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Technical Guide on Effective Design and Eurocodes:
Construction to Structural
EN 1993-1-1 Design of Steel Structures
Authors: K.F. Chung, M.C.H. Yam and H.C. Ho
The Hong Kong Polytechnic University
Publisher: Construction Industry Council, Hong Kong SAR
Supporting Organisation: Hong Kong Constructional Metal Structures Association
Copyright © 2015 reserved by the Construction Industry Council. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.
ISBN: 978-988-14432-0-5
i
Technical Guide on Effective Design and Eurocodes:
Construction to Structural
EN 1993-1-1 Design of Steel Structures
K.F. Chung, M.C.H. Yam and H.C. Ho
The Hong Kong Polytechnic University Publisher: Construction Industry Council, Hong Kong SAR
Supporting Organisation: Hong Kong Constructional Metal Structures Association
Copyright © 2015 reserved by the Construction Industry Council. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.
ISBN: 978-988-14432-0-5
i
Foreword The Construction Industry Council (www.hkcic.org) (CIC) was formed on 1 February 2007 in accordance with the Construction Industry Council Ordinance (Cap. 587) in Hong Kong. The main functions of the CIC are to forge consensus on long‐term strategic issues, to convey the industry’s needs and aspirations to the Government as well as to provide a communication channel for the Government to solicit advice on all construction‐related matters. The CIC Research Fund was established in September 2012 to enhance efficiency and competitiveness of the local construction industry. The CIC Research Fund encourages research and development activities as well as applications of innovative techniques that directly meet the needs of the industry. Moreover, it also promotes establishment of standards and good practices for the construction industry now and into the future. The project leading to the publication of this document is the first project funded by the CIC Research Fund announced in January 2013. It aims to facilitate technological upgrading of structural engineers and related construction professionals in Hong Kong to work effectively and efficiently in full accordance with the Structural Eurocodes, in particular, in structural steel design. Owing to the wide adoption of the Structural Eurocodes in many parts of the world beyond Member States of the European Union, the use of Structural Eurocodes presents huge opportunities for Hong Kong structural engineers and construction professionals to work on large scale infrastructure projects overseas. According to the World Steel Association (www.worldsteel.org), China has been the largest steel producer in the world since early 2000s. In 2013, China produces about 779 million metric tons (mmt) of steel materials, representing 49.2% of the world production. With the support of the Chinese Steel Construction Industry, Hong Kong construction professionals will be able to export their professional services to the international construction markets with quality structural steelwork through their international operation and practice. Hence, this will facilitate Hong Kong as a whole to develop into the International Engineering Centre for Design and Construction of Infrastructure for Asia and beyond.
ii
Foreword Since their official release in 2010, the Structural Eurocodes have been widely adopted in construction projects throughout the Member States of the European Community as well as a number of countries and cities in Southeast Asia such as Singapore, Malaysia and Hong Kong. Through effective design and construction using the Structural Eurocodes, designers, contractors and building materials suppliers are able to contribute to the international construction market with minimal technical barriers in the Region and beyond. The ability to produce steel materials to precise specifications and the associated quality control systems in addition to advanced skills in engineering design and construction will be essential. Jointly published by the Construction Industry Council, Hong Kong SAR, the Hong Kong Constructional Metal Structures Association and the Hong Kong Polytechnic University, the Technical Guide entitled “Effective Design and Construction to Structural Eurocodes: EN 1993‐1‐1 Design of Steel Structures” is considered to be highly relevant to the current needs of many design and construction engineers in Hong Kong as well as in many major cities in the Region. The Technical Guide provides detailed guidance on the design and construction of structural steelwork using European steel materials and products. More importantly, the Technical Guide also provides specific guidance on the use of Chinese steel materials, allowing engineers to select suitable steel materials and products according to generic project requirements on time and on budgets in meeting various specific project requirements. Consequently, design and construction engineers in Hong Kong and the Region will find the Technical Guide very helpful in providing practical advice on the selection of steel materials and products as well as technical guidance on the engineering design of structural steelwork conforming to Structural Eurocodes. It is expected that the Technical Guide will enable engineers to exploit new opportunities in international construction markets, striving for enhanced economic development of the construction industry in Hong Kong as well as in the Region. Mr Qing‐Rui YUE President Chinese National Engineering Research Centre for Steel Construction Beijing, China
iii
Foreword Roll forming is an established manufacturing process which has been developed for the mass production of profiles and sections over the past 100 years. In recent years, China has became the largest producer of roll formed profiles and sections in the world. Its annual production is estimated to be 127 million metric tons in 2013, i.e. over 50% of world production. The majority of the production includes thick gauge circular, rectangular and square hollow sections and thin gauge profiles in various sizes and thicknesses with different steel materials. The products are widely used as pipes and ducts in petroleum and chemical refineries, structural members in offshore structures and building frames as well as deckings, wall claddings and roof panels in buildings. Comprehensive design rules for applications of cold‐formed sections and profiles in construction are now available in the Structural Eurcodes. The Technical Guide “Effective Design and Construction to Structural Eurocodes – EN 1993‐1‐ 1 Design of Steel Structures” jointly published by the Construction Industry Council, Hong Kong SAR, the Hong Kong Constructional Metal Structures Association and the Hong Kong Polytechnic University is highly commendable. The Technical Guide is a major contribution to the Hong Kong Construction Industry, enabling its design and construction skills in structural steelwork to conform also to the Structural Eurocodes. In particular, the use of Chinese cold formed hollow sections is clearly illustrated in the document, and Design Tables are provided to facilitate adoption of Chinese cold formed hollow sections in construction projects. We believe that the Technical Guide will promote effective design and construction of structural steelwork using both European and Chinese steel materials and products. The Technical Guide will soon be regarded as the definitive reference for engineering design of cold formed hollow sections conforming to the Structural Eurocodes in many parts of the world, making a positive impact to the export of Chinese steel materials for overseas construction projects. Prof. Dr.‐Ing. Jing‐Tao Han President Chinese Confederation of Roll Forming Industry Professor University of Science and Technology Beijing Beijing, China iv
Preface This document is compiled by Ir Professor K.F. Chung, Ir Dr. Michael C.H. Yam and Dr. H.C. Ho of the Hong Kong Polytechnic University. The project leading to the publication of this document is fully funded by the CIC Research Fund of the Construction Industry Council (www.hkcic.org) (CIC) in Hong Kong. It is also supported by the Hong Kong Constructional Metal Structures Association (www.cmsa.org.hk). This document aims to facilitate the technological upgrading of structural engineers and related construction professionals in Hong Kong to work effectively and efficiently in full accordance with the Structural Eurocodes. Moreover, steel materials manufactured to selected European and Chinese steel materials specifications are covered in various chapters of the document. This provides a level playing field for both European and Chinese steel materials in the technical context of modern structural steel design. The project is also supported by the following professional associations:
the Steel Construction Institute (www.steel‐sci.org), the U.K.
the Institution of Structural Engineers (www.istructe.org), the U.K., and
the Institution of Civil Engineers, Hong Kong Association (www.ice.org.hk). An International Advisory Committee has been established to provide technical guidance for the project, and a member list of the Committee is as follows: The U.K. Dr. Graham Couchman The Steel Construction Institute Professor Leroy Gardner Imperial College London Professor Dennis S.H. Lam Bradford University Professor David A. Nethercot Imperial College London Mr. Y. K. Cheng The Institution of Structural Engineers, U.K. Mr. C.M. Lee The Institution of Civil Engineers – Hong Kong Association Singapore Professor S.P. Chiew Nanyang University of Technology Mr. W.B. Ho Singapore Structural Steel Society Professor Richard J.Y. Liew National University of Singapore Mr. K. Thanabal Building and Construction Authority v
Hong Kong Ir Professor Francis T.K. Au The University of Hong Kong Dr. C.M. Chan The Hong Kong University of Science and Technology Dr. T.M. Chan The Hong Kong Polytechnic University Ir Dr. Gary S.K. Chou Chun Wo Construction and Engineering Co. Ltd. Ir Dr. Goman W.M. Ho Ove Arup & Partners Hong Kong Ltd. Ir K.S. Kwan Housing Department, the Government of Hong Kong SAR Ir K.K. Kwan Ove Arup & Partners Hong Kong Ltd. Dr. Paul H.F. Lam The City University of Hong Kong Dr. Jackson C.K. Lau Hong Kong Institute of Vocational Education (Tsing Yi) Ir H.Y. Lee Hong Kong Constructional Metal Structures Association Ir M.K. Leung Architectural Services Department, the Government of Hong Kong SAR Ir Alan H.N. Yau AECOM Building Engineering Co. Ltd. The manuscript of the document was prepared by Ir Professor K.F. Chung, Ir Dr. Michael C.H. Yam and Dr. H.C. Ho assisted by Mr. K. Wang and Mr. T.Y. Ma. The worked examples were compiled by Ir Professor K.F. Chung and Dr. H.C. Ho, and checked by Ir Dr. Michael C.H. Yam and Dr. T.M. Chan. All the Design Tables were compiled by Mr. K. Wang and Dr. H.C. Ho under the supervision of Ir Professor K.F. Chung. During the compilation of the document, various drafts have been critically reviewed by the Engineering Technology Committee of the Hong Kong Constructional Metal Structures Association as well as various senior engineers and experts on steel construction. Hence, the final version of the document has been revised according to all of these technical comments, after rigorous consideration to attain a balanced view taking into account international trends, local practices, levels of structural accuracy and adequacy as well as user‐friendliness in practical design.
K.F. Chung, M.C.H. Yam and H.C. Ho The Hong Kong Polytechnic University Hong Kong Constructional Metal Structures Association
vi
EXECUTIVE SUMMARY This document provides technical guidance on the key structural steel design rules for both rolled and welded sections given in the Structural Eurocode EN1993‐1‐1 Design of Steel Structures (2005) and the associated UK National Annex together with relevant non‐ contradictory complementary information (NCCI). This document is compiled to assist structural engineers and related construction professionals in Hong Kong and the neighbouring areas to perform modern structural steel design to EN1993‐1‐1 in an effective and efficient manner. Technical information is presented in the context of the local construction industry, and references to prevailing regulations and codes of practice are made whenever necessary. In addition to European steel materials, selected Chinese steel materials are also included as equivalent steel materials which are readily accepted for construction projects designed to EN 1993‐1‐1. This provides a level playing field for both European and Chinese steel materials in the technical context of modern structural steel design. In general, all the key design rules given in EN 1993‐1‐1 are described and supplemented with explanatory notes in the same sequence as that found in the Eurocode: General Basis of design Materials Durability Structural analysis Ultimate limit states Serviceability limit states In order to illustrate various structural design procedures, a total of 8 worked examples with different cross‐section properties and resistances as well as different member buckling resistances are provided. Comprehensive design procedures for the following structural members are also presented in a rational manner: i) column members undergoing flexural buckling, ii) beam members undergoing lateral torsional buckling, and iii) beam‐column members undergoing buckling under combined compression and bending. Detailed design information and parameters are also presented in a tabulated format for easy reference. A complete chapter together with a total of 45 Design Tables is compiled to facilitate practical design of the following: vii
Rolled sections of S275 and S355 steel materials rolled I‐ and H‐sections hot‐finished circular, rectangular and square hollow sections
Equivalent welded sections of Q235, Q275, Q345 and Q460 steel materials welded I‐ and H‐sections cold‐formed circular, rectangular and square hollow sections
Hence, rolled sections complying to European steel materials specifications and equivalent welded sections with selected Chinese steel materials have been included for structural engineers and related construction professionals to use in large scale construction projects in Hong Kong and neighbouring cities whenever necessary.
viii
ix
Contents Section 1 Adopting Structural Eurocodes 1.1 1.2 1.3 1.4 1.4.1 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.7 1.8 1.9
Organization of Eurocodes Composition of EN1993 Aims and Scope Modern Structural Design Codes Modern design approach Harmonized Design Rules Member buckling check for hot‐rolled steel sections Member buckling check using normalized slenderness Member buckling check for composite columns Member buckling check for steel and composite columns at elevated temperatures Symbols and Terminology Conventions for Member Axes Format Equivalent Steel Materials
1 2 2 5 6 7 7 9 11 13 15 16 17 17
Section 2
Basis of Structural Design
2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.3.1 2.4.3.2 2.4.4 2.4.5
General Requirements Basic requirements Reliability management Design working life Principles of Limit State Design Design situations Ultimate limit states Serviceability limit states Basic Variables and Limit State Design Actions and environmental influences Material and product properties Limit state design Verification by Partial Factor Method Design values Ultimate limit states Combination of actions at ULS General Persistent or transient design situations Serviceability Limit States Combination of actions for SLS
x
22 22 23 24 24 24 25 25 26 26 26 27 27 27 29 29 29 29 32 32
Section 3
Materials
3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.3 3.3.1 3.3.2
General Structural Steel Material properties Ductility requirements Fracture toughness Through‐thickness properties Tolerances Design values of material coefficients Connecting Devices Fasteners Welding consumables
33 34 34 35 35 36 36 37 37 37 37
Durability
38
Section 4
Section 5
Structural Analysis
5.1 5.1.1 5.2 5.2.1 5.2.2 5.3 5.3.1 5.4 5.4.1 5.4.2 5.4.3 5.5 5.5.1 5.5.2 5.6
Structural Modeling for Analysis Structural Modeling and basic assumptions Global Analysis Effects of deformed geometry of a structure Structural stability of frames Imperfections Basis Methods of Analysis Allowing for Material Non‐linearities General Elastic global analysis Plastic global analysis Classification of Cross‐sections Basis Classification Cross‐section Requirements for Plastic Global Analysis
x
40 40 40 40 42 42 42 43 43 44 44 45 45 45 46
Section 6
Ultimate Limit States
6.1 6.2 6.2.1 6.2.2 6.2.2.1 6.2.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.2.7 6.2.8 6.2.9 6.2.9.1 6.2.9.2 6.2.10 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3
Partial Factors for Resistances Resistances of Cross‐sections General Section properties Gross cross‐section Net section Tension force Compression force Bending moment Shear force Torsion Bending and shear force Bending and axial force Class 1 and 2 cross‐sections Class 3 cross‐sections Bending, shear and axial forces Buckling Resistances of Members Uniform members in compression Buckling resistance Buckling curves Uniform members in bending Buckling resistance Lateral torsional buckling curves – general case Lateral torsional buckling curves for rolled sections or equivalent welded sections An alternative procedure recommended by the Steel Designers’ Manual Uniform members in bending and axial compression Columns in simple construction
6.3.2.4 6.3.3 6.3.4
Section 7
Serviceability Limit States
7.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.4
General Serviceability Limit States for Buildings Vertical deflections Horizontal deflections Dynamic effects Wind‐induced Oscillation Wind Sensitive Buildings and Structures
xii
49 49 49 50 50 50 50 51 51 52 54 54 56 56 57 58 59 59 59 59 63 63 64 65 67 72 73
75 75 75 75 75 77 77
Section 8
Design Data for Rolled and Welded Sections
8.1 General 8.2 Design Strengths 8.3 Section Classification 8.4 Rolled Sections 8.5 Equivalent Welded Sections 8.5.1 Equivalent welded I‐sections 8.5.2 Equivalent welded H‐sections 8.5.3 Equivalent cold‐formed circular hollow sections 8.5.4 Equivalent cold‐formed rectangular and square hollow sections 8.6 Design Tables on Section Dimensions, Properties and Resistances 8.6.1 Section dimensions and properties 8.6.2 Section resistances 8.6.2.1 Moment resistances 8.6.2.2 Shear resistances 8.6.2.3 Axial compression resistances Design Tables on Section Dimensions, Properties and Resistances for Rolled and Welded Sections
78 82 83 87 89 89 90 91 92 94 94 96 96 96 96 99 – 166
167
References
Appendices Appendix A
Design procedure of a pinned‐pinned column to EN 1993
A1
Appendix B
Design procedures of an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2
B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3
B7
B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded sections using the design method given in Steel Designer’s Manual
B14
B1
Appendix C
Design procedure of a column member under combined axial compression and bending to EN 1993
C1 Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex xiii
C1
Appendix D
Worked examples to BS EN 1993‐1‐1
Part I Section analysis and section resistance
Worked Example I‐1 Determination of section resistances
D1
Worked Example I‐2 Cross section resistance under combined bending and shear force
D7
Worked Example I‐3 Cross section resistance under combined bending and axial force
D9
Part II Member design
Worked Example II‐1 Design of a fully restrained steel beam
D14
Worked Example II‐2
D17
Worked Example II‐3 Design of a steel column under axial compression
D26
Worked Example II‐4 Design of a beam‐column under combined axial compression and bending
D29
Worked Example II‐5 Column in simple construction
D36
Design of an unrestrained steel beam against lateral torsional buckling Solution to Procedure B2 Solution to Procedure B3
xiv
List of tables Table 1.1
Comparison on key symbols
15
Table 1.2
Important changes on terminology
16
Table 1.3
Difference in the notation of axes
16
Table 2.1
Partial factor for actions, F
31
Table 2.2
Values of factors for buildings
31
Table 2.3
Values of factors for bridges
31
Table 3.1a
33
European Steel Materials
Table 3.1b
34
Chinese Steel Materials
Table 3.2
Choice of quality class according to EN 10164
36
Table 4.1
39
Exposure conditions
Table 5.1a
Maximum c/t ratios of compression parts
46
Table 5.1b
Maximum c/t ratios of compression parts
47
Table 5.1c
Maximum c/t ratios of compression parts
48
Table 6.1
Imperfection factors for flexural buckling curves
60
Table 6.2
Selection of flexural buckling curve for a cross‐section
61
Table 6.3
Buckling curves for lateral torsion buckling
64
Table 6.4
Imperfection factors for lateral torsion buckling curves
64
Table 6.5
Selection of buckling curves for rolled sections and equivalent welded sections
65
Table 6.6
Correction factors kc
66
Table 6.7
Values of
1 and C1 for various moment conditions C1
68
(load is not destabilizing )
Table 6.8
Imperfection factors for lateral torsion buckling curves
68
Table 6.9
Recommendations for the selection of lateral torsional buckling curves
69
Table 6.10
Comparison and design procedure of an unrestrained beam to EN 1993‐1‐1
xv
69
Table 7.1
Suggested limits for vertical deflection due to characteristic combination (variable actions only)
76
Table 8.1
Ranges of rolled and welded sections
78
Table 8.2
Summary of design information for rolled sections
80
Table 8.3
Summary of design information for equivalent welded sections
81
Table 8.4
Design strengths of different steel grades of rolled sections Class E1 Steel Materials with Mc 1.0
82
Table 8.5
Design strengths of different steel grades of welded sections Class E2 Steel Materials with Mc 1.1
82
Table 8.6
Section classification rules for I‐ and H‐sections
83
Table 8.7
Limiting ratios of section classification for I‐ and H‐sections
84
Table 8.8
Section classification of hollow sections
85
Table 8.9
Limiting ratios of section classification for hollow sections
86
Table 8.10
Full ranges of typical rolled sections available for application
88
Table 8.11
Allowable corner radii of hot‐finished and cold‐formed RHS and SHS
93
Table 8.12
Corner radii and local residual strains in cold‐formed zones
93
Table 8.13
Proposed corner radii of EWRHS and EWSHS
94
Table 8.14
Full ranges of proposed equivalent welded sections for application
95
Table 8.15
Summary of Design Tables
97
List of figures Figure 1.1
Cross‐sections typical rolled sections and welded sections
4
Figure 1.2
Member buckling curves to BS5950 Part 1
8
Figure 1.3
Member buckling curves to EN 1993‐1‐1
11
Figure 1.4
Member buckling curves to EN 1994‐1‐1
12
Figure 1.5
Strength reduction factors at elevated temperatures
13
Figure 1.6
Harmonized design of member buckling at both normal and elevated temperatures
14
Figure 6.1
Shear areas for various rolled and welded sections [Cl. 6.2.6 (3)]
53
Figure 6.2
Buckling curves for axial compression in members
62
xvi
Figure 6.3
Lateral torsional buckling curves for rolled sections
70
Figure 6.4
Lateral torsional buckling curves for welded sections
70
Figure 8.1
Cross‐sections of typical rolled sections and welded sections
79
Figure 8.2
Design method of equivalent welded I‐sections
89
Figure 8.3
Design method of equivalent welded H‐sections
90
Figure 8.4
Design method for equivalent cold‐formed circular hollow sections
91
Figure 8.5
Design method for equivalent cold‐formed rectangular hollow sections
92
Figure 8.6
Design method for equivalent cold‐formed square hollow sections
92
xvii
Section 1 Adopting Structural Eurocodes (1) The Structural Eurocodes are a new set of European design codes for building and civil engineering works. Conceived and developed over the past 40 years with the combined expertise of the member states of the European Union, they are arguably the most advanced structural codes in the world. The Structural Eurocodes are intended to be mandatory for European public works and likely to become the de‐facto standard for the private sector – both in Europe and world‐wide. The Eurocodes had been available as European pre‐standards (ENVs) for several years, and all of them were published as full European Standards (ENs) in 2007. (2) Owing to the withdrawal of various British structural design standards in March 2010, the Works Department of the Government of Hong Kong SAR has been migrating to the Eurocodes in stages, for the design of public works and civil engineering structures. Mandatory adoption of the Eurocodes will commence in 2015. Since a number of countries outside the European Union, in particular some Asian countries, have already adopted the structural Eurocodes for design and construction of building structures, there is a growing need for design and construction engineers in Hong Kong to acquire the new skills. 1.1 Organization of Eurocodes (1)
A total of 58 parts of the Eurocodes are published under 10 area headings:
(2)
Eurocode 0 – EN 1990: Basis of Structural Design Eurocode 1 – EN 1991: Actions on Structures Eurocode 2 – EN 1992: Design of Concrete Structures Eurocode 3 – EN 1993: Design of Steel Structures Eurocode 4 – EN 1994: Design of Composite Steel and Concrete Structures Eurocode 5 – EN 1995: Design of Timber Structures Eurocode 6 – EN 1996: Design of Masonry Structures Eurocode 7 – EN 1997: Geotechnical Design Eurocode 8 – EN 1998: Design of Structures for Earthquake Resistance Eurocode 9 – EN 1999: Design of Aluminium Structures
It should be noted that i)
the first two areas, namely, EN 1990 and EN 1991, are common to all designs – basis and actions; ii) the other six areas, namely, from EN 1992 to EN 1996 and EN 1999, are material‐ specific – concrete, steel, composite steel and concrete, timber, masonry, aluminum; and iii) the other two areas, namely, EN 1997 and EN 1998, cover geotechnical and seismic aspects. (3)
In order to avoid duplication of design rules as well as problems in updating various parts at different times, one of the prevailing regulations in drafting the Eurocodes is
1
that no design rule should be presented twice within the entire set of the Eurocodes. As a consequence, there is extensive cross‐referencing. 1.2 (1)
Composition of EN 1993 Various parts of EN 1993 are listed follows: Part
1‐1: 1‐2: 1‐3: 1‐4: 1‐5:
1‐6: 1‐7:
1‐8: 1‐9: 1‐10: 1‐11: 1‐12:
General rules and rules for buildings General – Structural fire design General – Cold formed thin gauge members and sheeting General – Structures in stainless steel General – Strength and stability of planar plated structures without transverse loading General – Strength and stability of shell structures General – Design values for plated structures subjected to out of plane loading General – Design of joints General – Fatigue strength General – Material toughness and through thickness assessment General – Design of structures with tension components General – Supplementary rules for high strength steels
Part 2‐1:
Bridges
Part Part
3‐1: 3‐2:
Towers, masts and chimneys – Towers and masts Towers, masts and chimneys – Chimneys
4‐1: 4‐2: 4‐3:
Silos, tanks and pipelines – Silos Silos, tanks and pipelines – Tanks Silos, tanks and pipelines – Pipelines
Part 5:
Piling
Part 6: (2)
1.3 (1)
Crane supporting structures
As indicated by the name, Part 1.1 provides the general rules for structural steel design which are formulated for direct application in building design while the other 11 sections in Part 1 are supplementary to Part 1.1 for application to various steel structures. Owing to the importance of these sections within the Eurocodes, design and construction engineers in Hong Kong need a good understanding of EN 1993‐1‐1 to make the most of the advantages offered by the Eurocodes. Aims and Scope This document provides technical guidance on key design rules for structural steel design for both the rolled and the welded sections given in the Structural Eurocode EN 1993‐1‐1 Design of Steel Structures (2005) and the associated UK National Annex together with relevant non‐contradictory complementary information. Technical
2
information is presented in the context of the local construction industry, and references to prevailing regulations and codes of practice are made whenever necessary. Figure 1.1 illustrates various cross‐sections of typical welded and rolled sections covered in this document. (2)
(3)
All the Nationally Determined Parameters (NDPs) recommended by the Works Bureau of the Government of Hong Kong SAR and provided in the updated design manuals of various government departments have been adopted. These items include load factors, loads, and methods for calculating certain loads, partial safety factors and advice where a choice of design approach is allowed. In general, all the key design rules given in EN 1993‐1‐1 are described and supplemented with explanatory notes in the same sequence as found in the Eurocode:
(4)
General Basis of design Materials - yield strengths Durability Structural analysis Ultimate limit states - resistances of cross‐sections under single actions - resistances of cross‐sections under combined actions - buckling resistances of members under single actions - buckling resistances of members under combined actions Serviceability limit states
In order to illustrate various design procedures for structural design, a total of 8 worked examples with different cross‐section properties and resistances as well as different member buckling resistances are provided. Comprehensive design procedures for the following buckling failure criteria are also provided: i) column members undergoing flexural buckling, ii) beam members undergoing lateral torsional buckling, and iii) beam‐column members undergoing buckling under combined compression and bending Detailed design information and parameters are also presented in tabulated format for easy reference. A complete section together with a total of 45 Design Tables has been compiled to facilitate the practical design of both rolled and welded sections assuming steel materials of different yield strengths.
3
Rolled sections: z z
y
y
H-section
I-section z
z
z
y
y
y
Circular hollow section CHS
Rectangular hollow section RHS
Square hollow section SHS
Welded sections: z z
y
y
Equivalent welded H-section EWH-section
Equivalent welded I-section EWI-section
z
z
z
y
Equivalent cold-formed circular hollow section EWCHS
Figure 1.1
y
Equivalent cold-formed rectangular hollow section EWRHS
y
Equivalent cold-formed square hollow section EWSHS
Cross‐sections of typical rolled and welded sections
4
(5)
A complete section is compiled to facilitate practical design of the following:
Rolled sections of S275 and S355 steel materials rolled I‐ and H‐sections hot‐finished circular, rectangular and square hollow sections
Welded sections of Q235, Q275, Q345 and Q460 steel materials welded I‐ and H‐sections cold‐formed circular, rectangular and square hollow sections
(6)
1.4 (1)
(2)
Hence, rolled sections complying to European steel materials specifications, and welded sections of selected Chinese steel materials have been included for design and construction engineers to use on large scale construction projects in Hong Kong and neighbouring cities. Modern Structural Design Codes Traditionally, a design code is expected to provide all key design requirements and considerations enabling a structural engineer to perform structural design. Proven lower bound design methods are also provided to assist the structural engineer to justify the structural adequacy of a structure in a prescriptive manner, i.e. if a structure is designed and confirmed to satisfy all the design rules, structural adequacy of the structure is deemed to be achieved. However, there is an overriding implicit assumption behind this, i.e. the structure being designed is assumed to behave in an essentially similar fashion to those structures for which the design methods have been developed and derived. While the extreme situation of structural failure would have been prevented, there is little information on how the structure is actually going to behave in relation to some specific requirements, in particular, during serviceability limit states. A review of the organization of many modern structural design codes reveals a typical layout as follows:
a) Materials Material types and manufacturing processes Physical, chemical and mechanical properties Requirements on structural performance
b) Sections and dimensions Typical shapes and sizes, limiting dimensions and scope of applications
c) Cross‐section resistances Cross‐section resistances under single actions Cross‐section resistances under combined actions
d) Member resistances Member resistances under single actions Member resistances under combined actions
5
e) System behaviour
f) Connection design Force analysis methods Basic resistances of fasteners, fixings and connectors Resistances and deformations of joints Detailing rules (3)
(4)
All these topics are considered to be essential for effective control of the design of a structure, and the given layout is considered to be a simple, effective, and structured arrangement to assist a structural engineer to perform his design in a straight forward manner. In practice, the design code is often considered to be a legal document enabling a structural engineer to perform his statutory duty to his client as well as to the regulatory authority. Consequently, the design clauses in the code are often written and compiled adopting a prescriptive approach, i.e. everything is spelled out with every use cautioned and every limit defined. However, while most of the design clauses are well controlled, there are occasions when the design becomes grossly conservative or things become unnecessarily complicated when interpretation between the lines of the design clauses is required, or the design lies outside the intended use of the design clauses. Hence, the prescriptive approach is generally considered to be restrictive, and little information is provided once the limits of the design clauses are crossed. Moreover, it is generally difficult to know how efficient the design is.
1.4.1 Modern design approach (1) With recent advances in development of structural design codes, the performance‐ based approach should be considered a major advance which enables the rational design and analysis of structural behaviour against well‐defined requirements at specific levels of acceptability. This approach is commonly adopted in seismic design as well as in fire resistant design of building structures and bridges whilst the levels of structural responses and acceptability are explicitly defined for specific structures. It is obvious that adopting effective performance‐based design requires a high level of understanding of the structural behaviour and the responses of structures. Hence, the structural examination of selected critical members is, in general, insufficient, and it is necessary to perform a numerical simulation of the structural behaviour of the entire structure under specific performance requirements. Supplementary member checks may be carried out, whenever necessary. (2) Ideally, a design method in a modern design code should be formulated in such a way that a structural engineer is able to perform the design while understanding the underlying principles when working through the design procedures. Moreover, the design procedures should be complied with in a fashion that enables the structural engineer to compromise on the calculation efforts he is prepared to make against the structural accuracy and economy of the structure. He should be able to decide
6
whether it is sufficient to adopt simple and yet conservative data, or if it is necessary to evaluate specific design parameters precisely, depending on the situation he is dealing with. When the structural engineer is making choices and decisions as the design proceeds, he is able to control the design rationally, i.e. to engineer not just the final product, but also the design process. 1.5 (1)
Harmonized Design Rules It is interesting to review the development of a number of national steel codes, and to examine some of the design methods and clauses which have evolved over the years; an illustration based on the checking of member buckling is given below. It concerns the use of the ‘slenderness’ parameter of a member, which is derived from elastic buckling theory, to facilitate simple and direct evaluation of member resistances for steel columns and beams as well as steel‐concrete composite columns.
1.5.1 Member buckling check for hot‐rolled steel sections (1) Consider the member buckling check in the British Steel Code BS5950 published by the British Standards Institution (2000) and the “Code of Practice for the Structural Use of Steel” published by the Buildings Department of the Government of Hong Kong SAR (2011). For a column susceptible to axial buckling, the slenderness of the column, λ, has been established for many years, and is defined as follows:
LE ry
(1.1)
where L E is the effective length of the column, depending on its boundary conditions; and ry is the radius of gyration of the cross‐section of the column, a function of its cross‐section geometry.
(2)
(3)
It should be noted that λ is an important structural parameter of a column and is a direct measure of the tendency of the column to undergo elastic buckling. Through a non‐linear interaction curve, which is commonly referred as the Perry‐Robertson formula, the effect of axial buckling in a real column is expressed as a reduction in its design strength from its yield value, i.e. its compressive strength. The compressive strength of a real column with material and geometrical initial imperfections is readily obtained using a specific column buckling curve after considering material yielding and geometrical instability. It should be noted that based on section shapes and sizes as well as bending axes during buckling, the value of the imperfection parameter, α , is determined after careful calibration against test data. Thus, a total of four column buckling curves are established, and they are plotted onto the same graph as shown in Figure 1.2a). For columns with welded sections made of thick steel plates, the design methodology is the same although the design yield strengths of the columns should be reduced by 20 N/mm2 to allow for the presence of
7
high residual stresses due to welding. 250
a= 3.5 a= 5.5
200
a= 8.0 150
100
50
0
20
40
60
80
100
120
140
160
180
200
140
160
180
200
Slenderness ratio, λ
a) Column buckling curves
300
250
a= 7.0
200
150
100
50
0 0
20
40
60
80
100
120
Equivalent slenderness ratio,LT
b) Beam buckling curve Figure 1.2
(4)
Design strength, py = 275 N/mm2
a= 2.0
0
Bending strength, p b Compressive
Compressive strength, p Compressive
300
Member buckling curves to BS5950 Part 1
For a beam susceptible to lateral buckling, an equivalent slenderness of the beam, LT , is devised and defined as follows:
LT
u v
(1.2)
where u and v
are secondary section properties of the beam related to lateral bending and torsion.
8
(5)
(6)
(7)
The adoption of the equivalent slenderness beam parameter is a good example of harmonized codification, and both design parameters, u and v, may be considered as correction factors which enable the lateral buckling check of a beam to be performed in a way similar to the axial buckling check of a column. Hence, the effect of lateral buckling in a real beam is expressed as a reduction in its design strength from its yield value, i.e. its bending strength. The bending strength of a real beam with material and geometrical initial imperfections is readily obtained after considering material yielding and geometrical instability, as shown in Figure 1.2b). It should be noted that in BS5950, there is only one beam buckling curve while different design coefficients are adopted for rolled and welded beam sections in calculating various parameters. For standardized steel sections, tabulated values of u and v are readily found in section dimensions and properties tables. Hence, it is demonstrated that in buckling checks of both columns and beams, the design methods are considered to be highly structured and rational, and all design parameters and coefficients are derived explicitly with analytical formulation. However, it should be noted that the structural adequacy and economy of the design methods often hinge on one single value, the effective length of the member. Up to the very present, there is still little or no effective means of examining the buckling behaviour of a particular member in a structure except through advanced finite element modelling, and the determination of the effective length of the member, and hence, the member slenderness, remains, otherwise, largely empirical.
1.5.2 Member buckling check using normalized slenderness (1) It is interesting to note that the harmonized design checks for both axial and lateral buckling of steel members given in BS5950 have been adopted in EN 1993‐1‐1 (2005) with a different formulation. The design rules are re‐formulated in such a way that the effect of member buckling in real steel columns and beams are expressed as a reduction to the resistances of the cross‐sections, i.e. a strength reduction factor, multiplied by the axial compression resistances of the cross‐sections of the column members, and a strength reduction factor, b multiplied by the moment resistances of the cross‐sections of the beam members respectively. (2)
Moreover, modified slenderness ratios are adopted, which are defined as follows:
N c,Rd or for axial or flexural buckling of columns N cr 1
(1.3)
and
LT
M c,Rd LT or for lateral buckling of beams M cr 1
where
9
(1.4)
1
is a material parameter given by:
=
E
is the elastic modulus of steel; is the yield strength of steel;
N c,Rd is the design axial resistance of the column;
fy
Ncr
E fy
is the elastic critical buckling resistance of the column; EI = 2 2 L cr is the second moment of area of the cross‐section of the column; is the buckling length;
I L cr
M c ,Rd is the design moment resistance of the beam; and
(3)
M cr is the elastic critical buckling moment resistance of the beam
(4)
It should be noted that the modified slenderness ratio, , is defined either as a ratio of the geometrical slenderness to the material parameter of the member, or a ratio of the square root of the ratio of the cross‐sectional axial resistance of the member to its corresponding elastic critical buckling resistance. Hence, the design methods are “normalized” against the mechanical properties of the members, and they are equally applicable to other materials, such as other metal and timber members, provided that calibration against geometrical and mechanical initial imperfections has been performed. As shown in Figure 1.3, there are five different buckling curves for columns and four for beams. The selection on the imperfection parameter, α , depends on section types and sizes as well as bending axes, if applicable.
10
Strength reduction factor, χ Compressive
1.2
α = 0.13
1.0
α = 0.21 0.8
α = 0.34 α = 0.49
0.6
α = 0.76 0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
1.75
2.00
Slenderness ratio, LT a) Column buckling curves
1.2
Compressive
Strength reduction factor, χLT
1.0
α = 0.21 α = 0.34
0.8
α = 0.49 0.6
α = 0.76
0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
Equivalent slenderness ratio, LT b) Beam buckling curves
Figure 1.3 Member buckling curves to EN 1993‐1‐1 1.5.3 Member buckling check for composite columns (1) For composite columns of concrete encased H sections or concrete in‐filled hollow sections, the same design methodology has been adopted in EN 1994‐1‐1 (2004), and the axial buckling resistances of the composite columns are based on the modified slenderness ratio which is defined as follows:
N pl,Rd N cr
for axial or flexural buckling of columns
11
(1.5)
where
N pl,Rd is the design plastic resistance of the composite column, which is equal to the
Ncr
sum of the section capacities of the individual components: concrete core, steel section and steel reinforcement; is the elastic axial buckling resistance of the composite column;
= 2
EIeff is the effective flexural rigidity of the composite column, which is equal to the
sum of the effective flexural rigidities of the individual components: concrete core, steel section and steel reinforcement; and is the buckling length.
L cr
(2)
(3)
L2cr
1.2
1.0
Strength reduction factor, Compressive
EI eff
α = 0.21 α = 0.34
0.8
α = 0.49 0.6
0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Slenderness ratio,
Figure 1.4 Member buckling curves to EN 1994‐1‐1 Hence, the effect of axial buckling in real composite columns is expressed as a strength reduction to the resistances of the cross‐sections of the column members, i.e. a strength reduction factor, χ , multiplied by the compression resistances of the cross‐ sections of the composite columns. As shown in Figure 1.4, there are three different column buckling curves. The selection depends on section types as well as bending axes, if applicable. Consequently, it is demonstrated that by adopting the same design methodology, i.e. the slenderness ratio of a member or its associated resistance ratio, the effect of buckling is readily expressed as a strength reduction factor multiplied by the resistance of the cross‐section of the member. The same methodology is shown to be highly satisfactory in steel beams and columns as well as composite columns. Moreover, the adoption of different buckling curves enables wide coverage of the many cross‐ sections of different shapes and sizes as well as bending axes.
12
1.5.4 Member buckling check for steel and composite columns at elevated temperatures (1) It should be noted that based on rigorous material tests of a number of constructional materials at elevated temperatures, various sets of strength reduction factors are given in EN 1993‐1‐2 (2005) and EN1994‐1‐2 (2005) for general use. Figure 1.5 plots these factors for different constructional materials for easy reference. It is interesting to note that all of these materials retain only 50% of their original strengths when their temperatures reach 500 to 600 oC. 1.1 Profiled steel decking (EN)
1.0
Reinforcement
Reduction factor
0.9
Structural steel
0.8
Normal weight concrete (NWC)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
100
200
300
400
500
600
700
800
900 1000 1100 1200
Temperature ( )
Figure 1.5 (2)
(3)
Strength reduction factors at elevated temperatures
Based on a known temperature distribution within a structural member obtained either from fire tests or numerical heat transfer analyses, the resistance of the member at elevated temperatures may be readily evaluated according to EN 1993‐1‐2 and EN 1994‐1‐2. A flow chart of various design procedures on steel beams and columns as well as composite columns at both normal and elevated temperatures is provided in Figure 1.6 to facilitate the use of these design procedures in practical design. Owing to the effective design development of member buckling in the Structural Eurocodes, the normalized slenderness ratios of steel beams and columns as well as composite columns are shown to be effective in determining corresponding strength reduction factors due to member buckling, as shown in Figure 1.6. Moreover, the same design formulation for member buckling design of various types of structural members is readily used at both normal and elevated temperatures with parameters having different values according to the materials of the members.
13
Design procedures
Key design parameters Normal temperatures
Elevated temperatures
1. Evaluate both the design and the characteristic resistances.
a. Steel column:
Ncr & N pl ,Rd
N fi , ,cr & N fi , ,Rd
b. Steel beam:
Not applicable
Not applicable
c. Composite column:
Ncr & N pl ,Rd
N fi , ,cr & N fi , ,Rd
2. Evaluate various structural parameters.
a. Steel column:
-
,
b. Steel beam:
-
,
c. Composite column:
(EI)eff
(EI)fi,eff
3. Evaluate the non‐ dimensional slenderness.
a. Steel column:
a. Steel column: b. Steel beam: c. Composite column:
5. Evaluate the buckling resistance.
b. Steel beam: c. Composite column:
4. Determine the imperfection factor and the reduction factor.
& & &
& &
&
a. Steel column: b. Steel beam: c. Composite column:
Figure 1.6 Harmonized design of member buckling at both normal and elevated temperatures
14
1.6 (1)
(2)
Symbols and Terminology The Eurocode system for symbols generally adopts a common notation for the principal variables. Differentiation between related variables, such as axial force and compression resistance, is achieved by the use of subscripts. Multiple subscripts are used where necessary, for example to distinguish between design bending resistances about the y‐y and the z‐z axes; each component is separated by a comma. In general, the Eurocode system for symbols is particular and precise, being effective in providing clarity and avoiding ambiguity. In general, symbols are defined where they are used within the text. A list of the most common symbols used is given in Clause 1.6 of EN 1993‐1‐1 for easy reference. Table 1.1 presents a comparison of some of the key symbols adopted in the U.K. and Hong Kong to those adopted in EN 1993‐1‐1. Table 1.1
Comparison of key symbols
U.K. and Hong Kong
EN 1993‐1‐1
U.K. and Hong Kong
EN 1993‐1‐1
A
A
P
N
Z
Wel
Mx
My
S
Wpl
V
V
Ix
Iy
H
Iw
Iy
Iz
J
It
U.K. and Hong Kong
EN 1993‐1‐1
py
fy
pb
LT f y
pc
fy
r
i
(3)
In this document, a dot is used as the decimal separator, in line with the existing U.K. and Hong Kong practice. However, it should be noted that the Eurocodes themselves use a comma as the separator.
15
(4)
1.7 (1) (2)
The Eurocodes contain alternative terms to those familiar to the U.K. and Hong Kong designers, and some important changes are summarized in Table 1.2. Table 1.2
Important changes on terminology
U.K. and Hong Kong terms
Eurocode terms
Loads
Actions
Dead load
Permanent action
Imposed or live load; wind load
Variable action
Ultimate loads
Design value of actions
Check
Verification
Internal forces and bending moments which result from the application of the actions
Effects of actions
Capacity, or Resistance
Resistance
Second‐order effects
Effects of deformed geometry
Conventions for Member Axes The convention for member axes is: x – x axis y – y axis z – z axis
along a member major axis of a cross‐section minor axis of a cross‐section
For typical I‐ and H‐sections and structural hollow sections, the convention used for cross‐section axes are: y – y axis z – z axis
major axis of the cross‐section which is parallel to the flanges minor axis of the cross‐section which is perpendicular to the flanges
The cross‐section axes of typical sections are illustrated in Figure 1.1. Table 1.3 summarizes the differences in the notation of the axes in both members and cross‐ sections. Table 1.3 Difference in the notation of axes
U.K. and Hong Kong
Eurocodes
X (?)
X
Major axis of a cross‐section
X
Y
Minor axis of a cross‐section
Y
Z
Longitudinal axis along the member
16
1.8 (1) (2)
Format All the clauses and paragraphs in this document are numbered consecutively. In the Eurocodes, a distinction is made between Principles and Application Rules: i. Principles are identified by the letter P following the paragraph number. ii. Application Rules are generally recognized rules which comply with the Principles and satisfy their requirements.
1.9 (1)
This distinction is retained in this document. Equivalent Steel Materials For many years, almost all steel structures in Hong Kong were designed to the British structural steel design code, BS5950, and all the steel materials were specified correspondingly to the British steel materials specifications such as BS4360. However, as early as the 1990s, non‐British steel materials found their way to Hong Kong as well as Singapore and other neighbouring cities in Southeast Asia. Occasionally, contractors wanted to use non‐British steel materials, such as Japanese, Australian and Chinese steel materials. The proposed changes ranged from merely adopting such materials for some members of temporary structures to their use for complete beam‐column frames of building structures. Over the years, many successful projects were reported in Hong Kong which benefited from good quality non‐British steel materials, timely supply and delivery as well as improved structural economy. However, there were also a few bad examples of the use of non‐British steel materials having inconsistent chemical compositions, inadequate mechanical properties and lack of traceability.
(2)
In the 2000s, owing to large fluctuations in the costs of steel materials on the global markets, Chinese steel materials became practical alternatives to British steel materials in a number of construction projects in Asia, in particular, in Hong Kong, Macau and Singapore. During the drafting of the “Code of Practice for the Structural Use of Steel” for the Buildings Department of the Government of Hong Kong SAR from February 2003 to August 2005, it was decided necessary to devise a means to allow, or more accurately, to formalize the use of Chinese steel materials as equivalent steel materials for structures which were originally designed to BS5950. Various parts of Section 3 of the Hong Kong Steel Code provide basic principles and considerations for accepting, as well as qualifying, steel materials manufactured to the following national materials specifications:
Australian / New Zealand standards, Chinese standards, Japanese standards, and American standards.
A practical classification system for non‐British steel materials is introduced in the Code
17
in which the design strengths of these non‐British steel materials depend on a newly defined factor, namely, the material class factor, γ Mc . (3)
(4)
(5)
Similar use of non‐British steel materials was also formally adopted in Singapore with the issue of a technical guide entitled “Design Guide on Use of Alternative Steel Materials to BS5950” in 2008, and then its revised version entitled “Design Guide on Use of Alternative Structural Steel to BS5950 and Eurocode 3” by the Building and Construction Authority of the Ministry of National Development. These Design Guides aimed to provide technical guidelines and design information on the use of non‐British steel materials, and the classification system for various steel materials given in the “Code of Practice for the Structural Use of Steel” was adopted after modification. Under the provisions of these Design Guides, alternative steel materials not manufactured to British and European steel materials standards may be allowed in structural design based on the Structural Eurocodes for construction projects in Singapore. In 2014, the use of non‐British steel materials in Hong Kong, Singapore and other neighbouring cities in Asia was further promoted through the publication of a Professional Guide on “Selection of Equivalent Steel Materials to European Steel Materials Specifications” (Publication CMSA‐PG01). The Professional Guide is jointly published by the Hong Kong Constructional Metal Structures, Macau Society of Metal Structures and Chinese National Engineering Research Centre for Steel Construction. It presents essential technical guidance to design and construction engineers as well as engineers from regulatory authorities on the selection of steel materials equivalent to material requirements specified in the European steel materials specifications. Through the use of the Professional Guide, selected steel materials manufactured to the modern materials specifications of Australia/New Zealand, China, Japan, and the United States of America are fully endorsed to be equivalent to steel materials manufactured to the European steel materials specifications, provided that all of these steel materials have been demonstrated to be in full compliance with the requirements of both material performance and quality control as detailed in the Professional Guide. Consequently, these equivalent steel materials can be readily employed on construction projects for which the structural steelwork is designed to EN 1993 and EN 1994. Given a satisfactory demonstration of both the material performance and the quality assurance procedures adopted during their manufacturing processes, steel materials with yield strengths from 235 to 690 N/mm2 are classified as follows:
18
Class E1 Steel Materials with γ Mc = 1.0
Steel materials which are
i) manufactured in accordance with one of the Acceptable Materials Specifications listed in Appendix A of the Professional Guide with a fully demonstrated compliance on their material performance, and
ii) manufactured in accordance with an Acceptable Quality Assurance System with full demonstration of effective implementation.
Thus, compliance with all the material requirements has been demonstrated through intensive routine testing conducted during the effective implementation of a certificated Factory Production Control system which accords with European steel materials specifications. The Factory Production Control System must be certified by an independent qualified certification body.
Class E2 Steel Materials with γ Mc = 1.1
Steel materials which are
i) manufactured in accordance with one of the Acceptable Materials Specifications listed in Appendix A of the Professional Guide with a fully demonstrated compliance on their material performance, and
ii) manufactured in accordance with an effectively implemented quality assurance system which is different to a Factory Control Production System.
Thus, the steel materials are manufactured in accordance with all the material requirements given in one of the Acceptable Materials Specifications, but without a certified Factory Production Control System which accords with European steel materials specifications.
In general, although many steel manufacturers will have already established a form of quality assurance during the manufacturing processes, the high level of consistency in the material performance of the steel materials required in European steel materials specifications cannot be verified in the absence of a certified Factory Production Control System. Hence, a demonstration of the conformity of the steel materials is required, and additional material tests with sufficient sampling should be conducted for various batches of supply to demonstrate full compliance with both the material performance and the quality assurance requirements.
Class E3 Steel Materials
Steel materials for which they cannot be demonstrated they were
i) manufactured in accordance with any of the Acceptable Materials Specifications listed in Appendix A; nor
ii) manufactured in accordance with an Acceptable Quality Assurance System.
Hence, any steel material which cannot be demonstrated to be either Class E1 Steel Material or Class E2 Steel Material will be classified as Class E3 Steel Material, and the nominal value of yield strength of the steel material is limited to 170 N/mm2 for
19
structural design; no additional material test is needed in general. However, the design yield strength of the steel material may be increased if additional material tests with sufficient sampling have been conducted for various batches of supply before use.
(6)
For details of specific requirements on material performance and quality assurance, refer to the Professional Guide. Also refer to Section 3.2.3 of the Professional Guide for details of additional materials tests. Table 1.4 summarizes the classification system applying to the various classes of steel materials.
Table 1.4
(7)
Nominal yield strength (N/mm2) ≥ 235 and ≤ 690
Classification system for various classes of steel materials Class
Material class factor, MC for minimum ultimate yield tensile strength, strength, ReH Rm
Compliance with material performance requirements
Compliance with quality assurance requirements
Additional material tests
E1
Y
Y
N
1.0
1.0
E2
Y
N
Y
1.1
1.1
E3
N
N
N
‐‐‐
‐‐‐
A newly defined factor, namely, the material class factor, MC , is adopted as a result of the classification, and hence, the nominal values of the yield strength and of the ultimate tensile strength of the equivalent steel materials are given as follows:
Nominal value of yield strength
fy
=
ReH / MC
(6a)
(6b)
Nominal value of ultimate tensile strength
fu
=
Rm / MC
where ReH Rm MC
is the minimum yield strength to product standards; is the ultimate tensile strength to product standards; and is the material class factor given in Table 1.4.
It should be noted that
a) Plastic analysis and design is permitted for Classes E1 and E2 Steel Materials assuming yield strengths not larger than 460 N/mm2.
20
b) For Classes E1 and E2 Steel Materials with yield strengths larger than 460 N/mm2 but smaller than or equal to 690 N/mm2, design rules given in EN 1993‐1‐12 should be used.
c) Only elastic analysis and design should be used for Class E3 Steel Materials.
21
Section 2 Basis of Structural Design This Section presents the key principles as well as the relevant application rules in EN 1990 that relate to the design of steel structures together with specific requirements given in EN 1993‐1‐1. These include specific rules on basic requirements, reliability management, principles of limit state design, partial factor method as well as combinations of action. It is important to be familiar with the various terminologies and mathematical formats of the expressions, formulae and equations adopted in the Eurocodes. 2.1 General Requirements Design of a structure requires the demonstration of structural adequacy under various effects of actions in extreme events, i.e. the ultimate limit state, and of full compliance against various requirements in deformation, vibration and durability during its intended life, i.e. serviceability limit states. 2.1.1 Basic requirements (1)P A structure shall be designed and executed in such a way that during its intended life, with appropriate degrees of reliability and in an economical way, it will sustain all actions likely to occur during execution and use, and meet specified serviceability requirements. (2)P A structure shall be designed to have adequate structural resistance, serviceability and durability. (3)P In the case of fire, the structural resistance shall be adequate for the required period of time. (4)P A structure shall be designed and executed in such a way that it will not be damaged by events such as explosion, impact, and consequences of human errors, to an extent disproportionate to the original cause. (5)P Potential damage shall be avoided or limited by appropriate choice of one or more of the following: – avoiding, eliminating or reducing the hazards to which the structure can be subjected; – selecting a structural form which has low sensitivity to the hazards considered; – selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage; – avoiding structural systems that can collapse without warning; – tying structural members together.
22
(6)
The basic requirements should be met by the use of appropriate materials, design and detailing, and quality control.
2.1.2 Reliability management (1)P The reliability required for structures within the scope of EN 1990 shall be achieved by: a) design in accordance with EN 1990 to EN 1999, and b) appropriate execution and quality management measures. (2) Different levels of reliability may be adopted, among other things: – for structural resistance; – for serviceability. (3) The choice of the levels of reliability for a particular structure should take account of various relevant factors, including: –possible cause and mode of attaining a limit state; – possible consequences of failure in terms of risk to life, injury, potential economical losses; – public aversion to failure; –expenses and procedures necessary to reduce the risk of failure. (4) The levels of reliability that apply to a particular structure may be specified in one or both of the following ways: ‐ by classification of the whole structure; ‐ by classification of its individual components. (5) The levels of reliability relating to structural resistance and serviceability can be achieved by suitable combinations of: a) preventative protective measures; b) measures relating to design calculations: ‐ representative values of actions; ‐ choice of partial factors; c) measures relating to quality management; d) measures aimed to reduce errors in design and execution of the structure, and gross human errors e) other measures relating to the following design matters: ‐ basic requirements; ‐ degree of robustness (structural integrity) ‐ durability, including the choice of the design working life; ‐ extent and quality of preliminary investigations of soils and possible environmental influences ‐ accuracy of mechanical models; ‐ detailing
23
(6)
(7) (8)
f) efficient execution, e.g. in accordance with the execution standards referred to in EN 1991 to EN 1999. g) adequate inspection and maintenance according procedures specified in the project documentation. The measures to prevent potential causes of failure and to reduce their consequences may, in appropriate circumstances, be interchanged to a limited extent provided that the required reliability levels are maintained. The level of reliability should be achieved by the use of appropriate quality management in design and execution. In general, execution should be performed in accordance with EN 1090‐2, and execution class EXC2 should be specified. EN 1090‐2 gives 4 classes of requirements for execution of the structure as a whole or for components of a structure, namely, Classes EXC1 to EXC4, with increasing strictness requirements. For common buildings and structures, Class EXC2 for the whole structure is normally considered to be sufficient.
2.1.3 Design working life (1) Common building structures should be designed for a working life of at least 50 years. In general, 50 years is the normal design working life for building structures, and this is implicitly adopted in the usual characteristic values of actions selected together with the various associated partial factors of safety. 2.2 Principles of Limit State Design (1) The resistances of cross‐sections and members specified in this document for the ultimate limit states as defined in Section 3.3 of EN 1991‐1‐3 are based on tests in which the steel materials exhibited sufficient ductility to allow to application of simplified design methods. Various design situations are introduced which should be considered for design against both ultimate and serviceability limit states. 2.2.1 Design situations (1)P The relevant design situations shall be selected taking into account the circumstances under which the structure is required to fulfill its function.
24
(2)P
Design situations shall be classified as follows: Persistent design situations Transient design situations Accidental design situations Seismic design situations
‐ ‐ ‐ ‐
normal conditions of use temporary conditions applicable to the structure exceptional conditions applicable to the structure or to its exposure, e.g. to fire, explosion, impact or the consequences of localised failure conditions applicable to the structure when subjected to seismic events
In general, the persistent design situation is the most common in practice while transient design situations occur during the construction stages as well as during renovation and refurbishment. (3)P The selected design situations shall be sufficiently severe and varied so as to encompass all conditions that can reasonably be foreseen to occur during the execution as well as the use of the structure. 2.2.2 Ultimate limit states (1)P The limit states that concern the safety of people and the safety of the structure shall be classified as ultimate limit states. (2) In some circumstances, the limit states that concern the protection of the contents should be classified as ultimate limit states. (3) States prior to structural collapse, which, for simplicity, are considered in place of the collapse itself, may be treated as ultimate limit states. (4)P The following ultimate limit states shall be verified where they are relevant: – loss of equilibrium of the structure or any part of it, considered as a rigid body; – failure by excessive deformation, transformation of the structure or any part of it into a mechanism, rupture, loss of stability of the structure, or any part of it, including supports and foundations; – failure caused by fatigue or other time‐dependent effects. Different sets of partial factors are associated with the various ultimate limit states. 2.2.3 Serviceability limit states (1)P The limit states that concern the functioning of a structure or its structural members under normal use, comfort of people, and deformation of construction works (leading to extensive cracking) shall be classified as serviceability limit states.
25
(2)P A distinction shall be made between reversible and irreversible serviceability limit states. (3) Verification of serviceability limit states should be based on criteria concerning the following aspects: a) deformations that affect – appearance, – comfort of users, or – functioning of the structure (including functioning of machines or services), or that cause damages to finishes or non‐structural members; b) vibrations that adversely affect – comfort to people, or – functional effectiveness of the structure; c) damages that are likely to adversely affect – appearance, – durability, or – functioning of the structure. 2.3 Basic Variables and Limit State Design 2.3.1 Actions and environmental influences (1) Actions for the design of steel structures should be taken from EN 1991. For the combination of actions and partial factors of actions, refer to Annex A to EN 1990. (2) The actions to be considered in the erection stage should be obtained from EN 1991‐ 1‐6. (3) Where the effects of predicted absolute and differential settlements need to be considered, best estimates of imposed deformations should be used. 2.3.2 Material and product properties (1) Material properties for steels and other construction products and the geometrical data to be used for design should be those specified in the relevant ENs, ETAGs or ETAs unless otherwise indicated in this document.
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2.3.3 Limit state design (1)P Design for limit states shall be based on the use of structural and load models for relevant limit states. (2)P It shall be verified that no limit state is exceeded when relevant design values for – actions, – material properties, or – product properties, and – geometrical data are used in these models. (3)P Verifications shall be carried out for all relevant design situations and load cases. (4) The requirements of Clause (1)P above should be achieved by the partial factor method described in Clause 2.4 Verification by Partial Factor Method. (5) As an alternative, a design directly based on probabilistic methods may be used. (6)P The selected design situations shall be considered and critical load cases identified. (7) For a particular verification, load cases should be selected, identifying compatible load arrangements, sets of deformations and imperfections that should be considered simultaneously with fixed variable and permanent actions. (8)P Possible deviations from assumed directions or positions of actions shall be taken into account. (9) Structural and load models can be either physical models or mathematical models. 2.4 Verification by Partial Factor Method 2.4.1 Design values (1) The design value Fd of an action F is expressed as:
Fd F Fk
where F Fk
(2.1)
is a partial factor for the action F; is the combination factor and is equal to 1.0 for permanent actions, or to 0 1 , or 2 for variable actions; and , is the characteristic value of the action, F.
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(2)
In general, the design value of an action is usually expressed as F Fk rather than Fd for clarity. Moreover, permanent and variable actions are distinguished symbolically by the use of G k for permanent actions and Q k for variable actions, i.e. G G k and Q Q k respectively. The design value X d of a material property is expressed as: X Xd k M where X k is a characteristic value of the material; and M is a partial factor for a material property.
(2.2)
In general, the design value of a material property is usually expressed as
Xk rather M
than X d for clarity. (3)
Geometrical data for cross‐sections and systems may be taken from product standards hEN or drawings for the execution to EN 1090 and treated as nominal values.
Design values of geometrical imperfections specified in this document are equivalent geometric imperfections that take into account the effects of: ‐ geometrical imperfections of members as governed by geometrical tolerances in product standards or the execution standard; ‐ structural imperfections due to fabrication and erection; ‐ residual stresses; and ‐ variation of yield strengths (4)
The design value of resistance is expressed as a function of the design value of a material property and a geometrical data: X R d R k ;a (2.3a) M where a
is the geometric parameter.
Alternatively, the design resistance may be obtained directly from the characteristic value of a material by: R (2.3b) Rd k M where Rk is the characteristic value of the particular resistance determined with characteristic or nominal values for the material properties and dimensions; and M is the global partial factor for the particular resistance.
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2.4.2 Ultimate limit states (1)P The following ultimate limit states of a structure shall be verified: EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body. STR Failure or excessive deformation of the structure or its structural members including supports where the strength of the structural material governs. GEO Failure or excessive deformation of the ground where the strengths of soils or rocks are significant in providing resistances. FAT Fatigue failure of the structure or its structural members. In general, the STR limit state is the only limit state that needs to be considered. (2)P When considering a limit state of rupture or excessive deformation of a section, a member or a connection, i.e. STR limit state, it shall be verified that: Ed R d (2.4) where E d is the design value of the effect of actions such as internal force, moment or a vector representing several internal forces or moments; and R d is the design value of the corresponding resistance. 2.4.3 Combination of actions at ULS 2.4.3.1 General (1) For each design situation, the design values of the effects of the actions should be determined from the combination of the actions that may occur simultaneously. (2) Each combination of actions should include a leading or main variable action, or an accidental action. 2.4.3.2 Persistent or transient design situations (1) The combination of effects of actions to be considered should be based on: the design value of the leading variable action, and the design combination values of the accompanying variable actions.
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j1
G k , j "" P P "" Q ,1 0,1Q k ,1 ""
G, j
i 1
Q ,i
0,i Q k ,i (2.5) [Eqn. 6.10 of EN 1990]
i 1
Q ,i
0,i Q k ,i (2.5a) [Eqn. 6.10a of EN 1990]
G k , j "" P P "" Q ,1Q k ,1"" Q ,i 0,i Q k ,i
j G, j
j1
or alternatively, for the STR limit state, the less favourable of the two following expressions:
j1
G k , j "" P P "" Q ,1Q k ,1 ""
G, j
(2.5b) [Eqn. 6.10b of EN 1990]
i 1
where “+” implies “to be combined with”; implies “the combined effect of”; G k , j are the characteristic values of the permanent actions;
Q k ,1 is the characteristic value of one of the variable actions; Q k ,i are the characteristic values of the other variable actions;
G, j is the partial factor for the permanent action G k , j ; Q,i is the partial factor for the variable action Q k ,i ; 0,i is the 0 factor for the combination value of the variable action Q k ,i ;
(3)
j
is a reduction factor applied to unfavorable permanent actions (in
Expression 6.10b of EN 1990); = 0.925 according to NA of EN 1990.
v According to the Eurocodes approach, it is necessary to apply all variable actions to the structure under consideration to examine the effects of actions on the structure. It should be noted that each variable action is in turn considered as the “leading” variable action while all the other variable actions are applied correspondingly with each of them multiplied by a relevant factor. It is thought that Expression (6.10) of EN 1990 gives a quick, but conservative approach when compared to Expressions (6.10a) and (6.10b) of EN 1990, which are slightly more involved. In general, it is expected that Expression (6.10b) of EN 1990 will normally be the governing case.
The partial factors to be used in the combination of actions and the factors on accompanying actions are given in Table 2.1 which are extracted from Tables N.A.A1.2(a) and N.A.A1.2(b) of UK NA to EN 1990 and modified accordingly to local practice. The corresponding partial factors for buildings and bridges are also presented in Tables 2.2 and 2.3 for easy reference.
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Table 2.1 Partial factors for actions, F
Ultimate Limit State EQU STR
Buildings Permanent Actions Leading or Main G, j Variable Action Q,1 Unfavorable Favorable 1.40 1.40
1.00 1.00
Accompanying Variable Action Q,i
1.60 1.60
1.60 1.60
Civil engineering works Permanent Leading or Main Traffic Actions Rail Wind Actions Variable Action Traffic (gr1a, gr1b, Ultimate Actions G, j Q,1 Actions gr2, gr3, gr4, Limit State gr5, gr6) Unfavorable Favorable EQU 1.05 0.95 1.35 To be agreed 2.10 STR 1.35 0.95 1.35 To be agreed 2.10 Note: When variable actions are favourable, Q k should be taken as zero. For building structures, reference should be made to “Code of Practices for the Structural Use of Steel 2011” for the detailed design values of actions. For civil engineering works, reference should be made to “Structures Design Manual for Highways and Railways 2013” for the detailed design values of actions.
Table 2.2 Values of factors for buildings Action Permanent actions + General variable actions Permanent actions + Equivalent horizontal actions Permanent actions + Wind actions + General variable actions Temperature (non‐fire) in buildings
0 0.875 0.875 0.75 0.75
1 0.75 0.75 0.75 0.75
2 0.75 0.75 0.75 0.75
1
2
a
On roofs, imposed loads should not be combined with wind loads.
Table 2.3 Values of factors for bridges 0
Action
Imposed loads in buildings, category (see “Structures Design Manual for Highways and Railways”) Traffic loads gr1a: TS, UDL 0.75 0.75 0.0 Traffic loads gr1b: Single axle 0.00 0.75 0.0 Traffic loads gr2: Horizontal forces 0.00 0.00 0.0 Traffic loads gr3: Pedestrain loads 0.00 0.40 0.0 Traffic loads gr4: Crowd loading 0.00 ‐ 0.0 Traffic loads gr5: Vertical forces from SV and SOV vehicles 0.00 ‐ 0.0 Traffic loads gr6: Horizontal forces from SV and SOV vehicles 0.00 0.00 0.0
Wind loads: Permanent design situation Wind loads: During erection Thermal actions
0.50 1.00 0.60
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0.20 ‐ 0.60
0.0 0.0 0.50
2.4.4 Serviceability limit states (1)P It shall be verified that:
Ed Cd
(2.6)
where E d is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination; and C d is the limiting design value of the relevant combination. As the partial factors for actions F are implicitly taken as 1.0, they are therefore not shown in the expressions for the effects of actions for clarity.
2.4.5 Combination of actions for SLS (1) The combinations of actions for serviceability limit states are: Characteristic applicable for irreversible limit states; Frequent applicable for reversible limit states; and Quasi‐permanent applicable for long‐term effects and the appearance of the structure. (2) The expressions for the effects due to the combinations of actions are: Characteristic combination
G j1
k, j
"" P "" Q k ,1 ""
Frequent combination
G j1
k, j
i 1
"" P "" 1,1Q k ,1 ""
Quasi‐permanent combination
G j1
k, j
"" P ""
i 1
2,i
0,i
Q k ,i
i 1
2,i
Q k ,i
Q k ,i
(2.7)
(2.8)
(2.9)
where 1,1 is the factor for the frequent value of the variable action Q k , i (see Table 2.2) 2 ,1 is the factor for the quasi‐permanent value of the variable action Q k , i (see
Table 2.2).
Advice on which combination to use is given in EN 1993‐1‐1 and its National Annex. The National Annex to EN 1993‐1‐1 states that serviceability deflections should be based on the unfactored variable actions, and that permanent actions need not be included. Refer to Section 7 of this document for further information.
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Section 3 Materials 3.1 General (1) The nominal values of material properties given in this Section should be adopted as characteristic values in design calculations. (2) This Part of EN 1993 covers the design of steel structures fabricated from steel materials conforming to the steel grades listed in Table 3.1. (3) In general, EN 1993‐1‐1 covers steel materials conforming to EN 10025 Parts 2, 3, 4, 5 and 6, EN 10210‐1 and EN 10219‐1 in grades S235 to S460. However, for quality steel materials which are manufactured to other materials specifications but satisfy both material performance and quality assurance requirements, they are readily considered to be equivalent steel materials. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details. (4) Depending on the supply sources of these steel materials, if it can be demonstrated that these steel materials satisfy both material performance and quality control requirements as described in Section 1.9, they are then considered as Class E1 Steel Materials, and the corresponding material class factor, Mc , is taken to be 1.0. However, if these steel materials are demonstrated to satisfy only the material performance requirements but not the quality control requirements as described in Section 1.9, they are then considered as Class E2 Steel Materials, and the corresponding material class factor, Mc , is taken to be 1.1. (5) Table 3.1 presents all the steel grades given in Table 3.1 of EN 1993‐1‐1: Table 3.1 European Steel Materials: EN 10025 – 2 • S235 • S275 • S355 • S450
EN 10025 – 3 • S275 N/NL • S355 N/NL • S420 N/NL • S460 N/NL
EN 10025 – 4 • S275 M/ML • S355 M/ML • S420 M/ML • S460 M/ML
EN 10210 – 1 • S235 H • S275 H • S355 H • S275 NH/NLH • S355 NH/NLH • S420 NH/NHL • S460 NH/NLH
EN 10219 – 1 • S235 H • S275 H • S355 H • S275 NH/NLH • S355 NH/NLH • S460 NH/NLH
• • • •
S275MH/MLH S355 MH/MLH S420 MH/MLH S460 MH/MLH
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EN 10025 – 5 • S235 W • S355 W
EN 10025 – 6 • S460 Q/QL/QL1
(6)
Table 3.2 presents commonly used Chinese steel grades which are considered to be equivalent steel materials for adoption in structural design to EN 1993: Table 3.2 Chinese steel materials: GB/T 700‐2006 • Q235B/C/D • Q275B/C/D
GB/T 1591‐2008 • Q345B/C/D/E • Q390B/C/D/E • Q420B/C/D/E • Q460C/D/E
GB/T 6725‐2008 • Q235 • Q345 • Q390
GB/T 8162‐2008 • Q235 • Q275 • Q345 • Q390
GB/T 4171‐2008 • Q265GNH • Q295GNH • Q310GNH • Q355GNH • Q235NH • Q295NH • Q355NH • Q415NH • Q460NH
GB/T 19879‐2005 • Q235GJB/C/D/E • Q345GJB/C/D/E • Q390GJC/D/E • Q420GJC/D/E • Q460GJC/D/E
• Q420 • Q460
Refer to the Professional Guide entitled “Selection of Equivalent Steel Materials to European Steel Materials Specifications” (2015) for further details on equivalent steel materials manufactured to different materials specifications.
3.2 Structural Steel 3.2.1 Material properties (1) The nominal values of the yield strength f y and of the ultimate strength fu for structural steel should be obtained either by a) adopting the values of f y R eH and f u R m directly from the product standard, or b) using the values given in Table 3.1 of EN 1993‐1‐1.
In general, both fy and fu are material strengths of the steel materials measured either along the longitudinal or in the transverse directions with respect to the rolling direction during manufacturing. Both fy and fu are determined in standard tensile tests to EN 10002 which specifies details of testing procedures (material sampling, dimensions of coupon sizes, straining rates) and data analyses.
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3.2.2 Ductility requirements (1) For steel materials for which a minimum ductility is required, the following three requirements should all be satisfied: the ratio f u / f y : f u / f y 1 .0
where
(3.1a)
fu fy
is the ultimate strength, and is the yield strength.
the elongation at failure : elongation at failure 15%
(3.1b)
which is based on a standard gauge length of 5.65 A 0 where A 0 is the original cross‐sectional area of the coupon.
the ultimate strain u : ε u 15 ε y
where u y
(3.1c)
is the strain corresponding to the ultimate strength f u , and is the yield strain, i.e. y f y / E .
Ductility is one of the most important mechanical properties of modern steel materials which allow steel structures to undergo large deformations without fracture, especially in highly stressed parts of members or joints. Moreover, ductility facilitates mobilization of cross‐sectional resistances, and simplifies the determination of cross‐sectional resistances without the need to examine the actual stress distribution within a cross‐section. Hence, these three limits on ductility requirements are effective measures in providing a safety margin for steel structures against failure by plastic collapse through large or even excessive deformations in the strain‐hardening range of the steel materials.
3.2.3 Fracture toughness (1) The material should have sufficient fracture toughness to avoid brittle fracture of tension elements at the lowest service temperature expected to occur within the intended design life of the structure. The lowest service temperature for building and civil engineering structures in Hong Kong is 0 oC. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details.
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3.2.4 Through‐thickness properties (1) Where steel materials with improved through‐thickness properties are necessary according to EN 1993‐1‐10, steel materials according to the required quality class in EN 10164 should be used. Table 3.3 Choice of quality class according to EN 10164
Target value of Z Ed according to EN 1993‐1‐10
Required value of Z Rd expressed in terms of design Z ‐values according to EN 10164
Z Ed 10
‐
10 Z Ed 20
Z15
20 Z Ed 30
Z25
Z Ed 30
Z35
The through‐thickness property is a measure of the ability of steel plates to ensure integrity against lamination (or separation) when they are subject to high tensile stresses acting in the through‐thickness direction.
For those welded steel plates with high tensile residual stresses induced in the through‐thickness direction, lamination within the plate thickness may occur leading to extensive local cracks in the welded zones. Hence, it is necessary to specify an appropriate target value for the permissible reduction in cross‐sectional area of the steel material in the through‐thickness direction, Z Ed . Particular care should be given to welded beam‐to‐column connections, and welded end plates where there is tension in the through‐thickness direction.
3.2.5 Tolerances (1) The dimensional and mass tolerances of plates, rolled sections, and hollow sections should conform to the relevant product standards unless more severe tolerances are specified. (2) (3)
For welded components, the tolerances given in EN 1090 should be applied. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details. For structural analysis and design, the nominal values of dimensions should be used.
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3.2.6 Design values of material coefficients Modulus of elasticity E = 210,000 N / mm2 Shear modulus G = E /21 = 81,000 N / mm2 Poisson’s ratio = 0.3 Coefficient of linear thermal expansion = 14 10 6 C Density 7850 kg / m3 3.3 Connecting Devices 3.3.1 Fasteners Requirements for fasteners are given in EN 1993‐1‐8. 3.3.2 Welding consumables Requirements for welding consumables are given in EN 1993‐1‐8.
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4 (1)
Durability The basic requirements for durability are set out in EN 1090. The durability of a structure is its ability to remain fit for use during its design working life given appropriate maintenance
According to EN 1990, a structure should be so designed that deterioration over its design working life does not impair the performance of the structure. Moreover, it is essential for a designer to identify various requirements that need to be allowed for during the design stage to achieve a high level of durability according to the expected design working life of the structure.
A structure should be designed in such a way, and provided with protection as necessary, so that no significant deterioration is likely to occur within the period between successive inspections. Critical parts of the structure need to be available for inspection, without complicated dismantling.
Other interrelated factors that need to be taken into account to ensure an adequately durable structure are given below:
(2)
intended and future use of the structure required performance criteria expected environmental influences composition, properties and performance of materials choice of structural system shape of members, structural detailing, and buildability quality of workmanship and level of control particular protective measures maintenance during the intended life
The means of executing the protective treatment undertaken off‐site and on‐site should be in accordance with EN 1090.
(3)
Parts susceptible to corrosion, mechanical wear or fatigue should be designed such that inspection, maintenance and reconstruction can be carried out satisfactorily and access is available for in‐service inspection and maintenance.
(4)B
For building structures, no fatigue assessment is normally required except as follows:
a) b) c) d)
members supporting lifting appliances or rolling loads members subject to repeated stress cycles from vibrating machinery members subject to wind‐induced vibrations members subject to crowd‐induced oscillations.
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(5)
For elements that cannot be inspected, an appropriate corrosion allowance should be included.
(6)B
Corrosion protection does not need to be applied to internal building structures if the internal relative humidity does not exceed 80%. The following factors should be taken into account in design of corrosion protective systems for a structure in order to ensure its durability under conditions relevant both to its intended use and to its design working life.
The environment of the structure, whether bimetallic corrosion is possible and the degree of exposure of the structure. Accessibility of the structure for inspection and maintenance, (i.e. easy, difficult or impossible). Access, safety and member shapes, and structural detailing are relevant. The relationship between corrosion protection and fire protection systems.
Typical examples of commonly occurring exposure conditions are given below.
Table 4.1 Exposure conditions Exposure Class 1 2 3
Type of Exposure
Non‐corrosive Mild (typically internal) Moderate (internal or external)
4
Severe
5
Extreme
Examples Steelwork in an internal controlled (i.e. dry) environment. Steel piles driven into undisturbed and non‐corrosive ground. Steelwork in an internal humid environment. Steelwork built into perimeter cladding. External steelwork in a dry climate. External steelwork exposed to rain and humidity. Internal steelwork over a swimming pool, kitchen or water tank. External steelwork in a marine environment. Steel piles driven into corrosive ground. Steelwork exposed to salt water.
Refer to the Code of Practice for the Structural Use of Steel (2011) for further details.
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Section 5 Structural Analysis 5.1 Structural Modeling for Analysis 5.1.1 Structural Modeling and basic assumptions (1) Analysis should be based upon calculation models of the structure that are appropriate for the limit state under consideration. Generally, a structural model is established in accordance with the geometry and the member configuration of a structure. An allowance for inevitable imperfections present within a structure is also made. It should be noted that no member imperfection is incorporated into the structural model since these are implicitly allowed for during structural design in accordance with Section 6. (2) The calculation model and the basic assumptions for the calculations should reflect the structural behaviour at the relevant limit state with appropriate accuracy, and reflect the anticipated type of behaviour of the cross‐sections, members, joints and bearings. (3) The method used for the analysis should be consistent with the design assumptions. When a designer considers connections in a steel structure to be either pinned joints or rigid joints during structural analysis, he needs to design these connections correspondingly. For a nominally pinned base of a structure, a 10% of the column EI stiffness is often assumed in structural analysis at ultimate limit state, in L particular, in assessing frame stability; and 20% at a serviceability limit state. 5.2 Global Analysis 5.2.1 Effects of deformed geometry of a structure (1) The internal forces and moments within a structure may generally be determined using either:
(2)
first order analysis, using the initial geometry of the structure or
second order analysis, taking into account the influence of the deformation of the structure.
The effects of deformed geometry (or the second‐order effects) should be considered if they increase the action effects significantly or modify significantly the structural behaviour. In general, the effects of deformed geometry of a structure are considered to be non‐ advantageous owing to large reduction in the resistances of the members.
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(3)
First order analysis may be used for the structure if the increase of the relevant internal forces or moments or any other change in the structural behaviour caused by deformations can be neglected.
(4)B
This condition may be assumed to be fulfilled if the following criterion is satisfied: F cr cr 10 for elastic analysis (5.1a) FEd or F cr cr 15 for plastic analysis (5.1b) FEd where cr is the factor by which the loading would have to be increased to cause elastic instability in a global mode; FEd is the design load acting on the structure; and
Fcr is the elastic critical buckling load for the global instability model based on initial elastic stiffnesses. Portal frames with shallow roof slopes and regular beam‐column plane frames in buildings may be checked for sway mode failure with first order analysis if Expression (5.1) is satisfied for each storey.
In these structures, cr may be calculated using the following approximate formula, provided that the axial compression in the beams or rafters is not significant: H h cr Ed VEd H , Ed
(5.2)
where: H Ed is the design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal forces (which are applied to produce the effects of sway imperfections to the structure as given in Clause 5.3.2); VEd is the total design vertical load on the structure acting at the bottom of the storey; H , Ed is the horizontal displacement at the top of the storey, relative to the bottom of the storey, when the frame is loaded with horizontal loads (e.g. wind) and fictitious horizontal forces which are applied at each floor level; and is the storey height.
h In the U.K., Expression 5.2 above is considered to be inappropriate for portal frames. A modified expression for portal frames cr ,est should be calculated following the
recommended approach given in the paper entitled “Eurocode 3 and the in‐plane stability of portal frames” which was published in the November 2005 issue of The Structural Engineer.
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5.2.2 Structural stability of frames (1) If, according to Clause 5.2.1, the influence of the deformation of the structure has to be taken into account, (2) to (6) should be applied to consider these effects and to verify its structural stability. (2) Verification of the structural stability of frames or their parts should be carried out considering: i) imperfections, and ii) second order effects. (3) According to the type of the frame and of the global analysis, imperfections and second order effects may be accounted for by one of the following methods: a) both totally by global analysis; b) partially by global analysis and partially through individual stability checks of members according to Clause 6.3; and c) for basic cases by individual stability checks of equivalent members according to Clause 6.3 using appropriate buckling lengths according to the global buckling mode of the structure. (4)
(5)B
Second order effects may be calculated by using an analysis appropriate to the structure (including step‐by‐step or other iterative procedures). For frames where the first sway buckling mode is predominant, first order elastic analysis should be carried out with subsequent amplification of relevant action effects (e.g. additional bending moments) by appropriate factors. For single storey frames designed on the basis of elastic global analysis, second order sway effects due to vertical loads may be calculated by increasing the horizontal loads HEd (e.g. wind) and equivalent loads VEd φ due to imperfections (see Clause 5.3.2(7)), and other possible sway effects according to first order theory by the factor:
1 1
1 cr
provided that αcr ≥ 3.0,
(5.3)
where cr may be calculated according to Expression (5.2) in Clause 5.2.1(4)B, provided that the roof slope is shallow and that the axial compression in the beams or rafters is not significant as defined in Clause 5.2.1(4)B. 5.3 Imperfections 5.3.1 Basis (1) Appropriate allowances should be incorporated in the structural model to cover the effects of imperfections, including residual stresses and geometrical imperfections such as lack of verticality, lack of straightness, lack of flatness, lack of fit and any minor eccentricities present in joints of the unloaded structure.
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(2)
(3)
Equivalent geometric imperfections should be used with values which reflect the possible effects of all types of imperfections unless these effects are included in the resistance formula for member design. The following imperfections should be taken into account: a) global imperfections for frames and bracing systems b) local imperfections for individual members
It is essential to incorporate imperfections in the structural model of a structure. Global imperfections may be taken into account by modelling the frame out‐of‐ plumb, or by a series of equivalent horizontal forces applied to a frame modelled vertically. In general, the latter approach is recommended. It should be noted that i) imperfections in individual members may be modelled, or ii) members may be modelled as straight whilst imperfections are implicitly allowed for by verifying member resistances in accordance with Section 6. 5.4 Methods of Analysis Allowing for Material Non‐linearities 5.4.1 General (1) The internal forces and moments in a structure may be determined using either a) elastic global analysis, or b) plastic global analysis. (2) (3)
(4)B
Elastic global analysis may be used in all cases. Plastic global analysis may be used only where the structure has sufficient rotation capacity at the actual locations of the plastic hinges, whether this is in the members or in the joints. Where a plastic hinge occurs in a member, the member cross‐section should be doubly symmetric or singly symmetric with a plane of symmetry in the same plane as the rotation of the plastic hinge, and it should satisfy the requirements specified in 5.6. Where a plastic hinge occurs in a joint, the joint should have sufficient strength to ensure the hinge remains in the member, i.e. it should be able to sustain the plastic resistance of the member for a sufficient rotation. As a simplified method for a limited plastic re‐distribution of moments in continuous beams where following an elastic analysis, some peak moments exceed the plastic bending resistances by a maximum of 15%, the parts in excess of these peak moments may be re‐distributed in any member, provided that:
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a) the internal forces and moments in the frame remain in equilibrium with the applied loads, b) all the members in which the moments are reduced have Class 1 or Class 2 cross sections, and c) lateral torsional buckling of the members in prevented. 5.4.2 Elastic global analysis (1) Elastic global analysis should be based on the assumption that the stress‐strain behaviour of the material is linear, whatever the stress level is. (2) Internal forces and moments may be calculated according to elastic global analysis even if the resistance of a cross‐section is based on its plastic resistance. (3) Elastic global analysis may also be used for cross‐sections of which the resistances are limited by local buckling. 5.4.3 Plastic global analysis (1) Plastic global analysis allows for the effects of material non‐linearity in calculating the action effects of a structural system. The behaviour should be modelled by one of the following methods: ‐ by elastic‐plastic analysis with plastified sections and joints as plastic hinges, ‐ by non‐linear plastic analysis considering the partial plastification of members in plastic zones, or ‐ by rigid plastic analysis neglecting the elastic behaviour between hinges. (2) Plastic global analysis may be used where the members have sufficient rotation capacity to enable the required re‐distributions of bending moments to develop. (3) Plastic global analysis should only be used where stability of the members at plastic hinges can be assured. (4) A bi‐linear stress‐strain relationship may be used for the grades of structural steel specified in Section 3. (5) Rigid plastic analysis may be applied if no effects of the deformed geometry (e.g. second‐order effects) have to be considered. In this case, joints are classified only by strengths. (6) The effects of deformed geometry of the structures and the corresponding structural stability of the frame should be verified according to the principles in 5.2.
44
5.5
Classification of Cross‐sections
5.5.1 Basis (1)
The role of cross section classification is to identify the extent to which the moment resistances and the rotation capacities of the cross‐sections are limited by their local buckling resistances.
5.5.2 Classification (1)
Four classes of cross‐sections are defined, as follows:
Class 1 cross‐sections are those which can form a plastic hinge with the rotation capacity required for plastic analysis without reduction of the resistance.
Class 2 cross‐sections are those which can develop their plastic moment resistance, but which have limited rotation capacity because of occurrence of local buckling.
Class 3 cross‐sections are those in which the stresses in the extreme compression parts of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance.
Class 4 cross‐sections are those in which local buckling will occur before the attainment of yield strength in one or more parts of the cross‐sections. Class 4 cross‐sections are outside the scope of this document.
(2) (3) (4) (5)
Compression parts include every part of a cross‐section which is either totally or partially in compression under the load combination considered. A cross‐section is classified according to the highest (least favourable) class of its compression parts. The limiting proportions for Class 1, 2, and 3 compression parts should be obtained from Table 5.1. A part which fails to satisfy the limits for Class 3 should be taken as Class 4.
45
5.6 (1)
Cross‐section Requirements for Plastic Global Analysis At plastic hinge locations, the cross‐section of the member which contains the plastic hinge should have a rotation capacity of not less than that required at the plastic hinge location.
(2)
In a uniform member, sufficient rotation capacity may be assumed at a plastic hinge if both the following requirements are satisfied:
a) The member has a Class 1 cross‐section at the plastic hinge location; and b) Where a transverse force that exceeds 10% of the shear resistance of the cross‐ section is applied to the web at the plastic hinge location, web stiffeners should be provided within a distance along the member of h/2 from the plastic hinge location, where h is the height of the cross‐section at this location. Table 5.1a
Maximum c/t ratios of compression parts Outstand flanges c
t
Class Stress distribution in parts (compression positive)
1 2 Stress distribution in parts (compression positive)
3
Rolled sections Welded sections Part subject to bending and compression Part subject to compression Tip in compression Tip in compression
v+
+
v+
v-
c 9 ε t c 10 ε t
v-
c 9 ε t c 10 ε t
+
-
c 9 ε t c 10 ε t
+
c 21 ε k t For k see EN 1993‐1‐5
c 14 ε t
46
+
-
Table 5.1b
Maximum c/t ratios of compression parts Internal compression parts
Axis of bending
c c
t t
t
Class Stress distribution in parts (compression positive)
Axis of bending
c
Part subject to bending
Part subject to compression
Part subject to bending and compression
+
+ +
-
-
1
2
Stress distribution in parts (compression positive)
3
c 72 t
c 33 t
c 83 t
c 38 t
when 0.5
396 c t 13 1
when 0.5
c 36 t
when 0.5
456 c t 13 1
when 0.5
c 41.5 t
+
+
c
+
-
c 124 t
-
c 42 t
The values of and are given by
N Ed 1 1 2 f y c t w N (2) Ed 1 A fy
(1)
where N Ed is positive in compression.
47
when 1
c 42 t 0 .67 0 .33
when 1
c 62 1 t
Table 5.1c
Maximum c/t ratios of compression parts
t
d
t
d
Class
Section in bending and/or compression d 50 ε 2 t d 70 ε 2 t d 90 ε 2 t
1 2 3
48
Section 6 Ultimate Limit States 6.1 Partial Factors for Resistances (1) The partial factors M should be applied to the various characteristic values of resistances in this section as follows:
Resistances Resistances of cross-section in tension, compression, shear, and
6.2
UKNA
Hong Kong
bending, and any of their combination,
M0
1.0
1.0
1.0
Resistances of members to instability,
M1
1.0
1.0
1.0
1.25
1.1
1.1
Resistances of cross-sections in tension to fracture,
EC3
M2
M 2 is used with ultimate material strengths, for example when verifying net areas subject to tension (see Clause 6.2.3(3)(b)) and when verifying net areas subject to a shear force in connection design. A different value of M 2 is used when calculating the resistance of connection components. Resistances of Cross‐Sections
6.2.1 General (1)P The design value of an action effect in each cross‐section, Ed , should not exceed the corresponding resistance, Rd. Ed
≤
Rd
Ed 1 Rd
Design checking against a cross‐section resistance rather than a limiting stress within the cross‐section allows economical design as the post‐yielding strength or even the plastic resistance of the cross‐section is mobilized. Moreover, the formulation is consistent for various degrees of strength mobilization including i) elastic, ii) elastro‐ plastic, and iii) plastic stress blocks.
(2)
(3)
or
(6.1)
If several action effects act simultaneously, the combined effect should not exceed the resistance for that combination. Shear lag effects and local buckling effects should be included by an effective width according to EN 1993‐1‐5. Shear buckling effects should also be considered according to EN 1993‐1‐5. The design values of resistances should depend on the classification of the cross‐ section.
49
(4)
(5)
Elastic verification according to the elastic resistance may be carried out for all cross sectional classes provided the effective cross sectional properties are used for the verification of Class 4 cross sections. The plastic resistance of cross sections should be verified by finding a stress distribution which is in equilibrium with the internal forces and moments without exceeding the yield strength. This stress distribution should be compatible with the associated plastic deformations.
6.2.2 Section properties
6.2.2.1 Gross cross‐section (1) The properties of the gross cross‐section should be determined using the nominal dimensions. Section analysis should be performed to determine various section properties using the nominal dimensions of the gross cross‐section, and typically these include:
Cross‐sectional area, A; Second moment of area, I; Radius of gyration, i; Section modulus – elastic, Wel and plastic, Wpl
Refer to Appendix D for a worked example on section analysis of a rolled I‐section. Holes for fasteners need not be deducted, but allowance should be made for larger openings. Splice materials should not be included.
6.2.2.2 Net section
(1) (2)
The net area of a cross‐section should be taken as its gross area less appropriate deductions for all holes and other openings. For calculating net section properties, the deduction for a single fastener hole should be the gross cross‐sectional area of the hole in the plane of its axis. For countersunk holes, appropriate allowance should be made for the countersunk portion. For deductions where the holes are staggered, refer to BS EN 1993‐1‐1 Clause 6.2.2.2(4).
6.2.3 Tension force (1)P The design value of the tension force N Ed at each cross‐section should satisfy:
N Ed N t ,Rd
1.0
(6.2)
50
(2)
For a section without holes, the design tension resistance N t , Rd should be taken as the smaller of: a) the design plastic resistance of the gross cross‐section, N pl,Rd , which should be
determined as follows: Af N pl,Rd y M0
(6.3a)
b) the design ultimate resistance of the net cross‐section at holes for fasteners, N u , Rd , which should be determined as follows:
N u ,Rd (3)
0.9A net f u M2
(6.3b)
For an angle connected through one leg, see BS EN 1993‐1‐8 Clause 3.10.3. Similar consideration should also be given to other types of sections connected through outstands. As the action is applied at an eccentricity to the centroid of the cross‐section, additional moment is induced. For simplicity, instead of designing the cross‐section under combined axial force and bending, the cross‐sectional area is reduced instead.
6.2.4 Compression force (1)P The design value of the compression force N Ed at each cross‐section should satisfy: N Ed 1.0 (6.4) N c,Rd (2)
(3)
The design resistance of the cross‐section for uniform compression N c ,Rd should be determined as follows: Af N c,Rd y N pl,Rd for Class 1, 2 or 3 cross‐sections (6.5) M0 where N pl,Rd is the design plastic resistance of the cross‐section for compression. Fastener holes, except for oversize and slotted holes as defined in EN 1090, need not be allowed for in compression members, provided that they are filled by fasteners.
6.2.5 Bending moment (1)P The design value of the bending moment M Ed at each cross‐section should satisfy: M Ed 1.0 (6.6) M c,Rd
where M c ,Rd is determined considering fastener holes, see (3) to (5).
51
(2)
The design resistance of the cross‐section for bending about one principal axis of the cross‐section, M c ,Rd , should be determined as follows:
M c,Rd M pl,Rd
M c,Rd M el,Rd
where Wel ,min
Wplf y
M0
Wel,min f y M0
for Class 1 or 2 cross‐sections
(6.7a)
for Class 3 cross‐sections
(6.7b)
is the minimum elastic section modulus which corresponds with the
maximum elastic stress; M pl,Rd is the design plastic resistance for bending; and
M el,Rd (3) (4)
(5)
(6)
is the design elastic resistance for bending.
For bending about both axes, the methods given in Clause 6.2.9 should be used. Fastener holes in the tension flange may be ignored in determining the bending resistance provided that for the tension flange:
Af f y A f ,net 0.9f u M2 M0 where Af A f ,net
(6.8)
is the area of the tension flange; and is the net area of the tension flange.
Fastener holes in the tension zone of the web need not be allowed for, provided that the limit given in (4) is satisfied for the complete tension zone comprising the tension flange plus the tension zone of the web. Fastener holes, except for oversize and slotted holes, in the compression zone of the cross‐section need not be allowed for, provided they are filled by fasteners.
6.2.6 Shear force (1)P The design value of the shear force VEd at each cross‐section should satisfy: VEd (6.9) 1.0 V c,Rd where: Vc,Rd is the design shear resistance.
For plastic design, Vc,Rd is the design plastic shear resistance, Vpl ,Rd , as given in (2).
For elastic design, Vc,Rd is the design elastic shear resistance calculated using (4) and (5).
52
In the absence of torsion, the design plastic resistance for shear, Vpl, Rd , is given by:
(2)
Vpl,Rd
Av fy / 3 M0
where Av
(6.10)
is the shear area.
(3)
The shear area Av should be determined as shown in Figure 6.1.
tw + 2r 0.5tf hw
hw
tw
hw
tw
0.5tf b
Av = a) Rolled I‐ and H‐sections, load parallel to web
h
w
t w where 1.0
b) Welded I, H and box sections, load parallel to web
tf
tf
b
b
b
tf
Av 2 b tf
c) Rolled I‐ and H‐sections, load parallel to flange
b
d) Welded I, H and box sections, load parallel to flange
h
b
h
e) Rolled rectangular hollow sections of uniform thickness
Figure 6.1
f) Rolled circular hollow sections of uniform thickness
Shear areas for various rolled and welded sections [Cl. 6.2.6.(3)]
53
(4)
Shear buckling in webs without intermediate stiffeners is avoided if:
hw tw
(5)
72 where may be taken conservatively as 1.
(6.11)
Otherwise, the shear buckling resistance must be verified in accordance with EN 1993‐1‐5. Fastener holes need not be allowed for in shear verification except in verifying the design shear resistance at connection zones as given in EN 1991‐1‐8. A deduction for fastener holes is made when checking block tearing in accordance with EN 1991‐1‐8 Clause 3.10.2. Refer to Worked Example I‐1 Determination of section resistances of Part I of Appendix D for details. Also refer to Worked Example II‐1 Design of a fully restrained steel beam of Part II of Appendix D for details.
6.2.7 Torsion (1) For members subject to torsion for which distortional deformations may be disregarded, the design value of the torsional moment, TEd , at each cross‐section should satisfy: (2)
TEd 1.0 TRd
(6.12)
where TRd is the design torsional resistance of the cross‐section. As a simplification, in the case of a member with a closed hollow cross‐section, such as a structural hollow section, it may be assumed that the effects of torsional warping can be neglected. Also as a simplification, in the case of a member with open cross‐section, such as a I‐ or a H‐section, it may be assumed that the effects of St. Venant torsion can be neglected.
6.2.8 Bending and shear force (1) For a cross‐section under a shear force, allowance should be made for its effect on the bending resistance of the cross‐section. (2) When VEd 0.5Vpl,Rd (see Clause 6.2.6(2)), the effect of the shear force on the bending resistance may be neglected, except where shear buckling reduces the section resistance. See EN 1993‐1‐5.
54
(3)
When VEd 0.5Vpl,Rd , the reduced moment resistance, M y ,V ,Rd should be taken as the design resistance of the cross‐section, calculated using a reduced yield strength, 2
1 f y , for the shear area, where 2V Ed 1 , and V pl,Rd is obtained from V pl ,Rd Clause 6.2.6 (2).
2
(4)
2VEd When torsion is present should be obtained from 1 , see V pl, T , Rd Clause 6.2.7, but should be taken as 0 for VEd 0.5Vpl, T , Rd .
(5)
The reduced plastic moment resistance allowing for the effect of the shear force may be obtained for I‐sections with equal flanges and bending about the major axis as follows: A 2w W pl , y f y 4t w M y ,V ,Rd but M y ,V ,Rd M y ,c,Rd (6.13) M0 where: M y ,c,Rd is obtained from Clause 6.2.5(2)
Aw h w t w
For I‐ and H‐sections as well as rectangular and square hollow sections, the interaction of bending moments and shear forces is not severe as the induced stresses do not act along the same direction. Hence,
when VEd 0.5Vpl,Rd , the webs are fully effective to resist both the shear forces and the bending moments. The flanges are fully effective to resist the bending moments.
when VEd 0.5Vpl,Rd , the webs are primarily assigned to resist the shear forces although they may also contribute to resist the bending moments together with the flanges.
when VEd Vpl, Rd , the webs are fully utilized to resist the shear forces with no contribution to resist the bending moment. The flanges remain to be fully effective to resist the bending moments.
Refer to Worked Example I‐2 Cross section resistance under combined bending and shear of Part I of Appendix D for details.
55
6.2.9 Bending and axial force 6.2.9.1 Class 1 and 2 cross‐sections (1) When an axial force is present, allowance should be made for its effect on the plastic moment resistance. (2)P For Class 1 and 2 cross‐sections, the following criteria should be satisfied: M Ed 1 (6.14) M N ,Rd (3) (4)
where M N ,Rd is the reduced design plastic moment resistance under the axial force N Ed . For a rectangular solid section without fastener holes, N 2 M N ,Rd M pl,Rd 1 Ed N pl,Rd
N Ed 0.25 N pl ,Rd and
N Ed
(5)
, should be taken as: (6.15)
For doubly symmetric I‐ and H‐sections or other flanged sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the y‐y axis when both the following are satisfied:
,
(6.16a)
0.5h w t w f y
(6.16b) M0 For doubly symmetrical I‐ and H‐sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the z‐z axis when: h t f N Ed w w y (6.16c) M0 The following approximations may be used for standard rolled I‐ or H‐sections and for welded I‐ or H‐sections with equal flanges:
1 n
M N,y,Rd Mpl,y,Rd
for n a :
M N ,z ,Rd M pl,z ,Rd
(6.17a)
for n a :
n a 2 M N ,z ,Rd M pl ,z ,Rd 1 1 a
(6.17b)
where
n
a
1 0.5a
but M N ,y,Rd M pl,y ,Rd
N Ed N pl ,Rd
A 2bt f but a 0.5 A
56
(6.17)
(6)
The following approximations may be used for rectangular structural hollow sections of uniform thickness and for welded box sections with equal flanges and equal webs: 1 n M N,y,Rd M pl,y,Rd but M N ,y,Rd M pl,y ,Rd (6.17c) 1 0.5a w 1 n M N ,z ,Rd M pl,z ,Rd but M N ,z ,Rd M pl,z ,Rd (6.17d) 1 0.5a f where A 2bt f but a w 0.5 aw A A 2ht w but a f 0.5 af A In general, the effect of combined bending and axial force is more pronounced than that of the effect of combined bending and shear as the induced stresses act along the same (longitudinal) direction. The design formulation using plastic stress blocks utilizes the cross‐section resistance more effectively. For biaxial bending, the following criterion may be used:
M y ,Ed M z ,Ed 1 M N ,y ,Rd M N ,z ,Rd
(6.18)
in which and are constants and they may be taken as follows:
I‐ and H‐ sections Circular hollow sections Rectangular hollow sections
α 2 2 1.66 / (1‐1.13n2)
β 5n; but 1 2 1.66 / (1‐1.13n2)
where
Refer to Worked Example I‐3 Cross section resistance under combined bending and axial force of Part I of Appendix D for details.
n
N Ed N pl ,Rd
6.2.9.2 Class 3 cross‐sections (1) For Class 3 cross‐sections, the maximum longitudinal stress due to moment and axial force, taking account of fastener holes where relevant, should not exceed f y / M 0 .
For Class 3 cross‐sections, linear elastic interaction of the bending moment with the axial force should be used to determine the maximum longitudinal stress, which should not exceed the design yield strength, f y / M 0 , i.e. elastic design.
57
6.2.10 Bending, shear and axial forces (1)
Where shear and axial force are present in a cross-section, allowance should be made for the effect of both shear force and axial force on the moment resistance of the cross-section.
(2)
Where VEd 0.5Vpl, Rd , no reduction of the resistances defined for bending and axial force in 6.2.9 need be made, except where shear buckling reduces the section resistance, see EN 1993-1-5.
(3)
Where VEd 0.5Vpl, Rd , the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength, 2
1 f y , for the shear area, where 2VEd 1 , and Vpl , Rd is obtained from Vpl, Rd 6.2.6 (2). Instead of reducing the yield strength, it is also possible to reduce the plate thickness of the relevant part of the cross-section. In general, this approach requires more calculation, but gives smaller reductions, when compared with a reduction in yield strength.
58
6.3
Buckling Resistances of Members
6.3.1 Uniform members in compression EN 1993‐1‐1 covers three modes of buckling when subject to axial compression:
flexural buckling which may be critical in I‐ and H‐sections, and hollow sections
torsional buckling which may be critical for cruciform sections with wide outstands
torsional‐flexural buckling which may be critical for asymmetric sections
In general, torsional buckling and torsional flexural buckling are not the critical buckling modes for doubly symmetric I‐ or H‐sections or hollow sections of practical cross‐section dimensions and member lengths. Flexural buckling is also commonly known as axial buckling or Euler buckling.
6.3.1.1 Buckling resistance (1) A compression member should be verified against buckling as follows:
N Ed 1.0 N b , Rd
where: N Ed is the design value of the compression force
Nb,Rd is the design buckling resistance of the compression member
(2)
The design buckling resistance of a compression member should be taken as:
N b, Rd
Afy M1
(6.19)
for Class 1, 2 and 3 cross‐sections
(6.20)
where: is the reduction factor for the relevant buckling mode
6.3.1.2 Buckling curves (1) For axial compression in members, the value of for the appropriate non‐dimensional slenderness should be determined from the relevant buckling curve according to:
1
where
2 2
2
but 1.0
2 0.51 0.2 is an imperfection factor
is the non‐dimensional slenderness
59
(6.21)
(2)
Lcr 1 i
L cr N cr
is the buckling length in the buckling plane considered is the radius of gyration about the relevant axis is the elastic critical force for the relevant buckling mode
N cr
i
Af y
N cr
for Class 1, 2 and 3 cross sections
2 EI L2
for Class 1, 2 and 3 cross sections
For rolled or welded I‐ and H‐sections, torsional and torsional‐flexural buckling modes are not critical in practical cases. The imperfection factor corresponding to the appropriate buckling curve should be obtained from Tables 6.1 and 6.2, and Figure 6.2.
Table 6.1
Imperfection factors for flexural buckling curves
Buckling curve Imperfection factor
a0 0.13
a 0.21
b 0.34
c 0.49
d 0.76
(3)
The values of corresponding to the non‐dimensional slenderness may be obtained from Appendix A. The values of are tabulated in Table A1 of Appendix A for direct determination of the buckling curves for various steel materials.
(4)
For slenderness 0.2 or for N Ed / Ncr 0.04 , the buckling effects may be ignored and only cross‐sectional checks apply.
For a column member with a slenderness 0.2 , the column behaves essentially as a short column. Hence, axial buckling is not critical. Refer to Worked Example II‐3 Design of a steel column under axial compression of Part II of Appendix D for details.
60
Table 6.2
Selection of flexural buckling curve for a cross‐section Buckling curve Buckling about axis
S 235 S 275 S 355 S 420
S460
tf ≤ 40 mm
y‐y z‐z
a b
a0 a0
40 ≤ tf ≤ 100 mm
y‐y z‐z
b c
a a
tf ≤ 100 mm
y‐y z‐z
b c
a a
tf > 100 mm
y‐y z‐z
d d
c c
tf ≤ 40 mm
y‐y z‐z
b c
b c
tf > 40 mm
y‐y z‐z
c d
c d
hot‐finished
any
a
a0
cold‐formed
any
c
c
generally applicable except as below
any
b
b
thick welds: a > 0.5 tf b/tf < 30 b/tw < 30
any
c
c
Cross section
z
h/b > 1.2
Rolled sections
tf
Limits
y
h/b ≤ 1.2
y
z b
Welded sections
z
z
tf
y
y
y
tf y
z
Welded box sections
Hollow sections
z
z h
y
tf y
tw z b
61
1.2
1.0
0.8 a0 Curve a0
Curve a
0.6
Curve b Curve c
0.4
Curve d 0.2
0.0 0.0
0.5
1.0
1.5
2.0
slenderness, ̅
Figure 6.2
Buckling curves for axial compression in members
62
6.3.2 Uniform members in bending 6.3.2.1 Buckling resistance (1) A laterally unrestrained member subject to major axis bending should be verified against lateral‐torsional buckling as follows:
M Ed 1.0 M b , Rd
where MEd is the design value of the moment
M b , Rd is the design buckling resistance moment.
(2)
(3)
(6.22)
Beams with sufficient restraint to the compression flange are not susceptible to lateral‐ torsional buckling. In addition, beams with cross‐sections of circular or square hollow section`s, fabricated circular tubes or square box sections are not susceptible to lateral‐torsional buckling. The design buckling moment resistance of a laterally unrestrained beam should be taken as
fy
Mb, Rd LT Wy
where Wy is the appropriate section modulus as follows:
Wy Wpl, y
for Class 1 and 2 cross‐sections
Wy Wel, y
for Class 3cross‐sections
LT
is the reduction factor for lateral‐torsional buckling.
The following three different design procedures for members in bending are presented:
Procedure B1‐ Clause 6.3.2.2 Lateral torsional buckling curves – General case
Procedure B2‐ Clause 6.3.2.3 Lateral torsional buckling curves for rolled sections or equivalent welded sections
Procedure B3‐ An alternative procedure recommended by the Steel Designer’s Manual
M1
(6.23)
63
6.3.2.2 Lateral torsional buckling curves ‐ general case (1) For members of constant cross‐sections under bending, the value of for the ̅ appropriate non‐dimensional slenderness , should be determined from: LT
1 2
LT LT LT
2
but LT 1.0
(6.24)
where 2 LT 0.5 1 LT LT 0.2 LT
LT LT
is an imperfection factor Wyf y M cr
Mcr is the elastic critical moment for lateral‐torsional buckling Table 6.3 Buckling curves for lateral torsional buckling Cross‐section
Limits h / b ≤ 2 h / b > 2 h / b ≤ 2 h / b > 2 ‐
Rolled I‐sections Welded sections Other cross‐sections
Buckling curve a b c d d
Table 6.4
Imperfection factors for lateral torsional buckling curves
Buckling curve Imperfection factor LT
a 0.21
b 0.34
c 0.49
d 0.76
(2)
M cr is based on the gross cross‐sectional properties, and takes into account the loading conditions, the real moment distribution and the lateral restraints. An expression to evaluate M cr is not given in EN 1993‐1‐1. Refer to Appendix B1 for determination of M cr . Alternatively, the value of M cr may be determined using standard software with eigenvalue analysis.
(3)
For slenderness LT LT 0 or for
M Ed LT 0 2 , the lateral torsional buckling effects may M cr
be ignored, and only cross‐sectional checks apply.
For a beam member with a slenderness LT LT 0 , the beam behaves essentially as a short beam. Hence, lateral torsional buckling is not critical. A similar conclusion may be drawn for a beam with
M Ed LT 0 2 . M cr
Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details. 64
6.3.2.3 Lateral torsional buckling curves for rolled sections or equivalent welded sections (1) For rolled or equivalent welded sections in bending, the value of LT for the appropriate non‐dimensional slenderness LT should be determined from:
LT
1 2
LT LT LT
2
but LT 1.0 and LT
1 LT
2
(6.25)
where 2 LT 0.5 1 LT LT LT 0 LT
LT0 0.40 (maximum value)
0.75 (minimum value)
Table 6.5 Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h / b ≤ 2 h / b > 2 h / b ≤ 2 h / b > 2
Rolled I‐sections Welded sections
Buckling curve b c c d
Values of LT may be obtained from Figure 6.3. (2)
When taking into account the moment distribution between the lateral restraints of members, the reduction factor LT may be modified as follows:
LT , mod
LT f
but LT, mod 1.0
(6.26)
where f f kc
is the correction factor for the moment distribution 1 0.5 1 k c 1 2.0 LT 0.8 2 is a correction factor according to Table B2.4
Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details.
65
Table 6.6 Correction factors kc kc
Moment distribution =1
1.0
1 1.33 0.33
1 1
0.94
0.90
0.91 0.86
0.77
0.82
66
6.3.2.4 An alternative procedure recommended by the Steel Designers’ Manual (1) (2)
As an alternative to calculating M cr and hence LT , the value of LT may be calculated directly from the expression given below. Where loads are not destabilising, for simply supported rolled I‐, H‐sections and channel sections, the non‐dimensional slenderness LT is given by: 1 UVD z w C1
LT
where: 1 is a parameter dependant on the shape of the bending moment diagram, which C1
(6.27)
may conservatively be taken as 1.0, or otherwise given in Table 6.7 for loads which are not destabilizing.
U
is a section property which is given in section property tables, or may conservatively be taken as 0.9.
V
is a parameter related to slenderness, and for symmetric rolled sections where the loads are not destabilising, may be conservatively taken as 1.0 or as 1 V 2 z 1 4 1 20 h / t f
Conservatively, the product of U and V may be taken as 0.9.
z
z
L
is the distance between points of lateral restraint;
1
is a material parameter;
λ1
π
w
kL , in which k may conservatively be taken as 1.0 for beams supported and iz restrained against twist at both ends. With certain additional restraint conditions, k may be less than 1.0.
z 1
E 93.9 ε fy
Wy Wpl,y
67
It is conservative to assume that the product UV 0.9 and that w 1.0
(3)
Where loads are destabilizing, a parameter D should be introduced in the expression for LT . The value of D should be taken as 1.2 for simply supported beams. For cantilever beams, the value of D may range from 1.7 to 2.5, depending on the restraints provided at supports. Refer to NCCI SN002 for details.
Table 6.7
Values of
1 and C1 for various moment conditions C1
(load is not destabilizing) End Moment Loading
M
M 1
1
1 C1
C1
+1.00
1.00
1.00
+0.75
0.92
1.17
+0.50
0.86
1.36
+0.25
0.80
1.56
0.00
0.75
1.77
‐0.25
0.71
2.00
‐0.50
0.67
2.24
‐0.75
0.63
2.49
‐1.00
0.60
2.76
0.94
1.13
0.62
2.60
0.86
1.35
0.77
1.69
Intermediate Transverse Loading
2/3 1/3
The value of the imperfection parameter LT corresponding to the appropriate buckling curve is given by Table 6.8.
Table 6.8
Imperfection factors for lateral torsional buckling curves
Buckling curve Imperfection factor LT
a 0.21
68
b 0.34
c 0.49
d 0.76
(4)
Recommendations for the buckling curves are given in Table 6.9. Table 6.9
Recommendations for the selection of lateral torsional buckling curve
Cross‐section
Limits
Rolled doubly symmetric I and H sections, and hot‐ finished hollow sections Angles (for moments in the major principal plane) All other hot‐rolled sections
h/b 2 h/b 2
Cold‐formed hollow sections
h/b 2 2 h / b 3 .1 h / b 3 .1
Buckling curve b c d d d c d
Values of the reduction factor LT for the appropriate non‐dimensional slenderness
LT may be obtained from Figures 6.3 and 6.4. (5)
Values of LT may alternatively be determined from Tables B2.4 and B2.5 in Appendix B. Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details.
69
1.20
1.00 Curve b 0.80
Curve c Curve d
0.60
0.40
0.20
0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
Slenderness ratio, ̅
Figure 6.3
Lateral torsional buckling curves for rolled sections
1.20
1.00 Curve b 0.80
Curve c Curve d
0.60
0.40
0.20
0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
Slenderness ratio, ̅
Figure 6.4
Lateral torsional buckling curves for welded sections
70
2.00
Table 6.10
Comparison and design procedure of an unrestrained beam to EN 1993‐1‐1
Step
Procedure B1
Procedure B2
Procedure B3
Cl. 6.3.2.2 General case
Cl. 6.3.2.3 Rolled sections or equivalent welded sections
Steel Designer’s Manual
1
Mcr , Wyf y 2
C1, U, V, z , w
M cr is based on gross sectional properties and taken into account
C1 is based on the shape of the
loading conditions, moment distributions and lateral restrainsts.
LT
3
Wy f y
Rolled I‐sections Welded sections
h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
M cr
Buckling curves
5
a b c d
Rolled I‐sections Welded sections
C1
h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
b c c d
h/b ≤ 2 2 < h/b ≤ 3.1 h/b > 3.1 h/b ≤ 2 h/b > 2
Rolled I‐sections Welded sections
a
b
c
d
LT
0.21
0.34
0.49
0.76
LT,0 0.20
LT,0 0.40 (max.)
1 .00
1 .00 (min.)
b c d c d
For rolled sections, hot‐finished and cold‐formed hollow sections,
For rolled and equivalent welded sections,
UV z w
Buckling curves
Buckling curve
For all sections,
6
1
LT
Buckling curves 4
bending moment diagram.
LT,0 0.40 1 .00
For welded sections,
LT,0 0.20 1 .00
8
9
10
LT 0.5 1 LT LT LT 0 LT 2
7
LT
1 2
LT LT LT
M b,Rd LT
-
Wy f y M1
2
LT
1 2
LT LT LT
LT,mod
2
LT f
where f is based on the moment distribution between lateral restraints of the member.
M b,Rd LT,mod
71
Wy f y M1
LT
1 LT LT 2 LT 2
M b,Rd LT
-
Wy f y M1
6.3.3 Uniform members in bending and axial compression (1)
(2)
For members of structural systems, verification of buckling resistance of doubly symmetric cross‐sections may be carried out on the basis of the individual single span members regarded as cut out of the system. Second order effects of the sway system ( P effects) should be taken into account, either by considering the end moments of the member or by means of appropriate buckling lengths about each axis for the global buckling mode. Members which are subjected to combined bending and axial compression should satisfy: M y,Ed M z ,Ed N Ed k yy k yz 1 N b , y ,Rd M b ,Rd M cb ,z ,Rd M y ,Ed M z ,Ed N Ed k zy k zz 1 M cb ,z ,Rd N b ,z ,Rd M b ,Rd
where: N Ed , M y ,Ed and M z ,Ed are the design values of the compression force and the maximum moments about the y‐y and the z‐z axes along the member, respectively N b ,y ,Rd and N b ,z ,Rd are the design buckling resistances of the member about the
M b ,Rd
major and the minor axes respectively from Clause 6.3.1.1 (2) is the design buckling resistance moment from Clause 6.3.2.1(3)
M cb,z ,Rd
Wpl,z f y M1 Wel,z f y
for Class 1 and 2 sections
for Class 3 sections M1 k yy , k yz , k zy , k zz are interaction factors, which may be determined from Annex A or B of BS EN 1993‐1‐1. The above criteria are based on the expressions in Clause 6.3.3(4) of EN 1993‐1‐1, interpreted in accordance with ECCS TC8 Rules for Member Stability in EN 1993‐1‐1 Background documentation and design guidelines. Annex B is recommended as the simpler approach for manual calculations. Use of either Annex is permitted by the National Annex. In some cases, conservative values of the k factors may be sufficient for initial design. The following table gives maximum values, based on Annex B of the Standard, and assuming the sections are susceptible to torsional deformations (i.e. not hollow sections).
72
Interaction factor
k yy
Maximum values Class 1 and 2 Class 3 Cmy 1.8 Cmy 1.6
k yz
0.6 k zz
k zz
k zy
1.0
1.0
k zz
C my 2.4
C mz 2.4
Appendix D summarizes all the equations necessary to calculate the interaction factors. Alternatively, the values of the interaction factors may simply be read off from various graphs. Refer to Worked Example II‐4 Design of a beam‐column under combined compression and major axis bending of Part II of Appendix D for details.
6.3.4 Columns in simple construction The rules in this clause are based on the NCCI in Access Steel document SN048 (available from www.access‐steel.com) with some different symbols following modifications to the design value given in Clause 6.3.3. (1) When the criteria given in Clause 6.3.4(2) are satisfied, a column in simple construction subject to combined bending and axial compression may be verified against buckling failure as follows:
M y ,Ed M z ,Ed N Ed 1 .5 1 M cb,z ,Rd N min,b ,Rd M b,Rd
where: N Ed , My,Ed and M z,Ed are the design values of the compression force and the maximum
design bending moments about the y‐y and the z‐z axes along the member. y Af y z Af y N min,b ,Ed is the lesser of and M1 M1
M b ,Rd
LT
Wpl,y f y M1
Wpl,z f y
M cb,z ,Rd
(2)
The following criteria must be satisfied to use the verification given in (1):
M1
The column is a rolled H‐section, or equivalent welded sections. The cross‐section is Class 1, 2 or 3 under compression. The bending moment diagram about each axis is linear. The column is restrained laterally in both the y‐y and the z‐z directions at each floor, but it is unrestrained between floors. 0.11 where is the ratio of the moments at the two ends. For a pin ended column ( 0 ), the following alternative criterion must be satisfied to use the simplified interaction expression: 73
(3) (4)
y Af y N Ed (the resistance in the major axis) 0.83 in which N b,y,Rd M1 N b ,y,Rd
Note: 0 if there is a true pin at one end of the column (such as a base). In this case the simplified interaction expression is only valid if the axial force in the column is less than 83% of its resistance in the major axis. Where the criteria in Clause 6.3.4(2) are not satisfied, the method given in Clause 6.3.3 should be used. The design bending moments should be determined by considering the vertical beam reactions to act at a distance of 100 mm from the face of the column (web or flange).
74
Section 7 Serviceability Limit States 7.1 General (1)
(2)
A steel structure should be designed and constructed such that all relevant serviceability criteria are satisfied. Serviceability limit states consider service requirements for a structure or a structural member under normally applied actions. Examples are deflection, human induced vibration, wind induced oscillation and durability. The basic requirements for serviceability limit states are given in Clause 3.4 of EN 1990.
(3)
Any serviceability limit state and the associated loading model as well as the associated analysis model should be specified for a structure.
(4)
Where plastic global analysis is used for ultimate limit state design, plastic redistribution of forces and moments at the serviceability limit state should be considered accordingly.
The serviceability actions should be taken as the characteristic values of the actions, i.e. unfactored. 7.2 Serviceability Limit States for Buildings 7.2.1 Vertical deflections (1) With reference to EN 1990 – Annex 1.4 limits for vertical deflection according to Figure A1.1 should be specified for each structure and agreed with the client. 7.2.2 Horizontal deflections (1) With reference to EN 1990 – Annex 1.4 limits for horizontal deflection according to Figure A1.2 should be specified for each structure and agreed with the client. 7.2.3 Dynamic effects (1) With reference to EN 1990 – Annex 1.4.4, vibrations of structures which are accessible to the public should be limited to avoid significant discomfort to users, and limits should be specified for each structure and agreed with the client. Deflections or deformations under all actions should not impair the resistance or the effective functioning of a structure, a structural member, a supporting member or its components, nor cause damage to finishes. For typical structures, the deflection limits given in the following table are recommended.
75
Table 7.1
Suggested limits for vertical deflection due to characteristic combination (variable actions only)
a) Deflection of profiled steel sheeting Vertical deflection during construction when the effects of ponding are not taken into account Vertical deflection during construction when the effects of ponding are taken into account Vertical deflection of roof cladding under self‐weight and wind action Lateral deflection of wall cladding under wind action
Span/180 (but ≤ 20 mm) Span/130 (but ≤ 30 mm) Span/90 (but ≤ 30 mm) Span/120 (but ≤ 30 mm)
b) Vertical deflection of composite slab Due to imposed actions Due to the total actions plus due to prop removal (if any) less due to self‐weight of the slab
Span/350 (but ≤ 20 mm) Span/250
c) Vertical deflection of beams ‐ due to imposed actions Cantilevers Beams carrying plasters or other brittle finishes Other beams except purlins and sheeting rails Purlins and sheeting rails
Length/180 Span/360 Span/200 To suit cladding
d) Horizontal deflection of columns ‐ due to imposed actions and wind actions Horizontal drift at topmost storey of buildings Horizontal drift at top of a single storey portal not supporting human Relative inter‐storey drift Columns in portal frame buildings Columns supporting crane runways
Height/500 To suit cladding Storey height/400 To suit cladding To suit crane runway
e) Crane girders Vertical deflection due to static vertical wheel actions from overhead traveling cranes Horizontal deflection (calculated on the top flange properties alone) due to horizontal crane actions
Span/600 Span/500
f) Trusses Typical trusses not carrying brittle panels
Span/200
Note: Pre‐camber in an unloaded structural member may be used to reduce the calculated deflection of that member under the loading conditions.
76
7.3
7.4
Wind‐induced Oscillation Vibration and oscillation of a structure should be limited to avoid discomfort to users and damage to contents. For special structures, including long‐span bridges, large stadium roofs and chimneys, wind tunnel model tests are recommended to provide data for wind resistant design to meet serviceability limits. Wind Sensitive Buildings and Structures A design procedure which incorporates dynamic analysis in addition to static analysis should be undertaken for wind sensitive buildings and structures. Structures with low natural frequencies or large height‐to‐least dimension ratios should receive special checking. Reference should be made to the Code of Practice on Wind Effects in Hong Kong (2004). For slender, flexible and lightly damped tall buildings and structures, those with a long afterbody or complex geometry, and those with an eccentricity between mass and stiffness centres, aeroelastic instabilities such as lock‐in, galloping and flutter may cause large amplitude crosswind responses. Specialist advice and wind tunnel model test are recommended to provide data for wind resistant design to meet serviceability limits. Refer to the Code of Practice for the Structural Use of Steel (2011) for details.
77
Section 8 Design Data for Rolled and Welded Sections 8.1 General Tabulated design data are essential for practicing engineers to perform structural design. For structural steel design, section dimensions are the basic data, and rational use of these data gives important structural quantities, i.e. section properties and resistances of both rolled and welded sections, enabling designers to establish structural adequacy against strength requirements in ultimate limit states as well as structural performance against deformation or vibration in serviceability limit states. In this Section, design data on section dimensions and properties as well as section resistances of both rolled and welded sections with practical steel materials are provided to assist structural engineers to perform effective structural steel design. Table 8.1 presents the types of rolled and welded sections covered in the present Section. Typical cross‐sections of these rolled and welded sections are illustrated in Figure 8.1.
Table 8.1
Ranges of rolled and welded sections
Rolled sections Rolled I‐section: I‐section Rolled H‐section: H‐section Hot‐finished circular hollow section: CHS Hot‐finished rectangular hollow section: RHS Hot‐finished square hollow section: SHS
Welded sections Equivalent welded I‐section: EWI‐section Equivalent welded H‐section: EWH‐section Equivalent cold‐formed circular hollow section: EWCHS Equivalent cold‐formed rectangular hollow section: EWRHS Equivalent cold‐formed square hollow section: EWRHS
Rolled Sections It should be noted that both I‐ and H‐sections are manufactured to BS 4‐1 while all the hot‐finished hollow sections are manufactured to EN 10210‐2. All rolled I‐ and H‐ sections given in BS 4‐1 have been included in the present Section, but only selected hot‐finished hollow sections specified in EN 10210‐2 with a dimension larger than 100 mm are considered. All of these rolled sections are assumed to be manufactured to EN 10025 and EN10210‐1, and hence, they are commonly considered as steel Class E1 Steel Materials with a material class factor, Mc = 1.0 as discussed in Section 1.9. Resistances of all these sections with common steel grades, i.e. S275 and S355 steel materials, are tabulated in a systematic manner for practical design. Table 8.2 summarizes various design information provided for the rolled sections covered in this Section.
78
Rolled sections: I‐ and H‐sections to: ‐ ‐
EN 10025 on materials BS4‐1 on dimensions
CHS, RHS and SHS to: I‐section
Circular hollow section CHS
‐ ‐
H‐section
EN 10210‐1 on materials EN 10210‐2 on dimensions
Rectangular hollow section RHS
Square hollow section SHS
Welded sections: EWIS and EWHS to: ‐ GB/T 700 & GB/T 1591 on materials ‐ design methods in Section 8.4
EWCHS, EWRHS and EWSHS to: Equivalent welded I‐section EWI‐section
Equivalent welded H‐section EWH‐section
Equivalent cold‐formed Equivalent cold‐formed rectangular circular hollow section hollow section EWRHS EWCHS
‐ GB/T 6725 & GB/T 8162 on materials ‐ design methods in Section 8.4 as well as GB/T 6728 & GB/T 17395 on dimensions.
Equivalent cold‐formed square hollow section EWSHS
Figure 8.1 Cross‐sections of typical rolled and welded sections Detailing rules of welding for I‐ and H‐sections (1) The height of the weld root, r, is assumed to be equal to the thickness of the web, tw, or at least 0.7 times the flange thickness, i.e. 0.7 tf , whichever is smaller. (2) To ensure welding quality, r should not be smaller than 8.0 mm nor larger than 16.0 mm.
79
Table 8.2 Summary of design information for rolled sections
I‐section z
H‐section
CHS
RHS
SHS
z
z
z
z
y
y
y
y
y
Dimensions and properties Resistances for S275 steel Resistances for S355 steel
72 sections
31 sections
55 sections
44 sections
32 sections
Note: All these rolled sections are assumed to be Class E1 Steel Materials with a material class factor
Mc 1.0 as discussed in Section 1.9.
Welded sections Equivalent welded I‐ and H‐sections All the equivalent welded I‐ and H‐sections are fabricated with steel plates to GB/T 700 and GB/T 1591 with standard thicknesses. For simplicity, the following plate thicknesses are assumed: 6.0 mm 8.0 mm 10.0 mm 12.0 mm 16.0 mm 20.0 mm 25.0 mm 30.0 mm 40.0 mm 50.0 mm 60.0 mm 80.0 mm It is envisaged that with a rational combination of these plate thicknesses in the flanges and the webs of the sections, a series of welded sections with similar section depths and flange widths are readily manufactured covering a wide range of section properties and resistances for practical design. These section properties and resistances are similar to those rolled sections in the same series of section designations. Moreover, resistances of all these sections with common steel grades, i.e. Q235, Q275, Q345 and Q460 steel materials, are tabulated in a systematic manner for practical design. Equivalent cold formed hollow sections All the equivalent cold‐formed hollow sections are manufactured with steel plates to GB/T 6725 and GB/T 8162 while their dimensions are manufactured to GB/T 6728 and GB/T 17395. The following plate thicknesses are assumed: 6.0 mm 8.0 mm 10.0 mm 12.0 mm 16.0 mm 20.0 mm
80
Depending on the performance of material properties as well as the demonstration of quality assurance system during manufacturing, Chinese Steel Materials may be classified as Class E1 or E2 Steel Materials with a material class factor, Mc 1.0 or 1.1 respectively as discussed in Section 1.9. Resistances of all these sections with common steel grades, i.e. Q275, Q345 and Q460 steel materials, are tabulated in a systematic manner for practical design. All of these welded sections are proposed as equivalent welded sections to those rolled sections based on various structural requirements, such as compression and bending resistances. Standard welding procedures are assumed to be applied effectively during their fabrication. Table 8.3 summarizes various items of design information provided for the equivalent welded sections covered in this Section. Table 8.3 Summary of design information for equivalent welded sections EWI‐ EWH‐ EWCHS EWRHS EWSHS section section z
z
z
y
y
y
z
z
y
y
Dimensions and properties
72 sections
31 sections
55 sections
44 sections
32 sections
Resistances for Q235 steel
‐‐‐
‐‐‐
‐‐‐
Resistances for Q275 steel
Resistances for Q345 steel
Resistances for Q460 steel
Note: Depending on the performance of material properties as well as the demonstration of quality assurance system during manufacturing, Chinese Steel Materials may be classified as Class E1 or E2 Steel Materials with a material class factor, Mc = 1.0 or 1.1 respectively, as discussed in Section 1.9. For ease of presentation, all welded sections presented in Design Tables 19 to 45 are conservatively assumed to be made of Class E2 Steel Materials. However, if Class E1 Steel Materials are used in the welded sections, Mc should then be taken as 1.0 and all the resistances presented in Design Tables 19 to 45 should be increased by a factor of 1.1 accordingly.
81
8.2
Design strengths For rolled sections with S275 and S355 Class E1 Steel Materials, the design strengths of the steel sections with steel plates of various thicknesses are presented in Table 8.4. Table 8.4 Design strengths of different steel grades of rolled sections Class E1 Steel Materials with Mc 1.0 Steel grade
S275
S355
Thickness, t (mm) t 16 16 < t 40 40 < t 63 63 < t 80 t 16 16 < t 40 40 < t 63 63 < t 80
Design strength (N/mm2) 275 265 255 245 355 345 335 325
For welded sections with Q235, Q275, Q345 and Q460 Class E2 Steel Materials, the design strengths of the steel sections with steel plates of different thicknesses are presented in Table 8.5. Table 8.5 Design strengths of different steel grades of welded sections Class E2 Steel Materials with Mc 1.1 Design strength, fy Thickness, t (N/mm2) (mm) t 16 213.6 16 < t 40 204.5 Q235 40 < t 60 195.5 60 < t 80 195.5 t 16 250.0 16 < t 40 240.9 Q275 40 < t 60 231.8 60 < t 80 222.7 t 16 313.6 16 < t 40 304.5 Q345 40 < t 63 295.5 63 < t 80 286.4 t 16 418.2 16 < t 40 400.0 Q460 40 < t 63 381.8 63 < t 80 363.6 Note: For ease of presentation, all welded sections are conservatively assumed to be made of Class E2 Steel Materials. However, if Class E1 Steel Materials are used in the Steel grade
welded sections, Mc should then be taken as 1.0 and all the resistances presented in Design Tables 19 to 45 should be increased by a factor of 1.1 accordingly.
82
8.3
Section Classification Section classification of all the rolled and the welded sections are performed according to Clause 5.5 of EN 1993‐1‐1. Depending on the susceptibility of various plate elements of the sections against local buckling under compression, plastic or elastic cross‐section resistances may be readily mobilized for Class 1, 2 or 3 sections. For Class 4 sections, elastic properties are not applicable, and provisions given in EN 1993‐1‐8 should be considered. Table 8.6 presents the section classification rules given in Table 5.2 of EN 1993‐1‐1 for I‐ and H‐sections while Table 8.7 presents various limiting ratios of the geometric parameters of the sections, namely, cf / tf and d / tw for section classification under i) compression, ii) bending about the major axis, and iii) bending about the minor axis. Table 8.6 Section classification rules for I‐ and H‐sections z z
y
cf
y
d
d
cf
Rolled I‐section
Rolled H‐section
z z
y cf
cf
d
Plate element Internal part under compression, d/tw Internal part under bending, d/tw Outstanding part under compression, cf / tf
ε = 235/fy
Class 1 ≤ 33 ε ≤ 72 ε ≤ 9 ε
d
Class 2 ≤ 38 ε ≤ 83 ε ≤ 10 ε
fy (N/mm2)
235
275
345
355
460
ε
1.00
0.92
0.83
0.81
0.71
83
y
Class 3 ≤ 42 ε ≤ 124 ε ≤ 14 ε
Class 4 > 42 ε > 124 ε >14 ε
Table 8.7 Limiting ratios of section classification for I‐ and H‐sections I‐ and H‐sections under compression Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
Class 1
Class 2
Class3
8.3 7.3 9.0 8.3 7.4 6.4
9.3 8.1 10.0 9.2 8.3 7.1
12.9 11.4 14.0 12.9 11.6 10.0
30.5 26.8 33.0 30.5 27.2 23.6
35.1 30.9 38.0 35.1 31.4 27.2
38.8 34.2 42.0 38.8 34.7 30.0
I‐ and H‐sections under bending about the major axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
Class 1
Class 2
Class3
8.3 7.3 9.0 8.3 7.4 6.4
9.2 8.1 10.0 9.2 8.3 7.1
12.9 11.4 14.0 12.9 11.6 10.0
66.6 58.6 72.0 66.6 59.4 51.5
76.7 67.5 83.0 76.7 68.5 59.3
114.6 100.9 124.0 114.6 102.3 88.6
I‐ and H‐sections under bending about the minor axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
8.3 7.3 9.0 8.3 7.4 6.4
9.2 8.1 10.0 9.2 8.3 7.1
12.8 11.2 13.8 12.8 11.4 9.9
84
Class 1
Class 2
Class3
Not applicable
Not applicable
Table 8.8 presents the section classification rules given in Table 5.2 of EN 1993‐1‐1 for hot‐finished and cold‐formed hollow sections while Table 8.9 presents various limiting ratios of the geometric parameters of the hollow sections, namely, cf / t and cw / t for section classification under i) compression, ii) bending about the major axis, and iii) bending about the minor axis. Table 8.8 Section classification of hollow sections z
z
z y
y
cw
cw
h
cf
cf
t d
b
Hot‐finished circular hollow section CHS
Hot‐finished rectangular hollow section RHS
t
Hot‐finished square hollow section SHS
z
z
y
z
cw
y
cw
h
t
cf
d
t
b
Equivalent cold‐formed circular hollow section EWCHS
b
Equivalent cold‐formed square hollow section EWSHS
Equivalent cold‐formed rectangular hollow section EWRHS
Plate element Internal parts under compression, cf / t Internal parts under bending, cw / t
Class 1 ≤ 33 ε ≤ 72 ε
Class 2 ≤ 38 ε ≤ 83 ε
Class 3 ≤ 42 ε ≤ 124 ε
Class 4 > 42 ε > 124 ε
Circular section under compression and / or bending, d / t
≤ 50ε2
≤ 70ε2
≤ 90ε2
> 90ε2
ε = 235/fy
fy (N/mm2)
235
275
345
355
460
ε
1.00
0.92
0.83
0.81
0.71
85
Table 8.9 Limiting ratios of section classification for hollow sections a) Rectangular and square hollow sections Rectangular and square hollow sections under compression Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Flange
Web
cf / t
cw / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Rectangular and square hollow sections under bending about the major axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Flange
Web
cf / t
cw / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Class 1 66.6 58.6 72.0 66.6 59.4 51.5
Class 2 76.7 67.5 83.0 76.7 68.5 59.3
Class 3 114.6 100.9 124.0 114.6 102.3 88.6
Rectangular and square hollow sections under bending about the minor axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Web
Flange
cw / t
cf / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
86
Class 1 66.6 58.6 72.0 66.6 59.4 51.5
Class 2 76.7 67.5 83.0 76.7 68.5 59.3
Class3 114.6 100.9 124.0 114.6 102.3 88.6
b)
Circular hollow sections
Circular hollow sections under i) compression, and ii) bending Plate element
Circular section
Geometrical parameter Section classification Rolled section
Welded section
S275 S355 Q235 Q275 Q345 Q460
d / t Class 1
Class 2
Class 3
42.7 33.1 50.0 42.7 34.1 25.5
59.8 46.3 70.0 59.8 47.7 35.8
76.9 59.6 90.0 76.9 61.3 46.0
8.4
Rolled Sections A wide range of rolled sections covered in this Section for application are summarized in Table 8.10. It should be noted that i) all rolled I‐sections available in BS 4‐1 are included in the Design Tables, i.e. I‐ sections from 127 x 76 x 13 kg/m to 914 x 419 x 388 kg/m with a total of 72 sections. ii) all rolled H‐sections available in BS 4‐1 are included in the Design Tables, i.e. H‐ sections from 152 x152 x 23 kg/m to 356 x 406 x 634 kg/m with a total of 31 sections. iii) selected hot‐finished circular hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. CHS from 139.7 x 6.3 mm to 813.0 x 20.0 mm with a total of 55 sections. iv) selected hot‐finished rectangular hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. RHS from 120 x 80 x 6.3 mm to 500 x 300 x 20.0 mm with a total of 44 sections. v) selected hot‐finished square hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. SHS from 100 x 100 x 6.3 mm to 400 x 400 x 20.0 mm with a total of 32 sections.
87
Table 8.10
Full ranges of typical rolled sections available for application
I-section
H-section
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
29
43
Number of sections: Total:
72
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
31
Hot-finished circular hollow section 139.7x6.3 x8.0 x10.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 x16.0 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.0x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Hot-finished rectangular hollow section 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
55
44
Hot-finished square hollow section 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.3 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
32 234
# Limited availability. Full series of I‐ and H‐sections have been provided while only selected hot‐finished circular, rectangular and square hollow sections are included. Section resistances for S275 and S355 steel materials are tabulated separately.
88
8.5
Equivalent Welded Sections Design data on equivalent welded sections are provided to assist structural engineers to use welded sections readily whenever necessary. The design methods for equivalent welded sections are described in the following sections.
8.5.1 Equivalent welded I‐Sections (1) The section depth h of the welded I‐sections is selected to be equal to that of the rolled I‐sections under consideration plus a maximum of 5 mm. (2) The plate thicknesses of the flanges and the webs of the welded I‐sections are:
6.0 mm 12.0 mm 25.0 mm (3)
8.0 mm 16.0 mm 30.0 mm
10.0 mm 20.0 mm 40.0 mm
In most cases, both the web thickness and the flange thickness of the equivalent welded I‐sections are taken to be larger than those of the rolled I‐sections as far as rational, as shown in Figure 8.2. Moreover, the flange width of the welded I‐sections is selected in such a way as to achieve a value of cross‐sectional area which is at least 10% larger than that of the rolled I‐sections. z
z tf
tf 5 max.
y
y
h
h 5 max.
tw 5 max.
tw
b 30 typ.
b
Equivalent welded I‐section
Typical rolled I‐section
Figure 8.2 Design method of equivalent welded I‐sections (4)
For a rolled I‐section with a web thickness or a flange thickness of odd values, for example, tw = 8.7 mm or tf = 13.2 mm, the web thickness and the flange thickness of the welded I‐section are then selected to be 8.0 mm and 12.0 mm (rather than 10.0 mm and 16.0 mm) respectively, i.e. of thinner plates. In order to achieve equivalency, the flange width of the welded I‐section will then be increased significantly, when compared with that of the rolled I‐section, in order to acquire a larger moment resistance of that of the rolled I‐section.
89
8.5.2 Equivalent welded H‐sections
(1) (2)
The section depth h of the welded H‐sections is selected to be equal to that of the rolled H‐sections under consideration plus a maximum of 5 mm. The plate thicknesses of the flanges and the webs of the welded H‐sections are:
6.0 mm 12.0 mm 25.0 mm 50.0 mm
(3)
8.0 mm 16.0 mm 30.0 mm 60.0 mm
10.0 mm 20.0 mm 40.0 mm 80.0 mm
In most cases, both the web thickness and the flange thickness of the welded H‐ sections are taken to be larger than those of the rolled H‐sections as far as rational, as shown in Figure 8.3. Moreover, the flange width of the welded H‐sections is selected in such a way as to achieve a value of cross‐sectional area which is at least 10% larger than that of the rolled H‐sections. z
z
tf
tf+10 max.
hw
y
O
hw
h
h + 5 max. O
tw + 5
tw
b
b 50 typ.
Typical rolled H‐section
Equivalent welded H‐section
Figure 8.3 Design method of equivalent welded H‐sections (4)
y
As there is a significant reduction in the yield strengths of thick steel plates, especially when tf ≥ 40 mm, the flange thicknesses of the proposed welded H‐ sections may be significantly larger than those of the rolled H‐sections. Nevertheless, the maximum increase in the flange thickness is limited to 10 mm.
90
8.5.3 Equivalent cold‐formed circular hollow sections
(1)
(2)
The external diameter d of the EWCHS is selected to be equal to that of the hot‐ finished CHS under consideration plus a maximum of 5 mm. The plate thicknesses of the EWCHS are:
6.0 mm 12.0 mm
8.0 mm 16.0 mm
10.0 mm 20.0 mm
It should be noted that the plate thickness of the EWCHS is selected to be equal to that of the hot‐finished CHS under consideration ± 0.5 mm, as shown in Figure 8.4. z
z
t
t 0.5 max
y
y
d
d 5 max
Typical hot‐finished circular hollow section CHS
Equivalent cold‐formed circular hollow section EWCHS
Figure 8.4 Design method for equivalent cold‐formed circular hollow sections (3)
It should be noted that the largest EWCHS covered in GB/T 6728 has an external diameter equal to 610.0 mm. For those EWCHS with external diameters equal to 711.0 and 813.0 mm, refer to GB/T 21835 for details.
91
8.5.4 Equivalent cold‐formed rectangular and square hollow sections (1) The external dimensions, h and b, of the EWRHS and the EWSHS are selected to be equal to those of the hot‐finished sections under consideration, as shown in Figures 8.5 and 8.6. (2) The plate thicknesses of the EWRHS and the EWSHS are:
6.0 mm 12.0 mm
8.0 mm 16.0 mm
10.0 mm 20.0 mm z
r
ro
cf
r
ro
cw
y
y h
h
t
b
t
b
Typical hot‐finished rectangular hollow section RHS
Equivalent cold‐formed rectangular hollow section EWRHS
Figure 8.5 Design method for equivalent cold‐formed rectangular hollow sections z ri
z
ro
cf
ri
ro
cw
y
y h
h t
t 0.5 b Equivalent cold‐formed square hollow section EWSHS
b Typical Hot‐finished square hollow section SHS
Figure 8.6 Design method for equivalent cold‐formed square hollow sections
92
(3)
It should be noted that both the inner and the outer corner radii, ri and ro , for cold‐ formed RHS and SHS given in EN 10219‐2 are considered to be very stringent, as shown in Table 8.11. In some cases, these limiting values are even smaller than those given in EN 10210‐2 for hot‐finished RHS and SHS. Table 8.11 Allowable corner radii of hot‐finished and cold‐formed RHS and SHS EN 10210‐2: Hot‐finished structural hollow sections of non‐alloy and fine grain steels Thickness All range Hot finished ri 2.0 t RHS, SHS ro 3.0 t EN 10219‐2: Cold‐formed welded structural hollow sections of non‐alloy and fine grain steels Thickness t = 6 mm t = 8, 10 mm t = 12, 16, 20 mm Cold‐formed ri 0.6 t ~ 1.4 t 1.0 t ~ 2.0 t 1.4 t ~ 2.6 t RHS, SHS ro 1.6 t ~ 2.4 t 2.0 t ~ 3.0 t 2.4 t ~ 3.6 t GB/T 6728: Cold‐formed steel hollow sections of general structures Thickness t = 6, 8, 10 mm t = 12, 16, 20 mm ri 1.0 t ~ 2.0 t 1.0 t ~ 2.5 t Q235 Q275 ro 2.0 t ~ 3.0 t 2.0 t ~ 3.5 t Q345 ri 1.0 t ~ 2.5 t 1.5 t ~ 3.0 t Q460 ro 2.0 t ~ 3.5 t 2.5 t ~ 4.0 t Moreover, according to Table 8.12, large local strains are always induced in the corners of the cold‐formed RHS and SHS with small corner radii. Hence, welding in the immediate vicinity of the corners requires caution, otherwise significant cracking may be induced. Table 8.12 Corner radii and local residual strains in cold‐formed zones BS EN 1993‐1‐8: Design of steel structures: Design of joints Maximum thickness (mm) Residual ri / t strain Static load control Fatigue control Killed steel 25 ≤ 2% Any Any Any 10 ≤ 5% Any 16 Any 3.0 ≤ 14% 24 12 24 2.0 ≤ 20% 12 10 12 1.5 ≤ 25% 8 8 8 1.0 ≤ 33% 4 4 4 Note: Conflict with EN 10219 will be assumed satisfied if t ≤ 12.5 mm.
93
(4)
Table 8.13 presents the proposed corner radii of EWRHS and EWSHS for various steel grades. It should be noted that these corner radii are less stringent when compared to those given in Table 8.11 for both hot‐finished and cold‐formed RHS and SHS to EN10210‐2 and 10219‐2 respectively. Nevertheless, these corner radii are permitted according to GB/T 6728.
Table 8.13 Proposed corner radii of EWRHS and EWSHS Equivalent cold‐formed Corner radii t = 6, 8, 10 mm hollow sections 2.5 t ri EWRHS
t = 12, 16, 20 mm 3.0 t
EWSHS (5) (6) 8.6
ro
3.5 t
4.0 t
For further details on the dimensions of cold‐formed rectangular and square hollow sections, refer to GB/T 6728. A full list of the rolled and of the welded sections are presented in Tables 8.10 and 8.14 respectively. Design Tables on Section Dimensions, Properties and Resistances According to the comprehensive design rules given in EN 1993‐1‐1, a total of 45 Design Tables are compiled to assist structural engineers to use both rolled and welded sections whenever appropriate in practical design. These Design Tables include:
12 Design Tables on section dimensions and properties; 12 Design Tables on section resistances of rolled sections; and 21 Design Tables on section resistances of welded sections.
Section resistances for a total of 468 rolled and welded sections are calculated and tabulated for a wide range of section types and dimensions as well as a wide range of steel materials with different yield strengths. Table 8.15 summarizes various key design parameters of structural steel design of the Design Tables. 8.6.1 Section dimensions and properties For details on the selection of section dimensions for various rolled and welded sections, refer to Sections 8.4 and 8.5 respectively. Expressions for the calculations of various section properties are fully presented in Steel Building Design: Design Data (2013).
94
Table 8.14
Full ranges of proposed equivalent welded sections for application
Welded I-section
Welded H-section
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
460x190x102 x94 x83 x76 x64 460x160x85 x75 x68 x59 x54 405x180x76 x70 x59 x53 400x140x45 x39 355x180x72 x61 x54 x49 355x170x44 x38 305x160x58 x44 x38 305x125x50 x42 x39 305x110x36 x32 x26 265x140x43 x38 x30 265x100x28 x25 x22 205x135x30 x26 205x100x25 180x100x19 150x90x17 125x75x14
29
43
Number of sections Total
72
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Cold-formed circular hollow section 140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
Cold-formed rectangular hollow section 120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 x16.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
Cold-formed square hollow section 100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
55
44
32
31
234
Notes: (1) All equivalent welded sections are proposed to match the structural performance of those rolled sections given in Table 8.10. (2) Design data for welded sections with Q235, Q275, Q345 and Q460 steel materials are tabulated.
95
8.6.2 Section resistances The resistances of the cross‐sections of various rolled and welded sections against bending moments, shear forces and axial compression forces have been calculated and tabulated. It should be noted that for all the Design Tables, Class E1 Steel Materials are assumed in all rolled sections while Class E2 Steel Materials are assumed in all welded sections. If Class E1 Steel Materials are used in the welded sections, Mc should be taken as 1.0, and all the resistances should be increased by a factor of 1.1 accordingly. 8.6.2.1 Moment resistances All rolled and welded sections are doubly symmetrical, and most of them have two distinctive moment resistances, namely i) ii)
My,Rd about the major y‐y axis, and Mz,Rd about the minor z‐z axis.
However, only a moment resistance, MRd, is provided for both circular and square hollow sections. The corresponding flexural rigidities as well as the section classifications of the sections for bending about the major and the minor axes are also given as appropriate. However, it should be noted that no resistance is given for any Class 4 section owing to the occurrence of local buckling in plate elements of the section, leading to low structural efficiency. 8.6.2.2 Shear resistances The shear resistances of the sections are calculated conservatively with the factor for shear area, η , being taken to 1.0 as recommended in Clause 6.2.6(3) of EN1993‐1‐1. Hence, there is no need to check against shear buckling in the web plate elements when the following conditions apply: i) ii)
d 72 t hw 72 t
for rolled sections
for welded sections
It should be noted that only the shear resistances of the sections acting along the direction of the webs of the sections are provided. 8.6.2.3 Axial compression resistances In most sections, the gross areas of the sections are fully effective owing to the stocky nature of the plate elements. Hence, full compression resistances of these sections are readily mobilized.
96
However, for both rolled and welded I‐sections, RHS and CHS with large d / t values under high compressive stress levels, local buckling in the plate elements of these cross‐sections is critical. Hence, they are taken as Class 4 sections, and effective areas should be used, instead of their gross areas, in the calculation of the cross‐ section resistances against axial compression forces. These resistances are printed in italics in the Design Tables. Refer to Section 4.4 of EN 1993‐1‐5 for details of the design rule for evaluation of effective areas using the reduction factor for plate buckling, ρ . As a whole, the Design Tables provide practical design data for structural engineers to assess the structural performance of various sections against material yielding as well as member buckling during practical design. Table 8.15 Summary of Design Tables Rolled Section type Design Table sections I‐section 01A / 01B 02A / 02B Dimensions H‐section 03A / 03B and CHS 04 properties RHS 05 SHS 06 Steel materials Section resistances Mc = 1.0
Welded sections Dimensions and properties
S355
07 08 09 10 11 12
13 14 15 16 17 18
I‐section H‐section CHS RHS SHS Section type
Design Table
EWI‐section
19A / 19B 20A / 20B 21A / 21B 22 23 24
EWH‐section EWCHS EWRHS EWSHS Steel materials
Section resistances Mc = 1.1
S275
EWI‐section EWH‐section EWCHS EWRHS EWSHS
Q235
Q275
Q345
Q460
25 26 27
28 29 30 31 32 33
34 35 36 37 38 39
40 41 42 43 44 45
Not applicable
97
98
Design Tables on Section Dimensions, Properties and Resistances for Rolled and Welded Sections
99
Rolled sections Table No. Design Table 01A Design Table 01B Design Table 02A Design Table 02B Design Table 03A Design Table 03B Design Table 04 Design Table 05 Design Table 06
Title Section dimensions of rolled I-sections (1) Section properties of rolled I-sections (1) Section dimensions of rolled I-sections (2) Section properties of rolled I-sections (2) Section dimensions of rolled H-sections Section properties of rolled H-sections Section dimensions and properties of hot-finished CHS Section dimensions and properties of hot-finished RHS Section dimensions and properties of hot-finished SHS
Design Table 07 Design Table 08 Design Table 09 Design Table 10 Design Table 11 Design Table 12
Section resistances of rolled I-sections: S275 steel (1) Section resistances of rolled I-sections: S275 steel (2) Section resistances of rolled H-sections: S275 steel Section resistances of hot-finished CHS: S275 steel Section resistances of hot-finished RHS: S275 steel Section resistances of hot-finished SHS: S275 steel
114 115 116 117 118 119
Design Table 13 Design Table 14 Design Table 15 Design Table 16 Design Table 17 Design Table 18
Section resistances of rolled I-sections: S355 steel (1) Section resistances of rolled I-sections: S355 steel (2) Section resistances of rolled H-sections: S355 steel Section resistances of hot-finished CHS: S355 steel Section resistances of hot-finished RHS: S355 steel Section resistances of hot-finished SHS: S355 steel
122 123 124 125 126 127
100
Page 104 105 106 107 108 109 110 111 112
Welded sections Table No. Design Table 19A Design Table 19B Design Table 20A Design Table 20B Design Table 21A Design Table 21B Design Table 22 Design Table 23 Design Table 24
Title Section dimensions of welded I-sections (1) Section properties of welded I-sections (1) Section dimensions of welded I-sections (2) Section properties of welded I-sections (2) Section dimensions of welded H-sections Section properties of welded H-sections Section dimensions and properties of cold-formed CHS Section dimensions and properties of cold-formed RHS Section dimensions and properties of cold-formed SHS
Page 130 131 132 133 134 135 136 137 138
Design Table 25 Design Table 26 Design Table 27
Section resistances of welded I-sections: Q235 steel (1) Section resistances of welded I-sections: Q235 steel (2) Section resistances of welded H-sections: Q235 steel
140 141 142
Design Table 28 Design Table 29 Design Table 30 Design Table 31 Design Table 32 Design Table 33
Section resistances of welded I-sections: Q275 steel (1) Section resistances of welded I-sections: Q275 steel (2) Section resistances of welded H-sections: Q275 steel Section resistances of cold-formed CHS: Q275 steel Section resistances of cold-formed RHS: Q275 steel Section resistances of cold-formed SHS: Q275 steel
144 145 146 147 148 149
Design Table 34 Design Table 35 Design Table 36 Design Table 37 Design Table 38 Design Table 39
Section resistances of welded I-sections: Q345 steel (1) Section resistances of welded I-sections: Q345 steel (2) Section resistances of welded H-sections: Q345 steel Section resistances of cold-formed CHS: Q345 steel Section resistances of cold-formed RHS: Q345 steel Section resistances of cold-formed SHS: Q345 steel
152 153 154 155 156 157
Design Table 40 Design Table 41 Design Table 42 Design Table 43 Design Table 44 Design Table 45
Section resistances of welded I-sections: Q460 steel (1) Section resistances of welded I-sections: Q460 steel (2) Section resistances of welded H-sections: Q460 steel Section resistances of cold-formed CHS: Q460 steel Section resistances of cold-formed RHS: Q460 steel Section resistances of cold-formed SHS: Q460 steel
160 161 162 163 164 165
101
102
Design Tables 01 to 06 for Section Dimensions and Properties of Rolled Sections I-sections H-sections CHS RHS SHS
103
Design Table 01A Section dimensions of rolled I-sections (1) tf
z
r y
tw
d h
cf
b Mass per Depth Width Meter of Section of Section I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
kg/m 388.0 343.3 289.1 253.4 224.2 200.9 226.5 193.8 175.9 196.8 173.0 146.9 133.9 170.2 152.4 140.1 125.2 238.1 179.0 149.2 139.9 125.1 113.0 101.2 122.0 109.0 101.0 92.1 82.2
mm 921.0 911.8 926.6 918.4 910.4 903.0 850.9 840.7 834.9 769.8 762.2 754.0 750.0 692.9 687.5 683.5 677.9 635.8 620.2 612.4 617.2 612.2 607.6 602.6 544.5 539.5 536.7 533.1 528.3
mm 420.5 418.5 307.7 305.5 304.1 303.3 293.8 292.4 291.7 268.0 266.7 265.2 264.4 255.8 254.5 253.7 253.0 311.4 307.1 304.8 230.2 229.0 228.2 227.6 211.9 210.8 210.0 209.3 208.8
Thickness Web tw mm 21.4 19.4 19.5 17.3 15.9 15.1 16.1 14.7 14.0 15.6 14.3 12.8 12.0 14.5 13.2 12.4 11.7 18.4 14.1 11.8 13.1 11.9 11.1 10.5 12.7 11.6 10.8 10.1 9.6
Root Radius
Depth between Fillets
r mm 24.1 24.1 19.1 19.1 19.1 19.1 17.8 17.8 17.8 16.5 16.5 16.5 16.5 15.2 15.2 15.2 15.2 16.5 16.5 16.5 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7
d mm 799.6 799.6 824.4 824.4 824.4 824.4 761.7 761.7 761.7 686.0 686.0 686.0 686.0 615.1 615.1 615.1 615.1 540.0 540.0 540.0 547.6 547.6 547.6 547.6 476.5 476.5 476.5 476.5 476.5
Flange tf mm 36.6 32.0 32.0 27.9 23.9 20.2 26.8 21.7 18.8 25.4 21.6 17.5 15.5 23.7 21.0 19.0 16.2 31.4 23.6 19.7 22.1 19.6 17.3 14.8 21.3 18.8 17.4 15.6 13.2
Limited availability.
104
Ratios for Local Buckling
Surface Area per Meter per Tonne
cf/tf
d/tw
4.8 5.5 3.9 4.5 5.2 6.2 4.5 5.6 6.4 4.3 5.1 6.3 7.1 4.4 5.0 5.6 6.5 4.1 5.5 6.6 4.3 4.9 5.5 6.5 4.1 4.6 5.0 5.6 6.6
37.4 41.2 42.3 47.7 51.8 54.6 47.3 51.8 54.4 44.0 48.0 53.6 57.2 42.4 46.6 49.6 52.6 29.3 38.3 45.8 41.8 46.0 49.3 52.2 37.5 41.1 44.1 47.2 49.6
m2 3.44 3.42 3.01 2.99 2.97 2.96 2.81 2.79 2.78 2.55 2.53 2.51 2.51 2.35 2.34 2.33 2.32 2.45 2.41 2.39 2.11 2.09 2.08 2.07 1.89 1.88 1.87 1.86 1.85
m2 8.87 10.0 10.4 11.8 13.2 14.7 12.4 14.4 15.8 13.0 14.6 17.1 18.7 13.8 15.4 16.6 18.5 10.3 13.5 16.0 15.1 16.7 18.4 20.5 15.5 17.2 18.5 20.2 22.5
Design Table 01B Section properties of rolled I-sections (1) z
tf r y
d h tw
cf b
I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
Second Moment of Area
Elastic Modulus
cm4 720000 626000 504000 436000 376000 325000 340000 279000 246000 240000 205000 169000 151000 170000 150000 136000 118000 209000 153000 126000 112000 98600 87300 75800 76000 66800 61500 55200 47500
cm3 15600 13700 10900 9500 8270 7200 7980 6640 5890 6230 5390 4470 4020 4920 4370 3990 3480 6590 4930 4110 3620 3220 2870 2520 2790 2480 2290 2070 1800
,
cm4 45400 39200 15600 13300 11200 9420 11400 9070 7800 8170 6850 5460 4790 6630 5780 5210 4380 15800 11400 9310 4510 3930 3430 2910 3390 2940 2690 2390 2010
,
cm3 2160 1870 1010 871 739 621 773 620 535 610 514 411 362 518 455 409 346 1020 743 611 391 343 301 256 320 279 256 228 192
Plastic Modulus ,
cm3 17700 15500 12600 10900 9530 8350 9160 7640 6810 7170 6200 5160 4640 5630 5000 4560 3990 7490 5550 4590 4140 3680 3280 2880 3200 2830 2610 2360 2060
Buckling Parameter
Torsional Index
Warping Constant
Torsional Constant
Area of Section
26.7 30.1 31.9 36.2 41.3 46.9 35.0 41.6 46.5 33.1 38.0 45.2 49.8 31.8 35.4 38.6 43.8 21.3 27.7 32.7 30.6 34.0 38.0 43.0 27.6 30.9 32.8 36.4 41.6
dm6 88.9 75.8 31.2 26.4 22.1 18.4 19.3 15.2 13.0 11.3 9.39 7.40 6.46 7.42 6.42 5.72 4.80 14.5 10.2 8.17 3.99 3.45 2.99 2.52 2.32 1.99 1.81 1.60 1.33
cm4 1730 1190 926 626 427 291 514 306 221 404 267 159 119 308 220 169 116 785 340 200 216 154 111 77 178 126 101 75.7 51.5
cm2 494 437 368 323 286 256 289 247 224 251 220 187 171 217 194 178 159 303 228 190 178 159 144 129 155 139 127 117 105
A
,
cm3 3340 2890 1600 1370 1160 982 1210 974 842 958 807 647 570 811 710 638 542 1570 1140 937 611 535 469 400 500 436 399 355 300
Limited availability.
105
0.885 0.883 0.867 0.865 0.866 0.853 0.869 0.862 0.856 0.869 0.865 0.858 0.853 0.872 0.871 0.872 0.863 0.886 0.885 0.886 0.875 0.875 0.870 0.863 0.878 0.875 0.874 0.873 0.863
Design Table 02A Section dimensions of rolled I-sections (2) z
tf r y
d h tw
cf b Mass per Depth Width Meter of Section of Section I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
kg/m 98.3 89.3 82.0 74.3 67.1 82.1 74.2 67.2 59.8 52.3 74.2 67.1 60.1 54.1 46.0 39.0 67.1 57.0 51.0 45.0 39.1 33.1 54.0 46.1 40.3 48.1 41.9 37.0 32.8 28.2 24.8 43.0 37.0 31.1 28.3 25.2 22.0 30.0 25.1 23.1 19.0 16.0 13.0
Mm 467.2 463.4 460.0 457.0 453.4 465.8 462.0 458.0 454.6 449.8 412.8 409.4 406.4 402.6 403.2 398.0 363.4 358.0 355.0 351.4 353.4 349.0 310.4 306.6 303.4 311.0 307.2 304.4 312.7 308.7 305.1 259.6 256.0 251.4 260.4 257.2 254.0 206.8 203.2 203.2 177.8 152.4 127.0
mm 192.8 191.9 191.3 190.4 189.9 155.3 154.4 153.8 152.9 152.4 179.5 178.8 177.9 177.7 142.2 141.8 173.2 172.2 171.5 171.1 126.0 125.4 166.9 165.7 165.0 125.3 124.3 123.4 102.4 101.8 101.6 147.3 146.4 146.1 102.2 101.9 101.6 133.9 133.2 101.8 101.2 88.7 76.0
Root Radius
Thickness Web tw mm 11.4 10.5 9.9 9.0 8.5 10.5 9.6 9.0 8.1 7.6 9.5 8.8 7.9 7.7 6.8 6.4 9.1 8.1 7.4 7.0 6.6 6.0 7.9 6.7 6.0 9.0 8.0 7.1 6.6 6.0 5.8 7.2 6.3 6.0 6.3 6.0 5.7 6.4 5.7 5.4 4.8 4.5 4.0
Flange tf mm 19.6 17.7 16.0 14.5 12.7 18.9 17.0 15.0 13.3 10.9 16.0 14.3 12.8 10.9 11.2 8.6 15.7 13.0 11.5 9.7 10.7 8.5 13.7 11.8 10.2 14.0 12.1 10.7 10.8 8.8 7.0 12.7 10.9 8.6 10.0 8.4 6.8 9.6 7.8 9.3 7.9 7.7 7.6
106
Depth between Fillets
Ratios for Local Buckling
Surface Area per Meter per Tonne
r mm 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 8.9 8.9 8.9 8.9 8.9 8.9 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6
d mm 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 360.4 360.4 360.4 360.4 360.4 360.4 311.6 311.6 311.6 311.6 311.6 311.6 265.2 265.2 265.2 265.2 265.2 265.2 275.9 275.9 275.9 219.0 219.0 219.0 225.2 225.2 225.2 172.4 172.4 169.4 146.8 121.8 96.6
cf/tf
d/tw
4.1 4.6 5.0 5.6 6.3 3.3 3.7 4.2 4.7 5.7 4.1 4.7 5.2 5.8 5.1 6.7 4.6 5.5 6.3 7.4 4.6 5.8 5.2 6.0 6.9 3.5 4.1 4.6 3.7 4.6 5.8 4.9 5.7 7.3 4.0 4.8 5.9 5.9 7.2 4.4 5.1 4.5 3.7
35.8 38.8 41.2 45.3 48.0 38.8 42.5 45.3 50.3 53.6 33.1 37.9 41.0 45.6 53.0 56.3 34.2 38.5 42.1 44.5 47.2 51.9 33.6 39.6 44.2 29.5 33.2 37.4 41.8 46.0 47.6 30.4 34.8 36.5 35.7 37.5 39.5 26.9 30.2 31.4 30.6 27.1 24.2
m2 1.67 1.66 1.65 1.64 1.63 1.51 1.50 1.50 1.49 1.48 1.51 1.50 1.49 1.48 1.34 1.33 1.38 1.37 1.36 1.36 1.18 1.17 1.26 1.25 1.24 1.09 1.08 1.07 1.01 1.00 0.992 1.08 1.07 1.06 0.904 0.897 0.890 0.923 0.915 0.790 0.738 0.638 0.537
m2 17.0 18.6 20.1 22.1 24.3 18.4 20.2 22.3 24.9 28.3 20.4 22.3 24.8 27.3 29.1 34.1 20.6 24.1 26.7 30.2 30.2 35.4 23.3 27.1 30.8 22.7 25.8 28.9 30.8 35.5 40.0 25.1 28.9 34.0 31.9 35.7 40.5 30.8 36.5 34.2 38.7 40.0 41.4
Design Table 02B Section properties of rolled I-sections (2) z
tf r y
d h tw
cf b Second Moment of Area I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Elastic Modulus ,
,
Plastic Modulus ,
Buckling Parameter
Torsional Index
Warping Constant
Torsional Constant
Area of Section A
dm6
cm4
cm2
1.18 1.04 0.922 0.818 0.705 0.591 0.518 0.448 0.387 0.311 0.608 0.533 0.466 0.392 0.207 0.155 0.412 0.330 0.286 0.237 0.105 0.081 0.234 0.195 0.164 0.102 0.0846 0.0725 0.0442 0.0349 0.0270 0.103 0.0857 0.0660 0.0280 0.0230 0.0182 0.0374 0.0294 0.0154 0.00990 0.00470 0.00200
121 90.7 69.2 51.8 37.1 89.2 65.9 47.7 33.8 21.4 62.8 46.1 33.3 23.1 19.0 10.7 55.7 33.4 23.8 15.8 15.1 8.79 34.8 22.2 14.7 31.8 21.1 14.8 12.2 7.40 4.77 23.9 15.3 8.55 9.57 6.42 4.15 10.3 5.96 7.02 4.41 3.56 2.85
125 114 104 94.6 85.5 105 94.5 85.6 76.2 66.6 94.5 85.5 76.5 69.0 58.6 49.7 85.5 72.6 64.9 57.3 49.8 42.1 68.8 58.7 51.3 61.2 53.4 47.2 41.8 35.9 31.6 54.8 47.2 39.7 36.1 32.0 28.0 38.2 32.0 29.4 24.3 20.3 16.5
,
cm4
cm4
cm3
cm3
cm3
cm3
45700 41000 37100 33300 29400 36600 32700 28900 25500 21400 27300 24300 21600 18700 15700 12500 19500 16000 14100 12100 10200 8250 11700 9900 8500 9570 8200 7170 6500 5370 4460 6540 5540 4410 4000 3410 2840 2900 2340 2100 1360 834 473
2350 2090 1870 1670 1450 1180 1050 913 795 645 1550 1360 1200 1020 538 410 1360 1110 968 811 358 280 1060 896 764 461 389 336 194 155 123 677 571 448 179 149 119 385 308 164 137 89.8 55.7
1960 1770 1610 1460 1300 1570 1410 1260 1120 950 1320 1190 1060 930 778 629 1070 896 796 687 576 473 754 646 560 616 534 471 416 348 292 504 433 351 308 266 224 280 230 207 153 109 74.6
243 218 196 176 153 153 136 119 104 84.6 172 153 135 115 75.7 57.8 157 129 113 94.8 56.8 44.7 127 108 92.6 73.6 62.6 54.5 37.9 30.5 24.2 92.0 78.0 61.3 34.9 29.2 23.5 57.5 46.2 32.2 27.0 20.2 14.7
2230 2010 1830 1650 1470 1810 1630 1450 1290 1100 1500 1350 1200 1050 888 724 1210 1010 896 775 659 543 846 720 623 711 614 539 481 403 342 566 483 393 353 306 259 314 258 234 171 123 84.2
379 338 304 272 237 240 213 187 163 133 267 237 209 178 118 90.8 243 199 174 147 89.0 70.2 196 166 142 116 98.4 85.4 60.0 48.4 38.8 141 119 94.1 54.8 46.0 37.3 88.2 70.9 49.7 41.6 31.2 22.6
107
0.881 0.878 0.879 0.877 0.873 0.872 0.872 0.868 0.868 0.859 0.882 0.880 0.880 0.871 0.871 0.858 0.886 0.882 0.881 0.874 0.871 0.863 0.889 0.890 0.889 0.873 0.872 0.872 0.867 0.859 0.846 0.891 0.890 0.879 0.873 0.866 0.856 0.882 0.876 0.888 0.886 0.890 0.894
25.8 28.3 30.8 33.8 37.8 27.4 30.1 33.6 37.5 43.8 27.5 30.4 33.7 38.3 39.0 47.4 24.4 28.8 32.1 36.8 35.2 42.1 23.6 27.1 31.0 23.3 26.5 29.7 31.6 37.3 43.4 21.1 24.3 29.6 27.5 31.4 36.3 21.5 25.6 22.4 22.6 19.5 16.3
Design Table 03A Section dimensions of rolled H-sections z
tf r h
y
tw d h
cf
b Mass per Depth Width Meter of Section of Section H-Sections
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
kg/m 633.9 551.0 467.0 393.0 339.9 287.1 235.1 201.9 177.0 152.9 129.0 282.9 240.0 198.1 158.1 136.9 117.9 96.9 167.1 132.0 107.1 88.9 73.1 86.1 71.0 60.0 52.0 46.1 37.0 30.0 23.0
mm 474.6 455.6 436.6 419.0 406.4 393.6 381.0 374.6 368.2 362.0 355.6 365.3 352.5 339.9 327.1 320.5 314.5 307.9 289.1 276.3 266.7 260.3 254.1 222.2 215.8 209.6 206.2 203.2 161.8 157.6 152.4
mm 424.0 418.5 412.2 407.0 403.0 399.0 394.8 374.7 372.6 370.5 368.6 322.2 318.4 314.5 311.2 309.2 307.4 305.3 265.2 261.3 258.8 256.3 254.6 209.1 206.4 205.8 204.3 203.6 154.4 152.9 152.2
Thickness Web tw mm 47.6 42.1 35.8 30.6 26.6 22.6 18.4 16.5 14.4 12.3 10.4 26.8 23.0 19.1 15.8 13.8 12.0 9.9 19.2 15.3 12.8 10.3 8.6 12.7 10.0 9.4 7.9 7.2 8.0 6.5 5.8
Root Radius
Depth between Fillets
r mm 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 12.7 12.7 12.7 12.7 12.7 10.2 10.2 10.2 10.2 10.2 7.6 7.6 7.6
d mm 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 246.7 246.7 246.7 246.7 246.7 246.7 246.7 200.3 200.3 200.3 200.3 200.3 160.8 160.8 160.8 160.8 160.8 123.6 123.6 123.6
Flange tf mm 77.0 67.5 58.0 49.2 42.9 36.5 30.2 27.0 23.8 20.7 17.5 44.1 37.7 31.4 25.0 21.7 18.7 15.4 31.7 25.3 20.5 17.3 14.2 20.5 17.3 14.2 12.5 11.0 11.5 9.4 6.8
Ratios for Local Buckling
Surface Area per Meter per Tonne
Limited availability.
108
cf/tf
d/tw
2.3 2.6 3.0 3.5 4.0 4.7 5.7 6.1 6.9 7.9 9.4 3.0 3.5 4.2 5.3 6.1 7.1 8.6 3.5 4.4 5.4 6.4 7.8 4.3 5.1 6.2 7.0 8.0 5.7 7.0 9.7
6.1 6.9 8.1 9.5 10.9 12.8 15.8 17.6 20.2 23.6 27.9 9.2 10.7 12.9 15.6 17.9 20.6 24.9 10.4 13.1 15.6 19.4 23.3 12.7 16.1 17.1 20.4 22.3 15.5 19.0 21.3
m2 2.52 2.47 2.42 2.38 2.35 2.31 2.28 2.19 2.17 2.16 2.14 1.94 1.91 1.87 1.84 1.82 1.81 1.79 1.58 1.55 1.52 1.50 1.49 1.24 1.22 1.21 1.20 1.19 0.912 0.901 0.889
m2 3.98 4.48 5.18 6.06 6.91 8.05 9.70 10.8 12.3 14.1 16.6 6.86 7.96 9.44 11.6 13.3 15.4 18.5 9.46 11.7 14.2 16.9 20.4 14.4 17.2 20.2 23.1 25.8 24.7 30.0 38.7
Design Table 03B Section properties of rolled H-sections z
tf r h
y
tw d h
cf
b
H-Sections
Second Moment of Area
Elastic Modulus ,
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
cm4 275000 227000 183000 147000 123000 99900 79100 66300 57100 48600 40200 78900 64200 50900 38700 32800 27700 22200 30000 22500 17500 14300 11400 9450 7620 6130 5260 4570 2210 1750 1250
cm4 98100 82700 67800 55400 46900 38700 31000 23700 20500 17600 14600 24600 20300 16300 12600 10700 9060 7310 9870 7530 5930 4860 3910 3130 2540 2070 1780 1550 706 560 400
cm3 11600 9960 8380 7000 6030 5070 4150 3540 3100 2680 2260 4320 3640 3000 2370 2050 1760 1450 2080 1630 1310 1100 898 850 706 584 510 450 273 222 164
,
cm3 4630 3950 3290 2720 2330 1940 1570 1260 1100 948 793 1530 1280 1040 808 692 589 479 744 576 458 379 307 299 246 201 174 152 91.5 73.3 52.6
Buckling Parameter
Plastic Modulus ,
cm3 14200 12100 10000 8220 7000 5810 4690 3970 3460 2960 2480 5110 4250 3440 2680 2300 1960 1590 2420 1870 1480 1220 992 977 799 656 567 497 309 248 182
Torsional Index
Warping Constant
Torsional Constant
Area of Section
5.46 6.05 6.86 7.86 8.85 10.2 12.1 13.4 15.0 17.0 19.9 7.65 8.74 10.2 12.5 14.2 16.2 19.3 8.49 10.3 12.4 14.5 17.3 10.2 11.9 14.1 15.8 17.7 13.3 16.0 20.7
dm6 38.8 31.1 24.3 18.9 15.5 12.3 9.54 7.16 6.09 5.11 4.18 6.35 5.03 3.88 2.87 2.39 1.98 1.56 1.63 1.19 0.898 0.717 0.562 0.318 0.250 0.197 0.167 0.143 0.0399 0.0308 0.0212
cm4 13700 9240 5810 3550 2340 1440 812 558 381 251 153 2030 1270 734 378 249 161 91.2 626 319 172 102 57.6 137 80.2 47.2 31.8 22.2 19.2 10.5 4.63
A cm2 808 702 595 501 433 366 299 257 226 195 164 360 306 252 201 174 150 123 213 168 136 113 93.1 110 90.4 76.4 66.3 58.7 47.1 38.3 29.2
,
cm3 7110 6060 5030 4150 3540 2950 2380 1920 1670 1430 1200 2340 1950 1580 1230 1050 895 726 1140 878 697 575 465 456 374 305 264 231 140 112 80.1
Limited availability.
109
0.843 0.841 0.839 0.837 0.836 0.835 0.834 0.844 0.844 0.844 0.844 0.855 0.854 0.854 0.851 0.851 0.850 0.850 0.851 0.850 0.848 0.850 0.849 0.850 0.853 0.846 0.848 0.847 0.848 0.849 0.840
Design Table 04 Section dimensions and properties of hot-finished CHS z
t
y
CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Mass per Area of Meter Section m A kg/m 20.7 26.0 25.2 31.6 39.0 48.0 33.1 41.6 51.6 63.7 41.4 52.3 64.9 80.3 49.3 62.3 77.4 96.0 121 54.3 68.6 85.2 106 134 78.6 97.8 121 154 191 88.6 110 137 174 216 98.6 123 153 194 241 119 148 184 234 291 173 215 274 349 198 247 314 391
cm2 26.4 33.1 32.1 40.3 49.7 61.2 42.1 53.1 65.7 81.1 52.8 66.6 82.6 102 62.9 79.4 98.6 122 155 69.1 87.4 109 135 171 100 125 155 196 243 113 140 175 222 275 126 156 195 247 307 151 188 235 299 371 173 215 274 341 252 314 401 498
d
Ratio for Local Second Moment Buckling of Area d/t I 22.2 17.5 26.7 21.0 16.8 13.5 34.8 27.4 21.9 17.5 43.3 34.1 27.3 21.8 51.4 40.5 32.4 25.9 20.2 56.4 44.5 35.6 28.4 22.2 50.8 40.6 32.5 25.4 20.3 57.1 45.7 36.6 28.6 22.9 63.5 50.8 40.6 31.8 25.4 76.3 61.0 48.8 38.1 30.5 71.1 56.9 44.4 35.6 81.3 65.0 50.8 40.7
cm4 589 720 1050 1300 1560 1870 2390 2960 3600 4350 4700 5850 7150 8700 7930 9910 12200 14800 18400 10500 13200 16200 19900 24700 19900 24500 30000 37400 45430 28400 35100 43100 54000 65680 39300 48500 59800 74900 91400 84900 104800 118000 131800 161500 135300 167300 211000 259400 203400 251900 318200 391900
Elastic Modulus Wel cm3 84.3 103 125 154 186 222 218 270 328 397 344 429 524 637 490 612 751 917 1140 593 742 912 1120 1390 978 1210 1480 1840 2240 1250 1540 1890 2360 2870 1550 1910 2350 2950 3600 2250 2780 3450 4320 5300 3810 4710 5940 7300 5000 6200 7830 9640
110
Plastic Modulus Wpl cm3 112 139 165 206 251 304 285 357 438 534 448 562 692 849 636 799 986 1210 1520 769 967 1200 1470 1850 1270 1570 1940 2440 2989 1610 2000 2470 3110 3822 2000 2480 3070 3870 4770 2900 3600 4460 5650 6970 4914 6100 7730 9550 6450 8010 10200 12600
Torsional Constants IT Wt cm4 1180 1440 2110 2600 3130 3740 4770 5920 7200 8690 9390 11700 14300 17400 15900 19800 24300 29700 36800 21100 26400 32400 39700 49300 39700 49000 60100 74900 90860 56900 70200 86300 108000 131000 78600 97000 120000 150000 182900 137100 169700 209600 263600 323000 270600 334700 422100 518700 406800 503700 636400 783800
cm3 169 206 250 308 372 444 436 540 657 793 688 857 1050 1270 979 1220 1500 1830 2270 1190 1490 1830 2230 2770 1960 2410 2960 3690 4470 2490 3070 3780 4720 5750 3090 3820 4710 5900 7199 4495 5564 6869 8641 10590 7612 9415 11870 14590 10010 12390 15660 19280
Surface Area per Meter m2 0.439 0.439 0.529 0.529 0.529 0.529 0.688 0.688 0.688 0.688 0.858 0.858 0.858 0.858 1.02 1.02 1.02 1.02 1.02 1.12 1.12 1.12 1.12 1.12 1.28 1.28 1.28 1.28 1.28 1.44 1.44 1.44 1.44 1.44 1.60 1.60 1.60 1.60 1.60 1.90 1.90 1.90 1.90 1.90 2.23 2.23 2.23 2.23 2.55 2.55 2.55 2.55
per Tonne m2 21.2 16.9 21.0 16.7 13.6 11.0 20.8 16.5 13.3 10.8 20.7 16.4 13.2 10.7 20.6 16.3 13.1 10.6 8.41 20.6 16.3 13.1 10.5 8.34 16.2 13.1 10.6 8.29 6.68 16.2 13.1 10.5 8.25 6.65 16.2 13.0 10.4 8.23 6.62 16.1 12.9 10.4 8.19 6.59 12.9 10.4 8.15 6.40 12.9 10.3 8.13 6.53
Design Table 05 Section dimensions and properties of hot-finished RHS z
cw
y
h
cf b RHS bxhxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Mass per Meter m kg/m 17.2 21.0 21.2 26.0 31.2 27.1 33.5 40.6 32.0 39.8 48.4 37.0 46.1 56.3 68.3 40.9 51.1 62.6 76.2 93.9 46.9 58.6 72.0 88.0 109 56.8 71.2 87.7 108 134 56.8 71.2 87.7 108 134 83.8 103 127 159 96.3 119 147 184 225
Area of Section A cm2 21.9 26.7 26.9 33.1 39.7 34.5 42.7 51.7 40.8 50.7 61.7 47.1 58.7 71.7 87.0 52.1 65.1 79.7 97.0 120 59.7 74.7 91.7 112 139 72.3 90.7 112 137 171 72.3 90.7 112 137 171 107 132 162 203 123 152 187 235 287
Ratio for Local Buckling cw/t cf/t 13.0 9.0 19.4 14.0 10.0 25.7 19.0 14.0 25.7 19.0 14.0 33.7 25.3 19.0 14.0 35.3 26.5 20.0 14.8 10.3 41.6 31.5 24.0 18.0 12.8 49.6 37.8 29.0 22.0 15.9 57.5 44.0 34.0 26.0 19.0 50.3 39.0 30.0 22.1 56.5 44.0 34.0 25.3 19.0
6.7 4.0 6.7 4.0 2.0 9.9 6.5 4.0 17.8 12.8 9.0 17.8 12.8 9.0 6.0 22.6 16.5 12.0 8.4 5.3 25.7 19.0 14.0 10.0 6.5 33.7 25.3 19.0 14.0 9.6 25.7 19.0 14.0 10.0 6.5 25.3 19.0 14.0 9.6 31.5 24.0 18.0 12.8 9.0
Second Moment of Area Iy cm4 394 451 821 959 1080 1700 2030 2340 2290 2760 3250 3940 4790 5670 6600 4950 6040 7200 8450 9860 7540 9250 11100 13100 15500 12800 15800 19100 22900 27500 15200 18700 22600 27000 32400 29000 35300 42500 51500 42400 51700 62700 76600 90700
Iz cm4 210 240 279 324 362 581 688 790 1480 1780 2080 1800 2180 2570 2990 2820 3440 4090 4790 5570 4070 4980 5960 7040 8290 7680 9480 11400 13700 16400 5250 6450 7760 9240 11000 11800 14300 17200 20800 19500 23700 28600 34900 41200
111
Elastic Modulus Wel,y cm3 65.6 75.2 103 120 135 170 203 234 229 276 325 315 383 454 528 381 465 554 650 758 503 617 740 873 1030 731 903 1090 1310 1570 760 935 1130 1350 1620 1290 1570 1890 2290 1700 2070 2510 3060 3630
Wel,z cm3 52.5 60.0 69.8 81.0 90.5 116 138 158 197 237 277 240 291 343 399 313 382 454 532 619 407 498 596 704 829 614 758 912 1100 1310 525 645 776 924 1100 944 1140 1380 1660 1300 1580 1910 2330 2750
t Plastic Modulus Wpl,y cm3 83.3 98.2 132 158 183 216 261 309 277 338 404 386 475 570 677 458 565 682 814 974 605 748 907 1090 1320 870 1080 1320 1600 1950 935 1160 1420 1710 2090 1580 1930 2340 2880 2050 2510 3070 3800 4560
Wpl,z cm3 63.1 74.2 81.6 97.3 112 133 161 190 228 278 332 273 335 402 476 357 440 531 633 756 460 568 689 826 997 693 862 1050 1270 1550 582 722 879 1060 1290 1060 1290 1570 1930 1450 1780 2170 2680 3210
Surface Area per Meter m2 0.384 0.379 0.464 0.459 0.454 0.584 0.579 0.574 0.684 0.679 0.674 0.784 0.779 0.774 0.768 0.860 0.860 0.850 0.850 0.840 0.984 0.979 0.974 0.968 0.962 1.180 1.180 1.170 1.170 1.160 1.18 1.18 1.17 1.17 1.16 1.38 1.37 1.37 1.36 1.58 1.57 1.57 1.56 1.55
per Tonne m2 21.1 16.8 20.9 16.6 13.5 20.8 16.5 13.3 20.7 16.4 13.2 20.6 16.4 13.2 10.6 23.8 19.0 15.4 12.5 10.0 20.6 16.3 13.1 10.6 8.7 17.3 13.7 11.1 9.0 7.1 20.4 16.2 13.0 10.5 7.1 16.1 12.9 10.4 8.21 16.1 12.9 10.4 8.17 6.59
Design Table 06 Section dimensions and properties of hot-finished SHS z y c t
b Mass per Area of Meter Section bxbxt m A
SHS
mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
kg/m 17.2 21.0 27.1 33.5 40.6 37.0 46.1 56.3 68.3 40.9 51.1 62.6 76.2 93.9 46.9 58.6 72.0 88.0 109 56.8 71.2 87.7 108 134 83.8 103 127 159 96.3 119 147 184 225
cm2 21.9 26.7 34.5 42.7 51.7 47.1 58.7 71.7 87.0 52.1 65.1 79.7 97.0 120 59.7 74.7 91.7 112 139 72.3 90.7 112 137 171 107 132 162 203 123 152 187 235 287
Ratio for Local Buckling c/t
Second Moment of Area I
9.9 6.5 17.8 12.8 9.0 25.7 19.0 14.0 10.0 28.9 21.5 16.0 11.6 7.8 33.7 25.3 19.0 14.0 9.63 41.6 31.5 24.0 18.0 12.8 37.8 29.0 22.0 15.9 44.0 34.0 26.0 19.0 14.0
cm4 304 349 1150 1370 1590 2880 3500 4150 4840 3890 4750 5660 6650 7760 5810 7130 8550 10100 12000 10300 12700 15300 18300 22000 20500 24900 30000 36400 31000 37800 45800 56000 66400
112
Elastic Modulus Wel cm3 60.7 69.7 153 183 212 288 350 415 484 354 432 515 605 706 465 570 684 808 960 687 847 1020 1220 1470 1170 1420 1710 2080 1550 1890 2290 2800 3320
Plastic Modulus Wpl cm3 74.4 87.8 182 221 262 338 415 499 592 413 509 614 733 878 540 668 810 974 1180 790 982 1200 1450 1770 1360 1660 2020 2480 1790 2200 2680 3320 3990
Surface Area per Meter m2 0.368 0.359 0.568 0.559 0.548 0.768 0.759 0.748 0.736 0.848 0.839 0.828 0.816 0.798 0.968 0.959 0.948 0.936 0.918 1.17 1.16 1.15 1.14 1.12 1.36 1.35 1.34 1.32 1.56 1.55 1.54 1.52 1.50
per Tonne m2 21.4 17.1 21.0 16.7 13.5 20.8 16.5 13.3 10.8 20.7 16.4 13.2 10.7 8.50 20.6 16.4 13.2 10.6 8.42 20.6 16.3 13.1 10.6 8.34 16.2 13.0 10.5 8.28 16.2 13.0 10.5 8.23 6.65
Design Tables 07 to 12 for Section Resistances of Rolled Sections: S275 steel I-sections H-sections CHS RHS SHS
113
Design Table 07 Section resistances of rolled I-sections: S275 steel (1) z
tf r y
d h tw
cf b I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
Flexural Rigidity EIy 103*kNm2 1510 1310 1060 916 790 683 714 586 517 504 431 355 317 357 315 286 248 439 321 265 235 207 183 159 160 140 129 116 100
EIz 103*kNm2 95.3 82.3 32.8 27.9 23.5 19.8 23.9 19.0 16.4 17.2 14.4 11.5 10.1 13.9 12.1 10.9 9.20 33.2 23.9 19.6 9.47 8.25 7.20 6.11 7.12 6.17 5.65 5.02 4.22
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
114
Moment Resistance My,Rd Mz,Rd kNm kNm 4690 885 4110 766 3340 424 2890 363 2530 307 2210 260 2430 321 2020 258 1800 223 1900 254 1640 214 1370 171 1280 157 1490 215 1330 188 1210 169 1060 144 1980 416 1470 302 1220 248 1100 162 975 142 869 124 792 110 848 133 750 116 692 106 649 97.6 567 82.5
Shear Resistance Vz,Rd kN 3240 2920 2900 2570 2350 2210 2220 2000 1890 1950 1760 1560 1520 1630 1470 1370 1280 1890 1440 1200 1300 1170 1090 1060 1110 1020 921 909 865
Axial Resistance Na,Rd kN 13000 11200 9340 7930 6840 5990 7130 5910 5260 6310 5390 4420 4100 5520 4810 4340 3790 8030 5960 4790 4540 3960 3520 3210 4060 3560 3200 3010 2650
Design Table 08 Section resistances of rolled I-sections: S275 steel (2) z
tf r y
d h tw
cf b I-Sections 457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Flexural Rigidity EIy 103*kNm2 93.7 84.1 76.1 68.3 60.3 75.0 67.0 59.2 52.3 43.9 56.0 49.8 44.3 38.3 32.2 25.6 40.0 32.8 28.9 24.8 20.9 16.9 24.0 20.3 17.4 19.6 16.8 14.7 13.3 11.0 9.14 13.4 11.4 9.04 8.20 6.99 5.82 5.95 4.80 4.31 2.79 1.71 0.970
EIz 103*kNm2 4.82 4.28 3.83 3.42 2.97 2.42 2.15 1.87 1.63 1.32 3.18 2.79 2.46 2.09 1.10 0.841 2.79 2.28 1.98 1.66 0.734 0.574 2.17 1.84 1.57 0.945 0.797 0.689 0.398 0.318 0.252 1.39 1.17 0.918 0.367 0.305 0.244 0.789 0.631 0.336 0.281 0.184 0.114
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
115
Moment Resistance My,Rd Mz,Rd kNm kNm 591 100 533 89.6 485 80.6 454 74.8 404 65.2 480 63.6 432 56.4 399 51.4 355 44.8 303 36.6 398 70.8 371 65.2 330 57.5 289 49.0 244 32.5 199 25.0 333 66.8 278 54.7 246 47.9 213 40.4 181 24.5 149 19.3 233 53.9 198 45.7 171 39.1 196 31.9 169 27.1 148 23.5 132 16.5 111 13.3 94.1 10.7 156 38.8 133 32.7 108 25.9 97.1 15.1 84.2 12.7 71.2 10.3 86.4 24.3 71.0 19.5 64.4 13.7 47.0 11.4 33.8 8.60 23.2 6.20
Shear Resistance Vz,Rd kN 852 789 729 693 650 798 721 697 624 578 640 612 549 529 473 438 568 501 455 425 408 366 422 357 319 474 420 372 350 315 299 321 280 260 283 265 248 231 204 197 157 130 102
Axial Resistance Na,Rd kN 3310 2960 2670 2460 2190 2730 2400 2220 1920 1630 2470 2280 1990 1780 1460 1200 2350 1970 1720 1500 1280 1050 1890 1580 1360 1680 1470 1280 1100 921 797 1510 1300 1090 990 868 749 1050 880 809 668 558 454
Design Table 09 Section resistances of rolled H-sections: S275 steel z
tf r tw d h
h
y
cf
b H-Sections 356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
Flexural Rigidity EIy 103*kNm2 578 477 384 309 258 210 166 139 120 102 84.4 166 135 107 81.3 68.9 58.2 46.6 63.0 47.3 36.8 30.0 23.9 19.8 16.0 12.9 11.0 9.60 4.64 3.68 2.63
EIz 103*kNm2 206 174 142 116 98.5 81.3 65.1 49.8 43.1 37.0 30.7 51.7 42.6 34.2 26.5 22.5 19.0 15.4 20.7 15.8 12.5 10.2 8.21 6.57 5.33 4.35 3.74 3.26 1.48 1.18 0.840
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Limited availability.
116
Moment Resistance My,Rd Mz,Rd kNm kNm 3480 1960 2960 1670 2550 1380 2100 1140 1790 974 1540 811 1240 655 1050 528 917 459 784 393 599 218 1300 644 1130 536 912 435 710 338 610 289 519 246 437 200 641 314 496 241 392 192 323 158 273 128 259 125 212 103 180 83.9 156 72.6 137 63.5 85.0 38.5 68.2 30.8 45.1 14.5
Shear Resistance Vz,Rd kN 3040 2630 2290 1920 1640 1440 1150 1030 907 772 645 1490 1320 1070 871 756 657 558 903 705 577 467 407 475 371 352 298 269 226 184 158
Axial Resistance Na,Rd kN 19800 17200 15200 12800 11000 9700 7920 6810 5990 5170 4350 9180 8110 6680 5330 4610 3980 3380 5640 4450 3600 2990 2560 2920 2400 2100 1820 1610 1300 1050 803
Design Table 10 Section resistances of hot-finished CHS: S275 steel z
t
y
d
S275 CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 1.24 1.51 2.21 2.73 3.28 3.93 5.02 6.22 7.56 9.14 9.87 12.3 15.0 18.3 16.7 20.8 25.6 31.1 38.6 22.1 27.7 34.0 41.8 51.9 41.8 51.5 63.0 78.5 95.4 59.6 73.7 90.5 113 138 82.5 102 126 157 192 178 220 248 277 339 284 351 443 545 427 529 668 823
Section Classification
1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 2 1 1 1 3 2 1 1 1 3 3 2 1 1 3 2 2 1 4 3 2 1
Moment Resistance My,Rd kNm 30.8 38.2 45.4 56.7 69.0 83.6 78.4 98.2 120 147 123 155 190 233 175 220 271 333 418 211 266 330 404 509 349 432 534 671 792 443 550 679 855 1010 426 682 844 1060 1260 619 765 1230 1550 1850 1050 1680 2130 2530 1710 2810 3340
117
Shear Resistance Vz,Rd kN 267 335 324 407 502 619 426 537 664 820 534 673 835 1031 636 803 997 1230 1570 698 883 1100 1360 1730 1010 1260 1570 1980 2370 1140 1420 1770 2240 2680 1270 1580 1970 2500 2990 1530 1900 2380 3020 3610 1750 2170 2770 3320 3170 4050 4850
Axial Resistance Na,Rd kN 726 910 883 1110 1370 1680 1160 1460 1810 2230 1450 1830 2270 2810 1730 2180 2710 3360 4260 1900 2400 3000 3710 4700 2750 3440 4260 5390 6440 3110 3850 4810 6110 7290 3470 4290 5360 6790 8140 4150 5170 6460 8220 9830 4760 5910 7540 9040 8640 11000 13200
Design Table 11 Section resistances of hot-finished RHS: S275 steel z
cw
y
h
cf t
b S275 RHS hxbxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.827 0.948 1.72 2.01 2.27 3.57 4.26 4.91 4.81 5.80 6.83 8.27 10.1 11.9 13.9 10.4 12.7 15.1 17.7 20.7 15.8 19.4 23.3 27.5 32.6 26.9 33.2 40.1 48.1 57.8 31.9 39.3 47.5 56.7 68.0 60.9 74.1 89.3 108 89.0 109 132 161 190
EIz 103*kNm2 0.441 0.504 0.586 0.680 0.760 1.22 1.44 1.66 3.11 3.74 4.37 3.78 4.58 5.40 6.28 5.92 7.22 8.59 10.1 11.7 8.55 10.5 12.5 14.8 17.4 16.1 19.9 23.9 28.8 34.4 11.0 13.5 16.3 19.4 23.1 24.8 30.0 36.1 43.7 41.0 49.8 60.1 73.3 86.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 4 1 2 1 1 1 1 1 1 2 4 1 3 1 1 1 1 1 1 1 4 1 4 1 2 1 1 1 1 1 4 1 4 1 1 1 1 2 4 1 4 1 2 1 1 1 1
Moment resistance My,Rd Mz,Rd kNm kNm 22.9 17.3 27.0 20.4 36.3 22.5 43.5 26.7 50.4 30.9 59.3 36.7 71.9 44.4 84.8 52.2 76.0 62.6 93.0 76.5 111 91.2 106 75.0 131 92.1 157 111 186 131 126 86.2 155 121 187 146 224 174 268 208 166 206 156 250 189 300 227 363 274 239 297 209 363 289 440 349 536 426 257 319 391 242 470 292 575 355 435 531 644 432 792 531 564 690 844 597 1050 737 1210 851
118
Shear Resistance
Axial Resistance
Vz,Rd kN 209 254 285 350 420 365 452 547 370 460 560 467 582 712 864 489 611 748 910 1120 569 712 874 1070 1320 670 840 1030 1270 1580 765 960 1180 1450 1810 1090 1340 1650 2070 1220 1510 1860 2330 2740
Na,Rd kN 602 734 741 910 1090 949 1170 1420 1120 1390 1700 1300 1610 1970 2390 1430 1790 2190 2670 3290 1600 2050 2520 3080 3820 1880 2470 3070 3770 4700 1810 2390 3070 3770 4700 2750 3560 4460 5580 3100 4020 5140 6460 7600
Design Table 12 Section resistances of hot-finished SHS: S275 steel z
y c b
t
S275 SHS bxbxt mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.638 0.732 2.42 2.88 3.34 6.05 7.35 8.72 10.2 8.17 10.0 11.9 14.0 16.3 12.2 15.0 18.0 21.2 25.2 21.6 26.7 32.1 38.4 46.2 43.1 52.3 63.0 76.4 65.1 79.4 96.2 118 139
Section Classification Bending y-y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 4 2 1 1 1 3 1 1 1 4 2 1 1 1
Moment Resistance My,Rd kNm 20.5 24.1 50.1 60.9 72.0 92.8 114 137 163 114 140 169 202 241 149 184 223 268 324 270 330 399 487 322 457 556 682 605 737 913 1060
119
Shear Resistance Vz,Rd kN 174 212 274 339 410 374 466 569 691 414 517 633 770 950 474 593 728 889 1100 574 720 887 1090 1360 847 1050 1290 1610 974 1200 1480 1860 2280
Axial Resistance Na,Rd kN 602 734 949 1170 1420 1300 1610 1970 2390 1430 1790 2190 2670 3290 1640 2050 2520 3080 3820 1900 2490 3070 3770 4700 2880 3620 4460 5580 3180 4170 5140 6460 7890
120
Design Tables 13 to 18 for Section Resistances of Rolled Sections: S355 steel I-sections H-sections CHS RHS SHS
121
Design Table 13 Section resistances of rolled I-sections: S355 steel (1) z
tf r y
d h tw
cf b I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
Flexural Rigidity EIy 103*kNm2 1510 1310 1060 916 790 683 714 586 517 504 431 355 317 357 315 286 248 439 321 265 235 207 183 159 160 140 129 116 100
EIz 103*kNm2 95.3 82.3 32.8 27.9 23.5 19.8 23.9 19.0 16.4 17.2 14.4 11.5 10.1 13.9 12.1 10.9 9.20 33.2 23.9 19.6 9.47 8.25 7.20 6.11 7.12 6.17 5.65 5.02 4.22
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Limited availability.
122
Moment Resistance My,Rd Mz,Rd kNm kNm 6110 1150 5350 997 4350 552 3760 473 3290 400 2880 339 3160 417 2640 336 2420 299 2470 331 2140 278 1780 223 1600 197 1940 280 1730 245 1570 220 1380 187 2580 542 1910 393 1630 333 1430 211 1270 185 1130 162 1020 142 1140 178 1000 155 927 142 838 126 731 107
Shear Resistance Vz,Rd kN 4220 3800 3780 3350 3060 2870 2900 2610 2460 2530 2290 2040 1970 2120 1920 1790 1670 2460 1880 1570 1690 1520 1420 1370 1450 1330 1200 1170 1120
Axial Resistance Na,Rd kN 16500 14200 11800 10000 8590 7500 8980 7430 6590 7950 6770 5540 5090 6960 6060 5460 4760 10500 7570 6080 5740 5000 4430 3990 5130 4500 4040 3760 3310
Design Table 14 Section resistances of rolled I-sections: S355 steel (2) z
tf r y
tw d h cf b
I-Sections 457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Flexural Rigidity EIy 103*kNm2 93.7 84.1 76.1 68.3 60.3 75.0 67.0 59.2 52.3 43.9 56.0 49.8 44.3 38.3 32.2 25.6 40.0 32.8 28.9 24.8 20.9 16.9 24.0 20.3 17.4 19.6 16.8 14.7 13.3 11.0 9.14 13.4 11.4 9.04 8.20 6.99 5.82 5.95 4.80 4.31 2.79 1.71 0.970
EIz 103*kNm2 4.82 4.28 3.83 3.42 2.97 2.42 2.15 1.87 1.63 1.32 3.18 2.79 2.46 2.09 1.10 0.841 2.79 2.28 1.98 1.66 0.734 0.574 2.17 1.84 1.57 0.945 0.797 0.689 0.398 0.318 0.252 1.39 1.17 0.918 0.367 0.305 0.244 0.789 0.631 0.336 0.281 0.184 0.114
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
123
Moment Resistance My,Rd Mz,Rd kNm kNm 792 135 693 117 631 105 586 96.6 522 84.1 643 85.2 562 73.5 515 66.4 458 57.9 391 47.2 533 94.8 479 84.1 426 74.2 373 63.2 315 41.9 257 32.2 430 86.3 359 70.6 318 61.8 275 52.2 234 31.6 193 24.9 300 69.6 256 58.9 221 50.4 252 41.2 218 34.9 191 30.3 171 21.3 143 17.2 121 13.8 201 50.1 171 42.2 140 33.4 125 19.5 109 16.3 91.9 13.2 111 31.3 91.6 25.2 83.1 17.6 60.7 14.8 43.7 11.1 29.9 8.02
Shear Resistance Vz,Rd kN 1110 1030 949 895 839 1040 938 899 806 747 833 790 709 683 611 566 733 646 587 549 527 472 545 461 411 612 542 481 452 407 386 415 361 336 365 341 320 299 263 254 203 167 131
Axial Resistance Na,Rd kN 4200 3770 3380 3100 2750 3460 3040 2780 2400 2040 3140 2870 2510 2230 1830 1500 2990 2480 2170 1890 1600 1310 2420 2010 1720 2170 1880 1610 1380 1150 992 1950 1650 1370 1250 1090 938 1360 1140 1040 863 721 586
Design Table 15 Section resistances of rolled H-sections: S355 steel tf
z
h
y
r tw d h
cf
b H-Sections 356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
Flexural Rigidity EIy 103*kNm2 578 477 384 309 258 210 166 139 120 102 84.4 166 135 107 81.3 68.9 58.2 46.6 63.0 47.3 36.8 30.0 23.9 19.8 16.0 12.9 11.0 9.60 4.64 3.68 2.63
EIz 103*kNm2 206 174 142 116 98.5 81.3 65.1 49.8 43.1 37.0 30.7 51.7 42.6 34.2 26.5 22.5 19.0 15.4 20.7 15.8 12.5 10.2 8.21 6.57 5.33 4.35 3.74 3.26 1.48 1.18 0.840
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 3 3
Limited availability.
124
Moment Resistance My,Rd Mz,Rd kNm kNm 4620 2520 3930 2150 3350 1790 2750 1470 2350 1260 2000 1050 1620 821 1370 662 1190 576 1020 493 780 274 1710 784 1470 673 1190 545 925 424 794 362 676 309 515 170 835 393 645 303 511 240 421 198 352 165 337 157 276 129 233 108 201 93.7 176 82.0 110 49.7 88.0 39.8 58.2 18.7
Shear Resistance Vz,Rd kN 4040 3490 3000 2520 2160 1870 1500 1340 1180 1000 839 1950 1710 1400 1130 984 856 721 1180 918 751 607 525 619 483 455 385 347 292 238 204
Axial Resistance Na,Rd kN 26300 22800 19900 16800 14500 12600 10300 8870 7800 6730 5660 12100 10600 8690 6930 6000 5180 4370 7350 5800 4690 3900 3310 3800 3120 2710 2350 2080 1670 1360 1040
Design Table 16 Section resistances of hot-finished CHS: S355 steel z
t
y
d
S355 CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 1.24 1.51 2.21 2.73 3.28 3.93 5.02 6.22 7.56 9.14 9.87 12.3 15.0 18.3 16.7 20.8 25.6 31.1 38.6 22.1 27.7 34.0 41.8 51.9 41.8 51.5 63.0 78.5 95.4 59.6 73.7 90.5 113 138 82.5 102 126 157 192 178 220 248 277 339 284 351 443 545 427 529 668 823
Section Classification
1 1 1 1 1 1 2 1 1 1 2 2 1 1 3 2 1 1 1 3 2 2 1 1 3 2 1 1 1 3 2 2 1 1 4 3 2 1 1 4 4 3 2 1 4 3 2 2 4 4 3 2
Moment Resistance My,Rd kNm 39.8 49.3 58.6 73.1 89.1 108 101 127 155 190 159 200 246 301 174 284 350 430 540 211 343 426 522 657 347 557 689 866 1060 444 710 877 1100 1360 678 1090 1370 1690 1220 2010 2470 1670 2740 3390 3420 4470
125
Shear Resistance Vz,Rd kN 344 432 419 526 649 799 549 693 857 1060 689 869 1080 1330 821 1040 1290 1590 2020 902 1140 1420 1760 2230 1300 1630 2020 2560 3170 1470 1830 2280 2900 3590 2040 2540 3220 4010 3070 3900 4840 2810 3580 4450 5230 6500
Axial Resistance Na,Rd kN 937 1180 1140 1430 1760 2170 1490 1890 2330 2880 1870 2360 2930 3620 2230 2820 3500 4330 5500 2450 3100 3870 4790 6070 3550 4440 5500 6960 8630 4010 4970 6210 7880 9760 5540 6920 8770 10900 8340 10600 13200 7630 9730 12100 14200 17700
Design Table 17 Section resistances of hot-finished RHS: S355 steel z
cw
y
h cf t
b S355 RHS hxbxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.827 0.948 1.72 2.01 2.27 3.57 4.26 4.91 4.81 5.80 6.83 8.27 10.1 11.9 13.9 10.4 12.7 15.1 17.7 20.7 15.8 19.4 23.3 27.5 32.6 26.9 33.2 40.1 48.1 57.8 31.9 39.3 47.5 56.7 68.0 60.9 74.1 89.3 108 89.0 109 132 161 190
EIz 103*kNm2 0.441 0.504 0.586 0.680 0.760 1.22 1.44 1.66 3.11 3.74 4.37 3.78 4.58 5.40 6.28 5.92 7.22 8.59 10.1 11.7 8.55 10.5 12.5 14.8 17.4 16.1 19.9 23.9 28.8 34.4 11.0 13.5 16.3 19.4 23.1 24.8 30.0 36.1 43.7 41.0 49.8 60.1 73.3 86.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 4 1 3 1 1 1 1 1 1 3 4 1 4 1 2 1 1 1 1 1 4 1 4 1 3 1 1 1 1 1 4 1 4 1 2 1 1 3 4 1 4 1 3 1 1 1 1
Moment resistance My,Rd Mz,Rd kNm kNm 29.6 22.4 34.9 26.4 46.9 29.0 56.1 34.5 65.0 39.9 76.5 47.4 92.8 57.3 110 67.4 98.2 80.8 120 98.7 143 118 137 85.2 169 119 203 143 240 169 163 201 156 242 188 289 225 346 269 215 266 177 322 244 387 293 469 354 260 383 469 373 568 451 692 550 332 412 504 276 607 376 742 458 561 685 831 557 1020 685 604 891 1090 678 1350 951 1570 1110
126
Shear Resistance
Axial Resistance
Vz,Rd kN 269 328 368 452 543 472 583 707 478 594 723 603 752 919 1120 632 788 965 1180 1450 734 919 1130 1380 1710 865 1080 1340 1640 2040 988 1240 1530 1870 2330 1410 1740 2140 2670 1570 1940 2400 3010 3670
Na,Rd kN 778 948 957 1170 1410 1230 1520 1840 1450 1800 2190 1650 2080 2550 3090 1810 2310 2830 3450 4240 2020 2650 3260 3980 4930 2350 3120 3970 4870 6060 2280 3010 3900 4870 6060 3470 4490 5750 7200 3910 5060 6540 8330 10200
Design Table 18 Section resistances of hot-finished SHS: S355 steel z
y c b
t
S355 SHS bxbxt mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.638 0.732 2.42 2.88 3.34 6.05 7.35 8.72 10.2 8.17 10.0 11.9 14.0 16.3 12.2 15.0 18.0 21.2 25.2 21.6 26.7 32.1 38.4 46.2 43.1 52.3 63.0 76.4 65.1 79.4 96.0 118 139
Section Classification Bending y-y 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 3 1 1 1 4 2 1 1 4 3 1 1 1
Moment Resistance My,Rd kNm 26.4 31.2 64.7 78.6 92.9 120 147 177 210 147 181 218 260 312 165 237 288 346 418 301 426 515 628 589 717 880 671 951 1180 1380
127
Shear Resistance Vz,Rd kN 225 274 354 438 530 483 601 735 892 534 667 817 990 1230 612 765 940 1150 1420 741 929 1140 1400 1750 1090 1350 1660 2080 1260 1550 1920 2410 2860
Axial Resistance Na,Rd kN 778 948 1230 1520 1840 1670 2080 2550 3090 1850 2310 2830 3450 4240 2080 2650 3260 3980 4930 2360 3210 3970 4860 6060 3590 4680 5750 7200 3940 5260 6640 8330 9610
128
Design Tables 19 to 24 for Section Dimensions and Properties of Welded Sections I-sections (EWIS) H-sections (EWHS) EWCHS EWRHS EWSHS
129
Design Table 19A Section dimensions of welded I-sections (1) z
tf r y
d h tw
cf b
I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
EWIS
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Mass per Meter kg/m 420.8 352.5 312.4 282.4 249.4 217.9 245.8 213.5 184.4 220.1 194.0 166.5 147.4 198.2 172.6 150.5 133.3 257.5 185.5 159.6 158.0 137.6 121.7 111.5 147.5 127.9 112.6 103.5 87.8
Depth Width of of Section Section mm 920 915 930 920 910 900 850 840 840 770 760 750 750 690 690 680 680 640 620 610 620 610 610 600 550 540 540 530 530
mm 450 450 360 360 350 340 360 350 340 320 320 310 310 290 280 280 280 340 330 330 260 260 260 260 250 250 250 250 250
Thickness Web Flange tw tf mm mm 20 40 20 30 20 30 20 25 16 25 16 20 16 25 16 20 12 20 16 25 16 20 12 20 12 16 16 25 16 20 12 20 12 16 20 30 12 25 12 20 12 25 12 20 12 16 10 16 12 25 12 20 12 16 10 16 10 12
Limited availability.
130
Depth Fillet between Height Fillets
Ratios for Local Buckling
Surface Area per Meter per Tonne
r mm 16 16 16 16 16 14 16 14 12 16 14 12 11 16 14 12 11 20 12 12 12 12 11 10 12 12 11 10 8
d mm 808 823 838 838 828 832 768 772 776 688 692 686 696 608 622 616 626 540 546 546 546 546 556 548 476 476 486 478 490
b/tf
d/tw
5.0 6.6 5.1 6.2 6.0 7.4 6.2 7.7 7.6 5.4 6.9 6.9 8.6 4.8 5.9 6.1 7.7 4.7 5.9 7.4 4.5 5.6 7.1 7.2 4.3 5.4 6.8 6.9 9.3
42.0 42.8 43.5 43.5 53.8 53.8 50.0 50.0 66.7 45.0 45.0 59.2 59.8 40.0 40.6 53.3 54.0 29.0 47.5 47.5 47.5 47.5 48.2 56.8 41.7 41.7 42.3 49.8 50.6
m2 3.60 3.59 3.26 3.24 3.19 3.13 3.11 3.05 3.02 2.79 2.77 2.72 2.72 2.51 2.47 2.46 2.46 2.60 2.54 2.52 2.26 2.24 2.24 2.22 2.08 2.06 2.06 2.04 2.04
m2 8.60 10.3 10.5 11.5 12.8 14.4 12.6 14.3 16.4 12.7 14.3 16.3 18.4 12.7 14.3 16.3 18.4 10.1 13.7 15.8 14.3 16.3 18.4 19.9 14.1 16.1 18.3 19.7 23.2
Design Table 19B Section properties of welded I-sections (1) z
tf r y
d h tw
cf b Second Moment of Area I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
EWIS
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Elastic Modulus ,
cm4 796000 633000 547000 470000 428000 348000 375000 304000 280000 272000 225000 201000 171000 195000 162000 148000 126000 222000 165000 133000 134000 109100 92700 86200 98700 80100 68000 63100 51100
cm4 60800 45600 23400 19500 17900 13130 19500 14310 13110 13670 10940 9940 7950 10180 7330 7320 5860 19700 15000 11980 7330 5860 4690 4690 6510 5210 4170 4170 3120
cm3 17300 13800 11800 10220 9410 7730 8820 7240 6670 7060 5920 5360 4560 5650 4700 4350 3710 6940 5320 4360 4320 3580 3040 2870 3590 2970 2520 2380 1930
Plastic Modulus ,
,
cm3 2700 2030 1300 1083 1023 772 1083 818 771 854 684 641 513 702 524 523 419 1159 909 726 564 451 361 361 521 417 334 334 250
cm3 19600 15800 13700 12100 10900 9110 10200 8450 7610 8220 6950 6140 5270 6620 5570 5020 4310 8130 5960 4950 4920 4120 3540 3290 4100 3420 2930 2730 2230
Limited availability.
131
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section A
,
cm3 4140 3130 2040 1710 1590 1216 1680 1280 1190 1330 1080 989 797 1100 831 810 653 1810 1380 1110 868 699 564 557 802 646 521 514 389
0.896 0.878 0.868 0.859 0.872 0.855 0.876 0.860 0.878 0.876 0.861 0.879 0.864 0.876 0.859 0.880 0.864 0.881 0.899 0.887 0.894 0.880 0.866 0.878 0.896 0.884 0.869 0.883 0.864
24.4 32.3 33.5 38.3 39.9 47.2 36.9 43.7 46.3 33.4 39.4 41.2 49.8 29.8 35.8 37.2 45.1 22.2 26.2 32.4 26.9 33.2 40.3 40.8 23.5 29.0 35.3 35.6 45.1
dm6 117.7 89.3 47.4 39.0 35.0 25.4 33.2 24.1 22.0 19.0 14.98 13.24 10.71 11.25 8.23 7.97 6.46 18.3 13.3 10.43 6.49 5.10 4.14 4.00 4.49 3.52 2.86 2.75 2.09
cm4 2140 1040 880 607 482 299 484 296 227 432 269 206 126 389 238 186 114 767 377 209 304 171 104 89.9 289 162 97.5 84.9 45.7
mm2 533 446 395 359 318 278 313 272 235 280 247 212 188 253 220 192 170 328 236 203 201 175 155 142 188 163 143 132 112
Design Table 20A Section dimensions of welded I-sections (2) z
tf r y
tw
d h
cf b
I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
EWIS
460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Mass per Meter kg/m 111.8 103.6 90.4 83.1 69.8 91.1 80.4 73.1 62.3 56.3 84.8 77.5 64.8 58.5 48.9 42.5 72.5 61.3 53.8 48.7 43.5 38.1 58.7 44.6 39.3 53.6 45.3 40.6 36.8 33.3 28.4 47.9 42.8 33.4 32.7 28.8 24.7 33.5 28.5 26.8 18.7 17.8 14.6
Depth Width of of Section Section mm 470 460 460 460 460 460 460 460 460 450 420 410 410 410 400 400 360 360 355 355 355 350 310 310 300 310 310 300 315 310 305 260 260 250 260 260 255 210 200 200 180 150 130
mm 220 220 220 220 220 180 180 180 180 180 210 210 210 210 160 150 180 180 170 170 170 170 160 160 160 140 140 140 110 110 110 170 170 170 130 130 130 150 150 110 100 100 80
Thickness Web tw mm 12 10 10 8 8 10 10 8 8 8 10 8 8 8 6 6 10 10 8 8 6 6 8 6 6 8 8 8 8 8 6 8 8 6 6 6 6 6 6 6 4 4 4
132
Flange tf mm 20 20 16 16 12 20 16 16 12 10 16 16 12 10 12 10 16 12 12 10 10 8 16 12 10 16 12 10 10 8 8 12 10 8 10 8 6 10 8 10 8 8 8
Fillet Height
Depth between Fillets
r mm 12 10 10 8 8 10 10 8 8 8 10 8 8 8 8 8 10 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
d mm 406 400 408 412 420 400 408 412 420 414 368 362 370 374 360 364 308 320 315 319 319 318 262 270 264 262 270 264 279 278 273 220 224 218 224 228 227 174 168 164 148 118 98
Ratios for Local Buckling
Surface Area per Meter per Tonne
b/tf 4.6 4.8 5.9 6.1 8.2 3.8 4.7 4.9 6.5 7.8 5.6 5.8 7.8 9.3 5.8 6.4 4.7 6.4 6.1 7.3 7.4 9.3 4.3 5.8 6.9 3.6 4.8 5.8 4.3 5.4 5.5 6.1 7.3 9.3 5.4 6.8 9.0 6.4 8.0 4.4 5.0 5.0 3.8
d/tw 31.8 38.0 38.8 49.5 50.5 38.0 38.8 49.5 50.5 49.8 34.8 43.3 44.3 44.8 57.3 58.0 28.8 30.4 37.4 37.9 50.5 50.3 30.8 42.3 41.3 30.8 31.8 31.0 32.9 32.8 42.8 25.5 26.0 33.7 34.7 35.3 35.2 26.3 25.3 24.7 33.0 25.5 20.5
m2 1.80 1.78 1.78 1.78 1.78 1.62 1.62 1.62 1.62 1.60 1.66 1.64 1.64 1.64 1.43 1.39 1.42 1.42 1.37 1.37 1.38 1.37 1.24 1.25 1.23 1.16 1.16 1.14 1.05 1.04 1.04 1.18 1.18 1.17 1.028 1.028 1.018 1.008 0.988 0.828 0.752 0.692 0.572
m2 16.1 17.2 19.7 21.5 25.5 17.8 20.2 22.2 26.1 28.5 19.6 21.2 25.4 28.1 29.2 32.7 19.6 23.2 25.5 28.2 31.7 35.9 21.2 28.0 31.2 21.7 25.7 28.2 28.6 31.4 36.5 24.7 27.7 35.0 31.4 35.7 41.2 30.1 34.7 31.0 40.2 38.9 39.1
Design Table 20B Section properties of welded I-sections (2) z
tf r d h
y tw
cf b Second Moment of Area I-Sections
Elastic Modulus
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section
EWIS ,
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Plastic Modulus
460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
,
,
cm4
cm3
cm3
cm3
cm3
50500 49200 40000 38600 31100 43100 36700 33600 27300 23000 29400 28400 22100 19400 17100 12600 21300 17300 15800 13900 12000 10100 12500 9690 8420 10080 8220 7250 6570 5340 4550 6980 5770 5170 4420 3560 2950 3450 2480 2540 1440 847 496
3090 3090 2130 2130 1600 1940 1550 1310 985 685 1560 1550 1160 974 552 367 1550 1160 984 820 819 656 1090 820 683 522 392 327 223 135 97.7 676 458 367 168 134 100 563 293 222 178 114 56.3
2150 2090 1700 1640 1320 1830 1560 1430 1160 979 1400 1350 1050 924 855 630 1150 935 854 751 676 569 806 625 543 650 530 468 424 345 294 517 427 383 327 264 219 329 236 242 160 112 75.4
294 294 213 213 160 216 172 154 116 85.6 173 172 129 108 78.8 56.4 172 129 116 96.5 96.4 77.1 136 102 85.4 83.5 62.7 52.3 40.6 26.9 21.7 90.1 65.5 56.4 33.5 26.8 20.1 75.1 45.1 40.4 32.3 24.1 15.0
2510 2390 1980 1860 1530 2120 1830 1650 1360 1170 1660 1580 1220 1080 1029 748 1340 1090 992 879 776 666 925 713 624 760 629 561 516 433 366 601 505 447 401 322 274 384 279 286 188 134 93.2
459 453 333 328 248 336 272 239 181 136 276 271 202 169 128 88.6 269 204 180 151 148 119 210 157 131 130 99.2 83.6 66.0 45.6 35.8 140 103 87.5 54.9 43.0 33.0 116 70.1 62.9 49.7 37.2 23.6
133
dm6
cm4
A mm2
1.56 1.56 1.10 1.10 0.839 0.982 0.799 0.675 0.516 0.362 0.637 0.632 0.483 0.409 0.208 0.139 0.486 0.372 0.315 0.266 0.244 0.197 0.236 0.182 0.154 0.113 0.0870 0.0735 0.0502 0.0307 0.0223 0.1125 0.0775 0.0620 0.0283 0.0230 0.0175 0.0563 0.0299 0.0222 0.01313 0.00577 0.00210
137 126 69.2 62.1 30.7 110 63.8 53.9 27.2 18.3 71.5 62.1 27.5 18.8 28.7 11.4 60.4 32.3 25.5 17.3 13.7 8.24 48.4 20.5 12.8 38.9 19.3 13.3 12.3 8.43 5.19 21.5 13.6 10.47 10.93 5.24 3.30 13.2 5.83 8.70 4.10 3.53 2.80
138 129 110 100 85.0 117 103 90.7 77.8 69.3 107 98.4 76.2 69.3 72.5 50.1 93.4 79.1 69.8 63.3 55.4 48.8 74.7 56.8 50.7 63.5 54.2 49.5 46.5 40.8 33.3 57.0 49.3 42.3 41.3 32.5 28.8 46.5 33.7 34.7 25.4 21.8 17.8
,
cm4
0.883 0.893 0.879 0.891 0.875 0.887 0.874 0.886 0.866 0.850 0.866 0.879 0.874 0.861 0.848 0.869 0.883 0.862 0.877 0.865 0.885 0.872 0.897 0.897 0.887 0.890 0.872 0.860 0.853 0.833 0.848 0.882 0.869 0.886 0.856 0.861 0.843 0.869 0.876 0.888 0.898 0.897 0.897
25.2 25.3 31.8 32.1 42.4 25.8 32.1 32.7 43.1 49.7 27.4 28.3 37.8 43.7 34.3 45.4 24.5 31.2 32.9 38.3 38.5 47.0 20.3 27.6 33.2 20.9 27.8 32.2 32.4 36.9 42.6 23.4 27.5 29.1 28.1 36.3 43.3 20.8 27.0 22.2 23.8 19.6 17.1
Design Table 21A Section dimensions of welded H-sections tf
z
r h
y
tw d h
cf b
H-Sections
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
EWHS
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Mass per Meter
kg/m 716 563 532 456 368 300 275 218 217 172 167 316 260 213 177 152 142 114 184 151 121 116 93.2 101 84.8 73.3 57.9 49.8 42.2 33.8 28.5
Depth Width of of Section Section
mm 470 460 440 420 400 390 380 380 370 360 360 370 350 340 330 320 320 310 290 280 270 260 260 220 220 210 210 200 170 160 160
mm 470 480 480 480 480 490 490 440 440 440 440 330 340 350 350 360 360 360 300 300 310 310 310 210 220 230 240 240 170 170 170
Thickness Web tw mm 50 40 30 30 25 25 16 16 16 12 10 25 20 20 16 16 12 10 20 16 12 10 8 12 10 10 8 8 8 6 6
Limited availability.
134
Flange tf mm 80 60 60 50 40 30 30 25 25 20 20 50 40 30 25 20 20 16 30 25 20 20 16 25 20 16 12 10 12 10 8
Fillet Height
Depth between Fillets
r mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 12 10 20 16 12 10 8 12 10 10 8 8 8 8 8
d mm 278 308 288 288 288 298 288 298 288 288 288 238 238 248 248 248 256 258 190 198 206 200 212 146 160 158 170 164 130 124 128
Ratios for Local Buckling
Surface Area per Meter per Tonne
cf/tf
d/tw
2.4 3.4 3.5 4.2 5.3 7.2 7.4 7.8 7.8 9.9 10.0 2.7 3.6 5.0 6.0 7.8 8.1 10.3 4.0 5.0 6.9 7.0 8.9 3.5 4.8 6.3 9.0 10.8 6.1 7.4 9.3
5.6 7.7 9.6 9.6 11.5 11.9 18.0 18.6 18.0 24.0 28.8 9.5 11.9 12.4 15.5 15.5 21.3 25.8 9.5 12.4 17.2 20.0 26.5 12.2 16.0 15.8 21.3 20.5 16.3 20.7 21.3
m2 2.72 2.72 2.66 2.58 2.51 2.49 2.47 2.37 2.33 2.30 2.30 2.09 2.04 2.02 1.99 1.97 1.98 1.94 1.72 1.69 1.68 1.64 1.64 1.28 1.30 1.28 1.30 1.26 1.00 0.97 0.97
m2 3.80 4.83 5.00 5.66 6.82 8.31 9.0 10.9 10.7 13.3 13.7 6.61 7.85 9.5 11.3 12.9 13.9 17.0 9.36 11.2 13.8 14.1 17.6 12.7 15.3 17.5 22.5 25.3 23.8 28.2 33.2
Design Table 21B Section properties of welded H-sections tf
z h
y
r tw d h
cf b
Second Moment of Area H-Sections
Elastic Modulus
#
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section
EWHS ,
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
Plastic Modulus
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
,
,
,
cm4
cm4
cm3
cm3
cm3
cm3
302000 245000 218000 173000 132000 103000 94600 74200 69900 54200 53700 89300 69000 54300 43700 35400 34600 26700 32600 26100 20600 18800 15600 10500 9310 7410 6080 4720 2750 2050 1720
139000 111000 110700 92200 73800 58900 58800 35500 35500 28400 28400 30000 26200 21500 17900 15600 15600 12400 13500 11300 9930 9930 7940 3860 3550 3240 2760 2300 983 819 655
12900 10700 9910 8240 6600 5280 4980 3910 3780 3010 2980 4830 3940 3190 2650 2210 2160 1720 2250 1860 1530 1450 1200 955 846 706 579 472 324 256 215
5910 4620 4610 3840 3080 2400 2400 1610 1610 1290 1290 1820 1540 1230 1020 864 864 691 901 750 641 641 512 368 323 282 230 192 116 96 77
15900 12800 11800 9730 7630 6050 5630 4420 4280 3380 3330 5800 4650 3720 3050 2540 2430 1910 2690 2180 1740 1630 1330 1130 978 810 651 532 374 293 247
9050 7060 6990 5840 4670 3660 3630 2450 2450 1950 1950 2770 2350 1870 1560 1320 1310 1050 1390 1150 972 968 773 560 490 429 349 292 177 146 118
Limited availability.
135
A 0.811 0.813 0.802 0.786 0.775 0.759 0.752 0.804 0.794 0.791 0.794 0.857 0.845 0.829 0.827 0.809 0.816 0.809 0.823 0.820 0.805 0.794 0.802 0.848 0.844 0.819 0.812 0.794 0.840 0.833 0.829
5.0 6.8 6.5 7.6 9.2 12.0 12.0 14.7 14.2 17.6 17.6 6.6 8.0 10.7 12.7 15.3 15.5 19.0 9.0 10.6 12.9 12.4 15.7 8.1 10.4 12.6 17.0 19.3 13.7 15.7 19.7
dm6
cm4
cm2
52.8 44.3 40.0 31.6 23.9 19.1 18.0 11.2 10.6 8.21 8.21 7.68 6.29 5.17 4.16 3.50 3.50 2.69 2.28 1.83 1.55 1.43 1.18 0.367 0.355 0.305 0.271 0.208 0.0614 0.0461 0.0379
17300 7640 7200 4290 2210 1050 926 503 502 253 245 2890 1520 705 403 230 208 108 601 344 179 173 88.5 229 123.3 68.7 30.8 19.1 22.1 12.3 6.84
912 717 677 581 469 382 350 278 276 220 213 403 331 271 225 194 180 145 234 192 154 148 119 128 108 93.4 73.8 63.7 53.8 43.7 37.1
Design Table 22 Section dimensions and properties of cold-formed CHS z
t
y
Area of Section
dxt
Mass per Meter m
mm 140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
kg/m 19.8 26.0 32.1 24.3 32.0 39.5 46.8 31.7 41.8 51.8 61.6 39.1 51.7 64.1 76.3 100 46.5 61.6 76.4 91.1 120 52.4 69.4 86.3 103 136 77.3 96.2 115 152 187 89.2 111 133 175 217 97.1 121 144 191 237 119 148 177 234 291 173 207 274 340 197 236 313 390
cm2 25.3 33.2 40.8 30.9 40.7 50.3 59.6 40.3 53.3 66.0 78.4 49.8 65.8 81.7 97.3 128 59.2 78.4 97.4 116 153 66.7 88.5 110 131 173 98.5 123 146 193 239 114 141 169 223 276 124 154 184 243 302 151 188 225 299 371 220 263 349 434 251 301 399 496
EWCHS CHS
139.7x6.3 x8.0 x10.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 x16.0 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.0x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
A
Ratio for Local Buckling d/t
23.3 17.5 14.0 28.3 21.3 17.0 14.2 36.7 27.5 22.0 18.3 45.0 33.8 27.0 22.5 16.9 53.3 40.0 32.0 26.7 20.0 60.0 45.0 36.0 30.0 22.5 50.0 40.0 33.3 25.0 20.0 57.5 46.0 38.3 28.8 23.0 62.5 50.0 41.7 31.3 25.0 76.3 61.0 50.8 38.1 30.5 71.0 59.2 44.4 35.5 81.0 67.5 50.6 40.5
d
Second Moment of Area I cm4 568 725 868 1041 1340 1610 1870 2310 3000 3640 4250 4340 5660 6910 8110 10300 7300 9500 11700 13800 17700 10460 13700 16900 19900 25600 18900 23300 27600 35600 43200 29000 35800 42400 55100 67000 37400 46200 54800 71300 87000 68500 84800 100800 131800 161000 135000 160000 210000 258000 201000 240000 315000 387000
136
Elastic Modulus
Plastic Modulus
Wel
Wpl
cm3 81.1 104 124 122 158 189 220 210 273 331 386 321 419 512 601 766 456 594 731 863 1110 581 761 939 1110 1420 945 1170 1380 1780 2160 1260 1560 1840 2400 2910 1500 1850 2190 2850 3480 2250 2780 3300 4320 5280 3800 4510 5920 7270 4960 5930 7780 9560
cm3 108 139 169 161 210 256 300 275 360 441 519 418 549 676 799 1030 592 779 961 1140 1480 752 991 1230 1450 1890 1230 1520 1810 2360 2890 1630 2030 2410 3150 3870 1940 2400 2860 3750 4610 2900 3600 4290 5650 6960 4900 5850 7710 9520 6400 7640 10100 12500
Torsional Constants IT cm4 1140 1450 1740 2080 2680 3220 3740 4620 6000 7280 8500 8680 11300 13800 16200 20700 14600 19000 23400 27600 35400 20900 27400 33800 39800 51200 37800 46600 55200 71200 86400 58000 71600 84800 110000 134000 74800 92400 110000 143000 174000 137000 170000 202000 264000 322000 270000 320000 420000 516000 402000 480000 630000 774000
Wt cm3 162 207 248 245 315 379 440 420 545 662 773 643 839 1020 1200 1530 913 1190 1460 1730 2220 1160 1520 1880 2220 2840 1890 2340 2760 3560 4320 2520 3120 3680 4800 5820 3000 3700 4380 5700 6960 4500 5560 6600 8640 10560 7600 9020 11800 14500 9920 11900 15600 19100
Surface Area per Meter m2 0.440 0.440 0.440 0.535 0.535 0.535 0.535 0.692 0.692 0.692 0.692 0.849 0.849 0.849 0.849 0.849 1.01 1.01 1.01 1.01 1.01 1.13 1.13 1.13 1.13 1.13 1.26 1.26 1.26 1.26 1.26 1.45 1.45 1.45 1.45 1.45 1.57 1.57 1.57 1.57 1.57 1.92 1.92 1.92 1.92 1.92 2.23 2.23 2.23 2.23 2.55 2.55 2.55 2.55
per Tonne m2 22.2 16.9 13.7 22.0 16.7 13.6 11.4 21.9 16.5 13.4 11.2 21.7 16.4 13.2 11.1 8.47 21.7 16.3 13.2 11.0 8.39 21.6 16.3 13.1 11.0 8.33 16.3 13.1 10.9 8.30 6.71 16.2 13.0 10.9 8.25 6.66 16.2 13.0 10.9 8.23 6.64 16.1 13.0 10.8 8.18 6.59 12.9 10.8 8.15 6.56 12.9 10.8 8.12 6.53
Design Table 23 Section dimensions and properties of cold-formed RHS z
y
h
cw cf
t
b
hxb
t
Mass per Meter m
mm 120x80
mm x6.0 x8.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x20.0
kg/m 16.5 21.0 20.3 26.0 31.2 25.9 33.5 40.6 30.6 39.8 48.4 35.3 46.1 56.3 64.0 39.1 51.1 62.6 71.6 44.8 58.6 72.0 82.9 105 54.2 71.2 87.7 102 131 54.2 71.2 87.7 102 131 83.8 103 121 156 96.3 119 139 181 220
EWRHS RHS
120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
160x80 200x100 200x150 250x150
260x180
300x200
350x250
400x200
450x250
500x300
Area of Section A cm2 21.0 26.7 25.8 33.1 39.7 33.0 42.7 51.7 39.0 50.7 61.7 45.0 58.7 71.7 81.6 49.8 65.1 79.7 91.2 57.0 74.7 91.7 106 134 69.0 90.7 112 130 166 69.0 90.7 112 130 166 107 132 154 198 123 152 178 230 280
Ratio for Local Buckling cw/t cf/t 14.0 9.0 20.7 14.0 10.0 27.3 19.0 14.0 27.3 19.0 14.0 35.7 25.3 19.0 12.8 37.3 26.5 20.0 13.7 44.0 31.5 24.0 17.0 10.8 52.3 37.8 29.0 21.2 13.9 60.7 44.0 34.0 25.3 17.0 50.3 39.0 29.5 20.1 56.5 44.0 33.7 23.3 17.0
7.3 4.0 7.3 4.0 2.0 10.7 6.5 4.0 19.0 12.8 9.0 19.0 12.8 9.0 4.5 24.0 16.5 12.0 7.0 27.3 19.0 14.0 8.7 4.5 35.7 25.3 19.0 12.8 7.6 27.3 19.0 14.0 8.7 4.5 25.3 19.0 12.8 7.6 31.5 24.0 17.0 10.8 7.0
137
Second Moment of Area Iy Iz cm4 382 451 793 959 1080 1640 2030 2340 2200 2760 3250 3780 4790 5670 5980 4750 6040 7200 7730 7220 9250 11090 12100 14400 12300 15800 19100 21300 25900 14500 18700 22600 25100 30400 29000 35300 39700 49000 42400 51700 58900 73600 85800
cm4 204 240 270 324 362 560 688 790 1420 1780 2080 1730 2180 2570 2740 2710 3440 4090 4420 3900 4980 5960 6540 7750 7360 9480 11400 12800 15500 5030 6450 7760 8660 10500 11800 14300 16200 19900 19500 23700 27100 33800 39300
Elastic Modulus
Plastic Modulus
Wel,y
Wel,z
Wpl,y
Wpl,z
cm3 63.6 75.2 99.2 120 135 164 203 234 220 276 325 302 383 454 478 365 465 554 595 481 617 739 807 960 703 903 1091 1217 1480 725 935 1130 1260 1520 1290 1570 1760 2180 1700 2070 2360 2940 3430
cm3 51.0 60.1 67.4 80.9 90.4 112 138 158 189 237 277 231 291 343 365 301 382 454 491 390 498 596 654 775 589 758 912 1020 1240 503 645 776 866 1050 940 1140 1300 1590 1300 1580 1810 2250 2620
cm3 80.3 98.2 127 158 183 207 261 309 265 338 404 370 475 570 623 439 565 682 753 578 748 907 1010 1240 830 1080 1320 1500 1870 893 1160 1420 1600 1990 1580 1930 2200 2780 2050 2510 2900 3680 4380
cm3 60.9 74.2 78.6 97.3 112 128 161 190 218 278 332 261 335 402 440 342 440 531 588 440 568 689 772 946 663 862 1050 1190 1490 556 722 879 1000 1240 1060 1290 1480 1860 1450 1780 2050 2610 3100
Surface Area per Meter m2 0.369 0.359 0.449 0.439 0.428 0.569 0.559 0.548 0.669 0.659 0.648 0.769 0.759 0.748 0.718 0.849 0.839 0.828 0.798 0.969 0.959 0.948 0.918 0.890 1.17 1.16 1.15 1.12 1.09 1.17 1.16 1.15 1.12 1.09 1.36 1.35 1.32 1.29 1.56 1.55 1.52 1.49 1.46
per Tonne m2 22.4 17.1 22.2 16.9 13.7 22.0 16.7 13.5 21.8 16.6 13.4 21.8 16.5 13.3 11.2 21.7 16.4 13.2 11.1 21.7 16.4 13.2 11.1 8.44 21.6 16.3 13.1 11.0 8.35 21.6 16.3 13.1 11.0 8.35 16.2 13.0 10.9 8.28 16.2 13.0 10.9 8.24 6.66
Design Table 24 Section dimensions and properties of cold-formed SHS
z
y c b
EWSHS SHS
100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
b mm 100 150 200
220
250
300
350
400
t mm x6.0 x8.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x20.0
Mass per Meter m kg/m 16.5 21.0 25.9 33.5 40.6 35.3 46.1 56.3 64.0 39.1 51.1 62.6 71.6 90.4 44.8 58.6 72.0 82.9 105 54.2 71.2 87.7 102 131 83.8 103 121 156 96.3 119 139 181 220
Area of section A cm2 21.0 26.7 33.0 42.7 51.7 45.0 58.7 71.7 81.6 49.8 65.1 79.7 91.2 115.2 57.0 74.7 91.7 105.6 134.4 69.0 90.7 112 130 166 107 132 154 198 123 152 178 230 280
Ratio for Local Buckling c/t 10.7 6.5 19.0 12.8 9.0 27.3 19.0 14.0 8.7 30.7 21.5 16.0 10.3 5.8 35.7 25.3 19.0 12.8 7.6 44.0 31.5 24.0 17.0 10.8 37.8 29.0 21.2 13.9 44.0 34.0 25.3 17.0 12.0
138
Second Moment of area Iy cm4 294 349 1110 1370 1590 2770 3500 4150 4410 3730 4750 5660 6110 7110 5570 7130 8550 9380 11160 9820 12700 15300 17100 20800 20500 24900 28200 34900 31000 37800 43200 54000 63200
t
Elastic Modulus
Plastic Modulus
Wel cm3 58.9 69.7 148 183 212 277 350 415 441 339 432 515 555 646 446 570 684 750 893 655 847 1020 1140 1390 1170 1420 1610 1990 1550 1890 2160 2700 3160
Wpl cm3 71.8 87.8 175 221 262 323 415 499 546 395 509 614 680 822 516 668 810 908 1110 755 982 1200 1360 1700 1360 1660 1900 2400 1790 2200 2530 3220 3840
Surface Area per Meter m2 0.369 0.359 0.569 0.559 0.548 0.769 0.759 0.748 0.718 0.849 0.839 0.828 0.798 0.770 0.969 0.959 0.948 0.918 0.890 1.17 1.16 1.15 1.12 1.09 1.36 1.35 1.32 1.29 1.56 1.55 1.52 1.49 1.46
per Tonne m2 22.4 17.1 22.0 16.7 13.5 21.8 16.5 13.3 11.2 21.7 16.4 13.2 11.1 8.52 21.7 16.4 13.2 11.1 8.44 21.6 16.3 13.1 11.0 8.35 16.2 13.0 10.9 8.28 16.2 13.0 10.9 8.24 6.66
Design Tables 25 to 27 for Section Resistances of Welded Sections: Q235 steel EWI-sections (EWIS) EWH-sections (EWHS)
139
Design Table 25 Section resistances of welded I-sections: Q235 steel (1) z
tf r y
d h tw
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
Moment Resistance My,Rd Mz,Rd kNm kNm 4010 847 3230 640 2800 417 2480 350 2230 325 1860 249 2080 344 1730 262 1560 243 1680 273 1420 220 1260 202 1130 170 1350 225 1140 170 1030 166 921 139 1660 370 1220 282 1010 228 1010 178 843 143 756 120 703 119 839 164 700 132 626 111 583 110 476 83.0
140
Shear Resistance Vz,Rd kN 2170 2160 2200 2170 1720 1700 1610 1590 1190 1450 1440 1060 1110 1300 1300 964 1010 1510 879 864 879 864 903 740 779 765 799 654 654
Axial Resistance Na,Rd kN 10700 8920 7840 7100 5970 5140 6020 5170 4200 5530 4850 3910 3550 5120 4430 3630 3310 6710 4670 3990 3950 3420 3120 2770 3790 3280 2990 2660 2220
Design Table 26 Section resistances of welded I-sections: Q235 steel (2) z
tf r y
d h tw
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 532 103 495 102 440 85.4 419 84.4 340 63.7 423 68.8 380 58.0 357 57.0 295 43.2 254 36.3 378 77.8 348 76.8 284 58.0 250 48.6 210 33.7 176 24.9 276 57.5 226 43.5 201 38.4 178 32.2 166 31.7 140 25.5 198 44.9 152 33.5 128 28.0 177 34.6 146 26.3 124 22.1 113 14.1 97.7 11.5 86.5 11.1 135 38.0 119 31.9 91.0 25.3 91.1 18.7 78.3 15.1 63.7 11.5 78.2 24.6 62.5 19.7 57.4 13.4 37.3 8.81 29.9 8.79 20.9 5.69
141
Shear Resistance Vz,Rd kN 666 543 567 454 454 543 567 454 454 444 518 405 405 405 296 296 444 444 350 350 263 259 306 229 222 306 306 296 311 306 226 257 257 185 192 192 189 155 148 148 88.8 74.0 64.1
Axial Resistance Na,Rd kN 2910 2710 2470 2180 1810 2380 2200 1910 1600 1440 2320 2080 1730 1550 1240 1060 1990 1680 1470 1330 1130 984 1610 1200 1060 1470 1240 1110 1010 912 759 1310 1170 914 896 789 676 918 781 733 513 487 401
Design Table 27 Section resistances of welded H-sections: Q235 steel tf
z
r y
h
cf
tw
d h
b EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 2 2
Moment Resistance My,Rd Mz,Rd kNm kNm 3110 1770 2500 1380 2310 1370 1900 1140 1560 955 1240 749 1150 743 904 501 875 501 691 399 681 399 1130 541 951 481 761 383 624 319 520 270 497 268 367 148 550 284 446 235 356 199 333 198 284 165 231 115 200 100 173 91.7 139 74.7 101 40.9 79.9 37.7 62.6 31.3 51.7 25.1
142
Shear Resistance Vz,Rd kN 2650 2080 1490 1420 1180 1150 718 718 699 510 425 1040 827 803 624 605 453 382 685 529 383 307 257 312 260 259 207 197 168 118 118
Axial Resistance Na,Rd kN 17800 14000 13200 11400 9600 7810 7170 5680 5650 4490 4360 7870 6770 5550 4600 3970 3690 3100 4790 3930 3160 3030 2540 2620 2210 2000 1580 1360 1150 933 793
Design Tables 28 to 33 for Section Resistances of Welded Sections: Q275 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
143
Design Table 28 Section resistances of welded I-sections: Q275 steel (1) z
tf r d h
y tw
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 4750 1000 3830 756 3320 491 2920 414 2630 383 2190 293 2450 405 2040 309 1830 286 1980 321 1670 259 1480 238 1320 199 1590 265 1340 200 1210 195 1080 163 1960 436 1440 332 1190 268 1190 209 993 168 885 141 823 139 988 193 824 156 733 130 683 129 483 62.4
144
Shear Resistance Vz,Rd kN 2560 2550 2590 2560 2030 2000 1890 1870 1710 1690 1250 1300 1540 1540 1130 1180 1780 1030 1020 1030 1020 1060 866 918 901 935 765 765
Axial Resistance Na,Rd kN 12500 10400 9110 8190 6880 5910 6950 5960 4850 6380 5590 4520 4070 5920 5110 4190 3790 7900 5420 4630 4580 3950 3580 3180 4400 3790 3430 3060 2550
Design Table 29 Section resistances of welded I-sections: Q275 steel (2) z
tf r tw d h
y cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 626 121 583 120 515 100 490 98.7 398 74.6 499 81.0 445 67.9 418 66.7 345 50.6 298 42.4 443 91.0 408 89.9 333 67.9 254 36.7 245 39.4 206 29.2 323 67.3 265 50.9 235 44.9 208 37.7 194 37.1 140 19.1 231 52.5 178 39.2 150 32.8 208 40.5 171 30.8 145 25.8 132 16.5 114 13.5 101 12.9 158 44.5 139 37.3 92.4 19.1 107 21.8 91.7 17.6 74.5 13.4 91.5 28.7 73.2 23.1 67.2 15.7 43.7 10.3 34.9 10.3 24.5 6.66
145
Shear Resistance Vz,Rd kN 784 640 664 531 531 640 664 531 531 520 606 473 473 473 346 346 520 520 410 410 307 303 358 268 260 358 358 346 364 358 264 300 300 217 225 225 221 182 173 173 104 86.6 75.1
Axial Resistance Na,Rd kN 3430 3140 2830 2500 2060 2760 2510 2180 1820 1640 2700 2390 1980 1770 1420 1210 2310 1950 1700 1530 1290 1120 1870 1380 1220 1710 1440 1290 1170 1060 865 1520 1360 1060 1040 918 787 1070 908 852 596 566 466
Design Table 30 Section resistances of welded H-sections: Q275 steel tf
z
r h
y
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 3 3 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 3540 2020 2970 1640 2740 1620 2260 1350 1840 1130 1460 882 1360 875 1060 590 1030 590 725 311 718 311 1340 642 1120 566 896 451 735 376 612 318 585 315 430 173 648 335 525 276 419 234 393 233 333 193 272 135 236 118 203 107 163 87.4 118 47.9 93.5 44.1 73.3 36.6 61.7 19.3
146
Shear Resistance Vz,Rd kN 3020 2460 1770 1690 1390 1360 846 846 823 601 501 1240 974 946 734 712 534 447 807 623 451 362 300 367 306 303 242 231 196 139 139
Axial Resistance Na,Rd kN 20300 16600 15700 13500 11300 9190 8440 6700 6660 5290 5130 9330 7980 6530 5420 4670 4350 3630 5640 4620 3720 3570 2970 3090 2600 2340 1840 1590 1340 1090 928
Design Table 31 Section resistances of cold-formed CHS: Q275 steel z
t
y
d
Q275 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 3 2 1 1 1 2 1 1 1 1 2 2 1 1 1 3 2 1 1 1 3 3 2 1 1 3 2 2 1 4 3 2 1
Moment Resistance My,Rd kNm 26.9 34.8 42.3 40.3 52.5 64.0 74.9 68.7 89.9 110 130 105 137 169 200 258 148 195 240 285 370 145 248 308 363 473 308 380 453 590 696 408 508 603 788 932 375 600 715 938 1110 563 695 1070 1410 1680 950 1460 1930 2290 1480 2520 3010
147
Shear Resistance Vz,Rd kN 232 305 375 284 374 462 547 371 490 606 721 457 605 751 894 1170 544 721 895 1070 1400 613 813 1010 1210 1590 905 1130 1340 1770 2110 1040 1300 1550 2050 2450 1140 1410 1690 2240 2670 1390 1730 2070 2740 3280 2020 2420 3210 3840 2760 3670 4400
Axial Resistance Na,Rd kN 631 829 1020 773 1020 1260 1490 1010 1330 1650 1960 1240 1650 2040 2430 3190 1480 1960 2430 2900 3820 1670 2210 2750 3280 4320 2460 3060 3660 4830 5750 2840 3530 4220 5580 6660 3090 3850 4600 6080 7270 3780 4710 5640 7460 8930 5500 6580 8720 10400 7520 9980 12000
Design Table 32 Section resistances of cold-formed RHS: Q275 steel z
cw
y
h
cf t
b Q275 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.6 9.98 12.7 15.1 16.2 15.2 19.4 23.3 25.4 30.2 25.8 33.2 40.1 44.7 54.4 30.5 39.3 47.5 52.7 63.8 60.9 74.1 83.4 103 89.0 109 124 155 180
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.75 5.69 7.22 8.59 9.28 8.19 10.5 12.5 13.7 16.3 15.5 19.9 23.9 26.9 32.6 10.6 13.5 16.3 18.2 22.1 24.8 30.0 34.0 41.8 41.0 49.8 56.9 71.0 82.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 2 1 1 1 1 1 1 3 4 1 3 1 1 1 1 1 1 1 4 1 4 1 2 1 1 1 1 1 4 1 4 1 1 1 1 2 4 1 4 1 2 1 1 1 1
Moment resistance My,Rd kNm 20.1 24.5 31.8 39.5 45.8 51.7 65.3 77.1 66.3 84.5 101 92.5 119 143 156 110 141 170 188 145 187 227 253 310 176 270 330 375 468 223 290 355 400 498 395 483 550 695 513 628 725 920 1060
148
Mz,Rd kNm 15.2 18.6 19.7 24.3 28.1 32.0 40.4 47.5 54.6 69.5 82.9 57.7 83.7 100 110 75.3 110 133 147 142 172 193 236 190 263 298 373 220 250 310 370 465 513 653 747
Shear Resistance
Axial Resistance
Vz,Rd kN 182 231 248 318 382 318 411 498 322 418 509 406 529 647 736 425 555 680 778 494 647 794 914 1160 581 764 941 1090 1400 873 1070 1250 1600 990 1220 1430 1840 1110 1370 1600 2080 2430
Na,Rd kN 525 667 645 827 993 825 1070 1290 975 1270 1540 1120 1470 1790 2040 1230 1630 1990 2280 1370 1870 2290 2640 3360 1620 2240 2790 3240 4160 1550 2180 2790 3240 4160 2500 3240 3840 4960 2820 3650 4440 5760 6740
Design Table 33 Section resistances of cold-formed SHS: Q275 steel z
y c b
Flexural rigidity EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
Section Classification
1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 2 1 1 1 3 1 1 1 4 2 1 1 1
Q275 Moment Resistance My,Rd kNm 17.9 22.0 43.8 55.3 65.4 80.8 104 125 137 98.8 127 154 170 206 111 167 203 227 279 246 300 340 425 293 415 475 600 550 633 805 925
149
Shear Resistance Vz,Rd kN 152 193 238 308 373 325 424 518 589 360 470 575 658 831 411 539 662 762 970 498 655 806 935 1200 770 951 1110 1430 885 1090 1280 1660 1870
t
Axial Resistance Na,Rd kN 525 667 825 1070 1290 1130 1470 1790 2040 1250 1630 1990 2280 2880 1420 1870 2290 2640 3360 1620 2270 2790 3240 4160 2620 3290 3840 4960 2890 3790 4440 5760 6740
150
Design Tables 34 to 39 for Section Resistances of Welded Sections: Q345 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
151
Design Table 34 Section resistances of welded I-sections: Q345 steel (1) z
tf r y
tw
d h
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 163 12.5 130 9.35 112 4.80 96.4 4.00 87.7 3.67 71.3 2.69 76.9 4.00 62.3 2.93 57.4 2.69 55.8 2.80 46.1 2.24 41.2 2.04 35.1 1.63 40.0 2.09 33.2 1.50 30.3 1.50 25.8 1.20 45.5 4.04 33.8 3.08 27.3 2.46 27.5 1.50 22.4 1.20 19.0 0.961 17.7 0.961 20.2 1.33 16.4 1.07 13.9 0.855 12.9 0.855 10.5 0.640
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 5970 1260 4810 953 4170 621 3690 521 3330 484 2770 370 3100 512 2570 390 2320 362 2500 406 2120 327 1870 301 1430 161 2020 335 1700 253 1530 247 1350 205 2480 551 1820 420 1510 339 1500 264 1250 213 1110 177 1030 175 1250 244 1040 197 919 163 856 161 605 78.3
152
Shear Resistance Vz,Rd kN 3240 3220 3270 3240 2560 2530 2390 2360 2170 2140 1940 1940 1430 1480 2250 1310 1290 1310 1290 1330 1090 1160 1140 1170 960 960
Axial Resistance Na,Rd kN 15400 12700 11100 10000 8440 7210 8540 7280 5970 7850 6830 5560 4940 7280 6260 5160 4600 9990 6720 5720 5660 4860 4350 3880 5440 4680 4190 3740 3090
Design Table 35 Section resistances of welded I-sections: Q345 steel (2) z
tf r y
tw
d h
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 1 1 2 2 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 792 153 737 151 646 125 615 124 499 93.5 630 102 558 85.2 524 83.7 433 63.4 373 53.2 555 114 511 113 417 85.2 318 46.0 308 49.5 259 36.6 405 84.4 332 63.9 295 56.3 261 47.3 243 46.5 176 24.0 290 65.9 224 49.2 188 41.2 260 50.8 214 38.6 182 32.4 166 20.7 143 16.9 127 16.2 198 55.8 174 46.8 116 24.0 134 27.4 115 22.1 77.0 10.6 115 36.0 91.8 29.0 84.3 19.7 54.8 12.9 43.8 12.9 30.7 8.36
153
Shear Resistance Vz,Rd kN 992 809 833 666 666 809 833 666 666 652 761 594 594 594 435 435 652 652 514 514 386 380 449 337 326 449 449 435 456 449 331 377 377 272 282 282 277 228 217 217 130 109 94.0
Axial Resistance Na,Rd kN 4330 3900 3480 3070 2530 3420 3070 2670 2220 2000 3330 2940 2420 2160 1740 1480 2900 2450 2080 1870 1590 1370 2340 1710 1500 2140 1810 1620 1460 1320 1050 1910 1710 1320 1290 1130 960 1340 1140 1070 744 710 585
Design Table 36 Section resistances of welded H-sections: Q345 steel tf
z
r h
y
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1 2 2 2 2 3 3 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 3 3 3 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 4550 2590 3780 2090 3490 2070 2870 1730 2320 1420 1840 1120 1710 1110 1350 746 1300 746 917 393 908 393 1710 818 1420 716 1130 570 929 475 774 402 740 399 539 217 819 423 664 349 530 296 496 295 376 161 344 171 298 149 254 135 182 72.1 148 60.1 117 55.4 91.9 45.9 67.4 24.2
154
Shear Resistance Vz,Rd kN 3890 3140 2250 2150 1760 1710 1070 1070 1040 760 633 1580 1230 1200 928 900 675 561 1020 788 570 457 377 557 464 456 365 348 296 209 174
Axial Resistance Na,Rd kN 26100 21200 20000 17200 14300 11600 10700 8460 8420 6690 6490 11900 10100 8260 6850 5910 5500 4550 7130 5840 4700 4510 3720 3910 3290 2930 2310 2000 1690 1370 1160
Design Table 37 Section resistances of cold-formed CHS: Q345 steel z
t
y
d
Q345 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 3 2 1 1 1 3 2 2 1 1 3 2 1 1 1 3 2 2 1 1 4 3 2 1 1 4 3 3 2 1 4 3 2 2 4 4 3 2
Moment Resistance My,Rd kNm 33.8 43.7 53.0 50.6 65.8 80.3 94.0 86.2 113 138 163 131 172 212 251 324 143 244 301 358 464 182 311 386 455 593 296 477 568 740 880 395 637 756 988 1180 580 897 1180 1400 872 1040 1770 2120 1410 2420 2900 2440 3800
155
Shear Resistance Vz,Rd kN 291 382 471 356 469 579 687 465 614 761 904 574 759 942 1120 1470 682 904 1120 1340 1760 769 1020 1270 1510 1990 1140 1410 1690 2230 2670 1310 1630 1950 2570 3090 1770 2120 2800 3380 2170 2600 3440 4150 3030 4020 4850 4600 5560
Axial Resistance Na,Rd kN 792 1040 1280 970 1280 1580 1870 1270 1670 2070 2460 1560 2070 2560 3050 4000 1860 2460 3050 3640 4790 2090 2770 3450 4110 5420 3090 3840 4590 6050 7270 3560 4430 5300 7000 8420 4830 5770 7630 9180 5910 7070 9360 11300 8250 10900 13200 12500 15100
Design Table 38 Section resistances of cold-formed RHS: Q345 steel z
cw
y
h
cf t
b Q345 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.9 9.98 12.7 15.1 16.7 15.2 19.4 23.3 26.0 31.3 25.8 33.2 40.1 45.6 55.9 30.5 39.3 47.5 53.6 65.5 60.9 74.1 84.6 105 89.0 109 125 157 184
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.90 5.69 7.22 8.59 9.49 8.19 10.5 12.5 14.0 16.8 15.5 19.9 24.0 27.2 33.4 10.6 13.5 16.3 18.4 22.4 24.8 30.0 34.4 42.6 41.0 49.8 57.3 71.8 84.2
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1 1 1 2 4 1 3 1 1 1 1 1 1 4 4 1 4 1 2 1 1 1 1 2 4 1 4 1 3 1 1 1 1 1 4 1 4 1 2 1 1 3 4 1 4 1 3 1 1 1 1
Moment resistance My,Rd kNm 25.2 30.8 39.9 49.5 57.4 64.9 81.9 96.8 83.1 106 127 116 149 179 195 138 177 214 236 181 235 284 317 389 339 414 470 587 280 364 445 502 624 496 605 690 872 533 787 910 1150 1330
156
Mz,Rd kNm 19.1 23.3 24.7 30.5 35.2 40.2 50.6 59.6 68.4 87.2 104 105 126 138 138 166 184 156 216 242 297 329 373 467 243 314 389 464 583 568 819 944
Shear Resistance
Axial Resistance
Vz,Rd kN 228 290 312 399 479 399 515 624 404 525 639 509 664 812 923 533 696 853 976 619 812 996 1150 1460 729 958 1180 1370 1760 1090 1350 1560 2010 1240 1530 1790 2310 1390 1720 2010 2610 3080
Na,Rd kN 659 837 810 1040 1250 1040 1340 1620 1220 1590 1940 1380 1840 2250 2560 1520 2040 2500 2860 1690 2340 2880 3310 4210 1960 2760 3500 4060 5220 1910 2670 3510 4060 5220 3070 3980 4820 6220 3460 4490 5510 7230 8530
Design Table 39 Section resistances of cold-formed SHS: Q345 steel z
y c b
Flexural rigidity
Section Classification
EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
1 1 1 1 1 2 1 1 1 2 1 1 1 1 4 1 1 1 1 4 3 1 1 1 4 2 1 1 4 3 1 1 1
Q345 Moment Resistance My,Rd kNm 22.5 27.5 54.9 69.4 82.1 101 130 156 171 124 160 193 213 258 210 254 285 350 266 376 427 533 521 596 753 593 794 1010 1170
157
Shear Resistance Vz,Rd kN 190 242 299 387 468 408 531 649 739 451 589 722 826 1040 516 676 830 956 1220 625 821 1010 1170 1510 966 1190 1390 1800 1110 1370 1610 2090 2460
t
Axial Resistance Na,Rd kN 659 837 1040 1340 1620 1410 1840 2250 2560 1560 2040 2500 2860 3610 1780 2340 2880 3310 4210 2040 2840 3500 4060 5220 3290 4130 4820 6220 3620 4760 5570 7230 8530
158
Design Tables 40 to 45 for Section Resistances of Welded Sections: Q460 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
159
Design Table 40 Section resistances of welded I-sections: Q460 steel (1) z
tf r y
tw
cf
d h
b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 2 2 1 1 1 1 2 1 3 3 1 1 3 3 3 3 1 1 2 2 2 2 3 3 1 1 1 1 2 1 3 3 1 1 1 1 3 3 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 7840 1660 6320 1250 5480 816 4840 684 4370 636 3090 309 4080 672 2900 327 2670 308 3290 533 2780 430 2140 396 1920 215 2650 440 2230 332 2010 324 1560 176 3250 724 2380 552 1740 290 1970 347 1650 280 1490 237 1380 234 1640 321 1370 258 1230 219 1150 216 811 105
160
Shear Resistance Vz,Rd kN 4250 4230 4300 4250 3280 3240 2970 2940 2670 2670 2960 1800 1770 1800 1770 1770 1590 1560 1560 1280 1280
Axial Resistance Na,Rd kN 19700 16100 14000 12600 10700 9060 10800 9170 7580 9940 8610 7060 6330 9230 7880 6540 5890 13000 8610 7290 7210 6170 5570 4990 6950 5950 5380 4820 3960
Design Table 41 Section resistances of welded I-sections: Q460 steel (2) z
tf r y
tw
d h
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 2 2 3 3 1 1 1 1 3 3 3 3 2 1 2 1 1 1 2 2 1 1 3 3 3 3 3 3 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 2 2 3 3 1 1 3 3 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 1040 201 968 199 865 168 823 166 584 81.3 828 135 748 114 701 112 580 84.9 424 45.3 743 153 685 151 487 74.0 426 61.6 412 66.2 347 49.0 542 113 445 85.6 395 75.4 298 63.3 284 40.0 235 32.1 388 88.2 299 65.9 252 55.1 349 68.1 287 51.7 244 43.4 222 27.8 192 22.7 170 21.7 265 74.8 201 40.0 155 32.1 179 36.7 154 29.6 103 14.2 154 48.3 106 25.2 113 26.4 73.4 17.3 58.7 17.3 41.2 11.2
161
Shear Resistance Vz,Rd kN 1300 1060 1110 888 888 1060 1110 888 888 869 1010 792 792 792 869 869 686 686 514 507 599 449 435 599 599 579 608 599 442 502 502 362 377 377 369 304 290 290 174 145 126
Axial Resistance Na,Rd kN 5550 5000 4500 4000 3260 4360 3970 3460 2860 2560 4320 3830 3140 2790 2260 1910 3830 3190 2690 2410 2060 1770 3070 2220 1950 2800 2350 2100 1870 1690 1350 2550 2280 1720 1670 1460 1240 1780 1520 1430 974 947 779
Design Table 42 Section resistances of welded H-sections: Q460 steel tf
z
r y
h
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 3 3 3 3 4 4 1 1 1 1 2 2 2 2 3 3 1 1 1 1 1 1 3 3 4 4 1 1 3 3 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 5490 3120 4670 2580 4310 2550 3550 2130 3050 1870 2110 960 1990 960 1560 644 1510 644 1200 516 1190 516 2120 1010 1860 940 1490 748 1220 624 884 346 864 346 1060 556 861 459 687 389 644 387 498 215 446 224 386 196 336 180 240 96.6 155 74.2 106 40.5 89.2 32.4
162
Shear Resistance Vz,Rd kN 4930 4060 2910 2780 2310 2250 1400 1400 1370 1000 831 2040 1620 1570 1220 1180 887 748 1340 1030 748 600 502 610 508 507 406 386 328 232 232
Axial Resistance Na,Rd kN 31500 26200 24700 21200 18800 15300 14000 11100 11100 8780 8220 14700 13200 10800 9000 7760 7220 6090 9360 7680 6180 5920 4990 5130 4320 3920 3100 2670 2260 1830 1560
Design Table 43 Section resistances of cold-formed CHS: Q460 steel z
t
y
d
Q460 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 2 1 1 1 3 2 1 1 3 2 2 1 1 4 3 2 2 1 4 3 3 2 1 4 3 2 1 1 4 4 3 2 1 4 4 3 2 1 4 4 4 3 2 4 4 3 2 4 4 4 3
Moment Resistance My,Rd kNm 45.1 58.3 70.7 67.5 87.8 107 125 87.8 150 184 217 134 230 283 334 432 248 402 477 619 318 393 606 790 489 757 987 1210 769 1320 1620 916 1570 1930 1810 2780 2480 3810 3820
163
Shear Resistance Vz,Rd kN 388 510 628 475 626 773 916 620 819 1010 1210 765 1010 1260 1490 1960 1210 1500 1780 2350 1360 1690 2020 2660 1880 2250 2970 3510 2600 3430 4060 2830 3740 4430 4590 5450 5360 6370 7300
Axial Resistance Na,Rd kN 1060 1390 1710 1290 1700 2100 2490 1690 2230 2760 3280 2080 2750 3420 4070 5340 3280 4070 4860 6390 3700 4600 5490 7230 5120 6120 8070 9550 7060 9330 11100 7690 10200 12100 12500 14800 14600 17300 19900
Design Table 44 Section resistances of cold-formed RHS: Q460 steel z
cw
y
h
cf t
b Q460 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.9 9.98 12.7 15.1 16.7 15.2 19.4 23.3 26.0 31.3 25.8 33.2 40.1 45.6 55.9 30.5 39.3 47.5 53.6 65.5 60.9 74.1 84.6 105 89.0 109 125 157 184
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.90 5.69 7.22 8.59 9.49 8.19 10.5 12.5 14.0 16.8 15.5 19.9 24.0 27.2 33.4 10.6 13.5 16.3 18.4 22.4 24.8 30.0 34.4 42.6 41.0 49.8 57.3 71.8 84.2
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 4 1 2 1 1 1 1 2 4 1 2 1 1 1 1 3 4 1 4 1 2 1 1 1 1 4 4 2 4 1 3 1 1 1 1 3 4 1 4 1 4 1 2 1 1 2 4 1 4 1 4 1 1 4 4 2 4 1 4 1 2 1 1
Moment resistance My,Rd kNm 33.6 41.1 53.2 66.1 76.6 86.5 109 129 111 141 169 155 199 238 260 183 236 285 315 201 313 379 422 519 452 552 627 782 303 485 594 669 832 661 807 920 1160 1050 1210 1540 1750
164
Mz,Rd kNm 25.4 31.2 33.0 40.9 47.2 47.0 67.8 79.8 79.5 117 139 141 169 185 185 223 247 289 324 397 441 500 626 420 521 781 1150 1360
Shear Resistance
Axial Resistance
Vz,Rd kN 306 388 417 535 642 534 690 836 541 702 855 682 890 1090 1240 714 933 1140 1310 830 1090 1330 1540 1960 976 1280 1580 1830 2350 1470 1810 2090 2690 1660 2050 2390 3090 1860 2300 2690 3490 4240
Na,Rd kN 879 1120 1080 1380 1660 1380 1790 2160 1630 2120 2580 1800 2450 3000 3410 1980 2720 3330 3810 2200 3050 3840 4420 5620 2500 3600 4630 5420 6960 2470 3460 4490 5420 6960 3980 5160 6340 8300 4430 5820 7160 9630 11700
Design Table 45 Section resistances of cold-formed SHS: Q460 steel z
y c b
Flexural rigidity
Section Classification
EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
1 1 1 1 1 3 1 1 1 4 1 1 1 1 4 2 1 1 1 4 4 2 1 1 4 3 1 1 4 4 2 1 1
Q460 Moment Resistance My,Rd kNm 30.0 36.7 73.2 92.6 110 116 174 209 229 213 257 285 344 280 339 380 466 502 569 711 594 795 1000 1060 1350 1540
165
Shear Resistance Vz,Rd kN 254 322 399 515 624 543 709 866 985 601 786 962 1100 1390 688 902 1110 1270 1620 833 1090 1350 1560 2010 1290 1590 1850 2390 1480 1830 2140 2780 3230
t
Axial Resistance Na,Rd kN 879 1120 1380 1790 2160 1880 2450 3000 3410 2020 2720 3330 3810 4820 2210 3120 3840 4420 5620 2510 3650 4670 5420 6960 4070 5420 6420 8300 4470 5970 7430 9630 11200
166
References European Steel Material Specifications: EN 10020, Definition and classification of grades of steel. 2000. EN 10021, General technical delivery requirements for steel and iron products. 2006. EN 10025, Hot rolled products of structural steels — Part 1: General technical delivery conditions. 2004. Part 2: Technical delivery conditions for non‐alloy structural steels. 2004. Part 3: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels. 2004. Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels. 2004. Part 5: Technical delivery conditions for structural steels with improved atmospheric corrosion resistance. 2004. Part 6: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition. 2004. BS EN 10029, Hot‐rolled steel plates 3 mm thick or above: Tolerances on dimensions and shape. 2010. EN 10034, Structural steel I and H sections: Tolerances on shape and dimensions. 1993. EN 10149, Specification for hot‐rolled flat products made of high yield strength steels for cold forming — Part 1: General delivery conditions. 2013. Part 2: Delivery conditions for thermomechanically rolled steels. 2013. Part 3. Delivery conditions for normalized or normalized rolled steels. 2013. EN 10210, Hot finished structural hollow sections of non‐alloy and fine grain steels — Part 1: Technical delivery conditions. 2006. Part 2: Tolerances, dimensions and sectional properties. 2006. EN 10219, Cold formed welded structural hollow sections of non‐alloy and fine grain steels — Part 1: Technical delivery conditions. 2006. Part 2: Tolerances, dimensions and sectional properties. 2006. BS 4‐1, Structural steel sections — Part 1: Specification for hot‐rolled sections. 2005.
167
Chinese Steel Material Specifications: GB/T 700, Carbon structural steels. 2006. GB/T 709, Dimension, shape, weight and tolerances for hot‐rolled steel plates and sheets. 2006. GB/T 912, Hot‐rolled sheets and strips of carbon structural steels and high strength low alloy structural steels. 2008. GB/T 1591, High strength low alloy structural steels. 2008. GB/T 3274, Carbon structural and low alloy steel rolled plates and strips. 2007. GB/T 4171, Atmospheric corrosion resisting structural steel. 2008. GB/T 5313, Steel plates with through‐thickness characteristics. 2010. GB/T 6725, Cold‐formed steel sections. 2002. GB/T 6728, Cold‐formed steel hollow sections of general structures: Dimensions, shapes, weight and permissible deviations. 2002. GB/T 8162, Seamless steel tubes for structural purposes. 2008. GB/T 17395, Dimensions, shapes, masses, and tolerances of seamless steel tubes. 2008. GB/T 19879, Steel plates for building structures. 2005. YB 4104, Steel plates for high rise building structures. 2000. Code of Practices for Design of Steel Structures: BS5950 Structural use of steelwork in building, Part 1: Code of practice for design of hot rolled and welded sections, 2000. Code of Practice for the Structural Use of Steel, 2011. Building Department, Government of Hong Kong SAR. EN 1993‐1‐1, Eurocode 3: Design of steel structures. General rules and rules for building. 2005. EN 1993‐1‐2, Eurocode 3: Design of steel structures. General rules — Structural fire design. 2005. EN 1993‐1‐3, Eurocode 3: Design of steel structures, General rules — Supplementary rules for cold‐formed members and sheeting. 2005. EN 1993‐1‐5, Eurocode 3: Design of steel structures, Plated structural elements. 2006. EN 1993‐1‐8, Eurocode 3: Design of steel structures, Design of steel joints. 2005.
GB 50017: Code for design of steel structures. 2003.
168
Technical Guidance for Design of Steel Structures: Chung, K.F., Harmonized member buckling design in Structural Eurocodes. Innovation in Construction, Research Journal 2014, Construction Industry Council, Hong Kong, 2014. Design of Steel Structures with Worked Examples to EN 1993‐1‐1 and EN 1993‐1‐8. F. Wald, K. H. Tan and S. P. Chiew. Research Publishing. 2012. Selection of equivalent steel materials to European steel materials specifications. Professional Guide CMSA‐PG01: 2015. Steel Building Design: Introduction to the Eurocodes. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association. SCI Publication No. P361, 2009. Steel Building Design: Concise Eurocodes. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association. SCI Publication No. P362. 2010. Steel Building Design: Design Data. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association, SCI Publication No.P363, 2013. Steel Designers’ Manual. 7th Edition. Buick Davidson & Graham W. Owens. Steel Construction Institute, Wiley‐Blackwell, 2012. Structural Steelwork, Design to Limit State Theory. 4th Edition. D. Lam, T. C. Ang, and S. P. Chiew. CRC Press, Taylor & Francis Group, 2013. The Behaviour and Design of Steel Structures to EC3. 4th Edition. N S Trahair, M A Bradford, D A Nethercot, and L Gardner. Taylor & Francis Group, 2008.
169
170
Appendices Appendix A Design procedure for a pinned‐pinned column to EN 1993
A1
Appendix B Design procedures for an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2
B1
B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3
B7
B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded I, H or channel sections using the design method given in Steel Designers’ Manual
B14
Appendix C Design procedure for a column member under combined axial compression and bending to EN 1993
C1 Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex Appendix D Worked examples to BS EN 1993‐1‐1
C1
Part I Section analysis and section resistance Worked Example I‐1 Determination of section resistances
Worked Example I‐2 Cross section resistance under combined bending and shear force
D7
Worked Example I‐3 Cross section resistance under combined bending and axial force
D9
Part II Member design Worked Example II‐1 Design of a fully restrained steel beam
Worked Example II‐2
Worked Example II‐3 Design of a steel column under axial compression
D26
Worked Example II‐4 Design of a beam‐column under combined compression and bending Worked Example II‐5 Column in simple construction
D29
Design of an unrestrained steel beam against lateral torsional buckling Solution to Procedure B2 Solution to Procedure B3
171
D1
D14 D17
D36
172
Appendix A Design procedure for a pinned‐pinned column to EN 1993:1‐1 A Design of a steel column against axial buckling 1. Determine the buckling length of the steel column for both axes. 2.
Calculate N cr and Afy .
3.
Calculate the non‐dimensional slenderness, of the steel column.
Af y N cr
A eff f y N cr
5.
L cr 1 i 1
L cr 1 i 1
A eff A
for Class 1, 2 and 3 cross‐sections for Class 4 cross‐sections
where A is the cross‐sectional area, A eff is the effective cross‐sectional area of Class 4 sections, fy is the yield strength,
2 EI which is the critical flexual buckling load/elastic critical force 2 L cr
N cr
4.
and
L cr
1
is the buckling length in the buckling plane considered,
E 235 93.9 , where fy fy
Choose a suitable flexural buckling curve for rolled and equivalent welded sections in Table A1, and hence, the imperfection factor, is obtained from Table A2. Determine the parameter ϕ.
2
0 .5 1 0 .2
6.
Calculate the buckling reduction factor,
1 2
2
but 1.0
7.
Calculate the design buckling resistance, N b , Rd .
N b, Rd
Af y M1
where M1 is the partial factor for resistance of the steel column to instability.
A1
Table A1: Selection of flexural buckling curves for rolled and equivalent welded cross‐ section
Cross section
z
y
y‐y z‐z
a b
a0 a0
40 ≤ tf ≤ 100 mm
y‐y z‐z
b c
a a
y
tf ≤ 100 mm
y‐y z‐z
b c
a a
tf > 100 mm
y‐y z‐z
d d
c c
tf ≤ 40 mm
y‐y z‐z
b c
b c
tf > 40 mm
y‐y z‐z
c d
c d
hot finished
any
a
a0
cold formed
any
c
c
generally (except as below)
any
b
b
thick welds: a > 0.5tf b/tf < 30 h/tw < 30
any
c
c
y
z
z
b
b
h/b ≤ 1.2
Rolled sections
t f
y
tf ≤ 40 mm
h/b > 1.2
z tf
Buckling about axis
Limits
Buckling curve S 235 S 275 S460 S 355 S 420
Welded sections
z
z
tf
tf y
y
y z
y z
Welded box sections
Hollow sections
z h
y tw
tf y
z b
Table A2: Recommended values for imperfection factor, α, for various flexural buckling curves Buckling curve Imperfection factor
a0 0.13
a 0.21
A2
b 0.34
c 0.49
d 0.76
Table A3: Reduction factor, χ for flexural buckling
̅ 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Reduction factor, χ
Buckling curve
a0
a
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.995 0.992 0.989 0.986 0.983 0.980 0.977 0.973 0.970 0.967 0.963 0.959 0.955 0.951 0.947 0.943 0.938 0.933 0.928 0.922 0.916 0.910 0.903 0.896 0.889 0.881 0.872 0.863 0.853 0.843 0.832 0.821 0.809 0.796 0.783 0.769 0.755 0.740 0.725
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.991 0.987 0.982 0.977 0.973 0.968 0.963 0.958 0.953 0.947 0.942 0.936 0.930 0.924 0.918 0.911 0.905 0.897 0.890 0.882 0.874 0.866 0.857 0.848 0.838 0.828 0.818 0.807 0.796 0.784 0.772 0.760 0.747 0.734 0.721 0.707 0.693 0.680 0.666
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
A3
Reduction factor, χ ̅ 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve a0
a
b
c
d
0.725 0.710 0.695 0.679 0.664 0.648 0.633 0.618 0.603 0.588 0.573 0.559 0.545 0.531 0.518 0.505 0.493 0.481 0.469 0.457 0.446 0.435 0.425 0.415 0.405 0.395 0.386 0.377 0.369 0.360 0.352 0.344 0.337 0.329 0.322 0.315 0.308 0.302 0.295 0.289 0.283 0.277 0.272 0.266 0.261 0.256 0.251 0.246 0.241 0.237 0.232
0.666 0.652 0.638 0.624 0.610 0.596 0.582 0.569 0.556 0.543 0.530 0.518 0.505 0.493 0.482 0.470 0.459 0.448 0.438 0.428 0.418 0.408 0.399 0.390 0.381 0.372 0.364 0.356 0.348 0.341 0.333 0.326 0.319 0.312 0.306 0.299 0.293 0.287 0.281 0.276 0.270 0.265 0.260 0.255 0.250 0.245 0.240 0.236 0.231 0.227 0.223
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2 1. Determine the buckling length of the steel beam. 2. Calculate M cr and Wpl , y f y .
2 EI z M cr C1 2 L cr
0.5 2 I L cr GI t 2 w C z C z C z C z 2 g 3 j 2 g 3 j 2 EI z I z
where I z , I t , I w are the section properties, E is the Young’s modulus, E , 21 is the buckling length of the steel beam, L cr kL , and k is the
is the shear modulus, G
G
L cr
effective length coefficient, C1 , C 2 , C 3 are the factors depending on the shape of the bending moment diagram, end restraint conditions and loading conditions as listed in Table B1.1, zg is the vertical distance of the loading position above the shear
zj
centre, is the relative distance to the shear centre. It is simply taken as 0 for uniform doubly symmetric cross‐sections.
3.
Calculate the non‐dimensional slenderness, LT of the steel beam.
LT
Wy f y M cr
where w
LT w 1
Wy Wpl , Rd
, and
Wy Wpl , y for Class 1 and 2 cross‐sections,
Wel , y for Class 3 cross‐sections,
Weff , y for Class 4 cross‐sections,
Wpl,y
is the plastic section modulus for Class 1 and 2 sections,
Wel, y
is the elastic section modulus for Class 3 sections,
Weff , y
is the effective elastic section modulus for Class 4 sections,
fy
is the yield strength.
B1
Table B1.1a Values of factors C1 , C 2 and C 3 corresponding to k factor under different end moment loading Loading and support conditions
Bending moment Diagram = +1
= +3/4
= +1/2
= +1/4
M
M = 0
= ‐1/4
= ‐1/2
= ‐3/4
= ‐1
B2
Value of k
Values of factors C3 C1 C2
1.0 0.7 0.5
1.000 1.000 1.000
‐
1.000 1.113 1.144
1.0 0.7 0.5
1.141 1.270 1.305
‐
0.998 1.565 2.283
1.0 0.7 0.5
1.323 1.473 1.514
‐
0.992 1.556 2.271
1.0 0.7 0.5
1.563 1.739 1.788
‐
0.977 1.531 2.235
1.0 0.7 0.5
1.879 2.092 2.150
‐
0.939 1.473 2.150
1.0 0.7 0.5
2.281 2.538 2.609
‐
0.855 1.340 1.957
1.0 0.7 0.5
2.704 3.009 3.093
‐
0.676 1.059 1.546
1.0 0.7 0.5
2.927 3.009 3.093
‐
0.366 0.575 0.837
1.0 0.7 0.5
2.752 3.063 3.149
‐
0.000 0.000 0.000
Table B1.1b Values of factors C1, C2 and C3 corresponding to k factor under transverse loading cases Loading and support conditions
w
w
Value of k
Bending moment Diagram
1.0 0.5
1.132 0.972
0.459 0.304
0.525 0.980
1.0 0.5
1.285 0.712
1.562 0.652
0.753 1.070
1.0 0.5
1.365 1.070
0.553 0.432
1.730 3.050
1.0 0.5
1.565 0.938
1.267 0.715
2.640 4.800
1.0 0.5
1.046 1.010
0.430 0.410
1.120 1.890
4.
Values of factors C1 C2 C3
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B1.2, and hence, the imperfection factor, LT , can be obtained from Table B1.3.
Table B1.2. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits
Buckling curve a b c d
h/b 2 h/b 2 h/b 2 h/b 2
Rolled I‐sections Welded sections
Table B1.3. Recommended imperfection factor values for lateral torsional buckling curves
Buckling curve
a
b
c
d
Imperfection factor, LT
0.21
0.34
0.49
0.76
B3
5.
Determine the parameter LT .
LT 0.5 1 LT LT 0.2 LT
6.
Calculate the reduction factor, LT .
LT
7. 8.
2
1 LT 2LT 2LT
but LT 1.0
Alternatively, reduction factor, LT can be obtained from Table B1.4. Calculate the buckling moment resistance, M b, Rd .
M b, Rd
LT Wy f y M1
where M1 is the partial factor for resistance of the beam to instability.
B4
Reduction factor, LT for lateral torsional buckling
Table B1.4.
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Reduction factor, LT
Buckling curve
a
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.991 0.987 0.982 0.977 0.973 0.968 0.963 0.958 0.953 0.947 0.942 0.936 0.930 0.924 0.918 0.911 0.905 0.897 0.890 0.882 0.874 0.866 0.857 0.848 0.838 0.828 0.818 0.807 0.796 0.784 0.772 0.760 0.747 0.734 0.721 0.707 0.693 0.680 0.666
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
B5
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve a
b
c
d
0.666 0.652 0.638 0.624 0.610 0.596 0.582 0.569 0.556 0.543 0.530 0.518 0.505 0.493 0.482 0.470 0.459 0.448 0.438 0.428 0.418 0.408 0.399 0.390 0.381 0.372 0.364 0.356 0.348 0.341 0.333 0.326 0.319 0.312 0.306 0.299 0.293 0.287 0.281 0.276 0.270 0.265 0.260 0.255 0.250 0.245 0.240 0.236 0.231 0.227 0.223
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3 1. Determine the buckling length of the steel beam. 2. Calculate M cr and Wpl , y f y .
2 EI M cr C1 2 z L cr
0. 5 I L2cr GI t w C z C z 2 C z C z 2 g 3 j 2 g 3 j 2 I z EI z
where I z , I t , I w are the section properties, E is the Young’s modulus, G
is the shear modulus, G
E , 2 21 L cr is the buckling length of the steel beam, L cr kL , and k is the effective length coefficient, C1 , C 2 , C 3 are the factors depending on the shape of the bending moment diagram, end restraint conditions and loading conditions as listed in Table B1.1, is the vertical distance of the loading position above the shear zg
zj
centre, is the relative distance to the shear centre. It is simply taken as 0
for uniform doubly symmetric cross‐sections. 3.
Calculate the non‐dimensional slenderness, LT of the steel beam.
LT
Wy f y M cr
where w
LT w 1
Wy Wpl , Rd
,
Wy Wpl , y for Class 1 and 2 cross‐sections,
Wel,y for Class 3 cross‐sections,
Weff,y for Class 4 cross‐sections,
Wpl, y
is the plastic section modulus for Class 1 and 2 sections,
Wel, y
is the elastic section modulus for Class 3 sections,
Weff , y
is the effective elastic section modulus for Class 4 sections,
fy
is the yield strength.
B6
4.
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B2.1, and hence, the imperfection factor, LT can be obtained from Table B2.2.
Table B2.1. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
Rolled I‐sections Welded sections
Buckling curve b c c d
Table B2.2. Recommended imperfection factor values for lateral torsional buckling curves Buckling curve Imperfection factor, LT
a
b
c
d
0.21
0.34
0.49
0.76
5.
Determine the parameter LT .
LT 0.5 1 LT LT LT,0 2LT
For rolled sections, LT ,0 = 0.4 (maximum value) = 0.75 (minimum value) For welded sections, LT ,0 = 0.2 (maximum value) = 1.0 (minimum value)
6.
Calculate the reduction factor, LT .
LT
Reduction factor, LT can also be obtained from Tables B2.4 and B2.5.
1 2
LT LT LT
2
but LT 1.0 and LT
B7
1 LT
2
7.
Calculate the modified reduction factor, LT , mod
LT, mod
LT but LT, mod 1.0 f
where f
is the correction factor for the moment distribution
1 0.51 k c 1 2.0 LT 0.8
f
2
kc is a correction factor according to Table B3.3. Table B2.3. Correction factors k c Moment distribution
kc
1
1.0
1 1
1 1.33 0.33
0.94
0.90
0.91
0.86
0.77
0.82
8.
Calculate the buckling moment resistance, M b,Rd
M b, Rd LT ,mod Wy where M1
fy M1
is the partial factor for resistance of the steel beam to instability.
B8
Table B2.4. Reduction factor, LT for lateral torsional buckling of rolled sections Reduction factor, LT
Buckling curve
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.984 0.976 0.968 0.960 0.952 0.943 0.935 0.926 0.917 0.908 0.899 0.889 0.880 0.870 0.860 0.849 0.839 0.828 0.817 0.806 0.795 0.783 0.772 0.760 0.748 0.736 0.724 0.712 0.700
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.989 0.978 0.966 0.955 0.944 0.932 0.921 0.909 0.898 0.886 0.874 0.862 0.850 0.838 0.826 0.813 0.801 0.789 0.776 0.764 0.751 0.739 0.726 0.713 0.701 0.688 0.676 0.664 0.651 0.639
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.983 0.966 0.949 0.932 0.916 0.900 0.883 0.867 0.852 0.836 0.820 0.805 0.790 0.775 0.760 0.745 0.730 0.716 0.702 0.688 0.674 0.660 0.647 0.634 0.621 0.608 0.596 0.584 0.572 0.560
B9
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve b
c
d
0.700 0.687 0.675 0.663 0.651 0.639 0.626 0.614 0.603 0.591 0.579 0.568 0.556 0.545 0.534 0.524 0.513 0.503 0.493 0.483 0.473 0.463 0.454 0.445 0.436 0.427 0.419 0.410 0.402 0.394 0.387 0.379 0.372 0.365 0.358 0.351 0.344 0.338 0.332 0.326 0.320 0.314 0.308 0.302 0.297 0.292 0.287 0.282 0.277 0.272 0.267
0.639 0.627 0.615 0.603 0.592 0.580 0.569 0.557 0.546 0.536 0.525 0.514 0.504 0.494 0.484 0.475 0.465 0.456 0.447 0.438 0.429 0.421 0.413 0.405 0.397 0.389 0.382 0.374 0.367 0.360 0.353 0.347 0.340 0.334 0.328 0.322 0.316 0.310 0.305 0.299 0.294 0.289 0.284 0.279 0.274 0.269 0.265 0.260 0.256 0.252 0.247
0.560 0.548 0.537 0.526 0.515 0.505 0.494 0.484 0.474 0.465 0.455 0.446 0.437 0.428 0.420 0.412 0.403 0.395 0.388 0.380 0.373 0.366 0.359 0.352 0.345 0.339 0.332 0.326 0.320 0.314 0.309 0.303 0.298 0.292 0.287 0.282 0.277 0.272 0.268 0.263 0.259 0.254 0.250 0.246 0.242 0.238 0.234 0.230 0.227 0.223 0.219
Table B2.5. Reduction factor, LT for lateral torsional buckling of welded sections Reduction factor, LT
Buckling curve
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
B10
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve b
c
d
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded I, H or channel sections using the design method given in the Steel Designer’s Manual 1. Determine the buckling length of the steel beam. 2.
Calculate the non‐dimensional slenderness LT of the steel beam.
LT
1 UV z w for rolled I‐, H‐ and channel sections C1
where C1
U
V
is a factor that depends on the shape of bending moment diagram as listed in Table B3.1, is a section property (given in section property tables, which may conservatively be taken as 0.9), is a parameter related to slenderness, and for symmetric rolled sections where the loads are not destabilising, may be conservatively taken as 1.0, 1 or as V , 2 z 1 4 1 20 h / t f
L cr in which L cr is the buckling length in the buckling plane iz considered. z z , 1 is the distance between points of lateral restraints, L
1
w
Wy Wpl, y for Class 1 and 2 cross‐sections,
Wel , y for Class 3 cross‐sections,
Weff , y for Class 4 cross‐sections,
where z
235 E 93.9 , where , fy fy
Wy Wpl , Rd
, and
Wpl,y
is the plastic section modulus of Class 1 and 2 sections,
Wel ,y
is the elastic section modulus of Class 3 sections,
Weff ,y
is the effective elastic section modulus of Class 4 sections,
fy
is the yield strength.
It is conservative to assume that the product UV 0.9 and that w 1.0
B11
Table B3.1. Values of C1 for various moment conditions (load is not destabilising) 1 End Moment Loading C1 +1.00 +0.75 +0.50 +0.25 0.00 ‐0.25 ‐0.50 ‐0.75 ‐1.00
M
M
1 1
Intermediate transverse loading
2/3 1/3
3.
C1
1.00 0.92 0.86 0.80 0.75 0.71 0.67 0.63 0.60
1.00 1.17 1.36 1.56 1.77 2.00 2.24 2.49 2.76
0.94 0.62
1.13 2.60
0.86 0.77
1.35 1.69
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B3.2, and hence, the imperfection factor, LT , is obtained from Table B3.3.
Table B3.2. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h/b 2 2 h / b 3. 1 h / b 3 .1 h/b 2 h/b 2
Rolled I‐sections Welded sections
Buckling curve b c d c d
Table B3.3. Recommended values for imperfection factor for lateral torsional buckling curves Buckling curve Imperfection factor, LT
a
b
c
d
0.21
0.34
0.49
0.76
B12
4. 5. 6.
Determine the parameter LT .
LT 0.5 1 LT LT LT ,0 2LT
For rolled sections, LT,0 = 0.4 (maximum value)
= 0.75 (minimum value)
For welded sections, LT,0 = 0.2 (maximum value)
= 1.0 (minimum value)
Calculate the reduction factor, LT .
LT
1 2
LT LT LT
2
but LT 1.0 and LT
1 LT
2
Reduction factor, LT can also be obtained from Tables B2.4 and B2.5. Calculate the buckling moment resistance, M b,Rd .
M b,Rd
LT Wy f y M1
where M1
is the partial factor for resistance of the beam to instability.
B13
Appendix C C1 1.
Design procedures for a column member under combined axial compression and bending to EN 1993: 1‐1
Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex Members subjected to combined bending and axial compression should satisfy:
M M y , Ed M z , Ed M N Ed k yy y , Ed k yz z , Ed 1 , and M z , Rk y N Rk LT M y , Rk M1 M1 M1
M M y , Ed M z , Ed M N Ed k zy y , Ed k zz z , Ed 1 M z , Rk z N Rk LT M y , Rk M1 M1 M1
where N Ed M y , Ed
is the design value of the compression force, is the design value of the maximum moment about the y‐y axis,
M z , Ed
is the design value of the maximum moment about the z‐z axis,
M y , Ed
is the moment due to the shift of the centroidal axis about the
M z , Ed
major axis for Class 4 sections, is the moment due to the shift of the centroidal axis about the
N Rk
M y ,Rk
minor axis for Class 4 sections, is the design resistance of the cross‐section for uniform compression. is the design moment resistance of the cross‐section about the y‐y
M z , Rk
axis. is the design moment resistance of the cross‐section about the z‐z
axis. k yy , k yz , k zy , k zz are the interaction factors to be calculated by Method A and B as illustrated in Annexes A and B of EN 1993‐1‐1: 2005.
2.
Method B is recommended by SCI‐P362 as a simplified approach for manual calculations. Use of either method is permitted by the U. K. National Annex.
C1
3. Calculate interaction factors, kij by Method A Table C.1 Interaction factors for combined axial compression and bending Interaction factors
k yy
Design assumptions Elastic cross‐sectional properties Plastic cross‐sectional properties Class 3, class 4 Class 1, class 2 C myC mLT
k zy
C myC mLT
C mz
z N 1 Ed N cr , y
y 1 N 1 Ed C yy N cr , y
y wz 1 0 .6 N Ed C yz w y 1 N cr , z
C myCmLT
z N 1 Ed N cr , z
C mz
k zz
CmyC mLT
y N 1 Ed N cr , z
Cmz
k yz
y N 1 Ed N cr, y
wy z 1 0.6 N wz 1 Ed Czy N cr , y
C mz
z 1 N Ed C zz 1 N cr , z
Auxiliary terms: Wel, y 1.6 2 1.6 2 2 C yy 1 w y 1 2 C my max C my max n pl b LT wy wy Wpl, y
N Ed N cr , y y N 1 y Ed N cr , y
1
N 1 Ed N cr , z z N 1 z Ed N cr , z wy wz
n pl
Wpl, y Wel, y Wpl, z Wel, z
1. 5 1 .5
N Ed N Rk / M1
C my see Table A.2
a LT
I 1 T 0 Iy
with b LT 0.5a LT 20
M y, Ed
LT M pl, y , Rd M pl, z , Rd
C2 2 w z Wel, z C yz 1 w z 1 2 14 mz 5max n pl c LT 0.6 w y Wpl, z wz with cLT 10a LT
20
M y, Ed
5 4z
CmyLTM pl, y, Rd
C 2my 2max w y Wel, y C zy 1 w y 1 2 14 n pl d LT 0.6 5 w z Wpl, y w y
with d LT 2a LT
M y , Ed
0 0 .1
4z
M z , Ed
C my LT M pl, y , Rd C mz M pl, z , Rd
1.6 2 W 1.6 2 2 Czz 1 w z 1 2 Cmz max Cmz max n pl eLT el, z wz wz Wpl, z with e LT 1.7a LT
M y, Ed 0 0.1 4z C my LT M pl, y, Rd
M z , Ed
C2
Table C.1
(continued)
y max max z 0 = non‐dimensional slenderness for lateral‐torsional buckling due to uniform bending moment,
i.e. y 1.0 in Table C.2
LT = non‐dimensional slenderness for lateral‐torsional buckling
N N If 0 0.2 C1 4 1 Ed 1 Ed N cr , z N cr ,TF
C my C my ,0
Cmz Cmz,0 C mLT 1 .0
N N If 0 0.2 C1 4 1 Ed 1 Ed N N cr , z cr , TF
C my Cmy,0 1 C my,0
Cmz Cmz,0
C mLT C 2my
y y
M y, Ed
A for class 1,2 and 3 cross‐sections N Ed Wel, y
M y , Ed A eff for class 4 cross‐sections N Ed Weff , y
N cr , y = elastic flexural buckling force about the y‐y axis
Ncr, z = elastic flexural buckling force about the z‐z axis N cr ,T = elastic torsional buckling force IT
= St. Venant torsional constant
Iy
= second moment of area about y‐y axis
C3
y a LT
1 y a LT
a LT 1 N Ed N cr , z
1 N Ed N cr , T
1
Table C2 Equivalent uniform moment factors, Cmi,0 Cmi,0
Moment diagram
C mi,0 0.79 0.21 i 0.36 i 0.33
-1 ψ 1
2 EI N i x 1 Ed C mi ,0 1 2 L M x N cr ,i i ,Ed Mi, Ed x is the maximum moment M y,Ed or M z, Ed
M x M x
x is the maximum member displacement along the member
C mi , 0 1 0.18
N Ed N cr , i
C mi , 0 1 0.03
N Ed N cr , i
N Ed N cr ,i
C4
4. Calculate interaction factors, kij by Method B Table C.3 Interaction factors for combined axial compression and bending Design assumptions Interaction factors
Type of sections
Elastic cross‐sectional properties Class 3, class 4
Plastic cross‐sectional properties Class 1, class 2
k yy
I‐sections RHS‐sections
N Ed C my 1 0.6 y N / y Rk M 1 N Ed C my 1 0.6 N y Rk / M1
N Ed C my 1 y 0.2 N / y Rk M 1 N Ed C my 1 0.8 N y Rk / M1
k yz
I‐sections RHS‐sections
k zz
0.6 k zz
k zy
I‐sections RHS‐sections
0.8 k yy
0.6 k yy
N Ed C mz 1 2 z 0.6 z N Rk / M1 N Ed C mz 1 1.4 N / z Rk M1
I‐sections N Ed C mz 1 0.6 z z N Rk / M1 N Ed C mz 1 0.6 N / z Rk M1
k zz
RHS‐sections
N Ed C mz 1 z 0.2 N / z Rk M1 N Ed C mz 1 0.8 N / z Rk M1
For I‐ and H‐sections and rectangular hollow sections under axial compression and uniaxial bending M y,Ed , the coefficient k zy may be k zy 0 .
C5
Interaction factors k ij for members susceptible to torsional deformations
Table C.4
Design assumptions Interaction Elastic cross‐sectional properties Plastic cross‐sectional properties factors Class 3, class 4 Class 1, class 2 k yy
k yy from Table C.3
k yy from Table C.3
k yz
k yz from Table C.3
k yz from Table C.3
N Ed 0.05 z 1 C mLT 0.25 z N Rk / M1
k zy
N Ed 0.1 z 1 C mLT 0.25 z N Rk / M1 N Ed 0.1 N Ed 0.05 1 1 C mLT 0.25 z N Rk / M1 C mLT 0.25 z N Rk / M1 for z 0.4 :
k zz
k zy 0.6 z 1
k zz from Table C.3
k zz from Table C.3
C6
N Ed 0.1 z C mLT 0.25 z N Rk / M1
Table C.5
Equivalent uniform moment factors, C m in Tables C.3 and C.4 Cmy and Cmz and CmLT
Moment diagram
Range Uniform loading
M1
1 1
ψM1
Concentrated load
0 . 6 0 .4 0 .4
0 s 1 Mh
ψM h
h Ms / Mh
Ms
h M h / Ms
0.2 0.8 s 0.4
0.2 0.8 s 0.4
0 1
0.1 0.8 s 0.4
0.8 s 0.4
1 0
0.11 0.8 s 0.4
0.2 0.8 s 0.4
1 1
0 .95 0 .05 h
0 .90 0 .10 h
0 1
0.95 0.05 h
0.90 0.10 h
1 0
0.95 0.05 h 1 2
0.90 0.10 h 1 2
1 s 0
0 s 1
ψM h
Mh
1 1
1 s 0
For members with sway buckling mode the equivalent uniform moment factor should be taken C my 0.9 or C mz 0.9 respectively. C my , C mz and C mLT should be obtained according to the bending moment diagram between the
relevant braced points as follows: moment factor Bending axis C my y‐y
Points braced in direction z‐z
C mz
z‐z
y‐y
C mLT
y‐y
y‐y
C7
Table C.6
Interaction factors for combined axial compression and bending Design Assumptions Criteria
Section
Class 1 and 2 cross‐sections
Class 3 cross‐sections
k yy
‐
All
Figure C.1
Figure C.2
C my
k yz
‐
All
0.6 k zz
k zz
‐
Member not susceptible to torsional deformation
RHS sections
Figure C.1
Figure C.2
C mz
Member susceptible to torsional deformation
I sections
Figure C.1
Figure C.2
C mz
Member not susceptible to torsional deformation
All
0.6
0.8
‐
Member susceptible to torsional deformation
All
Figure C.1
Figure C.2
C mLT
k zz
k zy
(1) C ‐Factors may be obtained from Table C.5. (2) In Figure C.1 and Figure C.2, k zy is based on the conservative assumption that C mLT 1.0 .
C Factor
Interaction Factors
C8
2.8
2.0 N N ,
1.8
2.6
N N ,
1.0 ,
2.4
1.0 ,
2.2
0.8
0.8
2.0
1.6 k C
k C
0.6
0.6 1.8 0.4
1.6
1.4 0.4
1.4 0.2
1.2
0.2
1.2 1.0
1.0
0.8 0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
Non‐dimensional slenderness λ
Non‐dimensional slenderness λ
a) Interaction factor kyy
b) Interaction factor kzz
1.00
2.0
2.0 N N ,
0.2 ,
1.8
0.4
0.95
N N ,
1.0 ,
0.8
0.6 1.6 k C
0.90
k C
0.8
0.6 1.4
0.2
0.4
0.85 1.2
0.2
1.0
0.80 0.0
0.5
1.0
1.5
0.0
2.0
0.5
1.0
Non‐dimensional slenderness λ
c) Interaction factor kzy
Interaction factor kij for Class 1 and 2 sections
Figure C.1.
2.0
d) Interaction factor kzz for RH Sections
1.5
Non‐dimensional slenderness λ
C9
1.7
1.7 N N ,
1.6
1.0
1.6
,
1.0 ,
0.8
1.5
0.8
1.5
N N ,
1.4 k C
1.4
k C
0.6
0.6
1.3 0.4
1.3 0.4
1.2 0.2
1.2 1.1 0.2 1.1
1.0
1.0
0.9 0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
Non‐dimensional slenderness λ
Non‐dimensional slenderness λ
a) Interaction factor kyy
b) Interaction factor kzz
1.00 N N ,
0.99
0.2 ,
0.98 0.4 0.97 k
0.6
0.96 0.95
0.8
0.94 1.0 0.93 0.92 0.0
0.5
1.0
1.5
2.0
Non‐dimensional slenderness ̅
c) Interaction factor kzy for I sections
Figure C.2.
Interaction factor kij for Class 3 sections
1.5
C10
2.0
Appendix D Worked Examples to EN 1993‐1‐1 Part I Section analysis and section resistance Worked Example I-1 Determination of section resistances Question Determine the section resistance of a steel beam as shown: 457 × 152 × 52 kg/m I‐section S355
t f = 10.9
219.45
203.8
hw = 428.0
h = 449.8
tw = 7.6
b = 152.4
D1
Solution Section properties of 457 × 152 × 52 kg/m I‐section: h = 449.8 mm b = 152.4 mm d = 407.6 mm tw = 7.6 mm tf = 10.9 mm r = 10.2 mm
b z
tw h
d
y
r
Calculate cross‐sectional area, A A
A fillet
Ag
y
= A w 2A f z = h 2t f t w 2 b t f = (449.8- 2 ×10.9)× 7.6 + 2 ×152.4×10.9 = 3253 mm2 + 3322 mm2 (c.f. 66.6 cm2 or 6660 mm2 from tabulated data) = 6575 mm2
t
= 4 10.2 2 1 89.3 mm2 4 = A A fillet = 6575 + 89.3 = 6664.3 mm2
In general, fillets are neglected in most design. Calculate second moment of area, I Iy
Ifillet
7.6 428 .0 3 152 .4 10 .9 3 = 2 152 .4 10 .9 219 .45 2 12 12 = 2 16.45 10 3 80.0 10 6 49.66 10 6 = 160.03 10 6 49.66 10 6 = 209.69 10 6 mm4 or 20969 cm4 2 10 .2 4 10 .2 2 10 .2 4 =4 10 .2 4 10 .2 2 214 12 2 16 9 4 2 4 10 .2 214 10 .2 3 = 4 902 4540 10 3 594 3540 10 3 = 4.00 10 6 mm4
Ig
= I y I fillet = 213 .69 10 6 mm4
D2
Calculate the elastic section modulus, Wel
Wel,y
Iy
213.69 10 6 h/2 449.8 / 2 = 950.2 103 mm3 = 950.2 cm3
=
49.66 10 6 449 .8 / 2 = 220 .8 10 3 mm3 = 220.8 cm3
Wel,y,w =
160.03 10 6 449.8 / 2 = 711.6 103 mm3 = 711.6 cm3
Wel,y,f =
Wel, y,w Wel,y
=
220.8 = 950.2
0.232
=
711.6 = 950.2
0.749
Wel,y,f Wel,y
D3
Calculate the plastic section modulus, Wpl
Wpl,y0
= b t f h w t f h w t w
hw 4
= 152.4 10.9 428.0 10.9
428.0 2 7.6 4
= 729.1 10 348.0 10 = 1077 .1 103 mm3 or 1077 cm3 3
3
2 h r r 2 h w 4r r Wpl,y,fillet = 4 r 2 w 3 2 2 4 2 = 4 21.7 103 17.0 103 = 18.8 103 mm3
Wpl,y
= Wpl, y0 Wpl,fillet = 1077 .1 103 18.8 103 mm3 = 1095.9 103 mm3 or 1096 cm3 (c.f. 1100 cm2 from tabulated data)
Wpl , y , w Wpl , y
Wpl , y , f Wpl , y
=
348 .0 = 0.318 1096
=
729 .1 = 0.665 1096
The shape factor of I‐section =
Wpl, y Wel, y
=
1096 = 1.18 932
2
Wpl,z
b2tf h w tf 4 4 10.9 7.62 428 = 2 152.42 4 4 3 3 = 126.6 10 6.18 10
= 2
= 132.8 cm3
(c.f. 133 cm2 from tabulated data)
D4
hw
tw
Typical section properties in an I‐section Area A
Elements
Second moment of area I
(cm2)
ratio
(cm4)
ratio
Flanges Web Fillet
3322 3253 89
0.498 0.488 0.014
16003 4966 400
0.750 0.232 0.018
Total
6664
1
21369
1
Elastic modulus Wel
Elements
Plastic modulus Wpl
(cm3)
ratio
(cm3)
ratio
Flanges Web Fillet
711.6 220.8 17.8
0.749 0.232 0.019
729.1 348.0 18.8
0.665 0.318 0.017
Total
950.2
1
1095.9
1
Perform section classification Since tf = 10.9 mm and tw = 7.6 mm, i.e. the nominal material thickness is less than 16 mm, the nominal value of yield strength fy for grade S355 steel is 355 N/mm2. f y 355 N / mm 2
=
235 / f y 235 / 355 0.81
[Cl. 5.5]
Web – subject to bending:
[Table 5.2]
⇒
= cw cw / tw =
h – 2tf – 2r 407.6 / 7.6
= 407.6 mm = 53.6
Limit for Class 1 web = 72 = 58.32
⇒
The web is Class 1.
D5
53.6
[Table 5.2]
Flange under compression: cf = b t w 2r / 2 ⇒
= 62.2 mm
cf / t f = 62.2 / 10.9
= 5.71
Limit for Class 1 flange = 9 ⇒
5.71
= 7.3
The flanges are Class 1.
The overall cross‐section classification is Class 1 subject to bending.
Summary Hence, the design resistance of the cross‐section for uniform compression, Nc,Rd is
N c, Rd =
A fy
M0
6660 355 103 1.0
[Cl. 6.2.4 (2)]
= 2364 kN The design resistance for bending about y‐y axis, M c, y, Rd is
M c, y, Rd =
Wpl, y f y
M0
1100 103 355 106 1.0
[Cl. 6.2.5 (2)]
= 390.5 kNm The design resistance for bending about z‐z axis, M c , z , Rd is
M c,z ,Rd =
Wpl, z f y
M0
133 103 355 106 1.0
tw + 2r
= 47.2 kNm
0.5tf
The design shear resistance, Vc, Rd is
Vpl, Rd =
Av fy / 3 M0
, where
M0
hw
[Cl. 6.2.6 (2)]
1.0
where
and
0.5t b
Av
= A 2 b t f t w 2r t f but not less than h w t w
Av
= 6660 2 152.4 10.9 7.6 2 10.2 10.9 = 3642.9 mm2
Av
> h w t w = 1.0 × (449.8 – 2 × 10.9) × 7.6 = 3252.8 mm2
Vpl, Rd =
3642.9 355 / 3 10 3 = 746.6 kN 1.00
D6
Part I Section analysis and section resistance Worked Example I-2 Cross section resistance under combined bending and shear force Question Determine the design moment resistance of a steel beam under high shear with the following details:
457 × 152 × 52 kg/m I‐section S355 Shear force ratio, VEd / Vpl, Rd = 0.8
t f = 10.9
219.45
203.8 h = 449.8
hw = 428
tw = 7.6
b = 152.4
D7
Solution Resistance against bending and shear force For 457 x 152 x 52 kg/m I‐section S355
M y , V , Rd
A 2w Wpl , y 4 t f y w M0
but M y,V,Rd M y,c,Rd
[Cl. 6.2.8]
where 2
2V Ed 1 V pl,Rd
A 2w h 2w t w 4282 7.6 348.0 103 mm3 4t w 4 4
Wpl,w
=
Wpl,y
= 1100 103 mm3
Wpl,w / Wpl,y = 0.316
M y,c,Rd
= 355 1100 103 10 6
= 390.5 kNm
Moment resistance contributed by the top and the bottom flanges: = 390.5 1 0.316 = 267.1 kNm
Mpl,f
VEd / Vpl ,Rd
M y ,V ,Rd (kNm)
M y ,V ,Rd / M y ,c ,Rd
0.5 0.6 0.7 0.8 0.9 1.0
0.00 0.04 0.16 0.36 0.64 1.00
390.5 385.6 370.7 346.0 311.4 267.0
1.000 0.987 0.949 0.886 0.798 0.684
1.2
UNSAFE
1.0
Moment ratio,
0.8
SAFE
0.6 0.4 0.2
Cl.6.2.8(5)
0.0 0.0
0.2
0.4
0.6
0.8
Shear ratio, VEd / Vpl,Rd
For a high shear load at VEd / Vpl,Rd = 0.8 M y ,V ,Rd
= 346.0 kNm
D8
1.0
1.2
Part I Section analysis and section resistance Worked Example I-3 Cross section resistance under combined bending and axial force Question Determine the design moment resistance of a steel beam under combined bending and axial force with the following details: 457 × 152 × 52 kg/m I‐section S355 Axial compression force ratio, N Ed / N pl ,Rd = 0.8 a) Determine the design plastic resistance for bending about the y‐y axis reduced due to the axial force NEd . b) Determine the design plastic resistance for bending about the z‐z axis reduced due to the axial force NEd . c) Plot the failure criterion of the cross section under an interaction of bi‐axial bending and axial force.
t f = 10.9
219.45
203.8
hw = 428
h = 449.8
tw = 7.6
b = 152.4
D9
Solution Resistance under combined bending and axial force a) For 457 × 152 × 52 kg/m I‐section S355 subjected to combined major axis bending and axial force
N c, Rd = 2,334 kN If N Ed
N Ed
0.25 N c , Rd = 583.5 kN, and
0.5h w t w f y M0
[Cl. 6.2.9]
0.5 428 7.6 355 10 3 577.4 kN , 1
Then allowance needs not be made for the effect of axial force on the plastic resistance moment. Otherwise, the design plastic resistance for bending about y‐y axis reduce due to the axial force is: 1 n M N , y, Rd M pl, y, Rd , but M N, y, Rd M pl, y,Rd 1 0.5a where N n Ed N pl, Rd
a
A 2bt f
but a 0.5
A
1.20 1.00
Moment ratio,
0.80 0.60 0.40 0.20 0.00 0.0
0.2
0.4
0.6
0.8
Axial force ratio, N Ed / N pl, Rd
D10
1.0
1.2
N Ed
N pl,Rd
n
a
0.0
2,334
0.0
0.49
1.00
233.4 466.8 700.2 933.6 1167.0
2,334 2,334 2,334 2,334 2,334
0.1 0.2 0.3 0.4 0.5
0.49 0.49 0.49 0.49 0.49
1.00 1.00 0.93 0.80 0.66
1400.4 1633.8 1867.2 2100.6
2,334 2,334 2,334 2,334
0.6 0.7 0.8 0.9
0.49 0.49 0.49 0.49
0.53 0.40 0.27 0.13
2,334.0
2,334
1.0
0.49
0.00
For a high axial load at N Ed / N pl , Rd 0.8 M N , y , Rd 0.27 390.5 105.4 kNm
M N, y, Rd / M pl, y, Rd
D11
b) For 457 x 152 x 52 kg/m I‐section S355 subjected to combined minor axis bending and axial force N c , Rd 2,334 kNm
If N Ed
h w t wfy
M0
428 7.6 355 10 3 1,154.7 kN , 1.00
then allowance needs not be made for the effect of axial force on the design plastic resistance for bending. Otherwise, the design resistance for bending about the z‐z axis reduced due to the axial force is: For n a :
M N , z , Rd M pl , z , Rd
For n a :
n a 2 M N , z , Rd M pl, z , Rd 1 1 a
[Cl. 6.2.9]
1.20 1.00
Moment ratio,
0.80 0.60 0.40 0.20 0.00 0.0
0.2
0.4
0.6
0.8
1.0
Axial force ratio, NEd / Npl, Rd N Ed
N pl,Rd
n
a
M N, z, Rd / Mpl, z, Rd
0.0 233.4 466.8 700.2
2,334 2,334 2,334 2,334
0.0 0.1 0.2
0.49 0.49 0.49
1.00 1.00 1.00
933.6 1167.0 1400.4 1633.8
2,334 2,334 2,334 2,334
0.3 0.4 0.5 0.6 0.7
0.49 0.49 0.49 0.49 0.49
1.00 1.00 1.00 0.96 0.83
1867.2 2100.6 2,334.0
2,334 2,334 2,334
0.8 0.9 1.0
0.49 0.49 0.49
0.63 0.36 0.00
For high axial load at N Ed / N pl, Rd 0.8 M N , z , Rd 0.63 47.2 29.7 kNm
D12
1.2
c) For biaxial bending, Clause 6.2.9.1 gives 2
M y , Ed M z , Ed M N , z , Rd M N , y , Rd
5n
1
[Cl. 6.2.9 (6)]
For 457 x 152 x 52 kg/m I‐section of S355 subjected to bi‐axial bending and axial force
N c , Rd 2,334 kN
For a high axial compression, N Ed 0.8 N c , Rd 1867 kN , the following criterion should be used: 2
as n 0.8
A graphical presentation of the interaction curve is shown as follows: Moment ratio about minor axis,
4
M y, Ed M z , Ed 1 M N , z , Rd M N , y, Rd
1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
Moment ratio about major axis, M y ,Ed / M N ,y ,Rd M y ,Ed / M N , y ,Rd
M z ,Ed / M N ,z ,Rd
0.00
1.00
0.10
1.00
0.20
0.99
0.30
0.98
0.40
0.96
0.50
0.93
0.60
0.89
0.70
0.85
0.80
0.77
0.90
0.66
1.00
0.00
D13
1.20
Part II Member design Worked Example II‐1 Design of a fully restrained steel beam Question Design a steel beam under the following condition: Span = 10 m (assuming simply supported) Beam spacing = 3 m Loadings Permanent actions Dead load, G k ,1 = 3.0 kN/m2 = 1.0 kN/m2
Superimposed dead load, G k , 2
Variable actions Imposed load, Q k ,1
= 3.0 kN/m2
Try 457 × 152 × 52 kg/m I‐section S355. Check against bending, shear and deflection.
Note:
Deflection limit under variable action
D14
L 360
b z
Solution Section properties of 457 × 152 × 52 kg/m I‐section: h = 449.8 mm b = 152.4 mm = 7.6 mm tf = 10.9 mm tw r = 10.2 mm Wpl,y
= 1,100 10 mm
Iy Iw A
= 21,400 104 mm4 = 311 109 mm6 = 6660 mm2
3
tw h
d
y
y
3
r
Iz = 645 10 4 mm4 It = 21.4 10 4 mm4 z
Material property: Since tf = 10.9 mm and tw = 7.6 mm, i.e. the nominal material thickness is less than 16 mm, the nominal value of the yield strength for grade S355 steel is: fy E G
= 355 N/mm2 2 = 210,000 N/mm = 0.3 = 81000 N/mm2
Span = 10 m Contributive area 10 3 30 m 2 This beam is assumed to be simply supported. a) Loading.
Dead load, G k ,1
= 3.0 kN/m2
Superimposed dead load, G k , 2
= 1.0 kN/m2
Live load, Q k ,1
= 3.0 kN/m2
Factored load Design moment, M Ed Design shear force, VEd
or
= 1.40 3 1 1.60 3 = 10.4 kN/m2 = 31.2 kN/m for a width of 3 m = 31.2 10 10 / 8 = 390.0 kNm = 31.2 10 0.5 = 156.0 kN
b) Try 457 × 152 × 52 kg/m I‐section S355. c) Perform section classification. As demonstrated in Worked Example I‐1, the cross‐section classification is Class 1.
D15
d) Check for moment. As demonstrated in Worked Example I‐1, the design resistance for bending about y‐y axis, M c,Rd is:
M c, Rd 390.5 kNm
M Ed 390.0 kNm
[Cl. 6.2.5 (2)]
OK
e) Check for shear force. As demonstrated in Worked Example I‐1, the design shear resistance Vpl,Rd is: Vpl , Rd
Av fy / 3 M0
, where
M0
1.0
[Cl. 6.2.6 (2)]
Vpl, Rd 746.6 kN VEd 156.0 kN
OK
f) Check for deflection. Serviceability load
= 3 kN/m2 = 9 kN/m for a width of 3 m
5 WL4 5 9 10,0004 26.1 mm 384 EI 384 210,000 21,400 104
L / 360 10,000 / 360 27.8 mm
OK
Therefore, 457 × 152 × 52 kg/m I‐section S355 satisfies the design.
D16
Part II Member design Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling Question As the structural details stated in Worked Example II‐1, Loading during construction = 1.5 kN/m2 Case I) Span Case II) Span
= 10 m with no intermediate restraint = 10 m with one restraint at mid‐span
Other design data are given in Worked Example II‐1.
D17
Solution to Procedure B2 – Use design method given in Appendix B2 Case I) Span = 10 m with no intermediate restraint a) Evaluate the design load and the design moment. Factored construction load, w = 1.5 kN/m2 x 1.6 = 2.4 kN/m2 = 7.2 kN/m over a width of 3 m = 7.2 x 102 / 8 = 90.0 kNm Factored design moment, MEd w = 6.75 kN/m 10 m
b) Buckling length, L cr , z = 10 m. c) Try 457 x 152 x 52 kg/m I-section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the elastic critical moment and the plastic moment resistance. 0.5
2 2 EIz I w Lcr , z GIT M cr C1 2 2 EIz Lcr , z I z
For a simply supported beam under uniformly distributed loading, C1 1.132 .
2 210,000 645 10 4 311 109 10,000 2 81,000 21.4 10 4 10 6 M cr 1.132 4 2 4 10,0002 645 10 210,000 645 10
0.5
= 1.132 133,684 48,217 129,664 106 0.5
= 63.8 kNm For Class 1 section,
M pl, Rd
Wpl, yf y M0
1100 103 355 10 6 390.5 kNm where M 0 1.0 [Cl. 6.2.5 (2)]
f) Calculate the non‐dimensional slenderness, LT . LT
Wpl, y f y M cr
390.5 2.47 63.8
g) Determine the imperfection factor, LT .
D18
[Cl. 6.3.2.2]
Buckling curve c is used for sections with h / b 2 , LT 0.49
[Cl. 6.3.2.3]
h) Calculate the reduction factor for lateral torsional buckling, LT . For rolled sections, LT,0 0.4 and 0.75
2
LT 0.5 1 LT LT LT , 0 LT
[Cl. 6.3.2.3]
[Cl. 6.3.2.3(2)]
0.5 1 0.49 2.47 0.4 0.75 2.472 3.29 LT
1
0.17
3.29 3.292 0.75 2.47 2
but LT 1.0 and LT
1 LT
2
1 0.16 2.47 2
LT 0.16 i) Calculate the modified reduction factor, LT, mod .
f 1 0.5 1 - k c 1 - 2.0 LT 0.8
2
1 0.5 1 0.94 1 - 2.0 2.47 - 0.8 2
1.14 1 f 1 LT , mod LT 0.16 j) Calculate the design buckling resistance moment and check for structural adequacy. M b , Rd LT , mod
Wpl , y f y M1
0.16 390.5 62.5 kNm where M1 1.0
M Ed 90.0 kNm
Not OK.
D19
[Cl. 6.3.2.1]
Case II) Span = 10 m with one restraint at mid‐span a) Evaluate the design load and the design moment. The factored design moment is the same as that in case I), i.e. M Ed 90.0 kNm
5m
w = 6.75 kN/m
10 m
b) Buckling length, Lcr, z 5 m . c) Try 457x152x52 I‐section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the elastic critical moment and the plastic moment resistance.
2 EI z M cr C1 2 L cr , z
0 .5
I w L cr , z 2GI T 2 Iz EI z
Conservatively, take C1 1.0 . 0. 5
2 210,000 645 104 311 109 10,0002 81,000 21.4 104 10 6 M cr 1.0 4 2 4 5,0002 645 10 210,000 645 10
= 1.0 534,735 48,217 129,664 106 0.5
= 225.5 kNm and M pl , Rd
Wpl , y f y M0
390.5 kNm
where M0 1.0
[Cl. 6.2.5 (2)]
f) Calculate the non‐dimensional slenderness, LT . LT
Wpl, y f y M cr
390.5 1.31 225.5
g) Determine the imperfection factor, LT . Buckling curve c is used for sections with h / b 2 , LT 0.49
D20
[Cl. 6.3.2.3]
h) Calculate the reduction factor of lateral torsional buckling, LT . For rolled sections, LT,0 0.4 and 0.75
2
LT 0.5 1 LT LT LT,0 LT
[Cl. 6.3.2.3]
0.5 1 0.49 1.31 0.4 0.75 1.312 1.37 LT
1 1.37 1.37 0.75 1.312 2
0.47
but LT 1.0 and LT
1 LT
2
1 0.58 1.312
LT 0.47 i) Calculate the modified reduction factor, LT, mod .
f 1 0.5 1 - k c 1 - 2.0 LT 0.8
2
where k c = 1.0 conservatively.
[Cl. 6.3.2.3(2)]
1 0.5 1 1 1 - 2.0 1.31 - 0.8 2
1 LT,mod LT 0.47 j) Calculate the design buckling resistance and check for structural adequacy.
M b,Rd LT,mod M Ed
Wpl,y f y
0.47 390.5 183.5 kNm where M1 1.0 M1 90.0 kNm OK.
[Cl. 6.3.2.1]
Therefore, 457 × 152 × 52 kg/m I‐section S355 with an intermediate restraint at mid‐span satisfies the design check.
D21
Solution to Procedure B3 – Use design method given in Appendix B3 Case I) Span = 10 m with no intermediate restraint a) Evaluate the design load and the design moment. Factored construction load, w = 1.5 kN/m2 x 1.6 = 2.4 kN/m2 = 7.2 kN/m over a width of 3 m MEd = 7.2 x 102 / 8 = 90.0 kNm Factored design moment, w = 6.75 kN/m
10 m
b) Try 457 x 152 x 52 kg/m I-section S355. c) Perform cross‐section classification – as demonstrated in Worked Example I‐1. d) Determine the buckling length, Lcr , z = 10 m. e) Calculate the non‐dimensional slenderness, LT . LT
1 UV z w C1
where
C1
1.13 ;
U
0.859 ; E 210,000 76.4 ; fy 355
1
i
31.1 mm ;
z
10,000 / 31.1 321.5 mm ;
V
1 4
LT
1
1 z 20 h / t f
2
1 1 321.5 4 1 20 449.8 / 10.9
z
z / 1 321.5 / 76.4 4.21
w
1
for Class 1 sections
1 UV z w C1
D22
2
0.706 ;
0.94 0.859 0.706 4.21 1 2.40 g) Determine the imperfection factor, LT , and the paramenter LT . Buckling curve b is used for sections with 2 h / b 3.1 , LT 0.49 .
h) Calculate the reduction factor for lateral torsional buckling, LT .
LT 0.5 1 0.49 2.40 0.4 0.75 2.402 3.15 LT
1 3.15 3.152 0.75 2.42
0.18 1.0
i) Calculate the design buckling resistance moment and check for structural adequacy.
M b,Rd LT
Wpl,y f y M1
0.18 390.5 70.3 kNm
where M0 1.0 M b ,Rd M Ed 90.0 kNm
Not OK.
D23
Case II) Span = 10 m with one restraint at mid‐span a) Evaluate the design load and the design moment. Factored design moment is same as that in case I), i.e. MEd = 90.0 kNm 5m
w = 6.75 kN/m
10 m
b) Determine the buckling length, L cr , z 5 m . c) Try 457 x 152 x 52 kg/m I‐section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the non‐dimensional slenderness, LT . LT
1 UV z w C1
where C1 U
E 210,000 76.4 fy 355
1
=
i z
= 31.1 mm = L cr , z / i 5,000 / 31.1 160.8
V
=
z
= z / 1 160.8 / 76.4 2.10 = 1 for Class 1 sections
w
= 1.00 for a conservative apprach; = 0.859;
LT =
1 1 z 4 1 20 h / t f
2
1 1 160.8 4 1 20 449.8 / 10.9
2
0.87
1 UV z w C1
= 1.00 0.859 0.87 2.10 1 = 1.57 g) Determine the imperfection factor, LT , and the paramenter LT . Buckling curve b is used for sections with 2 h / b 3.1 , LT 0.49 .
D24
h) Calculate the reduction factor of lateral torsional buckling, LT .
LT 0.5 1 0.49 1.57 - 0.4 0.75 1.572 1.71 LT
1 1.71 1.712 0.75 1.57 2
0.36 1.0
i) Calculate the design buckling resistance moment and check for structural adequacy.
M b,Rd LT
Wpl,y f y M1
0.36 390.5 140.6 kNm
where M1 1.0
M Ed 90.0 kNm
OK.
Therefore, 457 × 152 × 52 kg/m I‐section S355 with an intermediate restraint at mid‐span satisfies the design check. Summary of the reduction factors for lateral torsional buckling, χ LT Procedure B2: Design method given in Cl.6.3.2.3 Case I: LT = 2.48 LT = 3.32 LT = 0.17 f = 0.16 LT , mod = 0.16 Case II: LT = 1.31 LT = 1.37 LT = 0.47 f = 1.00 LT, mod = 0.47
Procedure B3: Design method given in Steel Designers’ Manual Case I: LT = 2.40 LT = 3.15 LT = 0.18
Case II: LT = 1.57 LT = 1.71 LT = 0.36
Design method according to Procedure B3 gives a more safe design to lateral torsional buckling.
D25
Part II Member design Worked Example II‐3 Design of a steel column under axial compression Question Design a steel column under the following condition: Factored axial load, Effective length, , ,
= 1000 kN = 9.0 m = 6.3 m
Try 254 x 254 x 73 kg/m H‐section S355.
D26
Solution Section properties of 254 x 254 x 73 kg/m H‐section S355: b
h = 254.1 mm b = 254.6 mm t w = 8.6 mm
tf r
A Iy
z tw
= 14.2 mm = 12.7 mm = 93.1 102 mm2 = 11,400 104 mm4
y
d
h
r
Iz = 3,910 10 mm I w = 562 109 mm6 4
It
3
y tf
4
z
4
= 576 10 mm
Wel, y
= 898 103 mm3
Wpl , y
= 992 103 mm3
Material properties: Since t f = 14.2 mm and t w = 8.6 mm, i.e. the nominal material thickness is smaller than 16 mm, the nominal value of the yield strength for grade S355 steel is: = 355 N/mm2 = 210,000 N/mm2 = 0.3 = 81,000 N/mm2
fy E G
a) Evaluate the design load. N Ed 1000 kN
b) Try 254 x 254 x 73 kg/m H‐section S355. c) Perform section classification.
235 / f y 235 / 355 0.81
Web – internal compression part: c w = h 2t f 2r cw / t w
= 200.3 / 8.6
Limit for Class 1 web = 33 Outstand flanges: cf = b t w 2r / 2
cf / t f = 110.3 / 14.2 Limit for Class 1 flange = 10
[Table 5.2] =
200.3 mm
=
23.3
=
26.7
23.3
⇒ The web is Class 1. [Table 5.2]
=
110.3 mm
= =
7.8 8.1
7.8
⇒ The flanges are Class 2.
The overall cross‐section classification is Class 2 under pure compression.
D27
d) Determine the effective length for both axes.
Effective length, L cr , y
= 9.0 m
L cr ,z
= 6.3 m
e) Calculate N cr and Af y . N cr , y N cr , z
2 EI y L cr , y
2
2 EI z L cr , z
2
2 210,000 114,000,000 10 3 2,917 kN 2 9,000
2 210,000 39,100,000 10 3 2,042 kN 6,300 2
N c ,Rd Af y 9,310 355 10 3 3,305 kN
f) Calculate the non‐dimensional slenderness, .
y z
Af y N cr ,y Af y N cr ,z
3,305 1.06 2,917
[Cl.6.3.1.2]
3,305 1.27 2,042
[Cl.6.3.1.2]
g) Determine the imperfection factor, . For a section with h / b 1.2 ,
use buckling curve b with = 0.34 for buckling about y‐y axis. use buckling curve c with = 0.49 for buckling about z‐z axis.
h) Calculate the parameter, and the buckling reduction factor, z . Buckling about y‐y axis:
[Cl.6.3.1.2]
[Cl.6.3.1.2]
y 0.5 1 0.34 1.06 - 0.2 1.06 2 1.21
y
1 1.21 1.212 1.06 2
0.56
Buckling about z‐z axis:
z 0.5 1 0.49 1.27 - 0.2 1.27 2 1.57
y
1 1.57 1.57 2 1.27 2
0.40
z 0.40 critical i&j) Calculate the design buckling resistance, N b ,Rd and check for structural adequacy: N b ,Rd
N c ,Rd 0.40 3,305 1,322 kN 1000 kN M1 1.00
OK.
Therefore, 254 x 254 x 73 kg/m H‐section S355 steel satisfies the design. D28
Part II Member design Worked Example II‐4 Design of a beam-column under combined compression and bending Question Design a steel column under the following condition: Design axial load, N Ed
= 1000 kN
Design moment, M y , Ed
= 60 kNm
M z ,Ed
= 0 kNm
Effective length,
L cr , y
= 9.0 m
L cr ,z
= 6.3 m
Try 254 x 254 x 73 kg/m H‐section S355.
60 kNm
0
0 My,Ed
0 Mz,Ed
D29
Solution Section properties of 254 × 254 × 73 kg/m H‐section S355:
h = 254.1 mm b = 254.6 mm t w = 8.6 mm
tf r
A Iy
= = = =
b z
14.2 mm 12.7 mm 93.1 10 2 mm2 11,400 104 mm4
tw y
d
h
y
Iz = 3,910 10 mm I w = 562 109 mm6 I t = 576 10 3 mm4 4
4
Wel, y
= 898 10 3 mm3
Wpl , y
= 992 10 3 mm3
r
tf
z
Material properties: Since t f = 14.2 mm and t w = 8.6 mm, i.e. the nominal material thickness is smaller than 16 mm, the nominal value of the yield strength for grade S355 steel is:
= 355 N/mm2 = 210,000 N/mm2 = 0.3 = 81,000 N/mm2
fy E G
a) Evaluate the design load.
N Ed M y , Ed
= 1000 kN = 60 kNm
M z , Ed
= 0 kNm
b) Try 254 x 254 x 73 kg/m H‐section S355 steel. c) Perform section classification.
235 / f y 235 / 355 0.81
Web – internal compression part: c w = h 2t f 2r
cw / t w
=
200.3 / 8.6
Limit for Class 1 web = 33
=
200.3 mm
=
23.3
=
26.7
D30
23.3
[Table 5.2]
⇒ The web is Class 1.
Outstand flanges: cf = b t w 2r / 2
cf / t f = 110.3 / 14.2 Limit for Class 2 flange = 10
=
110.3 mm
= =
7.8 8.1 7.8
⇒ The flanges are Class 2.
The overall cross‐section classification is Class 2. (Under pure compression) d) Determine the effective length for both axes.
Effective length, L cr , y
= 9.0 m
L cr ,z
= 6.3 m
e) Check the resistance of the cross‐section for combined bending and axial force. Compression: N c , Rd
Af y
[Cl. 6.2.4 (2)]
M0
The design compression resistance of the cross‐section is therefore:
N c, Rd
9,310 355 103 3,305 kN 1,000kN 1.00
OK.
Bending about y‐y axis:
M c,Rd M pl,Rd
Wpl, y f y
[Cl. 6.2.5 (2)]
M0
The design resistance of the cross‐section for bending is therefore:
M c, y,Rd
Wpl, y f y M0
992 103 355 10 6 1.00
352.2 kNm 60 kNm
OK.
Cross‐section capacity check for combined bending and axial force: f) Check the member buckling resistance in combined bending and axial compression. Buckling resistance in compression: Calculate the elastic critical force and Af y . N cr , y N cr , z
2 EI y L cr , y
2
2 EI z L cr , z
2
2 210,000 114,000,000 10 3 2,917 kN 9,000 2
2 210,000 39,100,000 10 3 2,042 kN 2 6,300
N c ,Rd Af y 9,310 355 10 3 3,305 kN
D31
Calculate the non‐dimensional slenderness. y
z
Af y N cr ,y
Af y N cr ,z
3,305 1.06 2,917
[Cl.6.3.1.2]
3,305 1.27 2,042
[Cl.6.3.1.2]
g) Determine the imperfection factor, . Choose a suitable buckling curve
[Table 6.1]
use buckling curve b with 0.34 for buckling about the y‐y axis. use buckling curve c with 0.49 for buckling about the z‐z axis.
Calculate the buckling reduction factor, . Buckling curve about y‐y axis: y 0.5 1 0.34 1.06 0.2 1.06 2 1.21
y
1 1.21 1.212 1.06 2
0.56
Buckling curve about z‐z axis: y 0.5 1 0.49 1.27 0.2 1.27 2 1.57
y
1 1.57 1.57 2 1.27 2
[Cl.6.3.1.2]
[Cl.6.3.1.2]
0.40
Buckling resistance in bending: h) Calculate the elastic critical moment, M cr and the plastic resistance moment M pl , Rd . 2 2 EI z I w L cr , z GI T 2 M cr C1 2 EI z L cr , z I z
0 .5
with a zero moment at one end, i.e. 0 , C1 1.879 .
M cr 1.879
2 210,000 39.110 6 6,300 2
0.5
562 10 9 6,300 2 81,000 576 10 3 10 6 2 6 6 210,000 39.110 39.110
1.879 2,041,807 14,373 22,850 106 740.2 kNm W f 992 103 355 106 M pl,Rd pl,y y 352.2 kNm where M 0 1.0 M0 1.0 0.5
i) Calculate the non‐dimensional slenderness. LT
W pl,y f y M cr
352.2 0.69 740.2
[Cl.6.3.2.2]
D32
j) Determine the imperfection factor for lateral torsional buckling, LT . Buckling curve a is used for sections with h / b 2.0 , LT 0.21 k) Calculate the buckling reduction factor.
2
LT 0.5 1 LT LT 0.2 LT
[Table 6.3 & 6.4]
[Cl. 6.3.2.2]
LT 0.5 1 0.21 0.69 0.2 0.69 2 0.79 LT
1 0.79 0.79 2 0.69 2
LT
M y,Rk M1
0.85
0.85
352.2 299.4 kNm 1.0
l) Resistance in combined bending and axial compression: A member subjected to combined bending and axial compression must satisfy both equations:
M y, Ed Mz , Ed N Ed k yy k yz 1 y N Rk / M1 LTM y, Rk / M1 M z , Rk / M1
[Cl. 6.3.3]
M y, Ed Mz , Ed N Ed k zy k zz 1 z N Rk / M1 LTM y, Rk / M1 Mz , Rk / M1 y N Rk / M1 0.56 9,310 355 103 1,850.8 kN y N Rk / M1 0.40 9,310 355 103 1,322.0 kN m) Determination of interaction factors
using Annex B
Since M z , Ed 0 kNm , only k yy and k zy are required. Since the member is susceptible to lateral torsional buckling, interaction factors k yy and k zy are determined according to Table B.2.
0 , C my C mLT 0.6 0.4 0.4 0.6 N Ed N Ed C my 1 0.8 k yy Cmy 1 y 0.2 y N Rk / M1 y N Rk / M1
1,000 = 0.60 1 1.06 0.2 0.95 1,850.8
1,000 0.60 1 0.8 0.86 1,850.8
D33
k yy 0.86 z 1.27 0.4 ,
0.1 z N Ed 0.1 N Ed 1 k zy 1 C mLT 0.25 z N Rk / M1 C mLT 0.25 z N Rk / M1
0.11.27 1,000 0.73 = 1 0.6 0.25 1,322
0.1 1,000 0.78 1 0.6 0.25 1,322
k yy 0.78
n) Check for structural adequacy. M y, Ed N Ed k yy y N Rk / M1 LTM y, Rk / M1
1,000 60 0.86 1,850.8 299.4
0.54 0.17 0.71 1.00
OK.
M y, Ed N Ed k zy z N Rk / M1 z M y, Rk / M1
1,000 60 0.78 1,322.0 299.4
0.76 0.16 0.92 1.00
OK.
Therefore, 254 x 254 x 73 kg/m H‐section S355 steel satisfies the design.
D34
Key parameters in Worked Example II‐4. C my 0.60 ;
CmLT 0.60
N Ed M y, Ed 0.47 1 N Rd M y, Rd
M y,Ed
N Ed k yy 0.71 1 y N Rk / M1 LT M y,Rk / M1
M y,Ed
N Ed k zy 0.92 1 z N Rk / M1 LT M y,Rk / M1
D35
Part II Member design Worked Example II‐5a Column in simple construction Question Design the column between Levels 1 and 2, i.e. Column C12, as shown in the figure below, with a S275 H‐section. The following assumptions are made:
The column forms part of a braced structure of simple construction. The column is effectively pinned at the base, and continuous at Level 2. Beam 2 is connected to the column flange of the column at Joint 2 with flexible end plates. Beam 3 Level 3 Column C23
P23,Ed 201.6 A
A
Level 2 Joint 2
201.8
Column C12
201.8
Column under consideration Section A-A R1,Ed, R2,Ed and R3,Ed are reaction
Level 1
forces from beams connected to the column at Joint 2.
Design data: P23,Ed P1, Ed P2, Ed P3, Ed
= 377 kN = 37 kN = 147 kN = 28 kN
Try 203 x 203 x 46 kg/m H‐section S275.
D36
Solution Section properties of 203 x 203 x 46 kg/m H‐section S275: b
h = 203.2 mm b = 203.6 mm t w = 7.2 mm
z tw
t f = 11.0 mm r = 10.2 mm
h
d
y
y
A = 5,870 mm2 I y = 4,570 10 4 mm4
r
I z = 1,550 10 mm I w = 143 10 9 mm6 4
tf
4
z
I t = 222 103 mm4
Wel,y
= 450 103 mm3
Wpl ,y
= 497 103 mm3
Wel ,z
= 152 103 mm3
Wpl ,z
= 231 103 mm3
U
= 0.847 (buckling parameter)
a) Nominal moments due to connected beams In simple construction, reaction forces from connected beams are assumed to act at 100 mm from the faces of the web or of the flanges of the column (NCCI SN005a). Nominal moments at Joint 2
h M 2, y ,Ed 100 R 2, Ed 10-3 kNm 29.6 kNm 2 tw -3 M 2,z , Ed 100 R 1, Ed R 3, Ed 10 kNm 0.9 kNm 2 These nominal moments are distributed between the column members above and below Level 2, i.e. Columns C12 and C23, in proportion to their bending stiffnesses, K12 and K23 respectively. K 23 K12 K 23 EI
EI L12
L 23 EI
L 23
EI
EI
3 5000 EI 8 3000 5000
The nominal moments acting onto Column C12 at Joint 2 after moment distribution are: 3 11.1 kNm 8 3 M 2, z , Ed 0.3 kNm 8
M y , Ed M 2, y , Ed M z , Ed
D37
The axial force and the bending moment diagrams are shown below. 377 Level 3 3000
377 37+147+28
Level 2
M2,y,Ed = 29.6
M2,y,Ed = 18.5
Joint 2
5000
0.6 0.3
11.1
589
Level 1
My
589
Mz
N
b) Buckling lengths About the y‐y axis
Lcr , y L 5,000 mm
About the z‐z axis
Lcr , z L 5,000 mm
c) Resistance to flexural buckling Flexural buckling about the z‐z axis is considered to be critical. Both the elastic critical force and the non‐dimensional slenderness for flexural buckling of column C12 are evaluated as follows: 2 EI z 2 210 103 1,548 10 4 10 3 1,283 kN L cr , z 2 5,000 2
N cr , z
N c , Rd Af y 5,870 275 10 3 1,614 kN
z
N c, Rd
N cr ,z
1,614 1.12 1,283
From Table 6.2 of EN 1993‐1‐1: For a H‐section (with h/b 1.2) and t f 100 mm, use buckling curve ‘c’, and hence,
0.49 .
[ Table 6.1 ]
According to Table 6.1 of EN 1993‐1‐1
z 0.5 1 z 0.2 z
z
1 z z z 2
2
2
0.5 1 0.49 1.12 0.2 1.12 1.35 2
1 1.35 1.352 1.122
0.48
D38
[Cl. 6.3.1.2]
z Af y M1
N b , Rd
0.48 1,614 774 kN N Ed 589 kN 1 .0
The resistance of Column C12 to flexural buckling is adequate. d) Design buckling resistance moment 1
V 4
LT
1
1 z 20 h tf
2
1 5,000 1 51.4 4 1 20 203.2 11.0
2
0.80
1 UV z w C1
(Refer to Appendix B3)
1 0.847 0.80 1.12 1.0 0.57 1.77
Alternatively, the non‐dimensional slenderness for lateral torsional buckling for the H‐section may be approximated (NCCI SN002a) as follows: LT 0.9 z 1.01
This assumes a uniform bending moment and a section symmetric about its major axis. From Table B3.2 in Appendix B of this Technical Guide, for a rolled H‐section (with h/b 2), use buckling curve ‘b’, and hence, LT 0.34 .
LT 0.5 1 LT LT LT, 0 LT
2
0.5 1 0.34 0.57 0.4 0.75 0.57 2 0.65
LT
1 2
LT LT LT
M b , Rd
2
1 0.65 0.65 0.75 0.572 2
0.93
0.93 497 10 3 275 10 6 127.1 kNm M y, Ed 11.1 kNm 1.0
The design buckling resistance moment of Column C12 is adequate. e) Resistance for bending about minor axis There is no reduction for buckling to the minor axis bending resistance M c, z , Rd . M c, z , Rd
Wpl, z f y M0
231 10 3 275 10 6 63.5 kNm 1.0
The resistance of Column C12 for bending about the minor axis is adequate.
D39
f) Combined compression and bending Using the simplified buckling check for combined bending and axial compression: M y , Ed M z , Ed N Ed k zy k zz 1 M c , z , Rd N b , z , Rd M b , Rd
[Clause 6.3.3, Eq. 6.62]
589 11.1 0.3 1.0 1.5 1 759 127.1 63.5
(Refer to NCCI SN048b)
Use k zy 1.0 and k zz 1.5 for columns in simple construction
0.76 0.09 0.01
0.86 1.0 The member resistance of Column C12 under combined bending and axial compression is
adequate.
Therefore, 203 x 203 x 46 kg/m H‐section S275 steel satisfies the design.
D40
Part II
Member design Worked Example II-5b Column in simple construction In Worked Example II‐5a, the factors k zy and k zz can be alternatively calculated according to Annex A in EN 1993‐1‐1 as follow: N Rk Af y 5,870 275 10-3 = 1,614 kN
N cr , y
N cr , z
y
z
2 EI y Lcr , y
2
2 210 103 4,568 104 10 3 3,787 kN 2 5,000
2 EI z 2 210 103 1,548 104 10 3 1,283 kN 2 5,0002 Lcr , z
Af y N cr , y Af y N cr ,z
1,614 0.65 3,787
1,614 1.12 1,283
For a H‐section (with h/b 1.2) and t f 100 mm , use curve ‘b’ for buckling about y‐y axis, and hence, 0.34 .
y 0.5 1 y 0.2 y
2
0.5 1 0.34 (0.65 0.2) 0.65 0.79 2
For a H‐section (with h/b 1.2) and t f 100 mm , use curve ‘c’ for buckling about z‐z axis, and hence, 0.49 .
z 0.5 1 z 0.2 z y
z
1 2
2
2
2
y y y
1 z z z
2
0.5 1 0.49 (1.12 0.2) 1.12 1.35 2
1 0.79 0.792 0.652
1 1.35 1.352 1.122
0.81
0.48
D41
For double symmetric H‐section with y o z o 0 2
2
2
2
2
io iy iz yo z o
Iy
A
N cr ,T
(Refer to EN 1993‐1‐3, Eq. 6.33b)
(Refer to EN 1993‐1‐3, Eq. 6.33a)
I z 4,570 104 1,550 104 10,426 mm2 A 5,870 5,870
2 EI w 1 GI T 2 2 i o Lcr ,T
1 2 210 103 0.143 1012 81 103 22.2 104 10 3 kN 10,426 2,5002
6,273 kN 2
y 1 o 1 io
N cr ,TF
(Refer to EN 1993‐1‐3, Eq. 6.35)
2 2 N cr ,T N cr , y N cr ,T y o N cr ,T 1 1 4 i o N cr , y 2 N cr , y N cr , y
(Refer to EN 1993‐1‐3, Eq. 6.35)
1 N cr ,y N cr ,T N cr ,y N cr ,T 2 1 N cr ,T
6,273 kN
Cmy,0 0.79 0.21y 0.36y 0.33
N Ed N cr , y
589 0.79 0.21 0 0.36 0 0.33 0.77 3,787 C mz , 0 0.79 0.21z 0.36z 0.33
N Ed N cr , z
589 0.79 0.21 0 0.36 0 0.33 0.74 1,283 N Ed 589 1 N cr , y 3,787 y 0.97 N Ed 589 1 y 1 0.81 N cr , y 3,787 1
D42
N Ed 589 1 N cr , z 1,283 z 0.69 589 N Ed 1 0.48 1 z 1,283 N cr , z 1
wy
Wpl, y
497 1.10 1.5 450
231 1.52 1.50 152
Wel, y
w y 1.10
wz
Wpl, z Wel, z
w z 1.50
n pl
N Ed 589 0.36 N Rk / M1 1,614 / 1.00
a LT 1
y
IT 22.2 1 1.00 Iy 4,570
M y, Ed A 11.1 106 5,870 0.25 3 N Ed Wel, y 589 10 450 103
2 EI z M cr C1 2 L cr ,z
0. 5 2 I w L cr ,z GI T 2 C z C z 2 g 2 g 2 I EI z z
(Refer to NCCI SN003a)
Since 0 is the non‐dimensional slenderness for lateral‐torsional buckling due to uniform bending moment, C1 1.00 and C 2 z g 0
2 210 103 1,550 10 4 0.143 1012 5,000 2 81 103 22.2 10 4 M cr 1.00 2 4 5,000 2 210 103 1,550 10 4 1,550 10 1.00 1,285,022 9,226 13,994 10 6 kNm 0.5
195.8 kNm 0
Wpl , y f y M cr
497 275 10 3 0.84 195.8
D43
0.5
10 6 kNm
0 0.84
N N 589 589 0.2 C1 4 1 Ed 1 Ed 0.2 1.77 4 1 0.22 1 1,283 6,273 N cr ,z N cr ,T
y a LT 0.25 1 Cmy Cmy,0 1 Cmy,0 0.77 1 0.77 0.85 1 y a LT 1 0.25 1 Cmz Cmz,0 0.74 C mLT C my
a LT
2
N N 1 Ed 1 Ed N N cr , z cr ,T
1.00
0.852
589 589 1 1 1,283 6,273
1.03 1
C mLT 1.03 LT 0.93 (Determined from Worked Example II‐5a)
y 0.65 max max max 1.12 z 1.12
d LT 2a LT
M y , Ed M z , Ed 0 4 0.1 z C my LT M pl , y , Rd C mz M pl, z , Rd
0.84 11.1 0.3 4 3 0.1 1.12 0.85 0.93 497 275 10 0.74 231 275 10 3 0.00066
2 1
2 2 C my max n pl d LT C zy 1 w y 1 2 14 5 wy
0.852 1.12 2 0.36 0.00066 0.79 1 1.10 1 2 14 5 1.10 w y Wel , y
0.6
w z Wpl , y
0.6
1.10 450 0.47 1.50 497
C zy 0.79
e LT 1.7a LT
M y, Ed 0 4 0.1 z C my LT M pl, y, Rd
0.84 11.1 0.09 1.7 1 4 0.1 1.12 0.85 0.93 497 275 10 3
D44
1.6 1.6 2 2 2 C mz max C mz max n pl e LT Czz 1 w z 1 2 wz wz 1.6 1.6 1 1.5 1 2 0.742 1.12 0.742 1.12 2 0.36 0.09 1.5 1.5 1.07 W 152 el, z 0.66 Wpl, z 231 C zz 1.07
k zy C my C mLT
k zz C mz
wy z 1.10 0.69 1 1 0.85 1.03 0.6 0.47 0.6 589 N Ed C zy 1 . 50 0 . 79 w z 1 1 3,787 N cr , y
1 0.69 1 z 0.74 0.88 N Ed Czz 589 1.07 1 1 N cr , z 1,283
D45
Part II
Member design Worked Example II-5c Column in simple construction In Worked Example II‐5a, the factors k zy and k zz can be alternatively calculated according to Annex B in EN 1993‐1‐1 as follows: Since H‐section is not susceptible to torsional deformation, use Table B.1. y z LT 0 C my C mz C mLT 0.6
As determined from Worked Example II‐5a, N Rk 1,614 kN
y 0.65
N cr, y 3,787 kN
y 0.81
z 1.12
N cr, z 1,283 kN
z 0.48
N Ed 589 0.61 0.65 0.2 k yy C my 1 y 0.2 0.72 0.81 1614 / 1.00 y N Rk / M1 N 589 Ed 0.61 0.8 C my 1 0.8 0.82 N / 0.81 1614 / 1.00 y Rk M 1 k yy 0.72 k zy 0.6k yy 0.6 0.72 0.43
N Ed 589 0.61 2 1.12 0.6 k zz C mz 1 2z 0.6 1.35 N / 0 . 48 1614 / 1 . 00 z Rk M1 N Ed C mz 1 1.4 z N Rk / M1
589 0.61 1.4 0 . 48 1614 / 1 . 00
1.24
k zz 1.24
Factors k zy and k zz according to different methods are summarized as follows:
BS EN 1993‐1‐1 BS EN 1993‐1‐1 NCCI SN048b Annex A Annex B
k zy
0.47
0.43
1.0
k zz
0.88
1.24
1.5
D46
Construction to Structural
EN 1993-1-1 Design of Steel Structures
Authors: K.F. Chung, M.C.H. Yam and H.C. Ho
The Hong Kong Polytechnic University
Publisher: Construction Industry Council, Hong Kong SAR
Supporting Organisation: Hong Kong Constructional Metal Structures Association
Copyright © 2015 reserved by the Construction Industry Council. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.
ISBN: 978-988-14432-0-5
i
Technical Guide on Effective Design and Eurocodes:
Construction to Structural
EN 1993-1-1 Design of Steel Structures
K.F. Chung, M.C.H. Yam and H.C. Ho
The Hong Kong Polytechnic University Publisher: Construction Industry Council, Hong Kong SAR
Supporting Organisation: Hong Kong Constructional Metal Structures Association
Copyright © 2015 reserved by the Construction Industry Council. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.
ISBN: 978-988-14432-0-5
i
Foreword The Construction Industry Council (www.hkcic.org) (CIC) was formed on 1 February 2007 in accordance with the Construction Industry Council Ordinance (Cap. 587) in Hong Kong. The main functions of the CIC are to forge consensus on long‐term strategic issues, to convey the industry’s needs and aspirations to the Government as well as to provide a communication channel for the Government to solicit advice on all construction‐related matters. The CIC Research Fund was established in September 2012 to enhance efficiency and competitiveness of the local construction industry. The CIC Research Fund encourages research and development activities as well as applications of innovative techniques that directly meet the needs of the industry. Moreover, it also promotes establishment of standards and good practices for the construction industry now and into the future. The project leading to the publication of this document is the first project funded by the CIC Research Fund announced in January 2013. It aims to facilitate technological upgrading of structural engineers and related construction professionals in Hong Kong to work effectively and efficiently in full accordance with the Structural Eurocodes, in particular, in structural steel design. Owing to the wide adoption of the Structural Eurocodes in many parts of the world beyond Member States of the European Union, the use of Structural Eurocodes presents huge opportunities for Hong Kong structural engineers and construction professionals to work on large scale infrastructure projects overseas. According to the World Steel Association (www.worldsteel.org), China has been the largest steel producer in the world since early 2000s. In 2013, China produces about 779 million metric tons (mmt) of steel materials, representing 49.2% of the world production. With the support of the Chinese Steel Construction Industry, Hong Kong construction professionals will be able to export their professional services to the international construction markets with quality structural steelwork through their international operation and practice. Hence, this will facilitate Hong Kong as a whole to develop into the International Engineering Centre for Design and Construction of Infrastructure for Asia and beyond.
ii
Foreword Since their official release in 2010, the Structural Eurocodes have been widely adopted in construction projects throughout the Member States of the European Community as well as a number of countries and cities in Southeast Asia such as Singapore, Malaysia and Hong Kong. Through effective design and construction using the Structural Eurocodes, designers, contractors and building materials suppliers are able to contribute to the international construction market with minimal technical barriers in the Region and beyond. The ability to produce steel materials to precise specifications and the associated quality control systems in addition to advanced skills in engineering design and construction will be essential. Jointly published by the Construction Industry Council, Hong Kong SAR, the Hong Kong Constructional Metal Structures Association and the Hong Kong Polytechnic University, the Technical Guide entitled “Effective Design and Construction to Structural Eurocodes: EN 1993‐1‐1 Design of Steel Structures” is considered to be highly relevant to the current needs of many design and construction engineers in Hong Kong as well as in many major cities in the Region. The Technical Guide provides detailed guidance on the design and construction of structural steelwork using European steel materials and products. More importantly, the Technical Guide also provides specific guidance on the use of Chinese steel materials, allowing engineers to select suitable steel materials and products according to generic project requirements on time and on budgets in meeting various specific project requirements. Consequently, design and construction engineers in Hong Kong and the Region will find the Technical Guide very helpful in providing practical advice on the selection of steel materials and products as well as technical guidance on the engineering design of structural steelwork conforming to Structural Eurocodes. It is expected that the Technical Guide will enable engineers to exploit new opportunities in international construction markets, striving for enhanced economic development of the construction industry in Hong Kong as well as in the Region. Mr Qing‐Rui YUE President Chinese National Engineering Research Centre for Steel Construction Beijing, China
iii
Foreword Roll forming is an established manufacturing process which has been developed for the mass production of profiles and sections over the past 100 years. In recent years, China has became the largest producer of roll formed profiles and sections in the world. Its annual production is estimated to be 127 million metric tons in 2013, i.e. over 50% of world production. The majority of the production includes thick gauge circular, rectangular and square hollow sections and thin gauge profiles in various sizes and thicknesses with different steel materials. The products are widely used as pipes and ducts in petroleum and chemical refineries, structural members in offshore structures and building frames as well as deckings, wall claddings and roof panels in buildings. Comprehensive design rules for applications of cold‐formed sections and profiles in construction are now available in the Structural Eurcodes. The Technical Guide “Effective Design and Construction to Structural Eurocodes – EN 1993‐1‐ 1 Design of Steel Structures” jointly published by the Construction Industry Council, Hong Kong SAR, the Hong Kong Constructional Metal Structures Association and the Hong Kong Polytechnic University is highly commendable. The Technical Guide is a major contribution to the Hong Kong Construction Industry, enabling its design and construction skills in structural steelwork to conform also to the Structural Eurocodes. In particular, the use of Chinese cold formed hollow sections is clearly illustrated in the document, and Design Tables are provided to facilitate adoption of Chinese cold formed hollow sections in construction projects. We believe that the Technical Guide will promote effective design and construction of structural steelwork using both European and Chinese steel materials and products. The Technical Guide will soon be regarded as the definitive reference for engineering design of cold formed hollow sections conforming to the Structural Eurocodes in many parts of the world, making a positive impact to the export of Chinese steel materials for overseas construction projects. Prof. Dr.‐Ing. Jing‐Tao Han President Chinese Confederation of Roll Forming Industry Professor University of Science and Technology Beijing Beijing, China iv
Preface This document is compiled by Ir Professor K.F. Chung, Ir Dr. Michael C.H. Yam and Dr. H.C. Ho of the Hong Kong Polytechnic University. The project leading to the publication of this document is fully funded by the CIC Research Fund of the Construction Industry Council (www.hkcic.org) (CIC) in Hong Kong. It is also supported by the Hong Kong Constructional Metal Structures Association (www.cmsa.org.hk). This document aims to facilitate the technological upgrading of structural engineers and related construction professionals in Hong Kong to work effectively and efficiently in full accordance with the Structural Eurocodes. Moreover, steel materials manufactured to selected European and Chinese steel materials specifications are covered in various chapters of the document. This provides a level playing field for both European and Chinese steel materials in the technical context of modern structural steel design. The project is also supported by the following professional associations:
the Steel Construction Institute (www.steel‐sci.org), the U.K.
the Institution of Structural Engineers (www.istructe.org), the U.K., and
the Institution of Civil Engineers, Hong Kong Association (www.ice.org.hk). An International Advisory Committee has been established to provide technical guidance for the project, and a member list of the Committee is as follows: The U.K. Dr. Graham Couchman The Steel Construction Institute Professor Leroy Gardner Imperial College London Professor Dennis S.H. Lam Bradford University Professor David A. Nethercot Imperial College London Mr. Y. K. Cheng The Institution of Structural Engineers, U.K. Mr. C.M. Lee The Institution of Civil Engineers – Hong Kong Association Singapore Professor S.P. Chiew Nanyang University of Technology Mr. W.B. Ho Singapore Structural Steel Society Professor Richard J.Y. Liew National University of Singapore Mr. K. Thanabal Building and Construction Authority v
Hong Kong Ir Professor Francis T.K. Au The University of Hong Kong Dr. C.M. Chan The Hong Kong University of Science and Technology Dr. T.M. Chan The Hong Kong Polytechnic University Ir Dr. Gary S.K. Chou Chun Wo Construction and Engineering Co. Ltd. Ir Dr. Goman W.M. Ho Ove Arup & Partners Hong Kong Ltd. Ir K.S. Kwan Housing Department, the Government of Hong Kong SAR Ir K.K. Kwan Ove Arup & Partners Hong Kong Ltd. Dr. Paul H.F. Lam The City University of Hong Kong Dr. Jackson C.K. Lau Hong Kong Institute of Vocational Education (Tsing Yi) Ir H.Y. Lee Hong Kong Constructional Metal Structures Association Ir M.K. Leung Architectural Services Department, the Government of Hong Kong SAR Ir Alan H.N. Yau AECOM Building Engineering Co. Ltd. The manuscript of the document was prepared by Ir Professor K.F. Chung, Ir Dr. Michael C.H. Yam and Dr. H.C. Ho assisted by Mr. K. Wang and Mr. T.Y. Ma. The worked examples were compiled by Ir Professor K.F. Chung and Dr. H.C. Ho, and checked by Ir Dr. Michael C.H. Yam and Dr. T.M. Chan. All the Design Tables were compiled by Mr. K. Wang and Dr. H.C. Ho under the supervision of Ir Professor K.F. Chung. During the compilation of the document, various drafts have been critically reviewed by the Engineering Technology Committee of the Hong Kong Constructional Metal Structures Association as well as various senior engineers and experts on steel construction. Hence, the final version of the document has been revised according to all of these technical comments, after rigorous consideration to attain a balanced view taking into account international trends, local practices, levels of structural accuracy and adequacy as well as user‐friendliness in practical design.
K.F. Chung, M.C.H. Yam and H.C. Ho The Hong Kong Polytechnic University Hong Kong Constructional Metal Structures Association
vi
EXECUTIVE SUMMARY This document provides technical guidance on the key structural steel design rules for both rolled and welded sections given in the Structural Eurocode EN1993‐1‐1 Design of Steel Structures (2005) and the associated UK National Annex together with relevant non‐ contradictory complementary information (NCCI). This document is compiled to assist structural engineers and related construction professionals in Hong Kong and the neighbouring areas to perform modern structural steel design to EN1993‐1‐1 in an effective and efficient manner. Technical information is presented in the context of the local construction industry, and references to prevailing regulations and codes of practice are made whenever necessary. In addition to European steel materials, selected Chinese steel materials are also included as equivalent steel materials which are readily accepted for construction projects designed to EN 1993‐1‐1. This provides a level playing field for both European and Chinese steel materials in the technical context of modern structural steel design. In general, all the key design rules given in EN 1993‐1‐1 are described and supplemented with explanatory notes in the same sequence as that found in the Eurocode: General Basis of design Materials Durability Structural analysis Ultimate limit states Serviceability limit states In order to illustrate various structural design procedures, a total of 8 worked examples with different cross‐section properties and resistances as well as different member buckling resistances are provided. Comprehensive design procedures for the following structural members are also presented in a rational manner: i) column members undergoing flexural buckling, ii) beam members undergoing lateral torsional buckling, and iii) beam‐column members undergoing buckling under combined compression and bending. Detailed design information and parameters are also presented in a tabulated format for easy reference. A complete chapter together with a total of 45 Design Tables is compiled to facilitate practical design of the following: vii
Rolled sections of S275 and S355 steel materials rolled I‐ and H‐sections hot‐finished circular, rectangular and square hollow sections
Equivalent welded sections of Q235, Q275, Q345 and Q460 steel materials welded I‐ and H‐sections cold‐formed circular, rectangular and square hollow sections
Hence, rolled sections complying to European steel materials specifications and equivalent welded sections with selected Chinese steel materials have been included for structural engineers and related construction professionals to use in large scale construction projects in Hong Kong and neighbouring cities whenever necessary.
viii
ix
Contents Section 1 Adopting Structural Eurocodes 1.1 1.2 1.3 1.4 1.4.1 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.7 1.8 1.9
Organization of Eurocodes Composition of EN1993 Aims and Scope Modern Structural Design Codes Modern design approach Harmonized Design Rules Member buckling check for hot‐rolled steel sections Member buckling check using normalized slenderness Member buckling check for composite columns Member buckling check for steel and composite columns at elevated temperatures Symbols and Terminology Conventions for Member Axes Format Equivalent Steel Materials
1 2 2 5 6 7 7 9 11 13 15 16 17 17
Section 2
Basis of Structural Design
2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.3.1 2.4.3.2 2.4.4 2.4.5
General Requirements Basic requirements Reliability management Design working life Principles of Limit State Design Design situations Ultimate limit states Serviceability limit states Basic Variables and Limit State Design Actions and environmental influences Material and product properties Limit state design Verification by Partial Factor Method Design values Ultimate limit states Combination of actions at ULS General Persistent or transient design situations Serviceability Limit States Combination of actions for SLS
x
22 22 23 24 24 24 25 25 26 26 26 27 27 27 29 29 29 29 32 32
Section 3
Materials
3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.3 3.3.1 3.3.2
General Structural Steel Material properties Ductility requirements Fracture toughness Through‐thickness properties Tolerances Design values of material coefficients Connecting Devices Fasteners Welding consumables
33 34 34 35 35 36 36 37 37 37 37
Durability
38
Section 4
Section 5
Structural Analysis
5.1 5.1.1 5.2 5.2.1 5.2.2 5.3 5.3.1 5.4 5.4.1 5.4.2 5.4.3 5.5 5.5.1 5.5.2 5.6
Structural Modeling for Analysis Structural Modeling and basic assumptions Global Analysis Effects of deformed geometry of a structure Structural stability of frames Imperfections Basis Methods of Analysis Allowing for Material Non‐linearities General Elastic global analysis Plastic global analysis Classification of Cross‐sections Basis Classification Cross‐section Requirements for Plastic Global Analysis
x
40 40 40 40 42 42 42 43 43 44 44 45 45 45 46
Section 6
Ultimate Limit States
6.1 6.2 6.2.1 6.2.2 6.2.2.1 6.2.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.2.7 6.2.8 6.2.9 6.2.9.1 6.2.9.2 6.2.10 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3
Partial Factors for Resistances Resistances of Cross‐sections General Section properties Gross cross‐section Net section Tension force Compression force Bending moment Shear force Torsion Bending and shear force Bending and axial force Class 1 and 2 cross‐sections Class 3 cross‐sections Bending, shear and axial forces Buckling Resistances of Members Uniform members in compression Buckling resistance Buckling curves Uniform members in bending Buckling resistance Lateral torsional buckling curves – general case Lateral torsional buckling curves for rolled sections or equivalent welded sections An alternative procedure recommended by the Steel Designers’ Manual Uniform members in bending and axial compression Columns in simple construction
6.3.2.4 6.3.3 6.3.4
Section 7
Serviceability Limit States
7.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.4
General Serviceability Limit States for Buildings Vertical deflections Horizontal deflections Dynamic effects Wind‐induced Oscillation Wind Sensitive Buildings and Structures
xii
49 49 49 50 50 50 50 51 51 52 54 54 56 56 57 58 59 59 59 59 63 63 64 65 67 72 73
75 75 75 75 75 77 77
Section 8
Design Data for Rolled and Welded Sections
8.1 General 8.2 Design Strengths 8.3 Section Classification 8.4 Rolled Sections 8.5 Equivalent Welded Sections 8.5.1 Equivalent welded I‐sections 8.5.2 Equivalent welded H‐sections 8.5.3 Equivalent cold‐formed circular hollow sections 8.5.4 Equivalent cold‐formed rectangular and square hollow sections 8.6 Design Tables on Section Dimensions, Properties and Resistances 8.6.1 Section dimensions and properties 8.6.2 Section resistances 8.6.2.1 Moment resistances 8.6.2.2 Shear resistances 8.6.2.3 Axial compression resistances Design Tables on Section Dimensions, Properties and Resistances for Rolled and Welded Sections
78 82 83 87 89 89 90 91 92 94 94 96 96 96 96 99 – 166
167
References
Appendices Appendix A
Design procedure of a pinned‐pinned column to EN 1993
A1
Appendix B
Design procedures of an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2
B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3
B7
B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded sections using the design method given in Steel Designer’s Manual
B14
B1
Appendix C
Design procedure of a column member under combined axial compression and bending to EN 1993
C1 Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex xiii
C1
Appendix D
Worked examples to BS EN 1993‐1‐1
Part I Section analysis and section resistance
Worked Example I‐1 Determination of section resistances
D1
Worked Example I‐2 Cross section resistance under combined bending and shear force
D7
Worked Example I‐3 Cross section resistance under combined bending and axial force
D9
Part II Member design
Worked Example II‐1 Design of a fully restrained steel beam
D14
Worked Example II‐2
D17
Worked Example II‐3 Design of a steel column under axial compression
D26
Worked Example II‐4 Design of a beam‐column under combined axial compression and bending
D29
Worked Example II‐5 Column in simple construction
D36
Design of an unrestrained steel beam against lateral torsional buckling Solution to Procedure B2 Solution to Procedure B3
xiv
List of tables Table 1.1
Comparison on key symbols
15
Table 1.2
Important changes on terminology
16
Table 1.3
Difference in the notation of axes
16
Table 2.1
Partial factor for actions, F
31
Table 2.2
Values of factors for buildings
31
Table 2.3
Values of factors for bridges
31
Table 3.1a
33
European Steel Materials
Table 3.1b
34
Chinese Steel Materials
Table 3.2
Choice of quality class according to EN 10164
36
Table 4.1
39
Exposure conditions
Table 5.1a
Maximum c/t ratios of compression parts
46
Table 5.1b
Maximum c/t ratios of compression parts
47
Table 5.1c
Maximum c/t ratios of compression parts
48
Table 6.1
Imperfection factors for flexural buckling curves
60
Table 6.2
Selection of flexural buckling curve for a cross‐section
61
Table 6.3
Buckling curves for lateral torsion buckling
64
Table 6.4
Imperfection factors for lateral torsion buckling curves
64
Table 6.5
Selection of buckling curves for rolled sections and equivalent welded sections
65
Table 6.6
Correction factors kc
66
Table 6.7
Values of
1 and C1 for various moment conditions C1
68
(load is not destabilizing )
Table 6.8
Imperfection factors for lateral torsion buckling curves
68
Table 6.9
Recommendations for the selection of lateral torsional buckling curves
69
Table 6.10
Comparison and design procedure of an unrestrained beam to EN 1993‐1‐1
xv
69
Table 7.1
Suggested limits for vertical deflection due to characteristic combination (variable actions only)
76
Table 8.1
Ranges of rolled and welded sections
78
Table 8.2
Summary of design information for rolled sections
80
Table 8.3
Summary of design information for equivalent welded sections
81
Table 8.4
Design strengths of different steel grades of rolled sections Class E1 Steel Materials with Mc 1.0
82
Table 8.5
Design strengths of different steel grades of welded sections Class E2 Steel Materials with Mc 1.1
82
Table 8.6
Section classification rules for I‐ and H‐sections
83
Table 8.7
Limiting ratios of section classification for I‐ and H‐sections
84
Table 8.8
Section classification of hollow sections
85
Table 8.9
Limiting ratios of section classification for hollow sections
86
Table 8.10
Full ranges of typical rolled sections available for application
88
Table 8.11
Allowable corner radii of hot‐finished and cold‐formed RHS and SHS
93
Table 8.12
Corner radii and local residual strains in cold‐formed zones
93
Table 8.13
Proposed corner radii of EWRHS and EWSHS
94
Table 8.14
Full ranges of proposed equivalent welded sections for application
95
Table 8.15
Summary of Design Tables
97
List of figures Figure 1.1
Cross‐sections typical rolled sections and welded sections
4
Figure 1.2
Member buckling curves to BS5950 Part 1
8
Figure 1.3
Member buckling curves to EN 1993‐1‐1
11
Figure 1.4
Member buckling curves to EN 1994‐1‐1
12
Figure 1.5
Strength reduction factors at elevated temperatures
13
Figure 1.6
Harmonized design of member buckling at both normal and elevated temperatures
14
Figure 6.1
Shear areas for various rolled and welded sections [Cl. 6.2.6 (3)]
53
Figure 6.2
Buckling curves for axial compression in members
62
xvi
Figure 6.3
Lateral torsional buckling curves for rolled sections
70
Figure 6.4
Lateral torsional buckling curves for welded sections
70
Figure 8.1
Cross‐sections of typical rolled sections and welded sections
79
Figure 8.2
Design method of equivalent welded I‐sections
89
Figure 8.3
Design method of equivalent welded H‐sections
90
Figure 8.4
Design method for equivalent cold‐formed circular hollow sections
91
Figure 8.5
Design method for equivalent cold‐formed rectangular hollow sections
92
Figure 8.6
Design method for equivalent cold‐formed square hollow sections
92
xvii
Section 1 Adopting Structural Eurocodes (1) The Structural Eurocodes are a new set of European design codes for building and civil engineering works. Conceived and developed over the past 40 years with the combined expertise of the member states of the European Union, they are arguably the most advanced structural codes in the world. The Structural Eurocodes are intended to be mandatory for European public works and likely to become the de‐facto standard for the private sector – both in Europe and world‐wide. The Eurocodes had been available as European pre‐standards (ENVs) for several years, and all of them were published as full European Standards (ENs) in 2007. (2) Owing to the withdrawal of various British structural design standards in March 2010, the Works Department of the Government of Hong Kong SAR has been migrating to the Eurocodes in stages, for the design of public works and civil engineering structures. Mandatory adoption of the Eurocodes will commence in 2015. Since a number of countries outside the European Union, in particular some Asian countries, have already adopted the structural Eurocodes for design and construction of building structures, there is a growing need for design and construction engineers in Hong Kong to acquire the new skills. 1.1 Organization of Eurocodes (1)
A total of 58 parts of the Eurocodes are published under 10 area headings:
(2)
Eurocode 0 – EN 1990: Basis of Structural Design Eurocode 1 – EN 1991: Actions on Structures Eurocode 2 – EN 1992: Design of Concrete Structures Eurocode 3 – EN 1993: Design of Steel Structures Eurocode 4 – EN 1994: Design of Composite Steel and Concrete Structures Eurocode 5 – EN 1995: Design of Timber Structures Eurocode 6 – EN 1996: Design of Masonry Structures Eurocode 7 – EN 1997: Geotechnical Design Eurocode 8 – EN 1998: Design of Structures for Earthquake Resistance Eurocode 9 – EN 1999: Design of Aluminium Structures
It should be noted that i)
the first two areas, namely, EN 1990 and EN 1991, are common to all designs – basis and actions; ii) the other six areas, namely, from EN 1992 to EN 1996 and EN 1999, are material‐ specific – concrete, steel, composite steel and concrete, timber, masonry, aluminum; and iii) the other two areas, namely, EN 1997 and EN 1998, cover geotechnical and seismic aspects. (3)
In order to avoid duplication of design rules as well as problems in updating various parts at different times, one of the prevailing regulations in drafting the Eurocodes is
1
that no design rule should be presented twice within the entire set of the Eurocodes. As a consequence, there is extensive cross‐referencing. 1.2 (1)
Composition of EN 1993 Various parts of EN 1993 are listed follows: Part
1‐1: 1‐2: 1‐3: 1‐4: 1‐5:
1‐6: 1‐7:
1‐8: 1‐9: 1‐10: 1‐11: 1‐12:
General rules and rules for buildings General – Structural fire design General – Cold formed thin gauge members and sheeting General – Structures in stainless steel General – Strength and stability of planar plated structures without transverse loading General – Strength and stability of shell structures General – Design values for plated structures subjected to out of plane loading General – Design of joints General – Fatigue strength General – Material toughness and through thickness assessment General – Design of structures with tension components General – Supplementary rules for high strength steels
Part 2‐1:
Bridges
Part Part
3‐1: 3‐2:
Towers, masts and chimneys – Towers and masts Towers, masts and chimneys – Chimneys
4‐1: 4‐2: 4‐3:
Silos, tanks and pipelines – Silos Silos, tanks and pipelines – Tanks Silos, tanks and pipelines – Pipelines
Part 5:
Piling
Part 6: (2)
1.3 (1)
Crane supporting structures
As indicated by the name, Part 1.1 provides the general rules for structural steel design which are formulated for direct application in building design while the other 11 sections in Part 1 are supplementary to Part 1.1 for application to various steel structures. Owing to the importance of these sections within the Eurocodes, design and construction engineers in Hong Kong need a good understanding of EN 1993‐1‐1 to make the most of the advantages offered by the Eurocodes. Aims and Scope This document provides technical guidance on key design rules for structural steel design for both the rolled and the welded sections given in the Structural Eurocode EN 1993‐1‐1 Design of Steel Structures (2005) and the associated UK National Annex together with relevant non‐contradictory complementary information. Technical
2
information is presented in the context of the local construction industry, and references to prevailing regulations and codes of practice are made whenever necessary. Figure 1.1 illustrates various cross‐sections of typical welded and rolled sections covered in this document. (2)
(3)
All the Nationally Determined Parameters (NDPs) recommended by the Works Bureau of the Government of Hong Kong SAR and provided in the updated design manuals of various government departments have been adopted. These items include load factors, loads, and methods for calculating certain loads, partial safety factors and advice where a choice of design approach is allowed. In general, all the key design rules given in EN 1993‐1‐1 are described and supplemented with explanatory notes in the same sequence as found in the Eurocode:
(4)
General Basis of design Materials - yield strengths Durability Structural analysis Ultimate limit states - resistances of cross‐sections under single actions - resistances of cross‐sections under combined actions - buckling resistances of members under single actions - buckling resistances of members under combined actions Serviceability limit states
In order to illustrate various design procedures for structural design, a total of 8 worked examples with different cross‐section properties and resistances as well as different member buckling resistances are provided. Comprehensive design procedures for the following buckling failure criteria are also provided: i) column members undergoing flexural buckling, ii) beam members undergoing lateral torsional buckling, and iii) beam‐column members undergoing buckling under combined compression and bending Detailed design information and parameters are also presented in tabulated format for easy reference. A complete section together with a total of 45 Design Tables has been compiled to facilitate the practical design of both rolled and welded sections assuming steel materials of different yield strengths.
3
Rolled sections: z z
y
y
H-section
I-section z
z
z
y
y
y
Circular hollow section CHS
Rectangular hollow section RHS
Square hollow section SHS
Welded sections: z z
y
y
Equivalent welded H-section EWH-section
Equivalent welded I-section EWI-section
z
z
z
y
Equivalent cold-formed circular hollow section EWCHS
Figure 1.1
y
Equivalent cold-formed rectangular hollow section EWRHS
y
Equivalent cold-formed square hollow section EWSHS
Cross‐sections of typical rolled and welded sections
4
(5)
A complete section is compiled to facilitate practical design of the following:
Rolled sections of S275 and S355 steel materials rolled I‐ and H‐sections hot‐finished circular, rectangular and square hollow sections
Welded sections of Q235, Q275, Q345 and Q460 steel materials welded I‐ and H‐sections cold‐formed circular, rectangular and square hollow sections
(6)
1.4 (1)
(2)
Hence, rolled sections complying to European steel materials specifications, and welded sections of selected Chinese steel materials have been included for design and construction engineers to use on large scale construction projects in Hong Kong and neighbouring cities. Modern Structural Design Codes Traditionally, a design code is expected to provide all key design requirements and considerations enabling a structural engineer to perform structural design. Proven lower bound design methods are also provided to assist the structural engineer to justify the structural adequacy of a structure in a prescriptive manner, i.e. if a structure is designed and confirmed to satisfy all the design rules, structural adequacy of the structure is deemed to be achieved. However, there is an overriding implicit assumption behind this, i.e. the structure being designed is assumed to behave in an essentially similar fashion to those structures for which the design methods have been developed and derived. While the extreme situation of structural failure would have been prevented, there is little information on how the structure is actually going to behave in relation to some specific requirements, in particular, during serviceability limit states. A review of the organization of many modern structural design codes reveals a typical layout as follows:
a) Materials Material types and manufacturing processes Physical, chemical and mechanical properties Requirements on structural performance
b) Sections and dimensions Typical shapes and sizes, limiting dimensions and scope of applications
c) Cross‐section resistances Cross‐section resistances under single actions Cross‐section resistances under combined actions
d) Member resistances Member resistances under single actions Member resistances under combined actions
5
e) System behaviour
f) Connection design Force analysis methods Basic resistances of fasteners, fixings and connectors Resistances and deformations of joints Detailing rules (3)
(4)
All these topics are considered to be essential for effective control of the design of a structure, and the given layout is considered to be a simple, effective, and structured arrangement to assist a structural engineer to perform his design in a straight forward manner. In practice, the design code is often considered to be a legal document enabling a structural engineer to perform his statutory duty to his client as well as to the regulatory authority. Consequently, the design clauses in the code are often written and compiled adopting a prescriptive approach, i.e. everything is spelled out with every use cautioned and every limit defined. However, while most of the design clauses are well controlled, there are occasions when the design becomes grossly conservative or things become unnecessarily complicated when interpretation between the lines of the design clauses is required, or the design lies outside the intended use of the design clauses. Hence, the prescriptive approach is generally considered to be restrictive, and little information is provided once the limits of the design clauses are crossed. Moreover, it is generally difficult to know how efficient the design is.
1.4.1 Modern design approach (1) With recent advances in development of structural design codes, the performance‐ based approach should be considered a major advance which enables the rational design and analysis of structural behaviour against well‐defined requirements at specific levels of acceptability. This approach is commonly adopted in seismic design as well as in fire resistant design of building structures and bridges whilst the levels of structural responses and acceptability are explicitly defined for specific structures. It is obvious that adopting effective performance‐based design requires a high level of understanding of the structural behaviour and the responses of structures. Hence, the structural examination of selected critical members is, in general, insufficient, and it is necessary to perform a numerical simulation of the structural behaviour of the entire structure under specific performance requirements. Supplementary member checks may be carried out, whenever necessary. (2) Ideally, a design method in a modern design code should be formulated in such a way that a structural engineer is able to perform the design while understanding the underlying principles when working through the design procedures. Moreover, the design procedures should be complied with in a fashion that enables the structural engineer to compromise on the calculation efforts he is prepared to make against the structural accuracy and economy of the structure. He should be able to decide
6
whether it is sufficient to adopt simple and yet conservative data, or if it is necessary to evaluate specific design parameters precisely, depending on the situation he is dealing with. When the structural engineer is making choices and decisions as the design proceeds, he is able to control the design rationally, i.e. to engineer not just the final product, but also the design process. 1.5 (1)
Harmonized Design Rules It is interesting to review the development of a number of national steel codes, and to examine some of the design methods and clauses which have evolved over the years; an illustration based on the checking of member buckling is given below. It concerns the use of the ‘slenderness’ parameter of a member, which is derived from elastic buckling theory, to facilitate simple and direct evaluation of member resistances for steel columns and beams as well as steel‐concrete composite columns.
1.5.1 Member buckling check for hot‐rolled steel sections (1) Consider the member buckling check in the British Steel Code BS5950 published by the British Standards Institution (2000) and the “Code of Practice for the Structural Use of Steel” published by the Buildings Department of the Government of Hong Kong SAR (2011). For a column susceptible to axial buckling, the slenderness of the column, λ, has been established for many years, and is defined as follows:
LE ry
(1.1)
where L E is the effective length of the column, depending on its boundary conditions; and ry is the radius of gyration of the cross‐section of the column, a function of its cross‐section geometry.
(2)
(3)
It should be noted that λ is an important structural parameter of a column and is a direct measure of the tendency of the column to undergo elastic buckling. Through a non‐linear interaction curve, which is commonly referred as the Perry‐Robertson formula, the effect of axial buckling in a real column is expressed as a reduction in its design strength from its yield value, i.e. its compressive strength. The compressive strength of a real column with material and geometrical initial imperfections is readily obtained using a specific column buckling curve after considering material yielding and geometrical instability. It should be noted that based on section shapes and sizes as well as bending axes during buckling, the value of the imperfection parameter, α , is determined after careful calibration against test data. Thus, a total of four column buckling curves are established, and they are plotted onto the same graph as shown in Figure 1.2a). For columns with welded sections made of thick steel plates, the design methodology is the same although the design yield strengths of the columns should be reduced by 20 N/mm2 to allow for the presence of
7
high residual stresses due to welding. 250
a= 3.5 a= 5.5
200
a= 8.0 150
100
50
0
20
40
60
80
100
120
140
160
180
200
140
160
180
200
Slenderness ratio, λ
a) Column buckling curves
300
250
a= 7.0
200
150
100
50
0 0
20
40
60
80
100
120
Equivalent slenderness ratio,LT
b) Beam buckling curve Figure 1.2
(4)
Design strength, py = 275 N/mm2
a= 2.0
0
Bending strength, p b Compressive
Compressive strength, p Compressive
300
Member buckling curves to BS5950 Part 1
For a beam susceptible to lateral buckling, an equivalent slenderness of the beam, LT , is devised and defined as follows:
LT
u v
(1.2)
where u and v
are secondary section properties of the beam related to lateral bending and torsion.
8
(5)
(6)
(7)
The adoption of the equivalent slenderness beam parameter is a good example of harmonized codification, and both design parameters, u and v, may be considered as correction factors which enable the lateral buckling check of a beam to be performed in a way similar to the axial buckling check of a column. Hence, the effect of lateral buckling in a real beam is expressed as a reduction in its design strength from its yield value, i.e. its bending strength. The bending strength of a real beam with material and geometrical initial imperfections is readily obtained after considering material yielding and geometrical instability, as shown in Figure 1.2b). It should be noted that in BS5950, there is only one beam buckling curve while different design coefficients are adopted for rolled and welded beam sections in calculating various parameters. For standardized steel sections, tabulated values of u and v are readily found in section dimensions and properties tables. Hence, it is demonstrated that in buckling checks of both columns and beams, the design methods are considered to be highly structured and rational, and all design parameters and coefficients are derived explicitly with analytical formulation. However, it should be noted that the structural adequacy and economy of the design methods often hinge on one single value, the effective length of the member. Up to the very present, there is still little or no effective means of examining the buckling behaviour of a particular member in a structure except through advanced finite element modelling, and the determination of the effective length of the member, and hence, the member slenderness, remains, otherwise, largely empirical.
1.5.2 Member buckling check using normalized slenderness (1) It is interesting to note that the harmonized design checks for both axial and lateral buckling of steel members given in BS5950 have been adopted in EN 1993‐1‐1 (2005) with a different formulation. The design rules are re‐formulated in such a way that the effect of member buckling in real steel columns and beams are expressed as a reduction to the resistances of the cross‐sections, i.e. a strength reduction factor, multiplied by the axial compression resistances of the cross‐sections of the column members, and a strength reduction factor, b multiplied by the moment resistances of the cross‐sections of the beam members respectively. (2)
Moreover, modified slenderness ratios are adopted, which are defined as follows:
N c,Rd or for axial or flexural buckling of columns N cr 1
(1.3)
and
LT
M c,Rd LT or for lateral buckling of beams M cr 1
where
9
(1.4)
1
is a material parameter given by:
=
E
is the elastic modulus of steel; is the yield strength of steel;
N c,Rd is the design axial resistance of the column;
fy
Ncr
E fy
is the elastic critical buckling resistance of the column; EI = 2 2 L cr is the second moment of area of the cross‐section of the column; is the buckling length;
I L cr
M c ,Rd is the design moment resistance of the beam; and
(3)
M cr is the elastic critical buckling moment resistance of the beam
(4)
It should be noted that the modified slenderness ratio, , is defined either as a ratio of the geometrical slenderness to the material parameter of the member, or a ratio of the square root of the ratio of the cross‐sectional axial resistance of the member to its corresponding elastic critical buckling resistance. Hence, the design methods are “normalized” against the mechanical properties of the members, and they are equally applicable to other materials, such as other metal and timber members, provided that calibration against geometrical and mechanical initial imperfections has been performed. As shown in Figure 1.3, there are five different buckling curves for columns and four for beams. The selection on the imperfection parameter, α , depends on section types and sizes as well as bending axes, if applicable.
10
Strength reduction factor, χ Compressive
1.2
α = 0.13
1.0
α = 0.21 0.8
α = 0.34 α = 0.49
0.6
α = 0.76 0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
1.75
2.00
Slenderness ratio, LT a) Column buckling curves
1.2
Compressive
Strength reduction factor, χLT
1.0
α = 0.21 α = 0.34
0.8
α = 0.49 0.6
α = 0.76
0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
Equivalent slenderness ratio, LT b) Beam buckling curves
Figure 1.3 Member buckling curves to EN 1993‐1‐1 1.5.3 Member buckling check for composite columns (1) For composite columns of concrete encased H sections or concrete in‐filled hollow sections, the same design methodology has been adopted in EN 1994‐1‐1 (2004), and the axial buckling resistances of the composite columns are based on the modified slenderness ratio which is defined as follows:
N pl,Rd N cr
for axial or flexural buckling of columns
11
(1.5)
where
N pl,Rd is the design plastic resistance of the composite column, which is equal to the
Ncr
sum of the section capacities of the individual components: concrete core, steel section and steel reinforcement; is the elastic axial buckling resistance of the composite column;
= 2
EIeff is the effective flexural rigidity of the composite column, which is equal to the
sum of the effective flexural rigidities of the individual components: concrete core, steel section and steel reinforcement; and is the buckling length.
L cr
(2)
(3)
L2cr
1.2
1.0
Strength reduction factor, Compressive
EI eff
α = 0.21 α = 0.34
0.8
α = 0.49 0.6
0.4
0.2
0.0 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Slenderness ratio,
Figure 1.4 Member buckling curves to EN 1994‐1‐1 Hence, the effect of axial buckling in real composite columns is expressed as a strength reduction to the resistances of the cross‐sections of the column members, i.e. a strength reduction factor, χ , multiplied by the compression resistances of the cross‐ sections of the composite columns. As shown in Figure 1.4, there are three different column buckling curves. The selection depends on section types as well as bending axes, if applicable. Consequently, it is demonstrated that by adopting the same design methodology, i.e. the slenderness ratio of a member or its associated resistance ratio, the effect of buckling is readily expressed as a strength reduction factor multiplied by the resistance of the cross‐section of the member. The same methodology is shown to be highly satisfactory in steel beams and columns as well as composite columns. Moreover, the adoption of different buckling curves enables wide coverage of the many cross‐ sections of different shapes and sizes as well as bending axes.
12
1.5.4 Member buckling check for steel and composite columns at elevated temperatures (1) It should be noted that based on rigorous material tests of a number of constructional materials at elevated temperatures, various sets of strength reduction factors are given in EN 1993‐1‐2 (2005) and EN1994‐1‐2 (2005) for general use. Figure 1.5 plots these factors for different constructional materials for easy reference. It is interesting to note that all of these materials retain only 50% of their original strengths when their temperatures reach 500 to 600 oC. 1.1 Profiled steel decking (EN)
1.0
Reinforcement
Reduction factor
0.9
Structural steel
0.8
Normal weight concrete (NWC)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
100
200
300
400
500
600
700
800
900 1000 1100 1200
Temperature ( )
Figure 1.5 (2)
(3)
Strength reduction factors at elevated temperatures
Based on a known temperature distribution within a structural member obtained either from fire tests or numerical heat transfer analyses, the resistance of the member at elevated temperatures may be readily evaluated according to EN 1993‐1‐2 and EN 1994‐1‐2. A flow chart of various design procedures on steel beams and columns as well as composite columns at both normal and elevated temperatures is provided in Figure 1.6 to facilitate the use of these design procedures in practical design. Owing to the effective design development of member buckling in the Structural Eurocodes, the normalized slenderness ratios of steel beams and columns as well as composite columns are shown to be effective in determining corresponding strength reduction factors due to member buckling, as shown in Figure 1.6. Moreover, the same design formulation for member buckling design of various types of structural members is readily used at both normal and elevated temperatures with parameters having different values according to the materials of the members.
13
Design procedures
Key design parameters Normal temperatures
Elevated temperatures
1. Evaluate both the design and the characteristic resistances.
a. Steel column:
Ncr & N pl ,Rd
N fi , ,cr & N fi , ,Rd
b. Steel beam:
Not applicable
Not applicable
c. Composite column:
Ncr & N pl ,Rd
N fi , ,cr & N fi , ,Rd
2. Evaluate various structural parameters.
a. Steel column:
-
,
b. Steel beam:
-
,
c. Composite column:
(EI)eff
(EI)fi,eff
3. Evaluate the non‐ dimensional slenderness.
a. Steel column:
a. Steel column: b. Steel beam: c. Composite column:
5. Evaluate the buckling resistance.
b. Steel beam: c. Composite column:
4. Determine the imperfection factor and the reduction factor.
& & &
& &
&
a. Steel column: b. Steel beam: c. Composite column:
Figure 1.6 Harmonized design of member buckling at both normal and elevated temperatures
14
1.6 (1)
(2)
Symbols and Terminology The Eurocode system for symbols generally adopts a common notation for the principal variables. Differentiation between related variables, such as axial force and compression resistance, is achieved by the use of subscripts. Multiple subscripts are used where necessary, for example to distinguish between design bending resistances about the y‐y and the z‐z axes; each component is separated by a comma. In general, the Eurocode system for symbols is particular and precise, being effective in providing clarity and avoiding ambiguity. In general, symbols are defined where they are used within the text. A list of the most common symbols used is given in Clause 1.6 of EN 1993‐1‐1 for easy reference. Table 1.1 presents a comparison of some of the key symbols adopted in the U.K. and Hong Kong to those adopted in EN 1993‐1‐1. Table 1.1
Comparison of key symbols
U.K. and Hong Kong
EN 1993‐1‐1
U.K. and Hong Kong
EN 1993‐1‐1
A
A
P
N
Z
Wel
Mx
My
S
Wpl
V
V
Ix
Iy
H
Iw
Iy
Iz
J
It
U.K. and Hong Kong
EN 1993‐1‐1
py
fy
pb
LT f y
pc
fy
r
i
(3)
In this document, a dot is used as the decimal separator, in line with the existing U.K. and Hong Kong practice. However, it should be noted that the Eurocodes themselves use a comma as the separator.
15
(4)
1.7 (1) (2)
The Eurocodes contain alternative terms to those familiar to the U.K. and Hong Kong designers, and some important changes are summarized in Table 1.2. Table 1.2
Important changes on terminology
U.K. and Hong Kong terms
Eurocode terms
Loads
Actions
Dead load
Permanent action
Imposed or live load; wind load
Variable action
Ultimate loads
Design value of actions
Check
Verification
Internal forces and bending moments which result from the application of the actions
Effects of actions
Capacity, or Resistance
Resistance
Second‐order effects
Effects of deformed geometry
Conventions for Member Axes The convention for member axes is: x – x axis y – y axis z – z axis
along a member major axis of a cross‐section minor axis of a cross‐section
For typical I‐ and H‐sections and structural hollow sections, the convention used for cross‐section axes are: y – y axis z – z axis
major axis of the cross‐section which is parallel to the flanges minor axis of the cross‐section which is perpendicular to the flanges
The cross‐section axes of typical sections are illustrated in Figure 1.1. Table 1.3 summarizes the differences in the notation of the axes in both members and cross‐ sections. Table 1.3 Difference in the notation of axes
U.K. and Hong Kong
Eurocodes
X (?)
X
Major axis of a cross‐section
X
Y
Minor axis of a cross‐section
Y
Z
Longitudinal axis along the member
16
1.8 (1) (2)
Format All the clauses and paragraphs in this document are numbered consecutively. In the Eurocodes, a distinction is made between Principles and Application Rules: i. Principles are identified by the letter P following the paragraph number. ii. Application Rules are generally recognized rules which comply with the Principles and satisfy their requirements.
1.9 (1)
This distinction is retained in this document. Equivalent Steel Materials For many years, almost all steel structures in Hong Kong were designed to the British structural steel design code, BS5950, and all the steel materials were specified correspondingly to the British steel materials specifications such as BS4360. However, as early as the 1990s, non‐British steel materials found their way to Hong Kong as well as Singapore and other neighbouring cities in Southeast Asia. Occasionally, contractors wanted to use non‐British steel materials, such as Japanese, Australian and Chinese steel materials. The proposed changes ranged from merely adopting such materials for some members of temporary structures to their use for complete beam‐column frames of building structures. Over the years, many successful projects were reported in Hong Kong which benefited from good quality non‐British steel materials, timely supply and delivery as well as improved structural economy. However, there were also a few bad examples of the use of non‐British steel materials having inconsistent chemical compositions, inadequate mechanical properties and lack of traceability.
(2)
In the 2000s, owing to large fluctuations in the costs of steel materials on the global markets, Chinese steel materials became practical alternatives to British steel materials in a number of construction projects in Asia, in particular, in Hong Kong, Macau and Singapore. During the drafting of the “Code of Practice for the Structural Use of Steel” for the Buildings Department of the Government of Hong Kong SAR from February 2003 to August 2005, it was decided necessary to devise a means to allow, or more accurately, to formalize the use of Chinese steel materials as equivalent steel materials for structures which were originally designed to BS5950. Various parts of Section 3 of the Hong Kong Steel Code provide basic principles and considerations for accepting, as well as qualifying, steel materials manufactured to the following national materials specifications:
Australian / New Zealand standards, Chinese standards, Japanese standards, and American standards.
A practical classification system for non‐British steel materials is introduced in the Code
17
in which the design strengths of these non‐British steel materials depend on a newly defined factor, namely, the material class factor, γ Mc . (3)
(4)
(5)
Similar use of non‐British steel materials was also formally adopted in Singapore with the issue of a technical guide entitled “Design Guide on Use of Alternative Steel Materials to BS5950” in 2008, and then its revised version entitled “Design Guide on Use of Alternative Structural Steel to BS5950 and Eurocode 3” by the Building and Construction Authority of the Ministry of National Development. These Design Guides aimed to provide technical guidelines and design information on the use of non‐British steel materials, and the classification system for various steel materials given in the “Code of Practice for the Structural Use of Steel” was adopted after modification. Under the provisions of these Design Guides, alternative steel materials not manufactured to British and European steel materials standards may be allowed in structural design based on the Structural Eurocodes for construction projects in Singapore. In 2014, the use of non‐British steel materials in Hong Kong, Singapore and other neighbouring cities in Asia was further promoted through the publication of a Professional Guide on “Selection of Equivalent Steel Materials to European Steel Materials Specifications” (Publication CMSA‐PG01). The Professional Guide is jointly published by the Hong Kong Constructional Metal Structures, Macau Society of Metal Structures and Chinese National Engineering Research Centre for Steel Construction. It presents essential technical guidance to design and construction engineers as well as engineers from regulatory authorities on the selection of steel materials equivalent to material requirements specified in the European steel materials specifications. Through the use of the Professional Guide, selected steel materials manufactured to the modern materials specifications of Australia/New Zealand, China, Japan, and the United States of America are fully endorsed to be equivalent to steel materials manufactured to the European steel materials specifications, provided that all of these steel materials have been demonstrated to be in full compliance with the requirements of both material performance and quality control as detailed in the Professional Guide. Consequently, these equivalent steel materials can be readily employed on construction projects for which the structural steelwork is designed to EN 1993 and EN 1994. Given a satisfactory demonstration of both the material performance and the quality assurance procedures adopted during their manufacturing processes, steel materials with yield strengths from 235 to 690 N/mm2 are classified as follows:
18
Class E1 Steel Materials with γ Mc = 1.0
Steel materials which are
i) manufactured in accordance with one of the Acceptable Materials Specifications listed in Appendix A of the Professional Guide with a fully demonstrated compliance on their material performance, and
ii) manufactured in accordance with an Acceptable Quality Assurance System with full demonstration of effective implementation.
Thus, compliance with all the material requirements has been demonstrated through intensive routine testing conducted during the effective implementation of a certificated Factory Production Control system which accords with European steel materials specifications. The Factory Production Control System must be certified by an independent qualified certification body.
Class E2 Steel Materials with γ Mc = 1.1
Steel materials which are
i) manufactured in accordance with one of the Acceptable Materials Specifications listed in Appendix A of the Professional Guide with a fully demonstrated compliance on their material performance, and
ii) manufactured in accordance with an effectively implemented quality assurance system which is different to a Factory Control Production System.
Thus, the steel materials are manufactured in accordance with all the material requirements given in one of the Acceptable Materials Specifications, but without a certified Factory Production Control System which accords with European steel materials specifications.
In general, although many steel manufacturers will have already established a form of quality assurance during the manufacturing processes, the high level of consistency in the material performance of the steel materials required in European steel materials specifications cannot be verified in the absence of a certified Factory Production Control System. Hence, a demonstration of the conformity of the steel materials is required, and additional material tests with sufficient sampling should be conducted for various batches of supply to demonstrate full compliance with both the material performance and the quality assurance requirements.
Class E3 Steel Materials
Steel materials for which they cannot be demonstrated they were
i) manufactured in accordance with any of the Acceptable Materials Specifications listed in Appendix A; nor
ii) manufactured in accordance with an Acceptable Quality Assurance System.
Hence, any steel material which cannot be demonstrated to be either Class E1 Steel Material or Class E2 Steel Material will be classified as Class E3 Steel Material, and the nominal value of yield strength of the steel material is limited to 170 N/mm2 for
19
structural design; no additional material test is needed in general. However, the design yield strength of the steel material may be increased if additional material tests with sufficient sampling have been conducted for various batches of supply before use.
(6)
For details of specific requirements on material performance and quality assurance, refer to the Professional Guide. Also refer to Section 3.2.3 of the Professional Guide for details of additional materials tests. Table 1.4 summarizes the classification system applying to the various classes of steel materials.
Table 1.4
(7)
Nominal yield strength (N/mm2) ≥ 235 and ≤ 690
Classification system for various classes of steel materials Class
Material class factor, MC for minimum ultimate yield tensile strength, strength, ReH Rm
Compliance with material performance requirements
Compliance with quality assurance requirements
Additional material tests
E1
Y
Y
N
1.0
1.0
E2
Y
N
Y
1.1
1.1
E3
N
N
N
‐‐‐
‐‐‐
A newly defined factor, namely, the material class factor, MC , is adopted as a result of the classification, and hence, the nominal values of the yield strength and of the ultimate tensile strength of the equivalent steel materials are given as follows:
Nominal value of yield strength
fy
=
ReH / MC
(6a)
(6b)
Nominal value of ultimate tensile strength
fu
=
Rm / MC
where ReH Rm MC
is the minimum yield strength to product standards; is the ultimate tensile strength to product standards; and is the material class factor given in Table 1.4.
It should be noted that
a) Plastic analysis and design is permitted for Classes E1 and E2 Steel Materials assuming yield strengths not larger than 460 N/mm2.
20
b) For Classes E1 and E2 Steel Materials with yield strengths larger than 460 N/mm2 but smaller than or equal to 690 N/mm2, design rules given in EN 1993‐1‐12 should be used.
c) Only elastic analysis and design should be used for Class E3 Steel Materials.
21
Section 2 Basis of Structural Design This Section presents the key principles as well as the relevant application rules in EN 1990 that relate to the design of steel structures together with specific requirements given in EN 1993‐1‐1. These include specific rules on basic requirements, reliability management, principles of limit state design, partial factor method as well as combinations of action. It is important to be familiar with the various terminologies and mathematical formats of the expressions, formulae and equations adopted in the Eurocodes. 2.1 General Requirements Design of a structure requires the demonstration of structural adequacy under various effects of actions in extreme events, i.e. the ultimate limit state, and of full compliance against various requirements in deformation, vibration and durability during its intended life, i.e. serviceability limit states. 2.1.1 Basic requirements (1)P A structure shall be designed and executed in such a way that during its intended life, with appropriate degrees of reliability and in an economical way, it will sustain all actions likely to occur during execution and use, and meet specified serviceability requirements. (2)P A structure shall be designed to have adequate structural resistance, serviceability and durability. (3)P In the case of fire, the structural resistance shall be adequate for the required period of time. (4)P A structure shall be designed and executed in such a way that it will not be damaged by events such as explosion, impact, and consequences of human errors, to an extent disproportionate to the original cause. (5)P Potential damage shall be avoided or limited by appropriate choice of one or more of the following: – avoiding, eliminating or reducing the hazards to which the structure can be subjected; – selecting a structural form which has low sensitivity to the hazards considered; – selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage; – avoiding structural systems that can collapse without warning; – tying structural members together.
22
(6)
The basic requirements should be met by the use of appropriate materials, design and detailing, and quality control.
2.1.2 Reliability management (1)P The reliability required for structures within the scope of EN 1990 shall be achieved by: a) design in accordance with EN 1990 to EN 1999, and b) appropriate execution and quality management measures. (2) Different levels of reliability may be adopted, among other things: – for structural resistance; – for serviceability. (3) The choice of the levels of reliability for a particular structure should take account of various relevant factors, including: –possible cause and mode of attaining a limit state; – possible consequences of failure in terms of risk to life, injury, potential economical losses; – public aversion to failure; –expenses and procedures necessary to reduce the risk of failure. (4) The levels of reliability that apply to a particular structure may be specified in one or both of the following ways: ‐ by classification of the whole structure; ‐ by classification of its individual components. (5) The levels of reliability relating to structural resistance and serviceability can be achieved by suitable combinations of: a) preventative protective measures; b) measures relating to design calculations: ‐ representative values of actions; ‐ choice of partial factors; c) measures relating to quality management; d) measures aimed to reduce errors in design and execution of the structure, and gross human errors e) other measures relating to the following design matters: ‐ basic requirements; ‐ degree of robustness (structural integrity) ‐ durability, including the choice of the design working life; ‐ extent and quality of preliminary investigations of soils and possible environmental influences ‐ accuracy of mechanical models; ‐ detailing
23
(6)
(7) (8)
f) efficient execution, e.g. in accordance with the execution standards referred to in EN 1991 to EN 1999. g) adequate inspection and maintenance according procedures specified in the project documentation. The measures to prevent potential causes of failure and to reduce their consequences may, in appropriate circumstances, be interchanged to a limited extent provided that the required reliability levels are maintained. The level of reliability should be achieved by the use of appropriate quality management in design and execution. In general, execution should be performed in accordance with EN 1090‐2, and execution class EXC2 should be specified. EN 1090‐2 gives 4 classes of requirements for execution of the structure as a whole or for components of a structure, namely, Classes EXC1 to EXC4, with increasing strictness requirements. For common buildings and structures, Class EXC2 for the whole structure is normally considered to be sufficient.
2.1.3 Design working life (1) Common building structures should be designed for a working life of at least 50 years. In general, 50 years is the normal design working life for building structures, and this is implicitly adopted in the usual characteristic values of actions selected together with the various associated partial factors of safety. 2.2 Principles of Limit State Design (1) The resistances of cross‐sections and members specified in this document for the ultimate limit states as defined in Section 3.3 of EN 1991‐1‐3 are based on tests in which the steel materials exhibited sufficient ductility to allow to application of simplified design methods. Various design situations are introduced which should be considered for design against both ultimate and serviceability limit states. 2.2.1 Design situations (1)P The relevant design situations shall be selected taking into account the circumstances under which the structure is required to fulfill its function.
24
(2)P
Design situations shall be classified as follows: Persistent design situations Transient design situations Accidental design situations Seismic design situations
‐ ‐ ‐ ‐
normal conditions of use temporary conditions applicable to the structure exceptional conditions applicable to the structure or to its exposure, e.g. to fire, explosion, impact or the consequences of localised failure conditions applicable to the structure when subjected to seismic events
In general, the persistent design situation is the most common in practice while transient design situations occur during the construction stages as well as during renovation and refurbishment. (3)P The selected design situations shall be sufficiently severe and varied so as to encompass all conditions that can reasonably be foreseen to occur during the execution as well as the use of the structure. 2.2.2 Ultimate limit states (1)P The limit states that concern the safety of people and the safety of the structure shall be classified as ultimate limit states. (2) In some circumstances, the limit states that concern the protection of the contents should be classified as ultimate limit states. (3) States prior to structural collapse, which, for simplicity, are considered in place of the collapse itself, may be treated as ultimate limit states. (4)P The following ultimate limit states shall be verified where they are relevant: – loss of equilibrium of the structure or any part of it, considered as a rigid body; – failure by excessive deformation, transformation of the structure or any part of it into a mechanism, rupture, loss of stability of the structure, or any part of it, including supports and foundations; – failure caused by fatigue or other time‐dependent effects. Different sets of partial factors are associated with the various ultimate limit states. 2.2.3 Serviceability limit states (1)P The limit states that concern the functioning of a structure or its structural members under normal use, comfort of people, and deformation of construction works (leading to extensive cracking) shall be classified as serviceability limit states.
25
(2)P A distinction shall be made between reversible and irreversible serviceability limit states. (3) Verification of serviceability limit states should be based on criteria concerning the following aspects: a) deformations that affect – appearance, – comfort of users, or – functioning of the structure (including functioning of machines or services), or that cause damages to finishes or non‐structural members; b) vibrations that adversely affect – comfort to people, or – functional effectiveness of the structure; c) damages that are likely to adversely affect – appearance, – durability, or – functioning of the structure. 2.3 Basic Variables and Limit State Design 2.3.1 Actions and environmental influences (1) Actions for the design of steel structures should be taken from EN 1991. For the combination of actions and partial factors of actions, refer to Annex A to EN 1990. (2) The actions to be considered in the erection stage should be obtained from EN 1991‐ 1‐6. (3) Where the effects of predicted absolute and differential settlements need to be considered, best estimates of imposed deformations should be used. 2.3.2 Material and product properties (1) Material properties for steels and other construction products and the geometrical data to be used for design should be those specified in the relevant ENs, ETAGs or ETAs unless otherwise indicated in this document.
26
2.3.3 Limit state design (1)P Design for limit states shall be based on the use of structural and load models for relevant limit states. (2)P It shall be verified that no limit state is exceeded when relevant design values for – actions, – material properties, or – product properties, and – geometrical data are used in these models. (3)P Verifications shall be carried out for all relevant design situations and load cases. (4) The requirements of Clause (1)P above should be achieved by the partial factor method described in Clause 2.4 Verification by Partial Factor Method. (5) As an alternative, a design directly based on probabilistic methods may be used. (6)P The selected design situations shall be considered and critical load cases identified. (7) For a particular verification, load cases should be selected, identifying compatible load arrangements, sets of deformations and imperfections that should be considered simultaneously with fixed variable and permanent actions. (8)P Possible deviations from assumed directions or positions of actions shall be taken into account. (9) Structural and load models can be either physical models or mathematical models. 2.4 Verification by Partial Factor Method 2.4.1 Design values (1) The design value Fd of an action F is expressed as:
Fd F Fk
where F Fk
(2.1)
is a partial factor for the action F; is the combination factor and is equal to 1.0 for permanent actions, or to 0 1 , or 2 for variable actions; and , is the characteristic value of the action, F.
27
(2)
In general, the design value of an action is usually expressed as F Fk rather than Fd for clarity. Moreover, permanent and variable actions are distinguished symbolically by the use of G k for permanent actions and Q k for variable actions, i.e. G G k and Q Q k respectively. The design value X d of a material property is expressed as: X Xd k M where X k is a characteristic value of the material; and M is a partial factor for a material property.
(2.2)
In general, the design value of a material property is usually expressed as
Xk rather M
than X d for clarity. (3)
Geometrical data for cross‐sections and systems may be taken from product standards hEN or drawings for the execution to EN 1090 and treated as nominal values.
Design values of geometrical imperfections specified in this document are equivalent geometric imperfections that take into account the effects of: ‐ geometrical imperfections of members as governed by geometrical tolerances in product standards or the execution standard; ‐ structural imperfections due to fabrication and erection; ‐ residual stresses; and ‐ variation of yield strengths (4)
The design value of resistance is expressed as a function of the design value of a material property and a geometrical data: X R d R k ;a (2.3a) M where a
is the geometric parameter.
Alternatively, the design resistance may be obtained directly from the characteristic value of a material by: R (2.3b) Rd k M where Rk is the characteristic value of the particular resistance determined with characteristic or nominal values for the material properties and dimensions; and M is the global partial factor for the particular resistance.
28
2.4.2 Ultimate limit states (1)P The following ultimate limit states of a structure shall be verified: EQU Loss of static equilibrium of the structure or any part of it considered as a rigid body. STR Failure or excessive deformation of the structure or its structural members including supports where the strength of the structural material governs. GEO Failure or excessive deformation of the ground where the strengths of soils or rocks are significant in providing resistances. FAT Fatigue failure of the structure or its structural members. In general, the STR limit state is the only limit state that needs to be considered. (2)P When considering a limit state of rupture or excessive deformation of a section, a member or a connection, i.e. STR limit state, it shall be verified that: Ed R d (2.4) where E d is the design value of the effect of actions such as internal force, moment or a vector representing several internal forces or moments; and R d is the design value of the corresponding resistance. 2.4.3 Combination of actions at ULS 2.4.3.1 General (1) For each design situation, the design values of the effects of the actions should be determined from the combination of the actions that may occur simultaneously. (2) Each combination of actions should include a leading or main variable action, or an accidental action. 2.4.3.2 Persistent or transient design situations (1) The combination of effects of actions to be considered should be based on: the design value of the leading variable action, and the design combination values of the accompanying variable actions.
29
j1
G k , j "" P P "" Q ,1 0,1Q k ,1 ""
G, j
i 1
Q ,i
0,i Q k ,i (2.5) [Eqn. 6.10 of EN 1990]
i 1
Q ,i
0,i Q k ,i (2.5a) [Eqn. 6.10a of EN 1990]
G k , j "" P P "" Q ,1Q k ,1"" Q ,i 0,i Q k ,i
j G, j
j1
or alternatively, for the STR limit state, the less favourable of the two following expressions:
j1
G k , j "" P P "" Q ,1Q k ,1 ""
G, j
(2.5b) [Eqn. 6.10b of EN 1990]
i 1
where “+” implies “to be combined with”; implies “the combined effect of”; G k , j are the characteristic values of the permanent actions;
Q k ,1 is the characteristic value of one of the variable actions; Q k ,i are the characteristic values of the other variable actions;
G, j is the partial factor for the permanent action G k , j ; Q,i is the partial factor for the variable action Q k ,i ; 0,i is the 0 factor for the combination value of the variable action Q k ,i ;
(3)
j
is a reduction factor applied to unfavorable permanent actions (in
Expression 6.10b of EN 1990); = 0.925 according to NA of EN 1990.
v According to the Eurocodes approach, it is necessary to apply all variable actions to the structure under consideration to examine the effects of actions on the structure. It should be noted that each variable action is in turn considered as the “leading” variable action while all the other variable actions are applied correspondingly with each of them multiplied by a relevant factor. It is thought that Expression (6.10) of EN 1990 gives a quick, but conservative approach when compared to Expressions (6.10a) and (6.10b) of EN 1990, which are slightly more involved. In general, it is expected that Expression (6.10b) of EN 1990 will normally be the governing case.
The partial factors to be used in the combination of actions and the factors on accompanying actions are given in Table 2.1 which are extracted from Tables N.A.A1.2(a) and N.A.A1.2(b) of UK NA to EN 1990 and modified accordingly to local practice. The corresponding partial factors for buildings and bridges are also presented in Tables 2.2 and 2.3 for easy reference.
30
Table 2.1 Partial factors for actions, F
Ultimate Limit State EQU STR
Buildings Permanent Actions Leading or Main G, j Variable Action Q,1 Unfavorable Favorable 1.40 1.40
1.00 1.00
Accompanying Variable Action Q,i
1.60 1.60
1.60 1.60
Civil engineering works Permanent Leading or Main Traffic Actions Rail Wind Actions Variable Action Traffic (gr1a, gr1b, Ultimate Actions G, j Q,1 Actions gr2, gr3, gr4, Limit State gr5, gr6) Unfavorable Favorable EQU 1.05 0.95 1.35 To be agreed 2.10 STR 1.35 0.95 1.35 To be agreed 2.10 Note: When variable actions are favourable, Q k should be taken as zero. For building structures, reference should be made to “Code of Practices for the Structural Use of Steel 2011” for the detailed design values of actions. For civil engineering works, reference should be made to “Structures Design Manual for Highways and Railways 2013” for the detailed design values of actions.
Table 2.2 Values of factors for buildings Action Permanent actions + General variable actions Permanent actions + Equivalent horizontal actions Permanent actions + Wind actions + General variable actions Temperature (non‐fire) in buildings
0 0.875 0.875 0.75 0.75
1 0.75 0.75 0.75 0.75
2 0.75 0.75 0.75 0.75
1
2
a
On roofs, imposed loads should not be combined with wind loads.
Table 2.3 Values of factors for bridges 0
Action
Imposed loads in buildings, category (see “Structures Design Manual for Highways and Railways”) Traffic loads gr1a: TS, UDL 0.75 0.75 0.0 Traffic loads gr1b: Single axle 0.00 0.75 0.0 Traffic loads gr2: Horizontal forces 0.00 0.00 0.0 Traffic loads gr3: Pedestrain loads 0.00 0.40 0.0 Traffic loads gr4: Crowd loading 0.00 ‐ 0.0 Traffic loads gr5: Vertical forces from SV and SOV vehicles 0.00 ‐ 0.0 Traffic loads gr6: Horizontal forces from SV and SOV vehicles 0.00 0.00 0.0
Wind loads: Permanent design situation Wind loads: During erection Thermal actions
0.50 1.00 0.60
31
0.20 ‐ 0.60
0.0 0.0 0.50
2.4.4 Serviceability limit states (1)P It shall be verified that:
Ed Cd
(2.6)
where E d is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination; and C d is the limiting design value of the relevant combination. As the partial factors for actions F are implicitly taken as 1.0, they are therefore not shown in the expressions for the effects of actions for clarity.
2.4.5 Combination of actions for SLS (1) The combinations of actions for serviceability limit states are: Characteristic applicable for irreversible limit states; Frequent applicable for reversible limit states; and Quasi‐permanent applicable for long‐term effects and the appearance of the structure. (2) The expressions for the effects due to the combinations of actions are: Characteristic combination
G j1
k, j
"" P "" Q k ,1 ""
Frequent combination
G j1
k, j
i 1
"" P "" 1,1Q k ,1 ""
Quasi‐permanent combination
G j1
k, j
"" P ""
i 1
2,i
0,i
Q k ,i
i 1
2,i
Q k ,i
Q k ,i
(2.7)
(2.8)
(2.9)
where 1,1 is the factor for the frequent value of the variable action Q k , i (see Table 2.2) 2 ,1 is the factor for the quasi‐permanent value of the variable action Q k , i (see
Table 2.2).
Advice on which combination to use is given in EN 1993‐1‐1 and its National Annex. The National Annex to EN 1993‐1‐1 states that serviceability deflections should be based on the unfactored variable actions, and that permanent actions need not be included. Refer to Section 7 of this document for further information.
32
Section 3 Materials 3.1 General (1) The nominal values of material properties given in this Section should be adopted as characteristic values in design calculations. (2) This Part of EN 1993 covers the design of steel structures fabricated from steel materials conforming to the steel grades listed in Table 3.1. (3) In general, EN 1993‐1‐1 covers steel materials conforming to EN 10025 Parts 2, 3, 4, 5 and 6, EN 10210‐1 and EN 10219‐1 in grades S235 to S460. However, for quality steel materials which are manufactured to other materials specifications but satisfy both material performance and quality assurance requirements, they are readily considered to be equivalent steel materials. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details. (4) Depending on the supply sources of these steel materials, if it can be demonstrated that these steel materials satisfy both material performance and quality control requirements as described in Section 1.9, they are then considered as Class E1 Steel Materials, and the corresponding material class factor, Mc , is taken to be 1.0. However, if these steel materials are demonstrated to satisfy only the material performance requirements but not the quality control requirements as described in Section 1.9, they are then considered as Class E2 Steel Materials, and the corresponding material class factor, Mc , is taken to be 1.1. (5) Table 3.1 presents all the steel grades given in Table 3.1 of EN 1993‐1‐1: Table 3.1 European Steel Materials: EN 10025 – 2 • S235 • S275 • S355 • S450
EN 10025 – 3 • S275 N/NL • S355 N/NL • S420 N/NL • S460 N/NL
EN 10025 – 4 • S275 M/ML • S355 M/ML • S420 M/ML • S460 M/ML
EN 10210 – 1 • S235 H • S275 H • S355 H • S275 NH/NLH • S355 NH/NLH • S420 NH/NHL • S460 NH/NLH
EN 10219 – 1 • S235 H • S275 H • S355 H • S275 NH/NLH • S355 NH/NLH • S460 NH/NLH
• • • •
S275MH/MLH S355 MH/MLH S420 MH/MLH S460 MH/MLH
33
EN 10025 – 5 • S235 W • S355 W
EN 10025 – 6 • S460 Q/QL/QL1
(6)
Table 3.2 presents commonly used Chinese steel grades which are considered to be equivalent steel materials for adoption in structural design to EN 1993: Table 3.2 Chinese steel materials: GB/T 700‐2006 • Q235B/C/D • Q275B/C/D
GB/T 1591‐2008 • Q345B/C/D/E • Q390B/C/D/E • Q420B/C/D/E • Q460C/D/E
GB/T 6725‐2008 • Q235 • Q345 • Q390
GB/T 8162‐2008 • Q235 • Q275 • Q345 • Q390
GB/T 4171‐2008 • Q265GNH • Q295GNH • Q310GNH • Q355GNH • Q235NH • Q295NH • Q355NH • Q415NH • Q460NH
GB/T 19879‐2005 • Q235GJB/C/D/E • Q345GJB/C/D/E • Q390GJC/D/E • Q420GJC/D/E • Q460GJC/D/E
• Q420 • Q460
Refer to the Professional Guide entitled “Selection of Equivalent Steel Materials to European Steel Materials Specifications” (2015) for further details on equivalent steel materials manufactured to different materials specifications.
3.2 Structural Steel 3.2.1 Material properties (1) The nominal values of the yield strength f y and of the ultimate strength fu for structural steel should be obtained either by a) adopting the values of f y R eH and f u R m directly from the product standard, or b) using the values given in Table 3.1 of EN 1993‐1‐1.
In general, both fy and fu are material strengths of the steel materials measured either along the longitudinal or in the transverse directions with respect to the rolling direction during manufacturing. Both fy and fu are determined in standard tensile tests to EN 10002 which specifies details of testing procedures (material sampling, dimensions of coupon sizes, straining rates) and data analyses.
34
3.2.2 Ductility requirements (1) For steel materials for which a minimum ductility is required, the following three requirements should all be satisfied: the ratio f u / f y : f u / f y 1 .0
where
(3.1a)
fu fy
is the ultimate strength, and is the yield strength.
the elongation at failure : elongation at failure 15%
(3.1b)
which is based on a standard gauge length of 5.65 A 0 where A 0 is the original cross‐sectional area of the coupon.
the ultimate strain u : ε u 15 ε y
where u y
(3.1c)
is the strain corresponding to the ultimate strength f u , and is the yield strain, i.e. y f y / E .
Ductility is one of the most important mechanical properties of modern steel materials which allow steel structures to undergo large deformations without fracture, especially in highly stressed parts of members or joints. Moreover, ductility facilitates mobilization of cross‐sectional resistances, and simplifies the determination of cross‐sectional resistances without the need to examine the actual stress distribution within a cross‐section. Hence, these three limits on ductility requirements are effective measures in providing a safety margin for steel structures against failure by plastic collapse through large or even excessive deformations in the strain‐hardening range of the steel materials.
3.2.3 Fracture toughness (1) The material should have sufficient fracture toughness to avoid brittle fracture of tension elements at the lowest service temperature expected to occur within the intended design life of the structure. The lowest service temperature for building and civil engineering structures in Hong Kong is 0 oC. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details.
35
3.2.4 Through‐thickness properties (1) Where steel materials with improved through‐thickness properties are necessary according to EN 1993‐1‐10, steel materials according to the required quality class in EN 10164 should be used. Table 3.3 Choice of quality class according to EN 10164
Target value of Z Ed according to EN 1993‐1‐10
Required value of Z Rd expressed in terms of design Z ‐values according to EN 10164
Z Ed 10
‐
10 Z Ed 20
Z15
20 Z Ed 30
Z25
Z Ed 30
Z35
The through‐thickness property is a measure of the ability of steel plates to ensure integrity against lamination (or separation) when they are subject to high tensile stresses acting in the through‐thickness direction.
For those welded steel plates with high tensile residual stresses induced in the through‐thickness direction, lamination within the plate thickness may occur leading to extensive local cracks in the welded zones. Hence, it is necessary to specify an appropriate target value for the permissible reduction in cross‐sectional area of the steel material in the through‐thickness direction, Z Ed . Particular care should be given to welded beam‐to‐column connections, and welded end plates where there is tension in the through‐thickness direction.
3.2.5 Tolerances (1) The dimensional and mass tolerances of plates, rolled sections, and hollow sections should conform to the relevant product standards unless more severe tolerances are specified. (2) (3)
For welded components, the tolerances given in EN 1090 should be applied. Refer to the Code of Practice for the Structural Use of Steel (2011) for further details. For structural analysis and design, the nominal values of dimensions should be used.
36
3.2.6 Design values of material coefficients Modulus of elasticity E = 210,000 N / mm2 Shear modulus G = E /21 = 81,000 N / mm2 Poisson’s ratio = 0.3 Coefficient of linear thermal expansion = 14 10 6 C Density 7850 kg / m3 3.3 Connecting Devices 3.3.1 Fasteners Requirements for fasteners are given in EN 1993‐1‐8. 3.3.2 Welding consumables Requirements for welding consumables are given in EN 1993‐1‐8.
37
4 (1)
Durability The basic requirements for durability are set out in EN 1090. The durability of a structure is its ability to remain fit for use during its design working life given appropriate maintenance
According to EN 1990, a structure should be so designed that deterioration over its design working life does not impair the performance of the structure. Moreover, it is essential for a designer to identify various requirements that need to be allowed for during the design stage to achieve a high level of durability according to the expected design working life of the structure.
A structure should be designed in such a way, and provided with protection as necessary, so that no significant deterioration is likely to occur within the period between successive inspections. Critical parts of the structure need to be available for inspection, without complicated dismantling.
Other interrelated factors that need to be taken into account to ensure an adequately durable structure are given below:
(2)
intended and future use of the structure required performance criteria expected environmental influences composition, properties and performance of materials choice of structural system shape of members, structural detailing, and buildability quality of workmanship and level of control particular protective measures maintenance during the intended life
The means of executing the protective treatment undertaken off‐site and on‐site should be in accordance with EN 1090.
(3)
Parts susceptible to corrosion, mechanical wear or fatigue should be designed such that inspection, maintenance and reconstruction can be carried out satisfactorily and access is available for in‐service inspection and maintenance.
(4)B
For building structures, no fatigue assessment is normally required except as follows:
a) b) c) d)
members supporting lifting appliances or rolling loads members subject to repeated stress cycles from vibrating machinery members subject to wind‐induced vibrations members subject to crowd‐induced oscillations.
38
(5)
For elements that cannot be inspected, an appropriate corrosion allowance should be included.
(6)B
Corrosion protection does not need to be applied to internal building structures if the internal relative humidity does not exceed 80%. The following factors should be taken into account in design of corrosion protective systems for a structure in order to ensure its durability under conditions relevant both to its intended use and to its design working life.
The environment of the structure, whether bimetallic corrosion is possible and the degree of exposure of the structure. Accessibility of the structure for inspection and maintenance, (i.e. easy, difficult or impossible). Access, safety and member shapes, and structural detailing are relevant. The relationship between corrosion protection and fire protection systems.
Typical examples of commonly occurring exposure conditions are given below.
Table 4.1 Exposure conditions Exposure Class 1 2 3
Type of Exposure
Non‐corrosive Mild (typically internal) Moderate (internal or external)
4
Severe
5
Extreme
Examples Steelwork in an internal controlled (i.e. dry) environment. Steel piles driven into undisturbed and non‐corrosive ground. Steelwork in an internal humid environment. Steelwork built into perimeter cladding. External steelwork in a dry climate. External steelwork exposed to rain and humidity. Internal steelwork over a swimming pool, kitchen or water tank. External steelwork in a marine environment. Steel piles driven into corrosive ground. Steelwork exposed to salt water.
Refer to the Code of Practice for the Structural Use of Steel (2011) for further details.
39
Section 5 Structural Analysis 5.1 Structural Modeling for Analysis 5.1.1 Structural Modeling and basic assumptions (1) Analysis should be based upon calculation models of the structure that are appropriate for the limit state under consideration. Generally, a structural model is established in accordance with the geometry and the member configuration of a structure. An allowance for inevitable imperfections present within a structure is also made. It should be noted that no member imperfection is incorporated into the structural model since these are implicitly allowed for during structural design in accordance with Section 6. (2) The calculation model and the basic assumptions for the calculations should reflect the structural behaviour at the relevant limit state with appropriate accuracy, and reflect the anticipated type of behaviour of the cross‐sections, members, joints and bearings. (3) The method used for the analysis should be consistent with the design assumptions. When a designer considers connections in a steel structure to be either pinned joints or rigid joints during structural analysis, he needs to design these connections correspondingly. For a nominally pinned base of a structure, a 10% of the column EI stiffness is often assumed in structural analysis at ultimate limit state, in L particular, in assessing frame stability; and 20% at a serviceability limit state. 5.2 Global Analysis 5.2.1 Effects of deformed geometry of a structure (1) The internal forces and moments within a structure may generally be determined using either:
(2)
first order analysis, using the initial geometry of the structure or
second order analysis, taking into account the influence of the deformation of the structure.
The effects of deformed geometry (or the second‐order effects) should be considered if they increase the action effects significantly or modify significantly the structural behaviour. In general, the effects of deformed geometry of a structure are considered to be non‐ advantageous owing to large reduction in the resistances of the members.
40
(3)
First order analysis may be used for the structure if the increase of the relevant internal forces or moments or any other change in the structural behaviour caused by deformations can be neglected.
(4)B
This condition may be assumed to be fulfilled if the following criterion is satisfied: F cr cr 10 for elastic analysis (5.1a) FEd or F cr cr 15 for plastic analysis (5.1b) FEd where cr is the factor by which the loading would have to be increased to cause elastic instability in a global mode; FEd is the design load acting on the structure; and
Fcr is the elastic critical buckling load for the global instability model based on initial elastic stiffnesses. Portal frames with shallow roof slopes and regular beam‐column plane frames in buildings may be checked for sway mode failure with first order analysis if Expression (5.1) is satisfied for each storey.
In these structures, cr may be calculated using the following approximate formula, provided that the axial compression in the beams or rafters is not significant: H h cr Ed VEd H , Ed
(5.2)
where: H Ed is the design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal forces (which are applied to produce the effects of sway imperfections to the structure as given in Clause 5.3.2); VEd is the total design vertical load on the structure acting at the bottom of the storey; H , Ed is the horizontal displacement at the top of the storey, relative to the bottom of the storey, when the frame is loaded with horizontal loads (e.g. wind) and fictitious horizontal forces which are applied at each floor level; and is the storey height.
h In the U.K., Expression 5.2 above is considered to be inappropriate for portal frames. A modified expression for portal frames cr ,est should be calculated following the
recommended approach given in the paper entitled “Eurocode 3 and the in‐plane stability of portal frames” which was published in the November 2005 issue of The Structural Engineer.
41
5.2.2 Structural stability of frames (1) If, according to Clause 5.2.1, the influence of the deformation of the structure has to be taken into account, (2) to (6) should be applied to consider these effects and to verify its structural stability. (2) Verification of the structural stability of frames or their parts should be carried out considering: i) imperfections, and ii) second order effects. (3) According to the type of the frame and of the global analysis, imperfections and second order effects may be accounted for by one of the following methods: a) both totally by global analysis; b) partially by global analysis and partially through individual stability checks of members according to Clause 6.3; and c) for basic cases by individual stability checks of equivalent members according to Clause 6.3 using appropriate buckling lengths according to the global buckling mode of the structure. (4)
(5)B
Second order effects may be calculated by using an analysis appropriate to the structure (including step‐by‐step or other iterative procedures). For frames where the first sway buckling mode is predominant, first order elastic analysis should be carried out with subsequent amplification of relevant action effects (e.g. additional bending moments) by appropriate factors. For single storey frames designed on the basis of elastic global analysis, second order sway effects due to vertical loads may be calculated by increasing the horizontal loads HEd (e.g. wind) and equivalent loads VEd φ due to imperfections (see Clause 5.3.2(7)), and other possible sway effects according to first order theory by the factor:
1 1
1 cr
provided that αcr ≥ 3.0,
(5.3)
where cr may be calculated according to Expression (5.2) in Clause 5.2.1(4)B, provided that the roof slope is shallow and that the axial compression in the beams or rafters is not significant as defined in Clause 5.2.1(4)B. 5.3 Imperfections 5.3.1 Basis (1) Appropriate allowances should be incorporated in the structural model to cover the effects of imperfections, including residual stresses and geometrical imperfections such as lack of verticality, lack of straightness, lack of flatness, lack of fit and any minor eccentricities present in joints of the unloaded structure.
42
(2)
(3)
Equivalent geometric imperfections should be used with values which reflect the possible effects of all types of imperfections unless these effects are included in the resistance formula for member design. The following imperfections should be taken into account: a) global imperfections for frames and bracing systems b) local imperfections for individual members
It is essential to incorporate imperfections in the structural model of a structure. Global imperfections may be taken into account by modelling the frame out‐of‐ plumb, or by a series of equivalent horizontal forces applied to a frame modelled vertically. In general, the latter approach is recommended. It should be noted that i) imperfections in individual members may be modelled, or ii) members may be modelled as straight whilst imperfections are implicitly allowed for by verifying member resistances in accordance with Section 6. 5.4 Methods of Analysis Allowing for Material Non‐linearities 5.4.1 General (1) The internal forces and moments in a structure may be determined using either a) elastic global analysis, or b) plastic global analysis. (2) (3)
(4)B
Elastic global analysis may be used in all cases. Plastic global analysis may be used only where the structure has sufficient rotation capacity at the actual locations of the plastic hinges, whether this is in the members or in the joints. Where a plastic hinge occurs in a member, the member cross‐section should be doubly symmetric or singly symmetric with a plane of symmetry in the same plane as the rotation of the plastic hinge, and it should satisfy the requirements specified in 5.6. Where a plastic hinge occurs in a joint, the joint should have sufficient strength to ensure the hinge remains in the member, i.e. it should be able to sustain the plastic resistance of the member for a sufficient rotation. As a simplified method for a limited plastic re‐distribution of moments in continuous beams where following an elastic analysis, some peak moments exceed the plastic bending resistances by a maximum of 15%, the parts in excess of these peak moments may be re‐distributed in any member, provided that:
43
a) the internal forces and moments in the frame remain in equilibrium with the applied loads, b) all the members in which the moments are reduced have Class 1 or Class 2 cross sections, and c) lateral torsional buckling of the members in prevented. 5.4.2 Elastic global analysis (1) Elastic global analysis should be based on the assumption that the stress‐strain behaviour of the material is linear, whatever the stress level is. (2) Internal forces and moments may be calculated according to elastic global analysis even if the resistance of a cross‐section is based on its plastic resistance. (3) Elastic global analysis may also be used for cross‐sections of which the resistances are limited by local buckling. 5.4.3 Plastic global analysis (1) Plastic global analysis allows for the effects of material non‐linearity in calculating the action effects of a structural system. The behaviour should be modelled by one of the following methods: ‐ by elastic‐plastic analysis with plastified sections and joints as plastic hinges, ‐ by non‐linear plastic analysis considering the partial plastification of members in plastic zones, or ‐ by rigid plastic analysis neglecting the elastic behaviour between hinges. (2) Plastic global analysis may be used where the members have sufficient rotation capacity to enable the required re‐distributions of bending moments to develop. (3) Plastic global analysis should only be used where stability of the members at plastic hinges can be assured. (4) A bi‐linear stress‐strain relationship may be used for the grades of structural steel specified in Section 3. (5) Rigid plastic analysis may be applied if no effects of the deformed geometry (e.g. second‐order effects) have to be considered. In this case, joints are classified only by strengths. (6) The effects of deformed geometry of the structures and the corresponding structural stability of the frame should be verified according to the principles in 5.2.
44
5.5
Classification of Cross‐sections
5.5.1 Basis (1)
The role of cross section classification is to identify the extent to which the moment resistances and the rotation capacities of the cross‐sections are limited by their local buckling resistances.
5.5.2 Classification (1)
Four classes of cross‐sections are defined, as follows:
Class 1 cross‐sections are those which can form a plastic hinge with the rotation capacity required for plastic analysis without reduction of the resistance.
Class 2 cross‐sections are those which can develop their plastic moment resistance, but which have limited rotation capacity because of occurrence of local buckling.
Class 3 cross‐sections are those in which the stresses in the extreme compression parts of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance.
Class 4 cross‐sections are those in which local buckling will occur before the attainment of yield strength in one or more parts of the cross‐sections. Class 4 cross‐sections are outside the scope of this document.
(2) (3) (4) (5)
Compression parts include every part of a cross‐section which is either totally or partially in compression under the load combination considered. A cross‐section is classified according to the highest (least favourable) class of its compression parts. The limiting proportions for Class 1, 2, and 3 compression parts should be obtained from Table 5.1. A part which fails to satisfy the limits for Class 3 should be taken as Class 4.
45
5.6 (1)
Cross‐section Requirements for Plastic Global Analysis At plastic hinge locations, the cross‐section of the member which contains the plastic hinge should have a rotation capacity of not less than that required at the plastic hinge location.
(2)
In a uniform member, sufficient rotation capacity may be assumed at a plastic hinge if both the following requirements are satisfied:
a) The member has a Class 1 cross‐section at the plastic hinge location; and b) Where a transverse force that exceeds 10% of the shear resistance of the cross‐ section is applied to the web at the plastic hinge location, web stiffeners should be provided within a distance along the member of h/2 from the plastic hinge location, where h is the height of the cross‐section at this location. Table 5.1a
Maximum c/t ratios of compression parts Outstand flanges c
t
Class Stress distribution in parts (compression positive)
1 2 Stress distribution in parts (compression positive)
3
Rolled sections Welded sections Part subject to bending and compression Part subject to compression Tip in compression Tip in compression
v+
+
v+
v-
c 9 ε t c 10 ε t
v-
c 9 ε t c 10 ε t
+
-
c 9 ε t c 10 ε t
+
c 21 ε k t For k see EN 1993‐1‐5
c 14 ε t
46
+
-
Table 5.1b
Maximum c/t ratios of compression parts Internal compression parts
Axis of bending
c c
t t
t
Class Stress distribution in parts (compression positive)
Axis of bending
c
Part subject to bending
Part subject to compression
Part subject to bending and compression
+
+ +
-
-
1
2
Stress distribution in parts (compression positive)
3
c 72 t
c 33 t
c 83 t
c 38 t
when 0.5
396 c t 13 1
when 0.5
c 36 t
when 0.5
456 c t 13 1
when 0.5
c 41.5 t
+
+
c
+
-
c 124 t
-
c 42 t
The values of and are given by
N Ed 1 1 2 f y c t w N (2) Ed 1 A fy
(1)
where N Ed is positive in compression.
47
when 1
c 42 t 0 .67 0 .33
when 1
c 62 1 t
Table 5.1c
Maximum c/t ratios of compression parts
t
d
t
d
Class
Section in bending and/or compression d 50 ε 2 t d 70 ε 2 t d 90 ε 2 t
1 2 3
48
Section 6 Ultimate Limit States 6.1 Partial Factors for Resistances (1) The partial factors M should be applied to the various characteristic values of resistances in this section as follows:
Resistances Resistances of cross-section in tension, compression, shear, and
6.2
UKNA
Hong Kong
bending, and any of their combination,
M0
1.0
1.0
1.0
Resistances of members to instability,
M1
1.0
1.0
1.0
1.25
1.1
1.1
Resistances of cross-sections in tension to fracture,
EC3
M2
M 2 is used with ultimate material strengths, for example when verifying net areas subject to tension (see Clause 6.2.3(3)(b)) and when verifying net areas subject to a shear force in connection design. A different value of M 2 is used when calculating the resistance of connection components. Resistances of Cross‐Sections
6.2.1 General (1)P The design value of an action effect in each cross‐section, Ed , should not exceed the corresponding resistance, Rd. Ed
≤
Rd
Ed 1 Rd
Design checking against a cross‐section resistance rather than a limiting stress within the cross‐section allows economical design as the post‐yielding strength or even the plastic resistance of the cross‐section is mobilized. Moreover, the formulation is consistent for various degrees of strength mobilization including i) elastic, ii) elastro‐ plastic, and iii) plastic stress blocks.
(2)
(3)
or
(6.1)
If several action effects act simultaneously, the combined effect should not exceed the resistance for that combination. Shear lag effects and local buckling effects should be included by an effective width according to EN 1993‐1‐5. Shear buckling effects should also be considered according to EN 1993‐1‐5. The design values of resistances should depend on the classification of the cross‐ section.
49
(4)
(5)
Elastic verification according to the elastic resistance may be carried out for all cross sectional classes provided the effective cross sectional properties are used for the verification of Class 4 cross sections. The plastic resistance of cross sections should be verified by finding a stress distribution which is in equilibrium with the internal forces and moments without exceeding the yield strength. This stress distribution should be compatible with the associated plastic deformations.
6.2.2 Section properties
6.2.2.1 Gross cross‐section (1) The properties of the gross cross‐section should be determined using the nominal dimensions. Section analysis should be performed to determine various section properties using the nominal dimensions of the gross cross‐section, and typically these include:
Cross‐sectional area, A; Second moment of area, I; Radius of gyration, i; Section modulus – elastic, Wel and plastic, Wpl
Refer to Appendix D for a worked example on section analysis of a rolled I‐section. Holes for fasteners need not be deducted, but allowance should be made for larger openings. Splice materials should not be included.
6.2.2.2 Net section
(1) (2)
The net area of a cross‐section should be taken as its gross area less appropriate deductions for all holes and other openings. For calculating net section properties, the deduction for a single fastener hole should be the gross cross‐sectional area of the hole in the plane of its axis. For countersunk holes, appropriate allowance should be made for the countersunk portion. For deductions where the holes are staggered, refer to BS EN 1993‐1‐1 Clause 6.2.2.2(4).
6.2.3 Tension force (1)P The design value of the tension force N Ed at each cross‐section should satisfy:
N Ed N t ,Rd
1.0
(6.2)
50
(2)
For a section without holes, the design tension resistance N t , Rd should be taken as the smaller of: a) the design plastic resistance of the gross cross‐section, N pl,Rd , which should be
determined as follows: Af N pl,Rd y M0
(6.3a)
b) the design ultimate resistance of the net cross‐section at holes for fasteners, N u , Rd , which should be determined as follows:
N u ,Rd (3)
0.9A net f u M2
(6.3b)
For an angle connected through one leg, see BS EN 1993‐1‐8 Clause 3.10.3. Similar consideration should also be given to other types of sections connected through outstands. As the action is applied at an eccentricity to the centroid of the cross‐section, additional moment is induced. For simplicity, instead of designing the cross‐section under combined axial force and bending, the cross‐sectional area is reduced instead.
6.2.4 Compression force (1)P The design value of the compression force N Ed at each cross‐section should satisfy: N Ed 1.0 (6.4) N c,Rd (2)
(3)
The design resistance of the cross‐section for uniform compression N c ,Rd should be determined as follows: Af N c,Rd y N pl,Rd for Class 1, 2 or 3 cross‐sections (6.5) M0 where N pl,Rd is the design plastic resistance of the cross‐section for compression. Fastener holes, except for oversize and slotted holes as defined in EN 1090, need not be allowed for in compression members, provided that they are filled by fasteners.
6.2.5 Bending moment (1)P The design value of the bending moment M Ed at each cross‐section should satisfy: M Ed 1.0 (6.6) M c,Rd
where M c ,Rd is determined considering fastener holes, see (3) to (5).
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(2)
The design resistance of the cross‐section for bending about one principal axis of the cross‐section, M c ,Rd , should be determined as follows:
M c,Rd M pl,Rd
M c,Rd M el,Rd
where Wel ,min
Wplf y
M0
Wel,min f y M0
for Class 1 or 2 cross‐sections
(6.7a)
for Class 3 cross‐sections
(6.7b)
is the minimum elastic section modulus which corresponds with the
maximum elastic stress; M pl,Rd is the design plastic resistance for bending; and
M el,Rd (3) (4)
(5)
(6)
is the design elastic resistance for bending.
For bending about both axes, the methods given in Clause 6.2.9 should be used. Fastener holes in the tension flange may be ignored in determining the bending resistance provided that for the tension flange:
Af f y A f ,net 0.9f u M2 M0 where Af A f ,net
(6.8)
is the area of the tension flange; and is the net area of the tension flange.
Fastener holes in the tension zone of the web need not be allowed for, provided that the limit given in (4) is satisfied for the complete tension zone comprising the tension flange plus the tension zone of the web. Fastener holes, except for oversize and slotted holes, in the compression zone of the cross‐section need not be allowed for, provided they are filled by fasteners.
6.2.6 Shear force (1)P The design value of the shear force VEd at each cross‐section should satisfy: VEd (6.9) 1.0 V c,Rd where: Vc,Rd is the design shear resistance.
For plastic design, Vc,Rd is the design plastic shear resistance, Vpl ,Rd , as given in (2).
For elastic design, Vc,Rd is the design elastic shear resistance calculated using (4) and (5).
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In the absence of torsion, the design plastic resistance for shear, Vpl, Rd , is given by:
(2)
Vpl,Rd
Av fy / 3 M0
where Av
(6.10)
is the shear area.
(3)
The shear area Av should be determined as shown in Figure 6.1.
tw + 2r 0.5tf hw
hw
tw
hw
tw
0.5tf b
Av = a) Rolled I‐ and H‐sections, load parallel to web
h
w
t w where 1.0
b) Welded I, H and box sections, load parallel to web
tf
tf
b
b
b
tf
Av 2 b tf
c) Rolled I‐ and H‐sections, load parallel to flange
b
d) Welded I, H and box sections, load parallel to flange
h
b
h
e) Rolled rectangular hollow sections of uniform thickness
Figure 6.1
f) Rolled circular hollow sections of uniform thickness
Shear areas for various rolled and welded sections [Cl. 6.2.6.(3)]
53
(4)
Shear buckling in webs without intermediate stiffeners is avoided if:
hw tw
(5)
72 where may be taken conservatively as 1.
(6.11)
Otherwise, the shear buckling resistance must be verified in accordance with EN 1993‐1‐5. Fastener holes need not be allowed for in shear verification except in verifying the design shear resistance at connection zones as given in EN 1991‐1‐8. A deduction for fastener holes is made when checking block tearing in accordance with EN 1991‐1‐8 Clause 3.10.2. Refer to Worked Example I‐1 Determination of section resistances of Part I of Appendix D for details. Also refer to Worked Example II‐1 Design of a fully restrained steel beam of Part II of Appendix D for details.
6.2.7 Torsion (1) For members subject to torsion for which distortional deformations may be disregarded, the design value of the torsional moment, TEd , at each cross‐section should satisfy: (2)
TEd 1.0 TRd
(6.12)
where TRd is the design torsional resistance of the cross‐section. As a simplification, in the case of a member with a closed hollow cross‐section, such as a structural hollow section, it may be assumed that the effects of torsional warping can be neglected. Also as a simplification, in the case of a member with open cross‐section, such as a I‐ or a H‐section, it may be assumed that the effects of St. Venant torsion can be neglected.
6.2.8 Bending and shear force (1) For a cross‐section under a shear force, allowance should be made for its effect on the bending resistance of the cross‐section. (2) When VEd 0.5Vpl,Rd (see Clause 6.2.6(2)), the effect of the shear force on the bending resistance may be neglected, except where shear buckling reduces the section resistance. See EN 1993‐1‐5.
54
(3)
When VEd 0.5Vpl,Rd , the reduced moment resistance, M y ,V ,Rd should be taken as the design resistance of the cross‐section, calculated using a reduced yield strength, 2
1 f y , for the shear area, where 2V Ed 1 , and V pl,Rd is obtained from V pl ,Rd Clause 6.2.6 (2).
2
(4)
2VEd When torsion is present should be obtained from 1 , see V pl, T , Rd Clause 6.2.7, but should be taken as 0 for VEd 0.5Vpl, T , Rd .
(5)
The reduced plastic moment resistance allowing for the effect of the shear force may be obtained for I‐sections with equal flanges and bending about the major axis as follows: A 2w W pl , y f y 4t w M y ,V ,Rd but M y ,V ,Rd M y ,c,Rd (6.13) M0 where: M y ,c,Rd is obtained from Clause 6.2.5(2)
Aw h w t w
For I‐ and H‐sections as well as rectangular and square hollow sections, the interaction of bending moments and shear forces is not severe as the induced stresses do not act along the same direction. Hence,
when VEd 0.5Vpl,Rd , the webs are fully effective to resist both the shear forces and the bending moments. The flanges are fully effective to resist the bending moments.
when VEd 0.5Vpl,Rd , the webs are primarily assigned to resist the shear forces although they may also contribute to resist the bending moments together with the flanges.
when VEd Vpl, Rd , the webs are fully utilized to resist the shear forces with no contribution to resist the bending moment. The flanges remain to be fully effective to resist the bending moments.
Refer to Worked Example I‐2 Cross section resistance under combined bending and shear of Part I of Appendix D for details.
55
6.2.9 Bending and axial force 6.2.9.1 Class 1 and 2 cross‐sections (1) When an axial force is present, allowance should be made for its effect on the plastic moment resistance. (2)P For Class 1 and 2 cross‐sections, the following criteria should be satisfied: M Ed 1 (6.14) M N ,Rd (3) (4)
where M N ,Rd is the reduced design plastic moment resistance under the axial force N Ed . For a rectangular solid section without fastener holes, N 2 M N ,Rd M pl,Rd 1 Ed N pl,Rd
N Ed 0.25 N pl ,Rd and
N Ed
(5)
, should be taken as: (6.15)
For doubly symmetric I‐ and H‐sections or other flanged sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the y‐y axis when both the following are satisfied:
,
(6.16a)
0.5h w t w f y
(6.16b) M0 For doubly symmetrical I‐ and H‐sections, allowance need not be made for the effect of the axial force on the plastic resistance moment about the z‐z axis when: h t f N Ed w w y (6.16c) M0 The following approximations may be used for standard rolled I‐ or H‐sections and for welded I‐ or H‐sections with equal flanges:
1 n
M N,y,Rd Mpl,y,Rd
for n a :
M N ,z ,Rd M pl,z ,Rd
(6.17a)
for n a :
n a 2 M N ,z ,Rd M pl ,z ,Rd 1 1 a
(6.17b)
where
n
a
1 0.5a
but M N ,y,Rd M pl,y ,Rd
N Ed N pl ,Rd
A 2bt f but a 0.5 A
56
(6.17)
(6)
The following approximations may be used for rectangular structural hollow sections of uniform thickness and for welded box sections with equal flanges and equal webs: 1 n M N,y,Rd M pl,y,Rd but M N ,y,Rd M pl,y ,Rd (6.17c) 1 0.5a w 1 n M N ,z ,Rd M pl,z ,Rd but M N ,z ,Rd M pl,z ,Rd (6.17d) 1 0.5a f where A 2bt f but a w 0.5 aw A A 2ht w but a f 0.5 af A In general, the effect of combined bending and axial force is more pronounced than that of the effect of combined bending and shear as the induced stresses act along the same (longitudinal) direction. The design formulation using plastic stress blocks utilizes the cross‐section resistance more effectively. For biaxial bending, the following criterion may be used:
M y ,Ed M z ,Ed 1 M N ,y ,Rd M N ,z ,Rd
(6.18)
in which and are constants and they may be taken as follows:
I‐ and H‐ sections Circular hollow sections Rectangular hollow sections
α 2 2 1.66 / (1‐1.13n2)
β 5n; but 1 2 1.66 / (1‐1.13n2)
where
Refer to Worked Example I‐3 Cross section resistance under combined bending and axial force of Part I of Appendix D for details.
n
N Ed N pl ,Rd
6.2.9.2 Class 3 cross‐sections (1) For Class 3 cross‐sections, the maximum longitudinal stress due to moment and axial force, taking account of fastener holes where relevant, should not exceed f y / M 0 .
For Class 3 cross‐sections, linear elastic interaction of the bending moment with the axial force should be used to determine the maximum longitudinal stress, which should not exceed the design yield strength, f y / M 0 , i.e. elastic design.
57
6.2.10 Bending, shear and axial forces (1)
Where shear and axial force are present in a cross-section, allowance should be made for the effect of both shear force and axial force on the moment resistance of the cross-section.
(2)
Where VEd 0.5Vpl, Rd , no reduction of the resistances defined for bending and axial force in 6.2.9 need be made, except where shear buckling reduces the section resistance, see EN 1993-1-5.
(3)
Where VEd 0.5Vpl, Rd , the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength, 2
1 f y , for the shear area, where 2VEd 1 , and Vpl , Rd is obtained from Vpl, Rd 6.2.6 (2). Instead of reducing the yield strength, it is also possible to reduce the plate thickness of the relevant part of the cross-section. In general, this approach requires more calculation, but gives smaller reductions, when compared with a reduction in yield strength.
58
6.3
Buckling Resistances of Members
6.3.1 Uniform members in compression EN 1993‐1‐1 covers three modes of buckling when subject to axial compression:
flexural buckling which may be critical in I‐ and H‐sections, and hollow sections
torsional buckling which may be critical for cruciform sections with wide outstands
torsional‐flexural buckling which may be critical for asymmetric sections
In general, torsional buckling and torsional flexural buckling are not the critical buckling modes for doubly symmetric I‐ or H‐sections or hollow sections of practical cross‐section dimensions and member lengths. Flexural buckling is also commonly known as axial buckling or Euler buckling.
6.3.1.1 Buckling resistance (1) A compression member should be verified against buckling as follows:
N Ed 1.0 N b , Rd
where: N Ed is the design value of the compression force
Nb,Rd is the design buckling resistance of the compression member
(2)
The design buckling resistance of a compression member should be taken as:
N b, Rd
Afy M1
(6.19)
for Class 1, 2 and 3 cross‐sections
(6.20)
where: is the reduction factor for the relevant buckling mode
6.3.1.2 Buckling curves (1) For axial compression in members, the value of for the appropriate non‐dimensional slenderness should be determined from the relevant buckling curve according to:
1
where
2 2
2
but 1.0
2 0.51 0.2 is an imperfection factor
is the non‐dimensional slenderness
59
(6.21)
(2)
Lcr 1 i
L cr N cr
is the buckling length in the buckling plane considered is the radius of gyration about the relevant axis is the elastic critical force for the relevant buckling mode
N cr
i
Af y
N cr
for Class 1, 2 and 3 cross sections
2 EI L2
for Class 1, 2 and 3 cross sections
For rolled or welded I‐ and H‐sections, torsional and torsional‐flexural buckling modes are not critical in practical cases. The imperfection factor corresponding to the appropriate buckling curve should be obtained from Tables 6.1 and 6.2, and Figure 6.2.
Table 6.1
Imperfection factors for flexural buckling curves
Buckling curve Imperfection factor
a0 0.13
a 0.21
b 0.34
c 0.49
d 0.76
(3)
The values of corresponding to the non‐dimensional slenderness may be obtained from Appendix A. The values of are tabulated in Table A1 of Appendix A for direct determination of the buckling curves for various steel materials.
(4)
For slenderness 0.2 or for N Ed / Ncr 0.04 , the buckling effects may be ignored and only cross‐sectional checks apply.
For a column member with a slenderness 0.2 , the column behaves essentially as a short column. Hence, axial buckling is not critical. Refer to Worked Example II‐3 Design of a steel column under axial compression of Part II of Appendix D for details.
60
Table 6.2
Selection of flexural buckling curve for a cross‐section Buckling curve Buckling about axis
S 235 S 275 S 355 S 420
S460
tf ≤ 40 mm
y‐y z‐z
a b
a0 a0
40 ≤ tf ≤ 100 mm
y‐y z‐z
b c
a a
tf ≤ 100 mm
y‐y z‐z
b c
a a
tf > 100 mm
y‐y z‐z
d d
c c
tf ≤ 40 mm
y‐y z‐z
b c
b c
tf > 40 mm
y‐y z‐z
c d
c d
hot‐finished
any
a
a0
cold‐formed
any
c
c
generally applicable except as below
any
b
b
thick welds: a > 0.5 tf b/tf < 30 b/tw < 30
any
c
c
Cross section
z
h/b > 1.2
Rolled sections
tf
Limits
y
h/b ≤ 1.2
y
z b
Welded sections
z
z
tf
y
y
y
tf y
z
Welded box sections
Hollow sections
z
z h
y
tf y
tw z b
61
1.2
1.0
0.8 a0 Curve a0
Curve a
0.6
Curve b Curve c
0.4
Curve d 0.2
0.0 0.0
0.5
1.0
1.5
2.0
slenderness, ̅
Figure 6.2
Buckling curves for axial compression in members
62
6.3.2 Uniform members in bending 6.3.2.1 Buckling resistance (1) A laterally unrestrained member subject to major axis bending should be verified against lateral‐torsional buckling as follows:
M Ed 1.0 M b , Rd
where MEd is the design value of the moment
M b , Rd is the design buckling resistance moment.
(2)
(3)
(6.22)
Beams with sufficient restraint to the compression flange are not susceptible to lateral‐ torsional buckling. In addition, beams with cross‐sections of circular or square hollow section`s, fabricated circular tubes or square box sections are not susceptible to lateral‐torsional buckling. The design buckling moment resistance of a laterally unrestrained beam should be taken as
fy
Mb, Rd LT Wy
where Wy is the appropriate section modulus as follows:
Wy Wpl, y
for Class 1 and 2 cross‐sections
Wy Wel, y
for Class 3cross‐sections
LT
is the reduction factor for lateral‐torsional buckling.
The following three different design procedures for members in bending are presented:
Procedure B1‐ Clause 6.3.2.2 Lateral torsional buckling curves – General case
Procedure B2‐ Clause 6.3.2.3 Lateral torsional buckling curves for rolled sections or equivalent welded sections
Procedure B3‐ An alternative procedure recommended by the Steel Designer’s Manual
M1
(6.23)
63
6.3.2.2 Lateral torsional buckling curves ‐ general case (1) For members of constant cross‐sections under bending, the value of for the ̅ appropriate non‐dimensional slenderness , should be determined from: LT
1 2
LT LT LT
2
but LT 1.0
(6.24)
where 2 LT 0.5 1 LT LT 0.2 LT
LT LT
is an imperfection factor Wyf y M cr
Mcr is the elastic critical moment for lateral‐torsional buckling Table 6.3 Buckling curves for lateral torsional buckling Cross‐section
Limits h / b ≤ 2 h / b > 2 h / b ≤ 2 h / b > 2 ‐
Rolled I‐sections Welded sections Other cross‐sections
Buckling curve a b c d d
Table 6.4
Imperfection factors for lateral torsional buckling curves
Buckling curve Imperfection factor LT
a 0.21
b 0.34
c 0.49
d 0.76
(2)
M cr is based on the gross cross‐sectional properties, and takes into account the loading conditions, the real moment distribution and the lateral restraints. An expression to evaluate M cr is not given in EN 1993‐1‐1. Refer to Appendix B1 for determination of M cr . Alternatively, the value of M cr may be determined using standard software with eigenvalue analysis.
(3)
For slenderness LT LT 0 or for
M Ed LT 0 2 , the lateral torsional buckling effects may M cr
be ignored, and only cross‐sectional checks apply.
For a beam member with a slenderness LT LT 0 , the beam behaves essentially as a short beam. Hence, lateral torsional buckling is not critical. A similar conclusion may be drawn for a beam with
M Ed LT 0 2 . M cr
Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details. 64
6.3.2.3 Lateral torsional buckling curves for rolled sections or equivalent welded sections (1) For rolled or equivalent welded sections in bending, the value of LT for the appropriate non‐dimensional slenderness LT should be determined from:
LT
1 2
LT LT LT
2
but LT 1.0 and LT
1 LT
2
(6.25)
where 2 LT 0.5 1 LT LT LT 0 LT
LT0 0.40 (maximum value)
0.75 (minimum value)
Table 6.5 Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h / b ≤ 2 h / b > 2 h / b ≤ 2 h / b > 2
Rolled I‐sections Welded sections
Buckling curve b c c d
Values of LT may be obtained from Figure 6.3. (2)
When taking into account the moment distribution between the lateral restraints of members, the reduction factor LT may be modified as follows:
LT , mod
LT f
but LT, mod 1.0
(6.26)
where f f kc
is the correction factor for the moment distribution 1 0.5 1 k c 1 2.0 LT 0.8 2 is a correction factor according to Table B2.4
Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details.
65
Table 6.6 Correction factors kc kc
Moment distribution =1
1.0
1 1.33 0.33
1 1
0.94
0.90
0.91 0.86
0.77
0.82
66
6.3.2.4 An alternative procedure recommended by the Steel Designers’ Manual (1) (2)
As an alternative to calculating M cr and hence LT , the value of LT may be calculated directly from the expression given below. Where loads are not destabilising, for simply supported rolled I‐, H‐sections and channel sections, the non‐dimensional slenderness LT is given by: 1 UVD z w C1
LT
where: 1 is a parameter dependant on the shape of the bending moment diagram, which C1
(6.27)
may conservatively be taken as 1.0, or otherwise given in Table 6.7 for loads which are not destabilizing.
U
is a section property which is given in section property tables, or may conservatively be taken as 0.9.
V
is a parameter related to slenderness, and for symmetric rolled sections where the loads are not destabilising, may be conservatively taken as 1.0 or as 1 V 2 z 1 4 1 20 h / t f
Conservatively, the product of U and V may be taken as 0.9.
z
z
L
is the distance between points of lateral restraint;
1
is a material parameter;
λ1
π
w
kL , in which k may conservatively be taken as 1.0 for beams supported and iz restrained against twist at both ends. With certain additional restraint conditions, k may be less than 1.0.
z 1
E 93.9 ε fy
Wy Wpl,y
67
It is conservative to assume that the product UV 0.9 and that w 1.0
(3)
Where loads are destabilizing, a parameter D should be introduced in the expression for LT . The value of D should be taken as 1.2 for simply supported beams. For cantilever beams, the value of D may range from 1.7 to 2.5, depending on the restraints provided at supports. Refer to NCCI SN002 for details.
Table 6.7
Values of
1 and C1 for various moment conditions C1
(load is not destabilizing) End Moment Loading
M
M 1
1
1 C1
C1
+1.00
1.00
1.00
+0.75
0.92
1.17
+0.50
0.86
1.36
+0.25
0.80
1.56
0.00
0.75
1.77
‐0.25
0.71
2.00
‐0.50
0.67
2.24
‐0.75
0.63
2.49
‐1.00
0.60
2.76
0.94
1.13
0.62
2.60
0.86
1.35
0.77
1.69
Intermediate Transverse Loading
2/3 1/3
The value of the imperfection parameter LT corresponding to the appropriate buckling curve is given by Table 6.8.
Table 6.8
Imperfection factors for lateral torsional buckling curves
Buckling curve Imperfection factor LT
a 0.21
68
b 0.34
c 0.49
d 0.76
(4)
Recommendations for the buckling curves are given in Table 6.9. Table 6.9
Recommendations for the selection of lateral torsional buckling curve
Cross‐section
Limits
Rolled doubly symmetric I and H sections, and hot‐ finished hollow sections Angles (for moments in the major principal plane) All other hot‐rolled sections
h/b 2 h/b 2
Cold‐formed hollow sections
h/b 2 2 h / b 3 .1 h / b 3 .1
Buckling curve b c d d d c d
Values of the reduction factor LT for the appropriate non‐dimensional slenderness
LT may be obtained from Figures 6.3 and 6.4. (5)
Values of LT may alternatively be determined from Tables B2.4 and B2.5 in Appendix B. Refer to Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling of Part II of Appendix D for details.
69
1.20
1.00 Curve b 0.80
Curve c Curve d
0.60
0.40
0.20
0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
Slenderness ratio, ̅
Figure 6.3
Lateral torsional buckling curves for rolled sections
1.20
1.00 Curve b 0.80
Curve c Curve d
0.60
0.40
0.20
0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
Slenderness ratio, ̅
Figure 6.4
Lateral torsional buckling curves for welded sections
70
2.00
Table 6.10
Comparison and design procedure of an unrestrained beam to EN 1993‐1‐1
Step
Procedure B1
Procedure B2
Procedure B3
Cl. 6.3.2.2 General case
Cl. 6.3.2.3 Rolled sections or equivalent welded sections
Steel Designer’s Manual
1
Mcr , Wyf y 2
C1, U, V, z , w
M cr is based on gross sectional properties and taken into account
C1 is based on the shape of the
loading conditions, moment distributions and lateral restrainsts.
LT
3
Wy f y
Rolled I‐sections Welded sections
h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
M cr
Buckling curves
5
a b c d
Rolled I‐sections Welded sections
C1
h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
b c c d
h/b ≤ 2 2 < h/b ≤ 3.1 h/b > 3.1 h/b ≤ 2 h/b > 2
Rolled I‐sections Welded sections
a
b
c
d
LT
0.21
0.34
0.49
0.76
LT,0 0.20
LT,0 0.40 (max.)
1 .00
1 .00 (min.)
b c d c d
For rolled sections, hot‐finished and cold‐formed hollow sections,
For rolled and equivalent welded sections,
UV z w
Buckling curves
Buckling curve
For all sections,
6
1
LT
Buckling curves 4
bending moment diagram.
LT,0 0.40 1 .00
For welded sections,
LT,0 0.20 1 .00
8
9
10
LT 0.5 1 LT LT LT 0 LT 2
7
LT
1 2
LT LT LT
M b,Rd LT
-
Wy f y M1
2
LT
1 2
LT LT LT
LT,mod
2
LT f
where f is based on the moment distribution between lateral restraints of the member.
M b,Rd LT,mod
71
Wy f y M1
LT
1 LT LT 2 LT 2
M b,Rd LT
-
Wy f y M1
6.3.3 Uniform members in bending and axial compression (1)
(2)
For members of structural systems, verification of buckling resistance of doubly symmetric cross‐sections may be carried out on the basis of the individual single span members regarded as cut out of the system. Second order effects of the sway system ( P effects) should be taken into account, either by considering the end moments of the member or by means of appropriate buckling lengths about each axis for the global buckling mode. Members which are subjected to combined bending and axial compression should satisfy: M y,Ed M z ,Ed N Ed k yy k yz 1 N b , y ,Rd M b ,Rd M cb ,z ,Rd M y ,Ed M z ,Ed N Ed k zy k zz 1 M cb ,z ,Rd N b ,z ,Rd M b ,Rd
where: N Ed , M y ,Ed and M z ,Ed are the design values of the compression force and the maximum moments about the y‐y and the z‐z axes along the member, respectively N b ,y ,Rd and N b ,z ,Rd are the design buckling resistances of the member about the
M b ,Rd
major and the minor axes respectively from Clause 6.3.1.1 (2) is the design buckling resistance moment from Clause 6.3.2.1(3)
M cb,z ,Rd
Wpl,z f y M1 Wel,z f y
for Class 1 and 2 sections
for Class 3 sections M1 k yy , k yz , k zy , k zz are interaction factors, which may be determined from Annex A or B of BS EN 1993‐1‐1. The above criteria are based on the expressions in Clause 6.3.3(4) of EN 1993‐1‐1, interpreted in accordance with ECCS TC8 Rules for Member Stability in EN 1993‐1‐1 Background documentation and design guidelines. Annex B is recommended as the simpler approach for manual calculations. Use of either Annex is permitted by the National Annex. In some cases, conservative values of the k factors may be sufficient for initial design. The following table gives maximum values, based on Annex B of the Standard, and assuming the sections are susceptible to torsional deformations (i.e. not hollow sections).
72
Interaction factor
k yy
Maximum values Class 1 and 2 Class 3 Cmy 1.8 Cmy 1.6
k yz
0.6 k zz
k zz
k zy
1.0
1.0
k zz
C my 2.4
C mz 2.4
Appendix D summarizes all the equations necessary to calculate the interaction factors. Alternatively, the values of the interaction factors may simply be read off from various graphs. Refer to Worked Example II‐4 Design of a beam‐column under combined compression and major axis bending of Part II of Appendix D for details.
6.3.4 Columns in simple construction The rules in this clause are based on the NCCI in Access Steel document SN048 (available from www.access‐steel.com) with some different symbols following modifications to the design value given in Clause 6.3.3. (1) When the criteria given in Clause 6.3.4(2) are satisfied, a column in simple construction subject to combined bending and axial compression may be verified against buckling failure as follows:
M y ,Ed M z ,Ed N Ed 1 .5 1 M cb,z ,Rd N min,b ,Rd M b,Rd
where: N Ed , My,Ed and M z,Ed are the design values of the compression force and the maximum
design bending moments about the y‐y and the z‐z axes along the member. y Af y z Af y N min,b ,Ed is the lesser of and M1 M1
M b ,Rd
LT
Wpl,y f y M1
Wpl,z f y
M cb,z ,Rd
(2)
The following criteria must be satisfied to use the verification given in (1):
M1
The column is a rolled H‐section, or equivalent welded sections. The cross‐section is Class 1, 2 or 3 under compression. The bending moment diagram about each axis is linear. The column is restrained laterally in both the y‐y and the z‐z directions at each floor, but it is unrestrained between floors. 0.11 where is the ratio of the moments at the two ends. For a pin ended column ( 0 ), the following alternative criterion must be satisfied to use the simplified interaction expression: 73
(3) (4)
y Af y N Ed (the resistance in the major axis) 0.83 in which N b,y,Rd M1 N b ,y,Rd
Note: 0 if there is a true pin at one end of the column (such as a base). In this case the simplified interaction expression is only valid if the axial force in the column is less than 83% of its resistance in the major axis. Where the criteria in Clause 6.3.4(2) are not satisfied, the method given in Clause 6.3.3 should be used. The design bending moments should be determined by considering the vertical beam reactions to act at a distance of 100 mm from the face of the column (web or flange).
74
Section 7 Serviceability Limit States 7.1 General (1)
(2)
A steel structure should be designed and constructed such that all relevant serviceability criteria are satisfied. Serviceability limit states consider service requirements for a structure or a structural member under normally applied actions. Examples are deflection, human induced vibration, wind induced oscillation and durability. The basic requirements for serviceability limit states are given in Clause 3.4 of EN 1990.
(3)
Any serviceability limit state and the associated loading model as well as the associated analysis model should be specified for a structure.
(4)
Where plastic global analysis is used for ultimate limit state design, plastic redistribution of forces and moments at the serviceability limit state should be considered accordingly.
The serviceability actions should be taken as the characteristic values of the actions, i.e. unfactored. 7.2 Serviceability Limit States for Buildings 7.2.1 Vertical deflections (1) With reference to EN 1990 – Annex 1.4 limits for vertical deflection according to Figure A1.1 should be specified for each structure and agreed with the client. 7.2.2 Horizontal deflections (1) With reference to EN 1990 – Annex 1.4 limits for horizontal deflection according to Figure A1.2 should be specified for each structure and agreed with the client. 7.2.3 Dynamic effects (1) With reference to EN 1990 – Annex 1.4.4, vibrations of structures which are accessible to the public should be limited to avoid significant discomfort to users, and limits should be specified for each structure and agreed with the client. Deflections or deformations under all actions should not impair the resistance or the effective functioning of a structure, a structural member, a supporting member or its components, nor cause damage to finishes. For typical structures, the deflection limits given in the following table are recommended.
75
Table 7.1
Suggested limits for vertical deflection due to characteristic combination (variable actions only)
a) Deflection of profiled steel sheeting Vertical deflection during construction when the effects of ponding are not taken into account Vertical deflection during construction when the effects of ponding are taken into account Vertical deflection of roof cladding under self‐weight and wind action Lateral deflection of wall cladding under wind action
Span/180 (but ≤ 20 mm) Span/130 (but ≤ 30 mm) Span/90 (but ≤ 30 mm) Span/120 (but ≤ 30 mm)
b) Vertical deflection of composite slab Due to imposed actions Due to the total actions plus due to prop removal (if any) less due to self‐weight of the slab
Span/350 (but ≤ 20 mm) Span/250
c) Vertical deflection of beams ‐ due to imposed actions Cantilevers Beams carrying plasters or other brittle finishes Other beams except purlins and sheeting rails Purlins and sheeting rails
Length/180 Span/360 Span/200 To suit cladding
d) Horizontal deflection of columns ‐ due to imposed actions and wind actions Horizontal drift at topmost storey of buildings Horizontal drift at top of a single storey portal not supporting human Relative inter‐storey drift Columns in portal frame buildings Columns supporting crane runways
Height/500 To suit cladding Storey height/400 To suit cladding To suit crane runway
e) Crane girders Vertical deflection due to static vertical wheel actions from overhead traveling cranes Horizontal deflection (calculated on the top flange properties alone) due to horizontal crane actions
Span/600 Span/500
f) Trusses Typical trusses not carrying brittle panels
Span/200
Note: Pre‐camber in an unloaded structural member may be used to reduce the calculated deflection of that member under the loading conditions.
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7.3
7.4
Wind‐induced Oscillation Vibration and oscillation of a structure should be limited to avoid discomfort to users and damage to contents. For special structures, including long‐span bridges, large stadium roofs and chimneys, wind tunnel model tests are recommended to provide data for wind resistant design to meet serviceability limits. Wind Sensitive Buildings and Structures A design procedure which incorporates dynamic analysis in addition to static analysis should be undertaken for wind sensitive buildings and structures. Structures with low natural frequencies or large height‐to‐least dimension ratios should receive special checking. Reference should be made to the Code of Practice on Wind Effects in Hong Kong (2004). For slender, flexible and lightly damped tall buildings and structures, those with a long afterbody or complex geometry, and those with an eccentricity between mass and stiffness centres, aeroelastic instabilities such as lock‐in, galloping and flutter may cause large amplitude crosswind responses. Specialist advice and wind tunnel model test are recommended to provide data for wind resistant design to meet serviceability limits. Refer to the Code of Practice for the Structural Use of Steel (2011) for details.
77
Section 8 Design Data for Rolled and Welded Sections 8.1 General Tabulated design data are essential for practicing engineers to perform structural design. For structural steel design, section dimensions are the basic data, and rational use of these data gives important structural quantities, i.e. section properties and resistances of both rolled and welded sections, enabling designers to establish structural adequacy against strength requirements in ultimate limit states as well as structural performance against deformation or vibration in serviceability limit states. In this Section, design data on section dimensions and properties as well as section resistances of both rolled and welded sections with practical steel materials are provided to assist structural engineers to perform effective structural steel design. Table 8.1 presents the types of rolled and welded sections covered in the present Section. Typical cross‐sections of these rolled and welded sections are illustrated in Figure 8.1.
Table 8.1
Ranges of rolled and welded sections
Rolled sections Rolled I‐section: I‐section Rolled H‐section: H‐section Hot‐finished circular hollow section: CHS Hot‐finished rectangular hollow section: RHS Hot‐finished square hollow section: SHS
Welded sections Equivalent welded I‐section: EWI‐section Equivalent welded H‐section: EWH‐section Equivalent cold‐formed circular hollow section: EWCHS Equivalent cold‐formed rectangular hollow section: EWRHS Equivalent cold‐formed square hollow section: EWRHS
Rolled Sections It should be noted that both I‐ and H‐sections are manufactured to BS 4‐1 while all the hot‐finished hollow sections are manufactured to EN 10210‐2. All rolled I‐ and H‐ sections given in BS 4‐1 have been included in the present Section, but only selected hot‐finished hollow sections specified in EN 10210‐2 with a dimension larger than 100 mm are considered. All of these rolled sections are assumed to be manufactured to EN 10025 and EN10210‐1, and hence, they are commonly considered as steel Class E1 Steel Materials with a material class factor, Mc = 1.0 as discussed in Section 1.9. Resistances of all these sections with common steel grades, i.e. S275 and S355 steel materials, are tabulated in a systematic manner for practical design. Table 8.2 summarizes various design information provided for the rolled sections covered in this Section.
78
Rolled sections: I‐ and H‐sections to: ‐ ‐
EN 10025 on materials BS4‐1 on dimensions
CHS, RHS and SHS to: I‐section
Circular hollow section CHS
‐ ‐
H‐section
EN 10210‐1 on materials EN 10210‐2 on dimensions
Rectangular hollow section RHS
Square hollow section SHS
Welded sections: EWIS and EWHS to: ‐ GB/T 700 & GB/T 1591 on materials ‐ design methods in Section 8.4
EWCHS, EWRHS and EWSHS to: Equivalent welded I‐section EWI‐section
Equivalent welded H‐section EWH‐section
Equivalent cold‐formed Equivalent cold‐formed rectangular circular hollow section hollow section EWRHS EWCHS
‐ GB/T 6725 & GB/T 8162 on materials ‐ design methods in Section 8.4 as well as GB/T 6728 & GB/T 17395 on dimensions.
Equivalent cold‐formed square hollow section EWSHS
Figure 8.1 Cross‐sections of typical rolled and welded sections Detailing rules of welding for I‐ and H‐sections (1) The height of the weld root, r, is assumed to be equal to the thickness of the web, tw, or at least 0.7 times the flange thickness, i.e. 0.7 tf , whichever is smaller. (2) To ensure welding quality, r should not be smaller than 8.0 mm nor larger than 16.0 mm.
79
Table 8.2 Summary of design information for rolled sections
I‐section z
H‐section
CHS
RHS
SHS
z
z
z
z
y
y
y
y
y
Dimensions and properties Resistances for S275 steel Resistances for S355 steel
72 sections
31 sections
55 sections
44 sections
32 sections
Note: All these rolled sections are assumed to be Class E1 Steel Materials with a material class factor
Mc 1.0 as discussed in Section 1.9.
Welded sections Equivalent welded I‐ and H‐sections All the equivalent welded I‐ and H‐sections are fabricated with steel plates to GB/T 700 and GB/T 1591 with standard thicknesses. For simplicity, the following plate thicknesses are assumed: 6.0 mm 8.0 mm 10.0 mm 12.0 mm 16.0 mm 20.0 mm 25.0 mm 30.0 mm 40.0 mm 50.0 mm 60.0 mm 80.0 mm It is envisaged that with a rational combination of these plate thicknesses in the flanges and the webs of the sections, a series of welded sections with similar section depths and flange widths are readily manufactured covering a wide range of section properties and resistances for practical design. These section properties and resistances are similar to those rolled sections in the same series of section designations. Moreover, resistances of all these sections with common steel grades, i.e. Q235, Q275, Q345 and Q460 steel materials, are tabulated in a systematic manner for practical design. Equivalent cold formed hollow sections All the equivalent cold‐formed hollow sections are manufactured with steel plates to GB/T 6725 and GB/T 8162 while their dimensions are manufactured to GB/T 6728 and GB/T 17395. The following plate thicknesses are assumed: 6.0 mm 8.0 mm 10.0 mm 12.0 mm 16.0 mm 20.0 mm
80
Depending on the performance of material properties as well as the demonstration of quality assurance system during manufacturing, Chinese Steel Materials may be classified as Class E1 or E2 Steel Materials with a material class factor, Mc 1.0 or 1.1 respectively as discussed in Section 1.9. Resistances of all these sections with common steel grades, i.e. Q275, Q345 and Q460 steel materials, are tabulated in a systematic manner for practical design. All of these welded sections are proposed as equivalent welded sections to those rolled sections based on various structural requirements, such as compression and bending resistances. Standard welding procedures are assumed to be applied effectively during their fabrication. Table 8.3 summarizes various items of design information provided for the equivalent welded sections covered in this Section. Table 8.3 Summary of design information for equivalent welded sections EWI‐ EWH‐ EWCHS EWRHS EWSHS section section z
z
z
y
y
y
z
z
y
y
Dimensions and properties
72 sections
31 sections
55 sections
44 sections
32 sections
Resistances for Q235 steel
‐‐‐
‐‐‐
‐‐‐
Resistances for Q275 steel
Resistances for Q345 steel
Resistances for Q460 steel
Note: Depending on the performance of material properties as well as the demonstration of quality assurance system during manufacturing, Chinese Steel Materials may be classified as Class E1 or E2 Steel Materials with a material class factor, Mc = 1.0 or 1.1 respectively, as discussed in Section 1.9. For ease of presentation, all welded sections presented in Design Tables 19 to 45 are conservatively assumed to be made of Class E2 Steel Materials. However, if Class E1 Steel Materials are used in the welded sections, Mc should then be taken as 1.0 and all the resistances presented in Design Tables 19 to 45 should be increased by a factor of 1.1 accordingly.
81
8.2
Design strengths For rolled sections with S275 and S355 Class E1 Steel Materials, the design strengths of the steel sections with steel plates of various thicknesses are presented in Table 8.4. Table 8.4 Design strengths of different steel grades of rolled sections Class E1 Steel Materials with Mc 1.0 Steel grade
S275
S355
Thickness, t (mm) t 16 16 < t 40 40 < t 63 63 < t 80 t 16 16 < t 40 40 < t 63 63 < t 80
Design strength (N/mm2) 275 265 255 245 355 345 335 325
For welded sections with Q235, Q275, Q345 and Q460 Class E2 Steel Materials, the design strengths of the steel sections with steel plates of different thicknesses are presented in Table 8.5. Table 8.5 Design strengths of different steel grades of welded sections Class E2 Steel Materials with Mc 1.1 Design strength, fy Thickness, t (N/mm2) (mm) t 16 213.6 16 < t 40 204.5 Q235 40 < t 60 195.5 60 < t 80 195.5 t 16 250.0 16 < t 40 240.9 Q275 40 < t 60 231.8 60 < t 80 222.7 t 16 313.6 16 < t 40 304.5 Q345 40 < t 63 295.5 63 < t 80 286.4 t 16 418.2 16 < t 40 400.0 Q460 40 < t 63 381.8 63 < t 80 363.6 Note: For ease of presentation, all welded sections are conservatively assumed to be made of Class E2 Steel Materials. However, if Class E1 Steel Materials are used in the Steel grade
welded sections, Mc should then be taken as 1.0 and all the resistances presented in Design Tables 19 to 45 should be increased by a factor of 1.1 accordingly.
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8.3
Section Classification Section classification of all the rolled and the welded sections are performed according to Clause 5.5 of EN 1993‐1‐1. Depending on the susceptibility of various plate elements of the sections against local buckling under compression, plastic or elastic cross‐section resistances may be readily mobilized for Class 1, 2 or 3 sections. For Class 4 sections, elastic properties are not applicable, and provisions given in EN 1993‐1‐8 should be considered. Table 8.6 presents the section classification rules given in Table 5.2 of EN 1993‐1‐1 for I‐ and H‐sections while Table 8.7 presents various limiting ratios of the geometric parameters of the sections, namely, cf / tf and d / tw for section classification under i) compression, ii) bending about the major axis, and iii) bending about the minor axis. Table 8.6 Section classification rules for I‐ and H‐sections z z
y
cf
y
d
d
cf
Rolled I‐section
Rolled H‐section
z z
y cf
cf
d
Plate element Internal part under compression, d/tw Internal part under bending, d/tw Outstanding part under compression, cf / tf
ε = 235/fy
Class 1 ≤ 33 ε ≤ 72 ε ≤ 9 ε
d
Class 2 ≤ 38 ε ≤ 83 ε ≤ 10 ε
fy (N/mm2)
235
275
345
355
460
ε
1.00
0.92
0.83
0.81
0.71
83
y
Class 3 ≤ 42 ε ≤ 124 ε ≤ 14 ε
Class 4 > 42 ε > 124 ε >14 ε
Table 8.7 Limiting ratios of section classification for I‐ and H‐sections I‐ and H‐sections under compression Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
Class 1
Class 2
Class3
8.3 7.3 9.0 8.3 7.4 6.4
9.3 8.1 10.0 9.2 8.3 7.1
12.9 11.4 14.0 12.9 11.6 10.0
30.5 26.8 33.0 30.5 27.2 23.6
35.1 30.9 38.0 35.1 31.4 27.2
38.8 34.2 42.0 38.8 34.7 30.0
I‐ and H‐sections under bending about the major axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
Class 1
Class 2
Class3
8.3 7.3 9.0 8.3 7.4 6.4
9.2 8.1 10.0 9.2 8.3 7.1
12.9 11.4 14.0 12.9 11.6 10.0
66.6 58.6 72.0 66.6 59.4 51.5
76.7 67.5 83.0 76.7 68.5 59.3
114.6 100.9 124.0 114.6 102.3 88.6
I‐ and H‐sections under bending about the minor axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Flange cf / tf
Web d / tw
Class 1
Class 2
Class 3
8.3 7.3 9.0 8.3 7.4 6.4
9.2 8.1 10.0 9.2 8.3 7.1
12.8 11.2 13.8 12.8 11.4 9.9
84
Class 1
Class 2
Class3
Not applicable
Not applicable
Table 8.8 presents the section classification rules given in Table 5.2 of EN 1993‐1‐1 for hot‐finished and cold‐formed hollow sections while Table 8.9 presents various limiting ratios of the geometric parameters of the hollow sections, namely, cf / t and cw / t for section classification under i) compression, ii) bending about the major axis, and iii) bending about the minor axis. Table 8.8 Section classification of hollow sections z
z
z y
y
cw
cw
h
cf
cf
t d
b
Hot‐finished circular hollow section CHS
Hot‐finished rectangular hollow section RHS
t
Hot‐finished square hollow section SHS
z
z
y
z
cw
y
cw
h
t
cf
d
t
b
Equivalent cold‐formed circular hollow section EWCHS
b
Equivalent cold‐formed square hollow section EWSHS
Equivalent cold‐formed rectangular hollow section EWRHS
Plate element Internal parts under compression, cf / t Internal parts under bending, cw / t
Class 1 ≤ 33 ε ≤ 72 ε
Class 2 ≤ 38 ε ≤ 83 ε
Class 3 ≤ 42 ε ≤ 124 ε
Class 4 > 42 ε > 124 ε
Circular section under compression and / or bending, d / t
≤ 50ε2
≤ 70ε2
≤ 90ε2
> 90ε2
ε = 235/fy
fy (N/mm2)
235
275
345
355
460
ε
1.00
0.92
0.83
0.81
0.71
85
Table 8.9 Limiting ratios of section classification for hollow sections a) Rectangular and square hollow sections Rectangular and square hollow sections under compression Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Flange
Web
cf / t
cw / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Rectangular and square hollow sections under bending about the major axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Flange
Web
cf / t
cw / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
Class 1 66.6 58.6 72.0 66.6 59.4 51.5
Class 2 76.7 67.5 83.0 76.7 68.5 59.3
Class 3 114.6 100.9 124.0 114.6 102.3 88.6
Rectangular and square hollow sections under bending about the minor axis Plate element Geometrical parameter Section classification S275 Rolled section S355 Q235 Q275 Welded section Q345 Q460
Class 1 30.5 26.8 33.0 30.5 27.2 23.6
Web
Flange
cw / t
cf / t
Class 2 35.1 30.9 38.0 35.1 31.4 27.2
Class 3 38.8 34.2 42.0 38.8 34.7 30.0
86
Class 1 66.6 58.6 72.0 66.6 59.4 51.5
Class 2 76.7 67.5 83.0 76.7 68.5 59.3
Class3 114.6 100.9 124.0 114.6 102.3 88.6
b)
Circular hollow sections
Circular hollow sections under i) compression, and ii) bending Plate element
Circular section
Geometrical parameter Section classification Rolled section
Welded section
S275 S355 Q235 Q275 Q345 Q460
d / t Class 1
Class 2
Class 3
42.7 33.1 50.0 42.7 34.1 25.5
59.8 46.3 70.0 59.8 47.7 35.8
76.9 59.6 90.0 76.9 61.3 46.0
8.4
Rolled Sections A wide range of rolled sections covered in this Section for application are summarized in Table 8.10. It should be noted that i) all rolled I‐sections available in BS 4‐1 are included in the Design Tables, i.e. I‐ sections from 127 x 76 x 13 kg/m to 914 x 419 x 388 kg/m with a total of 72 sections. ii) all rolled H‐sections available in BS 4‐1 are included in the Design Tables, i.e. H‐ sections from 152 x152 x 23 kg/m to 356 x 406 x 634 kg/m with a total of 31 sections. iii) selected hot‐finished circular hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. CHS from 139.7 x 6.3 mm to 813.0 x 20.0 mm with a total of 55 sections. iv) selected hot‐finished rectangular hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. RHS from 120 x 80 x 6.3 mm to 500 x 300 x 20.0 mm with a total of 44 sections. v) selected hot‐finished square hollow sections with standard plate thicknesses available in EN 10210‐2 are included in the Design Tables, i.e. SHS from 100 x 100 x 6.3 mm to 400 x 400 x 20.0 mm with a total of 32 sections.
87
Table 8.10
Full ranges of typical rolled sections available for application
I-section
H-section
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
29
43
Number of sections: Total:
72
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
31
Hot-finished circular hollow section 139.7x6.3 x8.0 x10.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 x16.0 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.0x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Hot-finished rectangular hollow section 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
55
44
Hot-finished square hollow section 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.3 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
32 234
# Limited availability. Full series of I‐ and H‐sections have been provided while only selected hot‐finished circular, rectangular and square hollow sections are included. Section resistances for S275 and S355 steel materials are tabulated separately.
88
8.5
Equivalent Welded Sections Design data on equivalent welded sections are provided to assist structural engineers to use welded sections readily whenever necessary. The design methods for equivalent welded sections are described in the following sections.
8.5.1 Equivalent welded I‐Sections (1) The section depth h of the welded I‐sections is selected to be equal to that of the rolled I‐sections under consideration plus a maximum of 5 mm. (2) The plate thicknesses of the flanges and the webs of the welded I‐sections are:
6.0 mm 12.0 mm 25.0 mm (3)
8.0 mm 16.0 mm 30.0 mm
10.0 mm 20.0 mm 40.0 mm
In most cases, both the web thickness and the flange thickness of the equivalent welded I‐sections are taken to be larger than those of the rolled I‐sections as far as rational, as shown in Figure 8.2. Moreover, the flange width of the welded I‐sections is selected in such a way as to achieve a value of cross‐sectional area which is at least 10% larger than that of the rolled I‐sections. z
z tf
tf 5 max.
y
y
h
h 5 max.
tw 5 max.
tw
b 30 typ.
b
Equivalent welded I‐section
Typical rolled I‐section
Figure 8.2 Design method of equivalent welded I‐sections (4)
For a rolled I‐section with a web thickness or a flange thickness of odd values, for example, tw = 8.7 mm or tf = 13.2 mm, the web thickness and the flange thickness of the welded I‐section are then selected to be 8.0 mm and 12.0 mm (rather than 10.0 mm and 16.0 mm) respectively, i.e. of thinner plates. In order to achieve equivalency, the flange width of the welded I‐section will then be increased significantly, when compared with that of the rolled I‐section, in order to acquire a larger moment resistance of that of the rolled I‐section.
89
8.5.2 Equivalent welded H‐sections
(1) (2)
The section depth h of the welded H‐sections is selected to be equal to that of the rolled H‐sections under consideration plus a maximum of 5 mm. The plate thicknesses of the flanges and the webs of the welded H‐sections are:
6.0 mm 12.0 mm 25.0 mm 50.0 mm
(3)
8.0 mm 16.0 mm 30.0 mm 60.0 mm
10.0 mm 20.0 mm 40.0 mm 80.0 mm
In most cases, both the web thickness and the flange thickness of the welded H‐ sections are taken to be larger than those of the rolled H‐sections as far as rational, as shown in Figure 8.3. Moreover, the flange width of the welded H‐sections is selected in such a way as to achieve a value of cross‐sectional area which is at least 10% larger than that of the rolled H‐sections. z
z
tf
tf+10 max.
hw
y
O
hw
h
h + 5 max. O
tw + 5
tw
b
b 50 typ.
Typical rolled H‐section
Equivalent welded H‐section
Figure 8.3 Design method of equivalent welded H‐sections (4)
y
As there is a significant reduction in the yield strengths of thick steel plates, especially when tf ≥ 40 mm, the flange thicknesses of the proposed welded H‐ sections may be significantly larger than those of the rolled H‐sections. Nevertheless, the maximum increase in the flange thickness is limited to 10 mm.
90
8.5.3 Equivalent cold‐formed circular hollow sections
(1)
(2)
The external diameter d of the EWCHS is selected to be equal to that of the hot‐ finished CHS under consideration plus a maximum of 5 mm. The plate thicknesses of the EWCHS are:
6.0 mm 12.0 mm
8.0 mm 16.0 mm
10.0 mm 20.0 mm
It should be noted that the plate thickness of the EWCHS is selected to be equal to that of the hot‐finished CHS under consideration ± 0.5 mm, as shown in Figure 8.4. z
z
t
t 0.5 max
y
y
d
d 5 max
Typical hot‐finished circular hollow section CHS
Equivalent cold‐formed circular hollow section EWCHS
Figure 8.4 Design method for equivalent cold‐formed circular hollow sections (3)
It should be noted that the largest EWCHS covered in GB/T 6728 has an external diameter equal to 610.0 mm. For those EWCHS with external diameters equal to 711.0 and 813.0 mm, refer to GB/T 21835 for details.
91
8.5.4 Equivalent cold‐formed rectangular and square hollow sections (1) The external dimensions, h and b, of the EWRHS and the EWSHS are selected to be equal to those of the hot‐finished sections under consideration, as shown in Figures 8.5 and 8.6. (2) The plate thicknesses of the EWRHS and the EWSHS are:
6.0 mm 12.0 mm
8.0 mm 16.0 mm
10.0 mm 20.0 mm z
r
ro
cf
r
ro
cw
y
y h
h
t
b
t
b
Typical hot‐finished rectangular hollow section RHS
Equivalent cold‐formed rectangular hollow section EWRHS
Figure 8.5 Design method for equivalent cold‐formed rectangular hollow sections z ri
z
ro
cf
ri
ro
cw
y
y h
h t
t 0.5 b Equivalent cold‐formed square hollow section EWSHS
b Typical Hot‐finished square hollow section SHS
Figure 8.6 Design method for equivalent cold‐formed square hollow sections
92
(3)
It should be noted that both the inner and the outer corner radii, ri and ro , for cold‐ formed RHS and SHS given in EN 10219‐2 are considered to be very stringent, as shown in Table 8.11. In some cases, these limiting values are even smaller than those given in EN 10210‐2 for hot‐finished RHS and SHS. Table 8.11 Allowable corner radii of hot‐finished and cold‐formed RHS and SHS EN 10210‐2: Hot‐finished structural hollow sections of non‐alloy and fine grain steels Thickness All range Hot finished ri 2.0 t RHS, SHS ro 3.0 t EN 10219‐2: Cold‐formed welded structural hollow sections of non‐alloy and fine grain steels Thickness t = 6 mm t = 8, 10 mm t = 12, 16, 20 mm Cold‐formed ri 0.6 t ~ 1.4 t 1.0 t ~ 2.0 t 1.4 t ~ 2.6 t RHS, SHS ro 1.6 t ~ 2.4 t 2.0 t ~ 3.0 t 2.4 t ~ 3.6 t GB/T 6728: Cold‐formed steel hollow sections of general structures Thickness t = 6, 8, 10 mm t = 12, 16, 20 mm ri 1.0 t ~ 2.0 t 1.0 t ~ 2.5 t Q235 Q275 ro 2.0 t ~ 3.0 t 2.0 t ~ 3.5 t Q345 ri 1.0 t ~ 2.5 t 1.5 t ~ 3.0 t Q460 ro 2.0 t ~ 3.5 t 2.5 t ~ 4.0 t Moreover, according to Table 8.12, large local strains are always induced in the corners of the cold‐formed RHS and SHS with small corner radii. Hence, welding in the immediate vicinity of the corners requires caution, otherwise significant cracking may be induced. Table 8.12 Corner radii and local residual strains in cold‐formed zones BS EN 1993‐1‐8: Design of steel structures: Design of joints Maximum thickness (mm) Residual ri / t strain Static load control Fatigue control Killed steel 25 ≤ 2% Any Any Any 10 ≤ 5% Any 16 Any 3.0 ≤ 14% 24 12 24 2.0 ≤ 20% 12 10 12 1.5 ≤ 25% 8 8 8 1.0 ≤ 33% 4 4 4 Note: Conflict with EN 10219 will be assumed satisfied if t ≤ 12.5 mm.
93
(4)
Table 8.13 presents the proposed corner radii of EWRHS and EWSHS for various steel grades. It should be noted that these corner radii are less stringent when compared to those given in Table 8.11 for both hot‐finished and cold‐formed RHS and SHS to EN10210‐2 and 10219‐2 respectively. Nevertheless, these corner radii are permitted according to GB/T 6728.
Table 8.13 Proposed corner radii of EWRHS and EWSHS Equivalent cold‐formed Corner radii t = 6, 8, 10 mm hollow sections 2.5 t ri EWRHS
t = 12, 16, 20 mm 3.0 t
EWSHS (5) (6) 8.6
ro
3.5 t
4.0 t
For further details on the dimensions of cold‐formed rectangular and square hollow sections, refer to GB/T 6728. A full list of the rolled and of the welded sections are presented in Tables 8.10 and 8.14 respectively. Design Tables on Section Dimensions, Properties and Resistances According to the comprehensive design rules given in EN 1993‐1‐1, a total of 45 Design Tables are compiled to assist structural engineers to use both rolled and welded sections whenever appropriate in practical design. These Design Tables include:
12 Design Tables on section dimensions and properties; 12 Design Tables on section resistances of rolled sections; and 21 Design Tables on section resistances of welded sections.
Section resistances for a total of 468 rolled and welded sections are calculated and tabulated for a wide range of section types and dimensions as well as a wide range of steel materials with different yield strengths. Table 8.15 summarizes various key design parameters of structural steel design of the Design Tables. 8.6.1 Section dimensions and properties For details on the selection of section dimensions for various rolled and welded sections, refer to Sections 8.4 and 8.5 respectively. Expressions for the calculations of various section properties are fully presented in Steel Building Design: Design Data (2013).
94
Table 8.14
Full ranges of proposed equivalent welded sections for application
Welded I-section
Welded H-section
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
460x190x102 x94 x83 x76 x64 460x160x85 x75 x68 x59 x54 405x180x76 x70 x59 x53 400x140x45 x39 355x180x72 x61 x54 x49 355x170x44 x38 305x160x58 x44 x38 305x125x50 x42 x39 305x110x36 x32 x26 265x140x43 x38 x30 265x100x28 x25 x22 205x135x30 x26 205x100x25 180x100x19 150x90x17 125x75x14
29
43
Number of sections Total
72
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Cold-formed circular hollow section 140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
Cold-formed rectangular hollow section 120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 x16.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
Cold-formed square hollow section 100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
55
44
32
31
234
Notes: (1) All equivalent welded sections are proposed to match the structural performance of those rolled sections given in Table 8.10. (2) Design data for welded sections with Q235, Q275, Q345 and Q460 steel materials are tabulated.
95
8.6.2 Section resistances The resistances of the cross‐sections of various rolled and welded sections against bending moments, shear forces and axial compression forces have been calculated and tabulated. It should be noted that for all the Design Tables, Class E1 Steel Materials are assumed in all rolled sections while Class E2 Steel Materials are assumed in all welded sections. If Class E1 Steel Materials are used in the welded sections, Mc should be taken as 1.0, and all the resistances should be increased by a factor of 1.1 accordingly. 8.6.2.1 Moment resistances All rolled and welded sections are doubly symmetrical, and most of them have two distinctive moment resistances, namely i) ii)
My,Rd about the major y‐y axis, and Mz,Rd about the minor z‐z axis.
However, only a moment resistance, MRd, is provided for both circular and square hollow sections. The corresponding flexural rigidities as well as the section classifications of the sections for bending about the major and the minor axes are also given as appropriate. However, it should be noted that no resistance is given for any Class 4 section owing to the occurrence of local buckling in plate elements of the section, leading to low structural efficiency. 8.6.2.2 Shear resistances The shear resistances of the sections are calculated conservatively with the factor for shear area, η , being taken to 1.0 as recommended in Clause 6.2.6(3) of EN1993‐1‐1. Hence, there is no need to check against shear buckling in the web plate elements when the following conditions apply: i) ii)
d 72 t hw 72 t
for rolled sections
for welded sections
It should be noted that only the shear resistances of the sections acting along the direction of the webs of the sections are provided. 8.6.2.3 Axial compression resistances In most sections, the gross areas of the sections are fully effective owing to the stocky nature of the plate elements. Hence, full compression resistances of these sections are readily mobilized.
96
However, for both rolled and welded I‐sections, RHS and CHS with large d / t values under high compressive stress levels, local buckling in the plate elements of these cross‐sections is critical. Hence, they are taken as Class 4 sections, and effective areas should be used, instead of their gross areas, in the calculation of the cross‐ section resistances against axial compression forces. These resistances are printed in italics in the Design Tables. Refer to Section 4.4 of EN 1993‐1‐5 for details of the design rule for evaluation of effective areas using the reduction factor for plate buckling, ρ . As a whole, the Design Tables provide practical design data for structural engineers to assess the structural performance of various sections against material yielding as well as member buckling during practical design. Table 8.15 Summary of Design Tables Rolled Section type Design Table sections I‐section 01A / 01B 02A / 02B Dimensions H‐section 03A / 03B and CHS 04 properties RHS 05 SHS 06 Steel materials Section resistances Mc = 1.0
Welded sections Dimensions and properties
S355
07 08 09 10 11 12
13 14 15 16 17 18
I‐section H‐section CHS RHS SHS Section type
Design Table
EWI‐section
19A / 19B 20A / 20B 21A / 21B 22 23 24
EWH‐section EWCHS EWRHS EWSHS Steel materials
Section resistances Mc = 1.1
S275
EWI‐section EWH‐section EWCHS EWRHS EWSHS
Q235
Q275
Q345
Q460
25 26 27
28 29 30 31 32 33
34 35 36 37 38 39
40 41 42 43 44 45
Not applicable
97
98
Design Tables on Section Dimensions, Properties and Resistances for Rolled and Welded Sections
99
Rolled sections Table No. Design Table 01A Design Table 01B Design Table 02A Design Table 02B Design Table 03A Design Table 03B Design Table 04 Design Table 05 Design Table 06
Title Section dimensions of rolled I-sections (1) Section properties of rolled I-sections (1) Section dimensions of rolled I-sections (2) Section properties of rolled I-sections (2) Section dimensions of rolled H-sections Section properties of rolled H-sections Section dimensions and properties of hot-finished CHS Section dimensions and properties of hot-finished RHS Section dimensions and properties of hot-finished SHS
Design Table 07 Design Table 08 Design Table 09 Design Table 10 Design Table 11 Design Table 12
Section resistances of rolled I-sections: S275 steel (1) Section resistances of rolled I-sections: S275 steel (2) Section resistances of rolled H-sections: S275 steel Section resistances of hot-finished CHS: S275 steel Section resistances of hot-finished RHS: S275 steel Section resistances of hot-finished SHS: S275 steel
114 115 116 117 118 119
Design Table 13 Design Table 14 Design Table 15 Design Table 16 Design Table 17 Design Table 18
Section resistances of rolled I-sections: S355 steel (1) Section resistances of rolled I-sections: S355 steel (2) Section resistances of rolled H-sections: S355 steel Section resistances of hot-finished CHS: S355 steel Section resistances of hot-finished RHS: S355 steel Section resistances of hot-finished SHS: S355 steel
122 123 124 125 126 127
100
Page 104 105 106 107 108 109 110 111 112
Welded sections Table No. Design Table 19A Design Table 19B Design Table 20A Design Table 20B Design Table 21A Design Table 21B Design Table 22 Design Table 23 Design Table 24
Title Section dimensions of welded I-sections (1) Section properties of welded I-sections (1) Section dimensions of welded I-sections (2) Section properties of welded I-sections (2) Section dimensions of welded H-sections Section properties of welded H-sections Section dimensions and properties of cold-formed CHS Section dimensions and properties of cold-formed RHS Section dimensions and properties of cold-formed SHS
Page 130 131 132 133 134 135 136 137 138
Design Table 25 Design Table 26 Design Table 27
Section resistances of welded I-sections: Q235 steel (1) Section resistances of welded I-sections: Q235 steel (2) Section resistances of welded H-sections: Q235 steel
140 141 142
Design Table 28 Design Table 29 Design Table 30 Design Table 31 Design Table 32 Design Table 33
Section resistances of welded I-sections: Q275 steel (1) Section resistances of welded I-sections: Q275 steel (2) Section resistances of welded H-sections: Q275 steel Section resistances of cold-formed CHS: Q275 steel Section resistances of cold-formed RHS: Q275 steel Section resistances of cold-formed SHS: Q275 steel
144 145 146 147 148 149
Design Table 34 Design Table 35 Design Table 36 Design Table 37 Design Table 38 Design Table 39
Section resistances of welded I-sections: Q345 steel (1) Section resistances of welded I-sections: Q345 steel (2) Section resistances of welded H-sections: Q345 steel Section resistances of cold-formed CHS: Q345 steel Section resistances of cold-formed RHS: Q345 steel Section resistances of cold-formed SHS: Q345 steel
152 153 154 155 156 157
Design Table 40 Design Table 41 Design Table 42 Design Table 43 Design Table 44 Design Table 45
Section resistances of welded I-sections: Q460 steel (1) Section resistances of welded I-sections: Q460 steel (2) Section resistances of welded H-sections: Q460 steel Section resistances of cold-formed CHS: Q460 steel Section resistances of cold-formed RHS: Q460 steel Section resistances of cold-formed SHS: Q460 steel
160 161 162 163 164 165
101
102
Design Tables 01 to 06 for Section Dimensions and Properties of Rolled Sections I-sections H-sections CHS RHS SHS
103
Design Table 01A Section dimensions of rolled I-sections (1) tf
z
r y
tw
d h
cf
b Mass per Depth Width Meter of Section of Section I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
kg/m 388.0 343.3 289.1 253.4 224.2 200.9 226.5 193.8 175.9 196.8 173.0 146.9 133.9 170.2 152.4 140.1 125.2 238.1 179.0 149.2 139.9 125.1 113.0 101.2 122.0 109.0 101.0 92.1 82.2
mm 921.0 911.8 926.6 918.4 910.4 903.0 850.9 840.7 834.9 769.8 762.2 754.0 750.0 692.9 687.5 683.5 677.9 635.8 620.2 612.4 617.2 612.2 607.6 602.6 544.5 539.5 536.7 533.1 528.3
mm 420.5 418.5 307.7 305.5 304.1 303.3 293.8 292.4 291.7 268.0 266.7 265.2 264.4 255.8 254.5 253.7 253.0 311.4 307.1 304.8 230.2 229.0 228.2 227.6 211.9 210.8 210.0 209.3 208.8
Thickness Web tw mm 21.4 19.4 19.5 17.3 15.9 15.1 16.1 14.7 14.0 15.6 14.3 12.8 12.0 14.5 13.2 12.4 11.7 18.4 14.1 11.8 13.1 11.9 11.1 10.5 12.7 11.6 10.8 10.1 9.6
Root Radius
Depth between Fillets
r mm 24.1 24.1 19.1 19.1 19.1 19.1 17.8 17.8 17.8 16.5 16.5 16.5 16.5 15.2 15.2 15.2 15.2 16.5 16.5 16.5 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7
d mm 799.6 799.6 824.4 824.4 824.4 824.4 761.7 761.7 761.7 686.0 686.0 686.0 686.0 615.1 615.1 615.1 615.1 540.0 540.0 540.0 547.6 547.6 547.6 547.6 476.5 476.5 476.5 476.5 476.5
Flange tf mm 36.6 32.0 32.0 27.9 23.9 20.2 26.8 21.7 18.8 25.4 21.6 17.5 15.5 23.7 21.0 19.0 16.2 31.4 23.6 19.7 22.1 19.6 17.3 14.8 21.3 18.8 17.4 15.6 13.2
Limited availability.
104
Ratios for Local Buckling
Surface Area per Meter per Tonne
cf/tf
d/tw
4.8 5.5 3.9 4.5 5.2 6.2 4.5 5.6 6.4 4.3 5.1 6.3 7.1 4.4 5.0 5.6 6.5 4.1 5.5 6.6 4.3 4.9 5.5 6.5 4.1 4.6 5.0 5.6 6.6
37.4 41.2 42.3 47.7 51.8 54.6 47.3 51.8 54.4 44.0 48.0 53.6 57.2 42.4 46.6 49.6 52.6 29.3 38.3 45.8 41.8 46.0 49.3 52.2 37.5 41.1 44.1 47.2 49.6
m2 3.44 3.42 3.01 2.99 2.97 2.96 2.81 2.79 2.78 2.55 2.53 2.51 2.51 2.35 2.34 2.33 2.32 2.45 2.41 2.39 2.11 2.09 2.08 2.07 1.89 1.88 1.87 1.86 1.85
m2 8.87 10.0 10.4 11.8 13.2 14.7 12.4 14.4 15.8 13.0 14.6 17.1 18.7 13.8 15.4 16.6 18.5 10.3 13.5 16.0 15.1 16.7 18.4 20.5 15.5 17.2 18.5 20.2 22.5
Design Table 01B Section properties of rolled I-sections (1) z
tf r y
d h tw
cf b
I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
Second Moment of Area
Elastic Modulus
cm4 720000 626000 504000 436000 376000 325000 340000 279000 246000 240000 205000 169000 151000 170000 150000 136000 118000 209000 153000 126000 112000 98600 87300 75800 76000 66800 61500 55200 47500
cm3 15600 13700 10900 9500 8270 7200 7980 6640 5890 6230 5390 4470 4020 4920 4370 3990 3480 6590 4930 4110 3620 3220 2870 2520 2790 2480 2290 2070 1800
,
cm4 45400 39200 15600 13300 11200 9420 11400 9070 7800 8170 6850 5460 4790 6630 5780 5210 4380 15800 11400 9310 4510 3930 3430 2910 3390 2940 2690 2390 2010
,
cm3 2160 1870 1010 871 739 621 773 620 535 610 514 411 362 518 455 409 346 1020 743 611 391 343 301 256 320 279 256 228 192
Plastic Modulus ,
cm3 17700 15500 12600 10900 9530 8350 9160 7640 6810 7170 6200 5160 4640 5630 5000 4560 3990 7490 5550 4590 4140 3680 3280 2880 3200 2830 2610 2360 2060
Buckling Parameter
Torsional Index
Warping Constant
Torsional Constant
Area of Section
26.7 30.1 31.9 36.2 41.3 46.9 35.0 41.6 46.5 33.1 38.0 45.2 49.8 31.8 35.4 38.6 43.8 21.3 27.7 32.7 30.6 34.0 38.0 43.0 27.6 30.9 32.8 36.4 41.6
dm6 88.9 75.8 31.2 26.4 22.1 18.4 19.3 15.2 13.0 11.3 9.39 7.40 6.46 7.42 6.42 5.72 4.80 14.5 10.2 8.17 3.99 3.45 2.99 2.52 2.32 1.99 1.81 1.60 1.33
cm4 1730 1190 926 626 427 291 514 306 221 404 267 159 119 308 220 169 116 785 340 200 216 154 111 77 178 126 101 75.7 51.5
cm2 494 437 368 323 286 256 289 247 224 251 220 187 171 217 194 178 159 303 228 190 178 159 144 129 155 139 127 117 105
A
,
cm3 3340 2890 1600 1370 1160 982 1210 974 842 958 807 647 570 811 710 638 542 1570 1140 937 611 535 469 400 500 436 399 355 300
Limited availability.
105
0.885 0.883 0.867 0.865 0.866 0.853 0.869 0.862 0.856 0.869 0.865 0.858 0.853 0.872 0.871 0.872 0.863 0.886 0.885 0.886 0.875 0.875 0.870 0.863 0.878 0.875 0.874 0.873 0.863
Design Table 02A Section dimensions of rolled I-sections (2) z
tf r y
d h tw
cf b Mass per Depth Width Meter of Section of Section I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
kg/m 98.3 89.3 82.0 74.3 67.1 82.1 74.2 67.2 59.8 52.3 74.2 67.1 60.1 54.1 46.0 39.0 67.1 57.0 51.0 45.0 39.1 33.1 54.0 46.1 40.3 48.1 41.9 37.0 32.8 28.2 24.8 43.0 37.0 31.1 28.3 25.2 22.0 30.0 25.1 23.1 19.0 16.0 13.0
Mm 467.2 463.4 460.0 457.0 453.4 465.8 462.0 458.0 454.6 449.8 412.8 409.4 406.4 402.6 403.2 398.0 363.4 358.0 355.0 351.4 353.4 349.0 310.4 306.6 303.4 311.0 307.2 304.4 312.7 308.7 305.1 259.6 256.0 251.4 260.4 257.2 254.0 206.8 203.2 203.2 177.8 152.4 127.0
mm 192.8 191.9 191.3 190.4 189.9 155.3 154.4 153.8 152.9 152.4 179.5 178.8 177.9 177.7 142.2 141.8 173.2 172.2 171.5 171.1 126.0 125.4 166.9 165.7 165.0 125.3 124.3 123.4 102.4 101.8 101.6 147.3 146.4 146.1 102.2 101.9 101.6 133.9 133.2 101.8 101.2 88.7 76.0
Root Radius
Thickness Web tw mm 11.4 10.5 9.9 9.0 8.5 10.5 9.6 9.0 8.1 7.6 9.5 8.8 7.9 7.7 6.8 6.4 9.1 8.1 7.4 7.0 6.6 6.0 7.9 6.7 6.0 9.0 8.0 7.1 6.6 6.0 5.8 7.2 6.3 6.0 6.3 6.0 5.7 6.4 5.7 5.4 4.8 4.5 4.0
Flange tf mm 19.6 17.7 16.0 14.5 12.7 18.9 17.0 15.0 13.3 10.9 16.0 14.3 12.8 10.9 11.2 8.6 15.7 13.0 11.5 9.7 10.7 8.5 13.7 11.8 10.2 14.0 12.1 10.7 10.8 8.8 7.0 12.7 10.9 8.6 10.0 8.4 6.8 9.6 7.8 9.3 7.9 7.7 7.6
106
Depth between Fillets
Ratios for Local Buckling
Surface Area per Meter per Tonne
r mm 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 8.9 8.9 8.9 8.9 8.9 8.9 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6 7.6
d mm 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 407.6 360.4 360.4 360.4 360.4 360.4 360.4 311.6 311.6 311.6 311.6 311.6 311.6 265.2 265.2 265.2 265.2 265.2 265.2 275.9 275.9 275.9 219.0 219.0 219.0 225.2 225.2 225.2 172.4 172.4 169.4 146.8 121.8 96.6
cf/tf
d/tw
4.1 4.6 5.0 5.6 6.3 3.3 3.7 4.2 4.7 5.7 4.1 4.7 5.2 5.8 5.1 6.7 4.6 5.5 6.3 7.4 4.6 5.8 5.2 6.0 6.9 3.5 4.1 4.6 3.7 4.6 5.8 4.9 5.7 7.3 4.0 4.8 5.9 5.9 7.2 4.4 5.1 4.5 3.7
35.8 38.8 41.2 45.3 48.0 38.8 42.5 45.3 50.3 53.6 33.1 37.9 41.0 45.6 53.0 56.3 34.2 38.5 42.1 44.5 47.2 51.9 33.6 39.6 44.2 29.5 33.2 37.4 41.8 46.0 47.6 30.4 34.8 36.5 35.7 37.5 39.5 26.9 30.2 31.4 30.6 27.1 24.2
m2 1.67 1.66 1.65 1.64 1.63 1.51 1.50 1.50 1.49 1.48 1.51 1.50 1.49 1.48 1.34 1.33 1.38 1.37 1.36 1.36 1.18 1.17 1.26 1.25 1.24 1.09 1.08 1.07 1.01 1.00 0.992 1.08 1.07 1.06 0.904 0.897 0.890 0.923 0.915 0.790 0.738 0.638 0.537
m2 17.0 18.6 20.1 22.1 24.3 18.4 20.2 22.3 24.9 28.3 20.4 22.3 24.8 27.3 29.1 34.1 20.6 24.1 26.7 30.2 30.2 35.4 23.3 27.1 30.8 22.7 25.8 28.9 30.8 35.5 40.0 25.1 28.9 34.0 31.9 35.7 40.5 30.8 36.5 34.2 38.7 40.0 41.4
Design Table 02B Section properties of rolled I-sections (2) z
tf r y
d h tw
cf b Second Moment of Area I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Elastic Modulus ,
,
Plastic Modulus ,
Buckling Parameter
Torsional Index
Warping Constant
Torsional Constant
Area of Section A
dm6
cm4
cm2
1.18 1.04 0.922 0.818 0.705 0.591 0.518 0.448 0.387 0.311 0.608 0.533 0.466 0.392 0.207 0.155 0.412 0.330 0.286 0.237 0.105 0.081 0.234 0.195 0.164 0.102 0.0846 0.0725 0.0442 0.0349 0.0270 0.103 0.0857 0.0660 0.0280 0.0230 0.0182 0.0374 0.0294 0.0154 0.00990 0.00470 0.00200
121 90.7 69.2 51.8 37.1 89.2 65.9 47.7 33.8 21.4 62.8 46.1 33.3 23.1 19.0 10.7 55.7 33.4 23.8 15.8 15.1 8.79 34.8 22.2 14.7 31.8 21.1 14.8 12.2 7.40 4.77 23.9 15.3 8.55 9.57 6.42 4.15 10.3 5.96 7.02 4.41 3.56 2.85
125 114 104 94.6 85.5 105 94.5 85.6 76.2 66.6 94.5 85.5 76.5 69.0 58.6 49.7 85.5 72.6 64.9 57.3 49.8 42.1 68.8 58.7 51.3 61.2 53.4 47.2 41.8 35.9 31.6 54.8 47.2 39.7 36.1 32.0 28.0 38.2 32.0 29.4 24.3 20.3 16.5
,
cm4
cm4
cm3
cm3
cm3
cm3
45700 41000 37100 33300 29400 36600 32700 28900 25500 21400 27300 24300 21600 18700 15700 12500 19500 16000 14100 12100 10200 8250 11700 9900 8500 9570 8200 7170 6500 5370 4460 6540 5540 4410 4000 3410 2840 2900 2340 2100 1360 834 473
2350 2090 1870 1670 1450 1180 1050 913 795 645 1550 1360 1200 1020 538 410 1360 1110 968 811 358 280 1060 896 764 461 389 336 194 155 123 677 571 448 179 149 119 385 308 164 137 89.8 55.7
1960 1770 1610 1460 1300 1570 1410 1260 1120 950 1320 1190 1060 930 778 629 1070 896 796 687 576 473 754 646 560 616 534 471 416 348 292 504 433 351 308 266 224 280 230 207 153 109 74.6
243 218 196 176 153 153 136 119 104 84.6 172 153 135 115 75.7 57.8 157 129 113 94.8 56.8 44.7 127 108 92.6 73.6 62.6 54.5 37.9 30.5 24.2 92.0 78.0 61.3 34.9 29.2 23.5 57.5 46.2 32.2 27.0 20.2 14.7
2230 2010 1830 1650 1470 1810 1630 1450 1290 1100 1500 1350 1200 1050 888 724 1210 1010 896 775 659 543 846 720 623 711 614 539 481 403 342 566 483 393 353 306 259 314 258 234 171 123 84.2
379 338 304 272 237 240 213 187 163 133 267 237 209 178 118 90.8 243 199 174 147 89.0 70.2 196 166 142 116 98.4 85.4 60.0 48.4 38.8 141 119 94.1 54.8 46.0 37.3 88.2 70.9 49.7 41.6 31.2 22.6
107
0.881 0.878 0.879 0.877 0.873 0.872 0.872 0.868 0.868 0.859 0.882 0.880 0.880 0.871 0.871 0.858 0.886 0.882 0.881 0.874 0.871 0.863 0.889 0.890 0.889 0.873 0.872 0.872 0.867 0.859 0.846 0.891 0.890 0.879 0.873 0.866 0.856 0.882 0.876 0.888 0.886 0.890 0.894
25.8 28.3 30.8 33.8 37.8 27.4 30.1 33.6 37.5 43.8 27.5 30.4 33.7 38.3 39.0 47.4 24.4 28.8 32.1 36.8 35.2 42.1 23.6 27.1 31.0 23.3 26.5 29.7 31.6 37.3 43.4 21.1 24.3 29.6 27.5 31.4 36.3 21.5 25.6 22.4 22.6 19.5 16.3
Design Table 03A Section dimensions of rolled H-sections z
tf r h
y
tw d h
cf
b Mass per Depth Width Meter of Section of Section H-Sections
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
kg/m 633.9 551.0 467.0 393.0 339.9 287.1 235.1 201.9 177.0 152.9 129.0 282.9 240.0 198.1 158.1 136.9 117.9 96.9 167.1 132.0 107.1 88.9 73.1 86.1 71.0 60.0 52.0 46.1 37.0 30.0 23.0
mm 474.6 455.6 436.6 419.0 406.4 393.6 381.0 374.6 368.2 362.0 355.6 365.3 352.5 339.9 327.1 320.5 314.5 307.9 289.1 276.3 266.7 260.3 254.1 222.2 215.8 209.6 206.2 203.2 161.8 157.6 152.4
mm 424.0 418.5 412.2 407.0 403.0 399.0 394.8 374.7 372.6 370.5 368.6 322.2 318.4 314.5 311.2 309.2 307.4 305.3 265.2 261.3 258.8 256.3 254.6 209.1 206.4 205.8 204.3 203.6 154.4 152.9 152.2
Thickness Web tw mm 47.6 42.1 35.8 30.6 26.6 22.6 18.4 16.5 14.4 12.3 10.4 26.8 23.0 19.1 15.8 13.8 12.0 9.9 19.2 15.3 12.8 10.3 8.6 12.7 10.0 9.4 7.9 7.2 8.0 6.5 5.8
Root Radius
Depth between Fillets
r mm 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 12.7 12.7 12.7 12.7 12.7 10.2 10.2 10.2 10.2 10.2 7.6 7.6 7.6
d mm 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 290.2 246.7 246.7 246.7 246.7 246.7 246.7 246.7 200.3 200.3 200.3 200.3 200.3 160.8 160.8 160.8 160.8 160.8 123.6 123.6 123.6
Flange tf mm 77.0 67.5 58.0 49.2 42.9 36.5 30.2 27.0 23.8 20.7 17.5 44.1 37.7 31.4 25.0 21.7 18.7 15.4 31.7 25.3 20.5 17.3 14.2 20.5 17.3 14.2 12.5 11.0 11.5 9.4 6.8
Ratios for Local Buckling
Surface Area per Meter per Tonne
Limited availability.
108
cf/tf
d/tw
2.3 2.6 3.0 3.5 4.0 4.7 5.7 6.1 6.9 7.9 9.4 3.0 3.5 4.2 5.3 6.1 7.1 8.6 3.5 4.4 5.4 6.4 7.8 4.3 5.1 6.2 7.0 8.0 5.7 7.0 9.7
6.1 6.9 8.1 9.5 10.9 12.8 15.8 17.6 20.2 23.6 27.9 9.2 10.7 12.9 15.6 17.9 20.6 24.9 10.4 13.1 15.6 19.4 23.3 12.7 16.1 17.1 20.4 22.3 15.5 19.0 21.3
m2 2.52 2.47 2.42 2.38 2.35 2.31 2.28 2.19 2.17 2.16 2.14 1.94 1.91 1.87 1.84 1.82 1.81 1.79 1.58 1.55 1.52 1.50 1.49 1.24 1.22 1.21 1.20 1.19 0.912 0.901 0.889
m2 3.98 4.48 5.18 6.06 6.91 8.05 9.70 10.8 12.3 14.1 16.6 6.86 7.96 9.44 11.6 13.3 15.4 18.5 9.46 11.7 14.2 16.9 20.4 14.4 17.2 20.2 23.1 25.8 24.7 30.0 38.7
Design Table 03B Section properties of rolled H-sections z
tf r h
y
tw d h
cf
b
H-Sections
Second Moment of Area
Elastic Modulus ,
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
cm4 275000 227000 183000 147000 123000 99900 79100 66300 57100 48600 40200 78900 64200 50900 38700 32800 27700 22200 30000 22500 17500 14300 11400 9450 7620 6130 5260 4570 2210 1750 1250
cm4 98100 82700 67800 55400 46900 38700 31000 23700 20500 17600 14600 24600 20300 16300 12600 10700 9060 7310 9870 7530 5930 4860 3910 3130 2540 2070 1780 1550 706 560 400
cm3 11600 9960 8380 7000 6030 5070 4150 3540 3100 2680 2260 4320 3640 3000 2370 2050 1760 1450 2080 1630 1310 1100 898 850 706 584 510 450 273 222 164
,
cm3 4630 3950 3290 2720 2330 1940 1570 1260 1100 948 793 1530 1280 1040 808 692 589 479 744 576 458 379 307 299 246 201 174 152 91.5 73.3 52.6
Buckling Parameter
Plastic Modulus ,
cm3 14200 12100 10000 8220 7000 5810 4690 3970 3460 2960 2480 5110 4250 3440 2680 2300 1960 1590 2420 1870 1480 1220 992 977 799 656 567 497 309 248 182
Torsional Index
Warping Constant
Torsional Constant
Area of Section
5.46 6.05 6.86 7.86 8.85 10.2 12.1 13.4 15.0 17.0 19.9 7.65 8.74 10.2 12.5 14.2 16.2 19.3 8.49 10.3 12.4 14.5 17.3 10.2 11.9 14.1 15.8 17.7 13.3 16.0 20.7
dm6 38.8 31.1 24.3 18.9 15.5 12.3 9.54 7.16 6.09 5.11 4.18 6.35 5.03 3.88 2.87 2.39 1.98 1.56 1.63 1.19 0.898 0.717 0.562 0.318 0.250 0.197 0.167 0.143 0.0399 0.0308 0.0212
cm4 13700 9240 5810 3550 2340 1440 812 558 381 251 153 2030 1270 734 378 249 161 91.2 626 319 172 102 57.6 137 80.2 47.2 31.8 22.2 19.2 10.5 4.63
A cm2 808 702 595 501 433 366 299 257 226 195 164 360 306 252 201 174 150 123 213 168 136 113 93.1 110 90.4 76.4 66.3 58.7 47.1 38.3 29.2
,
cm3 7110 6060 5030 4150 3540 2950 2380 1920 1670 1430 1200 2340 1950 1580 1230 1050 895 726 1140 878 697 575 465 456 374 305 264 231 140 112 80.1
Limited availability.
109
0.843 0.841 0.839 0.837 0.836 0.835 0.834 0.844 0.844 0.844 0.844 0.855 0.854 0.854 0.851 0.851 0.850 0.850 0.851 0.850 0.848 0.850 0.849 0.850 0.853 0.846 0.848 0.847 0.848 0.849 0.840
Design Table 04 Section dimensions and properties of hot-finished CHS z
t
y
CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Mass per Area of Meter Section m A kg/m 20.7 26.0 25.2 31.6 39.0 48.0 33.1 41.6 51.6 63.7 41.4 52.3 64.9 80.3 49.3 62.3 77.4 96.0 121 54.3 68.6 85.2 106 134 78.6 97.8 121 154 191 88.6 110 137 174 216 98.6 123 153 194 241 119 148 184 234 291 173 215 274 349 198 247 314 391
cm2 26.4 33.1 32.1 40.3 49.7 61.2 42.1 53.1 65.7 81.1 52.8 66.6 82.6 102 62.9 79.4 98.6 122 155 69.1 87.4 109 135 171 100 125 155 196 243 113 140 175 222 275 126 156 195 247 307 151 188 235 299 371 173 215 274 341 252 314 401 498
d
Ratio for Local Second Moment Buckling of Area d/t I 22.2 17.5 26.7 21.0 16.8 13.5 34.8 27.4 21.9 17.5 43.3 34.1 27.3 21.8 51.4 40.5 32.4 25.9 20.2 56.4 44.5 35.6 28.4 22.2 50.8 40.6 32.5 25.4 20.3 57.1 45.7 36.6 28.6 22.9 63.5 50.8 40.6 31.8 25.4 76.3 61.0 48.8 38.1 30.5 71.1 56.9 44.4 35.6 81.3 65.0 50.8 40.7
cm4 589 720 1050 1300 1560 1870 2390 2960 3600 4350 4700 5850 7150 8700 7930 9910 12200 14800 18400 10500 13200 16200 19900 24700 19900 24500 30000 37400 45430 28400 35100 43100 54000 65680 39300 48500 59800 74900 91400 84900 104800 118000 131800 161500 135300 167300 211000 259400 203400 251900 318200 391900
Elastic Modulus Wel cm3 84.3 103 125 154 186 222 218 270 328 397 344 429 524 637 490 612 751 917 1140 593 742 912 1120 1390 978 1210 1480 1840 2240 1250 1540 1890 2360 2870 1550 1910 2350 2950 3600 2250 2780 3450 4320 5300 3810 4710 5940 7300 5000 6200 7830 9640
110
Plastic Modulus Wpl cm3 112 139 165 206 251 304 285 357 438 534 448 562 692 849 636 799 986 1210 1520 769 967 1200 1470 1850 1270 1570 1940 2440 2989 1610 2000 2470 3110 3822 2000 2480 3070 3870 4770 2900 3600 4460 5650 6970 4914 6100 7730 9550 6450 8010 10200 12600
Torsional Constants IT Wt cm4 1180 1440 2110 2600 3130 3740 4770 5920 7200 8690 9390 11700 14300 17400 15900 19800 24300 29700 36800 21100 26400 32400 39700 49300 39700 49000 60100 74900 90860 56900 70200 86300 108000 131000 78600 97000 120000 150000 182900 137100 169700 209600 263600 323000 270600 334700 422100 518700 406800 503700 636400 783800
cm3 169 206 250 308 372 444 436 540 657 793 688 857 1050 1270 979 1220 1500 1830 2270 1190 1490 1830 2230 2770 1960 2410 2960 3690 4470 2490 3070 3780 4720 5750 3090 3820 4710 5900 7199 4495 5564 6869 8641 10590 7612 9415 11870 14590 10010 12390 15660 19280
Surface Area per Meter m2 0.439 0.439 0.529 0.529 0.529 0.529 0.688 0.688 0.688 0.688 0.858 0.858 0.858 0.858 1.02 1.02 1.02 1.02 1.02 1.12 1.12 1.12 1.12 1.12 1.28 1.28 1.28 1.28 1.28 1.44 1.44 1.44 1.44 1.44 1.60 1.60 1.60 1.60 1.60 1.90 1.90 1.90 1.90 1.90 2.23 2.23 2.23 2.23 2.55 2.55 2.55 2.55
per Tonne m2 21.2 16.9 21.0 16.7 13.6 11.0 20.8 16.5 13.3 10.8 20.7 16.4 13.2 10.7 20.6 16.3 13.1 10.6 8.41 20.6 16.3 13.1 10.5 8.34 16.2 13.1 10.6 8.29 6.68 16.2 13.1 10.5 8.25 6.65 16.2 13.0 10.4 8.23 6.62 16.1 12.9 10.4 8.19 6.59 12.9 10.4 8.15 6.40 12.9 10.3 8.13 6.53
Design Table 05 Section dimensions and properties of hot-finished RHS z
cw
y
h
cf b RHS bxhxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Mass per Meter m kg/m 17.2 21.0 21.2 26.0 31.2 27.1 33.5 40.6 32.0 39.8 48.4 37.0 46.1 56.3 68.3 40.9 51.1 62.6 76.2 93.9 46.9 58.6 72.0 88.0 109 56.8 71.2 87.7 108 134 56.8 71.2 87.7 108 134 83.8 103 127 159 96.3 119 147 184 225
Area of Section A cm2 21.9 26.7 26.9 33.1 39.7 34.5 42.7 51.7 40.8 50.7 61.7 47.1 58.7 71.7 87.0 52.1 65.1 79.7 97.0 120 59.7 74.7 91.7 112 139 72.3 90.7 112 137 171 72.3 90.7 112 137 171 107 132 162 203 123 152 187 235 287
Ratio for Local Buckling cw/t cf/t 13.0 9.0 19.4 14.0 10.0 25.7 19.0 14.0 25.7 19.0 14.0 33.7 25.3 19.0 14.0 35.3 26.5 20.0 14.8 10.3 41.6 31.5 24.0 18.0 12.8 49.6 37.8 29.0 22.0 15.9 57.5 44.0 34.0 26.0 19.0 50.3 39.0 30.0 22.1 56.5 44.0 34.0 25.3 19.0
6.7 4.0 6.7 4.0 2.0 9.9 6.5 4.0 17.8 12.8 9.0 17.8 12.8 9.0 6.0 22.6 16.5 12.0 8.4 5.3 25.7 19.0 14.0 10.0 6.5 33.7 25.3 19.0 14.0 9.6 25.7 19.0 14.0 10.0 6.5 25.3 19.0 14.0 9.6 31.5 24.0 18.0 12.8 9.0
Second Moment of Area Iy cm4 394 451 821 959 1080 1700 2030 2340 2290 2760 3250 3940 4790 5670 6600 4950 6040 7200 8450 9860 7540 9250 11100 13100 15500 12800 15800 19100 22900 27500 15200 18700 22600 27000 32400 29000 35300 42500 51500 42400 51700 62700 76600 90700
Iz cm4 210 240 279 324 362 581 688 790 1480 1780 2080 1800 2180 2570 2990 2820 3440 4090 4790 5570 4070 4980 5960 7040 8290 7680 9480 11400 13700 16400 5250 6450 7760 9240 11000 11800 14300 17200 20800 19500 23700 28600 34900 41200
111
Elastic Modulus Wel,y cm3 65.6 75.2 103 120 135 170 203 234 229 276 325 315 383 454 528 381 465 554 650 758 503 617 740 873 1030 731 903 1090 1310 1570 760 935 1130 1350 1620 1290 1570 1890 2290 1700 2070 2510 3060 3630
Wel,z cm3 52.5 60.0 69.8 81.0 90.5 116 138 158 197 237 277 240 291 343 399 313 382 454 532 619 407 498 596 704 829 614 758 912 1100 1310 525 645 776 924 1100 944 1140 1380 1660 1300 1580 1910 2330 2750
t Plastic Modulus Wpl,y cm3 83.3 98.2 132 158 183 216 261 309 277 338 404 386 475 570 677 458 565 682 814 974 605 748 907 1090 1320 870 1080 1320 1600 1950 935 1160 1420 1710 2090 1580 1930 2340 2880 2050 2510 3070 3800 4560
Wpl,z cm3 63.1 74.2 81.6 97.3 112 133 161 190 228 278 332 273 335 402 476 357 440 531 633 756 460 568 689 826 997 693 862 1050 1270 1550 582 722 879 1060 1290 1060 1290 1570 1930 1450 1780 2170 2680 3210
Surface Area per Meter m2 0.384 0.379 0.464 0.459 0.454 0.584 0.579 0.574 0.684 0.679 0.674 0.784 0.779 0.774 0.768 0.860 0.860 0.850 0.850 0.840 0.984 0.979 0.974 0.968 0.962 1.180 1.180 1.170 1.170 1.160 1.18 1.18 1.17 1.17 1.16 1.38 1.37 1.37 1.36 1.58 1.57 1.57 1.56 1.55
per Tonne m2 21.1 16.8 20.9 16.6 13.5 20.8 16.5 13.3 20.7 16.4 13.2 20.6 16.4 13.2 10.6 23.8 19.0 15.4 12.5 10.0 20.6 16.3 13.1 10.6 8.7 17.3 13.7 11.1 9.0 7.1 20.4 16.2 13.0 10.5 7.1 16.1 12.9 10.4 8.21 16.1 12.9 10.4 8.17 6.59
Design Table 06 Section dimensions and properties of hot-finished SHS z y c t
b Mass per Area of Meter Section bxbxt m A
SHS
mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
kg/m 17.2 21.0 27.1 33.5 40.6 37.0 46.1 56.3 68.3 40.9 51.1 62.6 76.2 93.9 46.9 58.6 72.0 88.0 109 56.8 71.2 87.7 108 134 83.8 103 127 159 96.3 119 147 184 225
cm2 21.9 26.7 34.5 42.7 51.7 47.1 58.7 71.7 87.0 52.1 65.1 79.7 97.0 120 59.7 74.7 91.7 112 139 72.3 90.7 112 137 171 107 132 162 203 123 152 187 235 287
Ratio for Local Buckling c/t
Second Moment of Area I
9.9 6.5 17.8 12.8 9.0 25.7 19.0 14.0 10.0 28.9 21.5 16.0 11.6 7.8 33.7 25.3 19.0 14.0 9.63 41.6 31.5 24.0 18.0 12.8 37.8 29.0 22.0 15.9 44.0 34.0 26.0 19.0 14.0
cm4 304 349 1150 1370 1590 2880 3500 4150 4840 3890 4750 5660 6650 7760 5810 7130 8550 10100 12000 10300 12700 15300 18300 22000 20500 24900 30000 36400 31000 37800 45800 56000 66400
112
Elastic Modulus Wel cm3 60.7 69.7 153 183 212 288 350 415 484 354 432 515 605 706 465 570 684 808 960 687 847 1020 1220 1470 1170 1420 1710 2080 1550 1890 2290 2800 3320
Plastic Modulus Wpl cm3 74.4 87.8 182 221 262 338 415 499 592 413 509 614 733 878 540 668 810 974 1180 790 982 1200 1450 1770 1360 1660 2020 2480 1790 2200 2680 3320 3990
Surface Area per Meter m2 0.368 0.359 0.568 0.559 0.548 0.768 0.759 0.748 0.736 0.848 0.839 0.828 0.816 0.798 0.968 0.959 0.948 0.936 0.918 1.17 1.16 1.15 1.14 1.12 1.36 1.35 1.34 1.32 1.56 1.55 1.54 1.52 1.50
per Tonne m2 21.4 17.1 21.0 16.7 13.5 20.8 16.5 13.3 10.8 20.7 16.4 13.2 10.7 8.50 20.6 16.4 13.2 10.6 8.42 20.6 16.3 13.1 10.6 8.34 16.2 13.0 10.5 8.28 16.2 13.0 10.5 8.23 6.65
Design Tables 07 to 12 for Section Resistances of Rolled Sections: S275 steel I-sections H-sections CHS RHS SHS
113
Design Table 07 Section resistances of rolled I-sections: S275 steel (1) z
tf r y
d h tw
cf b I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
Flexural Rigidity EIy 103*kNm2 1510 1310 1060 916 790 683 714 586 517 504 431 355 317 357 315 286 248 439 321 265 235 207 183 159 160 140 129 116 100
EIz 103*kNm2 95.3 82.3 32.8 27.9 23.5 19.8 23.9 19.0 16.4 17.2 14.4 11.5 10.1 13.9 12.1 10.9 9.20 33.2 23.9 19.6 9.47 8.25 7.20 6.11 7.12 6.17 5.65 5.02 4.22
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
114
Moment Resistance My,Rd Mz,Rd kNm kNm 4690 885 4110 766 3340 424 2890 363 2530 307 2210 260 2430 321 2020 258 1800 223 1900 254 1640 214 1370 171 1280 157 1490 215 1330 188 1210 169 1060 144 1980 416 1470 302 1220 248 1100 162 975 142 869 124 792 110 848 133 750 116 692 106 649 97.6 567 82.5
Shear Resistance Vz,Rd kN 3240 2920 2900 2570 2350 2210 2220 2000 1890 1950 1760 1560 1520 1630 1470 1370 1280 1890 1440 1200 1300 1170 1090 1060 1110 1020 921 909 865
Axial Resistance Na,Rd kN 13000 11200 9340 7930 6840 5990 7130 5910 5260 6310 5390 4420 4100 5520 4810 4340 3790 8030 5960 4790 4540 3960 3520 3210 4060 3560 3200 3010 2650
Design Table 08 Section resistances of rolled I-sections: S275 steel (2) z
tf r y
d h tw
cf b I-Sections 457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Flexural Rigidity EIy 103*kNm2 93.7 84.1 76.1 68.3 60.3 75.0 67.0 59.2 52.3 43.9 56.0 49.8 44.3 38.3 32.2 25.6 40.0 32.8 28.9 24.8 20.9 16.9 24.0 20.3 17.4 19.6 16.8 14.7 13.3 11.0 9.14 13.4 11.4 9.04 8.20 6.99 5.82 5.95 4.80 4.31 2.79 1.71 0.970
EIz 103*kNm2 4.82 4.28 3.83 3.42 2.97 2.42 2.15 1.87 1.63 1.32 3.18 2.79 2.46 2.09 1.10 0.841 2.79 2.28 1.98 1.66 0.734 0.574 2.17 1.84 1.57 0.945 0.797 0.689 0.398 0.318 0.252 1.39 1.17 0.918 0.367 0.305 0.244 0.789 0.631 0.336 0.281 0.184 0.114
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
115
Moment Resistance My,Rd Mz,Rd kNm kNm 591 100 533 89.6 485 80.6 454 74.8 404 65.2 480 63.6 432 56.4 399 51.4 355 44.8 303 36.6 398 70.8 371 65.2 330 57.5 289 49.0 244 32.5 199 25.0 333 66.8 278 54.7 246 47.9 213 40.4 181 24.5 149 19.3 233 53.9 198 45.7 171 39.1 196 31.9 169 27.1 148 23.5 132 16.5 111 13.3 94.1 10.7 156 38.8 133 32.7 108 25.9 97.1 15.1 84.2 12.7 71.2 10.3 86.4 24.3 71.0 19.5 64.4 13.7 47.0 11.4 33.8 8.60 23.2 6.20
Shear Resistance Vz,Rd kN 852 789 729 693 650 798 721 697 624 578 640 612 549 529 473 438 568 501 455 425 408 366 422 357 319 474 420 372 350 315 299 321 280 260 283 265 248 231 204 197 157 130 102
Axial Resistance Na,Rd kN 3310 2960 2670 2460 2190 2730 2400 2220 1920 1630 2470 2280 1990 1780 1460 1200 2350 1970 1720 1500 1280 1050 1890 1580 1360 1680 1470 1280 1100 921 797 1510 1300 1090 990 868 749 1050 880 809 668 558 454
Design Table 09 Section resistances of rolled H-sections: S275 steel z
tf r tw d h
h
y
cf
b H-Sections 356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
Flexural Rigidity EIy 103*kNm2 578 477 384 309 258 210 166 139 120 102 84.4 166 135 107 81.3 68.9 58.2 46.6 63.0 47.3 36.8 30.0 23.9 19.8 16.0 12.9 11.0 9.60 4.64 3.68 2.63
EIz 103*kNm2 206 174 142 116 98.5 81.3 65.1 49.8 43.1 37.0 30.7 51.7 42.6 34.2 26.5 22.5 19.0 15.4 20.7 15.8 12.5 10.2 8.21 6.57 5.33 4.35 3.74 3.26 1.48 1.18 0.840
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Limited availability.
116
Moment Resistance My,Rd Mz,Rd kNm kNm 3480 1960 2960 1670 2550 1380 2100 1140 1790 974 1540 811 1240 655 1050 528 917 459 784 393 599 218 1300 644 1130 536 912 435 710 338 610 289 519 246 437 200 641 314 496 241 392 192 323 158 273 128 259 125 212 103 180 83.9 156 72.6 137 63.5 85.0 38.5 68.2 30.8 45.1 14.5
Shear Resistance Vz,Rd kN 3040 2630 2290 1920 1640 1440 1150 1030 907 772 645 1490 1320 1070 871 756 657 558 903 705 577 467 407 475 371 352 298 269 226 184 158
Axial Resistance Na,Rd kN 19800 17200 15200 12800 11000 9700 7920 6810 5990 5170 4350 9180 8110 6680 5330 4610 3980 3380 5640 4450 3600 2990 2560 2920 2400 2100 1820 1610 1300 1050 803
Design Table 10 Section resistances of hot-finished CHS: S275 steel z
t
y
d
S275 CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 1.24 1.51 2.21 2.73 3.28 3.93 5.02 6.22 7.56 9.14 9.87 12.3 15.0 18.3 16.7 20.8 25.6 31.1 38.6 22.1 27.7 34.0 41.8 51.9 41.8 51.5 63.0 78.5 95.4 59.6 73.7 90.5 113 138 82.5 102 126 157 192 178 220 248 277 339 284 351 443 545 427 529 668 823
Section Classification
1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 2 1 1 1 3 2 1 1 1 3 3 2 1 1 3 2 2 1 4 3 2 1
Moment Resistance My,Rd kNm 30.8 38.2 45.4 56.7 69.0 83.6 78.4 98.2 120 147 123 155 190 233 175 220 271 333 418 211 266 330 404 509 349 432 534 671 792 443 550 679 855 1010 426 682 844 1060 1260 619 765 1230 1550 1850 1050 1680 2130 2530 1710 2810 3340
117
Shear Resistance Vz,Rd kN 267 335 324 407 502 619 426 537 664 820 534 673 835 1031 636 803 997 1230 1570 698 883 1100 1360 1730 1010 1260 1570 1980 2370 1140 1420 1770 2240 2680 1270 1580 1970 2500 2990 1530 1900 2380 3020 3610 1750 2170 2770 3320 3170 4050 4850
Axial Resistance Na,Rd kN 726 910 883 1110 1370 1680 1160 1460 1810 2230 1450 1830 2270 2810 1730 2180 2710 3360 4260 1900 2400 3000 3710 4700 2750 3440 4260 5390 6440 3110 3850 4810 6110 7290 3470 4290 5360 6790 8140 4150 5170 6460 8220 9830 4760 5910 7540 9040 8640 11000 13200
Design Table 11 Section resistances of hot-finished RHS: S275 steel z
cw
y
h
cf t
b S275 RHS hxbxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.827 0.948 1.72 2.01 2.27 3.57 4.26 4.91 4.81 5.80 6.83 8.27 10.1 11.9 13.9 10.4 12.7 15.1 17.7 20.7 15.8 19.4 23.3 27.5 32.6 26.9 33.2 40.1 48.1 57.8 31.9 39.3 47.5 56.7 68.0 60.9 74.1 89.3 108 89.0 109 132 161 190
EIz 103*kNm2 0.441 0.504 0.586 0.680 0.760 1.22 1.44 1.66 3.11 3.74 4.37 3.78 4.58 5.40 6.28 5.92 7.22 8.59 10.1 11.7 8.55 10.5 12.5 14.8 17.4 16.1 19.9 23.9 28.8 34.4 11.0 13.5 16.3 19.4 23.1 24.8 30.0 36.1 43.7 41.0 49.8 60.1 73.3 86.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 4 1 2 1 1 1 1 1 1 2 4 1 3 1 1 1 1 1 1 1 4 1 4 1 2 1 1 1 1 1 4 1 4 1 1 1 1 2 4 1 4 1 2 1 1 1 1
Moment resistance My,Rd Mz,Rd kNm kNm 22.9 17.3 27.0 20.4 36.3 22.5 43.5 26.7 50.4 30.9 59.3 36.7 71.9 44.4 84.8 52.2 76.0 62.6 93.0 76.5 111 91.2 106 75.0 131 92.1 157 111 186 131 126 86.2 155 121 187 146 224 174 268 208 166 206 156 250 189 300 227 363 274 239 297 209 363 289 440 349 536 426 257 319 391 242 470 292 575 355 435 531 644 432 792 531 564 690 844 597 1050 737 1210 851
118
Shear Resistance
Axial Resistance
Vz,Rd kN 209 254 285 350 420 365 452 547 370 460 560 467 582 712 864 489 611 748 910 1120 569 712 874 1070 1320 670 840 1030 1270 1580 765 960 1180 1450 1810 1090 1340 1650 2070 1220 1510 1860 2330 2740
Na,Rd kN 602 734 741 910 1090 949 1170 1420 1120 1390 1700 1300 1610 1970 2390 1430 1790 2190 2670 3290 1600 2050 2520 3080 3820 1880 2470 3070 3770 4700 1810 2390 3070 3770 4700 2750 3560 4460 5580 3100 4020 5140 6460 7600
Design Table 12 Section resistances of hot-finished SHS: S275 steel z
y c b
t
S275 SHS bxbxt mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.638 0.732 2.42 2.88 3.34 6.05 7.35 8.72 10.2 8.17 10.0 11.9 14.0 16.3 12.2 15.0 18.0 21.2 25.2 21.6 26.7 32.1 38.4 46.2 43.1 52.3 63.0 76.4 65.1 79.4 96.2 118 139
Section Classification Bending y-y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 4 2 1 1 1 3 1 1 1 4 2 1 1 1
Moment Resistance My,Rd kNm 20.5 24.1 50.1 60.9 72.0 92.8 114 137 163 114 140 169 202 241 149 184 223 268 324 270 330 399 487 322 457 556 682 605 737 913 1060
119
Shear Resistance Vz,Rd kN 174 212 274 339 410 374 466 569 691 414 517 633 770 950 474 593 728 889 1100 574 720 887 1090 1360 847 1050 1290 1610 974 1200 1480 1860 2280
Axial Resistance Na,Rd kN 602 734 949 1170 1420 1300 1610 1970 2390 1430 1790 2190 2670 3290 1640 2050 2520 3080 3820 1900 2490 3070 3770 4700 2880 3620 4460 5580 3180 4170 5140 6460 7890
120
Design Tables 13 to 18 for Section Resistances of Rolled Sections: S355 steel I-sections H-sections CHS RHS SHS
121
Design Table 13 Section resistances of rolled I-sections: S355 steel (1) z
tf r y
d h tw
cf b I-Sections 914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
Flexural Rigidity EIy 103*kNm2 1510 1310 1060 916 790 683 714 586 517 504 431 355 317 357 315 286 248 439 321 265 235 207 183 159 160 140 129 116 100
EIz 103*kNm2 95.3 82.3 32.8 27.9 23.5 19.8 23.9 19.0 16.4 17.2 14.4 11.5 10.1 13.9 12.1 10.9 9.20 33.2 23.9 19.6 9.47 8.25 7.20 6.11 7.12 6.17 5.65 5.02 4.22
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Limited availability.
122
Moment Resistance My,Rd Mz,Rd kNm kNm 6110 1150 5350 997 4350 552 3760 473 3290 400 2880 339 3160 417 2640 336 2420 299 2470 331 2140 278 1780 223 1600 197 1940 280 1730 245 1570 220 1380 187 2580 542 1910 393 1630 333 1430 211 1270 185 1130 162 1020 142 1140 178 1000 155 927 142 838 126 731 107
Shear Resistance Vz,Rd kN 4220 3800 3780 3350 3060 2870 2900 2610 2460 2530 2290 2040 1970 2120 1920 1790 1670 2460 1880 1570 1690 1520 1420 1370 1450 1330 1200 1170 1120
Axial Resistance Na,Rd kN 16500 14200 11800 10000 8590 7500 8980 7430 6590 7950 6770 5540 5090 6960 6060 5460 4760 10500 7570 6080 5740 5000 4430 3990 5130 4500 4040 3760 3310
Design Table 14 Section resistances of rolled I-sections: S355 steel (2) z
tf r y
tw d h cf b
I-Sections 457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 356x171x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Flexural Rigidity EIy 103*kNm2 93.7 84.1 76.1 68.3 60.3 75.0 67.0 59.2 52.3 43.9 56.0 49.8 44.3 38.3 32.2 25.6 40.0 32.8 28.9 24.8 20.9 16.9 24.0 20.3 17.4 19.6 16.8 14.7 13.3 11.0 9.14 13.4 11.4 9.04 8.20 6.99 5.82 5.95 4.80 4.31 2.79 1.71 0.970
EIz 103*kNm2 4.82 4.28 3.83 3.42 2.97 2.42 2.15 1.87 1.63 1.32 3.18 2.79 2.46 2.09 1.10 0.841 2.79 2.28 1.98 1.66 0.734 0.574 2.17 1.84 1.57 0.945 0.797 0.689 0.398 0.318 0.252 1.39 1.17 0.918 0.367 0.305 0.244 0.789 0.631 0.336 0.281 0.184 0.114
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
123
Moment Resistance My,Rd Mz,Rd kNm kNm 792 135 693 117 631 105 586 96.6 522 84.1 643 85.2 562 73.5 515 66.4 458 57.9 391 47.2 533 94.8 479 84.1 426 74.2 373 63.2 315 41.9 257 32.2 430 86.3 359 70.6 318 61.8 275 52.2 234 31.6 193 24.9 300 69.6 256 58.9 221 50.4 252 41.2 218 34.9 191 30.3 171 21.3 143 17.2 121 13.8 201 50.1 171 42.2 140 33.4 125 19.5 109 16.3 91.9 13.2 111 31.3 91.6 25.2 83.1 17.6 60.7 14.8 43.7 11.1 29.9 8.02
Shear Resistance Vz,Rd kN 1110 1030 949 895 839 1040 938 899 806 747 833 790 709 683 611 566 733 646 587 549 527 472 545 461 411 612 542 481 452 407 386 415 361 336 365 341 320 299 263 254 203 167 131
Axial Resistance Na,Rd kN 4200 3770 3380 3100 2750 3460 3040 2780 2400 2040 3140 2870 2510 2230 1830 1500 2990 2480 2170 1890 1600 1310 2420 2010 1720 2170 1880 1610 1380 1150 992 1950 1650 1370 1250 1090 938 1360 1140 1040 863 721 586
Design Table 15 Section resistances of rolled H-sections: S355 steel tf
z
h
y
r tw d h
cf
b H-Sections 356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
Flexural Rigidity EIy 103*kNm2 578 477 384 309 258 210 166 139 120 102 84.4 166 135 107 81.3 68.9 58.2 46.6 63.0 47.3 36.8 30.0 23.9 19.8 16.0 12.9 11.0 9.60 4.64 3.68 2.63
EIz 103*kNm2 206 174 142 116 98.5 81.3 65.1 49.8 43.1 37.0 30.7 51.7 42.6 34.2 26.5 22.5 19.0 15.4 20.7 15.8 12.5 10.2 8.21 6.57 5.33 4.35 3.74 3.26 1.48 1.18 0.840
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 3 3
Limited availability.
124
Moment Resistance My,Rd Mz,Rd kNm kNm 4620 2520 3930 2150 3350 1790 2750 1470 2350 1260 2000 1050 1620 821 1370 662 1190 576 1020 493 780 274 1710 784 1470 673 1190 545 925 424 794 362 676 309 515 170 835 393 645 303 511 240 421 198 352 165 337 157 276 129 233 108 201 93.7 176 82.0 110 49.7 88.0 39.8 58.2 18.7
Shear Resistance Vz,Rd kN 4040 3490 3000 2520 2160 1870 1500 1340 1180 1000 839 1950 1710 1400 1130 984 856 721 1180 918 751 607 525 619 483 455 385 347 292 238 204
Axial Resistance Na,Rd kN 26300 22800 19900 16800 14500 12600 10300 8870 7800 6730 5660 12100 10600 8690 6930 6000 5180 4370 7350 5800 4690 3900 3310 3800 3120 2710 2350 2080 1670 1360 1040
Design Table 16 Section resistances of hot-finished CHS: S355 steel z
t
y
d
S355 CHS dxt mmxmm 139.7x6.3 x8.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.8x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 1.24 1.51 2.21 2.73 3.28 3.93 5.02 6.22 7.56 9.14 9.87 12.3 15.0 18.3 16.7 20.8 25.6 31.1 38.6 22.1 27.7 34.0 41.8 51.9 41.8 51.5 63.0 78.5 95.4 59.6 73.7 90.5 113 138 82.5 102 126 157 192 178 220 248 277 339 284 351 443 545 427 529 668 823
Section Classification
1 1 1 1 1 1 2 1 1 1 2 2 1 1 3 2 1 1 1 3 2 2 1 1 3 2 1 1 1 3 2 2 1 1 4 3 2 1 1 4 4 3 2 1 4 3 2 2 4 4 3 2
Moment Resistance My,Rd kNm 39.8 49.3 58.6 73.1 89.1 108 101 127 155 190 159 200 246 301 174 284 350 430 540 211 343 426 522 657 347 557 689 866 1060 444 710 877 1100 1360 678 1090 1370 1690 1220 2010 2470 1670 2740 3390 3420 4470
125
Shear Resistance Vz,Rd kN 344 432 419 526 649 799 549 693 857 1060 689 869 1080 1330 821 1040 1290 1590 2020 902 1140 1420 1760 2230 1300 1630 2020 2560 3170 1470 1830 2280 2900 3590 2040 2540 3220 4010 3070 3900 4840 2810 3580 4450 5230 6500
Axial Resistance Na,Rd kN 937 1180 1140 1430 1760 2170 1490 1890 2330 2880 1870 2360 2930 3620 2230 2820 3500 4330 5500 2450 3100 3870 4790 6070 3550 4440 5500 6960 8630 4010 4970 6210 7880 9760 5540 6920 8770 10900 8340 10600 13200 7630 9730 12100 14200 17700
Design Table 17 Section resistances of hot-finished RHS: S355 steel z
cw
y
h cf t
b S355 RHS hxbxt mmxmmxmm 120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 x16.0 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.827 0.948 1.72 2.01 2.27 3.57 4.26 4.91 4.81 5.80 6.83 8.27 10.1 11.9 13.9 10.4 12.7 15.1 17.7 20.7 15.8 19.4 23.3 27.5 32.6 26.9 33.2 40.1 48.1 57.8 31.9 39.3 47.5 56.7 68.0 60.9 74.1 89.3 108 89.0 109 132 161 190
EIz 103*kNm2 0.441 0.504 0.586 0.680 0.760 1.22 1.44 1.66 3.11 3.74 4.37 3.78 4.58 5.40 6.28 5.92 7.22 8.59 10.1 11.7 8.55 10.5 12.5 14.8 17.4 16.1 19.9 23.9 28.8 34.4 11.0 13.5 16.3 19.4 23.1 24.8 30.0 36.1 43.7 41.0 49.8 60.1 73.3 86.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 4 1 3 1 1 1 1 1 1 3 4 1 4 1 2 1 1 1 1 1 4 1 4 1 3 1 1 1 1 1 4 1 4 1 2 1 1 3 4 1 4 1 3 1 1 1 1
Moment resistance My,Rd Mz,Rd kNm kNm 29.6 22.4 34.9 26.4 46.9 29.0 56.1 34.5 65.0 39.9 76.5 47.4 92.8 57.3 110 67.4 98.2 80.8 120 98.7 143 118 137 85.2 169 119 203 143 240 169 163 201 156 242 188 289 225 346 269 215 266 177 322 244 387 293 469 354 260 383 469 373 568 451 692 550 332 412 504 276 607 376 742 458 561 685 831 557 1020 685 604 891 1090 678 1350 951 1570 1110
126
Shear Resistance
Axial Resistance
Vz,Rd kN 269 328 368 452 543 472 583 707 478 594 723 603 752 919 1120 632 788 965 1180 1450 734 919 1130 1380 1710 865 1080 1340 1640 2040 988 1240 1530 1870 2330 1410 1740 2140 2670 1570 1940 2400 3010 3670
Na,Rd kN 778 948 957 1170 1410 1230 1520 1840 1450 1800 2190 1650 2080 2550 3090 1810 2310 2830 3450 4240 2020 2650 3260 3980 4930 2350 3120 3970 4870 6060 2280 3010 3900 4870 6060 3470 4490 5750 7200 3910 5060 6540 8330 10200
Design Table 18 Section resistances of hot-finished SHS: S355 steel z
y c b
t
S355 SHS bxbxt mmxmmxmm 100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
Flexural rigidity EIy 103*kNm2 0.638 0.732 2.42 2.88 3.34 6.05 7.35 8.72 10.2 8.17 10.0 11.9 14.0 16.3 12.2 15.0 18.0 21.2 25.2 21.6 26.7 32.1 38.4 46.2 43.1 52.3 63.0 76.4 65.1 79.4 96.0 118 139
Section Classification Bending y-y 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 3 1 1 1 4 2 1 1 4 3 1 1 1
Moment Resistance My,Rd kNm 26.4 31.2 64.7 78.6 92.9 120 147 177 210 147 181 218 260 312 165 237 288 346 418 301 426 515 628 589 717 880 671 951 1180 1380
127
Shear Resistance Vz,Rd kN 225 274 354 438 530 483 601 735 892 534 667 817 990 1230 612 765 940 1150 1420 741 929 1140 1400 1750 1090 1350 1660 2080 1260 1550 1920 2410 2860
Axial Resistance Na,Rd kN 778 948 1230 1520 1840 1670 2080 2550 3090 1850 2310 2830 3450 4240 2080 2650 3260 3980 4930 2360 3210 3970 4860 6060 3590 4680 5750 7200 3940 5260 6640 8330 9610
128
Design Tables 19 to 24 for Section Dimensions and Properties of Welded Sections I-sections (EWIS) H-sections (EWHS) EWCHS EWRHS EWSHS
129
Design Table 19A Section dimensions of welded I-sections (1) z
tf r y
d h tw
cf b
I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
EWIS
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Mass per Meter kg/m 420.8 352.5 312.4 282.4 249.4 217.9 245.8 213.5 184.4 220.1 194.0 166.5 147.4 198.2 172.6 150.5 133.3 257.5 185.5 159.6 158.0 137.6 121.7 111.5 147.5 127.9 112.6 103.5 87.8
Depth Width of of Section Section mm 920 915 930 920 910 900 850 840 840 770 760 750 750 690 690 680 680 640 620 610 620 610 610 600 550 540 540 530 530
mm 450 450 360 360 350 340 360 350 340 320 320 310 310 290 280 280 280 340 330 330 260 260 260 260 250 250 250 250 250
Thickness Web Flange tw tf mm mm 20 40 20 30 20 30 20 25 16 25 16 20 16 25 16 20 12 20 16 25 16 20 12 20 12 16 16 25 16 20 12 20 12 16 20 30 12 25 12 20 12 25 12 20 12 16 10 16 12 25 12 20 12 16 10 16 10 12
Limited availability.
130
Depth Fillet between Height Fillets
Ratios for Local Buckling
Surface Area per Meter per Tonne
r mm 16 16 16 16 16 14 16 14 12 16 14 12 11 16 14 12 11 20 12 12 12 12 11 10 12 12 11 10 8
d mm 808 823 838 838 828 832 768 772 776 688 692 686 696 608 622 616 626 540 546 546 546 546 556 548 476 476 486 478 490
b/tf
d/tw
5.0 6.6 5.1 6.2 6.0 7.4 6.2 7.7 7.6 5.4 6.9 6.9 8.6 4.8 5.9 6.1 7.7 4.7 5.9 7.4 4.5 5.6 7.1 7.2 4.3 5.4 6.8 6.9 9.3
42.0 42.8 43.5 43.5 53.8 53.8 50.0 50.0 66.7 45.0 45.0 59.2 59.8 40.0 40.6 53.3 54.0 29.0 47.5 47.5 47.5 47.5 48.2 56.8 41.7 41.7 42.3 49.8 50.6
m2 3.60 3.59 3.26 3.24 3.19 3.13 3.11 3.05 3.02 2.79 2.77 2.72 2.72 2.51 2.47 2.46 2.46 2.60 2.54 2.52 2.26 2.24 2.24 2.22 2.08 2.06 2.06 2.04 2.04
m2 8.60 10.3 10.5 11.5 12.8 14.4 12.6 14.3 16.4 12.7 14.3 16.3 18.4 12.7 14.3 16.3 18.4 10.1 13.7 15.8 14.3 16.3 18.4 19.9 14.1 16.1 18.3 19.7 23.2
Design Table 19B Section properties of welded I-sections (1) z
tf r y
d h tw
cf b Second Moment of Area I-Sections
914x419x388# x343# 914x305x289# x253# x224# x201# 838x292x226# x194# x176# 762x267x197 x173 x147 x134 686x254x170 x152 x140 x125 610x305x238 x179 x149 610x229x140 x125 x113 x101 533x210x122 x109 x101 x92 x82
#
EWIS
920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Elastic Modulus ,
cm4 796000 633000 547000 470000 428000 348000 375000 304000 280000 272000 225000 201000 171000 195000 162000 148000 126000 222000 165000 133000 134000 109100 92700 86200 98700 80100 68000 63100 51100
cm4 60800 45600 23400 19500 17900 13130 19500 14310 13110 13670 10940 9940 7950 10180 7330 7320 5860 19700 15000 11980 7330 5860 4690 4690 6510 5210 4170 4170 3120
cm3 17300 13800 11800 10220 9410 7730 8820 7240 6670 7060 5920 5360 4560 5650 4700 4350 3710 6940 5320 4360 4320 3580 3040 2870 3590 2970 2520 2380 1930
Plastic Modulus ,
,
cm3 2700 2030 1300 1083 1023 772 1083 818 771 854 684 641 513 702 524 523 419 1159 909 726 564 451 361 361 521 417 334 334 250
cm3 19600 15800 13700 12100 10900 9110 10200 8450 7610 8220 6950 6140 5270 6620 5570 5020 4310 8130 5960 4950 4920 4120 3540 3290 4100 3420 2930 2730 2230
Limited availability.
131
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section A
,
cm3 4140 3130 2040 1710 1590 1216 1680 1280 1190 1330 1080 989 797 1100 831 810 653 1810 1380 1110 868 699 564 557 802 646 521 514 389
0.896 0.878 0.868 0.859 0.872 0.855 0.876 0.860 0.878 0.876 0.861 0.879 0.864 0.876 0.859 0.880 0.864 0.881 0.899 0.887 0.894 0.880 0.866 0.878 0.896 0.884 0.869 0.883 0.864
24.4 32.3 33.5 38.3 39.9 47.2 36.9 43.7 46.3 33.4 39.4 41.2 49.8 29.8 35.8 37.2 45.1 22.2 26.2 32.4 26.9 33.2 40.3 40.8 23.5 29.0 35.3 35.6 45.1
dm6 117.7 89.3 47.4 39.0 35.0 25.4 33.2 24.1 22.0 19.0 14.98 13.24 10.71 11.25 8.23 7.97 6.46 18.3 13.3 10.43 6.49 5.10 4.14 4.00 4.49 3.52 2.86 2.75 2.09
cm4 2140 1040 880 607 482 299 484 296 227 432 269 206 126 389 238 186 114 767 377 209 304 171 104 89.9 289 162 97.5 84.9 45.7
mm2 533 446 395 359 318 278 313 272 235 280 247 212 188 253 220 192 170 328 236 203 201 175 155 142 188 163 143 132 112
Design Table 20A Section dimensions of welded I-sections (2) z
tf r y
tw
d h
cf b
I-Sections
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
EWIS
460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Mass per Meter kg/m 111.8 103.6 90.4 83.1 69.8 91.1 80.4 73.1 62.3 56.3 84.8 77.5 64.8 58.5 48.9 42.5 72.5 61.3 53.8 48.7 43.5 38.1 58.7 44.6 39.3 53.6 45.3 40.6 36.8 33.3 28.4 47.9 42.8 33.4 32.7 28.8 24.7 33.5 28.5 26.8 18.7 17.8 14.6
Depth Width of of Section Section mm 470 460 460 460 460 460 460 460 460 450 420 410 410 410 400 400 360 360 355 355 355 350 310 310 300 310 310 300 315 310 305 260 260 250 260 260 255 210 200 200 180 150 130
mm 220 220 220 220 220 180 180 180 180 180 210 210 210 210 160 150 180 180 170 170 170 170 160 160 160 140 140 140 110 110 110 170 170 170 130 130 130 150 150 110 100 100 80
Thickness Web tw mm 12 10 10 8 8 10 10 8 8 8 10 8 8 8 6 6 10 10 8 8 6 6 8 6 6 8 8 8 8 8 6 8 8 6 6 6 6 6 6 6 4 4 4
132
Flange tf mm 20 20 16 16 12 20 16 16 12 10 16 16 12 10 12 10 16 12 12 10 10 8 16 12 10 16 12 10 10 8 8 12 10 8 10 8 6 10 8 10 8 8 8
Fillet Height
Depth between Fillets
r mm 12 10 10 8 8 10 10 8 8 8 10 8 8 8 8 8 10 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
d mm 406 400 408 412 420 400 408 412 420 414 368 362 370 374 360 364 308 320 315 319 319 318 262 270 264 262 270 264 279 278 273 220 224 218 224 228 227 174 168 164 148 118 98
Ratios for Local Buckling
Surface Area per Meter per Tonne
b/tf 4.6 4.8 5.9 6.1 8.2 3.8 4.7 4.9 6.5 7.8 5.6 5.8 7.8 9.3 5.8 6.4 4.7 6.4 6.1 7.3 7.4 9.3 4.3 5.8 6.9 3.6 4.8 5.8 4.3 5.4 5.5 6.1 7.3 9.3 5.4 6.8 9.0 6.4 8.0 4.4 5.0 5.0 3.8
d/tw 31.8 38.0 38.8 49.5 50.5 38.0 38.8 49.5 50.5 49.8 34.8 43.3 44.3 44.8 57.3 58.0 28.8 30.4 37.4 37.9 50.5 50.3 30.8 42.3 41.3 30.8 31.8 31.0 32.9 32.8 42.8 25.5 26.0 33.7 34.7 35.3 35.2 26.3 25.3 24.7 33.0 25.5 20.5
m2 1.80 1.78 1.78 1.78 1.78 1.62 1.62 1.62 1.62 1.60 1.66 1.64 1.64 1.64 1.43 1.39 1.42 1.42 1.37 1.37 1.38 1.37 1.24 1.25 1.23 1.16 1.16 1.14 1.05 1.04 1.04 1.18 1.18 1.17 1.028 1.028 1.018 1.008 0.988 0.828 0.752 0.692 0.572
m2 16.1 17.2 19.7 21.5 25.5 17.8 20.2 22.2 26.1 28.5 19.6 21.2 25.4 28.1 29.2 32.7 19.6 23.2 25.5 28.2 31.7 35.9 21.2 28.0 31.2 21.7 25.7 28.2 28.6 31.4 36.5 24.7 27.7 35.0 31.4 35.7 41.2 30.1 34.7 31.0 40.2 38.9 39.1
Design Table 20B Section properties of welded I-sections (2) z
tf r d h
y tw
cf b Second Moment of Area I-Sections
Elastic Modulus
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section
EWIS ,
457x191x98 x89 x82 x74 x67 457x152x82 x74 x60 x60 x52 406x178x74 x67 x60 x54 406x140x46 x39 x67 x57 x51 x45 356x127x39 x33 305x165x54 x46 x40 305x127x48 x42 x37 305x102x33 x28 x25 254x146x43 x37 x31 254x102x28 x25 x22 203x133x30 x26 203x102x23 178x102x19 152x89x16 127x76x13
Plastic Modulus
460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
,
,
cm4
cm3
cm3
cm3
cm3
50500 49200 40000 38600 31100 43100 36700 33600 27300 23000 29400 28400 22100 19400 17100 12600 21300 17300 15800 13900 12000 10100 12500 9690 8420 10080 8220 7250 6570 5340 4550 6980 5770 5170 4420 3560 2950 3450 2480 2540 1440 847 496
3090 3090 2130 2130 1600 1940 1550 1310 985 685 1560 1550 1160 974 552 367 1550 1160 984 820 819 656 1090 820 683 522 392 327 223 135 97.7 676 458 367 168 134 100 563 293 222 178 114 56.3
2150 2090 1700 1640 1320 1830 1560 1430 1160 979 1400 1350 1050 924 855 630 1150 935 854 751 676 569 806 625 543 650 530 468 424 345 294 517 427 383 327 264 219 329 236 242 160 112 75.4
294 294 213 213 160 216 172 154 116 85.6 173 172 129 108 78.8 56.4 172 129 116 96.5 96.4 77.1 136 102 85.4 83.5 62.7 52.3 40.6 26.9 21.7 90.1 65.5 56.4 33.5 26.8 20.1 75.1 45.1 40.4 32.3 24.1 15.0
2510 2390 1980 1860 1530 2120 1830 1650 1360 1170 1660 1580 1220 1080 1029 748 1340 1090 992 879 776 666 925 713 624 760 629 561 516 433 366 601 505 447 401 322 274 384 279 286 188 134 93.2
459 453 333 328 248 336 272 239 181 136 276 271 202 169 128 88.6 269 204 180 151 148 119 210 157 131 130 99.2 83.6 66.0 45.6 35.8 140 103 87.5 54.9 43.0 33.0 116 70.1 62.9 49.7 37.2 23.6
133
dm6
cm4
A mm2
1.56 1.56 1.10 1.10 0.839 0.982 0.799 0.675 0.516 0.362 0.637 0.632 0.483 0.409 0.208 0.139 0.486 0.372 0.315 0.266 0.244 0.197 0.236 0.182 0.154 0.113 0.0870 0.0735 0.0502 0.0307 0.0223 0.1125 0.0775 0.0620 0.0283 0.0230 0.0175 0.0563 0.0299 0.0222 0.01313 0.00577 0.00210
137 126 69.2 62.1 30.7 110 63.8 53.9 27.2 18.3 71.5 62.1 27.5 18.8 28.7 11.4 60.4 32.3 25.5 17.3 13.7 8.24 48.4 20.5 12.8 38.9 19.3 13.3 12.3 8.43 5.19 21.5 13.6 10.47 10.93 5.24 3.30 13.2 5.83 8.70 4.10 3.53 2.80
138 129 110 100 85.0 117 103 90.7 77.8 69.3 107 98.4 76.2 69.3 72.5 50.1 93.4 79.1 69.8 63.3 55.4 48.8 74.7 56.8 50.7 63.5 54.2 49.5 46.5 40.8 33.3 57.0 49.3 42.3 41.3 32.5 28.8 46.5 33.7 34.7 25.4 21.8 17.8
,
cm4
0.883 0.893 0.879 0.891 0.875 0.887 0.874 0.886 0.866 0.850 0.866 0.879 0.874 0.861 0.848 0.869 0.883 0.862 0.877 0.865 0.885 0.872 0.897 0.897 0.887 0.890 0.872 0.860 0.853 0.833 0.848 0.882 0.869 0.886 0.856 0.861 0.843 0.869 0.876 0.888 0.898 0.897 0.897
25.2 25.3 31.8 32.1 42.4 25.8 32.1 32.7 43.1 49.7 27.4 28.3 37.8 43.7 34.3 45.4 24.5 31.2 32.9 38.3 38.5 47.0 20.3 27.6 33.2 20.9 27.8 32.2 32.4 36.9 42.6 23.4 27.5 29.1 28.1 36.3 43.3 20.8 27.0 22.2 23.8 19.6 17.1
Design Table 21A Section dimensions of welded H-sections tf
z
r h
y
tw d h
cf b
H-Sections
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
#
EWHS
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Mass per Meter
kg/m 716 563 532 456 368 300 275 218 217 172 167 316 260 213 177 152 142 114 184 151 121 116 93.2 101 84.8 73.3 57.9 49.8 42.2 33.8 28.5
Depth Width of of Section Section
mm 470 460 440 420 400 390 380 380 370 360 360 370 350 340 330 320 320 310 290 280 270 260 260 220 220 210 210 200 170 160 160
mm 470 480 480 480 480 490 490 440 440 440 440 330 340 350 350 360 360 360 300 300 310 310 310 210 220 230 240 240 170 170 170
Thickness Web tw mm 50 40 30 30 25 25 16 16 16 12 10 25 20 20 16 16 12 10 20 16 12 10 8 12 10 10 8 8 8 6 6
Limited availability.
134
Flange tf mm 80 60 60 50 40 30 30 25 25 20 20 50 40 30 25 20 20 16 30 25 20 20 16 25 20 16 12 10 12 10 8
Fillet Height
Depth between Fillets
r mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 12 10 20 16 12 10 8 12 10 10 8 8 8 8 8
d mm 278 308 288 288 288 298 288 298 288 288 288 238 238 248 248 248 256 258 190 198 206 200 212 146 160 158 170 164 130 124 128
Ratios for Local Buckling
Surface Area per Meter per Tonne
cf/tf
d/tw
2.4 3.4 3.5 4.2 5.3 7.2 7.4 7.8 7.8 9.9 10.0 2.7 3.6 5.0 6.0 7.8 8.1 10.3 4.0 5.0 6.9 7.0 8.9 3.5 4.8 6.3 9.0 10.8 6.1 7.4 9.3
5.6 7.7 9.6 9.6 11.5 11.9 18.0 18.6 18.0 24.0 28.8 9.5 11.9 12.4 15.5 15.5 21.3 25.8 9.5 12.4 17.2 20.0 26.5 12.2 16.0 15.8 21.3 20.5 16.3 20.7 21.3
m2 2.72 2.72 2.66 2.58 2.51 2.49 2.47 2.37 2.33 2.30 2.30 2.09 2.04 2.02 1.99 1.97 1.98 1.94 1.72 1.69 1.68 1.64 1.64 1.28 1.30 1.28 1.30 1.26 1.00 0.97 0.97
m2 3.80 4.83 5.00 5.66 6.82 8.31 9.0 10.9 10.7 13.3 13.7 6.61 7.85 9.5 11.3 12.9 13.9 17.0 9.36 11.2 13.8 14.1 17.6 12.7 15.3 17.5 22.5 25.3 23.8 28.2 33.2
Design Table 21B Section properties of welded H-sections tf
z h
y
r tw d h
cf b
Second Moment of Area H-Sections
Elastic Modulus
#
Buckling Torsional Warping Torsional Area of Parameter Index Constant Constant Section
EWHS ,
356x406x634# x551# x467# x393# x340# x287# x235# 356x368x202# x177# x153# x129# 305x305x283 x240 x198 x158 x137 x118 x97 254x254x167 x132 x107 x89 x73 203x203x86 x71 x60 x52 x46 152x152x37 x30 x23
Plastic Modulus
420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
,
,
,
cm4
cm4
cm3
cm3
cm3
cm3
302000 245000 218000 173000 132000 103000 94600 74200 69900 54200 53700 89300 69000 54300 43700 35400 34600 26700 32600 26100 20600 18800 15600 10500 9310 7410 6080 4720 2750 2050 1720
139000 111000 110700 92200 73800 58900 58800 35500 35500 28400 28400 30000 26200 21500 17900 15600 15600 12400 13500 11300 9930 9930 7940 3860 3550 3240 2760 2300 983 819 655
12900 10700 9910 8240 6600 5280 4980 3910 3780 3010 2980 4830 3940 3190 2650 2210 2160 1720 2250 1860 1530 1450 1200 955 846 706 579 472 324 256 215
5910 4620 4610 3840 3080 2400 2400 1610 1610 1290 1290 1820 1540 1230 1020 864 864 691 901 750 641 641 512 368 323 282 230 192 116 96 77
15900 12800 11800 9730 7630 6050 5630 4420 4280 3380 3330 5800 4650 3720 3050 2540 2430 1910 2690 2180 1740 1630 1330 1130 978 810 651 532 374 293 247
9050 7060 6990 5840 4670 3660 3630 2450 2450 1950 1950 2770 2350 1870 1560 1320 1310 1050 1390 1150 972 968 773 560 490 429 349 292 177 146 118
Limited availability.
135
A 0.811 0.813 0.802 0.786 0.775 0.759 0.752 0.804 0.794 0.791 0.794 0.857 0.845 0.829 0.827 0.809 0.816 0.809 0.823 0.820 0.805 0.794 0.802 0.848 0.844 0.819 0.812 0.794 0.840 0.833 0.829
5.0 6.8 6.5 7.6 9.2 12.0 12.0 14.7 14.2 17.6 17.6 6.6 8.0 10.7 12.7 15.3 15.5 19.0 9.0 10.6 12.9 12.4 15.7 8.1 10.4 12.6 17.0 19.3 13.7 15.7 19.7
dm6
cm4
cm2
52.8 44.3 40.0 31.6 23.9 19.1 18.0 11.2 10.6 8.21 8.21 7.68 6.29 5.17 4.16 3.50 3.50 2.69 2.28 1.83 1.55 1.43 1.18 0.367 0.355 0.305 0.271 0.208 0.0614 0.0461 0.0379
17300 7640 7200 4290 2210 1050 926 503 502 253 245 2890 1520 705 403 230 208 108 601 344 179 173 88.5 229 123.3 68.7 30.8 19.1 22.1 12.3 6.84
912 717 677 581 469 382 350 278 276 220 213 403 331 271 225 194 180 145 234 192 154 148 119 128 108 93.4 73.8 63.7 53.8 43.7 37.1
Design Table 22 Section dimensions and properties of cold-formed CHS z
t
y
Area of Section
dxt
Mass per Meter m
mm 140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
kg/m 19.8 26.0 32.1 24.3 32.0 39.5 46.8 31.7 41.8 51.8 61.6 39.1 51.7 64.1 76.3 100 46.5 61.6 76.4 91.1 120 52.4 69.4 86.3 103 136 77.3 96.2 115 152 187 89.2 111 133 175 217 97.1 121 144 191 237 119 148 177 234 291 173 207 274 340 197 236 313 390
cm2 25.3 33.2 40.8 30.9 40.7 50.3 59.6 40.3 53.3 66.0 78.4 49.8 65.8 81.7 97.3 128 59.2 78.4 97.4 116 153 66.7 88.5 110 131 173 98.5 123 146 193 239 114 141 169 223 276 124 154 184 243 302 151 188 225 299 371 220 263 349 434 251 301 399 496
EWCHS CHS
139.7x6.3 x8.0 x10.0 168.3x6.3 x8.0 x10.0 x12.5 219.1x6.3 x8.0 x10.0 x12.5 273.0x6.3 x8.0 x10.0 x12.5 x16.0 323.9x6.3 x8.0 x10.0 x12.5 x16.0 355.6x6.3 x8.0 x10.0 x12.5 x16.0 406.4x8.0 x10.0 x12.5 x16.0 x20.0 457.0x8.0 x10.0 x12.5 x16.0 x20.0 508.0x8.0 x10.0 x12.5 x16.0 x20.0 610.0x8.0 x10.0 x12.5 x16.0 x20.0 711.0x10.0 x12.5 x16.0 x20.0 813.0x10.0 x12.5 x16.0 x20.0
A
Ratio for Local Buckling d/t
23.3 17.5 14.0 28.3 21.3 17.0 14.2 36.7 27.5 22.0 18.3 45.0 33.8 27.0 22.5 16.9 53.3 40.0 32.0 26.7 20.0 60.0 45.0 36.0 30.0 22.5 50.0 40.0 33.3 25.0 20.0 57.5 46.0 38.3 28.8 23.0 62.5 50.0 41.7 31.3 25.0 76.3 61.0 50.8 38.1 30.5 71.0 59.2 44.4 35.5 81.0 67.5 50.6 40.5
d
Second Moment of Area I cm4 568 725 868 1041 1340 1610 1870 2310 3000 3640 4250 4340 5660 6910 8110 10300 7300 9500 11700 13800 17700 10460 13700 16900 19900 25600 18900 23300 27600 35600 43200 29000 35800 42400 55100 67000 37400 46200 54800 71300 87000 68500 84800 100800 131800 161000 135000 160000 210000 258000 201000 240000 315000 387000
136
Elastic Modulus
Plastic Modulus
Wel
Wpl
cm3 81.1 104 124 122 158 189 220 210 273 331 386 321 419 512 601 766 456 594 731 863 1110 581 761 939 1110 1420 945 1170 1380 1780 2160 1260 1560 1840 2400 2910 1500 1850 2190 2850 3480 2250 2780 3300 4320 5280 3800 4510 5920 7270 4960 5930 7780 9560
cm3 108 139 169 161 210 256 300 275 360 441 519 418 549 676 799 1030 592 779 961 1140 1480 752 991 1230 1450 1890 1230 1520 1810 2360 2890 1630 2030 2410 3150 3870 1940 2400 2860 3750 4610 2900 3600 4290 5650 6960 4900 5850 7710 9520 6400 7640 10100 12500
Torsional Constants IT cm4 1140 1450 1740 2080 2680 3220 3740 4620 6000 7280 8500 8680 11300 13800 16200 20700 14600 19000 23400 27600 35400 20900 27400 33800 39800 51200 37800 46600 55200 71200 86400 58000 71600 84800 110000 134000 74800 92400 110000 143000 174000 137000 170000 202000 264000 322000 270000 320000 420000 516000 402000 480000 630000 774000
Wt cm3 162 207 248 245 315 379 440 420 545 662 773 643 839 1020 1200 1530 913 1190 1460 1730 2220 1160 1520 1880 2220 2840 1890 2340 2760 3560 4320 2520 3120 3680 4800 5820 3000 3700 4380 5700 6960 4500 5560 6600 8640 10560 7600 9020 11800 14500 9920 11900 15600 19100
Surface Area per Meter m2 0.440 0.440 0.440 0.535 0.535 0.535 0.535 0.692 0.692 0.692 0.692 0.849 0.849 0.849 0.849 0.849 1.01 1.01 1.01 1.01 1.01 1.13 1.13 1.13 1.13 1.13 1.26 1.26 1.26 1.26 1.26 1.45 1.45 1.45 1.45 1.45 1.57 1.57 1.57 1.57 1.57 1.92 1.92 1.92 1.92 1.92 2.23 2.23 2.23 2.23 2.55 2.55 2.55 2.55
per Tonne m2 22.2 16.9 13.7 22.0 16.7 13.6 11.4 21.9 16.5 13.4 11.2 21.7 16.4 13.2 11.1 8.47 21.7 16.3 13.2 11.0 8.39 21.6 16.3 13.1 11.0 8.33 16.3 13.1 10.9 8.30 6.71 16.2 13.0 10.9 8.25 6.66 16.2 13.0 10.9 8.23 6.64 16.1 13.0 10.8 8.18 6.59 12.9 10.8 8.15 6.56 12.9 10.8 8.12 6.53
Design Table 23 Section dimensions and properties of cold-formed RHS z
y
h
cw cf
t
b
hxb
t
Mass per Meter m
mm 120x80
mm x6.0 x8.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x20.0
kg/m 16.5 21.0 20.3 26.0 31.2 25.9 33.5 40.6 30.6 39.8 48.4 35.3 46.1 56.3 64.0 39.1 51.1 62.6 71.6 44.8 58.6 72.0 82.9 105 54.2 71.2 87.7 102 131 54.2 71.2 87.7 102 131 83.8 103 121 156 96.3 119 139 181 220
EWRHS RHS
120x80x6.3 x8.0 160x80x6.3 x8.0 x10.0 200x100x6.3 x8.0 x10.0 200x150x6.3 x8.0 x10.0 250x150x6.3 x8.0 x10.0 x12.5 260x180x6.3 x8.0 x10.0 x12.5 300x200x6.3 x8.0 x10.0 x12.5 x16.0 350x250x6.3 x8.0 x10.0 x12.5 x16.0 400x200x6.3 x8.0 x10.0 x12.5 x16.0 450x250x8.0 x10.0 x12.5 x16.0 500x300x8.0 x10.0 x12.5 x16.0 x20.0
160x80 200x100 200x150 250x150
260x180
300x200
350x250
400x200
450x250
500x300
Area of Section A cm2 21.0 26.7 25.8 33.1 39.7 33.0 42.7 51.7 39.0 50.7 61.7 45.0 58.7 71.7 81.6 49.8 65.1 79.7 91.2 57.0 74.7 91.7 106 134 69.0 90.7 112 130 166 69.0 90.7 112 130 166 107 132 154 198 123 152 178 230 280
Ratio for Local Buckling cw/t cf/t 14.0 9.0 20.7 14.0 10.0 27.3 19.0 14.0 27.3 19.0 14.0 35.7 25.3 19.0 12.8 37.3 26.5 20.0 13.7 44.0 31.5 24.0 17.0 10.8 52.3 37.8 29.0 21.2 13.9 60.7 44.0 34.0 25.3 17.0 50.3 39.0 29.5 20.1 56.5 44.0 33.7 23.3 17.0
7.3 4.0 7.3 4.0 2.0 10.7 6.5 4.0 19.0 12.8 9.0 19.0 12.8 9.0 4.5 24.0 16.5 12.0 7.0 27.3 19.0 14.0 8.7 4.5 35.7 25.3 19.0 12.8 7.6 27.3 19.0 14.0 8.7 4.5 25.3 19.0 12.8 7.6 31.5 24.0 17.0 10.8 7.0
137
Second Moment of Area Iy Iz cm4 382 451 793 959 1080 1640 2030 2340 2200 2760 3250 3780 4790 5670 5980 4750 6040 7200 7730 7220 9250 11090 12100 14400 12300 15800 19100 21300 25900 14500 18700 22600 25100 30400 29000 35300 39700 49000 42400 51700 58900 73600 85800
cm4 204 240 270 324 362 560 688 790 1420 1780 2080 1730 2180 2570 2740 2710 3440 4090 4420 3900 4980 5960 6540 7750 7360 9480 11400 12800 15500 5030 6450 7760 8660 10500 11800 14300 16200 19900 19500 23700 27100 33800 39300
Elastic Modulus
Plastic Modulus
Wel,y
Wel,z
Wpl,y
Wpl,z
cm3 63.6 75.2 99.2 120 135 164 203 234 220 276 325 302 383 454 478 365 465 554 595 481 617 739 807 960 703 903 1091 1217 1480 725 935 1130 1260 1520 1290 1570 1760 2180 1700 2070 2360 2940 3430
cm3 51.0 60.1 67.4 80.9 90.4 112 138 158 189 237 277 231 291 343 365 301 382 454 491 390 498 596 654 775 589 758 912 1020 1240 503 645 776 866 1050 940 1140 1300 1590 1300 1580 1810 2250 2620
cm3 80.3 98.2 127 158 183 207 261 309 265 338 404 370 475 570 623 439 565 682 753 578 748 907 1010 1240 830 1080 1320 1500 1870 893 1160 1420 1600 1990 1580 1930 2200 2780 2050 2510 2900 3680 4380
cm3 60.9 74.2 78.6 97.3 112 128 161 190 218 278 332 261 335 402 440 342 440 531 588 440 568 689 772 946 663 862 1050 1190 1490 556 722 879 1000 1240 1060 1290 1480 1860 1450 1780 2050 2610 3100
Surface Area per Meter m2 0.369 0.359 0.449 0.439 0.428 0.569 0.559 0.548 0.669 0.659 0.648 0.769 0.759 0.748 0.718 0.849 0.839 0.828 0.798 0.969 0.959 0.948 0.918 0.890 1.17 1.16 1.15 1.12 1.09 1.17 1.16 1.15 1.12 1.09 1.36 1.35 1.32 1.29 1.56 1.55 1.52 1.49 1.46
per Tonne m2 22.4 17.1 22.2 16.9 13.7 22.0 16.7 13.5 21.8 16.6 13.4 21.8 16.5 13.3 11.2 21.7 16.4 13.2 11.1 21.7 16.4 13.2 11.1 8.44 21.6 16.3 13.1 11.0 8.35 21.6 16.3 13.1 11.0 8.35 16.2 13.0 10.9 8.28 16.2 13.0 10.9 8.24 6.66
Design Table 24 Section dimensions and properties of cold-formed SHS
z
y c b
EWSHS SHS
100x100x6.3 x8.0 150x150x6.3 x8.0 x10.0 200x200x6.3 x8.0 x10.0 x12.5 220x220x6.3 x8.0 x10.0 x12.5 x16.0 250x250x6.3 x8.0 x10.0 x12.5 x16.0 300x300x6.0 x8.0 x10.0 x12.5 x16.0 350x350x8.0 x10.0 x12.5 x16.0 400x400x8.0 x10.0 x12.5 x16.0 x20.0
b mm 100 150 200
220
250
300
350
400
t mm x6.0 x8.0 x6.0 x8.0 x10.0 x6.0 x8.0 x10.0 x12.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x6.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x8.0 x10.0 x12.0 x16.0 x20.0
Mass per Meter m kg/m 16.5 21.0 25.9 33.5 40.6 35.3 46.1 56.3 64.0 39.1 51.1 62.6 71.6 90.4 44.8 58.6 72.0 82.9 105 54.2 71.2 87.7 102 131 83.8 103 121 156 96.3 119 139 181 220
Area of section A cm2 21.0 26.7 33.0 42.7 51.7 45.0 58.7 71.7 81.6 49.8 65.1 79.7 91.2 115.2 57.0 74.7 91.7 105.6 134.4 69.0 90.7 112 130 166 107 132 154 198 123 152 178 230 280
Ratio for Local Buckling c/t 10.7 6.5 19.0 12.8 9.0 27.3 19.0 14.0 8.7 30.7 21.5 16.0 10.3 5.8 35.7 25.3 19.0 12.8 7.6 44.0 31.5 24.0 17.0 10.8 37.8 29.0 21.2 13.9 44.0 34.0 25.3 17.0 12.0
138
Second Moment of area Iy cm4 294 349 1110 1370 1590 2770 3500 4150 4410 3730 4750 5660 6110 7110 5570 7130 8550 9380 11160 9820 12700 15300 17100 20800 20500 24900 28200 34900 31000 37800 43200 54000 63200
t
Elastic Modulus
Plastic Modulus
Wel cm3 58.9 69.7 148 183 212 277 350 415 441 339 432 515 555 646 446 570 684 750 893 655 847 1020 1140 1390 1170 1420 1610 1990 1550 1890 2160 2700 3160
Wpl cm3 71.8 87.8 175 221 262 323 415 499 546 395 509 614 680 822 516 668 810 908 1110 755 982 1200 1360 1700 1360 1660 1900 2400 1790 2200 2530 3220 3840
Surface Area per Meter m2 0.369 0.359 0.569 0.559 0.548 0.769 0.759 0.748 0.718 0.849 0.839 0.828 0.798 0.770 0.969 0.959 0.948 0.918 0.890 1.17 1.16 1.15 1.12 1.09 1.36 1.35 1.32 1.29 1.56 1.55 1.52 1.49 1.46
per Tonne m2 22.4 17.1 22.0 16.7 13.5 21.8 16.5 13.3 11.2 21.7 16.4 13.2 11.1 8.52 21.7 16.4 13.2 11.1 8.44 21.6 16.3 13.1 11.0 8.35 16.2 13.0 10.9 8.28 16.2 13.0 10.9 8.24 6.66
Design Tables 25 to 27 for Section Resistances of Welded Sections: Q235 steel EWI-sections (EWIS) EWH-sections (EWHS)
139
Design Table 25 Section resistances of welded I-sections: Q235 steel (1) z
tf r y
d h tw
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
Moment Resistance My,Rd Mz,Rd kNm kNm 4010 847 3230 640 2800 417 2480 350 2230 325 1860 249 2080 344 1730 262 1560 243 1680 273 1420 220 1260 202 1130 170 1350 225 1140 170 1030 166 921 139 1660 370 1220 282 1010 228 1010 178 843 143 756 120 703 119 839 164 700 132 626 111 583 110 476 83.0
140
Shear Resistance Vz,Rd kN 2170 2160 2200 2170 1720 1700 1610 1590 1190 1450 1440 1060 1110 1300 1300 964 1010 1510 879 864 879 864 903 740 779 765 799 654 654
Axial Resistance Na,Rd kN 10700 8920 7840 7100 5970 5140 6020 5170 4200 5530 4850 3910 3550 5120 4430 3630 3310 6710 4670 3990 3950 3420 3120 2770 3790 3280 2990 2660 2220
Design Table 26 Section resistances of welded I-sections: Q235 steel (2) z
tf r y
d h tw
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 532 103 495 102 440 85.4 419 84.4 340 63.7 423 68.8 380 58.0 357 57.0 295 43.2 254 36.3 378 77.8 348 76.8 284 58.0 250 48.6 210 33.7 176 24.9 276 57.5 226 43.5 201 38.4 178 32.2 166 31.7 140 25.5 198 44.9 152 33.5 128 28.0 177 34.6 146 26.3 124 22.1 113 14.1 97.7 11.5 86.5 11.1 135 38.0 119 31.9 91.0 25.3 91.1 18.7 78.3 15.1 63.7 11.5 78.2 24.6 62.5 19.7 57.4 13.4 37.3 8.81 29.9 8.79 20.9 5.69
141
Shear Resistance Vz,Rd kN 666 543 567 454 454 543 567 454 454 444 518 405 405 405 296 296 444 444 350 350 263 259 306 229 222 306 306 296 311 306 226 257 257 185 192 192 189 155 148 148 88.8 74.0 64.1
Axial Resistance Na,Rd kN 2910 2710 2470 2180 1810 2380 2200 1910 1600 1440 2320 2080 1730 1550 1240 1060 1990 1680 1470 1330 1130 984 1610 1200 1060 1470 1240 1110 1010 912 759 1310 1170 914 896 789 676 918 781 733 513 487 401
Design Table 27 Section resistances of welded H-sections: Q235 steel tf
z
r y
h
cf
tw
d h
b EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 2 2
Moment Resistance My,Rd Mz,Rd kNm kNm 3110 1770 2500 1380 2310 1370 1900 1140 1560 955 1240 749 1150 743 904 501 875 501 691 399 681 399 1130 541 951 481 761 383 624 319 520 270 497 268 367 148 550 284 446 235 356 199 333 198 284 165 231 115 200 100 173 91.7 139 74.7 101 40.9 79.9 37.7 62.6 31.3 51.7 25.1
142
Shear Resistance Vz,Rd kN 2650 2080 1490 1420 1180 1150 718 718 699 510 425 1040 827 803 624 605 453 382 685 529 383 307 257 312 260 259 207 197 168 118 118
Axial Resistance Na,Rd kN 17800 14000 13200 11400 9600 7810 7170 5680 5650 4490 4360 7870 6770 5550 4600 3970 3690 3100 4790 3930 3160 3030 2540 2620 2210 2000 1580 1360 1150 933 793
Design Tables 28 to 33 for Section Resistances of Welded Sections: Q275 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
143
Design Table 28 Section resistances of welded I-sections: Q275 steel (1) z
tf r d h
y tw
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 4750 1000 3830 756 3320 491 2920 414 2630 383 2190 293 2450 405 2040 309 1830 286 1980 321 1670 259 1480 238 1320 199 1590 265 1340 200 1210 195 1080 163 1960 436 1440 332 1190 268 1190 209 993 168 885 141 823 139 988 193 824 156 733 130 683 129 483 62.4
144
Shear Resistance Vz,Rd kN 2560 2550 2590 2560 2030 2000 1890 1870 1710 1690 1250 1300 1540 1540 1130 1180 1780 1030 1020 1030 1020 1060 866 918 901 935 765 765
Axial Resistance Na,Rd kN 12500 10400 9110 8190 6880 5910 6950 5960 4850 6380 5590 4520 4070 5920 5110 4190 3790 7900 5420 4630 4580 3950 3580 3180 4400 3790 3430 3060 2550
Design Table 29 Section resistances of welded I-sections: Q275 steel (2) z
tf r tw d h
y cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 626 121 583 120 515 100 490 98.7 398 74.6 499 81.0 445 67.9 418 66.7 345 50.6 298 42.4 443 91.0 408 89.9 333 67.9 254 36.7 245 39.4 206 29.2 323 67.3 265 50.9 235 44.9 208 37.7 194 37.1 140 19.1 231 52.5 178 39.2 150 32.8 208 40.5 171 30.8 145 25.8 132 16.5 114 13.5 101 12.9 158 44.5 139 37.3 92.4 19.1 107 21.8 91.7 17.6 74.5 13.4 91.5 28.7 73.2 23.1 67.2 15.7 43.7 10.3 34.9 10.3 24.5 6.66
145
Shear Resistance Vz,Rd kN 784 640 664 531 531 640 664 531 531 520 606 473 473 473 346 346 520 520 410 410 307 303 358 268 260 358 358 346 364 358 264 300 300 217 225 225 221 182 173 173 104 86.6 75.1
Axial Resistance Na,Rd kN 3430 3140 2830 2500 2060 2760 2510 2180 1820 1640 2700 2390 1980 1770 1420 1210 2310 1950 1700 1530 1290 1120 1870 1380 1220 1710 1440 1290 1170 1060 865 1520 1360 1060 1040 918 787 1070 908 852 596 566 466
Design Table 30 Section resistances of welded H-sections: Q275 steel tf
z
r h
y
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 3 3 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 3540 2020 2970 1640 2740 1620 2260 1350 1840 1130 1460 882 1360 875 1060 590 1030 590 725 311 718 311 1340 642 1120 566 896 451 735 376 612 318 585 315 430 173 648 335 525 276 419 234 393 233 333 193 272 135 236 118 203 107 163 87.4 118 47.9 93.5 44.1 73.3 36.6 61.7 19.3
146
Shear Resistance Vz,Rd kN 3020 2460 1770 1690 1390 1360 846 846 823 601 501 1240 974 946 734 712 534 447 807 623 451 362 300 367 306 303 242 231 196 139 139
Axial Resistance Na,Rd kN 20300 16600 15700 13500 11300 9190 8440 6700 6660 5290 5130 9330 7980 6530 5420 4670 4350 3630 5640 4620 3720 3570 2970 3090 2600 2340 1840 1590 1340 1090 928
Design Table 31 Section resistances of cold-formed CHS: Q275 steel z
t
y
d
Q275 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 3 2 1 1 1 2 1 1 1 1 2 2 1 1 1 3 2 1 1 1 3 3 2 1 1 3 2 2 1 4 3 2 1
Moment Resistance My,Rd kNm 26.9 34.8 42.3 40.3 52.5 64.0 74.9 68.7 89.9 110 130 105 137 169 200 258 148 195 240 285 370 145 248 308 363 473 308 380 453 590 696 408 508 603 788 932 375 600 715 938 1110 563 695 1070 1410 1680 950 1460 1930 2290 1480 2520 3010
147
Shear Resistance Vz,Rd kN 232 305 375 284 374 462 547 371 490 606 721 457 605 751 894 1170 544 721 895 1070 1400 613 813 1010 1210 1590 905 1130 1340 1770 2110 1040 1300 1550 2050 2450 1140 1410 1690 2240 2670 1390 1730 2070 2740 3280 2020 2420 3210 3840 2760 3670 4400
Axial Resistance Na,Rd kN 631 829 1020 773 1020 1260 1490 1010 1330 1650 1960 1240 1650 2040 2430 3190 1480 1960 2430 2900 3820 1670 2210 2750 3280 4320 2460 3060 3660 4830 5750 2840 3530 4220 5580 6660 3090 3850 4600 6080 7270 3780 4710 5640 7460 8930 5500 6580 8720 10400 7520 9980 12000
Design Table 32 Section resistances of cold-formed RHS: Q275 steel z
cw
y
h
cf t
b Q275 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.6 9.98 12.7 15.1 16.2 15.2 19.4 23.3 25.4 30.2 25.8 33.2 40.1 44.7 54.4 30.5 39.3 47.5 52.7 63.8 60.9 74.1 83.4 103 89.0 109 124 155 180
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.75 5.69 7.22 8.59 9.28 8.19 10.5 12.5 13.7 16.3 15.5 19.9 23.9 26.9 32.6 10.6 13.5 16.3 18.2 22.1 24.8 30.0 34.0 41.8 41.0 49.8 56.9 71.0 82.5
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 2 1 1 1 1 1 1 3 4 1 3 1 1 1 1 1 1 1 4 1 4 1 2 1 1 1 1 1 4 1 4 1 1 1 1 2 4 1 4 1 2 1 1 1 1
Moment resistance My,Rd kNm 20.1 24.5 31.8 39.5 45.8 51.7 65.3 77.1 66.3 84.5 101 92.5 119 143 156 110 141 170 188 145 187 227 253 310 176 270 330 375 468 223 290 355 400 498 395 483 550 695 513 628 725 920 1060
148
Mz,Rd kNm 15.2 18.6 19.7 24.3 28.1 32.0 40.4 47.5 54.6 69.5 82.9 57.7 83.7 100 110 75.3 110 133 147 142 172 193 236 190 263 298 373 220 250 310 370 465 513 653 747
Shear Resistance
Axial Resistance
Vz,Rd kN 182 231 248 318 382 318 411 498 322 418 509 406 529 647 736 425 555 680 778 494 647 794 914 1160 581 764 941 1090 1400 873 1070 1250 1600 990 1220 1430 1840 1110 1370 1600 2080 2430
Na,Rd kN 525 667 645 827 993 825 1070 1290 975 1270 1540 1120 1470 1790 2040 1230 1630 1990 2280 1370 1870 2290 2640 3360 1620 2240 2790 3240 4160 1550 2180 2790 3240 4160 2500 3240 3840 4960 2820 3650 4440 5760 6740
Design Table 33 Section resistances of cold-formed SHS: Q275 steel z
y c b
Flexural rigidity EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
Section Classification
1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 2 1 1 1 3 1 1 1 4 2 1 1 1
Q275 Moment Resistance My,Rd kNm 17.9 22.0 43.8 55.3 65.4 80.8 104 125 137 98.8 127 154 170 206 111 167 203 227 279 246 300 340 425 293 415 475 600 550 633 805 925
149
Shear Resistance Vz,Rd kN 152 193 238 308 373 325 424 518 589 360 470 575 658 831 411 539 662 762 970 498 655 806 935 1200 770 951 1110 1430 885 1090 1280 1660 1870
t
Axial Resistance Na,Rd kN 525 667 825 1070 1290 1130 1470 1790 2040 1250 1630 1990 2280 2880 1420 1870 2290 2640 3360 1620 2270 2790 3240 4160 2620 3290 3840 4960 2890 3790 4440 5760 6740
150
Design Tables 34 to 39 for Section Resistances of Welded Sections: Q345 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
151
Design Table 34 Section resistances of welded I-sections: Q345 steel (1) z
tf r y
tw
d h
cf b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 163 12.5 130 9.35 112 4.80 96.4 4.00 87.7 3.67 71.3 2.69 76.9 4.00 62.3 2.93 57.4 2.69 55.8 2.80 46.1 2.24 41.2 2.04 35.1 1.63 40.0 2.09 33.2 1.50 30.3 1.50 25.8 1.20 45.5 4.04 33.8 3.08 27.3 2.46 27.5 1.50 22.4 1.20 19.0 0.961 17.7 0.961 20.2 1.33 16.4 1.07 13.9 0.855 12.9 0.855 10.5 0.640
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 5970 1260 4810 953 4170 621 3690 521 3330 484 2770 370 3100 512 2570 390 2320 362 2500 406 2120 327 1870 301 1430 161 2020 335 1700 253 1530 247 1350 205 2480 551 1820 420 1510 339 1500 264 1250 213 1110 177 1030 175 1250 244 1040 197 919 163 856 161 605 78.3
152
Shear Resistance Vz,Rd kN 3240 3220 3270 3240 2560 2530 2390 2360 2170 2140 1940 1940 1430 1480 2250 1310 1290 1310 1290 1330 1090 1160 1140 1170 960 960
Axial Resistance Na,Rd kN 15400 12700 11100 10000 8440 7210 8540 7280 5970 7850 6830 5560 4940 7280 6260 5160 4600 9990 6720 5720 5660 4860 4350 3880 5440 4680 4190 3740 3090
Design Table 35 Section resistances of welded I-sections: Q345 steel (2) z
tf r y
tw
d h
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 1 1 2 2 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 792 153 737 151 646 125 615 124 499 93.5 630 102 558 85.2 524 83.7 433 63.4 373 53.2 555 114 511 113 417 85.2 318 46.0 308 49.5 259 36.6 405 84.4 332 63.9 295 56.3 261 47.3 243 46.5 176 24.0 290 65.9 224 49.2 188 41.2 260 50.8 214 38.6 182 32.4 166 20.7 143 16.9 127 16.2 198 55.8 174 46.8 116 24.0 134 27.4 115 22.1 77.0 10.6 115 36.0 91.8 29.0 84.3 19.7 54.8 12.9 43.8 12.9 30.7 8.36
153
Shear Resistance Vz,Rd kN 992 809 833 666 666 809 833 666 666 652 761 594 594 594 435 435 652 652 514 514 386 380 449 337 326 449 449 435 456 449 331 377 377 272 282 282 277 228 217 217 130 109 94.0
Axial Resistance Na,Rd kN 4330 3900 3480 3070 2530 3420 3070 2670 2220 2000 3330 2940 2420 2160 1740 1480 2900 2450 2080 1870 1590 1370 2340 1710 1500 2140 1810 1620 1460 1320 1050 1910 1710 1320 1290 1130 960 1340 1140 1070 744 710 585
Design Table 36 Section resistances of welded H-sections: Q345 steel tf
z
r h
y
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 1 1 1 2 2 2 2 3 3 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 3 3 3 1 1 1 1 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 4550 2590 3780 2090 3490 2070 2870 1730 2320 1420 1840 1120 1710 1110 1350 746 1300 746 917 393 908 393 1710 818 1420 716 1130 570 929 475 774 402 740 399 539 217 819 423 664 349 530 296 496 295 376 161 344 171 298 149 254 135 182 72.1 148 60.1 117 55.4 91.9 45.9 67.4 24.2
154
Shear Resistance Vz,Rd kN 3890 3140 2250 2150 1760 1710 1070 1070 1040 760 633 1580 1230 1200 928 900 675 561 1020 788 570 457 377 557 464 456 365 348 296 209 174
Axial Resistance Na,Rd kN 26100 21200 20000 17200 14300 11600 10700 8460 8420 6690 6490 11900 10100 8260 6850 5910 5500 4550 7130 5840 4700 4510 3720 3910 3290 2930 2310 2000 1690 1370 1160
Design Table 37 Section resistances of cold-formed CHS: Q345 steel z
t
y
d
Q345 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 3 2 1 1 1 3 2 2 1 1 3 2 1 1 1 3 2 2 1 1 4 3 2 1 1 4 3 3 2 1 4 3 2 2 4 4 3 2
Moment Resistance My,Rd kNm 33.8 43.7 53.0 50.6 65.8 80.3 94.0 86.2 113 138 163 131 172 212 251 324 143 244 301 358 464 182 311 386 455 593 296 477 568 740 880 395 637 756 988 1180 580 897 1180 1400 872 1040 1770 2120 1410 2420 2900 2440 3800
155
Shear Resistance Vz,Rd kN 291 382 471 356 469 579 687 465 614 761 904 574 759 942 1120 1470 682 904 1120 1340 1760 769 1020 1270 1510 1990 1140 1410 1690 2230 2670 1310 1630 1950 2570 3090 1770 2120 2800 3380 2170 2600 3440 4150 3030 4020 4850 4600 5560
Axial Resistance Na,Rd kN 792 1040 1280 970 1280 1580 1870 1270 1670 2070 2460 1560 2070 2560 3050 4000 1860 2460 3050 3640 4790 2090 2770 3450 4110 5420 3090 3840 4590 6050 7270 3560 4430 5300 7000 8420 4830 5770 7630 9180 5910 7070 9360 11300 8250 10900 13200 12500 15100
Design Table 38 Section resistances of cold-formed RHS: Q345 steel z
cw
y
h
cf t
b Q345 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.9 9.98 12.7 15.1 16.7 15.2 19.4 23.3 26.0 31.3 25.8 33.2 40.1 45.6 55.9 30.5 39.3 47.5 53.6 65.5 60.9 74.1 84.6 105 89.0 109 125 157 184
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.90 5.69 7.22 8.59 9.49 8.19 10.5 12.5 14.0 16.8 15.5 19.9 24.0 27.2 33.4 10.6 13.5 16.3 18.4 22.4 24.8 30.0 34.4 42.6 41.0 49.8 57.3 71.8 84.2
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1 1 1 2 4 1 3 1 1 1 1 1 1 4 4 1 4 1 2 1 1 1 1 2 4 1 4 1 3 1 1 1 1 1 4 1 4 1 2 1 1 3 4 1 4 1 3 1 1 1 1
Moment resistance My,Rd kNm 25.2 30.8 39.9 49.5 57.4 64.9 81.9 96.8 83.1 106 127 116 149 179 195 138 177 214 236 181 235 284 317 389 339 414 470 587 280 364 445 502 624 496 605 690 872 533 787 910 1150 1330
156
Mz,Rd kNm 19.1 23.3 24.7 30.5 35.2 40.2 50.6 59.6 68.4 87.2 104 105 126 138 138 166 184 156 216 242 297 329 373 467 243 314 389 464 583 568 819 944
Shear Resistance
Axial Resistance
Vz,Rd kN 228 290 312 399 479 399 515 624 404 525 639 509 664 812 923 533 696 853 976 619 812 996 1150 1460 729 958 1180 1370 1760 1090 1350 1560 2010 1240 1530 1790 2310 1390 1720 2010 2610 3080
Na,Rd kN 659 837 810 1040 1250 1040 1340 1620 1220 1590 1940 1380 1840 2250 2560 1520 2040 2500 2860 1690 2340 2880 3310 4210 1960 2760 3500 4060 5220 1910 2670 3510 4060 5220 3070 3980 4820 6220 3460 4490 5510 7230 8530
Design Table 39 Section resistances of cold-formed SHS: Q345 steel z
y c b
Flexural rigidity
Section Classification
EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
1 1 1 1 1 2 1 1 1 2 1 1 1 1 4 1 1 1 1 4 3 1 1 1 4 2 1 1 4 3 1 1 1
Q345 Moment Resistance My,Rd kNm 22.5 27.5 54.9 69.4 82.1 101 130 156 171 124 160 193 213 258 210 254 285 350 266 376 427 533 521 596 753 593 794 1010 1170
157
Shear Resistance Vz,Rd kN 190 242 299 387 468 408 531 649 739 451 589 722 826 1040 516 676 830 956 1220 625 821 1010 1170 1510 966 1190 1390 1800 1110 1370 1610 2090 2460
t
Axial Resistance Na,Rd kN 659 837 1040 1340 1620 1410 1840 2250 2560 1560 2040 2500 2860 3610 1780 2340 2880 3310 4210 2040 2840 3500 4060 5220 3290 4130 4820 6220 3620 4760 5570 7230 8530
158
Design Tables 40 to 45 for Section Resistances of Welded Sections: Q460 steel EWI-sections (EWIS) EWH-sections (EWHS) EWCHS EWRHS EWSHS
159
Design Table 40 Section resistances of welded I-sections: Q460 steel (1) z
tf r y
tw
cf
d h
b EWI-Sections 920x450x420 x353 920x360x312 x282 x249 x218 840x350x246 x214 x184 760x320x220 x194 x167 x147 690x280x198 x173 x151 x133 620x330x258 x186 x160 610x260x158 x138 x122 x112 540x250x148 x128 x113 x104 x88
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 1670 128 1330 95.8 1150 49.1 987 41.0 899 37.6 731 27.6 788 41.0 638 30.1 588 27.5 571 28.7 473 23.0 422 20.9 359 16.7 410 21.4 340 15.4 311 15.4 265 12.3 466 41.4 347 31.5 279 25.2 281 15.4 229 12.3 195 9.85 181 9.85 207 13.7 168 10.9 143 8.76 133 8.76 107 6.55
Section Classification Bending Bending y-y z-z 1 1 2 2 1 1 1 1 2 1 3 3 1 1 3 3 3 3 1 1 2 2 2 2 3 3 1 1 1 1 2 1 3 3 1 1 1 1 3 3 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 7840 1660 6320 1250 5480 816 4840 684 4370 636 3090 309 4080 672 2900 327 2670 308 3290 533 2780 430 2140 396 1920 215 2650 440 2230 332 2010 324 1560 176 3250 724 2380 552 1740 290 1970 347 1650 280 1490 237 1380 234 1640 321 1370 258 1230 219 1150 216 811 105
160
Shear Resistance Vz,Rd kN 4250 4230 4300 4250 3280 3240 2970 2940 2670 2670 2960 1800 1770 1800 1770 1770 1590 1560 1560 1280 1280
Axial Resistance Na,Rd kN 19700 16100 14000 12600 10700 9060 10800 9170 7580 9940 8610 7060 6330 9230 7880 6540 5890 13000 8610 7290 7210 6170 5570 4990 6950 5950 5380 4820 3960
Design Table 41 Section resistances of welded I-sections: Q460 steel (2) z
tf r y
tw
d h
cf b EWI-Sections 460x220x112 x104 x90 x83 x70 460x180x91 x80 x73 x62 x56 410x210x85 x78 x65 x59 400x150x49 x43 355x180x73 x62 x54 x49 355x170x44 x38 310x160x59 x45 x39 310x140x54 x45 x41 310x110x37 x33 x28 260x170x48 x43 x33 260x130x33 x29 x25 210x150x34 x29 200x110x27 180x100x19 150x100x18 130x80x15
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 110 7.46 102 7.46 86.5 5.96 83.8 5.96 67.2 4.47 86.1 4.07 73.3 3.26 70.6 3.26 57.1 2.44 47.7 2.04 67.8 5.19 62.4 5.19 50.0 3.89 43.7 3.23 35.9 1.70 29.8 1.18 42.0 3.26 34.0 2.44 30.2 2.06 26.5 1.72 25.2 1.70 20.6 1.37 26.3 2.29 20.3 1.70 16.4 1.43 23.4 1.53 18.9 1.16 15.4 0.945 14.3 0.462 12.0 0.357 10.7 0.357 15.0 2.06 13.1 1.70 9.70 1.37 10.0 0.756 8.44 0.609 6.57 0.462 7.01 1.18 5.29 0.945 4.77 0.462 2.79 0.273 1.85 0.273 1.09 0.126
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 2 2 3 3 1 1 1 1 3 3 3 3 2 1 2 1 1 1 2 2 1 1 3 3 3 3 3 3 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 2 2 3 3 1 1 3 3 1 1 1 1 1 1 1 1
Moment Resistance My,Rd Mz,Rd kNm kNm 1040 201 968 199 865 168 823 166 584 81.3 828 135 748 114 701 112 580 84.9 424 45.3 743 153 685 151 487 74.0 426 61.6 412 66.2 347 49.0 542 113 445 85.6 395 75.4 298 63.3 284 40.0 235 32.1 388 88.2 299 65.9 252 55.1 349 68.1 287 51.7 244 43.4 222 27.8 192 22.7 170 21.7 265 74.8 201 40.0 155 32.1 179 36.7 154 29.6 103 14.2 154 48.3 106 25.2 113 26.4 73.4 17.3 58.7 17.3 41.2 11.2
161
Shear Resistance Vz,Rd kN 1300 1060 1110 888 888 1060 1110 888 888 869 1010 792 792 792 869 869 686 686 514 507 599 449 435 599 599 579 608 599 442 502 502 362 377 377 369 304 290 290 174 145 126
Axial Resistance Na,Rd kN 5550 5000 4500 4000 3260 4360 3970 3460 2860 2560 4320 3830 3140 2790 2260 1910 3830 3190 2690 2410 2060 1770 3070 2220 1950 2800 2350 2100 1870 1690 1350 2550 2280 1720 1670 1460 1240 1780 1520 1430 974 947 779
Design Table 42 Section resistances of welded H-sections: Q460 steel tf
z
r y
h
tw d h
cf b
EWH-Sections 420x480x716 x563 x532 x456 x368 x300 x275 360x440x218 x217 x172 x167 370x330x316 x260 x213 x177 x152 x142 x114 270x310x184 x151 x121 x116 x93 210x230x101 x85 x73 x58 x50 170x170x42 x34 x29
Flexural Rigidity EIy EIz 103*kNm2 103*kNm2 634 291 515 233 458 232 363 194 277 155 216 124 199 123 156 74.6 147 74.6 114 59.6 113 59.6 188 63.0 145 55.0 114 45.2 91.8 37.6 74.3 32.7 72.7 32.7 56.1 26.1 68.5 28.4 54.8 23.6 43.3 20.9 39.5 20.9 32.8 16.7 22.1 8.11 19.6 7.46 15.6 6.80 12.8 5.80 9.91 4.83 5.78 2.06 4.31 1.72 3.61 1.38
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 3 3 3 3 4 4 1 1 1 1 2 2 2 2 3 3 1 1 1 1 1 1 3 3 4 4 1 1 3 3 3 3
Moment Resistance My,Rd Mz,Rd kNm kNm 5490 3120 4670 2580 4310 2550 3550 2130 3050 1870 2110 960 1990 960 1560 644 1510 644 1200 516 1190 516 2120 1010 1860 940 1490 748 1220 624 884 346 864 346 1060 556 861 459 687 389 644 387 498 215 446 224 386 196 336 180 240 96.6 155 74.2 106 40.5 89.2 32.4
162
Shear Resistance Vz,Rd kN 4930 4060 2910 2780 2310 2250 1400 1400 1370 1000 831 2040 1620 1570 1220 1180 887 748 1340 1030 748 600 502 610 508 507 406 386 328 232 232
Axial Resistance Na,Rd kN 31500 26200 24700 21200 18800 15300 14000 11100 11100 8780 8220 14700 13200 10800 9000 7760 7220 6090 9360 7680 6180 5920 4990 5130 4320 3920 3100 2670 2260 1830 1560
Design Table 43 Section resistances of cold-formed CHS: Q460 steel z
t
y
d
Q460 Flexural rigidity EWCHS
140x6.0 x8.0 x10.0 170x6.0 x8.0 x10.0 x12.0 220x6.0 x8.0 x10.0 x12.0 270x6.0 x8.0 x10.0 x12.0 x16.0 320x6.0 x8.0 x10.0 x12.0 x16.0 360x6.0 x8.0 x10.0 x12.0 x16.0 400x8.0 x10.0 x12.0 x16.0 x20.0 460x8.0 x10.0 x12.0 x16.0 x20.0 500x8.0 x10.0 x12.0 x16.0 x20.0 610x8.0 x10.0 x12.0 x16.0 x20.0 710x10.0 x12.0 x16.0 x20.0 810x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 1.19 1.52 1.82 2.19 2.81 3.38 3.93 4.85 6.30 7.64 8.93 9.11 11.9 14.5 17.0 21.7 15.3 20.0 24.6 29.0 37.2 22.0 28.8 35.5 41.8 53.8 39.7 48.9 58.0 74.8 90.7 60.9 75.2 89.0 116 141 78.5 97.0 115 150 183 144 178 212 277 338 284 336 441 542 422 504 662 813
Section Classification
1 1 1 2 1 1 1 3 2 1 1 3 2 2 1 1 4 3 2 2 1 4 3 3 2 1 4 3 2 1 1 4 4 3 2 1 4 4 3 2 1 4 4 4 3 2 4 4 3 2 4 4 4 3
Moment Resistance My,Rd kNm 45.1 58.3 70.7 67.5 87.8 107 125 87.8 150 184 217 134 230 283 334 432 248 402 477 619 318 393 606 790 489 757 987 1210 769 1320 1620 916 1570 1930 1810 2780 2480 3810 3820
163
Shear Resistance Vz,Rd kN 388 510 628 475 626 773 916 620 819 1010 1210 765 1010 1260 1490 1960 1210 1500 1780 2350 1360 1690 2020 2660 1880 2250 2970 3510 2600 3430 4060 2830 3740 4430 4590 5450 5360 6370 7300
Axial Resistance Na,Rd kN 1060 1390 1710 1290 1700 2100 2490 1690 2230 2760 3280 2080 2750 3420 4070 5340 3280 4070 4860 6390 3700 4600 5490 7230 5120 6120 8070 9550 7060 9330 11100 7690 10200 12100 12500 14800 14600 17300 19900
Design Table 44 Section resistances of cold-formed RHS: Q460 steel z
cw
y
h
cf t
b Q460 Flexural rigidity EWRHS
120x80x6.0 x8.0 160x80x6.0 x8.0 x10.0 200x100x6.0 x8.0 x10.0 200x150x6.0 x8.0 x10.0 250x150x6.0 x8.0 x10.0 x12.0 260x180x6.0 x8.0 x10.0 x12.0 300x200x6.0 x8.0 x10.0 x12.0 x16.0 350x250x6.0 x8.0 x10.0 x12.0 x16.0 400x200x6.0 x8.0 x10.0 x12.0 x16.0 450x250x8.0 x10.0 x12.0 x16.0 500x300x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.801 0.948 1.67 2.01 2.27 3.44 4.26 4.91 4.62 5.80 6.83 7.94 10.1 11.9 12.9 9.98 12.7 15.1 16.7 15.2 19.4 23.3 26.0 31.3 25.8 33.2 40.1 45.6 55.9 30.5 39.3 47.5 53.6 65.5 60.9 74.1 84.6 105 89.0 109 125 157 184
EIz 103*kNm2 0.428 0.505 0.566 0.679 0.760 1.18 1.44 1.66 2.98 3.74 4.37 3.63 4.58 5.40 5.90 5.69 7.22 8.59 9.49 8.19 10.5 12.5 14.0 16.8 15.5 19.9 24.0 27.2 33.4 10.6 13.5 16.3 18.4 22.4 24.8 30.0 34.4 42.6 41.0 49.8 57.3 71.8 84.2
Section Classification Bending Bending y-y z-z 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 4 1 2 1 1 1 1 2 4 1 2 1 1 1 1 3 4 1 4 1 2 1 1 1 1 4 4 2 4 1 3 1 1 1 1 3 4 1 4 1 4 1 2 1 1 2 4 1 4 1 4 1 1 4 4 2 4 1 4 1 2 1 1
Moment resistance My,Rd kNm 33.6 41.1 53.2 66.1 76.6 86.5 109 129 111 141 169 155 199 238 260 183 236 285 315 201 313 379 422 519 452 552 627 782 303 485 594 669 832 661 807 920 1160 1050 1210 1540 1750
164
Mz,Rd kNm 25.4 31.2 33.0 40.9 47.2 47.0 67.8 79.8 79.5 117 139 141 169 185 185 223 247 289 324 397 441 500 626 420 521 781 1150 1360
Shear Resistance
Axial Resistance
Vz,Rd kN 306 388 417 535 642 534 690 836 541 702 855 682 890 1090 1240 714 933 1140 1310 830 1090 1330 1540 1960 976 1280 1580 1830 2350 1470 1810 2090 2690 1660 2050 2390 3090 1860 2300 2690 3490 4240
Na,Rd kN 879 1120 1080 1380 1660 1380 1790 2160 1630 2120 2580 1800 2450 3000 3410 1980 2720 3330 3810 2200 3050 3840 4420 5620 2500 3600 4630 5420 6960 2470 3460 4490 5420 6960 3980 5160 6340 8300 4430 5820 7160 9630 11700
Design Table 45 Section resistances of cold-formed SHS: Q460 steel z
y c b
Flexural rigidity
Section Classification
EWSHS
100x100x6.0 x8.0 150x150x6.0 x8.0 x10.0 200x200x6.0 x8.0 x10.0 x12.0 220x220x6.0 x8.0 x10.0 x12.0 x16.0 250x250x6.0 x8.0 x10.0 x12.0 x16.0 300x300x6.0 x8.0 x10.0 x12.0 x16.0 350x350x8.0 x10.0 x12.0 x16.0 400x400x8.0 x10.0 x12.0 x16.0 x20.0
EIy 103*kNm2 0.618 0.732 2.33 2.88 3.34 5.82 7.35 8.72 9.26 7.83 9.98 11.9 12.8 14.9 11.7 15.0 18.0 19.7 23.4 20.6 26.7 32.1 35.9 43.7 43.1 52.3 59.2 73.3 65.1 79.4 90.7 113 133
1 1 1 1 1 3 1 1 1 4 1 1 1 1 4 2 1 1 1 4 4 2 1 1 4 3 1 1 4 4 2 1 1
Q460 Moment Resistance My,Rd kNm 30.0 36.7 73.2 92.6 110 116 174 209 229 213 257 285 344 280 339 380 466 502 569 711 594 795 1000 1060 1350 1540
165
Shear Resistance Vz,Rd kN 254 322 399 515 624 543 709 866 985 601 786 962 1100 1390 688 902 1110 1270 1620 833 1090 1350 1560 2010 1290 1590 1850 2390 1480 1830 2140 2780 3230
t
Axial Resistance Na,Rd kN 879 1120 1380 1790 2160 1880 2450 3000 3410 2020 2720 3330 3810 4820 2210 3120 3840 4420 5620 2510 3650 4670 5420 6960 4070 5420 6420 8300 4470 5970 7430 9630 11200
166
References European Steel Material Specifications: EN 10020, Definition and classification of grades of steel. 2000. EN 10021, General technical delivery requirements for steel and iron products. 2006. EN 10025, Hot rolled products of structural steels — Part 1: General technical delivery conditions. 2004. Part 2: Technical delivery conditions for non‐alloy structural steels. 2004. Part 3: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels. 2004. Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels. 2004. Part 5: Technical delivery conditions for structural steels with improved atmospheric corrosion resistance. 2004. Part 6: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition. 2004. BS EN 10029, Hot‐rolled steel plates 3 mm thick or above: Tolerances on dimensions and shape. 2010. EN 10034, Structural steel I and H sections: Tolerances on shape and dimensions. 1993. EN 10149, Specification for hot‐rolled flat products made of high yield strength steels for cold forming — Part 1: General delivery conditions. 2013. Part 2: Delivery conditions for thermomechanically rolled steels. 2013. Part 3. Delivery conditions for normalized or normalized rolled steels. 2013. EN 10210, Hot finished structural hollow sections of non‐alloy and fine grain steels — Part 1: Technical delivery conditions. 2006. Part 2: Tolerances, dimensions and sectional properties. 2006. EN 10219, Cold formed welded structural hollow sections of non‐alloy and fine grain steels — Part 1: Technical delivery conditions. 2006. Part 2: Tolerances, dimensions and sectional properties. 2006. BS 4‐1, Structural steel sections — Part 1: Specification for hot‐rolled sections. 2005.
167
Chinese Steel Material Specifications: GB/T 700, Carbon structural steels. 2006. GB/T 709, Dimension, shape, weight and tolerances for hot‐rolled steel plates and sheets. 2006. GB/T 912, Hot‐rolled sheets and strips of carbon structural steels and high strength low alloy structural steels. 2008. GB/T 1591, High strength low alloy structural steels. 2008. GB/T 3274, Carbon structural and low alloy steel rolled plates and strips. 2007. GB/T 4171, Atmospheric corrosion resisting structural steel. 2008. GB/T 5313, Steel plates with through‐thickness characteristics. 2010. GB/T 6725, Cold‐formed steel sections. 2002. GB/T 6728, Cold‐formed steel hollow sections of general structures: Dimensions, shapes, weight and permissible deviations. 2002. GB/T 8162, Seamless steel tubes for structural purposes. 2008. GB/T 17395, Dimensions, shapes, masses, and tolerances of seamless steel tubes. 2008. GB/T 19879, Steel plates for building structures. 2005. YB 4104, Steel plates for high rise building structures. 2000. Code of Practices for Design of Steel Structures: BS5950 Structural use of steelwork in building, Part 1: Code of practice for design of hot rolled and welded sections, 2000. Code of Practice for the Structural Use of Steel, 2011. Building Department, Government of Hong Kong SAR. EN 1993‐1‐1, Eurocode 3: Design of steel structures. General rules and rules for building. 2005. EN 1993‐1‐2, Eurocode 3: Design of steel structures. General rules — Structural fire design. 2005. EN 1993‐1‐3, Eurocode 3: Design of steel structures, General rules — Supplementary rules for cold‐formed members and sheeting. 2005. EN 1993‐1‐5, Eurocode 3: Design of steel structures, Plated structural elements. 2006. EN 1993‐1‐8, Eurocode 3: Design of steel structures, Design of steel joints. 2005.
GB 50017: Code for design of steel structures. 2003.
168
Technical Guidance for Design of Steel Structures: Chung, K.F., Harmonized member buckling design in Structural Eurocodes. Innovation in Construction, Research Journal 2014, Construction Industry Council, Hong Kong, 2014. Design of Steel Structures with Worked Examples to EN 1993‐1‐1 and EN 1993‐1‐8. F. Wald, K. H. Tan and S. P. Chiew. Research Publishing. 2012. Selection of equivalent steel materials to European steel materials specifications. Professional Guide CMSA‐PG01: 2015. Steel Building Design: Introduction to the Eurocodes. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association. SCI Publication No. P361, 2009. Steel Building Design: Concise Eurocodes. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association. SCI Publication No. P362. 2010. Steel Building Design: Design Data. The Steel Construction Institute, Tata Steel and British Constructional Steelwork Association, SCI Publication No.P363, 2013. Steel Designers’ Manual. 7th Edition. Buick Davidson & Graham W. Owens. Steel Construction Institute, Wiley‐Blackwell, 2012. Structural Steelwork, Design to Limit State Theory. 4th Edition. D. Lam, T. C. Ang, and S. P. Chiew. CRC Press, Taylor & Francis Group, 2013. The Behaviour and Design of Steel Structures to EC3. 4th Edition. N S Trahair, M A Bradford, D A Nethercot, and L Gardner. Taylor & Francis Group, 2008.
169
170
Appendices Appendix A Design procedure for a pinned‐pinned column to EN 1993
A1
Appendix B Design procedures for an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2
B1
B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3
B7
B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded I, H or channel sections using the design method given in Steel Designers’ Manual
B14
Appendix C Design procedure for a column member under combined axial compression and bending to EN 1993
C1 Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex Appendix D Worked examples to BS EN 1993‐1‐1
C1
Part I Section analysis and section resistance Worked Example I‐1 Determination of section resistances
Worked Example I‐2 Cross section resistance under combined bending and shear force
D7
Worked Example I‐3 Cross section resistance under combined bending and axial force
D9
Part II Member design Worked Example II‐1 Design of a fully restrained steel beam
Worked Example II‐2
Worked Example II‐3 Design of a steel column under axial compression
D26
Worked Example II‐4 Design of a beam‐column under combined compression and bending Worked Example II‐5 Column in simple construction
D29
Design of an unrestrained steel beam against lateral torsional buckling Solution to Procedure B2 Solution to Procedure B3
171
D1
D14 D17
D36
172
Appendix A Design procedure for a pinned‐pinned column to EN 1993:1‐1 A Design of a steel column against axial buckling 1. Determine the buckling length of the steel column for both axes. 2.
Calculate N cr and Afy .
3.
Calculate the non‐dimensional slenderness, of the steel column.
Af y N cr
A eff f y N cr
5.
L cr 1 i 1
L cr 1 i 1
A eff A
for Class 1, 2 and 3 cross‐sections for Class 4 cross‐sections
where A is the cross‐sectional area, A eff is the effective cross‐sectional area of Class 4 sections, fy is the yield strength,
2 EI which is the critical flexual buckling load/elastic critical force 2 L cr
N cr
4.
and
L cr
1
is the buckling length in the buckling plane considered,
E 235 93.9 , where fy fy
Choose a suitable flexural buckling curve for rolled and equivalent welded sections in Table A1, and hence, the imperfection factor, is obtained from Table A2. Determine the parameter ϕ.
2
0 .5 1 0 .2
6.
Calculate the buckling reduction factor,
1 2
2
but 1.0
7.
Calculate the design buckling resistance, N b , Rd .
N b, Rd
Af y M1
where M1 is the partial factor for resistance of the steel column to instability.
A1
Table A1: Selection of flexural buckling curves for rolled and equivalent welded cross‐ section
Cross section
z
y
y‐y z‐z
a b
a0 a0
40 ≤ tf ≤ 100 mm
y‐y z‐z
b c
a a
y
tf ≤ 100 mm
y‐y z‐z
b c
a a
tf > 100 mm
y‐y z‐z
d d
c c
tf ≤ 40 mm
y‐y z‐z
b c
b c
tf > 40 mm
y‐y z‐z
c d
c d
hot finished
any
a
a0
cold formed
any
c
c
generally (except as below)
any
b
b
thick welds: a > 0.5tf b/tf < 30 h/tw < 30
any
c
c
y
z
z
b
b
h/b ≤ 1.2
Rolled sections
t f
y
tf ≤ 40 mm
h/b > 1.2
z tf
Buckling about axis
Limits
Buckling curve S 235 S 275 S460 S 355 S 420
Welded sections
z
z
tf
tf y
y
y z
y z
Welded box sections
Hollow sections
z h
y tw
tf y
z b
Table A2: Recommended values for imperfection factor, α, for various flexural buckling curves Buckling curve Imperfection factor
a0 0.13
a 0.21
A2
b 0.34
c 0.49
d 0.76
Table A3: Reduction factor, χ for flexural buckling
̅ 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Reduction factor, χ
Buckling curve
a0
a
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.995 0.992 0.989 0.986 0.983 0.980 0.977 0.973 0.970 0.967 0.963 0.959 0.955 0.951 0.947 0.943 0.938 0.933 0.928 0.922 0.916 0.910 0.903 0.896 0.889 0.881 0.872 0.863 0.853 0.843 0.832 0.821 0.809 0.796 0.783 0.769 0.755 0.740 0.725
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.991 0.987 0.982 0.977 0.973 0.968 0.963 0.958 0.953 0.947 0.942 0.936 0.930 0.924 0.918 0.911 0.905 0.897 0.890 0.882 0.874 0.866 0.857 0.848 0.838 0.828 0.818 0.807 0.796 0.784 0.772 0.760 0.747 0.734 0.721 0.707 0.693 0.680 0.666
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
A3
Reduction factor, χ ̅ 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve a0
a
b
c
d
0.725 0.710 0.695 0.679 0.664 0.648 0.633 0.618 0.603 0.588 0.573 0.559 0.545 0.531 0.518 0.505 0.493 0.481 0.469 0.457 0.446 0.435 0.425 0.415 0.405 0.395 0.386 0.377 0.369 0.360 0.352 0.344 0.337 0.329 0.322 0.315 0.308 0.302 0.295 0.289 0.283 0.277 0.272 0.266 0.261 0.256 0.251 0.246 0.241 0.237 0.232
0.666 0.652 0.638 0.624 0.610 0.596 0.582 0.569 0.556 0.543 0.530 0.518 0.505 0.493 0.482 0.470 0.459 0.448 0.438 0.428 0.418 0.408 0.399 0.390 0.381 0.372 0.364 0.356 0.348 0.341 0.333 0.326 0.319 0.312 0.306 0.299 0.293 0.287 0.281 0.276 0.270 0.265 0.260 0.255 0.250 0.245 0.240 0.236 0.231 0.227 0.223
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B1 Design of a steel beam against lateral torsional buckling using general design method to Clause 6.3.2.2 1. Determine the buckling length of the steel beam. 2. Calculate M cr and Wpl , y f y .
2 EI z M cr C1 2 L cr
0.5 2 I L cr GI t 2 w C z C z C z C z 2 g 3 j 2 g 3 j 2 EI z I z
where I z , I t , I w are the section properties, E is the Young’s modulus, E , 21 is the buckling length of the steel beam, L cr kL , and k is the
is the shear modulus, G
G
L cr
effective length coefficient, C1 , C 2 , C 3 are the factors depending on the shape of the bending moment diagram, end restraint conditions and loading conditions as listed in Table B1.1, zg is the vertical distance of the loading position above the shear
zj
centre, is the relative distance to the shear centre. It is simply taken as 0 for uniform doubly symmetric cross‐sections.
3.
Calculate the non‐dimensional slenderness, LT of the steel beam.
LT
Wy f y M cr
where w
LT w 1
Wy Wpl , Rd
, and
Wy Wpl , y for Class 1 and 2 cross‐sections,
Wel , y for Class 3 cross‐sections,
Weff , y for Class 4 cross‐sections,
Wpl,y
is the plastic section modulus for Class 1 and 2 sections,
Wel, y
is the elastic section modulus for Class 3 sections,
Weff , y
is the effective elastic section modulus for Class 4 sections,
fy
is the yield strength.
B1
Table B1.1a Values of factors C1 , C 2 and C 3 corresponding to k factor under different end moment loading Loading and support conditions
Bending moment Diagram = +1
= +3/4
= +1/2
= +1/4
M
M = 0
= ‐1/4
= ‐1/2
= ‐3/4
= ‐1
B2
Value of k
Values of factors C3 C1 C2
1.0 0.7 0.5
1.000 1.000 1.000
‐
1.000 1.113 1.144
1.0 0.7 0.5
1.141 1.270 1.305
‐
0.998 1.565 2.283
1.0 0.7 0.5
1.323 1.473 1.514
‐
0.992 1.556 2.271
1.0 0.7 0.5
1.563 1.739 1.788
‐
0.977 1.531 2.235
1.0 0.7 0.5
1.879 2.092 2.150
‐
0.939 1.473 2.150
1.0 0.7 0.5
2.281 2.538 2.609
‐
0.855 1.340 1.957
1.0 0.7 0.5
2.704 3.009 3.093
‐
0.676 1.059 1.546
1.0 0.7 0.5
2.927 3.009 3.093
‐
0.366 0.575 0.837
1.0 0.7 0.5
2.752 3.063 3.149
‐
0.000 0.000 0.000
Table B1.1b Values of factors C1, C2 and C3 corresponding to k factor under transverse loading cases Loading and support conditions
w
w
Value of k
Bending moment Diagram
1.0 0.5
1.132 0.972
0.459 0.304
0.525 0.980
1.0 0.5
1.285 0.712
1.562 0.652
0.753 1.070
1.0 0.5
1.365 1.070
0.553 0.432
1.730 3.050
1.0 0.5
1.565 0.938
1.267 0.715
2.640 4.800
1.0 0.5
1.046 1.010
0.430 0.410
1.120 1.890
4.
Values of factors C1 C2 C3
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B1.2, and hence, the imperfection factor, LT , can be obtained from Table B1.3.
Table B1.2. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits
Buckling curve a b c d
h/b 2 h/b 2 h/b 2 h/b 2
Rolled I‐sections Welded sections
Table B1.3. Recommended imperfection factor values for lateral torsional buckling curves
Buckling curve
a
b
c
d
Imperfection factor, LT
0.21
0.34
0.49
0.76
B3
5.
Determine the parameter LT .
LT 0.5 1 LT LT 0.2 LT
6.
Calculate the reduction factor, LT .
LT
7. 8.
2
1 LT 2LT 2LT
but LT 1.0
Alternatively, reduction factor, LT can be obtained from Table B1.4. Calculate the buckling moment resistance, M b, Rd .
M b, Rd
LT Wy f y M1
where M1 is the partial factor for resistance of the beam to instability.
B4
Reduction factor, LT for lateral torsional buckling
Table B1.4.
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Reduction factor, LT
Buckling curve
a
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.991 0.987 0.982 0.977 0.973 0.968 0.963 0.958 0.953 0.947 0.942 0.936 0.930 0.924 0.918 0.911 0.905 0.897 0.890 0.882 0.874 0.866 0.857 0.848 0.838 0.828 0.818 0.807 0.796 0.784 0.772 0.760 0.747 0.734 0.721 0.707 0.693 0.680 0.666
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
B5
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve a
b
c
d
0.666 0.652 0.638 0.624 0.610 0.596 0.582 0.569 0.556 0.543 0.530 0.518 0.505 0.493 0.482 0.470 0.459 0.448 0.438 0.428 0.418 0.408 0.399 0.390 0.381 0.372 0.364 0.356 0.348 0.341 0.333 0.326 0.319 0.312 0.306 0.299 0.293 0.287 0.281 0.276 0.270 0.265 0.260 0.255 0.250 0.245 0.240 0.236 0.231 0.227 0.223
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B2 Design of a steel beam against lateral torsional buckling using alternative design method to Clause 6.3.2.3 1. Determine the buckling length of the steel beam. 2. Calculate M cr and Wpl , y f y .
2 EI M cr C1 2 z L cr
0. 5 I L2cr GI t w C z C z 2 C z C z 2 g 3 j 2 g 3 j 2 I z EI z
where I z , I t , I w are the section properties, E is the Young’s modulus, G
is the shear modulus, G
E , 2 21 L cr is the buckling length of the steel beam, L cr kL , and k is the effective length coefficient, C1 , C 2 , C 3 are the factors depending on the shape of the bending moment diagram, end restraint conditions and loading conditions as listed in Table B1.1, is the vertical distance of the loading position above the shear zg
zj
centre, is the relative distance to the shear centre. It is simply taken as 0
for uniform doubly symmetric cross‐sections. 3.
Calculate the non‐dimensional slenderness, LT of the steel beam.
LT
Wy f y M cr
where w
LT w 1
Wy Wpl , Rd
,
Wy Wpl , y for Class 1 and 2 cross‐sections,
Wel,y for Class 3 cross‐sections,
Weff,y for Class 4 cross‐sections,
Wpl, y
is the plastic section modulus for Class 1 and 2 sections,
Wel, y
is the elastic section modulus for Class 3 sections,
Weff , y
is the effective elastic section modulus for Class 4 sections,
fy
is the yield strength.
B6
4.
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B2.1, and hence, the imperfection factor, LT can be obtained from Table B2.2.
Table B2.1. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h/b ≤ 2 h/b > 2 h/b ≤ 2 h/b > 2
Rolled I‐sections Welded sections
Buckling curve b c c d
Table B2.2. Recommended imperfection factor values for lateral torsional buckling curves Buckling curve Imperfection factor, LT
a
b
c
d
0.21
0.34
0.49
0.76
5.
Determine the parameter LT .
LT 0.5 1 LT LT LT,0 2LT
For rolled sections, LT ,0 = 0.4 (maximum value) = 0.75 (minimum value) For welded sections, LT ,0 = 0.2 (maximum value) = 1.0 (minimum value)
6.
Calculate the reduction factor, LT .
LT
Reduction factor, LT can also be obtained from Tables B2.4 and B2.5.
1 2
LT LT LT
2
but LT 1.0 and LT
B7
1 LT
2
7.
Calculate the modified reduction factor, LT , mod
LT, mod
LT but LT, mod 1.0 f
where f
is the correction factor for the moment distribution
1 0.51 k c 1 2.0 LT 0.8
f
2
kc is a correction factor according to Table B3.3. Table B2.3. Correction factors k c Moment distribution
kc
1
1.0
1 1
1 1.33 0.33
0.94
0.90
0.91
0.86
0.77
0.82
8.
Calculate the buckling moment resistance, M b,Rd
M b, Rd LT ,mod Wy where M1
fy M1
is the partial factor for resistance of the steel beam to instability.
B8
Table B2.4. Reduction factor, LT for lateral torsional buckling of rolled sections Reduction factor, LT
Buckling curve
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.984 0.976 0.968 0.960 0.952 0.943 0.935 0.926 0.917 0.908 0.899 0.889 0.880 0.870 0.860 0.849 0.839 0.828 0.817 0.806 0.795 0.783 0.772 0.760 0.748 0.736 0.724 0.712 0.700
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.989 0.978 0.966 0.955 0.944 0.932 0.921 0.909 0.898 0.886 0.874 0.862 0.850 0.838 0.826 0.813 0.801 0.789 0.776 0.764 0.751 0.739 0.726 0.713 0.701 0.688 0.676 0.664 0.651 0.639
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.983 0.966 0.949 0.932 0.916 0.900 0.883 0.867 0.852 0.836 0.820 0.805 0.790 0.775 0.760 0.745 0.730 0.716 0.702 0.688 0.674 0.660 0.647 0.634 0.621 0.608 0.596 0.584 0.572 0.560
B9
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve b
c
d
0.700 0.687 0.675 0.663 0.651 0.639 0.626 0.614 0.603 0.591 0.579 0.568 0.556 0.545 0.534 0.524 0.513 0.503 0.493 0.483 0.473 0.463 0.454 0.445 0.436 0.427 0.419 0.410 0.402 0.394 0.387 0.379 0.372 0.365 0.358 0.351 0.344 0.338 0.332 0.326 0.320 0.314 0.308 0.302 0.297 0.292 0.287 0.282 0.277 0.272 0.267
0.639 0.627 0.615 0.603 0.592 0.580 0.569 0.557 0.546 0.536 0.525 0.514 0.504 0.494 0.484 0.475 0.465 0.456 0.447 0.438 0.429 0.421 0.413 0.405 0.397 0.389 0.382 0.374 0.367 0.360 0.353 0.347 0.340 0.334 0.328 0.322 0.316 0.310 0.305 0.299 0.294 0.289 0.284 0.279 0.274 0.269 0.265 0.260 0.256 0.252 0.247
0.560 0.548 0.537 0.526 0.515 0.505 0.494 0.484 0.474 0.465 0.455 0.446 0.437 0.428 0.420 0.412 0.403 0.395 0.388 0.380 0.373 0.366 0.359 0.352 0.345 0.339 0.332 0.326 0.320 0.314 0.309 0.303 0.298 0.292 0.287 0.282 0.277 0.272 0.268 0.263 0.259 0.254 0.250 0.246 0.242 0.238 0.234 0.230 0.227 0.223 0.219
Table B2.5. Reduction factor, LT for lateral torsional buckling of welded sections Reduction factor, LT
Buckling curve
LT 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
b
c
d
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.986 0.979 0.971 0.964 0.957 0.949 0.942 0.934 0.926 0.918 0.910 0.902 0.893 0.884 0.875 0.866 0.857 0.847 0.837 0.827 0.816 0.806 0.795 0.784 0.772 0.761 0.749 0.737 0.724 0.712 0.699 0.687 0.674 0.661 0.648 0.635 0.623 0.610 0.597
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.990 0.980 0.969 0.959 0.949 0.939 0.929 0.918 0.908 0.897 0.887 0.876 0.865 0.854 0.843 0.832 0.820 0.809 0.797 0.785 0.773 0.761 0.749 0.737 0.725 0.712 0.700 0.687 0.675 0.662 0.650 0.637 0.625 0.612 0.600 0.588 0.575 0.563 0.552 0.540
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.984 0.969 0.954 0.938 0.923 0.909 0.894 0.879 0.865 0.850 0.836 0.822 0.808 0.793 0.779 0.765 0.751 0.738 0.724 0.710 0.696 0.683 0.670 0.656 0.643 0.630 0.617 0.605 0.592 0.580 0.568 0.556 0.544 0.532 0.521 0.510 0.499 0.488 0.477 0.467
B10
Reduction factor, LT LT 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00
Buckling curve b
c
d
0.597 0.584 0.572 0.559 0.547 0.535 0.523 0.512 0.500 0.489 0.478 0.467 0.457 0.447 0.437 0.427 0.417 0.408 0.399 0.390 0.382 0.373 0.365 0.357 0.350 0.342 0.335 0.328 0.321 0.314 0.308 0.302 0.295 0.289 0.284 0.278 0.273 0.267 0.262 0.257 0.252 0.247 0.243 0.238 0.234 0.229 0.225 0.221 0.217 0.213 0.209
0.540 0.528 0.517 0.506 0.495 0.484 0.474 0.463 0.453 0.443 0.434 0.424 0.415 0.406 0.397 0.389 0.380 0.372 0.364 0.357 0.349 0.342 0.335 0.328 0.321 0.315 0.308 0.302 0.296 0.290 0.284 0.279 0.273 0.268 0.263 0.258 0.253 0.248 0.243 0.239 0.235 0.230 0.226 0.222 0.218 0.214 0.210 0.207 0.203 0.200 0.196
0.467 0.457 0.447 0.438 0.428 0.419 0.410 0.401 0.393 0.384 0.376 0.368 0.361 0.353 0.346 0.339 0.332 0.325 0.318 0.312 0.306 0.299 0.293 0.288 0.282 0.277 0.271 0.266 0.261 0.256 0.251 0.247 0.242 0.237 0.233 0.229 0.225 0.221 0.217 0.213 0.209 0.206 0.202 0.199 0.195 0.192 0.189 0.186 0.183 0.180 0.177
Appendix B Design procedures for an unrestrained beam to EN 1993 B3 Design of a steel beam against lateral torsional buckling for rolled or equivalent welded I, H or channel sections using the design method given in the Steel Designer’s Manual 1. Determine the buckling length of the steel beam. 2.
Calculate the non‐dimensional slenderness LT of the steel beam.
LT
1 UV z w for rolled I‐, H‐ and channel sections C1
where C1
U
V
is a factor that depends on the shape of bending moment diagram as listed in Table B3.1, is a section property (given in section property tables, which may conservatively be taken as 0.9), is a parameter related to slenderness, and for symmetric rolled sections where the loads are not destabilising, may be conservatively taken as 1.0, 1 or as V , 2 z 1 4 1 20 h / t f
L cr in which L cr is the buckling length in the buckling plane iz considered. z z , 1 is the distance between points of lateral restraints, L
1
w
Wy Wpl, y for Class 1 and 2 cross‐sections,
Wel , y for Class 3 cross‐sections,
Weff , y for Class 4 cross‐sections,
where z
235 E 93.9 , where , fy fy
Wy Wpl , Rd
, and
Wpl,y
is the plastic section modulus of Class 1 and 2 sections,
Wel ,y
is the elastic section modulus of Class 3 sections,
Weff ,y
is the effective elastic section modulus of Class 4 sections,
fy
is the yield strength.
It is conservative to assume that the product UV 0.9 and that w 1.0
B11
Table B3.1. Values of C1 for various moment conditions (load is not destabilising) 1 End Moment Loading C1 +1.00 +0.75 +0.50 +0.25 0.00 ‐0.25 ‐0.50 ‐0.75 ‐1.00
M
M
1 1
Intermediate transverse loading
2/3 1/3
3.
C1
1.00 0.92 0.86 0.80 0.75 0.71 0.67 0.63 0.60
1.00 1.17 1.36 1.56 1.77 2.00 2.24 2.49 2.76
0.94 0.62
1.13 2.60
0.86 0.77
1.35 1.69
Choose a suitable lateral buckling curve for rolled sections or equivalent welded sections from Table B3.2, and hence, the imperfection factor, LT , is obtained from Table B3.3.
Table B3.2. Selection of buckling curves for rolled sections and equivalent welded sections Cross‐section
Limits h/b 2 2 h / b 3. 1 h / b 3 .1 h/b 2 h/b 2
Rolled I‐sections Welded sections
Buckling curve b c d c d
Table B3.3. Recommended values for imperfection factor for lateral torsional buckling curves Buckling curve Imperfection factor, LT
a
b
c
d
0.21
0.34
0.49
0.76
B12
4. 5. 6.
Determine the parameter LT .
LT 0.5 1 LT LT LT ,0 2LT
For rolled sections, LT,0 = 0.4 (maximum value)
= 0.75 (minimum value)
For welded sections, LT,0 = 0.2 (maximum value)
= 1.0 (minimum value)
Calculate the reduction factor, LT .
LT
1 2
LT LT LT
2
but LT 1.0 and LT
1 LT
2
Reduction factor, LT can also be obtained from Tables B2.4 and B2.5. Calculate the buckling moment resistance, M b,Rd .
M b,Rd
LT Wy f y M1
where M1
is the partial factor for resistance of the beam to instability.
B13
Appendix C C1 1.
Design procedures for a column member under combined axial compression and bending to EN 1993: 1‐1
Interaction of combined axial compression and bending to Clause 6.3.3 using the design method given in the U.K. National Annex Members subjected to combined bending and axial compression should satisfy:
M M y , Ed M z , Ed M N Ed k yy y , Ed k yz z , Ed 1 , and M z , Rk y N Rk LT M y , Rk M1 M1 M1
M M y , Ed M z , Ed M N Ed k zy y , Ed k zz z , Ed 1 M z , Rk z N Rk LT M y , Rk M1 M1 M1
where N Ed M y , Ed
is the design value of the compression force, is the design value of the maximum moment about the y‐y axis,
M z , Ed
is the design value of the maximum moment about the z‐z axis,
M y , Ed
is the moment due to the shift of the centroidal axis about the
M z , Ed
major axis for Class 4 sections, is the moment due to the shift of the centroidal axis about the
N Rk
M y ,Rk
minor axis for Class 4 sections, is the design resistance of the cross‐section for uniform compression. is the design moment resistance of the cross‐section about the y‐y
M z , Rk
axis. is the design moment resistance of the cross‐section about the z‐z
axis. k yy , k yz , k zy , k zz are the interaction factors to be calculated by Method A and B as illustrated in Annexes A and B of EN 1993‐1‐1: 2005.
2.
Method B is recommended by SCI‐P362 as a simplified approach for manual calculations. Use of either method is permitted by the U. K. National Annex.
C1
3. Calculate interaction factors, kij by Method A Table C.1 Interaction factors for combined axial compression and bending Interaction factors
k yy
Design assumptions Elastic cross‐sectional properties Plastic cross‐sectional properties Class 3, class 4 Class 1, class 2 C myC mLT
k zy
C myC mLT
C mz
z N 1 Ed N cr , y
y 1 N 1 Ed C yy N cr , y
y wz 1 0 .6 N Ed C yz w y 1 N cr , z
C myCmLT
z N 1 Ed N cr , z
C mz
k zz
CmyC mLT
y N 1 Ed N cr , z
Cmz
k yz
y N 1 Ed N cr, y
wy z 1 0.6 N wz 1 Ed Czy N cr , y
C mz
z 1 N Ed C zz 1 N cr , z
Auxiliary terms: Wel, y 1.6 2 1.6 2 2 C yy 1 w y 1 2 C my max C my max n pl b LT wy wy Wpl, y
N Ed N cr , y y N 1 y Ed N cr , y
1
N 1 Ed N cr , z z N 1 z Ed N cr , z wy wz
n pl
Wpl, y Wel, y Wpl, z Wel, z
1. 5 1 .5
N Ed N Rk / M1
C my see Table A.2
a LT
I 1 T 0 Iy
with b LT 0.5a LT 20
M y, Ed
LT M pl, y , Rd M pl, z , Rd
C2 2 w z Wel, z C yz 1 w z 1 2 14 mz 5max n pl c LT 0.6 w y Wpl, z wz with cLT 10a LT
20
M y, Ed
5 4z
CmyLTM pl, y, Rd
C 2my 2max w y Wel, y C zy 1 w y 1 2 14 n pl d LT 0.6 5 w z Wpl, y w y
with d LT 2a LT
M y , Ed
0 0 .1
4z
M z , Ed
C my LT M pl, y , Rd C mz M pl, z , Rd
1.6 2 W 1.6 2 2 Czz 1 w z 1 2 Cmz max Cmz max n pl eLT el, z wz wz Wpl, z with e LT 1.7a LT
M y, Ed 0 0.1 4z C my LT M pl, y, Rd
M z , Ed
C2
Table C.1
(continued)
y max max z 0 = non‐dimensional slenderness for lateral‐torsional buckling due to uniform bending moment,
i.e. y 1.0 in Table C.2
LT = non‐dimensional slenderness for lateral‐torsional buckling
N N If 0 0.2 C1 4 1 Ed 1 Ed N cr , z N cr ,TF
C my C my ,0
Cmz Cmz,0 C mLT 1 .0
N N If 0 0.2 C1 4 1 Ed 1 Ed N N cr , z cr , TF
C my Cmy,0 1 C my,0
Cmz Cmz,0
C mLT C 2my
y y
M y, Ed
A for class 1,2 and 3 cross‐sections N Ed Wel, y
M y , Ed A eff for class 4 cross‐sections N Ed Weff , y
N cr , y = elastic flexural buckling force about the y‐y axis
Ncr, z = elastic flexural buckling force about the z‐z axis N cr ,T = elastic torsional buckling force IT
= St. Venant torsional constant
Iy
= second moment of area about y‐y axis
C3
y a LT
1 y a LT
a LT 1 N Ed N cr , z
1 N Ed N cr , T
1
Table C2 Equivalent uniform moment factors, Cmi,0 Cmi,0
Moment diagram
C mi,0 0.79 0.21 i 0.36 i 0.33
-1 ψ 1
2 EI N i x 1 Ed C mi ,0 1 2 L M x N cr ,i i ,Ed Mi, Ed x is the maximum moment M y,Ed or M z, Ed
M x M x
x is the maximum member displacement along the member
C mi , 0 1 0.18
N Ed N cr , i
C mi , 0 1 0.03
N Ed N cr , i
N Ed N cr ,i
C4
4. Calculate interaction factors, kij by Method B Table C.3 Interaction factors for combined axial compression and bending Design assumptions Interaction factors
Type of sections
Elastic cross‐sectional properties Class 3, class 4
Plastic cross‐sectional properties Class 1, class 2
k yy
I‐sections RHS‐sections
N Ed C my 1 0.6 y N / y Rk M 1 N Ed C my 1 0.6 N y Rk / M1
N Ed C my 1 y 0.2 N / y Rk M 1 N Ed C my 1 0.8 N y Rk / M1
k yz
I‐sections RHS‐sections
k zz
0.6 k zz
k zy
I‐sections RHS‐sections
0.8 k yy
0.6 k yy
N Ed C mz 1 2 z 0.6 z N Rk / M1 N Ed C mz 1 1.4 N / z Rk M1
I‐sections N Ed C mz 1 0.6 z z N Rk / M1 N Ed C mz 1 0.6 N / z Rk M1
k zz
RHS‐sections
N Ed C mz 1 z 0.2 N / z Rk M1 N Ed C mz 1 0.8 N / z Rk M1
For I‐ and H‐sections and rectangular hollow sections under axial compression and uniaxial bending M y,Ed , the coefficient k zy may be k zy 0 .
C5
Interaction factors k ij for members susceptible to torsional deformations
Table C.4
Design assumptions Interaction Elastic cross‐sectional properties Plastic cross‐sectional properties factors Class 3, class 4 Class 1, class 2 k yy
k yy from Table C.3
k yy from Table C.3
k yz
k yz from Table C.3
k yz from Table C.3
N Ed 0.05 z 1 C mLT 0.25 z N Rk / M1
k zy
N Ed 0.1 z 1 C mLT 0.25 z N Rk / M1 N Ed 0.1 N Ed 0.05 1 1 C mLT 0.25 z N Rk / M1 C mLT 0.25 z N Rk / M1 for z 0.4 :
k zz
k zy 0.6 z 1
k zz from Table C.3
k zz from Table C.3
C6
N Ed 0.1 z C mLT 0.25 z N Rk / M1
Table C.5
Equivalent uniform moment factors, C m in Tables C.3 and C.4 Cmy and Cmz and CmLT
Moment diagram
Range Uniform loading
M1
1 1
ψM1
Concentrated load
0 . 6 0 .4 0 .4
0 s 1 Mh
ψM h
h Ms / Mh
Ms
h M h / Ms
0.2 0.8 s 0.4
0.2 0.8 s 0.4
0 1
0.1 0.8 s 0.4
0.8 s 0.4
1 0
0.11 0.8 s 0.4
0.2 0.8 s 0.4
1 1
0 .95 0 .05 h
0 .90 0 .10 h
0 1
0.95 0.05 h
0.90 0.10 h
1 0
0.95 0.05 h 1 2
0.90 0.10 h 1 2
1 s 0
0 s 1
ψM h
Mh
1 1
1 s 0
For members with sway buckling mode the equivalent uniform moment factor should be taken C my 0.9 or C mz 0.9 respectively. C my , C mz and C mLT should be obtained according to the bending moment diagram between the
relevant braced points as follows: moment factor Bending axis C my y‐y
Points braced in direction z‐z
C mz
z‐z
y‐y
C mLT
y‐y
y‐y
C7
Table C.6
Interaction factors for combined axial compression and bending Design Assumptions Criteria
Section
Class 1 and 2 cross‐sections
Class 3 cross‐sections
k yy
‐
All
Figure C.1
Figure C.2
C my
k yz
‐
All
0.6 k zz
k zz
‐
Member not susceptible to torsional deformation
RHS sections
Figure C.1
Figure C.2
C mz
Member susceptible to torsional deformation
I sections
Figure C.1
Figure C.2
C mz
Member not susceptible to torsional deformation
All
0.6
0.8
‐
Member susceptible to torsional deformation
All
Figure C.1
Figure C.2
C mLT
k zz
k zy
(1) C ‐Factors may be obtained from Table C.5. (2) In Figure C.1 and Figure C.2, k zy is based on the conservative assumption that C mLT 1.0 .
C Factor
Interaction Factors
C8
2.8
2.0 N N ,
1.8
2.6
N N ,
1.0 ,
2.4
1.0 ,
2.2
0.8
0.8
2.0
1.6 k C
k C
0.6
0.6 1.8 0.4
1.6
1.4 0.4
1.4 0.2
1.2
0.2
1.2 1.0
1.0
0.8 0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
Non‐dimensional slenderness λ
Non‐dimensional slenderness λ
a) Interaction factor kyy
b) Interaction factor kzz
1.00
2.0
2.0 N N ,
0.2 ,
1.8
0.4
0.95
N N ,
1.0 ,
0.8
0.6 1.6 k C
0.90
k C
0.8
0.6 1.4
0.2
0.4
0.85 1.2
0.2
1.0
0.80 0.0
0.5
1.0
1.5
0.0
2.0
0.5
1.0
Non‐dimensional slenderness λ
c) Interaction factor kzy
Interaction factor kij for Class 1 and 2 sections
Figure C.1.
2.0
d) Interaction factor kzz for RH Sections
1.5
Non‐dimensional slenderness λ
C9
1.7
1.7 N N ,
1.6
1.0
1.6
,
1.0 ,
0.8
1.5
0.8
1.5
N N ,
1.4 k C
1.4
k C
0.6
0.6
1.3 0.4
1.3 0.4
1.2 0.2
1.2 1.1 0.2 1.1
1.0
1.0
0.9 0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
Non‐dimensional slenderness λ
Non‐dimensional slenderness λ
a) Interaction factor kyy
b) Interaction factor kzz
1.00 N N ,
0.99
0.2 ,
0.98 0.4 0.97 k
0.6
0.96 0.95
0.8
0.94 1.0 0.93 0.92 0.0
0.5
1.0
1.5
2.0
Non‐dimensional slenderness ̅
c) Interaction factor kzy for I sections
Figure C.2.
Interaction factor kij for Class 3 sections
1.5
C10
2.0
Appendix D Worked Examples to EN 1993‐1‐1 Part I Section analysis and section resistance Worked Example I-1 Determination of section resistances Question Determine the section resistance of a steel beam as shown: 457 × 152 × 52 kg/m I‐section S355
t f = 10.9
219.45
203.8
hw = 428.0
h = 449.8
tw = 7.6
b = 152.4
D1
Solution Section properties of 457 × 152 × 52 kg/m I‐section: h = 449.8 mm b = 152.4 mm d = 407.6 mm tw = 7.6 mm tf = 10.9 mm r = 10.2 mm
b z
tw h
d
y
r
Calculate cross‐sectional area, A A
A fillet
Ag
y
= A w 2A f z = h 2t f t w 2 b t f = (449.8- 2 ×10.9)× 7.6 + 2 ×152.4×10.9 = 3253 mm2 + 3322 mm2 (c.f. 66.6 cm2 or 6660 mm2 from tabulated data) = 6575 mm2
t
= 4 10.2 2 1 89.3 mm2 4 = A A fillet = 6575 + 89.3 = 6664.3 mm2
In general, fillets are neglected in most design. Calculate second moment of area, I Iy
Ifillet
7.6 428 .0 3 152 .4 10 .9 3 = 2 152 .4 10 .9 219 .45 2 12 12 = 2 16.45 10 3 80.0 10 6 49.66 10 6 = 160.03 10 6 49.66 10 6 = 209.69 10 6 mm4 or 20969 cm4 2 10 .2 4 10 .2 2 10 .2 4 =4 10 .2 4 10 .2 2 214 12 2 16 9 4 2 4 10 .2 214 10 .2 3 = 4 902 4540 10 3 594 3540 10 3 = 4.00 10 6 mm4
Ig
= I y I fillet = 213 .69 10 6 mm4
D2
Calculate the elastic section modulus, Wel
Wel,y
Iy
213.69 10 6 h/2 449.8 / 2 = 950.2 103 mm3 = 950.2 cm3
=
49.66 10 6 449 .8 / 2 = 220 .8 10 3 mm3 = 220.8 cm3
Wel,y,w =
160.03 10 6 449.8 / 2 = 711.6 103 mm3 = 711.6 cm3
Wel,y,f =
Wel, y,w Wel,y
=
220.8 = 950.2
0.232
=
711.6 = 950.2
0.749
Wel,y,f Wel,y
D3
Calculate the plastic section modulus, Wpl
Wpl,y0
= b t f h w t f h w t w
hw 4
= 152.4 10.9 428.0 10.9
428.0 2 7.6 4
= 729.1 10 348.0 10 = 1077 .1 103 mm3 or 1077 cm3 3
3
2 h r r 2 h w 4r r Wpl,y,fillet = 4 r 2 w 3 2 2 4 2 = 4 21.7 103 17.0 103 = 18.8 103 mm3
Wpl,y
= Wpl, y0 Wpl,fillet = 1077 .1 103 18.8 103 mm3 = 1095.9 103 mm3 or 1096 cm3 (c.f. 1100 cm2 from tabulated data)
Wpl , y , w Wpl , y
Wpl , y , f Wpl , y
=
348 .0 = 0.318 1096
=
729 .1 = 0.665 1096
The shape factor of I‐section =
Wpl, y Wel, y
=
1096 = 1.18 932
2
Wpl,z
b2tf h w tf 4 4 10.9 7.62 428 = 2 152.42 4 4 3 3 = 126.6 10 6.18 10
= 2
= 132.8 cm3
(c.f. 133 cm2 from tabulated data)
D4
hw
tw
Typical section properties in an I‐section Area A
Elements
Second moment of area I
(cm2)
ratio
(cm4)
ratio
Flanges Web Fillet
3322 3253 89
0.498 0.488 0.014
16003 4966 400
0.750 0.232 0.018
Total
6664
1
21369
1
Elastic modulus Wel
Elements
Plastic modulus Wpl
(cm3)
ratio
(cm3)
ratio
Flanges Web Fillet
711.6 220.8 17.8
0.749 0.232 0.019
729.1 348.0 18.8
0.665 0.318 0.017
Total
950.2
1
1095.9
1
Perform section classification Since tf = 10.9 mm and tw = 7.6 mm, i.e. the nominal material thickness is less than 16 mm, the nominal value of yield strength fy for grade S355 steel is 355 N/mm2. f y 355 N / mm 2
=
235 / f y 235 / 355 0.81
[Cl. 5.5]
Web – subject to bending:
[Table 5.2]
⇒
= cw cw / tw =
h – 2tf – 2r 407.6 / 7.6
= 407.6 mm = 53.6
Limit for Class 1 web = 72 = 58.32
⇒
The web is Class 1.
D5
53.6
[Table 5.2]
Flange under compression: cf = b t w 2r / 2 ⇒
= 62.2 mm
cf / t f = 62.2 / 10.9
= 5.71
Limit for Class 1 flange = 9 ⇒
5.71
= 7.3
The flanges are Class 1.
The overall cross‐section classification is Class 1 subject to bending.
Summary Hence, the design resistance of the cross‐section for uniform compression, Nc,Rd is
N c, Rd =
A fy
M0
6660 355 103 1.0
[Cl. 6.2.4 (2)]
= 2364 kN The design resistance for bending about y‐y axis, M c, y, Rd is
M c, y, Rd =
Wpl, y f y
M0
1100 103 355 106 1.0
[Cl. 6.2.5 (2)]
= 390.5 kNm The design resistance for bending about z‐z axis, M c , z , Rd is
M c,z ,Rd =
Wpl, z f y
M0
133 103 355 106 1.0
tw + 2r
= 47.2 kNm
0.5tf
The design shear resistance, Vc, Rd is
Vpl, Rd =
Av fy / 3 M0
, where
M0
hw
[Cl. 6.2.6 (2)]
1.0
where
and
0.5t b
Av
= A 2 b t f t w 2r t f but not less than h w t w
Av
= 6660 2 152.4 10.9 7.6 2 10.2 10.9 = 3642.9 mm2
Av
> h w t w = 1.0 × (449.8 – 2 × 10.9) × 7.6 = 3252.8 mm2
Vpl, Rd =
3642.9 355 / 3 10 3 = 746.6 kN 1.00
D6
Part I Section analysis and section resistance Worked Example I-2 Cross section resistance under combined bending and shear force Question Determine the design moment resistance of a steel beam under high shear with the following details:
457 × 152 × 52 kg/m I‐section S355 Shear force ratio, VEd / Vpl, Rd = 0.8
t f = 10.9
219.45
203.8 h = 449.8
hw = 428
tw = 7.6
b = 152.4
D7
Solution Resistance against bending and shear force For 457 x 152 x 52 kg/m I‐section S355
M y , V , Rd
A 2w Wpl , y 4 t f y w M0
but M y,V,Rd M y,c,Rd
[Cl. 6.2.8]
where 2
2V Ed 1 V pl,Rd
A 2w h 2w t w 4282 7.6 348.0 103 mm3 4t w 4 4
Wpl,w
=
Wpl,y
= 1100 103 mm3
Wpl,w / Wpl,y = 0.316
M y,c,Rd
= 355 1100 103 10 6
= 390.5 kNm
Moment resistance contributed by the top and the bottom flanges: = 390.5 1 0.316 = 267.1 kNm
Mpl,f
VEd / Vpl ,Rd
M y ,V ,Rd (kNm)
M y ,V ,Rd / M y ,c ,Rd
0.5 0.6 0.7 0.8 0.9 1.0
0.00 0.04 0.16 0.36 0.64 1.00
390.5 385.6 370.7 346.0 311.4 267.0
1.000 0.987 0.949 0.886 0.798 0.684
1.2
UNSAFE
1.0
Moment ratio,
0.8
SAFE
0.6 0.4 0.2
Cl.6.2.8(5)
0.0 0.0
0.2
0.4
0.6
0.8
Shear ratio, VEd / Vpl,Rd
For a high shear load at VEd / Vpl,Rd = 0.8 M y ,V ,Rd
= 346.0 kNm
D8
1.0
1.2
Part I Section analysis and section resistance Worked Example I-3 Cross section resistance under combined bending and axial force Question Determine the design moment resistance of a steel beam under combined bending and axial force with the following details: 457 × 152 × 52 kg/m I‐section S355 Axial compression force ratio, N Ed / N pl ,Rd = 0.8 a) Determine the design plastic resistance for bending about the y‐y axis reduced due to the axial force NEd . b) Determine the design plastic resistance for bending about the z‐z axis reduced due to the axial force NEd . c) Plot the failure criterion of the cross section under an interaction of bi‐axial bending and axial force.
t f = 10.9
219.45
203.8
hw = 428
h = 449.8
tw = 7.6
b = 152.4
D9
Solution Resistance under combined bending and axial force a) For 457 × 152 × 52 kg/m I‐section S355 subjected to combined major axis bending and axial force
N c, Rd = 2,334 kN If N Ed
N Ed
0.25 N c , Rd = 583.5 kN, and
0.5h w t w f y M0
[Cl. 6.2.9]
0.5 428 7.6 355 10 3 577.4 kN , 1
Then allowance needs not be made for the effect of axial force on the plastic resistance moment. Otherwise, the design plastic resistance for bending about y‐y axis reduce due to the axial force is: 1 n M N , y, Rd M pl, y, Rd , but M N, y, Rd M pl, y,Rd 1 0.5a where N n Ed N pl, Rd
a
A 2bt f
but a 0.5
A
1.20 1.00
Moment ratio,
0.80 0.60 0.40 0.20 0.00 0.0
0.2
0.4
0.6
0.8
Axial force ratio, N Ed / N pl, Rd
D10
1.0
1.2
N Ed
N pl,Rd
n
a
0.0
2,334
0.0
0.49
1.00
233.4 466.8 700.2 933.6 1167.0
2,334 2,334 2,334 2,334 2,334
0.1 0.2 0.3 0.4 0.5
0.49 0.49 0.49 0.49 0.49
1.00 1.00 0.93 0.80 0.66
1400.4 1633.8 1867.2 2100.6
2,334 2,334 2,334 2,334
0.6 0.7 0.8 0.9
0.49 0.49 0.49 0.49
0.53 0.40 0.27 0.13
2,334.0
2,334
1.0
0.49
0.00
For a high axial load at N Ed / N pl , Rd 0.8 M N , y , Rd 0.27 390.5 105.4 kNm
M N, y, Rd / M pl, y, Rd
D11
b) For 457 x 152 x 52 kg/m I‐section S355 subjected to combined minor axis bending and axial force N c , Rd 2,334 kNm
If N Ed
h w t wfy
M0
428 7.6 355 10 3 1,154.7 kN , 1.00
then allowance needs not be made for the effect of axial force on the design plastic resistance for bending. Otherwise, the design resistance for bending about the z‐z axis reduced due to the axial force is: For n a :
M N , z , Rd M pl , z , Rd
For n a :
n a 2 M N , z , Rd M pl, z , Rd 1 1 a
[Cl. 6.2.9]
1.20 1.00
Moment ratio,
0.80 0.60 0.40 0.20 0.00 0.0
0.2
0.4
0.6
0.8
1.0
Axial force ratio, NEd / Npl, Rd N Ed
N pl,Rd
n
a
M N, z, Rd / Mpl, z, Rd
0.0 233.4 466.8 700.2
2,334 2,334 2,334 2,334
0.0 0.1 0.2
0.49 0.49 0.49
1.00 1.00 1.00
933.6 1167.0 1400.4 1633.8
2,334 2,334 2,334 2,334
0.3 0.4 0.5 0.6 0.7
0.49 0.49 0.49 0.49 0.49
1.00 1.00 1.00 0.96 0.83
1867.2 2100.6 2,334.0
2,334 2,334 2,334
0.8 0.9 1.0
0.49 0.49 0.49
0.63 0.36 0.00
For high axial load at N Ed / N pl, Rd 0.8 M N , z , Rd 0.63 47.2 29.7 kNm
D12
1.2
c) For biaxial bending, Clause 6.2.9.1 gives 2
M y , Ed M z , Ed M N , z , Rd M N , y , Rd
5n
1
[Cl. 6.2.9 (6)]
For 457 x 152 x 52 kg/m I‐section of S355 subjected to bi‐axial bending and axial force
N c , Rd 2,334 kN
For a high axial compression, N Ed 0.8 N c , Rd 1867 kN , the following criterion should be used: 2
as n 0.8
A graphical presentation of the interaction curve is shown as follows: Moment ratio about minor axis,
4
M y, Ed M z , Ed 1 M N , z , Rd M N , y, Rd
1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
Moment ratio about major axis, M y ,Ed / M N ,y ,Rd M y ,Ed / M N , y ,Rd
M z ,Ed / M N ,z ,Rd
0.00
1.00
0.10
1.00
0.20
0.99
0.30
0.98
0.40
0.96
0.50
0.93
0.60
0.89
0.70
0.85
0.80
0.77
0.90
0.66
1.00
0.00
D13
1.20
Part II Member design Worked Example II‐1 Design of a fully restrained steel beam Question Design a steel beam under the following condition: Span = 10 m (assuming simply supported) Beam spacing = 3 m Loadings Permanent actions Dead load, G k ,1 = 3.0 kN/m2 = 1.0 kN/m2
Superimposed dead load, G k , 2
Variable actions Imposed load, Q k ,1
= 3.0 kN/m2
Try 457 × 152 × 52 kg/m I‐section S355. Check against bending, shear and deflection.
Note:
Deflection limit under variable action
D14
L 360
b z
Solution Section properties of 457 × 152 × 52 kg/m I‐section: h = 449.8 mm b = 152.4 mm = 7.6 mm tf = 10.9 mm tw r = 10.2 mm Wpl,y
= 1,100 10 mm
Iy Iw A
= 21,400 104 mm4 = 311 109 mm6 = 6660 mm2
3
tw h
d
y
y
3
r
Iz = 645 10 4 mm4 It = 21.4 10 4 mm4 z
Material property: Since tf = 10.9 mm and tw = 7.6 mm, i.e. the nominal material thickness is less than 16 mm, the nominal value of the yield strength for grade S355 steel is: fy E G
= 355 N/mm2 2 = 210,000 N/mm = 0.3 = 81000 N/mm2
Span = 10 m Contributive area 10 3 30 m 2 This beam is assumed to be simply supported. a) Loading.
Dead load, G k ,1
= 3.0 kN/m2
Superimposed dead load, G k , 2
= 1.0 kN/m2
Live load, Q k ,1
= 3.0 kN/m2
Factored load Design moment, M Ed Design shear force, VEd
or
= 1.40 3 1 1.60 3 = 10.4 kN/m2 = 31.2 kN/m for a width of 3 m = 31.2 10 10 / 8 = 390.0 kNm = 31.2 10 0.5 = 156.0 kN
b) Try 457 × 152 × 52 kg/m I‐section S355. c) Perform section classification. As demonstrated in Worked Example I‐1, the cross‐section classification is Class 1.
D15
d) Check for moment. As demonstrated in Worked Example I‐1, the design resistance for bending about y‐y axis, M c,Rd is:
M c, Rd 390.5 kNm
M Ed 390.0 kNm
[Cl. 6.2.5 (2)]
OK
e) Check for shear force. As demonstrated in Worked Example I‐1, the design shear resistance Vpl,Rd is: Vpl , Rd
Av fy / 3 M0
, where
M0
1.0
[Cl. 6.2.6 (2)]
Vpl, Rd 746.6 kN VEd 156.0 kN
OK
f) Check for deflection. Serviceability load
= 3 kN/m2 = 9 kN/m for a width of 3 m
5 WL4 5 9 10,0004 26.1 mm 384 EI 384 210,000 21,400 104
L / 360 10,000 / 360 27.8 mm
OK
Therefore, 457 × 152 × 52 kg/m I‐section S355 satisfies the design.
D16
Part II Member design Worked Example II‐2 Design of an unrestrained steel beam against lateral torsional buckling Question As the structural details stated in Worked Example II‐1, Loading during construction = 1.5 kN/m2 Case I) Span Case II) Span
= 10 m with no intermediate restraint = 10 m with one restraint at mid‐span
Other design data are given in Worked Example II‐1.
D17
Solution to Procedure B2 – Use design method given in Appendix B2 Case I) Span = 10 m with no intermediate restraint a) Evaluate the design load and the design moment. Factored construction load, w = 1.5 kN/m2 x 1.6 = 2.4 kN/m2 = 7.2 kN/m over a width of 3 m = 7.2 x 102 / 8 = 90.0 kNm Factored design moment, MEd w = 6.75 kN/m 10 m
b) Buckling length, L cr , z = 10 m. c) Try 457 x 152 x 52 kg/m I-section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the elastic critical moment and the plastic moment resistance. 0.5
2 2 EIz I w Lcr , z GIT M cr C1 2 2 EIz Lcr , z I z
For a simply supported beam under uniformly distributed loading, C1 1.132 .
2 210,000 645 10 4 311 109 10,000 2 81,000 21.4 10 4 10 6 M cr 1.132 4 2 4 10,0002 645 10 210,000 645 10
0.5
= 1.132 133,684 48,217 129,664 106 0.5
= 63.8 kNm For Class 1 section,
M pl, Rd
Wpl, yf y M0
1100 103 355 10 6 390.5 kNm where M 0 1.0 [Cl. 6.2.5 (2)]
f) Calculate the non‐dimensional slenderness, LT . LT
Wpl, y f y M cr
390.5 2.47 63.8
g) Determine the imperfection factor, LT .
D18
[Cl. 6.3.2.2]
Buckling curve c is used for sections with h / b 2 , LT 0.49
[Cl. 6.3.2.3]
h) Calculate the reduction factor for lateral torsional buckling, LT . For rolled sections, LT,0 0.4 and 0.75
2
LT 0.5 1 LT LT LT , 0 LT
[Cl. 6.3.2.3]
[Cl. 6.3.2.3(2)]
0.5 1 0.49 2.47 0.4 0.75 2.472 3.29 LT
1
0.17
3.29 3.292 0.75 2.47 2
but LT 1.0 and LT
1 LT
2
1 0.16 2.47 2
LT 0.16 i) Calculate the modified reduction factor, LT, mod .
f 1 0.5 1 - k c 1 - 2.0 LT 0.8
2
1 0.5 1 0.94 1 - 2.0 2.47 - 0.8 2
1.14 1 f 1 LT , mod LT 0.16 j) Calculate the design buckling resistance moment and check for structural adequacy. M b , Rd LT , mod
Wpl , y f y M1
0.16 390.5 62.5 kNm where M1 1.0
M Ed 90.0 kNm
Not OK.
D19
[Cl. 6.3.2.1]
Case II) Span = 10 m with one restraint at mid‐span a) Evaluate the design load and the design moment. The factored design moment is the same as that in case I), i.e. M Ed 90.0 kNm
5m
w = 6.75 kN/m
10 m
b) Buckling length, Lcr, z 5 m . c) Try 457x152x52 I‐section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the elastic critical moment and the plastic moment resistance.
2 EI z M cr C1 2 L cr , z
0 .5
I w L cr , z 2GI T 2 Iz EI z
Conservatively, take C1 1.0 . 0. 5
2 210,000 645 104 311 109 10,0002 81,000 21.4 104 10 6 M cr 1.0 4 2 4 5,0002 645 10 210,000 645 10
= 1.0 534,735 48,217 129,664 106 0.5
= 225.5 kNm and M pl , Rd
Wpl , y f y M0
390.5 kNm
where M0 1.0
[Cl. 6.2.5 (2)]
f) Calculate the non‐dimensional slenderness, LT . LT
Wpl, y f y M cr
390.5 1.31 225.5
g) Determine the imperfection factor, LT . Buckling curve c is used for sections with h / b 2 , LT 0.49
D20
[Cl. 6.3.2.3]
h) Calculate the reduction factor of lateral torsional buckling, LT . For rolled sections, LT,0 0.4 and 0.75
2
LT 0.5 1 LT LT LT,0 LT
[Cl. 6.3.2.3]
0.5 1 0.49 1.31 0.4 0.75 1.312 1.37 LT
1 1.37 1.37 0.75 1.312 2
0.47
but LT 1.0 and LT
1 LT
2
1 0.58 1.312
LT 0.47 i) Calculate the modified reduction factor, LT, mod .
f 1 0.5 1 - k c 1 - 2.0 LT 0.8
2
where k c = 1.0 conservatively.
[Cl. 6.3.2.3(2)]
1 0.5 1 1 1 - 2.0 1.31 - 0.8 2
1 LT,mod LT 0.47 j) Calculate the design buckling resistance and check for structural adequacy.
M b,Rd LT,mod M Ed
Wpl,y f y
0.47 390.5 183.5 kNm where M1 1.0 M1 90.0 kNm OK.
[Cl. 6.3.2.1]
Therefore, 457 × 152 × 52 kg/m I‐section S355 with an intermediate restraint at mid‐span satisfies the design check.
D21
Solution to Procedure B3 – Use design method given in Appendix B3 Case I) Span = 10 m with no intermediate restraint a) Evaluate the design load and the design moment. Factored construction load, w = 1.5 kN/m2 x 1.6 = 2.4 kN/m2 = 7.2 kN/m over a width of 3 m MEd = 7.2 x 102 / 8 = 90.0 kNm Factored design moment, w = 6.75 kN/m
10 m
b) Try 457 x 152 x 52 kg/m I-section S355. c) Perform cross‐section classification – as demonstrated in Worked Example I‐1. d) Determine the buckling length, Lcr , z = 10 m. e) Calculate the non‐dimensional slenderness, LT . LT
1 UV z w C1
where
C1
1.13 ;
U
0.859 ; E 210,000 76.4 ; fy 355
1
i
31.1 mm ;
z
10,000 / 31.1 321.5 mm ;
V
1 4
LT
1
1 z 20 h / t f
2
1 1 321.5 4 1 20 449.8 / 10.9
z
z / 1 321.5 / 76.4 4.21
w
1
for Class 1 sections
1 UV z w C1
D22
2
0.706 ;
0.94 0.859 0.706 4.21 1 2.40 g) Determine the imperfection factor, LT , and the paramenter LT . Buckling curve b is used for sections with 2 h / b 3.1 , LT 0.49 .
h) Calculate the reduction factor for lateral torsional buckling, LT .
LT 0.5 1 0.49 2.40 0.4 0.75 2.402 3.15 LT
1 3.15 3.152 0.75 2.42
0.18 1.0
i) Calculate the design buckling resistance moment and check for structural adequacy.
M b,Rd LT
Wpl,y f y M1
0.18 390.5 70.3 kNm
where M0 1.0 M b ,Rd M Ed 90.0 kNm
Not OK.
D23
Case II) Span = 10 m with one restraint at mid‐span a) Evaluate the design load and the design moment. Factored design moment is same as that in case I), i.e. MEd = 90.0 kNm 5m
w = 6.75 kN/m
10 m
b) Determine the buckling length, L cr , z 5 m . c) Try 457 x 152 x 52 kg/m I‐section S355. d) Perform cross‐section classification – as demonstrated in Worked Example I‐1. e) Calculate the non‐dimensional slenderness, LT . LT
1 UV z w C1
where C1 U
E 210,000 76.4 fy 355
1
=
i z
= 31.1 mm = L cr , z / i 5,000 / 31.1 160.8
V
=
z
= z / 1 160.8 / 76.4 2.10 = 1 for Class 1 sections
w
= 1.00 for a conservative apprach; = 0.859;
LT =
1 1 z 4 1 20 h / t f
2
1 1 160.8 4 1 20 449.8 / 10.9
2
0.87
1 UV z w C1
= 1.00 0.859 0.87 2.10 1 = 1.57 g) Determine the imperfection factor, LT , and the paramenter LT . Buckling curve b is used for sections with 2 h / b 3.1 , LT 0.49 .
D24
h) Calculate the reduction factor of lateral torsional buckling, LT .
LT 0.5 1 0.49 1.57 - 0.4 0.75 1.572 1.71 LT
1 1.71 1.712 0.75 1.57 2
0.36 1.0
i) Calculate the design buckling resistance moment and check for structural adequacy.
M b,Rd LT
Wpl,y f y M1
0.36 390.5 140.6 kNm
where M1 1.0
M Ed 90.0 kNm
OK.
Therefore, 457 × 152 × 52 kg/m I‐section S355 with an intermediate restraint at mid‐span satisfies the design check. Summary of the reduction factors for lateral torsional buckling, χ LT Procedure B2: Design method given in Cl.6.3.2.3 Case I: LT = 2.48 LT = 3.32 LT = 0.17 f = 0.16 LT , mod = 0.16 Case II: LT = 1.31 LT = 1.37 LT = 0.47 f = 1.00 LT, mod = 0.47
Procedure B3: Design method given in Steel Designers’ Manual Case I: LT = 2.40 LT = 3.15 LT = 0.18
Case II: LT = 1.57 LT = 1.71 LT = 0.36
Design method according to Procedure B3 gives a more safe design to lateral torsional buckling.
D25
Part II Member design Worked Example II‐3 Design of a steel column under axial compression Question Design a steel column under the following condition: Factored axial load, Effective length, , ,
= 1000 kN = 9.0 m = 6.3 m
Try 254 x 254 x 73 kg/m H‐section S355.
D26
Solution Section properties of 254 x 254 x 73 kg/m H‐section S355: b
h = 254.1 mm b = 254.6 mm t w = 8.6 mm
tf r
A Iy
z tw
= 14.2 mm = 12.7 mm = 93.1 102 mm2 = 11,400 104 mm4
y
d
h
r
Iz = 3,910 10 mm I w = 562 109 mm6 4
It
3
y tf
4
z
4
= 576 10 mm
Wel, y
= 898 103 mm3
Wpl , y
= 992 103 mm3
Material properties: Since t f = 14.2 mm and t w = 8.6 mm, i.e. the nominal material thickness is smaller than 16 mm, the nominal value of the yield strength for grade S355 steel is: = 355 N/mm2 = 210,000 N/mm2 = 0.3 = 81,000 N/mm2
fy E G
a) Evaluate the design load. N Ed 1000 kN
b) Try 254 x 254 x 73 kg/m H‐section S355. c) Perform section classification.
235 / f y 235 / 355 0.81
Web – internal compression part: c w = h 2t f 2r cw / t w
= 200.3 / 8.6
Limit for Class 1 web = 33 Outstand flanges: cf = b t w 2r / 2
cf / t f = 110.3 / 14.2 Limit for Class 1 flange = 10
[Table 5.2] =
200.3 mm
=
23.3
=
26.7
23.3
⇒ The web is Class 1. [Table 5.2]
=
110.3 mm
= =
7.8 8.1
7.8
⇒ The flanges are Class 2.
The overall cross‐section classification is Class 2 under pure compression.
D27
d) Determine the effective length for both axes.
Effective length, L cr , y
= 9.0 m
L cr ,z
= 6.3 m
e) Calculate N cr and Af y . N cr , y N cr , z
2 EI y L cr , y
2
2 EI z L cr , z
2
2 210,000 114,000,000 10 3 2,917 kN 2 9,000
2 210,000 39,100,000 10 3 2,042 kN 6,300 2
N c ,Rd Af y 9,310 355 10 3 3,305 kN
f) Calculate the non‐dimensional slenderness, .
y z
Af y N cr ,y Af y N cr ,z
3,305 1.06 2,917
[Cl.6.3.1.2]
3,305 1.27 2,042
[Cl.6.3.1.2]
g) Determine the imperfection factor, . For a section with h / b 1.2 ,
use buckling curve b with = 0.34 for buckling about y‐y axis. use buckling curve c with = 0.49 for buckling about z‐z axis.
h) Calculate the parameter, and the buckling reduction factor, z . Buckling about y‐y axis:
[Cl.6.3.1.2]
[Cl.6.3.1.2]
y 0.5 1 0.34 1.06 - 0.2 1.06 2 1.21
y
1 1.21 1.212 1.06 2
0.56
Buckling about z‐z axis:
z 0.5 1 0.49 1.27 - 0.2 1.27 2 1.57
y
1 1.57 1.57 2 1.27 2
0.40
z 0.40 critical i&j) Calculate the design buckling resistance, N b ,Rd and check for structural adequacy: N b ,Rd
N c ,Rd 0.40 3,305 1,322 kN 1000 kN M1 1.00
OK.
Therefore, 254 x 254 x 73 kg/m H‐section S355 steel satisfies the design. D28
Part II Member design Worked Example II‐4 Design of a beam-column under combined compression and bending Question Design a steel column under the following condition: Design axial load, N Ed
= 1000 kN
Design moment, M y , Ed
= 60 kNm
M z ,Ed
= 0 kNm
Effective length,
L cr , y
= 9.0 m
L cr ,z
= 6.3 m
Try 254 x 254 x 73 kg/m H‐section S355.
60 kNm
0
0 My,Ed
0 Mz,Ed
D29
Solution Section properties of 254 × 254 × 73 kg/m H‐section S355:
h = 254.1 mm b = 254.6 mm t w = 8.6 mm
tf r
A Iy
= = = =
b z
14.2 mm 12.7 mm 93.1 10 2 mm2 11,400 104 mm4
tw y
d
h
y
Iz = 3,910 10 mm I w = 562 109 mm6 I t = 576 10 3 mm4 4
4
Wel, y
= 898 10 3 mm3
Wpl , y
= 992 10 3 mm3
r
tf
z
Material properties: Since t f = 14.2 mm and t w = 8.6 mm, i.e. the nominal material thickness is smaller than 16 mm, the nominal value of the yield strength for grade S355 steel is:
= 355 N/mm2 = 210,000 N/mm2 = 0.3 = 81,000 N/mm2
fy E G
a) Evaluate the design load.
N Ed M y , Ed
= 1000 kN = 60 kNm
M z , Ed
= 0 kNm
b) Try 254 x 254 x 73 kg/m H‐section S355 steel. c) Perform section classification.
235 / f y 235 / 355 0.81
Web – internal compression part: c w = h 2t f 2r
cw / t w
=
200.3 / 8.6
Limit for Class 1 web = 33
=
200.3 mm
=
23.3
=
26.7
D30
23.3
[Table 5.2]
⇒ The web is Class 1.
Outstand flanges: cf = b t w 2r / 2
cf / t f = 110.3 / 14.2 Limit for Class 2 flange = 10
=
110.3 mm
= =
7.8 8.1 7.8
⇒ The flanges are Class 2.
The overall cross‐section classification is Class 2. (Under pure compression) d) Determine the effective length for both axes.
Effective length, L cr , y
= 9.0 m
L cr ,z
= 6.3 m
e) Check the resistance of the cross‐section for combined bending and axial force. Compression: N c , Rd
Af y
[Cl. 6.2.4 (2)]
M0
The design compression resistance of the cross‐section is therefore:
N c, Rd
9,310 355 103 3,305 kN 1,000kN 1.00
OK.
Bending about y‐y axis:
M c,Rd M pl,Rd
Wpl, y f y
[Cl. 6.2.5 (2)]
M0
The design resistance of the cross‐section for bending is therefore:
M c, y,Rd
Wpl, y f y M0
992 103 355 10 6 1.00
352.2 kNm 60 kNm
OK.
Cross‐section capacity check for combined bending and axial force: f) Check the member buckling resistance in combined bending and axial compression. Buckling resistance in compression: Calculate the elastic critical force and Af y . N cr , y N cr , z
2 EI y L cr , y
2
2 EI z L cr , z
2
2 210,000 114,000,000 10 3 2,917 kN 9,000 2
2 210,000 39,100,000 10 3 2,042 kN 2 6,300
N c ,Rd Af y 9,310 355 10 3 3,305 kN
D31
Calculate the non‐dimensional slenderness. y
z
Af y N cr ,y
Af y N cr ,z
3,305 1.06 2,917
[Cl.6.3.1.2]
3,305 1.27 2,042
[Cl.6.3.1.2]
g) Determine the imperfection factor, . Choose a suitable buckling curve
[Table 6.1]
use buckling curve b with 0.34 for buckling about the y‐y axis. use buckling curve c with 0.49 for buckling about the z‐z axis.
Calculate the buckling reduction factor, . Buckling curve about y‐y axis: y 0.5 1 0.34 1.06 0.2 1.06 2 1.21
y
1 1.21 1.212 1.06 2
0.56
Buckling curve about z‐z axis: y 0.5 1 0.49 1.27 0.2 1.27 2 1.57
y
1 1.57 1.57 2 1.27 2
[Cl.6.3.1.2]
[Cl.6.3.1.2]
0.40
Buckling resistance in bending: h) Calculate the elastic critical moment, M cr and the plastic resistance moment M pl , Rd . 2 2 EI z I w L cr , z GI T 2 M cr C1 2 EI z L cr , z I z
0 .5
with a zero moment at one end, i.e. 0 , C1 1.879 .
M cr 1.879
2 210,000 39.110 6 6,300 2
0.5
562 10 9 6,300 2 81,000 576 10 3 10 6 2 6 6 210,000 39.110 39.110
1.879 2,041,807 14,373 22,850 106 740.2 kNm W f 992 103 355 106 M pl,Rd pl,y y 352.2 kNm where M 0 1.0 M0 1.0 0.5
i) Calculate the non‐dimensional slenderness. LT
W pl,y f y M cr
352.2 0.69 740.2
[Cl.6.3.2.2]
D32
j) Determine the imperfection factor for lateral torsional buckling, LT . Buckling curve a is used for sections with h / b 2.0 , LT 0.21 k) Calculate the buckling reduction factor.
2
LT 0.5 1 LT LT 0.2 LT
[Table 6.3 & 6.4]
[Cl. 6.3.2.2]
LT 0.5 1 0.21 0.69 0.2 0.69 2 0.79 LT
1 0.79 0.79 2 0.69 2
LT
M y,Rk M1
0.85
0.85
352.2 299.4 kNm 1.0
l) Resistance in combined bending and axial compression: A member subjected to combined bending and axial compression must satisfy both equations:
M y, Ed Mz , Ed N Ed k yy k yz 1 y N Rk / M1 LTM y, Rk / M1 M z , Rk / M1
[Cl. 6.3.3]
M y, Ed Mz , Ed N Ed k zy k zz 1 z N Rk / M1 LTM y, Rk / M1 Mz , Rk / M1 y N Rk / M1 0.56 9,310 355 103 1,850.8 kN y N Rk / M1 0.40 9,310 355 103 1,322.0 kN m) Determination of interaction factors
using Annex B
Since M z , Ed 0 kNm , only k yy and k zy are required. Since the member is susceptible to lateral torsional buckling, interaction factors k yy and k zy are determined according to Table B.2.
0 , C my C mLT 0.6 0.4 0.4 0.6 N Ed N Ed C my 1 0.8 k yy Cmy 1 y 0.2 y N Rk / M1 y N Rk / M1
1,000 = 0.60 1 1.06 0.2 0.95 1,850.8
1,000 0.60 1 0.8 0.86 1,850.8
D33
k yy 0.86 z 1.27 0.4 ,
0.1 z N Ed 0.1 N Ed 1 k zy 1 C mLT 0.25 z N Rk / M1 C mLT 0.25 z N Rk / M1
0.11.27 1,000 0.73 = 1 0.6 0.25 1,322
0.1 1,000 0.78 1 0.6 0.25 1,322
k yy 0.78
n) Check for structural adequacy. M y, Ed N Ed k yy y N Rk / M1 LTM y, Rk / M1
1,000 60 0.86 1,850.8 299.4
0.54 0.17 0.71 1.00
OK.
M y, Ed N Ed k zy z N Rk / M1 z M y, Rk / M1
1,000 60 0.78 1,322.0 299.4
0.76 0.16 0.92 1.00
OK.
Therefore, 254 x 254 x 73 kg/m H‐section S355 steel satisfies the design.
D34
Key parameters in Worked Example II‐4. C my 0.60 ;
CmLT 0.60
N Ed M y, Ed 0.47 1 N Rd M y, Rd
M y,Ed
N Ed k yy 0.71 1 y N Rk / M1 LT M y,Rk / M1
M y,Ed
N Ed k zy 0.92 1 z N Rk / M1 LT M y,Rk / M1
D35
Part II Member design Worked Example II‐5a Column in simple construction Question Design the column between Levels 1 and 2, i.e. Column C12, as shown in the figure below, with a S275 H‐section. The following assumptions are made:
The column forms part of a braced structure of simple construction. The column is effectively pinned at the base, and continuous at Level 2. Beam 2 is connected to the column flange of the column at Joint 2 with flexible end plates. Beam 3 Level 3 Column C23
P23,Ed 201.6 A
A
Level 2 Joint 2
201.8
Column C12
201.8
Column under consideration Section A-A R1,Ed, R2,Ed and R3,Ed are reaction
Level 1
forces from beams connected to the column at Joint 2.
Design data: P23,Ed P1, Ed P2, Ed P3, Ed
= 377 kN = 37 kN = 147 kN = 28 kN
Try 203 x 203 x 46 kg/m H‐section S275.
D36
Solution Section properties of 203 x 203 x 46 kg/m H‐section S275: b
h = 203.2 mm b = 203.6 mm t w = 7.2 mm
z tw
t f = 11.0 mm r = 10.2 mm
h
d
y
y
A = 5,870 mm2 I y = 4,570 10 4 mm4
r
I z = 1,550 10 mm I w = 143 10 9 mm6 4
tf
4
z
I t = 222 103 mm4
Wel,y
= 450 103 mm3
Wpl ,y
= 497 103 mm3
Wel ,z
= 152 103 mm3
Wpl ,z
= 231 103 mm3
U
= 0.847 (buckling parameter)
a) Nominal moments due to connected beams In simple construction, reaction forces from connected beams are assumed to act at 100 mm from the faces of the web or of the flanges of the column (NCCI SN005a). Nominal moments at Joint 2
h M 2, y ,Ed 100 R 2, Ed 10-3 kNm 29.6 kNm 2 tw -3 M 2,z , Ed 100 R 1, Ed R 3, Ed 10 kNm 0.9 kNm 2 These nominal moments are distributed between the column members above and below Level 2, i.e. Columns C12 and C23, in proportion to their bending stiffnesses, K12 and K23 respectively. K 23 K12 K 23 EI
EI L12
L 23 EI
L 23
EI
EI
3 5000 EI 8 3000 5000
The nominal moments acting onto Column C12 at Joint 2 after moment distribution are: 3 11.1 kNm 8 3 M 2, z , Ed 0.3 kNm 8
M y , Ed M 2, y , Ed M z , Ed
D37
The axial force and the bending moment diagrams are shown below. 377 Level 3 3000
377 37+147+28
Level 2
M2,y,Ed = 29.6
M2,y,Ed = 18.5
Joint 2
5000
0.6 0.3
11.1
589
Level 1
My
589
Mz
N
b) Buckling lengths About the y‐y axis
Lcr , y L 5,000 mm
About the z‐z axis
Lcr , z L 5,000 mm
c) Resistance to flexural buckling Flexural buckling about the z‐z axis is considered to be critical. Both the elastic critical force and the non‐dimensional slenderness for flexural buckling of column C12 are evaluated as follows: 2 EI z 2 210 103 1,548 10 4 10 3 1,283 kN L cr , z 2 5,000 2
N cr , z
N c , Rd Af y 5,870 275 10 3 1,614 kN
z
N c, Rd
N cr ,z
1,614 1.12 1,283
From Table 6.2 of EN 1993‐1‐1: For a H‐section (with h/b 1.2) and t f 100 mm, use buckling curve ‘c’, and hence,
0.49 .
[ Table 6.1 ]
According to Table 6.1 of EN 1993‐1‐1
z 0.5 1 z 0.2 z
z
1 z z z 2
2
2
0.5 1 0.49 1.12 0.2 1.12 1.35 2
1 1.35 1.352 1.122
0.48
D38
[Cl. 6.3.1.2]
z Af y M1
N b , Rd
0.48 1,614 774 kN N Ed 589 kN 1 .0
The resistance of Column C12 to flexural buckling is adequate. d) Design buckling resistance moment 1
V 4
LT
1
1 z 20 h tf
2
1 5,000 1 51.4 4 1 20 203.2 11.0
2
0.80
1 UV z w C1
(Refer to Appendix B3)
1 0.847 0.80 1.12 1.0 0.57 1.77
Alternatively, the non‐dimensional slenderness for lateral torsional buckling for the H‐section may be approximated (NCCI SN002a) as follows: LT 0.9 z 1.01
This assumes a uniform bending moment and a section symmetric about its major axis. From Table B3.2 in Appendix B of this Technical Guide, for a rolled H‐section (with h/b 2), use buckling curve ‘b’, and hence, LT 0.34 .
LT 0.5 1 LT LT LT, 0 LT
2
0.5 1 0.34 0.57 0.4 0.75 0.57 2 0.65
LT
1 2
LT LT LT
M b , Rd
2
1 0.65 0.65 0.75 0.572 2
0.93
0.93 497 10 3 275 10 6 127.1 kNm M y, Ed 11.1 kNm 1.0
The design buckling resistance moment of Column C12 is adequate. e) Resistance for bending about minor axis There is no reduction for buckling to the minor axis bending resistance M c, z , Rd . M c, z , Rd
Wpl, z f y M0
231 10 3 275 10 6 63.5 kNm 1.0
The resistance of Column C12 for bending about the minor axis is adequate.
D39
f) Combined compression and bending Using the simplified buckling check for combined bending and axial compression: M y , Ed M z , Ed N Ed k zy k zz 1 M c , z , Rd N b , z , Rd M b , Rd
[Clause 6.3.3, Eq. 6.62]
589 11.1 0.3 1.0 1.5 1 759 127.1 63.5
(Refer to NCCI SN048b)
Use k zy 1.0 and k zz 1.5 for columns in simple construction
0.76 0.09 0.01
0.86 1.0 The member resistance of Column C12 under combined bending and axial compression is
adequate.
Therefore, 203 x 203 x 46 kg/m H‐section S275 steel satisfies the design.
D40
Part II
Member design Worked Example II-5b Column in simple construction In Worked Example II‐5a, the factors k zy and k zz can be alternatively calculated according to Annex A in EN 1993‐1‐1 as follow: N Rk Af y 5,870 275 10-3 = 1,614 kN
N cr , y
N cr , z
y
z
2 EI y Lcr , y
2
2 210 103 4,568 104 10 3 3,787 kN 2 5,000
2 EI z 2 210 103 1,548 104 10 3 1,283 kN 2 5,0002 Lcr , z
Af y N cr , y Af y N cr ,z
1,614 0.65 3,787
1,614 1.12 1,283
For a H‐section (with h/b 1.2) and t f 100 mm , use curve ‘b’ for buckling about y‐y axis, and hence, 0.34 .
y 0.5 1 y 0.2 y
2
0.5 1 0.34 (0.65 0.2) 0.65 0.79 2
For a H‐section (with h/b 1.2) and t f 100 mm , use curve ‘c’ for buckling about z‐z axis, and hence, 0.49 .
z 0.5 1 z 0.2 z y
z
1 2
2
2
2
y y y
1 z z z
2
0.5 1 0.49 (1.12 0.2) 1.12 1.35 2
1 0.79 0.792 0.652
1 1.35 1.352 1.122
0.81
0.48
D41
For double symmetric H‐section with y o z o 0 2
2
2
2
2
io iy iz yo z o
Iy
A
N cr ,T
(Refer to EN 1993‐1‐3, Eq. 6.33b)
(Refer to EN 1993‐1‐3, Eq. 6.33a)
I z 4,570 104 1,550 104 10,426 mm2 A 5,870 5,870
2 EI w 1 GI T 2 2 i o Lcr ,T
1 2 210 103 0.143 1012 81 103 22.2 104 10 3 kN 10,426 2,5002
6,273 kN 2
y 1 o 1 io
N cr ,TF
(Refer to EN 1993‐1‐3, Eq. 6.35)
2 2 N cr ,T N cr , y N cr ,T y o N cr ,T 1 1 4 i o N cr , y 2 N cr , y N cr , y
(Refer to EN 1993‐1‐3, Eq. 6.35)
1 N cr ,y N cr ,T N cr ,y N cr ,T 2 1 N cr ,T
6,273 kN
Cmy,0 0.79 0.21y 0.36y 0.33
N Ed N cr , y
589 0.79 0.21 0 0.36 0 0.33 0.77 3,787 C mz , 0 0.79 0.21z 0.36z 0.33
N Ed N cr , z
589 0.79 0.21 0 0.36 0 0.33 0.74 1,283 N Ed 589 1 N cr , y 3,787 y 0.97 N Ed 589 1 y 1 0.81 N cr , y 3,787 1
D42
N Ed 589 1 N cr , z 1,283 z 0.69 589 N Ed 1 0.48 1 z 1,283 N cr , z 1
wy
Wpl, y
497 1.10 1.5 450
231 1.52 1.50 152
Wel, y
w y 1.10
wz
Wpl, z Wel, z
w z 1.50
n pl
N Ed 589 0.36 N Rk / M1 1,614 / 1.00
a LT 1
y
IT 22.2 1 1.00 Iy 4,570
M y, Ed A 11.1 106 5,870 0.25 3 N Ed Wel, y 589 10 450 103
2 EI z M cr C1 2 L cr ,z
0. 5 2 I w L cr ,z GI T 2 C z C z 2 g 2 g 2 I EI z z
(Refer to NCCI SN003a)
Since 0 is the non‐dimensional slenderness for lateral‐torsional buckling due to uniform bending moment, C1 1.00 and C 2 z g 0
2 210 103 1,550 10 4 0.143 1012 5,000 2 81 103 22.2 10 4 M cr 1.00 2 4 5,000 2 210 103 1,550 10 4 1,550 10 1.00 1,285,022 9,226 13,994 10 6 kNm 0.5
195.8 kNm 0
Wpl , y f y M cr
497 275 10 3 0.84 195.8
D43
0.5
10 6 kNm
0 0.84
N N 589 589 0.2 C1 4 1 Ed 1 Ed 0.2 1.77 4 1 0.22 1 1,283 6,273 N cr ,z N cr ,T
y a LT 0.25 1 Cmy Cmy,0 1 Cmy,0 0.77 1 0.77 0.85 1 y a LT 1 0.25 1 Cmz Cmz,0 0.74 C mLT C my
a LT
2
N N 1 Ed 1 Ed N N cr , z cr ,T
1.00
0.852
589 589 1 1 1,283 6,273
1.03 1
C mLT 1.03 LT 0.93 (Determined from Worked Example II‐5a)
y 0.65 max max max 1.12 z 1.12
d LT 2a LT
M y , Ed M z , Ed 0 4 0.1 z C my LT M pl , y , Rd C mz M pl, z , Rd
0.84 11.1 0.3 4 3 0.1 1.12 0.85 0.93 497 275 10 0.74 231 275 10 3 0.00066
2 1
2 2 C my max n pl d LT C zy 1 w y 1 2 14 5 wy
0.852 1.12 2 0.36 0.00066 0.79 1 1.10 1 2 14 5 1.10 w y Wel , y
0.6
w z Wpl , y
0.6
1.10 450 0.47 1.50 497
C zy 0.79
e LT 1.7a LT
M y, Ed 0 4 0.1 z C my LT M pl, y, Rd
0.84 11.1 0.09 1.7 1 4 0.1 1.12 0.85 0.93 497 275 10 3
D44
1.6 1.6 2 2 2 C mz max C mz max n pl e LT Czz 1 w z 1 2 wz wz 1.6 1.6 1 1.5 1 2 0.742 1.12 0.742 1.12 2 0.36 0.09 1.5 1.5 1.07 W 152 el, z 0.66 Wpl, z 231 C zz 1.07
k zy C my C mLT
k zz C mz
wy z 1.10 0.69 1 1 0.85 1.03 0.6 0.47 0.6 589 N Ed C zy 1 . 50 0 . 79 w z 1 1 3,787 N cr , y
1 0.69 1 z 0.74 0.88 N Ed Czz 589 1.07 1 1 N cr , z 1,283
D45
Part II
Member design Worked Example II-5c Column in simple construction In Worked Example II‐5a, the factors k zy and k zz can be alternatively calculated according to Annex B in EN 1993‐1‐1 as follows: Since H‐section is not susceptible to torsional deformation, use Table B.1. y z LT 0 C my C mz C mLT 0.6
As determined from Worked Example II‐5a, N Rk 1,614 kN
y 0.65
N cr, y 3,787 kN
y 0.81
z 1.12
N cr, z 1,283 kN
z 0.48
N Ed 589 0.61 0.65 0.2 k yy C my 1 y 0.2 0.72 0.81 1614 / 1.00 y N Rk / M1 N 589 Ed 0.61 0.8 C my 1 0.8 0.82 N / 0.81 1614 / 1.00 y Rk M 1 k yy 0.72 k zy 0.6k yy 0.6 0.72 0.43
N Ed 589 0.61 2 1.12 0.6 k zz C mz 1 2z 0.6 1.35 N / 0 . 48 1614 / 1 . 00 z Rk M1 N Ed C mz 1 1.4 z N Rk / M1
589 0.61 1.4 0 . 48 1614 / 1 . 00
1.24
k zz 1.24
Factors k zy and k zz according to different methods are summarized as follows:
BS EN 1993‐1‐1 BS EN 1993‐1‐1 NCCI SN048b Annex A Annex B
k zy
0.47
0.43
1.0
k zz
0.88
1.24
1.5
D46
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