Research ArticleThe Guidelines for Modelling the Preloading Bolts inthe Structural Connection Using Finite Element Methods
Paulina Krolo Davor GrandiT and Mladen BuliT
Department of Structural Engineering and Technical Mechanics Faculty of Civil Engineering University of RijekaRadmile Matejcic 3 51000 Rijeka Croatia
Correspondence should be addressed to Paulina Krolo paulinakrolounirihr
Received 30 March 2016 Revised 25 May 2016 Accepted 29 May 2016
Academic Editor Marek Krawczuk
Copyright copy 2016 Paulina Krolo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The aim of this paper is the development of the two different numerical techniques for the preloading of bolts by the finite elementmethod using the software Abaqus Standard Furthermore this paper gave detailed guidelines for modelling contact method forsolving the numerical error problems such as numerical singularity error and negative eigenvalues due to rigid body motion orthe problem of the extensive elongation of bolts after pretension which is occurring during the analysis The behaviour of boltedjoints depending on the two different approaches of pretension was shown on the example of an extended end-plate bolted beam-to-column connection under the monotonic loading The behaviour of beam-to-column connection was shown in the form andmoment-rotation (119872-120601) curves and validated by experimental test Advantages and disadvantages of pretension techniques as wellas the speed of numerical models were also presented in this paper
1 Introduction
The bolted joints remain the most common connectionmethod in the construction and machine design As a struc-tural component it is often considered the critical part of anassembly Due to the high cost of experimental test develop-ment of the computer programs especially the finite elementmodelling gives accurate prediction of the real behaviour ofsuch type of joints
There are a lot of articles [1ndash7] which analyzed the behav-iour of the assembly with bolted joints It takes into accountthe preload bolts in the joint Maggi et al [2] use the tem-perature gradient in the bolts to impose the pretension forceGuidelines formodelling the bolt load are available inAbaqus[8] using the bolt loadmethod and the adjust lengthmethod
The numerical problems such as numerical singularityerror negative eigenvalues rigid body motion and problemof the extensive elongation of bolts after pretension are veryoften during the numerical analysis All of these problemsmay stop the procedure or give the inaccurate results of theanalysis Contact surfaces with edges or corners alsomay cre-ate the convergence difficulties Sharp corners may producethe element distortion and high stress level in the contactzones Selamet and Garlock [9] give the solution for edges
and corner numerical problems as well as the comparison ofexplicit and implicit solution techniques
Two different approaches to preloading of the bolts willbe presented at the first part of the paper The first techniquewas standardized in Abaqus software and uses bolt load forpreloading During the numerical analysis using standard-ized Abaqus technique of preloading all of the aforemen-tioned numerical problemsmay occur In order to avoid thesenumerical errors the second technique of preloading willbe presented which uses the initial stress The comparisonbetween these preloading techniques will be shown on theexample of an extended end-plate bolted beam-to-columnconnection Results obtained from numerical analysis willbe compared with experimental test according to [10]
2 Finite Element Model of Bolted Joints
Numerical modelling of bolted joints is carried out by usingthe following parameters geometric and material nonlinear-ities of the elementary parts of the joints bolt pretensionforce contact between connected plates washers and platedelements bolt-shank and hole and friction The nut and thebolt-head were considered as a single body with bolt-shank
Hindawi Publishing CorporationJournal of Computational EngineeringVolume 2016 Article ID 4724312 8 pageshttpdxdoiorg10115520164724312
2 Journal of Computational Engineering
Figure 1 Bolted joint
(a) (b)
Figure 2 Finite element model of (a) plate element (b) bolt
together with washers on both ends of the boltThreaded partof the bolt-shank and the extended length of the bolt beyondeach nut were ignored Hexagonal shape of the bolt-head andnut was replaced with a cylinder The typical bolted joint ispresented in Figure 1
21 Finite Element Mesh and Contact Modelling The platedelements in the joint were meshed with 8-node first-order(linear) hexagon (brick) elements with incompatible modes(C3D8I) Each of these elements has 13 additional degrees offreedom (DOF) when compared to the fully integrated ele-ments (C3D8) providing superior performance in bendingdominant problems without shear locking behaviour or zeroenergy deformation modes see Figure 2(a) The 6-noddedlinear triangular prism element (C3D6) was used to modelthe bolts The details of the finite element mesh are shownin Figure 2(b) Structure mesh technique is used for all partsof assembly Previously the bolts as well as bolt-hole regionare quarter-partitioned Then they mesh with 16 elementsaround the circumference
Numerical results are highly sensitive to the contact prop-erties between components of the joints and the preloadedbolts Small sliding surface-to-surface discretization methodwas considered for all the contacts The surface contactproperties between the plate elements were modelled as atangential behaviour using penalty friction with the friction
coefficient value of 044 Normal behaviour contact proper-ties using Augmented Lagrangian Formulation were consid-ered for the normal forces between the same componentssee Figures 3(a) and 3(b) The tangential contact betweenbolt-shank and bolt-hole was considered to be frictionlesssee Figures 3(c) and 3(d) The hard contact was used for theconnection between bolt-headnut and plate elements Thebolts are usuallymore rigid than hot-rolled steelmember andthey are usually denoted as a master surface in the contactpairs see Figure 4
22 Simulation Procedure and Bolt Preload The analysis hasbeen performed through the steps in two different waysdepending on the type of the bolt pretension technique
Step 1 Bolt preloadingactivating the contact element
Step 2 Fixing the bolt length
Step 3 External load
The bolts are preloaded in the first step of the analysisaccording to bolt load method The pretension is simulated
Journal of Computational Engineering 3
(a) (b)
(c) (d)
Figure 3 Contact between bolt and plate elements (a) and (b) are friction and ldquohardrdquo contact and (c) and (d) are frictionless
S
S
S
S
S
S
S
S
M
M
M
M
M
M
M
M
Figure 4 Definition of master and slave surface in the contact zones M master surface S slave surface
by splitting the bolt body and applying a magnitude ofpreload force on two parallel surfaces in the bolt-shank AtAbaqusCAE are created the datum axes and the partition ofthe bolt body in themiddle of the shank as shown in Figure 5The magnitude of preload force is 70 of their minimumtensile strength of the bolt [11] After applying the pretensionto the bolts their length is fixed at their current positionThis technique helps to avoid the problem with extensiveelongation of the bolts under the loading During the first twosteps (Initial Step and Step 1) all three translational degreesof freedom (DOF) at the section of pretension are restrainedThis degree of freedom served as the artificial boundarycondition to prevent the numerical singularity error whichoccurs as a result of rigid body motion After the preloading
and activating the contact properties this artificial boundarycondition is then removed
Initial Step Boundary condition and initial state of stress inbolt-shank
Step 1 Activating the contact element with small load value
Step 2 External load
The preloading of bolt is simulated in the Initial Step asinitial state of stress in the bolt-shank which is defined in theload module as a Predefined Field In order to activate the
4 Journal of Computational Engineering
Figure 5 Preload bolt by bolt load method
contact between connected elements small loading will beacting on the element in the direction of pretensionThe valueof this load is small enough that it does not have an effect onthe overall behaviour of joint
Comparison between aforementioned analysis proce-dures will be shown on the numericalmodel of extended end-plate connection under the monotonic loadingThe accuracyof obtaining results will be compared with experimental testSC3 by [10] Advantages and disadvantages of pretensiontechnique as well as the speed of numerical models will bepresented in the next section
3 Finite Element Analysis of ExtendedBeam-to-Column Bolted Connection
Theextended end-plate connection consists of steelH-shapedbeam H-300 times 200 times 8 times 12mm H-shaped column H-300 times250 times 8 times 12mm and high-strength pretensioned bolts end-plate thickness was 20mm and column stiffeners thicknesswas 12mm The specimen was fabricated from Q345B steelThe end-plate was connected to the column flange with high-strength pretensioned bolts M20 with diameter 20mm andgrade 109Thepretension force valuewas 155 kN according toChinese Specification JGJ82-91 (1992)The friction coefficientof contact surface was considered as 044 Loading patternwas imposed on the end of the beamas shown in Figure 6Thethickness of the column flange is taken to be the same as thethickness of the end-plate within the length range of 100mmabove the extension of the end-plate and 100mm below theextension of the end-plate
In the finite element model the stress-strain relationshipof steel plates is elastic-perfectly plastic trilinear and Poissonrsquosratio is 03 Yield strength and ultimate strength value of steelplates thicker than 16mm are 363MPa and 537MPa respec-tively while its Youngmodulus is 204227MPa Yield strengthand ultimate strength value of steel plates thinner than orequal to 16mm are 391MPa and 559MPa respectively whileits Young modulus is 190707MPa The stress-strain relation-ship of high-strength bolts is trilinear andmaterial propertiesare shown in Table 1 Youngrsquos modulus of the bolts is takenas 206000Mpa The stress-strain relationship was shown inFigure 7
Table 1 Material properties of high strength bolts
Stress [MPa] 990 1160 1160Strain 000483 0136 015
Due to the symmetry about a vertical plane passingthrough the beam and columnwebs only one-half of the con-nection is considered in the numerical model see Figure 8Numerical modelling of connection is carried out by usingthe following parameters geometric and material nonlinear-ities of the elementary parts of connection bolt pretensionforce contact between column flange and end-plate washersand plated elements bolt-shank and hole and frictionStatic analysis was conducted for the monotonic loading asdisplacement control load with value of 125mm which wasacting on the beam end at the lever arm of 1200mm (distancefrom the loading point to the column flange) The constantaxial force with a value of 485 kN was acting on the top andthe bottom end of the column Axial force was modelled asthe pressure preentire surface of the cross section
4 Results and Discussions
In order to validate the accuracy of nonlinear finite elementmodel of end-plate connection obtained results are com-pared with experimental test by Shi et al [10] The behaviourof beam-to-column connection was shown in the form ofmoment-rotation (119872-120601) curves see Figure 9 Red curve rep-resents the results of model obtained from analysis with ldquoboltloadrdquo preloading technique while the green curve representsthe results of model obtained from analysis with ldquoinitialstressrdquo preload technique Both curves were comparable witha black curve which present the experiment test resultsLoading capacity and moment resistance of connection wereshown in Table 2
State of stress after pretension of the bolt using ldquobolt loadrdquotechnique is shown in Figure 10 Stress value in the preloadingdirection before the external loading was 49727MPa seeFigure 11 Figure 12(a) presents the initial stress on the firstframe of the analysis and had a value 840MPa After activat-ing the contact properties between the connected elementsredistribution of stresses was occurring between the bolt and
Journal of Computational Engineering 5
Constant axial force
Constant axial force
Load displacement control
Column stiffenersBeam
Column
End-plate
Bolt
1200
115
70
965
965
70
115
Restraint displacement in z-direction
Restraint displacement in z-direction
Restraint displacement in x- y- and z-directions
Figure 6 Details of end-plate beam-to-column connection (mm)
Table 2 Comparison of numerical and test results
FEA Test by Shi et al [10]Loading capacity [kN] Moment resistance [kNm] Loading capacity [kN] Moment resistance [kNm]
ldquoBolt loadrdquo case 25689 30828 2569 3083ldquoInitial stressrdquo case 24484 30342
plate elements Finally the stress value in the bolt was4946MPa
Figure 12(a) shows the failure modes of finite elementmodel and Figure 12(b) failure modes of the specimen SC3which is experimentally tested by Shi et al [10] Figure 12(b)shows the failure mode after bolt fracture
5 Conclusions
The behaviour of preload bolted joints was investigated fortwo different techniques of preloading using finite elementmethod in software Abaqus Standard The behaviour ofbolted joints was shown on the extended beam-to-columnend-plate connectionwhose results were then comparedwithexperimental test The static analysis for ldquobolt loadrdquo preload-ing techniquemodel gives the nonsignificant difference of the
loading capacity value compared with test results The staticanalysis for ldquoinitial stressrdquo preloading technique model gives492 lower value of the loading capacity compared withtest results If the loading process was continued the higherloading capacity was obtained showing the interrupted partof the curve in Figure 9 Such behaviour is the result ofthe simple constitutive model of steel which is used inthe finite element model In spite of that both numericalresults provide very good behaviour of the connection untilachieving the maximum moment resistance compared withexperimental test Finally the finite element method is acost-effective way to investigate and provide the satisfactoryprediction of the behaviour of connection
Comparing the ldquobolt loadrdquo and ldquoinitial stressrdquo preloadingtechnique the results show that the ldquoinitial stressrdquo preloadingtechnique gives satisfactory results This method also avoids
6 Journal of Computational Engineering
120590(M
Pa)
120590(M
Pa)
Steel plates t le 16mmSteel plates t gt 16mm998400998400
Bolts
Strain hardeningStrain hardening
005 010 015 020000120576 (mdash)
005 010 015 020000120576 (mdash)
0
200
400
600
800
1000
1200
1400
0
100
200
300
400
500
600
Figure 7 Stress-strain relationship of steel plates and bolts
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
Figure 2 Finite element model of (a) plate element (b) bolt
together with washers on both ends of the boltThreaded partof the bolt-shank and the extended length of the bolt beyondeach nut were ignored Hexagonal shape of the bolt-head andnut was replaced with a cylinder The typical bolted joint ispresented in Figure 1
21 Finite Element Mesh and Contact Modelling The platedelements in the joint were meshed with 8-node first-order(linear) hexagon (brick) elements with incompatible modes(C3D8I) Each of these elements has 13 additional degrees offreedom (DOF) when compared to the fully integrated ele-ments (C3D8) providing superior performance in bendingdominant problems without shear locking behaviour or zeroenergy deformation modes see Figure 2(a) The 6-noddedlinear triangular prism element (C3D6) was used to modelthe bolts The details of the finite element mesh are shownin Figure 2(b) Structure mesh technique is used for all partsof assembly Previously the bolts as well as bolt-hole regionare quarter-partitioned Then they mesh with 16 elementsaround the circumference
Numerical results are highly sensitive to the contact prop-erties between components of the joints and the preloadedbolts Small sliding surface-to-surface discretization methodwas considered for all the contacts The surface contactproperties between the plate elements were modelled as atangential behaviour using penalty friction with the friction
coefficient value of 044 Normal behaviour contact proper-ties using Augmented Lagrangian Formulation were consid-ered for the normal forces between the same componentssee Figures 3(a) and 3(b) The tangential contact betweenbolt-shank and bolt-hole was considered to be frictionlesssee Figures 3(c) and 3(d) The hard contact was used for theconnection between bolt-headnut and plate elements Thebolts are usuallymore rigid than hot-rolled steelmember andthey are usually denoted as a master surface in the contactpairs see Figure 4
22 Simulation Procedure and Bolt Preload The analysis hasbeen performed through the steps in two different waysdepending on the type of the bolt pretension technique
Step 1 Bolt preloadingactivating the contact element
Step 2 Fixing the bolt length
Step 3 External load
The bolts are preloaded in the first step of the analysisaccording to bolt load method The pretension is simulated
Journal of Computational Engineering 3
(a) (b)
(c) (d)
Figure 3 Contact between bolt and plate elements (a) and (b) are friction and ldquohardrdquo contact and (c) and (d) are frictionless
S
S
S
S
S
S
S
S
M
M
M
M
M
M
M
M
Figure 4 Definition of master and slave surface in the contact zones M master surface S slave surface
by splitting the bolt body and applying a magnitude ofpreload force on two parallel surfaces in the bolt-shank AtAbaqusCAE are created the datum axes and the partition ofthe bolt body in themiddle of the shank as shown in Figure 5The magnitude of preload force is 70 of their minimumtensile strength of the bolt [11] After applying the pretensionto the bolts their length is fixed at their current positionThis technique helps to avoid the problem with extensiveelongation of the bolts under the loading During the first twosteps (Initial Step and Step 1) all three translational degreesof freedom (DOF) at the section of pretension are restrainedThis degree of freedom served as the artificial boundarycondition to prevent the numerical singularity error whichoccurs as a result of rigid body motion After the preloading
and activating the contact properties this artificial boundarycondition is then removed
Initial Step Boundary condition and initial state of stress inbolt-shank
Step 1 Activating the contact element with small load value
Step 2 External load
The preloading of bolt is simulated in the Initial Step asinitial state of stress in the bolt-shank which is defined in theload module as a Predefined Field In order to activate the
4 Journal of Computational Engineering
Figure 5 Preload bolt by bolt load method
contact between connected elements small loading will beacting on the element in the direction of pretensionThe valueof this load is small enough that it does not have an effect onthe overall behaviour of joint
Comparison between aforementioned analysis proce-dures will be shown on the numericalmodel of extended end-plate connection under the monotonic loadingThe accuracyof obtaining results will be compared with experimental testSC3 by [10] Advantages and disadvantages of pretensiontechnique as well as the speed of numerical models will bepresented in the next section
3 Finite Element Analysis of ExtendedBeam-to-Column Bolted Connection
Theextended end-plate connection consists of steelH-shapedbeam H-300 times 200 times 8 times 12mm H-shaped column H-300 times250 times 8 times 12mm and high-strength pretensioned bolts end-plate thickness was 20mm and column stiffeners thicknesswas 12mm The specimen was fabricated from Q345B steelThe end-plate was connected to the column flange with high-strength pretensioned bolts M20 with diameter 20mm andgrade 109Thepretension force valuewas 155 kN according toChinese Specification JGJ82-91 (1992)The friction coefficientof contact surface was considered as 044 Loading patternwas imposed on the end of the beamas shown in Figure 6Thethickness of the column flange is taken to be the same as thethickness of the end-plate within the length range of 100mmabove the extension of the end-plate and 100mm below theextension of the end-plate
In the finite element model the stress-strain relationshipof steel plates is elastic-perfectly plastic trilinear and Poissonrsquosratio is 03 Yield strength and ultimate strength value of steelplates thicker than 16mm are 363MPa and 537MPa respec-tively while its Youngmodulus is 204227MPa Yield strengthand ultimate strength value of steel plates thinner than orequal to 16mm are 391MPa and 559MPa respectively whileits Young modulus is 190707MPa The stress-strain relation-ship of high-strength bolts is trilinear andmaterial propertiesare shown in Table 1 Youngrsquos modulus of the bolts is takenas 206000Mpa The stress-strain relationship was shown inFigure 7
Table 1 Material properties of high strength bolts
Stress [MPa] 990 1160 1160Strain 000483 0136 015
Due to the symmetry about a vertical plane passingthrough the beam and columnwebs only one-half of the con-nection is considered in the numerical model see Figure 8Numerical modelling of connection is carried out by usingthe following parameters geometric and material nonlinear-ities of the elementary parts of connection bolt pretensionforce contact between column flange and end-plate washersand plated elements bolt-shank and hole and frictionStatic analysis was conducted for the monotonic loading asdisplacement control load with value of 125mm which wasacting on the beam end at the lever arm of 1200mm (distancefrom the loading point to the column flange) The constantaxial force with a value of 485 kN was acting on the top andthe bottom end of the column Axial force was modelled asthe pressure preentire surface of the cross section
4 Results and Discussions
In order to validate the accuracy of nonlinear finite elementmodel of end-plate connection obtained results are com-pared with experimental test by Shi et al [10] The behaviourof beam-to-column connection was shown in the form ofmoment-rotation (119872-120601) curves see Figure 9 Red curve rep-resents the results of model obtained from analysis with ldquoboltloadrdquo preloading technique while the green curve representsthe results of model obtained from analysis with ldquoinitialstressrdquo preload technique Both curves were comparable witha black curve which present the experiment test resultsLoading capacity and moment resistance of connection wereshown in Table 2
State of stress after pretension of the bolt using ldquobolt loadrdquotechnique is shown in Figure 10 Stress value in the preloadingdirection before the external loading was 49727MPa seeFigure 11 Figure 12(a) presents the initial stress on the firstframe of the analysis and had a value 840MPa After activat-ing the contact properties between the connected elementsredistribution of stresses was occurring between the bolt and
Journal of Computational Engineering 5
Constant axial force
Constant axial force
Load displacement control
Column stiffenersBeam
Column
End-plate
Bolt
1200
115
70
965
965
70
115
Restraint displacement in z-direction
Restraint displacement in z-direction
Restraint displacement in x- y- and z-directions
Figure 6 Details of end-plate beam-to-column connection (mm)
Table 2 Comparison of numerical and test results
FEA Test by Shi et al [10]Loading capacity [kN] Moment resistance [kNm] Loading capacity [kN] Moment resistance [kNm]
ldquoBolt loadrdquo case 25689 30828 2569 3083ldquoInitial stressrdquo case 24484 30342
plate elements Finally the stress value in the bolt was4946MPa
Figure 12(a) shows the failure modes of finite elementmodel and Figure 12(b) failure modes of the specimen SC3which is experimentally tested by Shi et al [10] Figure 12(b)shows the failure mode after bolt fracture
5 Conclusions
The behaviour of preload bolted joints was investigated fortwo different techniques of preloading using finite elementmethod in software Abaqus Standard The behaviour ofbolted joints was shown on the extended beam-to-columnend-plate connectionwhose results were then comparedwithexperimental test The static analysis for ldquobolt loadrdquo preload-ing techniquemodel gives the nonsignificant difference of the
loading capacity value compared with test results The staticanalysis for ldquoinitial stressrdquo preloading technique model gives492 lower value of the loading capacity compared withtest results If the loading process was continued the higherloading capacity was obtained showing the interrupted partof the curve in Figure 9 Such behaviour is the result ofthe simple constitutive model of steel which is used inthe finite element model In spite of that both numericalresults provide very good behaviour of the connection untilachieving the maximum moment resistance compared withexperimental test Finally the finite element method is acost-effective way to investigate and provide the satisfactoryprediction of the behaviour of connection
Comparing the ldquobolt loadrdquo and ldquoinitial stressrdquo preloadingtechnique the results show that the ldquoinitial stressrdquo preloadingtechnique gives satisfactory results This method also avoids
6 Journal of Computational Engineering
120590(M
Pa)
120590(M
Pa)
Steel plates t le 16mmSteel plates t gt 16mm998400998400
Bolts
Strain hardeningStrain hardening
005 010 015 020000120576 (mdash)
005 010 015 020000120576 (mdash)
0
200
400
600
800
1000
1200
1400
0
100
200
300
400
500
600
Figure 7 Stress-strain relationship of steel plates and bolts
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
Figure 3 Contact between bolt and plate elements (a) and (b) are friction and ldquohardrdquo contact and (c) and (d) are frictionless
S
S
S
S
S
S
S
S
M
M
M
M
M
M
M
M
Figure 4 Definition of master and slave surface in the contact zones M master surface S slave surface
by splitting the bolt body and applying a magnitude ofpreload force on two parallel surfaces in the bolt-shank AtAbaqusCAE are created the datum axes and the partition ofthe bolt body in themiddle of the shank as shown in Figure 5The magnitude of preload force is 70 of their minimumtensile strength of the bolt [11] After applying the pretensionto the bolts their length is fixed at their current positionThis technique helps to avoid the problem with extensiveelongation of the bolts under the loading During the first twosteps (Initial Step and Step 1) all three translational degreesof freedom (DOF) at the section of pretension are restrainedThis degree of freedom served as the artificial boundarycondition to prevent the numerical singularity error whichoccurs as a result of rigid body motion After the preloading
and activating the contact properties this artificial boundarycondition is then removed
Initial Step Boundary condition and initial state of stress inbolt-shank
Step 1 Activating the contact element with small load value
Step 2 External load
The preloading of bolt is simulated in the Initial Step asinitial state of stress in the bolt-shank which is defined in theload module as a Predefined Field In order to activate the
4 Journal of Computational Engineering
Figure 5 Preload bolt by bolt load method
contact between connected elements small loading will beacting on the element in the direction of pretensionThe valueof this load is small enough that it does not have an effect onthe overall behaviour of joint
Comparison between aforementioned analysis proce-dures will be shown on the numericalmodel of extended end-plate connection under the monotonic loadingThe accuracyof obtaining results will be compared with experimental testSC3 by [10] Advantages and disadvantages of pretensiontechnique as well as the speed of numerical models will bepresented in the next section
3 Finite Element Analysis of ExtendedBeam-to-Column Bolted Connection
Theextended end-plate connection consists of steelH-shapedbeam H-300 times 200 times 8 times 12mm H-shaped column H-300 times250 times 8 times 12mm and high-strength pretensioned bolts end-plate thickness was 20mm and column stiffeners thicknesswas 12mm The specimen was fabricated from Q345B steelThe end-plate was connected to the column flange with high-strength pretensioned bolts M20 with diameter 20mm andgrade 109Thepretension force valuewas 155 kN according toChinese Specification JGJ82-91 (1992)The friction coefficientof contact surface was considered as 044 Loading patternwas imposed on the end of the beamas shown in Figure 6Thethickness of the column flange is taken to be the same as thethickness of the end-plate within the length range of 100mmabove the extension of the end-plate and 100mm below theextension of the end-plate
In the finite element model the stress-strain relationshipof steel plates is elastic-perfectly plastic trilinear and Poissonrsquosratio is 03 Yield strength and ultimate strength value of steelplates thicker than 16mm are 363MPa and 537MPa respec-tively while its Youngmodulus is 204227MPa Yield strengthand ultimate strength value of steel plates thinner than orequal to 16mm are 391MPa and 559MPa respectively whileits Young modulus is 190707MPa The stress-strain relation-ship of high-strength bolts is trilinear andmaterial propertiesare shown in Table 1 Youngrsquos modulus of the bolts is takenas 206000Mpa The stress-strain relationship was shown inFigure 7
Table 1 Material properties of high strength bolts
Stress [MPa] 990 1160 1160Strain 000483 0136 015
Due to the symmetry about a vertical plane passingthrough the beam and columnwebs only one-half of the con-nection is considered in the numerical model see Figure 8Numerical modelling of connection is carried out by usingthe following parameters geometric and material nonlinear-ities of the elementary parts of connection bolt pretensionforce contact between column flange and end-plate washersand plated elements bolt-shank and hole and frictionStatic analysis was conducted for the monotonic loading asdisplacement control load with value of 125mm which wasacting on the beam end at the lever arm of 1200mm (distancefrom the loading point to the column flange) The constantaxial force with a value of 485 kN was acting on the top andthe bottom end of the column Axial force was modelled asthe pressure preentire surface of the cross section
4 Results and Discussions
In order to validate the accuracy of nonlinear finite elementmodel of end-plate connection obtained results are com-pared with experimental test by Shi et al [10] The behaviourof beam-to-column connection was shown in the form ofmoment-rotation (119872-120601) curves see Figure 9 Red curve rep-resents the results of model obtained from analysis with ldquoboltloadrdquo preloading technique while the green curve representsthe results of model obtained from analysis with ldquoinitialstressrdquo preload technique Both curves were comparable witha black curve which present the experiment test resultsLoading capacity and moment resistance of connection wereshown in Table 2
State of stress after pretension of the bolt using ldquobolt loadrdquotechnique is shown in Figure 10 Stress value in the preloadingdirection before the external loading was 49727MPa seeFigure 11 Figure 12(a) presents the initial stress on the firstframe of the analysis and had a value 840MPa After activat-ing the contact properties between the connected elementsredistribution of stresses was occurring between the bolt and
Journal of Computational Engineering 5
Constant axial force
Constant axial force
Load displacement control
Column stiffenersBeam
Column
End-plate
Bolt
1200
115
70
965
965
70
115
Restraint displacement in z-direction
Restraint displacement in z-direction
Restraint displacement in x- y- and z-directions
Figure 6 Details of end-plate beam-to-column connection (mm)
Table 2 Comparison of numerical and test results
FEA Test by Shi et al [10]Loading capacity [kN] Moment resistance [kNm] Loading capacity [kN] Moment resistance [kNm]
ldquoBolt loadrdquo case 25689 30828 2569 3083ldquoInitial stressrdquo case 24484 30342
plate elements Finally the stress value in the bolt was4946MPa
Figure 12(a) shows the failure modes of finite elementmodel and Figure 12(b) failure modes of the specimen SC3which is experimentally tested by Shi et al [10] Figure 12(b)shows the failure mode after bolt fracture
5 Conclusions
The behaviour of preload bolted joints was investigated fortwo different techniques of preloading using finite elementmethod in software Abaqus Standard The behaviour ofbolted joints was shown on the extended beam-to-columnend-plate connectionwhose results were then comparedwithexperimental test The static analysis for ldquobolt loadrdquo preload-ing techniquemodel gives the nonsignificant difference of the
loading capacity value compared with test results The staticanalysis for ldquoinitial stressrdquo preloading technique model gives492 lower value of the loading capacity compared withtest results If the loading process was continued the higherloading capacity was obtained showing the interrupted partof the curve in Figure 9 Such behaviour is the result ofthe simple constitutive model of steel which is used inthe finite element model In spite of that both numericalresults provide very good behaviour of the connection untilachieving the maximum moment resistance compared withexperimental test Finally the finite element method is acost-effective way to investigate and provide the satisfactoryprediction of the behaviour of connection
Comparing the ldquobolt loadrdquo and ldquoinitial stressrdquo preloadingtechnique the results show that the ldquoinitial stressrdquo preloadingtechnique gives satisfactory results This method also avoids
6 Journal of Computational Engineering
120590(M
Pa)
120590(M
Pa)
Steel plates t le 16mmSteel plates t gt 16mm998400998400
Bolts
Strain hardeningStrain hardening
005 010 015 020000120576 (mdash)
005 010 015 020000120576 (mdash)
0
200
400
600
800
1000
1200
1400
0
100
200
300
400
500
600
Figure 7 Stress-strain relationship of steel plates and bolts
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
contact between connected elements small loading will beacting on the element in the direction of pretensionThe valueof this load is small enough that it does not have an effect onthe overall behaviour of joint
Comparison between aforementioned analysis proce-dures will be shown on the numericalmodel of extended end-plate connection under the monotonic loadingThe accuracyof obtaining results will be compared with experimental testSC3 by [10] Advantages and disadvantages of pretensiontechnique as well as the speed of numerical models will bepresented in the next section
3 Finite Element Analysis of ExtendedBeam-to-Column Bolted Connection
Theextended end-plate connection consists of steelH-shapedbeam H-300 times 200 times 8 times 12mm H-shaped column H-300 times250 times 8 times 12mm and high-strength pretensioned bolts end-plate thickness was 20mm and column stiffeners thicknesswas 12mm The specimen was fabricated from Q345B steelThe end-plate was connected to the column flange with high-strength pretensioned bolts M20 with diameter 20mm andgrade 109Thepretension force valuewas 155 kN according toChinese Specification JGJ82-91 (1992)The friction coefficientof contact surface was considered as 044 Loading patternwas imposed on the end of the beamas shown in Figure 6Thethickness of the column flange is taken to be the same as thethickness of the end-plate within the length range of 100mmabove the extension of the end-plate and 100mm below theextension of the end-plate
In the finite element model the stress-strain relationshipof steel plates is elastic-perfectly plastic trilinear and Poissonrsquosratio is 03 Yield strength and ultimate strength value of steelplates thicker than 16mm are 363MPa and 537MPa respec-tively while its Youngmodulus is 204227MPa Yield strengthand ultimate strength value of steel plates thinner than orequal to 16mm are 391MPa and 559MPa respectively whileits Young modulus is 190707MPa The stress-strain relation-ship of high-strength bolts is trilinear andmaterial propertiesare shown in Table 1 Youngrsquos modulus of the bolts is takenas 206000Mpa The stress-strain relationship was shown inFigure 7
Table 1 Material properties of high strength bolts
Stress [MPa] 990 1160 1160Strain 000483 0136 015
Due to the symmetry about a vertical plane passingthrough the beam and columnwebs only one-half of the con-nection is considered in the numerical model see Figure 8Numerical modelling of connection is carried out by usingthe following parameters geometric and material nonlinear-ities of the elementary parts of connection bolt pretensionforce contact between column flange and end-plate washersand plated elements bolt-shank and hole and frictionStatic analysis was conducted for the monotonic loading asdisplacement control load with value of 125mm which wasacting on the beam end at the lever arm of 1200mm (distancefrom the loading point to the column flange) The constantaxial force with a value of 485 kN was acting on the top andthe bottom end of the column Axial force was modelled asthe pressure preentire surface of the cross section
4 Results and Discussions
In order to validate the accuracy of nonlinear finite elementmodel of end-plate connection obtained results are com-pared with experimental test by Shi et al [10] The behaviourof beam-to-column connection was shown in the form ofmoment-rotation (119872-120601) curves see Figure 9 Red curve rep-resents the results of model obtained from analysis with ldquoboltloadrdquo preloading technique while the green curve representsthe results of model obtained from analysis with ldquoinitialstressrdquo preload technique Both curves were comparable witha black curve which present the experiment test resultsLoading capacity and moment resistance of connection wereshown in Table 2
State of stress after pretension of the bolt using ldquobolt loadrdquotechnique is shown in Figure 10 Stress value in the preloadingdirection before the external loading was 49727MPa seeFigure 11 Figure 12(a) presents the initial stress on the firstframe of the analysis and had a value 840MPa After activat-ing the contact properties between the connected elementsredistribution of stresses was occurring between the bolt and
Journal of Computational Engineering 5
Constant axial force
Constant axial force
Load displacement control
Column stiffenersBeam
Column
End-plate
Bolt
1200
115
70
965
965
70
115
Restraint displacement in z-direction
Restraint displacement in z-direction
Restraint displacement in x- y- and z-directions
Figure 6 Details of end-plate beam-to-column connection (mm)
Table 2 Comparison of numerical and test results
FEA Test by Shi et al [10]Loading capacity [kN] Moment resistance [kNm] Loading capacity [kN] Moment resistance [kNm]
ldquoBolt loadrdquo case 25689 30828 2569 3083ldquoInitial stressrdquo case 24484 30342
plate elements Finally the stress value in the bolt was4946MPa
Figure 12(a) shows the failure modes of finite elementmodel and Figure 12(b) failure modes of the specimen SC3which is experimentally tested by Shi et al [10] Figure 12(b)shows the failure mode after bolt fracture
5 Conclusions
The behaviour of preload bolted joints was investigated fortwo different techniques of preloading using finite elementmethod in software Abaqus Standard The behaviour ofbolted joints was shown on the extended beam-to-columnend-plate connectionwhose results were then comparedwithexperimental test The static analysis for ldquobolt loadrdquo preload-ing techniquemodel gives the nonsignificant difference of the
loading capacity value compared with test results The staticanalysis for ldquoinitial stressrdquo preloading technique model gives492 lower value of the loading capacity compared withtest results If the loading process was continued the higherloading capacity was obtained showing the interrupted partof the curve in Figure 9 Such behaviour is the result ofthe simple constitutive model of steel which is used inthe finite element model In spite of that both numericalresults provide very good behaviour of the connection untilachieving the maximum moment resistance compared withexperimental test Finally the finite element method is acost-effective way to investigate and provide the satisfactoryprediction of the behaviour of connection
Comparing the ldquobolt loadrdquo and ldquoinitial stressrdquo preloadingtechnique the results show that the ldquoinitial stressrdquo preloadingtechnique gives satisfactory results This method also avoids
6 Journal of Computational Engineering
120590(M
Pa)
120590(M
Pa)
Steel plates t le 16mmSteel plates t gt 16mm998400998400
Bolts
Strain hardeningStrain hardening
005 010 015 020000120576 (mdash)
005 010 015 020000120576 (mdash)
0
200
400
600
800
1000
1200
1400
0
100
200
300
400
500
600
Figure 7 Stress-strain relationship of steel plates and bolts
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
Figure 6 Details of end-plate beam-to-column connection (mm)
Table 2 Comparison of numerical and test results
FEA Test by Shi et al [10]Loading capacity [kN] Moment resistance [kNm] Loading capacity [kN] Moment resistance [kNm]
ldquoBolt loadrdquo case 25689 30828 2569 3083ldquoInitial stressrdquo case 24484 30342
plate elements Finally the stress value in the bolt was4946MPa
Figure 12(a) shows the failure modes of finite elementmodel and Figure 12(b) failure modes of the specimen SC3which is experimentally tested by Shi et al [10] Figure 12(b)shows the failure mode after bolt fracture
5 Conclusions
The behaviour of preload bolted joints was investigated fortwo different techniques of preloading using finite elementmethod in software Abaqus Standard The behaviour ofbolted joints was shown on the extended beam-to-columnend-plate connectionwhose results were then comparedwithexperimental test The static analysis for ldquobolt loadrdquo preload-ing techniquemodel gives the nonsignificant difference of the
loading capacity value compared with test results The staticanalysis for ldquoinitial stressrdquo preloading technique model gives492 lower value of the loading capacity compared withtest results If the loading process was continued the higherloading capacity was obtained showing the interrupted partof the curve in Figure 9 Such behaviour is the result ofthe simple constitutive model of steel which is used inthe finite element model In spite of that both numericalresults provide very good behaviour of the connection untilachieving the maximum moment resistance compared withexperimental test Finally the finite element method is acost-effective way to investigate and provide the satisfactoryprediction of the behaviour of connection
Comparing the ldquobolt loadrdquo and ldquoinitial stressrdquo preloadingtechnique the results show that the ldquoinitial stressrdquo preloadingtechnique gives satisfactory results This method also avoids
6 Journal of Computational Engineering
120590(M
Pa)
120590(M
Pa)
Steel plates t le 16mmSteel plates t gt 16mm998400998400
Bolts
Strain hardeningStrain hardening
005 010 015 020000120576 (mdash)
005 010 015 020000120576 (mdash)
0
200
400
600
800
1000
1200
1400
0
100
200
300
400
500
600
Figure 7 Stress-strain relationship of steel plates and bolts
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
Figure 11 Preload bolt by ldquoinitial stressrdquo preloading technique
(a) (b)
Figure 12 Failure mode of (a) finite element model and (b) specimen by Shi et al [10]
the numerical error problems such as numerical singularityand negative eigenvalues as the results of rigid body motionUsing this method of preloading in the connection the arti-ficial boundary condition before preloading is not necessaryIn addition problem of extensive elongation of bolts due toexternal load is also avoided Moreover the model with ldquoboltloadrdquo preloading technique completes the analysis with 34increments while the model with ldquoinitial stressrdquo preloadingtechnique has only 23 increments This computational effi-ciency plays an important role when the models are largerwith more contact surfaces
Competing Interests
The authors declare that there are no competing interestsregarding the publication of this paper
Acknowledgments
The research presented in this work was done within thescientific project Grant no 13051101 supported by theUniversity of Rijeka
8 Journal of Computational Engineering
References
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
[1] M R Bahaari and A N Sherbourne ldquoBehavior of eight-boltlarge capacity endplate connectionsrdquoComputers and Structuresvol 77 no 3 pp 315ndash325 2000
[2] Y I Maggi R M Goncalves R T Leon and L F L RibeiroldquoParametric analysis of steel bolted end plate connectionsusing finite element modelingrdquo Journal of Constructional SteelResearch vol 61 no 5 pp 689ndash708 2005
[3] C Dıaz M Victoria P Martı and O M Querin ldquoFE modelof beam-to-column extended end-plate jointsrdquo Journal of Con-structional Steel Research vol 67 no 10 pp 1578ndash1590 2011
[4] G Shi Y Shi Y Wang and M A Bradford ldquoNumericalsimulation of steel pretensioned bolted end-plate connectionsof different types and detailsrdquo Engineering Structures vol 30no 10 pp 2677ndash2686 2008
[5] M Gerami H Saberi V Saberi and A S Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4 pp690ndash705 2011
[6] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquo Journalof Constructional Steel Research vol 90 pp 140ndash152 2013
[7] R Kiamanesh A Abolmaali and M Razavi ldquoEffect of circularbolt pattern on behavior of extended end-plate connectionrdquoJournal of Structural Engineering vol 139 no 11 pp 1833ndash18412013
[8] ABAQUS Analysis Userrsquos Manual I V Version 612 ABAQUSDassault Systemes Fremont Calif USA 2012
[9] S Selamet and M Garlock ldquoGuidlines for modeling threedimensional structural conncetion models using finite elementmethodsrdquo in Proceedings of the International Symposium onSteel Structures Culture amp Sustainability p 14 Istanbul TurkeySeptember 2010
[10] G Shi Y Shi Y Wang and F Bijlaard ldquoMonotonic loadingtests on semi-rigid end-plate connections with welded I-shapedcolumns and beamsrdquoAdvances in Structural Engineering vol 13no 2 pp 215ndash229 2010
[11] EC3 Design of Steel Structures Part 1-8 Design of Joints (EN1993-1-8) European Committee for Standardization (CEN)Brusseles Belgium 2005
