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Engineering Structures 30 (2008) 2677–2686www.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 Chinab 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 2008Available online 22 April 2008

Abstract

This paper describes the development of a nite 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 thebasis of themodelling and itsnew functionsareused to simulate the interfacebetween the endplate and thecolumn ange, as well as the pretensionforce in thebolts.Modelling of this kind hashitherto not been reported. Thenite element model is compared with test results, which verify that thenumerical procedure can simulate and analyse the overall and detailed behaviour of a number of types of bolt-pretensioned end-plate connectionsand components accurately, including the generation of the moment–rotation ( M –φ ) relationship, the contact status between the end-plate and thecolumn ange, the behaviour of the end plate, the panel zone and bolts, and the inuences of the bolt pretension force. Moreover, the numericalmodel also provides some additional useful results which are difcult to measure during testing, including the distribution of the pressure andfrictional forces between the end plate and column ange induced by the bolt pretension and the moment at the joint, and the principal stress owin the connections. This knowledge provides a basis for developing mechanical models consistent with the Eurocode component method of jointdesign. The validated numerical model is used for additional parametric nite element analyses of a number of beam-to-column bolt-pretensionedend-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.ush and extended end-plate connections, are used widely insteel structures, [ 1–3]. Beam-to-column connections, includingend-plate types, often signicantly inuence the behaviour

of steel frames, with deformation of the connection incombination with the P-delta effect contributing to excessivelateral drift in unbraced multistorey frames [ 4]. For mostconnections under ambient conditions, the axial and shearingdeformations are usually small compared to the rotationaldeformation and consequently the rotational deformation is themost important characteristic of the connection. This rotationaldeformation 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).

moment in the connection [1–3,5]. In steel frame analysisconventional methods of analysis idealise the connectionssimplistically in two representations: rigid or pinned. However,the actual behaviour of frame connections lies between thesetwo extremes and is semi-rigid [ 1–6] and considerable attentionhas been directed in recent years towards modelling theresponse of semi-rigid connections. The so-called componentmethod adopted by the Eurocode [ 1,7] can quantify thebehaviour of semi-rigid connections and claims to be ableto establish a predictable degree of interaction between themembers based on the moment–rotation ( M –φ ) characteristicsof the joint. Although this somewhat advanced philosophy hasnot been adopted universally amongst design standards, theChinese steel structures design code [8] requires the M –φcharacteristics of the joint to be rst determined for the analysisof steel frames with semi-rigid connections.

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2678 G. Shi et al. / Engineering Structures 30 (2008) 2677–2686

Notwithstanding the usefulness of the component methodof the Eurocode for quantifying the behaviour of semi-rigid joints [1,7], the background research on which the M –φ curvesand the relevant coefcients are based is limited to end-plateconnections with unstiffened end plates and snug tightenedbolts. As a result, the component method is not applicable to

end-plate joints with either pretensioned bolts or to joints witha stiffened end plate and research into these types of end-plateconnections is therefore much needed [ 9].

Many tests on beam-to-column end-plate connections havebeen reported over the years. However, connection types anddetails are numerous and innovative with many parametersthat must be accounted for collectively to characterise thebehaviour; such parameters include whether the end plate isush or extended, whether the end plate extends beyond oneor both of the beam anges and the length of this extension,the diameter of the bolt, the number of bolt rows, the verticaland horizontal spacing of the bolts, the grade of the bolts,the end-plate thickness, stiffening of the end plate or columnpanel zone, the bolt pretension force, the dimensions of thebeam and column, the yield strength of the steel and thecoefcient of friction at the contact surface etc. Because of this,it is almost impossible to study the behaviour of these jointscomprehensively except by physical tests [ 10]. Furthermore,such testing can be costly and nite element modelling in lieuof physical modelling is an attractive option for developing adatabase of connection characteristics.

The nite element analysis (FEA) of end-plate connectionsappears to have been rst 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 developmentof the design procedure reported in Ref. [14]. Tarpyand Cardinal [ 15] carried out an elastic nite elementstudy of unstiffened end-plate connections that was veriedexperimentally and they also proposed a design methodologyfor these joints. Maxwell et al. [16] developed a predictionequation for the ultimate moment of connections, as well astheir M –φ relationships, based on a FEA and on experimentaltests. Jenkins et al. [ 17] did FEA on ush end-plate connectionsand those extended on one side, then put forward a bi-linear M –φ model for ush end-plate connections. Kukretiet al. [18] adopted 2-D FEA model to calculate 50 ushend-plate connections and veried the recommended M –φrelationship for this type of connection based on regressionanalysis. Chasten et al. [ 19] studied the contact between theend-plate and column ange so as to determine the pryingforce by using the commercial ADINA code. Sherbourneand Bahaari used rstly 2-D [ 20] and then 3-D [21] niteelement models to analyse end-plate connections. In additionto the overall behaviour, the contribution of the bolts, end-plateexibility and the column ange exibility to the connectionrotation was singled out in their work. Using FEA, Bahaariand Sherbourne [22] also studied the structural propertiesof an extended end-plate connected to a column ange andproduced a standardised M –φ function for extended end-plate

connections with or without stiffeners in the tension region by

curve tting [23,24]. Choi et al. [25] applied new solid elementsand ne mesh to analyse beam-to-beam and beam-to-columnend-plate connections extended on both sides. Bose et al. [ 26]used the commercial program LUSAS to analyse unstiffenedush end-plate connections. Bursi et al. [ 27] produced anoverview of the nite element method for the analysis of end-

plate connections and undertook a FEA of one extended end-plate connection using the commercial ABAQUS code. Morerecently, the present authors [ 28] carried out a FEA of two typesof end-plate connections in portal frames and used test resultsto verify the numerical results.

Over the last decade, some numerical simulation of the hysteretic behaviour of end-plate connections has beenconducted. Kukreti and Biswas [ 29] developed a computer codeand used it to analyse the moment–rotation behaviour of threeeight-bolt end-plate connections subjected to seismic loadingand they compared their numerical results with experiments.Deng et al. [30] formulated a hysteretic connection elementand 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 fracturebehaviour of isolated T-stub connections; these are elementalcomponents of extended end-plate connections and arefundamental elements of the Eurocode component method of design of connections [7]. A shell nite element was appliedby Adany et al. [32] to model the cyclic analysis of steel-to-concrete end-plate joints.

While the results of these aforementioned studies arevaluable, their drawbacks, from a numerical standpoint, arethe use of often specically-developed nite element modelsand some questions as to the assumptions made in modelling

a difcult and complex problem. These formulations wereoften seemingly governed by balancing accuracy with thecomputational prowess of the day and, while providingimportant results and insight into structural behaviour inlieu of physical testing, in most cases they do not providean entirely general means of describing quantitatively thebehaviour of semi-rigid connections by FEA. Large-scalegeneral purpose nite element software packages such asANSYS [33] and ABAQUS [ 34] have evolved in recentyears and their functions and capabilities are becoming moreadvanced and easier to implement. Software of this type canbe applied to model and simulate accurately the behaviourof different types of bolted end-plate connections in lieu of developing specic FEA programs for the simulation, or of conducting expensive and time-consuming physical testing. Inparticular, the most comprehensive version of ANSYS [ 33]provides many new functions that can simulate and analysethe mechanical behaviour of bolted end-plate connectionsaccurately, especially the contact between the end-plate and thecolumn ange and the pretension force in the bolts; these havehitherto proven to be difcult to model for computer simulation.

This paper simulates and analyses eight beam–column end-plate connections with pretensioned bolts having various typesand details using ANSYS. Hitherto, such joint types have notbeen modelled in this way, the connections are all typical of

those in multistorey steel frames. In implementing the FEA, the



G. Shi et al. / Engineering Structures 30 (2008) 2677–2686 2679

Table 1Types and details of specimens

Specimen number Connection type End-plate thickness (mm) Bolt diameter (mm) Number of bolts Column stiffener End-plate stiffener

SC1 Flush 20 20 6 Yes –SC2 Extended 20 20 8 Yes YesSC3 Extended 20 20 8 Yes No

SC4 Extended 20 20 8 No YesSC5 Extended 25 20 8 Yes YesSC6 Extended 20 24 8 Yes YesSC7 Extended 25 24 8 Yes YesSC8 Extended 16 20 8 Yes Yes

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

Sectiondepth

Webthickness

Flangewidth

Flange thickness

Beam 300 8 200 12Column 300 8 250 12

interaction between the end plate and column ange as wellas geometric and material nonlinearities are taken into accountand the modelling proposes a new andmore appropriate methodfor applying the pretension force in the bolts instead of themore conventional use of applied initial strains. These eightconnections have also been tested physically under monotonicloading in order to validate the FEA model and the results. Thenumerical simulations also provide some extra valuable resultswhich are usually very difcult to measure during physicaltesting, including the distribution of the pressure and frictionalforce between the end plate and the column ange due to thebolt 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 anew numerical scheme for the analysis of end-plate connectionsbut 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 connectionspecimens used in the FEA are shown in Table 1 and inFig. 1. All of the beams and columns in the joints had thesame dimensions, as listed in Table 2. In these connectionspecimens, SC2 can be regarded as a reference or controlspecimen and all the other connections differ from SC2 in onlyone or two geometric parameters, e.g. whether the joint is aush or extended end-plate type, whether the joint has an end-plate stiffener or a column panel zone stiffener, the thickness of the end-plate and the bolt diameter. The thickness of the columnange is taken to be the same as that of the end-plate, within thelength range of 100 mm above the extension of the end-plateand 100 mm below the extension of the end-plate ( Fig. 1). Thethicknesses 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 meshedby the 10-node tetrahedral solid structural elements SOLID92.The important interface between the end-plate and the columnange was simulated by creating contact pairs with the 3-D target surface elements TARGE170 and the 3-D 8-nodesurface-to-surface contact elements CONTA174. The PSMESHcommand was used to dene pretension sections in the middleof the bolt shanks and to generate the pretension elementsPRETS179 through which the pretension forces in the bolts areapplied by the command SLOAD. Because of their geometricalsymmetry about the central plane passing parallel throughthe beam and column webs, only one half of each of theconnection specimens was modelled for the FEA in order toreduce computation time. Fig. 3 shows a typical nite elementmodel of a connection and that of a high strength bolt is shown

in Fig. 4.




Table 3Material properties for high strength bolts

Stress (MPa) 0 990 1160 1160Strain (%) 0 0.483 13.6 15

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

2.3. Material properties

The stress–strain relationship for the steel plates was takenas elastically–perfect plastic with a Poisson’s ratio of 0.3.The yield strength and elastic modulus of steel plates thickerthan 16 mm were taken as 363 MPa and 204,227 MPa

respectively; those for plates thinner than 16 mm being391 MPa and 190,707 MPa. The stress–strain relationshipfor the high strength bolts (including the bolt heads, shanksand nuts) was taken as trilinear, with the points dening thestress–strain relationship being given in Table 3 . Von Mises’yield criterion was adopted as the yield criterion for all steelcomponents and the ow rule was adopted following yielding.The coefcient of friction for the contact surface between theend plate and column ange was taken as 0.44. All of thesematerial properties were taken from test data reported by theauthors [35].

2.4. Analysis methodology

The implementation of the analysis and solution of thenite element modelling involved two load steps. Firstly, alldisplacement restraints were applied at the restraint points thatare shown in Fig. 2 and the pretension forces were applied tothe bolts. The pretension forces were 155 kN and 225 kN forM20 and M24 bolts respectively, which were obtained fromthe Chinese design code for pretensioned high strength boltedconnections [ 36]. After solving the rst load step, the secondload step implemented consisted of a downward displacementload being applied at the loading point identied on the beam inFig. 2, for which the “Large Displacement Static” analysis type

was chosen to consider the P -delta effect.

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

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 theloading point shown in Fig. 2 was identied and its peak valuewas taken as the loading capacity of each of the connectionspecimens. The joint moment was taken as the product of theload and its lever arm of 1200 mm (which is the distance fromthe loading point to the column ange, 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 moment-shearing rotation ( M –φs ) curves for the FEA and test resultsfor all of the connection specimens are shown in Figs. 5 and6 respectively. In these gures, the rotation φ is the total jointrotation of the beam-to-column end-plate connection while φ sis the shearing rotation, which is that part of φ contributedto by the shearing deformation of the column panel zone.The detailed denition and method of calculating the joint

rotation is given in Ref. [ 37]. The M –φ curves describe the




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

overall characteristics of the joints, while the M –φ s curvesillustrate 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 theultimate failure modes for the other connection specimens wasfound to be similar. These two gures also show the detaileddeformations of the end-plate, the column ange and the end-

plate stiffener.




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

3.2. Discussion

When comparing the moment–rotation ( M –φ ) and moment-shearing rotation ( M –φ s ) 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 agreementbetween the FEA curves and the test results is extremely close.For most of the end-plate connections with bolt pretensionsthe agreement between the FEA and test results in the

nonlinear range of response is very close, with only minor




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

Fig. 8. Comparison of ultimate failure mode of connection specimen SC8.

Table 4Comparison of loading capacities between FEA and tests

Specimen number Test (kN) FEA (kN) FEA/TestSC1 155.3 156.2 1.01SC2 286.4 276.8 0.97SC3 256.9 244.2 0.95SC4 256.6 256.5 1.00SC5 268.4 289.2 1.08SC6 325.3 294.2 0.90SC7 342.3 301.9 0.88SC8 296.1 261.6 0.88

Average 0.96Standard deviation 0.07

discrepancies. In addition, the comparisons given in Table 4of the joint capacities derived by the FEA and tests areclose, with the numerical predictions of the capacities beingslightly conservative (average FEA to test ratio of 96% witha coefcient of variation of 7%). It can be concluded thatthe nite element modelling described here can simulate theresponse of the connections with acceptable accuracy and, bycorollary, it is able to simulate the contact status betweenthe end-plate and the column ange as well as the detailedcharacteristics of other components of the connections, viz. thepanel zone, end-plate, column ange, end-plate stiffener andpretension 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 thephysical tests need some discussion. Firstly, the stress–strain

relationship for the steel plates used in the FEA waselastic–perfectly plastic and so strain hardening was neglected.This idealisation is reected in the FEA results for connectionswhose capacities are governed by steel plates, including thepanel zone in shear and the end-plate in bending, wherethe discrepancies are larger owing to the post-yield steelstrength; the discrepancies of specimens SC6 and SC7 inparticular are attributable to the neglect of the strength of the panel zone after yielding, while those of specimens SC3and SC8 are attributable to the neglect of the strength of the end-plate in bending after yielding. The load capacitiesof the other connections are controlled by the bolts and theerror is much smaller. Secondly, the values of the applied

pretension force for all of the bolts were determined by thedesign values given in Ref. [ 36]. In conducting physical testsit is very difcult to induce a predetermined bolt force bypretensioning techniques because the bolt forces are veryhigh [38] and, as a consequence, this has been identiedas a reason for discrepancies between theoretical predictionsand test results [ 39,40]. Thirdly, fabrication errors in the testspecimens can lead to a geometric deviation between thephysical and numerical results.

3.3. Additional results from FEA study

The nite element results can also provide extra valuable

results for the mechanical behaviour of bolt-pretensioned end-




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

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

plate connections, which are difcult to measure in physicaltests.

Firstly, Fig. 9 shows the distribution of pressure between theend-plate and column ange for specimens SC2 and SC6 prior

to loading; the distributions in all of the other specimens aresimilar. Although the area of force distribution is governed bymany factors, such as the bolt diameter and the end-plate andcolumn ange thicknesses, it can be concluded from the FEAresults of all of the connections that this distribution regionis about ten times the bolt shank sectional area. This value isvery important in the theoretical analysis of the stiffness anddeformation of pretensioned bolted connections [35].

The distributions of the friction force between the end-plate and the column ange at ultimate loading for jointsSC1 and SC2 are shown in Fig. 10; the distributions for theother connections are similar to SC2. The FEA results canalso provide the friction force distribution for the connectionunder any loading, including that at rst yield. This observationprovides full details of the contact and friction forces in theconnection at any load level and is important in contrivinga mechanical model for use in practical design, especiallywhen studying the behaviour of the end-plate connection undercombined moment and shear force. This also has potential forincluding the large axial forces that are induced in a joint dueto re loading but which are not included in the study in thispaper.

Fig. 11 shows the distributions of principal stress owfor joints SC1 to SC 4; again the distributions for the otherconnections are similar to SC2. This gure makes transparent

the inuence of the connection details, e.g. ush or extended

end-plate type, end-plate stiffener and column panel zonestiffener, on the connection stress status. These results provideimportant information for a generic mechanical analysis of theoverall behaviour of the end-plate connection and the inuences

of its components and detailing.4. Concluding remarks

This paper has described the development of nite elementmodels to simulate and analyse the mechanical behaviourof beam–column bolt-pretensioned end-plate connections of different types and details. From the results of a comprehensivecomparison of the results of the nite element analysis andtests, the following conclusions can be made.

The nite element modelling that has been developed andthe methodology of its implementation can accurately andefciently simulate and analyse not only the overall behaviourof connections of this type, including the load capacity, themoment–rotation relationships and the mode of failure, but alsothe detailed characteristics of the joint and its components,including the mechanical behaviour and deformation of thepanel zone, the end-plate and the bolts.

The pretension force in the bolt and the contact between theend-plate and the column, which have proven to be difcult toinclude in nite element analyses, are simulated well with thepresent modelling.

Strain hardening of the steel should be taken into accountwhen the post-yielding behaviour of end-plate connections isneeded.

The nite element results which were validated well against

test results can provide extra valuable results for the mechanical




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

behaviour of joints which are difcult to measure in physicaltests, such as the distribution of pressure caused by boltpretension, the friction between the end-plate and the columnange and the principal stress ow in the connection.

The nite element method allows for further parametricanalyses of bolt-pretensioned end-plate connections to beimplemented so as to obtain comprehensive results that can beused to propose a complete analytical design procedure that isconsistent with the component method of joint design used inthe Eurocode.

Acknowledgments

This work was jointly supported by the National NaturalScience Foundation of China (No. 50578083) and Programfor Changjiang Scholars and Innovative Research Team inUniversity (IRT00736), and also partly through the AustralianResearch Council.

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