Analysis And Design Of Suspension Bridge

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Ministry of Higher Education University of Baghdad College of Engineering Civil Engineering Department

Analysis and Design of Suspension Bridge A Study Submitted to the Civil Engineering Department of the University of Baghdad in Partial Fulfillment for the Requirements of the Degree of B.Sc.

By Ahmed Adham Abdullah Supervised By Dr. Ala’a H. Al – Zuhairi 2012

2012

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Acknowledgment First of all, Father, Thank You, I am an Engineer; that is because of you. I would like to like to express my sincere thanks, appreciation and deepest gratitude to my supervisor (Dr. Ala’a Hussein Al-Zuhairi) for his help, support and guidance in the preparation for this study. Much thanks for my father, Dr. Ala’a and Dr. Salah Ruheima Al-Zaidi, to them the favor returned in making me a civil engineer during my four years of study.

All the respect and love to my department and my university, I will always be proud that I studied in it and spent many beautiful days inside it campus.

Ahmed Al-Fakhar May, 2012

I

Dedication To Iraq.. To my Family.. Father, Mother, Gaith and Zahraa. To my Grandfather.. Abdullah Al-Fakhar

II

Abstract

In this project, the structural analysis of suspension bridge is conducted using the computer program named as (CSi Bridge). The analysis is based on adopting AASHTO and Iraqi specifications standard for loading in bridges. The 14th – July suspension bridge built in Baghdad in 1963 was taken as a case study. The actual data (Bridge geometry in material properties) was input to the program with standard loading mentioned above. The results indicate that the max tensile stress in the main cable was 0.36 F u. The maximum compressive stress in the tower was 0.51 F y , while the maximum normal and shear stresses in the plate of the main girder were 0.8 F y and 0.33 F u respectively.

III

II

III

Table of Contents No. 1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 2.6 3.1 3.1.1 3.1.2 3.1.2.1 3.1.2.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.3 3.3.1 3.4 3.4.1 3.4.2 3.4.3 3.5 3.5.1 3.5.2

Title Chapter 1 Introduction What is a suspension bridge Importance and advantage Drawbacks Components of suspension bridge Loads Chapter 2 Historical aspects of suspension bridge development Early Precursor First Suspension Bridges From Past to Present Development of Cables and Anchorages Lists of Longest spans of Suspension Bridges 14th of July Suspension Bridge – Baghdad, Iraq Chapter 3 Analysis of suspension bridge Bridge Loading. Dead load Live Load AASHTO loading British Standard (BS5400 Part 2) Cable static analysis Equation of the cable Horizontal Thrust on the Cable & Second Equation (Force-related) Maximum tension in the cable Length of the cable The effect on the cable due to change in temperature Analysis problem Catenary Fabrication and types of cables 1Basic Types of Cables Deck – Stiffening girder Flexural stiffness in the vertical direction Torsional stiffness Supporting Condition Towers – Cable Anchors Guide pulley support for suspension cable

Page 2 2 3 3 5 7 8 8 8 21 23 26 26 26 26 28 30 31 32 34 37 40 42 42 43 44 45 46 47 48 52 52 52

Roller support for suspension cable Chapter 4 Case Study – 14th of July Using Computer Program (CSi Bridge)

4.1

Analysis Program – CSi Bridge.

54

4.2

Geometry of the Bridge

55

4.3

Steel types used

56

IV

4.4

Structural properties of the components of suspension bridge

57

4.5

Loading Cases

59

4.6

Analysis Results

61

4.6.1

Cable analysis

61

4.6.2

Tower analysis

66

4.6.3

Deck Analysis

69 Chapter 5 Conclusion and Recommendation

5.1

Conclusion

76

5.2

Recommendation

77

List of Figures No. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

2.11

2.12 2.13 2.14 2.15 2.16 2.17 2.18

Title Chapter 2 Historical aspects of suspension bridge development A diagram of one of the earliest known suspension bridges in the world, built in 1430, at Chushul, south of Lhasa in Tibet Jacob’s bridge, Pennsylvania Finley’s river over Merrimack river in Massachusetts Eyebar chains were very effective structural elements because each link could be constructed of multiple parallel eye bars Eyebar fail the Union Bridge Tweed River Telford’s Bridge the British Telford and his Eyebar chain bridge Wire-cable Bridge of Joseph Chaley Wire-cable of Charles Ellet This picture represents the actual system as was used by john Roebling and by his son Washington Roebling in the Brooklyn Bridge, 30 after it was first developed. Up on the top one can see the traveller attached to the haul rope carrying a loop of wire to the top of the tower This picture presents a cut away of the cable of the golden gate bridge, showing it was fabricated using Roebling method. (27,572 wires) A wire-cable problem in suspension bridge in Angers, France This an original drawings of john anchorage design it uses a series of massive rod iron eyebar chains one for each strand of the main cable Strands attached to a strand shoe Strand shoe attached to the anchor chain Akashi Kaikyo Bridge, Japan 14th July Bridge, A view from Tigris River

V

Page 7 9 9 10 11 12 12 13 15 15

16

17 18 19 20 20 23 24

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16

Chapter 3 Analysis of suspension bridge AASHTO truck loading Geometry of suspension bridge Cable geometry Horizontal thrust on cable Forces on cable Cable equilibrium Cable supported at different levels Cable supported at the same level ds, dy, dx Difference between catenary and parabola Seven-wire strand Comparison between the dead load moment in a 3 span continuous girder and in the girder of cable stayed bridge Distribution of the concentrated force by the deck A system with two cable planes and a deck without torsional rigidity A system with two cable planes as well as a torsionally stiff deck Supporting condition of a three span suspension bridge Inclination of the short hangers at midspan to transfer a longitudinal force from the deck to the main cable Cable supported bridge with the deck supported vertically on the end piers only, but laterally at the pylons as well as on the end piers Pylon of the Storebælt East Bridge without a cross beam below the deck Connection between the deck and the pylon through vertical sliding bearings for transmission of lateral forces Chapter 4 Case Study – 14th of July Using Computer Program (CSi Bridge) General view Deck cross section Girder cross section Floor beam and stringer cross sections Tower cross section Positive moment loading Negative moment loading General distribution loading Maximum shear loading Cable axial force diagram Cable embedment in deck Axial force Moment in tower Shear in tower Positive moment about horizontal axis Sections adequacy for positive moment

VI

27 30 31 32 32 33 35 37 38 42 44 45 46 47 48 49 49 51 51 52 55 57 58 58 59 60 60 60 61 61 64 66 66 66 69 69

4.17 4.18 4.19 4.20

Negative moment about horizontal axis Sections adequacy for negative moment Shear force 20 Sections adequacy for shear

71 71 73 73

List of Tables No. 2.1 3.1 3.2 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

Title Chapter 2 Historical aspects of suspension bridge development the world longest spans of suspension bridges Chapter 3 Analysis of suspension bridge Equivalent loading for trucks Comparison between cable steel and structural steel Chapter 4 Case Study – 14th of July Using Computer Program (CSi Bridge) Bridge geometry Girders, stringer, floor beams and towers Cables and Suspenders Concrete material: deck surface Deck floor beams, stringers and surface thickness Main cable Suspenders Element Forces – Frames (Main Cable) Element Forces – Frames (Tower)

VII

Page 22 28 44 55 56 56 56 57 59 59 62 67

CHAPTER ONE INTRODUCTION

1.1 What is a suspension bridge. 1.2 Importance and advantage. 1.3 Drawbacks. 1.4 Components of suspension bridge. 1.5 Loads.

Chapter 1

Introduction

1.1 What is a suspension bridge? It is a type of bridges in which a continuous deck (the load-bearing portion) is hung below the suspension cables on vertical suspenders that connect the deck with the main cable. The cables are connected to towers at either end of the bridge, and are balanced by anchors. The suspension bridge must be anchored at each end of the bridge, since any load applied to the bridge is transformed into tension in the main cables in which they transform that load to the main towers. 1.2 Importance and advantage • Because of the suspension bridge design that has one long span spread along the stream of the water flow , without any additional pillars in the flow, it provides : a) Free ships transportation. b) Does not cause corrosion to the bed of the river. • Capable of spanning long distance. While other types of bridges require intermediate supports, a suspension bridge can cover long distances using only

the

strength

of

its

cables.

• Less material may be required than other bridge types, even at spans they can achieve. • Except for the installation of the initial temporary cables, little or no access from below is required during construction, allowing the waterway to remain open while the bridge is built above. • May be better to withstand earthquake movements than heavier and more rigid bridges.

2

Chapter 1

Introduction

1.3 Drawbacks:

Suspension bridges are highly vulnerable to wind, and have been known to collapse or fail due to seemingly minor wind gusts. They must be carefully engineered and braced to minimize the risk of failure. This high level of technical engineering, combined with the difficulty of building over a long span, tends to make suspension bridge construction more

costly

than

that

of

other

bridge

designs.

1.4 Components of the suspension bridge

a) The superstructure part of the suspension bridge consists of:

1. Deck:

which

composed

is

either

a of

stiff plate

structural girders

part or

hung truss

by

suspenders

structure.

This

arrangement allows the deck to be level or arc upward for additional

clearance.

This

part

is

often

constructed

without

falsework.

2. Cables: The suspension bridge includes two main cables, which are stretched over the span to be bridged. The cables is flexible throughout, therefore it cannot resist any moment and can adopt any shape under the load. The main suspension cable in older bridges was often made from chain or linked bars, but modern bridge cables are made from multiple strands of wire. Assuming a negligible weight as compared to the weight of deck and vehicles being supported, the main cable of the suspension bridge

3

Chapter 1

Introduction will

form

a

parabola.

3. Main towers; which supports the main cables, since all the force on the pillars is vertically downwards and they are also stabilized by the main cables, the pillars can be made quite slender. Another function for the main tower, it works as a support to the deck

also.

In some circumstances the towers may sit on a bluff or canyon edge where the road may proceed directly to the main span, otherwise the bridge will usually have two smaller spans, running between either pair of pillars and the highway, which may be supported by suspender cables or may use a truss bridge to make this connection. In latter case there will be a very little arc in the outboard

main

cables.

b) Substructure part:

1. Cable

anchors:

The anchor block, on the other hand, resists the tensile pull from the

main

cable

primarily

through

its

mass.

The tensile pull or force from the main cable is balanced, or equilibrated (put into a state of equilibrium) by the gravitational pull on the mass of the anchor and the resulting frictional force between the anchorage and the foundation on which it sits. In most suspension bridges, the anchorage is a reinforced concrete block. 2. Concrete piers.

4

Chapter 1

Introduction

1.5 Loads:

Three kinds of forces operate on any bridge: the dead load, the live load, and the dynamic load.

1. Dead load: refers to the weight of the bridge itself. Like any other structure, a bridge has a tendency to collapse simply because of the gravitational forces acting on the materials of which the bridge is made.

2. Live load: refers to traffic that moves across the bridge as well as normal environmental factors such as changes in temperature, precipitation, and winds.

3. Dynamic load: refers to environmental factors that go beyond normal weather conditions, factors such as sudden gusts of wind and earthquakes. All three factors must be taken into consideration when building a bridge.

The relatively low deck stiffness compared to other (non-suspension) types of bridges makes it more difficult to carry heavy rail traffic where high concentrated LL occur. Loads calculation considerations will follow the AASHTO, BS 5400, and the Iraqi code.

5

CHAPTER TWO Historical Aspects of Suspension Bridge Development

2.1 Early Precursor. 2.2 First Suspension Bridges. 2.3 From Past to Present. 2.4 Development of Cables and Anchorages. 2.5 Lists of Longest spans of Suspension Bridges. 2.6 14th of July Suspension Bridge – Baghdad, Iraq.

Chapter 2

Historical aspects of suspension bridges development

CHAPTER 2 HISTORICAL ASPECTS OF SUSPENSION BRIDGES DEVELOPMENT 2.1 Early precursor The

Tibetan

originated bridges. only Gyalpo finally

the In

use

1433,

surviving Bridge washed

saint of

and

iron

Gyalpo

chains built

chain-linked in

in

in

his

eight

bridge

Duksum

away

bridge-builder

enroute

2004.

version

bridges

of

in

Gyalpo's

to

Gyalpo's

Thangtong

Trashi iron

of

early

eastern was

suspension

Bhutan.

the

Yangtse, chain

Gyalpo

The

Thangtong which

bridges

did

was not

include a suspended deck bridge which is the standard on all modern suspension

bridges

today.

Instead,

both

the

railing

and

the

walking

layer of Gyalpo's bridges used wires. Before the use of iron chains it is thought that Gyalpo used ropes from twisted willows or yak skins.

“Figure 2.1 - A diagram of one of the earliest known suspension bridges in the world, built in 1430, at Chushul, south of Lhasa in Tibet”

7

Chapter 2

Historical aspects of suspension bridges development

2.2 First Suspension Bridges: The first design for a bridge resembling the modern suspension bridge is attributed to Fausto Veranzio, whose 1595 book “Machinae Novae” included drawings both for a timber and rope suspension bridge, and a hybrid suspension and cable-stayed bridge using iron chains. 2.3 From Past to Present: For the last two centuries the suspension bridge has been the most effective means of building across vast distances. Throughout the history of suspension bridge development intensive engineering efforts have been at overcoming two persistent challenges that in general terms related to the structure system of the suspension bridge: 1. Constructing the main cables and the anchorages. 2. Controlling the suspension bridges susceptibility to vibrations caused by wind Some efforts to address these challenges have been quite successful but many have

not,

indeed

as

we

study

the

early

years

of

suspension

bridge

development we see at least as many failures as successes, one can wonder why engineers were persisted with suspension bridges at all, after these so many failures it would have been an entirely reasonable to just give up and try something else, the answer is that suspension bridges represent extraordinary potential for greatness. Because of the structural efficiency of that cable the world longest span has been for a suspension bridge for over 150 years of the past 200 years. 2.4 Development of Cables and Anchorages: The history of modern suspension bridge begins started from America with the very unlucky pioneer in 1801 an American named James Finley built the first suspension bridge capable of carrying vehicular traffic – Jacob’s

8

Chapter 2

Historical aspects of suspension bridges development

creek bridge in western Pennsylvania . Finley was a justice of a peace not an engineer and there is no evidence that he had any technical training at all.

“Figure 2.2 - Jacob’s bridge, Pennsylvania”

All Finley suspension bridges use cables made of conventional iron chains, the bridges were apparently quite successful at least for a while. Several of them have been collapsed. The only suspension bridge Finley built and still survived for this day is a bridge over Merrimack river in Massachusetts with many

components

have

been

replaced

since

that

“Figure 2.3 - Finley’s river over Merrimack river in Massachusetts”

9

time.

Chapter 2

Historical aspects of suspension bridges development

Finley has lacked the expertise and experience to design enduring structures. And the concept of a chain suspension bridge quickly spread to Britain. Their engineers with more tradition of empirical design set about the task of making the idea work. The royal navy did many of experiments to determine if they could replace the rope rigging in their ships with newly designed iron chains. These experiments produce an invention called the (eyebar chain) which turned out to be far superior to traditional chains made of individually O ring shapes of iron chains. It is like the chain of the bicycle.

“Figure 2.4 - Eyebar chains were very effective structural elements because each link could be constructed of multiple parallel eye bars”

10

Chapter 2

Historical aspects of suspension bridges development

This system was structurally redundant; if one individual eyebar failed, the chain itself would not necessarily fail. And it was the characteristic that inspired British engineers to begin experiments with the eyebar chains as a structural element in suspension bridges.

“Figure 2.5 - Eyebar fail”

In 1817 a royal navy officer Samuel brown developed and patented a system

of

eyebar

chains

British

suspension

bridge

incorporated capable

of

that

system

carrying

into

the

vehicular

very

first

traffic,

the

Union Bridge Tweed River in New Waterford. With 430 foot span used six eyebar chains three on each side, stacked one on the top of the other with the suspenders connected at the links which join the pins together. This arrangement worked so well that it established the general pattern for British suspension bridge development for the next 50 years, incredibly the Union bridge still stands and still caries vehicular traffic today.

11

Chapter 2

Historical aspects of suspension bridges development

“Figure 2.6 - the Union Bridge Tweed River”

In 1818 a Scottish engineer named Thomas Telford was employed to build a bridge across the Menai strait in northwestern wales, in response Telford created the world longest span and enduring a monument to British empirical engineering the Menai bridge 579 foot span suspended from two massive limestone towers the main cables in this bridge are 16 rod iron eyebar chains each composed of over 900 individual eyebars

“Figure 2.7 – Telford’s Bridge”

12

Chapter 2

Historical aspects of suspension bridges development

Telford was a typical British engineer of this era. He disdained math and

scientific

theory

but

Telford

was

also

a

strong

believer

in

experimentation, he conducted extensive laboratory tests on chains that would be used in his Menai Bridge. And he designed structures that chains would never exceed one third of their ultimate strength.

“Figure 2.8 - , the British Telford and his Eyebar chain bridge”

Meanwhile, across the channel the French was trying to catch up. During the late eighteen then early nineteen centuries as American and British were developing that first generations of suspension bridges, the French were quite slow to adopt new structural technologies, the turmoil of the recent French revolution had disrupted industrial development and driven many engineers out of the country. Recognizing the need to catch up, in 1794 the French government founded (Ecole polytechnique), in among of the first generation of graduates was Cloud Navier. in the early 1820s Navier traveled to U.S. to study American development in suspension bridge design, in 1823 he presented the world’s first

theoretical

treatment

of

suspension

bridge

design.

It

tremendous interests in this new structural configuration throughout France.

13

stimulated

Chapter 2

Historical aspects of suspension bridges development

In1820s French engineer began experimenting with the use of (wire cables) rather than eyebar chains in suspension bridge. In 1823 a Swiss engineer Guillaume-Henri Dufor constructed the world’s first permanent wire-cable suspension bridge, in Dufor system, the cables were composed of hundreds of parallel wires each about one eighth inch in diameter bundled together. Now in theory, wire cables are far superior to eyebar chains because of the manufacturing process; the iron steel in a wire is actually a lot stronger than a thicker bar. And wire cables have significantly greater redundancy than eyebar chains because there are so many parallel elements, one or two or even a ten that would have to break would not compromise the strength of the cable. In practice the effectiveness of a wire cable depends entirely on two aspects of its construction: 1. The wires need to be arranged such that all carry approximately the same tension 2. The ends of the cable have to be suitably anchored at their ends. By 1820s, French engineers had become the world leaders in science-based design, they were in fact the masters of theory, the British exemplified by Thomas

Tulford

disdained

theory

and

took

ride

in

practical

empirical

approach to design, this immense gap between the two approaches was manifested in the development of suspension bridges, theoretically adopt French

engineers

advocated

the

theoretically

superior

wire

cable

configuration, while practically minded British engineers held to their robust time tested iron chains system, the stage was set for an epic contest. Now in France based on Dufor’s success and Navie newly developed design theories of suspension bridge, there was an explosion of a wire cable construction. between 1823 – 1850 over 500 wire-cable suspension bridge built.

14

Chapter 2

Historical aspects of suspension bridges development

In 1834 a French engineer named joseph Chaley built a wire cable bridge at Fribourg, Switzerland surpassed Tulford Menai bridge as the world’s longest, it was nearly 900 feet in length. In 1849, an American named Charles Ellet, educated in a French system surpassed Chaley’s record with 1010 foot wire cable span in West Virginia.

“Figure 2.9 - Wire-cable Bridge of Joseph Chaley”

“Figure 2.10 – Wire-cable of Charles Ellet”

15

Chapter 2

Historical aspects of suspension bridges development

At this point, the battle of the cable appeared to have turned decisively in favor of wire cables. The early French bridges were all built by fabricating the cables on the ground and then installing them on the bridge, a very difficult process could compromise the strength of the cable by stretching some of the individual strands to tightly while leaving other slacked. But in 1844 the American bridge pioneer John Roebling devised a far superior system for fabricating cables in place on the bridge. He won a contract to build his very first bridge, and in this project he developed and perfected his system for fabricating wire cables. Made of a one long individual cable goes between the two anchorages back and forth along the gap by means of a traveller, the traveller moves on a temporary constructing cable (haul rope). And repeats this process hundreds of times to create a bundle of wires called (strand).

“Figure 2.11 - This picture represents the actual system as was used by john Roebling and by his son Washington Roebling in the Brooklyn Bridge, 30 after it was first developed. Up on the top one can see the traveller attached to the haul rope carrying a loop of wire to the top of the tower”

16

Chapter 2

Historical aspects of suspension bridges development

In the Brooklyn bridge, each strand has 278 individual wires and 19 strands are then bundled together in a pattern to form one single main cable. John Roebling patented this system in1847 and it has been used with only minor modifications, on every major suspension bridge since then.

“Figure 2.12 - This picture presents a cut away of the cable of the golden gate bridge, showing it was fabricated using Roebling method. (27,572 wires)”

In 1850 a wire-cable suspension bridge in Angers, France, collapsed when one of its main cables torn away from its anchor. The configuration of the anchorage system of this bridge was the same as had been used on most French bridges built since 1831. In this system the end of the cables were spread to multiple strands like Roebling system, and then anchored inside a shaft in the bedrock and sealed with lime mortar for protection. The post collapse investigations showed that the mortar sealant that was supposed to protect the strands from the elements had cracked over time allowing water to

17

Chapter 2

Historical aspects of suspension bridges development

penetrate into the anchorage and covering the wires of the cables. Corrosion reduced the strength of these individual wires until, ultimately, the cable failed.

“Figure 2.13 - a wire-cable problem in suspension bridge in Angers, France”

18

Chapter 2

Historical aspects of suspension bridges development

And immediate inspections of all other bridges showed the same problem was occurring at most of them many have been rebuilt. This disaster ended the carriers of entire generation of French suspension bridge designers it also effectively stopped suspension bridge development in France for the next twenty years, meanwhile in the U.S. john Roebling had developed a fundamentally different anchorage system and it was already used at first bridges in the united states.

“Figure 2.14 - This an original drawings of john anchorage design it uses a series of massive rod iron eyebar chains one for each strand of the main cable”

These chains are anchored to the bottom of a deep pit which is then filled with an enough stone masonry to counter balance the large tension force of the strand cable.

19

Chapter 2

Historical aspects of suspension bridges development

The upper most link of each anchor chain is then attached to a strand shoe; each shoe holds all the wires belonging to one strand of the main cable.

“Figure 2.15 – Strands attached to a strand shoe”

“Figure 2.16 Strand shoe attached to the anchor chain”

20

Chapter 2

Historical aspects of suspension bridges development

John Roebling system succeeded when the French system failed because its underground elements are robust corrosion resistant eyebar chains rather than the fragile wire strands that were underground in the French system. The system that emerged from this fifty years development process was actually hybrid of the two competing alternatives. As a result of Roebling ingenuity; leadership in the field of suspension bridges design passed from France to the United States, that leadership came with the Roebling’s magnificent Brooklyn Bridge. 2.5 list of the longest spans of suspension bridges: The world's longest suspension bridges are listed according to the length of their main span (i.e. the length of suspended roadway between the bridge's towers). The length of main span is the most common method of comparing the sizes of suspension bridges, often correlating with the height of the towers and the engineering complexity involved in designing and constructing the bridge. Suspension bridges have the longest spans of any type of bridge. Cable-stayed bridges, the next longest design, are practical for spans up to around 1 km. Therefore the 15 longest bridges on this list are suspension bridges that are currently the 15 longest spans of all types of vehicular bridges.

21

Chapter 2

Historical aspects of suspension bridges development Table 2.1 the world longest spans of suspension bridges

#

NAME

country

Span m

year

1

Akashi Kaikyō Bridge

Japan

1,991

1998

2

Xihoumen Bridge

China

1,650

2009

3

Great Belt Bridge

Denmark

1,624

1998

4

Runyang Bridge

China

1,490

2005

5

Humber Bridge

England

1,410

1981

6

Jiangyin Bridge

China

1,385

1999

7

Tsing Ma Bridge

Hong Kong

1,377

1997

8

Verrazano-Narrows Bridge

NY. U.S.

1,298

1964

9

Golden Gate Bridge

C.A. U.S.

1,280

1937

10

Yangluo Bridge

China

1,280

2007

11

Högakustenbron (High Coast Bridge)

Sweden

1,210

1997

12

Mackinac Bridge

U.S.

1,158

1957

13

Huangpu Bridge

China

1,108

2008

14

Minami Bisan-Seto Bridge

Japan

1,100

1989

Turkey

1,090

1988

15

Fatih Sultan Mehmet (2nd Bosporus Bridge)

16

Balinghe Bridge

China

1,088

2009

17

Boğaziçi (First Bosporus Bridge)

Turkey

1,074

1973

18

George Washington Bridge

U.S.

1,067

1931

19

Third Kurushima-Kaikyo Bridge

Japan

1,030

1999

20

Second Kurushima-Kaikyo Bridge

Japan

1,020

1999

Note that world’s longest suspension bridges are externally anchored type; longest self-anchored suspension bridge is 118th on the list of the world’s longest spans. Akashi Kaikyō Bridge is the world’s longest bridge since 1998 up to day. A Suspension

bridge

in

its

Preliminary

22

work

expected

to

break

this

Chapter 2

Historical aspects of suspension bridges development

record; Sunda Strait Bridge, Indonesia, This project has been approved by the Indonesian government. If completed, it will not only be the world's longest suspension bridge (26 km), but will also have a main span of about 3,000 m (9,800 ft), roughly fifty percent longer than the current record.

“Figure 2.17 - Akashi Kaikyo Bridge, Japan”

2.6 14th of July suspension bridge – Baghdad, Iraq Self-anchored

suspension

bridge

across

the

Tigris

River

designed

by

Steinman, Boynton and London in New York, U.S.A. implemented by Belgian company. It is the first suspension bridge in Iraq and Middle East joining (KarradatMariam) with (Zowiya/Karrada), it is one of the unique bridges built. Opened in 1964.

23

Chapter 2

Historical aspects of suspension bridges development

The bridge acquired its value when official government buildings constructed beside it like Al-Khuld Hall, ministry of transportation, and the Olympic swimming pool. It exposed to massive destruction in 1991, and it was built again with Iraqi efforts and opened again in 1995.

“Figure 2.18 – 14th July Bridge, A view from Tigris River”

24

CHAPTER THREE Analysis of Suspension Bridge

3.1 Bridge Loading. 3.2 Cable static analysis. 3.3 Fabrication and types of cables. 3.4 Deck – Stiffening girder. 3.5 Towers – Cable Anchors.

Chapter 3

Analysis of Suspension Bridge

CHAPTER 3 ANALYSIS OF SUSPENSION BRIDGE 3.1 Bridge Loading: When building a bridge, engineers need to consider the load types the bridge will encounter over a long period of time. These factors determine what material should be used to build the bridge as well as the type of structure that will best withstand the loads. Types of Loading: 3.1.1 Dead load: The dead load of a bridge is the bridge itself and all the parts and materials that are used in the construction of the bridge. This includes the foundation, beams, cement, cables, surfacing, guard rail, hand rail, power poles, and water lines. It is necessary to make a preliminary estimation for the dead load and perform the design based on the estimated value. The weight of the structure can then be calculated and then compared with the previously estimated weight. It might be necessary to make more cycles of design on new D.L. 3.1.2 Live Load: 3.1.2.1 AASHTO loading: a) Truck loading: Consist of H-10, H-15, H-20, H-25, HS-15, HS-20, and HS-25. • H-10 and H-15 are used for the design of lightly loaded state roads. • H-20 and HS-20 used for national and interstate highway system.

26

Chapter 3

Analysis of Suspension Bridge

“Figure 3.1 – AASHTO truck loading”

b) Uniform Loading: The design of live load consists of basic H-trucks preceded and followed by train of trucks weighing three quarter as much as the basic truck.

27

Chapter 3

Analysis of Suspension Bridge

Note: for the HS truck only one truck is to be used per span. For longer spans the equivalent loading produces greater stresses than the single truck. Equivalent Uniform Lane loading: • Composed of Uniform Distributed Load (UDL) as (KN/m) of lane width 10 ft. (3.05 m) and Knife Edge Load (KEL). • Only one concentrated load is used in a simply supported span or for a positive moment in continuous spans. • Two concentrated loads are used for negative moment. • The uniformly distributed load can be divided into segments, when applied to continuous spans.

Table 3.1 - Equivalent loading for trucks Truck

KEL (KN)

UDL (KN/m)

Moment

shear

HS20

9.3

80

116

H20

9.3

80

116

HS15

7.0

60

87

H15

7.0

60

87

3.1.2.2 British Standard (BS5400 Part 2): Two types of loading must be considered: 1. HA

–

loading:

The Design Manual for Roads and Bridges says that Type HA loading is the normal design loading for Great Britain and adequately covers the effects of all permitted normal vehicles other than those used for abnormal loads. Normal vehicles are governed by the Road Vehicles (Authorized Weight) Regulations 1998, referred to as the AW Vehicles and cover vehicles up to 44 ton gross vehicle weight.

28

Chapter 3

Analysis of Suspension Bridge

Loads from these AW vehicles are represented by a uniformly distributed load (UDL) and a Knife Edge Load (KEL) combined. • UDL: the uniformly distributed load (UDL) shall be taken as 30 KN per linear meter of national lane for loaded length up to 30m. And for loaded length in excess of 30 m it shall be derived from the equation: 1 𝑊 = 151 × ( )0.475 𝐿

but not less than 9 KN/m where: L: loaded length in (m).

W: load per meter of lane in KN. • Nominal KEL: The KEL per national lane shall be taken as 120 KN/Lane. Placed on position to obtain higher moment or shear needed.

2. HB

–

loading:

the Design Manual for Roads and Bridges says that Type HB loading requirements derive from the nature of exceptional industrial loads (e.g. electrical transformers, generators, pressure vessels, etc.) likely to

use

the

roads

in

the

area.

The vehicle load is represented by a four axle vehicle with four wheels equally spaced on each axle. The load on each axle is defined by a number of units which is dependent on the class of road. Motorways and trunk roads require 45 units, Principal roads require 37.5 units and other public roads require 30 units. One unit of HB is equal to 10kN per axle.

29

Chapter 3

Analysis of Suspension Bridge

3.2 Cable Static Analysis: Suspension bridge consists of two cables, which are stretched over the span to be bridged. Each cable, passing over two towers, anchored by backstays to a firm foundation, as shown in the figure.

“Figure 3.2 – Geometry of suspension bridge”

As the cables is flexible throughout, therefore it cannot resist any moment and can adopt any shape under the loads; that’s why the bending moment at every point of the cable is taken as zero.

The roadway is suspended from the cables by means of “Hangers” or “Suspenders”. Since the hangers are large in number, therefore the load transmitted by hangers, is taken as uniformly distributed load.

The central sag or dip of the cable generally varies from 1/10 to 1/15 of the span.

30

Chapter 3

Analysis of Suspension Bridge

3.2.1 Equation of the cable: By geometry:

“Figure 3.3 – Cable geometry”

Consider cable (ACB) as shown in figure (3.3) supported at A and B. let C be the lowest point of the cable as shown in the figure. Let: l = span of the cable Yc = Central dip of the cable The shape of the cable when the load is uniformly distributed is parabola. The equation of the parabola is:

When 𝑋 =

𝑙

2

, 𝑌 = 𝑌𝑐

𝑌 = 𝑘𝑋 2

Substituting these values of X and Y in the equation yields:

Now sub. Value of (K) in the eq.:

𝑘= 𝑌=

4𝑌𝐶 𝑙2

4𝑌𝐶 2 𝑋 𝑙2

This is the required eq. for Y at any X from A to B.

31

Chapter 3

Analysis of Suspension Bridge

3.2.2Horizontal Thrust on the Cable & Second Equation (Force-related):

“Figure 3.4 – Horizontal thrust on cable”

Consider a cable (ACB) as shown in figure (3.4) supported at A and B and carrying

a

uniformly

distributed

load

as

shown

in

the

figure.

Let C be the lowest point of the cable. A little consideration will show, that as a result of loading, the two supports at A and B will tend to come nearer to each other. Since these two supports are in equilibrium, therefore an outward force must act, on both the supports to keep them in balance. As the cables is supporting vertical load only, therefore the horizontal thrust at A must be equal to the horizontal thrust at B.

“Figure 3.5 – Forces on cable”

1. Horizontal pull (T o ). 2. Downward load (wx). 3. Tension in the cable at D (T).

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Chapter 3

Analysis of Suspension Bridge

We find that the magnitude W of the total load carried by the portion of the cable extending from C to the point D of coordinates x and y is W = wx Since all forces of this portion is in equilibrium,

𝑇 = �𝑇𝑜 2 + 𝑊 2

𝑡𝑎𝑛𝜃 =

𝑤𝑑 𝑇𝑜

“Figure 3.6 – Cable equilibrium”

Moreover, the distance from D to the line of action of the resultant W is equal to half the horizontal distance from C to D. Taking the summing moments about D equals zero then one can obtain: 𝑑 𝑤𝑑 − 𝑇𝑜 𝑑 = 0 � 𝑀𝐷 = 0 2 𝑤𝑑 2 𝑇𝑜 = 2𝑑

To find the value of the horizontal tension 𝑇𝑜 , applying any boundary condition, such as, at X = 𝑙 / 2, Y = Y C Therefore:

𝑙 2 𝑤� � 𝑤𝑙 2 2 = 𝑇𝑜 = 2𝑌𝑐 8𝑌𝑐

To is the horizontal thrust on the cable.

Consequently, equations above are used to know the value of the tension force and its direction at any point on the cable at X distance from the origin C.

33

Chapter 3

Analysis of Suspension Bridge

On the other hand: � 𝐹𝑥 = 0

𝑇 sin 𝜃 = 𝑇𝑜

the horizontal thrust is constant on all points of the cable. Since 𝑇𝑜 is a constant quantity, therefore the above equation 𝑇𝑜 =

𝑤𝑋 2 2𝑌

is that of a

parabola. It is thus obvious, that the cable hangs in the form of a parabola. 𝑤𝑑 2 𝑌= 2𝑇𝑜 Difference between two equations of the cable: 1. First eq. is related to a geometric shape, not related to forces and used only for analysis. 2. Second eq. is a force related, one can calculate the length of each hanger at specific equal distances (X) which is used at the design stage.

3.2.3 Maximum tension in the cable:

a. When supported at the same level. b. When supported at different level.

To prove that the maximum tension occurs at the supports of the cable: 𝑇 = �𝑇𝑜 2 + 𝑊 2

𝑇𝑚𝑎𝑥 = �𝑐𝑜𝑛𝑑𝑡𝑎𝑛𝑡 2 + (𝑐𝑜𝑛𝑑𝑡𝑎𝑛𝑡 × 𝑋𝑚𝑎𝑥 )2 𝑙

So T max occurs at the X max which is (support of the cable). 2

34

Chapter 3

Analysis of Suspension Bridge

a) Maximum tension when cable supported at the same level:

Since T max is at the supports A and B. So the tension at the supports will be:

Note:

𝑇𝑚𝑎𝑥 =

�𝑅 2

+ 𝑇𝑜

2

2

𝑙2 𝑤𝑙 2 𝑤𝑙 2 𝑤𝑙 ��1 + = �� � + � � = � 2 2 8𝑌𝐶 16𝑌𝐶 2

If the cable is subjected to point loads, with or without uniformly distributed load, then the magnitude of tension in the cable will be different at two supports. In such case, first of all find out the two vertical

reactions

V A and

V B considering

the

cable

as

a

simply

supported beam of length 𝑙. b) Maximum tension when cable supported at different levels:

Main purpose here is to find the coordinates of the lowest point.

“Figure 3.7 – Cable supported at different levels”

In order to locate position of the lowest point if the cable C, let us imagine the portion CB of the cable to be extended to CB 1 such that the new support B 1 is at the same level as that of A.

35

Chapter 3

Analysis of Suspension Bridge

Similarly, imagine the portion AC of the cable to be cut short to A 1 C such that the new support A 1 is at the same level as that of B. from the geometry of the figure, we find that the cable ACB 1 has a span of 2𝑙1 and a central dip of YC.

From

figure

(3.7),

now

in

the

cable

ACB 1

the

horizontal

thrust,

𝑤𝑙 2 𝑤(2𝑙1 )2 = 𝑇𝑜 = 8𝑌𝐶 8(𝑌𝐶 + 𝑑) Similarly in the cable A 1 CB the horizontal thrust, 𝑤𝑙 2 𝑤(2𝑙2 )2 𝑇𝑜 = = 8𝑌𝐶 8𝑌𝐶 Since the two horizontal thrusts are equal, therefore equating the both equations, 𝑤(2𝑙2 )2 𝑤(2𝑙1 )2 = 8(𝑌𝐶 + 𝑑) 8𝑌𝐶 𝑙2 2 𝑙1 2 = 𝑌𝐶 + 𝑑 𝑌𝐶

𝑙1 𝑌𝐶 + 𝑑 = � ≫≫≫ 1 𝑌𝐶 𝑙2 𝑙1 + 𝑙2 = 𝑙 From 1 and 2, it is possible to find 𝑙1 and 𝑙2 .

36

≫≫≫ 2

Chapter 3

Analysis of Suspension Bridge 𝑤𝑑 2 𝑤𝑙2 2 𝑤𝑙1 2 𝑇𝑜 = = = 2𝑌 2𝑌𝐶 2(𝑌𝑐 + 𝑑) 𝑅𝐴 = 𝑤𝑙1

𝑅𝐵 = 𝑤𝑙2 𝑇𝐴 = �𝑅𝐴 2 + 𝑇𝑜 2

𝑇𝐵 = �𝑅𝐵 2 + 𝑇𝑜 2 Since the value of R A (the support carrying more of the load) is more than R B therefore the maximum tension in the cable will be at A.

3.2.4 Length of the cable: It means the actual length of the cable required between the two supports A and B, when it is loaded with a uniformly distributed load, and hangs in the form of a parabola. Here we shall discuss the following two cases: a. When supported at the same levels b. When supported at different levels

a) Length of cables when supported at the same level:

“Figure 3.8 – Cable supported at the same level”

37

Chapter 3

Analysis of Suspension Bridge

Equation of the cable: 𝑤𝑋 2 𝑌= 2𝑇𝑜

Differentiating this equation with respect to X,

𝑑𝑑 2𝑤𝑑 𝑤𝑑 = = 𝑑𝑑 2𝑇𝑜 𝑇𝑜 Now consider a small length 𝑑𝑑 of the cable as shown in figure (3.9): ***REPAIRED***

𝑑𝑑 = �𝑑𝑑 2 + 𝑑𝑑 2 = 𝑑𝑑 ��1 +

𝑑𝑑

𝑑𝑑

𝑑𝑑

𝑑𝑑 2 � 𝑑𝑑

“Figure 3.9”

Substituting the value of

𝑑𝑦 𝑑𝑥

𝑤𝑑 2 � 𝑇𝑜

𝑑𝑑 = 𝑑𝑑 �1 + �

Now expanding the term inside the square root, by binomial theorem, 1/2

𝑤𝑑 2 𝑤 2𝑑2 𝑤 2𝑑2 �1 + � � = �1 + = �1 + � 𝑇𝑜 𝑇𝑜 2 𝑇𝑜 2

(Neglecting the higher powers of

1 𝑤 2𝑑2 +⋯ = 1+ × 2 𝑇𝑜 2 𝑤2𝑥2 𝑇𝑜 2

)

1 𝑤 2𝑑2 � ∴ 𝑑𝑑 = 𝑑𝑑 �1 + × 2 𝑇𝑜 2

Now integrating the above equation between the limits 𝑑 = 0 and 𝑑 =

38

𝑙

2

Chapter 3

Analysis of Suspension Bridge 𝑙 2

1 𝑤 2𝑑2 𝑑 = � �1 + × � 𝑑𝑑 2 𝑇𝑜 2 0 𝑙 𝑤 2 𝑙2 = + ∙ 2 2𝑇𝑜 2 24 𝑤 2 𝑙3 𝑙 = + 2 48𝑇𝑜 2

A little consideration will show that since the limits of integration where from 0 to 𝑙/2 (taking C as origin) therefore the above equation gives the length of half of the cable.

∴ Total length of the cable, Now substituting the value of 𝑇𝑜 =

𝑙 𝑤 2 𝑙3 𝐿= + 2 48𝑇𝑜 2

𝑤𝑙 2 8𝑌𝑐

in the above equation,

1 𝑤 2 𝑙3 × 𝐿=𝑙+ 2 24 𝑤𝑙 2 � � 8𝑌𝑐 8𝑌𝑐 2 =𝑙+ 3𝑙

b) Length of the cable, when supported at different levels From figure (3.7): • Length of the cable ACB 1 8(𝑌𝑐 + 𝑑)2 𝐿1 = 2𝑙1 + 3 × 2𝑙1 • Length of the cable A 1 CB

8(𝑌𝑐 + 𝑑)2 = 2𝑙1 + 6𝑙1

39

Chapter 3

Analysis of Suspension Bridge 8(𝑌𝑐 )2 𝐿2 = 2𝑙2 + 3 × 2𝑙2 8(𝑌𝑐 )2 = 2𝑙2 + 6𝑙2

Now the actual length of the cable ACB,

1 8(𝑌𝑐 + 𝑑)2 8𝑌𝑐 2 𝐿1 + 𝐿2 = �2𝑙1 + + 2𝑙2 + � 𝐿= 2 2 6𝑙1 6𝑙2 2(𝑌𝑐 + 𝑑)2 2𝑌𝑐 2 + =𝑙+ 3𝑙1 3𝑙2 3.2.5 The effect on the cable due to change in temperature: We know that the length of the cable must increase with the rise in temperature. Since the two supports of the cable cannot move under any displacement, therefore the downward movement of the point will increase the central dip Y c of the cable. Length of the cable: 8𝑌𝑐 2 𝐿= 𝑙+ 3𝑙

Differentiating the above equation with respect to Y c 𝑑𝐿 16𝑌𝑐 = 𝑑𝑌𝑐 3𝑙 𝑑𝐿 = 𝑑𝑌𝑐 =

16𝑌𝑐 𝑑𝑌𝑐 3𝑙 3𝑙 𝑑𝐿 16𝑌𝑐

40

… 𝑖

Chapter 3

Analysis of Suspension Bridge

As a result of rise in the temperature, increase in length of the cable, 8𝑌𝑐 2 � 𝛼𝑡 𝑑𝐿 = 𝐿 𝛼 𝑡 = �𝑙 + 3𝑙

Where 𝛼 = coefficient of linear expansion for the cable material. (Neglecting

∝𝑡8𝑌𝑐 2 3𝑙

as compared to 𝐿 𝛼 𝑡)

=𝑙𝛼𝑡

Substituting this value of 𝑑𝐿 in equation i

3𝑙 3𝑙2 𝑑𝑌𝑐 = ×𝑙𝛼𝑡 = 𝛼𝑡 16𝑌𝑐 16𝑌𝑐

We know that the horizontal thrust, 𝑤𝑙 2 𝑇𝑜 = 8𝑌𝑐

∴ 𝑇𝑜 ∝

1 𝑌𝑐

𝑑𝑌𝑐 𝑑𝑇𝑜 =− 𝑇𝑜 𝑌𝑐

We also know that the stress in the cable: 𝑓 ∝ 𝑇𝑜

𝑑𝑓 𝑑𝑇𝑜 𝑑𝑌𝑐 = =− 𝑓 𝑇𝑜 𝑌𝑐

3𝑙 2 𝑑𝑇𝑜 =− 𝛼𝑡 𝑇𝑜 16𝑌𝑐 2 Minus sign indicates that when the temperature rises: 1. The central dip increases. 2. Horizontal thrust decreases.

41

Chapter 3

Analysis of Suspension Bridge

3.2.7 Accuracy: 1. Since the weight of the cables is small compared to the weight of the road way so the shape of the of the suspension bridge cables is always parabolic. 2. Mathematically, the difference between the function of the parabola (X2) and the function of the catenary cosh(X) is very little and can be neglected.

“Figure 3.10 – Difference between catenary and parabola”

42

Chapter 3

Analysis of Suspension Bridge

3.3 Types and Fabrication of cables:

The basic element for all cables to be found in modern cable supported bridges is the steel wire characterized by a considerably larger tensile strength than that of ordinary structural steel. In most cases, the steel wire is of cylindrical shape with a diameter between 3 and 7 mm. Typically, a wire with a diameter of (5–5.5) mm is used in the main cables of suspension bridges whereas wires with diameters up to 7mm are used for parallel wire strands in cable stayed bridges. The steel material for the wires is manufactured by the Siemens–Martin process or as electro steel, with a chemical composition characterized by a higher carbon content than allowed for structural steel. Table below shows a comparison between different properties of cable steel and structural steel. In the chemical composition, the high carbon content of cable steel, about four times that of structural steel, is of special significance:

1. It appears that the strength of the cable steel is approximately four times that of mild structural steel and twice that of high-strength structural steel. 2. This increased strength is, however, paid for by a noticeable decrease of the ductility as the strain at breaking is only about one-fifth of that found for structural steel. 3. This high content of carbon makes the cable steel unsuited for welding.

43

Chapter 3

Analysis of Suspension Bridge

“Table 3.2 – Comparison between cable steel and structural steel”

3.3.1 Basic Types of Cables Although the single wire forms the basic element for cables, several wires are often shop-assembled to form pre-fabricated strands, subsequently used at the site as basic elements for the construction of the final cable. The simplest strand to be found within cable supported bridges is the sevenwire strand as used extensively in tendons for pre-stressed concrete. For cables, the strand is normally made from seven 5mmwires giving the strand a nominal diameter of 15mm.

“Figure 3.11 – Seven-wire strand”

The most common seven-wire strands comprise wires with tensile strengths between 1770 and 1860 MPa. The seven-wire strand consists of a single straight core wire surrounded by a single layer of six wires, all with the same direction of helix.

44

Chapter 3

Analysis of Suspension Bridge

3.4 Deck – Stiffening Girder: The deck is the structural element subjected to the major part of the external load on a cable supported bridge. This is because the total traffic load is applied directly to the deck, and in most cases both the dead load and the wind area are larger for the deck than for the cable system. Immediately the deck must be able to transfer the load locally whereas it will receive assistance from the cable system in the global transmission of the (vertical) load to the supporting points at the main piers. Immediately the deck must be able to transfer the load locally whereas it will receive strong decisive assistance from the cable system in the global transmission of the (vertical) load to the supporting points at the main piers. This feature is illustrated in Figure below showing at the top a typical dead load moment diagram for a continuous three span girder bridge, and at the bottom a possible dead load moment diagram for a three-span cable stayed bridge. It is seen that, even in the case of only four cable supported points in the main span the dead load moments are substantially reduced.

“Figure 3.12”

45

Chapter 3

Analysis of Suspension Bridge

3.4.1 Flexural stiffness in the vertical direction:

The participation of the deck in the transfer of vertical loads depends on the general arrangement of the total structural system. In principle, the action of the deck can be divided into:

1. To carry the load locally between cable anchor points. 2. To distribute concentrated forces. 3. To assist the cable system in carrying the load globally.

As the deck is subjected directly to the traffic load and its own weight, but only supported by the cable system at the cable anchor points, the deck must as a minimum be able to span between these points. The deck’s ability to distribute concentrated forces (Action 2) will be utilized primarily in bridges with a large number of cable supported points as found in suspension bridges cable system. Distributing a concentrated force between a number of cables, as indicated in Figure will reduce the maximum design force in the cables and give a more even curvature of the bridge deck at the concentrated force.

“Figure 3.13”

46

Chapter 3

Analysis of Suspension Bridge

3.4.2 Torsional stiffness

The eccentricity of the traffic load is totally dependent on the: 1. The cable system of the suspension bridge. 2. Torsional stiffness of the deck: a torsional stiffness of the deck is not essential but it might lead to a favorable distribution of forces between the two cable planes. The following two figures will demonstrates the relation in torsional stiffness between cable system and deck.

“Figure 3.14 - A system with two cable planes and a deck without torsional rigidity”

In System above, the eccentric force P can be distributed to the two cable planes according to the lever arm principle, and in that case no torsional moments will be induced in the deck.

47

Chapter 3

Analysis of Suspension Bridge

“Figure 3.15 - A system with two cable planes as well as a torsionally stiff deck”

In System above the torsional moment Pe is taken partly by the deck and partly by the cable system. As indicated, this reduces the difference between the two forces acting on the cable systems (compared to System before). Therefore, the torsional stiffness of the deck results in a more even force distribution between the two cable systems, and in a reduction of the twist angle. 3.4.3 Supporting Condition:

The interaction between the deck, the cable system and the pylons in the transmission of vertical and horizontal loads is decisively influenced by the choice of the supporting conditions for the deck. In the conventional three-span suspension bridge the deck often consists of three individual girders with simple supports at the pylons and the end piers (anchor blocks), as indicated in the figure below.

48

Chapter 3

Analysis of Suspension Bridge

“Figure 3.16”

Generally, the end pier supports will be longitudinally fixed whereas all other supports are made longitudinally movable, so that all expansion will take place in the two joints at the pylons. The supporting conditions shown in Figure are especially favorable for the deformations

under

temperature

change

as

the

largest

longitudinal

displacements of the deck will occur in the regions with the longest hangers. The change of inclination of the hangers will therefore be modest. In the dead load condition the bearings under the deck will be subjected to small forces as almost all dead load is carried by the cable system. With movable bearings at both ends, the deck of the main span will be supported longitudinally only by the cable system. Therefore, in conventional suspension

bridges

with

vertical

hangers

throughout

the

main

span

a

longitudinal displacement of the deck is required to ensure the transmission of a longitudinal force by inclination of the shorter hangers, as illustrated below:

“Figure 3.17 - Inclination of the short hangers at midspan to transfer a longitudinal force from the deck to the main cable”

49

Chapter 3

Analysis of Suspension Bridge

In bridges with moderate longitudinal forces, e.g. braking forces on road bridges, the required longitudinal displacement will be small, On the other hand, in bridges with large longitudinal forces a further restraint of the main span deck might be desirable. Such a restraint could be accomplished in the following ways:

1. By applying a fixed support at one of the pylons. 2. By connecting the deck and the main cable through a central clamp at midspan. 3. By installing shock absorbers at the pylons, allowing slow thermal movements but excluding movements from short-term loading such as braking forces.

A continuous deck can be applied in an earth anchored suspension bridge. Here the main advantage to be gained is that the large angular changes occurring

at

the

pylons

under

certain

traffic

load

conditions

will

be

eliminated. This might be of special importance in bridges carrying a train load. On the other hand, a suspension bridge with a continuous deck will have large negative moments induced in the deck at the supports on the pylons. This might result in stresses of such a magnitude that high tensile steels will be required for the deck sections near the pylons. In suspension bridges and cable stayed bridges with multi-cable systems where the deck is almost continuously supported by the cable system from one end to the other, it might be possible to omit the vertical supports of the deck at the pylons, as shown in Figure (3.18).

50

Chapter 3

Analysis of Suspension Bridge

“Figure 3.18 - Cable supported bridge with the deck supported vertically on the end piers only, but laterally at the pylons as well as on the end piers”

This will lead to a noticeable reduction of the bending moments in the deck at the pylons. For a major suspension bridge the system illustrated in Figure above was used for the first time in the Storebælt East Bridge. Here the lack of vertical deck support at the pylons is dearly indicated by omitting the traditional cross beam between the pylon legs beneath the deck.

“Figure 3.19 - Pylon of the Storebælt East Bridge without a cross beam below the deck”

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Chapter 3

Analysis of Suspension Bridge

In the lateral direction it will often be required to have bearings both at the end piers and at the pylons, as indicated on the plan of last Figure. This is due to the fact that the cable system in many cases does not render a very efficient lateral support to the deck. The lateral support of the deck at the-pylons can be accomplished by applying vertical sliding bearings between the deck and the inner faces of the pylon legs.

“Figure 3.20 - Connection between the deck and the pylon through vertical sliding bearings for transmission of lateral forces”

3.5 Tower – Cable anchors The suspension bridge is supported on two towers on both of its sides. The cable, after passing over the supporting tower, is anchored down into a huge mass of concrete. The following two arrangements of passing the cable over the supporting towers are important from the subject point of view: 3.5.1 Guide pulley support for suspension cable: • Tension equal on both sides of the cable. • Moment occurs on tower 3.5.2 Roller support for suspension cable: • Horizontal force equal on both side of cable. • No moment occurs – moment released.

52

CHAPTER FOUR Case Study – 14th of July Suspension Bridge Using Computer Program (CSi Bridge) 4.1 Analysis Program – CSi Bridge. 4.2 Geometry of the Bridge. 4.3 Steel types used. 4.4 Structural properties of the components of suspension bridge. 4.5 Loading Cases. 4.6 Analysis Results.

Chapter 4

Case Study

CHAPTER 4 CASE STUDY - 14TH JULY In this chapter, general analysis is performed to the (14th July) suspension bridge as a case study with different loadings to study the behavior of the bridge under these loadings. I would like to note that I have made some modifications in different parts of the suspension bridge to make the analysis process easier. 4.1 Analysis Program – CSiBridge CSiBridge program is a modeling, analysis and design program for bridge structures that have been integrated into CSiBridge to perform the maximum benefit from the computerized engineering tools. This program is a development version of SAP2000. The program has a facility in which the geometrical properties of the suspension bridge can be entered directly. The bridge model is generated directly saving in time and effort, In contrary to other programs like STAAD Pro which took a lot of time and effort to construct the main parts of the bridge.

54

Chapter 4

Case Study

4.2 Geometry of the Bridge: The 14th of July suspension bridge has the geometrical properties shown in table (4.1). Table 4.1 – Bridge geometry Total span (m)

336

Center span length (m)

168

Side span length (m)

84

Tower height (m)

25

Length of the tower over deck (m) Deck width (m)

23.308 15.9

Carriage way width (m)

14

Number of lanes

4

Cable sag at center span (m)

4

Number of suspenders in each side

45

Suspender spacing (m)

7

Length of the cable (m)

380.7

The simple shape of the bridge is shown in figure (4.1).

“Figure 4.1 – general view”

55

Chapter 4

Case Study

4.3 Steel types used: 1. Girders, stringer, floor beams and towers have the properties shown in table (4-2). Table 4-2 Weight per unit volume KN/m3

76.8

Modulus of elasticity( E) KN/m2

2 x 108

Poisson’s ratio U

0.28

Shear modulus (G) KN/m2

11.7 x 108

Yield stress (F y ) MPa

355

Effective yield stress (F ye ) MPa

213

Tensile stress (F u ) MPa

510

Effective tensile stress( F ue ) MPa

306

2. St-37 Cables and Suspenders: Table 4-3 Weight per unit volume KN/m3

59.94

Modulus of elasticity (E) KN/m2

1.655 x 108

Poisson’s ratio (U)

0.28

Tensile stress (F u ) MPa

1700

Effective tensile stress( F ue ) MPa

1020

3. Concrete material: deck surface Table 4-4 Fc’ MPa

25

Weight per unit volume KN/m3

25

56

Chapter 4

Case Study

4.4 Structural properties of the components of suspension bridge: The floor beam system of the deck is detailed in figure (4.2) and summarized in table (4.5).

“Figure 4.2 – Deck cross section”

Table 4-5 Deck floor beams, stringers and surface thickness Number of floor beams

49

Number of stringers

7

Spacing between stringers (m)

2.15

Concrete surface thickness (mm)

20

57

Chapter 4

Case Study

Cross sections: The geometrical and mechanical properties of the bridge components were entered in dialog input boxes of the program as shown in figures (4.3) , (4.4) and (4.5). All dimensions in (KN and m). 1. Girder:

“Figure 4.3 – Girder cross section” 2. Floor Beam – Stringer:

“Figure 4.4 - Floor beam and stringer cross sections”

58

Chapter 4

Case Study

3. Tower

“Figure 4.5 – Tower cross section” The properties of the main cable and suspenders were shown in tables (4.6) and (4.7) respectively. Table 4-6 Main Cable Properties Diameter

34 cm

Cable area

907.92cm2

Table 4-7 Suspender Properties Diameter

76 mm

Suspender area

45.8 cm2

4.5 Loading Cases: Bridge is subjected to different loading cases to measure a certain parameters in each case 1. Dead load: a. Steel Frames and Cables. b. Concrete of the deck and asphalt layer. c. Accessories like hand rail, Guard rail and light poles.

59

Chapter 4

Case Study

2. Positive moment: Truck HS-20

KEL

UDL: 9.3 KN/m

UDL

KEL: 80 KN

“Figure 4.6 - Positive moment loading” 3. Negative moment: Truck HS-20 UDL: 9.3 KN/m KEL: 80 KN

“Figure 4.7 - Negative moment loading” 4. General Distribution: UDL: 10.1827 KN/m KEL: 120.13 KN

“Figure 4.8 - General distribution loading”

60

Chapter 4

Case Study

5. Maximum Shear: UDL: 9.3 KN/m KEL: 116 KN

“Figure 4.9 Maximum shear loading” The ASD method suggested by AISC manual were adopted in analysis of the whole bridge. 1.6 Result of analysis: 1.6.1 Cable analysis: The result of analysis under the effect of (general distribution) loading case was summarized in figure (4.10) and table (4.8).

“Figure 4.10 – Cable axial force diagram”

Table (4-8) indicates the element forces of cable from mid span to the anchorage.

61

Chapter 4

Case Study

TABLE 4-8 : Element Forces - Frames Frame Station P Text m KN 168 0 21308.123 168 3.5006 21308.475 168 7.0012 21308.828 175 0 21634.828 175 3.50539 21635.886 175 7.01079 21636.944 182 0 22181.474 182 3.51496 22183.237 182 7.02992 22185 189 0 22810.781 189 3.52926 22813.249 189 7.05853 22815.717 196 0 23424.843 196 3.54824 23428.016 196 7.09649 23431.19 203 0 23980.631 203 3.57183 23984.51 203 7.14366 23988.388 210 0 24472.782 210 3.59992 24477.365 210 7.19985 24481.949 217 0 24912.913 217 3.63243 24918.202 217 7.26486 24923.491 224 0 25317.457 224 3.66922 25323.45 224 7.33845 25329.444 231 0 25698.737 231 3.71018 25705.436 231 7.42037 25712.135 238 0 26079.753 238 3.75517 26087.157 238 7.51034 26094.561 245 0 26420.935 245 3.80404 26429.045 245 7.60808 26437.154 250 0 27537.847 250 3.96419 27527.718 250 7.92838 27517.588

62

Chapter 4 257 257 257 264 264 264 271 271 271 278 278 278 285 285 285 292 292 292 299 299 299 306 306 306 313 313 313 320 320 320 327 327 327

0 3.89082 7.78163 0 3.82289 7.64577 0 3.7607 7.5214 0 3.70455 7.4091 0 3.65471 7.30942 0 3.61144 7.22289 0 3.57499 7.14997 0 3.54555 7.0911 0 3.52331 7.04663 0 3.50841 7.01682 0 3.50094 7.00187

Case Study 27061.503 27052.255 27043.006 26605.882 26597.514 26589.146 26186.181 26178.694 26171.207 25787.802 25781.196 25774.589 25389.085 25383.359 25377.634 24932.629 24927.785 24922.94 24269.001 24265.037 24261.073 22978.632 22975.549 22972.466 19814.939 19812.737 19810.535 11276.25 11274.929 11273.607 2070.379 2069.939 2069.498

Results: 1. Maximum cable tension = 27537.847 KN 2. Horizontal tension = 21308.123 KN

63

Chapter 4

Case Study

3. It is observed that the last three cable segments (327, 320, and 313) have low tension forces due to the fact that the cable is embedded in the deck girder (selfanchored) as shown in figure (4-11).

“Figure 4.11 - cable embedment in deck” A sample of the program output of the problem can be seen in the following computer sheet.

64

Chapter 4

Case Study

4.6.2 Tower analysis: Loading case: General Distribution. The axial force distribution in the tower can be shown in figure (4.12) and summarized in table (4.9)

“Figure 4.12 – Axial force” Neither bending moment nor shear force found in the tower as shown in figure (4.13) and (4.14)

“Figure 4.13 – Moment in tower”

66

Chapter 4

Case Study

“Figure 4.14 – Shear in tower” TABLE 4-9 : Element Forces - Frames Frame Station P Text m KN 338 0 -23911.549 338 11.654 -23676.656 338 23.308 -23441.764

•

V2 KN

V3 KN 0 0 0

0 0 0

T KN-m 0 0 0

M2 KN-m

M3 KN-m 0 0 0

0 0 0

Max axial force = 23441.8 KN

From these figures and tables, the following can be concluded: 1. The max axial force in the tower is recorded to be 23441.8 KN. 2. Sudden change in axial force occurred near the deck supporting, the extra force comes from the deck which is not carried by the cable system. 3. Bending moment, shear force and torques are vanished because the main cable sits on a saddle, which is supported on rollers.

67

Chapter 4

Case Study

4.6.3 Deck Analysis: 1. Positive moment : Loading case : POSITIVE MOMENT

“Figure 4.15 – Positive moment about horizontal axis” • Max positive moment = 401.2 KN.m • Max negative moment = 456.2 KN.m

“Figure 4.16 – Sections adequacy for positive moment”

69

Chapter 4

Case Study

1. Negative moment: Loading case : NEGATIVE MOMENT

“Figure 4.17 – Negative moment about horizontal axis” • Max positive moment = 379.8 KN.m • Max negative moment = 508 KN.m

“Figure 4.18 – Sections adequacy for negative moment”

71

Chapter 4

Case Study

1. Shear: Loading case : MAX SHEAR

“Figure 4.19 – Shear force” • Max shear force = 554.6

“Figure 4.20 Sections adequacy for shear”

73

Chapter 4

Case Study

Main Cable Suspender Tower Main Girder Positive Negative Shear

Table 4-10 Analysis Summary for Critical Sections Critical Axial Bending Axial Comp. Frame Tension Moment (KN) Number (KN) (KN.m) 250 27538 None -43 777.4 None None 338 None 23442 None 167 252 86

-

-

43795 41876 -

Shear Force (KN) 29.1 None None 2401

Table 4-11 Stresses State in Members Bridge Component

Main Cable

Tower

Girder

Girder

Girder

Critical Force Axial Tension (KN) Axial Comp. (KN) Positive Moment (KN.m) Negative Moment (KN.m) Shear (KN)

Critical Allowable Stress Frame Magnitude Capacity (MPa) Number

As a Ratio of Yield Stress

Status Check

250

27538

77171

302.6

0.178F u

O.K.

338

23442

45551

89

0.25F y

O.K.

167

43795

54485

148

0.42F y

O.K.

252

41876

54485

176

0.5F y

O.K.

86

2401

7260

26.96

0.08F y

O.K.

75

CSiBridge Steel Design

Project Job Number Engineer

AISC360-05/IBC2006 STEEL SECTION CHECK Units : KN, m, C

(Summary for Combo and Station)

Frame : 250 Length: 7.928 Loc : 0.000

X Mid: 87.500 Y Mid: -7.950 Z Mid: 21.447

Combo: general distributDesign Type: Brace Shape: Main Cable Frame Type: Special Moment Frame Class: Compact Princpl Rot: 0.000 degrees

Provision: ASD D/C Limit=0.950 AlphaPr/Py=0.285

Analysis: Direct Analysis 2nd Order: General 2nd Order AlphaPr/Pe=2.585 Tau_b=1.000

OmegaB=1.670 OmegaV=1.670

OmegaC=1.670 OmegaV-RI=1.500

OmegaTY=1.670 OmegaVT=1.670

OmegaTF=2.000

A=0.091 J=0.001 E=165500000.0 RLLF=1.000

I33=6.560E-04 I22=6.560E-04 fy=1700000.000 Fu=1700000.000

r33=0.085 r22=0.085 Ry=1.000

S33=0.004 S22=0.004 z33=0.007 z22=0.007

HSS Welding: ERW

Reduce HSS Thickness? No

Reduction: Tau-b Fixed EA factor=0.800 EI factor=0.800

STRESS CHECK FORCES & MOMENTS (Combo general distribution) Location Pr Mr33 Mr22 Vr2 0.000 27537.847 33.441 -82.853 15.675

Av3=0.068 Av2=0.068

Vr3 -10.488

Tr -1.978

PMM DEMAND/CAPACITY RATIO (H1.2,H1-1a) D/C Ratio: 0.369 = 0.357 + 0.004 + 0.011 = (Pr/Pc) + (8/9)(Mr33/Mc33) + (8/9)(Mr22/Mc22) AXIAL FORCE & BIAXIAL MOMENT DESIGN (H1.2,H1-1a) Factor L K1 K2 Major Bending 1.000 1.000 1.000 Minor Bending 1.000 1.000 1.000 LTB

Axial

Major Moment Minor Moment

Torsion SHEAR CHECK Major Shear Minor Shear

Lltb 1.000

Kltb 1.000

Cb 4.045

Pr Force 27537.847

Pnc/Omega Capacity 8951.525

Pnt/Omega Capacity 77170.553

Mr Moment 33.441 -82.853

Mn/Omega Capacity 6668.342 6668.342

Mn/Omega No LTB 6668.342

Tr Moment -1.978

Tn Capacity 7917.699

Tn/Omega Capacity 4741.137

Vr Force 15.675 10.488

Vn/Omega Capacity 27725.947 27725.947

Stress Ratio 0.001 0.000

BRACE MAXIMUM AXIAL LOADS Axial

P Comp 27537.847

B1 1.000 1.000

B2 1.000 1.000

Cm 1.000 1.000

Status Check OK OK

P Tens N/C

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CSiBridge Steel Design

Project Job Number Engineer

AISC360-05/IBC2006 STEEL SECTION CHECK Units : KN, m, C

(Summary for Combo and Station)

Frame : 338 Length: 23.308 Loc : 23.308

X Mid: 84.000 Y Mid: -7.950 Z Mid: 11.654

Combo: general distributDesign Type: Column Shape: Tower Frame Type: Special Moment Frame Class: Slender Princpl Rot: 0.000 degrees

Provision: ASD D/C Limit=0.950 AlphaPr/Py=0.403

Analysis: Direct Analysis 2nd Order: General 2nd Order AlphaPr/Pe=0.088 Tau_b=1.000

OmegaB=1.670 OmegaV=1.670

OmegaC=1.670 OmegaV-RI=1.500

OmegaTY=1.670 OmegaVT=1.670

OmegaTF=2.000

A=0.262 J=0.176 E=200000000.0 RLLF=1.000

I33=0.118 I22=0.118 fy=355000.000 Fu=510000.000

r33=0.670 r22=0.670 Ry=1.000

S33=0.140 S22=0.140 z33=0.161 z22=0.161

HSS Welding: ERW

Reduce HSS Thickness? No

Reduction: Tau-b Fixed EA factor=0.800 EI factor=0.800

STRESS CHECK FORCES & MOMENTS (Combo general distribution) Location Pr Mr33 Mr22 Vr2 23.308 -23441.764 0.000 0.000 0.000

Av3=0.134 Av2=0.134

Vr3 0.000

Tr 0.000

B2 1.000 1.000

Cm 1.000 1.000

PMM DEMAND/CAPACITY RATIO (H1.3b,H1-2) D/C Ratio: 0.515 = 0.515 + 0.000 + 0.000 = (Pr/Pc) + (Mr33/Mc33)^2 + (Mr22/Mc22) AXIAL FORCE & BIAXIAL MOMENT DESIGN (H1.3b,H1-2) Factor L K1 K2 Major Bending 1.000 1.000 1.000 Minor Bending 1.000 1.000 1.000 Lltb 1.000

Kltb 2.204

Cb 1.000

Pr Force -23441.764

Pnc/Omega Capacity 45551.421

Pnt/Omega Capacity 55779.641

Major Moment Minor Moment

Mr Moment 0.000 0.000

Mn/Omega Capacity 27212.116 27212.116

Mn/Omega No LTB 27212.116

Torsion

Tr Moment 0.000

Tn Capacity 45778.126

Tn/Omega Capacity 27412.051

Vr Force 0.000 0.000

Vn/Omega Capacity 15917.605 15917.605

Stress Ratio 0.000 0.000

LTB

Axial

SHEAR CHECK Major Shear Minor Shear

B1 1.000 1.000

Status Check OK OK

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CSiBridge Steel Design

Project Job Number Engineer

AISC360-05/IBC2006 STEEL SECTION CHECK Units : KN, m, C

(Summary for Combo and Station)

Frame : 167 Length: 7.000 Loc : 0.000

X Mid: 3.500 Y Mid: -7.950 Z Mid: 0.000

Combo: positive moment Shape: Girder Class: Non-Compact

Design Type: Beam Frame Type: Special Moment Frame Princpl Rot: 0.000 degrees

Provision: ASD D/C Limit=0.950 AlphaPr/Py=0.136

Analysis: Direct Analysis 2nd Order: General 2nd Order AlphaPr/Pe=0.010 Tau_b=1.000

OmegaB=1.670 OmegaV=1.670

OmegaC=1.670 OmegaV-RI=1.500

OmegaTY=1.670 OmegaVT=1.670

OmegaTF=2.000

A=0.292 J=0.083 E=200000000.0 RLLF=1.000

I33=0.282 I22=0.036 fy=355000.000 Fu=510000.000

r33=0.983 r22=0.349 Ry=1.000

S33=0.238 S22=0.076 z33=0.269 z22=0.092

HSS Welding: ERW

Reduce HSS Thickness? No

Reduction: Tau-b Fixed EA factor=0.800 EI factor=0.800

STRESS CHECK FORCES & MOMENTS (Combo positive moment) Location Pr Mr33 Mr22 0.000 -8831.295 43794.977 1.087

Vr2 31.010

Av3=0.188 Av2=0.114

Vr3 0.518

Tr 19.899

B2 1.000 1.000

Cm 1.000 0.429

PMM DEMAND/CAPACITY RATIO (H1.3a,H1-1b) D/C Ratio: 0.894 = 0.090 + 0.804 + 0.000 = (1/2)(Pr/Pc) + (Mr33/Mc33) + (Mr22/Mc22) AXIAL FORCE & BIAXIAL MOMENT DESIGN (H1.3a,H1-1b) Factor L K1 K2 Major Bending 1.000 1.000 1.000 Minor Bending 1.000 1.000 1.000 Lltb 1.000

Kltb 1.000

Cb 1.005

Axial

Pr Force -8831.295

Pnc/Omega Capacity 48806.513

Pnt/Omega Capacity 62065.054

Major Moment Minor Moment

Mr Moment 43794.977 1.087

Mn/Omega Capacity 54485.147 10746.321

Mn/Omega No LTB 54485.147

Tr Moment 19.899

Tn Capacity 46071.283

Tn/Omega Capacity 27587.594

Vr Force 31.010 0.518

Vn/Omega Capacity 7260.142 22141.796

Stress Ratio 0.004 2.340E-05

LTB

Torsion SHEAR CHECK Major Shear Minor Shear

B1 1.000 1.000

Status Check OK OK

CONNECTION SHEAR FORCES FOR BEAMS VMajor VMajor Left Right Major (V2) 31.010 187.998

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CSiBridge Steel Design

Project Job Number Engineer

AISC360-05/IBC2006 STEEL SECTION CHECK Units : KN, m, C

(Summary for Combo and Station)

Frame : 252 Length: 7.000 Loc : 0.000

X Mid: 87.500 Y Mid: 7.950 Z Mid: 0.000

Combo: negative moment Shape: Girder Class: Non-Compact

Design Type: Beam Frame Type: Special Moment Frame Princpl Rot: 0.000 degrees

Provision: ASD D/C Limit=1.000 AlphaPr/Py=0.206

Analysis: Direct Analysis 2nd Order: General 2nd Order AlphaPr/Pe=0.015 Tau_b=1.000

OmegaB=1.670 OmegaV=1.670

OmegaC=1.670 OmegaV-RI=1.500

OmegaTY=1.670 OmegaVT=1.670

OmegaTF=2.000

A=0.292 J=0.083 E=200000000.0 RLLF=1.000

I33=0.282 I22=0.036 fy=355000.000 Fu=510000.000

r33=0.983 r22=0.349 Ry=1.000

S33=0.238 S22=0.076 z33=0.269 z22=0.092

HSS Welding: ERW

Reduce HSS Thickness? No

Reduction: Tau-b Fixed EA factor=0.800 EI factor=0.800

STRESS CHECK FORCES & MOMENTS (Combo negative moment) Location Pr Mr33 Mr22 0.000 -13363.231 -41875.841 53.791

Vr2 -658.647

Av3=0.188 Av2=0.114

Vr3 15.484

Tr -235.270

PMM DEMAND/CAPACITY RATIO (H1-1a) D/C Ratio: 0.961 = 0.274 + 0.683 + 0.004 = (Pr/Pc) + (8/9)(Mr33/Mc33) + (8/9)(Mr22/Mc22) AXIAL FORCE & BIAXIAL MOMENT DESIGN (H1-1a) Factor L K1 Major Bending 1.000 1.000 Minor Bending 1.000 1.000

K2 1.000 1.000

Lltb 1.000

Kltb 1.000

Cb 1.043

Axial

Pr Force -13363.231

Pnc/Omega Capacity 48806.513

Pnt/Omega Capacity 62065.054

Major Moment Minor Moment

Mr Moment -41875.841 53.791

Mn/Omega Capacity 54485.147 10746.321

Mn/Omega No LTB 54485.147

Tr Moment -235.270

Tn Capacity 46071.283

Tn/Omega Capacity 27587.594

Vr Force 658.647 15.484

Vn/Omega Capacity 7260.142 22141.796

Stress Ratio 0.091 0.001

LTB

Torsion SHEAR CHECK Major Shear Minor Shear

B1 1.000 1.000

B2 1.000 1.000

Cm 1.000 0.206

Status Check OK OK

CONNECTION SHEAR FORCES FOR BEAMS VMajor VMajor Left Right Major (V2) 658.647 501.660

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CSiBridge Steel Design

Project Job Number Engineer

AISC360-05/IBC2006 STEEL SECTION CHECK Units : KN, m, C

(Summary for Combo and Station)

Frame : 86 Length: 7.000 Loc : 0.000

X Mid: -80.500 Y Mid: 7.950 Z Mid: 0.000

Combo: max shear Shape: Girder Class: Non-Compact

Design Type: Beam Frame Type: Special Moment Frame Princpl Rot: 0.000 degrees

Provision: ASD D/C Limit=1.000 AlphaPr/Py=0.192

Analysis: Direct Analysis 2nd Order: General 2nd Order AlphaPr/Pe=0.014 Tau_b=1.000

OmegaB=1.670 OmegaV=1.670

OmegaC=1.670 OmegaV-RI=1.500

OmegaTY=1.670 OmegaVT=1.670

OmegaTF=2.000

A=0.292 J=0.083 E=200000000.0 RLLF=1.000

I33=0.282 I22=0.036 fy=355000.000 Fu=510000.000

r33=0.983 r22=0.349 Ry=1.000

S33=0.238 S22=0.076 z33=0.269 z22=0.092

HSS Welding: ERW

Reduce HSS Thickness? No

Reduction: Tau-b Fixed EA factor=0.800 EI factor=0.800

STRESS CHECK FORCES & MOMENTS (Combo max shear) Location Pr Mr33 Mr22 0.000 -12435.015 -41507.634 -55.818

Vr2 -2401.254

Av3=0.188 Av2=0.114

Vr3 -15.832

Tr -446.397

PMM DEMAND/CAPACITY RATIO (H1-1a) D/C Ratio: 0.937 = 0.255 + 0.677 + 0.005 = (Pr/Pc) + (8/9)(Mr33/Mc33) + (8/9)(Mr22/Mc22) AXIAL FORCE & BIAXIAL MOMENT DESIGN (H1-1a) Factor L K1 Major Bending 1.000 1.000 Minor Bending 1.000 1.000

K2 1.000 1.000

Lltb 1.000

Kltb 1.000

Cb 1.189

Axial

Pr Force -12435.015

Pnc/Omega Capacity 48806.513

Pnt/Omega Capacity 62065.054

Major Moment Minor Moment

Mr Moment -41507.634 -55.818

Mn/Omega Capacity 54485.147 10746.321

Mn/Omega No LTB 54485.147

Tr Moment -446.397

Tn Capacity 46071.283

Tn/Omega Capacity 27587.594

Vr Force 2401.254 15.832

Vn/Omega Capacity 7260.142 22141.796

Stress Ratio 0.331 0.001

LTB

Torsion SHEAR CHECK Major Shear Minor Shear

B1 1.000 1.000

B2 1.000 1.000

Cm 1.000 0.206

Status Check OK OK

CONNECTION SHEAR FORCES FOR BEAMS VMajor VMajor Left Right Major (V2) 2401.254 2244.267

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`

CHAPTER FIVE Conclusion And Recommendation

5.1 Conclusion. 5.2 Recommendation For Future Studies.

Chapter 5

Conclusion and Recommendation

5.1 Conclusion Reviewing the results of the case study (14th – July) suspension bridge the following points can be concluded: 1. The structural analysis of the 14th – July suspension bridge using (CSi Bridge) may be extended to analyze other suspension bridges. 2. Design of suspension bridge can be performed using the same computer program that used through the project. 3. The result of analysis which is based in adopting the Iraqi and AASHTO specification standards for bridge loading indicates the following: a. Main Cable: almost tensile force is dominated on the section of the cable with maximum value of (27538 KN) at the support on the tower. Accordingly, the maximum average tensile stress is (302.6 MPa) which represents (0.178 F u ). This finding indicates that the cable is in the safe side. b. Towers: The two towers of the bridge were subjected to a pure compression force. The maximum compression force was (23442 KN). The compression stress is (89 MPa) which represents (0.25 F y ) which is in the limit of the specification (0.5Fy). c. Main Girder: The analysis showed that the maximum normal stresses in the box girder of the bridge were as follows: 1. For Positive moment , stress = 148 MPa , which is (0.42Fy) at middle span which is within the limit of the specification (0.6Fy). 2. For negative moment, stress = 176 MPa, which is (0.5Fy) near the support which is within the limit of the specification (0.6Fy). 3. For Shear, stress = 26.96 MPa, which is (0.08 Fy) near the support. Which is within the limit of the specification (0.4Fy).

77

Chapter 5

Conclusion and Recommendation

5.2 Recommendation for future studies: The

following

suggestions

are

recommended

for

future

studies

that

concern the suspension bridge problem: 1. Wind load can be taken into consideration through the analysis and design of the suspension bridge. 2. Seismic analysis can be applied to the suspension bridge structure and foundation. 3. Study and design of the cable – Anchor Blocks that support the main cable of the suspension bridge.

78

References 1. Ali Laftah Abbas, “Linear and Non Linear Coupled Dynamic Response of Suspension Bridges”, A thesis for the degree of master of science in civil engineering, Civil Engineering Department, University of Baghdad, July 2000. 2. Niels J. Gimsing, Christos T. Georgakis, “Cable Supported Bridges, Concept and Design”, John Wiley and Sons, Third edition, 2012. 3. Dr. Khalid Shakir, Bridge Engineering Ph.D. lectures, Civil Engineering Department, University of Baghdad, 2001. 4. Colonel Stephen Ressler, Ph.D., Lecture 8, Lecture 15, U.S. Military Academy at West Point. 5. R.S. Khurmi, “Theory of Structures”, S.Chand and Company Ltd., 2010. 6. “Suspension Bridge”, Wikipedia, the Free Encyclopedia, 2011. 7. R.C. Hibbler, “Engineering Mechanics – Statics”, Pearson Education, 11th Edition, 2007. 8. J. L. Meriam, L. G. Kraige, “Engineering Mechanics – Statics”, John Wiley and Sons, Sixth edition, 2007.

79

Appendix A – Original Brochure of the building Company of 14th of July Suspension Bridge

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Appendix B – Section Properties of 14th of July Suspension Bridge.

Tower

Girder

Sec No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Floor 18 Beam Main 19 Cable Suspenders

Axial Area (cm2) 1678.92 1848.12 2038.92 2367.04 2197.84 2028.64 1859.44 1690.27 1859.44 1764.04 2937.12 2113.1 2305.1 21197.1 2552.11 2607.12 1363.2

I major (cm4) 17579803 19996067 22519449 27244837 24755235 22338971 19849369 17433105 19849369 18587678 10009153 7447427 6766356 5585284 7001025 8416765 14611588

I minor (cm4) 17579803 2589434 2634097 2763217 2638629 2514041 2389454 2204866 2389454 2367122 11245372 7947472 7925440 7903453 8255329 8607204 4095390

J (cm4) 7475691 8229085 9078656 10539669 9786275 9032882 8279489 7526096 8279489 7854703 19761029 12125100 12180445 12235790 12235790 10678764 9625751

Torsional Radius (cm) 66.73 66.73 66.73 66.73 66.73 66.73 66.73 66.73 66.73 66.73 82.0 75.75 72.69 70.0 67.0 64.0 84.0

423.4

2010818

20359

893

1.45

680.74

3690000

3690000

45.8

81

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