Shi 2008 Engineering-structures

Engineering Structures 30 (2008) 2677–2686 www.elsevier.com/locate/engstruct

Numerical simulation of steel pretensioned bolted end-plate connections of different types and details Gang Shi a,∗ , Yongjiu Shi a , Yuanqing Wang a , Mark A. Bradford b a Department of Civil Engineering, Tsinghua University, Beijing 100084, PR China b Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney,

NSW 2052, Australia Received 22 June 2007; received in revised form 22 February 2008; accepted 26 February 2008 Available online 22 April 2008

Abstract This paper describes the development of a finite element numerical model with the ability to simulate and analyse the mechanical behaviour of different types of beam–column end-plate connections in which all of the bolts are pretensioned. The general purpose ANSYS software forms the basis of the modelling and its new functions are used to simulate the interface between the end plate and the column flange, as well as the pretension force in the bolts. Modelling of this kind has hitherto not been reported. The finite element model is compared with test results, which verify that the numerical procedure can simulate and analyse the overall and detailed behaviour of a number of types of bolt-pretensioned end-plate connections and components accurately, including the generation of the moment–rotation (M–φ) relationship, the contact status between the end-plate and the column flange, the behaviour of the end plate, the panel zone and bolts, and the influences of the bolt pretension force. Moreover, the numerical model also provides some additional useful results which are difficult to measure during testing, including the distribution of the pressure and frictional forces between the end plate and column flange induced by the bolt pretension and the moment at the joint, and the principal stress flow in the connections. This knowledge provides a basis for developing mechanical models consistent with the Eurocode component method of joint design. The validated numerical model is used for additional parametric finite element analyses of a number of beam-to-column bolt-pretensioned end-plate connections so as to produce a comprehensive study of their behaviour. c 2008 Elsevier Ltd. All rights reserved.

Keywords: End plate connection; Finite element analysis; Pretensioned; Semi-rigid; Joints

1. Introduction End-plate connections, which consist of two main types, viz. flush and extended end-plate connections, are used widely in steel structures, [1–3]. Beam-to-column connections, including end-plate types, often significantly influence the behaviour of steel frames, with deformation of the connection in combination with the P-delta effect contributing to excessive lateral drift in unbraced multistorey frames [4]. For most connections under ambient conditions, the axial and shearing deformations are usually small compared to the rotational deformation and consequently the rotational deformation is the most important characteristic of the connection. This rotational deformation is customarily expressed as a function of the ∗ Corresponding author. Tel.: +86 10 6279 2330; fax: +86 10 6278 8623.

E-mail address: [email protected] (G. Shi). c 2008 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2008.02.013

moment in the connection [1–3,5]. In steel frame analysis conventional methods of analysis idealise the connections simplistically in two representations: rigid or pinned. However, the actual behaviour of frame connections lies between these two extremes and is semi-rigid [1–6] and considerable attention has been directed in recent years towards modelling the response of semi-rigid connections. The so-called component method adopted by the Eurocode [1,7] can quantify the behaviour of semi-rigid connections and claims to be able to establish a predictable degree of interaction between the members based on the moment–rotation (M–φ) characteristics of the joint. Although this somewhat advanced philosophy has not been adopted universally amongst design standards, the Chinese steel structures design code [8] requires the M–φ characteristics of the joint to be first determined for the analysis of steel frames with semi-rigid connections.

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Notwithstanding the usefulness of the component method of the Eurocode for quantifying the behaviour of semi-rigid joints [1,7], the background research on which the M–φ curves and the relevant coefficients are based is limited to end-plate connections with unstiffened end plates and snug tightened bolts. As a result, the component method is not applicable to end-plate joints with either pretensioned bolts or to joints with a stiffened end plate and research into these types of end-plate connections is therefore much needed [9]. Many tests on beam-to-column end-plate connections have been reported over the years. However, connection types and details are numerous and innovative with many parameters that must be accounted for collectively to characterise the behaviour; such parameters include whether the end plate is flush or extended, whether the end plate extends beyond one or both of the beam flanges and the length of this extension, the diameter of the bolt, the number of bolt rows, the vertical and horizontal spacing of the bolts, the grade of the bolts, the end-plate thickness, stiffening of the end plate or column panel zone, the bolt pretension force, the dimensions of the beam and column, the yield strength of the steel and the coefficient of friction at the contact surface etc. Because of this, it is almost impossible to study the behaviour of these joints comprehensively except by physical tests [10]. Furthermore, such testing can be costly and finite element modelling in lieu of physical modelling is an attractive option for developing a database of connection characteristics. The finite element analysis (FEA) of end-plate connections appears to have been first reported by Krishnamurthy [11– 13]. An exhaustive numerical study of four-bolt, unstiffened, extended end-plate connections, along with the results of a series of experimental investigations, led to the development of the design procedure reported in Ref. [14]. Tarpy and Cardinal [15] carried out an elastic finite element study of unstiffened end-plate connections that was verified experimentally and they also proposed a design methodology for these joints. Maxwell et al. [16] developed a prediction equation for the ultimate moment of connections, as well as their M–φ relationships, based on a FEA and on experimental tests. Jenkins et al. [17] did FEA on flush end-plate connections and those extended on one side, then put forward a bilinear M–φ model for flush end-plate connections. Kukreti et al. [18] adopted 2-D FEA model to calculate 50 flush end-plate connections and verified the recommended M–φ relationship for this type of connection based on regression analysis. Chasten et al. [19] studied the contact between the end-plate and column flange so as to determine the prying force by using the commercial ADINA code. Sherbourne and Bahaari used firstly 2-D [20] and then 3-D [21] finite element models to analyse end-plate connections. In addition to the overall behaviour, the contribution of the bolts, end-plate flexibility and the column flange flexibility to the connection rotation was singled out in their work. Using FEA, Bahaari and Sherbourne [22] also studied the structural properties of an extended end-plate connected to a column flange and produced a standardised M–φ function for extended end-plate connections with or without stiffeners in the tension region by

curve fitting [23,24]. Choi et al. [25] applied new solid elements and fine mesh to analyse beam-to-beam and beam-to-column end-plate connections extended on both sides. Bose et al. [26] used the commercial program LUSAS to analyse unstiffened flush end-plate connections. Bursi et al. [27] produced an overview of the finite element method for the analysis of endplate connections and undertook a FEA of one extended endplate connection using the commercial ABAQUS code. More recently, the present authors [28] carried out a FEA of two types of end-plate connections in portal frames and used test results to verify the numerical results. Over the last decade, some numerical simulation of the hysteretic behaviour of end-plate connections has been conducted. Kukreti and Biswas [29] developed a computer code and used it to analyse the moment–rotation behaviour of three eight-bolt end-plate connections subjected to seismic loading and they compared their numerical results with experiments. Deng et al. [30] formulated a hysteretic connection element and implemented it to simulate the hysteretic response of unstiffened extended end-plate connections. Bursi et al. [31] performed a numerical analysis of the low-cycle fracture behaviour of isolated T-stub connections; these are elemental components of extended end-plate connections and are fundamental elements of the Eurocode component method of design of connections [7]. A shell finite element was applied ´ any et al. [32] to model the cyclic analysis of steel-toby Ad´ concrete end-plate joints. While the results of these aforementioned studies are valuable, their drawbacks, from a numerical standpoint, are the use of often specifically-developed finite element models and some questions as to the assumptions made in modelling a difficult and complex problem. These formulations were often seemingly governed by balancing accuracy with the computational prowess of the day and, while providing important results and insight into structural behaviour in lieu of physical testing, in most cases they do not provide an entirely general means of describing quantitatively the behaviour of semi-rigid connections by FEA. Large-scale general purpose finite element software packages such as ANSYS [33] and ABAQUS [34] have evolved in recent years and their functions and capabilities are becoming more advanced and easier to implement. Software of this type can be applied to model and simulate accurately the behaviour of different types of bolted end-plate connections in lieu of developing specific FEA programs for the simulation, or of conducting expensive and time-consuming physical testing. In particular, the most comprehensive version of ANSYS [33] provides many new functions that can simulate and analyse the mechanical behaviour of bolted end-plate connections accurately, especially the contact between the end-plate and the column flange and the pretension force in the bolts; these have hitherto proven to be difficult to model for computer simulation. This paper simulates and analyses eight beam–column endplate connections with pretensioned bolts having various types and details using ANSYS. Hitherto, such joint types have not been modelled in this way, the connections are all typical of those in multistorey steel frames. In implementing the FEA, the

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G. Shi et al. / Engineering Structures 30 (2008) 2677–2686 Table 1 Types and details of specimens Specimen number

Connection type

End-plate thickness (mm)

Bolt diameter (mm)

Number of bolts

Column stiffener

End-plate stiffener

SC1 SC2 SC3 SC4 SC5 SC6 SC7 SC8

Flush Extended Extended Extended Extended Extended Extended Extended

20 20 20 20 25 20 25 16

20 20 20 20 20 24 24 20

6 8 8 8 8 8 8 8

Yes Yes Yes No Yes Yes Yes Yes

– Yes No Yes Yes Yes Yes Yes

Table 2 Dimensions of beam and column cross-sections (mm)

Beam Column

Section depth

Web thickness

Flange width

Flange thickness

300 300

8 8

200 250

12 12

interaction between the end plate and column flange as well as geometric and material nonlinearities are taken into account and the modelling proposes a new and more appropriate method for applying the pretension force in the bolts instead of the more conventional use of applied initial strains. These eight connections have also been tested physically under monotonic loading in order to validate the FEA model and the results. The numerical simulations also provide some extra valuable results which are usually very difficult to measure during physical testing, including the distribution of the pressure and frictional force between the end plate and the column flange due to the bolt pretension force and the moment at the joint, as well as the principal stresses in the connection. 2. Finite element analysis As has been noted, the purpose of this paper is not to derive a new numerical scheme for the analysis of end-plate connections but rather to illustrate the use of recent advanced features of ANSYS software for the FEA of these connection types. 2.1. Geometric details of connections The details of the eight bolted end-plate connection specimens used in the FEA are shown in Table 1 and in Fig. 1. All of the beams and columns in the joints had the same dimensions, as listed in Table 2. In these connection specimens, SC2 can be regarded as a reference or control specimen and all the other connections differ from SC2 in only one or two geometric parameters, e.g. whether the joint is a flush or extended end-plate type, whether the joint has an endplate stiffener or a column panel zone stiffener, the thickness of the end-plate and the bolt diameter. The thickness of the column flange is taken to be the same as that of the end-plate, within the length range of 100 mm above the extension of the end-plate and 100 mm below the extension of the end-plate (Fig. 1). The thicknesses of the column panel zone stiffener and the end-plate rib stiffener are 12 mm and 10 mm respectively.

Fig. 1. Details of connections (dimensions in mm).

2.2. Finite element model In the modelling herein, all elements of the beams, columns, end-plates, stiffeners and the high strength bolts were meshed by the 10-node tetrahedral solid structural elements SOLID92. The important interface between the end-plate and the column flange was simulated by creating contact pairs with the 3D target surface elements TARGE170 and the 3-D 8-node surface-to-surface contact elements CONTA174. The PSMESH command was used to define pretension sections in the middle of the bolt shanks and to generate the pretension elements PRETS179 through which the pretension forces in the bolts are applied by the command SLOAD. Because of their geometrical symmetry about the central plane passing parallel through the beam and column webs, only one half of each of the connection specimens was modelled for the FEA in order to reduce computation time. Fig. 3 shows a typical finite element model of a connection and that of a high strength bolt is shown in Fig. 4.

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Table 3 Material properties for high strength bolts Stress (MPa) Strain (%)

0 0

990 0.483

1160 13.6

1160 15

Fig. 3. Typical finite element model of a connection.

Fig. 2. Typical connection prototype model (dimensions in mm).

2.3. Material properties The stress–strain relationship for the steel plates was taken as elastically–perfect plastic with a Poisson’s ratio of 0.3. The yield strength and elastic modulus of steel plates thicker than 16 mm were taken as 363 MPa and 204,227 MPa respectively; those for plates thinner than 16 mm being 391 MPa and 190,707 MPa. The stress–strain relationship for the high strength bolts (including the bolt heads, shanks and nuts) was taken as trilinear, with the points defining the stress–strain relationship being given in Table 3. Von Mises’ yield criterion was adopted as the yield criterion for all steel components and the flow rule was adopted following yielding. The coefficient of friction for the contact surface between the end plate and column flange was taken as 0.44. All of these material properties were taken from test data reported by the authors [35]. 2.4. Analysis methodology The implementation of the analysis and solution of the finite element modelling involved two load steps. Firstly, all displacement restraints were applied at the restraint points that are shown in Fig. 2 and the pretension forces were applied to the bolts. The pretension forces were 155 kN and 225 kN for M20 and M24 bolts respectively, which were obtained from the Chinese design code for pretensioned high strength bolted connections [36]. After solving the first load step, the second load step implemented consisted of a downward displacement load being applied at the loading point identified on the beam in Fig. 2, for which the “Large Displacement Static” analysis type was chosen to consider the P-delta effect.

Fig. 4. Finite element model of high strength bolt.

3. Results and discussion 3.1. Comparison of results from FEA and experiments For post-processing the results of the FEA, the force at the loading point shown in Fig. 2 was identified and its peak value was taken as the loading capacity of each of the connection specimens. The joint moment was taken as the product of the load and its lever arm of 1200 mm (which is the distance from the loading point to the column flange, as shown in Fig. 2). Table 4 presents comparisons of the load capacities of all of these connections. Comparisons of the moment–rotation (M–φ) and momentshearing rotation (M–φs ) curves for the FEA and test results for all of the connection specimens are shown in Figs. 5 and 6 respectively. In these figures, the rotation φ is the total joint rotation of the beam-to-column end-plate connection while φ s is the shearing rotation, which is that part of φ contributed to by the shearing deformation of the column panel zone. The detailed definition and method of calculating the joint rotation is given in Ref. [37]. The M–φ curves describe the

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Fig. 5. Comparison of moment–rotation (M–φ) curves for all connections.

overall characteristics of the joints, while the M–φ s curves illustrate the detailed behaviour of one of the components of the connection. Comparisons of the ultimate failure modes from the FEA and test results for two typical connection specimens (SC1

and SC8) are shown in Figs. 7 and 8. The comparison of the ultimate failure modes for the other connection specimens was found to be similar. These two figures also show the detailed deformations of the end-plate, the column flange and the endplate stiffener.

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Fig. 6. Comparison of moment-shearing rotation (M–φs ) curves for all connections.

3.2. Discussion When comparing the moment–rotation (M–φ) and momentshearing rotation (M–φs ) curves that are shown in Figs. 5 and 6, it can be seen that the initial stages of loading for

all of the connections are linear and that the agreement between the FEA curves and the test results is extremely close. For most of the end-plate connections with bolt pretensions the agreement between the FEA and test results in the nonlinear range of response is very close, with only minor

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Fig. 7. Comparison of ultimate failure mode of connection specimen SC1.

Fig. 8. Comparison of ultimate failure mode of connection specimen SC8. Table 4 Comparison of loading capacities between FEA and tests Specimen number

Test (kN)

FEA (kN)

FEA/Test

SC1 SC2 SC3 SC4 SC5 SC6 SC7 SC8

155.3 286.4 256.9 256.6 268.4 325.3 342.3 296.1

156.2 276.8 244.2 256.5 289.2 294.2 301.9 261.6

1.01 0.97 0.95 1.00 1.08 0.90 0.88 0.88

Average Standard deviation

0.96 0.07

discrepancies. In addition, the comparisons given in Table 4 of the joint capacities derived by the FEA and tests are close, with the numerical predictions of the capacities being slightly conservative (average FEA to test ratio of 96% with a coefficient of variation of 7%). It can be concluded that the finite element modelling described here can simulate the response of the connections with acceptable accuracy and, by corollary, it is able to simulate the contact status between the end-plate and the column flange as well as the detailed characteristics of other components of the connections, viz. the panel zone, end-plate, column flange, end-plate stiffener and pretension forces in the bolts. Because the FEA modelling herein purports to provide an accurate representation of the joint behaviour, the

small discrepancies between the numerical results and the physical tests need some discussion. Firstly, the stress–strain relationship for the steel plates used in the FEA was elastic–perfectly plastic and so strain hardening was neglected. This idealisation is reflected in the FEA results for connections whose capacities are governed by steel plates, including the panel zone in shear and the end-plate in bending, where the discrepancies are larger owing to the post-yield steel strength; the discrepancies of specimens SC6 and SC7 in particular are attributable to the neglect of the strength of the panel zone after yielding, while those of specimens SC3 and SC8 are attributable to the neglect of the strength of the end-plate in bending after yielding. The load capacities of the other connections are controlled by the bolts and the error is much smaller. Secondly, the values of the applied pretension force for all of the bolts were determined by the design values given in Ref. [36]. In conducting physical tests it is very difficult to induce a predetermined bolt force by pretensioning techniques because the bolt forces are very high [38] and, as a consequence, this has been identified as a reason for discrepancies between theoretical predictions and test results [39,40]. Thirdly, fabrication errors in the test specimens can lead to a geometric deviation between the physical and numerical results. 3.3. Additional results from FEA study The finite element results can also provide extra valuable results for the mechanical behaviour of bolt-pretensioned end-

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Fig. 9. Distribution of pressure between the end-plate and column flange caused by bolt pretension force.

Fig. 10. Distribution of friction force between the end-plate and column flange at ultimate load.

plate connections, which are difficult to measure in physical tests. Firstly, Fig. 9 shows the distribution of pressure between the end-plate and column flange for specimens SC2 and SC6 prior to loading; the distributions in all of the other specimens are similar. Although the area of force distribution is governed by many factors, such as the bolt diameter and the end-plate and column flange thicknesses, it can be concluded from the FEA results of all of the connections that this distribution region is about ten times the bolt shank sectional area. This value is very important in the theoretical analysis of the stiffness and deformation of pretensioned bolted connections [35]. The distributions of the friction force between the endplate and the column flange at ultimate loading for joints SC1 and SC2 are shown in Fig. 10; the distributions for the other connections are similar to SC2. The FEA results can also provide the friction force distribution for the connection under any loading, including that at first yield. This observation provides full details of the contact and friction forces in the connection at any load level and is important in contriving a mechanical model for use in practical design, especially when studying the behaviour of the end-plate connection under combined moment and shear force. This also has potential for including the large axial forces that are induced in a joint due to fire loading but which are not included in the study in this paper. Fig. 11 shows the distributions of principal stress flow for joints SC1 to SC 4; again the distributions for the other connections are similar to SC2. This figure makes transparent the influence of the connection details, e.g. flush or extended

end-plate type, end-plate stiffener and column panel zone stiffener, on the connection stress status. These results provide important information for a generic mechanical analysis of the overall behaviour of the end-plate connection and the influences of its components and detailing. 4. Concluding remarks This paper has described the development of finite element models to simulate and analyse the mechanical behaviour of beam–column bolt-pretensioned end-plate connections of different types and details. From the results of a comprehensive comparison of the results of the finite element analysis and tests, the following conclusions can be made. The finite element modelling that has been developed and the methodology of its implementation can accurately and efficiently simulate and analyse not only the overall behaviour of connections of this type, including the load capacity, the moment–rotation relationships and the mode of failure, but also the detailed characteristics of the joint and its components, including the mechanical behaviour and deformation of the panel zone, the end-plate and the bolts. The pretension force in the bolt and the contact between the end-plate and the column, which have proven to be difficult to include in finite element analyses, are simulated well with the present modelling. Strain hardening of the steel should be taken into account when the post-yielding behaviour of end-plate connections is needed. The finite element results which were validated well against test results can provide extra valuable results for the mechanical

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Fig. 11. Distribution of principal stress flow in connections.

behaviour of joints which are difficult to measure in physical tests, such as the distribution of pressure caused by bolt pretension, the friction between the end-plate and the column flange and the principal stress flow in the connection. The finite element method allows for further parametric analyses of bolt-pretensioned end-plate connections to be implemented so as to obtain comprehensive results that can be used to propose a complete analytical design procedure that is consistent with the component method of joint design used in the Eurocode. Acknowledgments This work was jointly supported by the National Natural Science Foundation of China (No. 50578083) and Program for Changjiang Scholars and Innovative Research Team in University (IRT00736), and also partly through the Australian Research Council. References [1] Trahair NS, Bradford MA, Nethercot DA, Gardner L. The behaviour and design of steel structures to EC3. 4th edn. British. London: Spon Press; 2007. [2] Owens GW, Cheal BD. Structural steelwork connections. London: Butterworths; 1989.

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