AnalysisoftheMechanicalBehaviorofBoltedBeam-Column … · 2018. 11. 7. · beam webs, the contact between the end plates and the columnﬂanges,thecontactbetweentheT-sectionsteelsand

Research ArticleAnalysis of the Mechanical Behavior of Bolted Beam-ColumnConnections with Different Structural Forms

Rongqian Yang1 and Xuejun Zhou 2

1School of Civil Engineering Shandong University Jinan 250101 China2School of Civil Engineering Shandong Jianzhu University Jinan 250101 China

Correspondence should be addressed to Xuejun Zhou xuejunzhousdjzueducn

Received 7 November 2018 Accepted 30 December 2018 Published 3 March 2019

Academic Editor Rosario Montuori

Copyright copy 2019 Rongqian Yang and Xuejun Zhou is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

In order to study the mechanical behavior of bolted beam-column connections the accuracy and applicability of the finite elementmodel were firstly validated according to the published experiments on end-plate connections using ABAQUS en in order todiscuss the mechanical behavior of connections three semirigid connections which are convenient for prefabricated constructionincluding top-and-seat angle connections with web and ear plate extended end-plate connection and T-stub connection wereexamined using numerical simulation analysis to study and compare their capacity hysteretic behavior ductility and degradationcharacteristics in detail e results showed that the finite element models that were built could effectively simulate the loadbearing behavior of bolted connections under both single-direction loading and cyclic loading e three connections showedgood load bearing capacity e connectors significantly affected the energy dissipation capacity under load e extended end-plate connection demonstrated the best performance in both mechanical behavior and manufacture and installation so it wouldtherefore be the preferred option

1 Introduction

Bolted beam-column connection joints have the advantagessuch as a high degree of assemblage quick speed of con-struction energy conservation and environmental pro-tection which meet the requirements of industrial buildingIn the Northridge earthquake in the United States in 1994and in the Kobe earthquake in Japan in 1995 a large numberof beam column welded joints displayed brittle fracturefailure at the welded seams of the lower flanges [1] resultingin casualties while the bolted joints were only lightlydamaged and showed excellent seismic performance

Relevant research [2ndash5] shows that the mechanicalcharacteristics of bolted beam-column connection joints arebounded by perfectly rigid joints and ideal articulated jointsshowing the characteristics of semirigid jointse semirigidnature of the joints has a significant effect on the overallperformance of the structure and its good deformationcapacity can optimize the distribution of bending moments

in the steel frame making the structure better both in stressand required quantity of steel [6ndash8] ere are variousstructural types of semirigid bolted joints common end-plate connections steel angle connections and T-sectionsteel connections e mechanical properties of these threekinds of joints at home and abroad have been studied [9ndash19]however load tests and variable analysis have basically beenonly carried out on one kind of joint without systematiccomparison and analysis of the seismic performance ofcommon types of semirigid structural joints which cannotbe used to guide engineering design

Firstly based on the existing experimental research thispaper used the finite element analysis software ABAQUS toestablish an analytic finite element model of the end-plateconnection which was then compared with the experi-mental results to verify the accuracy and applicability of themodel Secondly an analytic finite element model of the top-seat angle connections with web and ear plate of extendedendplate connections and T-section steel connections was

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 1967253 11 pageshttpsdoiorg10115520191967253

established to contrast and analyze the performance pa-rameters such as load-bearing capacity hysteretic perfor-mance ductility performance and failure modes emechanical properties of semirigid joints of differentstructural types structures and proposed designs have beendiscussed in depth Designers can then select the appropriatejoint types according to the design requirements

2 Finite Element Model andExperimental Verification

In order to verify the accuracy and applicability of the finiteelement model that has been established in this paper themonotonic loading test of end-plate connections establishedby Guo et al [19] was selected

21 Finite Element Model e finite element model con-sisted of steel beams steel columns end-plates ribbed webstiffeners and high-strength friction type bolts An eight-joint hexahedral linear reduced integral unit C3D8R wasselected for the simulation and mesh refinement wasmanually performed on the areas of stress concentrationsuch as bolt holes e constitutive relationship of the steeladopted the experimental material property data from theliterature e lateral constraints boundary conditions andloading systems of the finite element model were all con-sistent with the experiment

22 Experimental Verification e experimental specimensfrom Guo et al were designed at a reduced scale of 1 2 esectional dimensions of each member are shown in Table 1e sectional plastic modulus ratio of the beams and col-umns was 143 which meets the design requirements ofstrong columns and weak beams of the ldquoCode for SeismicDesign of Buildingsrdquo (2016 Edition) (GB50011-2010) [20]e specimen loading device is shown in Figure 1

e comparison curve of the bending moment anglebetween the finite element analysis and the experiment isshown in Figure 2 and the comparison of the typical failuremodes is shown in Figure 3 It can be seen that it is feasible tosimulate the mechanical properties of semirigid joints byusing the established finite element model

3 Comparison of the Mechanical Behavior ofSemirigid Joints

31 Details of the Connections is paper selected threekinds of common semirigid joints including the top-seatangle connection with web and ear plate (J-1) the extendedendplate connection (J-2) and the T-section steel connec-tion (J-3) to establish finite element models to contrast andanalyze their mechanical properties e joint structures areshown in Figure 4 e sectional dimensions and specifi-cations of each member of the joint are shown in Table 2

32 Establishment of the Finite Element Model e consti-tutive relationship of the steel used the simplified classic

three-straight-line model and the parameters were de-termined according to the material property test of thesubject and Poissonrsquos ratio is taken as 03 e constitutiverelationship of the high-strength bolts was determinedaccording to the literature [21] e stress-strain curves ofthe steel and the bolts are shown in Figure 5

e surfaces for building the contact relation include thecontact between the bolts and the ear plates the steel anglesthe end-plates the T-section steels the beam flanges thebeam webs and the column flanges the contact between thesteel angles with column flanges and beam flanges thecontact between the steel angles with the column flanges andthe beam flanges the contact between the ear plates and thebeam webs the contact between the end plates and thecolumn flanges the contact between the T-section steels andthe column flange and the beam flange and the contactbetween the bar bolts and the bolt holes e contact typewas surface-to-surface contact and the tangential Coulombfriction was set on the contact surface with a friction co-efficient of 035

According to the actual stress condition of the joint theboundary condition of the finite element model was set as apinned base column joint and the top column limited thedisplacement in the translational direction of X and Y andthe rotation direction around Z axis In order to prevent thelateral torsional-flexural buckling of the beam its out-of-plane freedom (UY) was restrained at the end of the beamjoints e loads applied to the joint model included axialcolumn forces beam end loads and bolt pretighteningforces e loads were applied in three stages in the firststage a bolt pretightening force was applied to the middlesurface of the bolt using bolt load and the bolt pretighteningforce was considered to be 100 kN in the second stage axialpressure was applied to the column top in the manner of aconcentrated force and the axial pressure ratio for thecolumn was 02 in the third stage a beam end load wasapplied in the manner of displacement increment controland the loading device and the loading systems are shown inFigures 6 and 7e overall finite element models of the jointare shown in Figure 8

33 ComparisonofMechanical Behavior e analysis resultsof the load bearing capacity of the joints are shown in Table 3and Figures 9 and 10 It can be seen that the maximumbending moments of the three kinds of joints were7758 kNmiddotm 7856 kNmiddotm and 8442 kNmiddotm respectivelywhich were all greater than twice the total sectional plasticmoment of the beam (3568 kNmiddotm) and met the re-quirements for ldquostrong joint and weak memberrdquo e plastic

Table 1 Specification and material of the specimen

Parts Specification (mm) MaterialColumn H180times180times 8times10

Q235Beam H200times150times 6times 8Column stiffener 160times 86times 8End plate 380times150times16Bolt 8M20 level 109

2 Advances in Civil Engineering

500 50027

018

060

040

0

P

Displacementsensor

Anchor bolt

Column

BeamJack

SupportDial indicator

(a) (b)

Figure 1 Test setup (a) Design setup (b) Practical setup

0 002 004 006 008 010 012 0140

20

40

60

80

100

TestFinite element analysis

M (k

Nmiddotm

)

θ (rad)

Figure 2 Comparison of the M-θ curve

(a) (b)

Figure 3 Comparison of the failure mode (a) Experiment (b) FEM

Advances in Civil Engineering 3

hinge would not generate on the joints but the beam-ende load bearing capacity and elastic rigidity of J-3 were thehighest and J-3rsquos load bearing capacity was 75 and 88higher and J-3rsquos stiffness was 17 and 211 higher thanthat of J-1 and J-2 respectively e next was the loadbearing capacity and rigidity of J-2 which was 13 and190 higher than that of J-1 respectively e load bearingcapacity of J-1 was the worst

34 Comparison of Hysteretic Behavior It can be seen fromFigure 11 that the hysteresis curves of the three kinds of

joints were all full in shape but due to the large plasticdeformation of the connecting pieces the hysteresis curvesof the J-1 and J-3 joints had a certain reduction of pinchwhich showed that the hysteretic performance was not as

2525

3555

35

50 405515

5050

5050

24 42 2455 55

6M16

4M16Column

Beam8

Angle steel

Ear plate

Joint region

(a)

4545

846

6746

845

45

35 75 3528 28

End plate

8M16Column

BeamJoint region

(b)

4050

4540

740

4550

40

25 40 2555 55

70 65 40

T-stub

8M16

8M16

Column

Joint region Beam

(c)

Figure 4 Joint details (a) J-1 (b) J-2 (c) J-3

Table 2 Specification and material of the specimens

Parts Specificationmm MaterialColumn HW200times 200times 8times12

Q235

Beam HN175times 90times 5times 8Column stiffener 176times 96times 8Steel angle L140times 90times12Ear plate 65times125times12End plate 355times145times 24T-stub T175times175times 7times11Bolt M16 109 grade

0025 0050 0075 0100 0125 0150 0175 02000

200

400

600

800

1000

1400

Q235 steel

Bolt

263

467

1130

σ (M

Pa)

ε

940

1200

Figure 5 Stress-strain curve of Q235 steel and the high-strengthbolts


good as the J-2 joint e hysteresis curves of the joint modelare all lower than that of the monotonic loading curves isis because under cyclic loading and due to the Bauschingereffect the plastic deformation of the joints continuouslyaccumulates and the local buckling phenomenon becomesmore obvious resulting in the degradation of the strengthand rigidity

It can be seen from the skeleton curve in Figure 12 thatthe skeleton curves of the J-1 and J-2 joints were roughly thesame as the monotonic loading curve In the initial hys-teresis the skeleton curve and the monotonic loading curveof J-3 joint basically coincided With the increase of the loadthe skeleton curve was no longer smooth and although theload bearing capacity kept rising it was not stable It has

1000

1000

200

200

1212

8

8

5

8

90

175

Axial force

Column

Beam

Figure 6 Loading device

5∆y

ndash5∆y

t

6∆y5∆y4∆y

3∆y

∆y2∆y

075∆y

ndash05∆y

ndash6∆yndash5∆y


ndash2∆y

∆y

ndash∆y

δ (m

m)

ndash∆y

Figure 7 Loading scheme

(a) (b) (c)

Figure 8 Finite element models of the joints (a) J-1 (b) J-2 (c) J-3


been speculated that the connecting pieces at the area of thebeam flanges (top-and-seat steel angles and T-section steels)have a larger plastic deformation during the late stages ofloading

35 Comparison of the Energy Dissipation Capacity eenergy dissipation capacity of a joint can be measured by theenergy dissipation coefficient e larger the value thestronger the energy dissipation capacity e energy dissi-pation coefficient is calculated according to the followingformula

E S(ABC+CDA)

S(OBE+ODF)

(1)

where S(ABC+CDA) represents the area enclosed by the hys-teresis loop and S(OBE+ODF) represents the area enclosed bythe corresponding triangle as shown in Figure 13

Figure 14 shows that after entering the yield phase theenergy dissipation coefficient of the J-2 joints was greaterthan 23 and the energy dissipation capacity was excellentHowever the energy dissipation coefficient of the J-3 jointwas 10sim15 the energy dissipation coefficient of the J-1 jointwas about 10 and their energy dissipation performance wasnot good e reason for this is that the screw shear forceborne around the bolt holes of the top-and-seat steel anglesand T-section steel webs produced plastic deformation andwas gradually accumulated and the deformation of the boltholes was obvious and the energy dissipation capacity of theconnection under cyclic loading was not fully realized evalue of the energy dissipation coefficient was consistentwith the full degree of the hysteresis loop of the joint

36 Comparison of Degradation Characteristics e plasticdeformation generated by the joint under cyclic loading wascontinuously accumulated which might cause the degra-dation of the load-bearing capacity and rigidity e load-bearing capacity degradation can be measured by the re-duced loading coefficient λi (formula (2)) and the rigiditydegradation can be calculated by the secant stiffness Ki

under the same cycle

λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)

In the formula when j is the displacement ductilityfactor Fi

j is the peak load of the ith cycle and when j is thedisplacement ductility factor Fi+1

j is the peak load of the i +

1th cycle plusmnFi is the peak load of the cycle and plusmnXi is thedisplacement of the peak of the cycle

Figure 15 shows the variation trend of the decreasingload coefficient of the joint with load It can be seen that thedecreasing load-bearing capacity coefficient of the joint wasgreater than 093 indicating that the load-bearing capacitydegradation of each cycle of the same loading stage was smalland its stability was good Comparing the three kinds ofjoints the decreasing load coefficients of the J-2 and J-3joints were greater than that of J-1 joint without drasticchange indicating that the stability of the load-bearingcapacity was better than that of the J-1 joint Howeverbecause the plastic deformation of J-1 joint occurs in the topand bottom steel angle area where the web bolts are keptcontinuously and gradually accumulates resulting in rela-tively unstable bearing capacity the producing plastic de-formation at the area of the top-and-seat steel angle and theweb bolt resulted in a relatively less stable load bearingcapacity of J-1 joint After entering the yield phase the

Table 3 Comparison of load bearing behavior

Joint number Yield load (kN) Peak load (kN) Elastic stiffness(kNmiddotm)

J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3

Figure 9 Comparison of the monotonic curves

0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3

Figure 10 Comparison of the moment-rotation curves


stability of the load-bearing capacity of the J-2 joint wasbetter than that of J-3

Table 4 and Figure 16 show that the initial rigidity of theJ-3 joint was the largest followed by J-2 and then J-1 which

ndash100 ndash80 ndash60 ndash40 ndash20 0 20 40 60 80 100ndash120ndash100

ndash80ndash60ndash40ndash20

020406080

100120

P (k

N)

δ (mm)

Monotonic curveHysteretic curve

(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)

Figure 11 Hysteretic curves of the joints (a) J-1 (b) J-2 (c) J-3

P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1

Figure 12 Skeleton curves of the joints

COF

D

AE

B

P

δ

Figure 13 Calculation of dissipative coefficient


was consistent with the monotonic loading analysis resultse rigidity of the three types of joints degenerated rapidly inthe initial stage of loading and the final rigidity degradationdegrees were all at 90with the final ratio of rigidity (ratio ofthe secant stiffness of each cycle to the secant stiffness of thefirst cycle) tending to be 01 e rigidity degradation curvesof the J-2 and J-3 joints basically coincided while under thesame loading level the ratio of the rigidity of J-1 was lowerthan that of the J-2 and J-3 joints indicating that the rigidityof J-1 degraded faster under stress which was not conduciveto seismic resistance

37 Comparison of Failure Mode Figure 17 shows that thestress level of the J-2 joint was the lowest followed by the J-3joint while the J-1 joint was the higheste failure of the J-1joint was mainly displayed as the deformation of the area ofthe top-and-seat steel angle and the bolt holes of the beamweb (Figure 18(a)) e failure of the J-3 nodes was mainly

concentrated on the area of the bolt holes of the T-sectionsteel webs under the shearing force of the screws and a largeamount of plastic deformation was accumulated(Figure 18(b)) For J-2 due to the thicker end-plate therewas almost no plastic deformation on the connection be-tween the end-plates and the bolt and the failure of the jointwas mainly displayed in the bending deformation at the endsof the beams e ductility and bearing capacity of the jointswere increased with good seismic performance due to theoutward hinged plastic movement

38 Comparison of Joint Performance In conclusion acomprehensive contrastive analysis of the three types ofsemirigid joints is shown in Table 5

4 Conclusions

Based on the analysis of the three kinds of beam-columnbolted connections the following conclusions can be drawnfor the connections

(1) e finite element models that were built could ef-fectively simulate the load-bearing behavior of boltedconnections under single-direction loading and cy-clic loading e rationality of the element type andconstitutive relation was verified to be correct

(2) e three connections all showed stable and goodload-bearing capacity hysteretic behavior and energydissipation capacity which could make the plastichinge generate on the beam-end instead of theconnections erefore the ductility of steel framecould be promoted effectively

(3) e extended end-plate connection had the bestenergy dissipation capacity because no obvious de-formation generated on the end-plate e con-nectors such as the steel angle and T-stub had large

0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1

Figure 14 Comparison of the dissipative coefficient

ndash80 ndash70 ndash60 ndash50 ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50 60 70 80093009350940094509500955096009650970097509800985099009951000

λ j

δ (mm)

J-3

J-1J-2

Figure 15 Comparison of the capacity degeneration coefficient

Table 4 Stiffness of the joints

Loading grade J-1 J-2 J-3025Δy 1213 1301 135405Δy 1172 1286 1344075Δy 1092 1255 1311Δy 975 1196 12402Δy 613 775 8193Δy 430 553 5664Δy 348 432 4455Δy 294 356 3676Δy 254 304 3157Δy 226 267 2768Δy 196 238 2489Δy 173 214 22410Δy 165 195 20511Δy 155 179 18912Δy 151 165 17513Δy 141 153 16314Δy 136 143 15315Δy 131 134 14516Δy 126 127 137


0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3

Figure 16 Comparison of stiffness degeneration

S Mises(Avg 75)

+7066e minus 01+8398e + 01+1673e + 02+2505e + 02+3338e + 02+4171e + 02+5004e + 02+5836e + 02+6669e + 02+7502e + 02+8335e + 02+9167e + 02+1000e + 03

(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)

Figure 17 Stress nephogram of the joints (a) J-1 (b) J-2 (c) J-3


deformation and significantly affected the energydissipation capacity and the failure mode

(4) Comprehensive consideration the extended end-plate connection showed good mechanical perfor-mance in manufacture and installation and it shouldbe used for preference e T-stub connection tooksecond place e top-and-seat angle connectionwith the web and ear plate requires the highest in-stallation precision and its manufacture is tediouswhich means it should be avoided in buildingconstruction

Data Availability

No data were used to support this study

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

References

[1] F Hu G Shi Y Shi et al ldquoFinite element analysis on seismicperformance of specifically pre-fabricated beam-columnconnectionsrdquo Engineering Mechanics vol 32 no 6 pp 69ndash75 2015

[2] W F Chen Steel Beam-to-Column Building ConnectionsElsevier Science Publishing Co Inc New York NY USA1988

[3] W F Chen and F M Lui Stability Design of Steel FramesCRC Press Boca Raton FL USA 1991

[4] J Y R Liew C H Yu Y H Ng and N E ShanmugamldquoTesting of semi-rigid unbraced frames for calibration ofsecond-order inelastic analysisrdquo Journal of ConstructionalSteel Research vol 41 no 2-3 pp 159ndash195 1997

[5] D A Nethercot T Q Li and B Ahmed ldquoUnified classifi-cation system for beam-to-column connectionsrdquo Journal ofConstructional Steel Research vol 45 no 1 pp 39ndash65 1998

[6] J M Cabrero and E Bayo ldquoDevelopment of practical designmethods for steel structures with semi-rigid connectionsrdquoEngineering Structures vol 27 no 8 pp 1125ndash1137 2005

[7] J Hao andW Li ldquoFinite element analysis for the top-and-seatangle minor axis connection of semi-rigid steel beam-columnjointsrdquo China Civil Engineering Journal vol 40 no 9pp 36ndash42 2007

[8] G Li W Shi and J Wang Design of Steel Frames with Semi-Rigid Connections China Architecture amp Building PressBeijing China 2009

[9] A R Kukreti M Ghassemieh and T M Murray ldquoBehaviorand design of large-capacity moment end platesrdquo Journal ofStructural Engineering vol 116 no 3 pp 809ndash828 1990

[10] B T Adey G Y Grondin and J J Cheng ldquoCyclic loading ofend plate moment connectionsrdquo Canadian Journal of CivilEngineering vol 27 no 4 pp 68ndash701 2000

[11] J Shen and A Astaneh-Asl ldquoHysteretic behavior of bolted-angle connectionsrdquo Journal of Constructional Steel Researchvol 51 no 3 pp 201ndash218 1991

[12] V Piluso and G Rizzano ldquoExperimental analysis andmodelling of bolted T-stubs under cyclic loadsrdquo Journal ofConstructional Steel Research vol 64 no 6 pp 655ndash6692008

[13] 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

(a) (b)

Figure 18 Local deformation (a) J-1 (b) J-2

Table 5 Comparison of joint performance

Number Bearing behavior Hysteretic behavior Energy dissipation Bearing degradation Stiffness degradation Failure modeJ-1 times times times times times times

J-2 radic radic radic radic radicJ-3 radic times radic times

Note radic good medium times poor


[14] B M Broderick and A W omson ldquoe response of flushend-plate joints under earthquake loadingrdquo Journal of Con-structional Steel Research vol 58 no 9 pp 1161ndash1175 2002

[15] M Wang Y Shi Y Wang and G Shi ldquoNumerical study onseismic behaviors of steel frame end-plate connectionsrdquoJournal of Constructional Steel Research vol 90 pp 140ndash1522013

[16] M Gerami H Saberi V Saberi and A Saedi Daryan ldquoCyclicbehavior of bolted connections with different arrangement ofboltsrdquo Journal of Constructional Steel Research vol 67 no 4pp 690ndash705 2011

[17] O S Bursi and J P Jaspart ldquoBenchmarks for finite elementmodelling of bolted steel connectionsrdquo Journal of Construc-tional Steel Research vol 43 no 1ndash3 pp 17ndash42 1997

[18] Z Li X Li X Zheng and K Zhang ldquoExperimental study andnumercial investigation on hysteretic behavior of T-stubsemi-rigid beam-to-column connectionsrdquo Journal of BuildingStructures vol 35 no 7 pp 61ndash68 2014

[19] B Guo L Wang Y Wang et al ldquoExperimental study onrotational stiffness of steel frame beam-column connectionsrdquoJournal of Building Structures vol 32 no 10 pp 82ndash89 2011

[20] GB50011-2010 Code for Seismic Design of Buildings ChinaArchitecture amp Building Press Beijing China 2016

[21] T Wang Study on Moment-Rotation Relationship of End-Plate Connections and Seismic Behavior of Semi-Rigid SteelFrames South China University of Technology GuangzhouChina 2013


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established to contrast and analyze the performance pa-rameters such as load-bearing capacity hysteretic perfor-mance ductility performance and failure modes emechanical properties of semirigid joints of differentstructural types structures and proposed designs have beendiscussed in depth Designers can then select the appropriatejoint types according to the design requirements

2 Finite Element Model andExperimental Verification

In order to verify the accuracy and applicability of the finiteelement model that has been established in this paper themonotonic loading test of end-plate connections establishedby Guo et al [19] was selected

21 Finite Element Model e finite element model con-sisted of steel beams steel columns end-plates ribbed webstiffeners and high-strength friction type bolts An eight-joint hexahedral linear reduced integral unit C3D8R wasselected for the simulation and mesh refinement wasmanually performed on the areas of stress concentrationsuch as bolt holes e constitutive relationship of the steeladopted the experimental material property data from theliterature e lateral constraints boundary conditions andloading systems of the finite element model were all con-sistent with the experiment

22 Experimental Verification e experimental specimensfrom Guo et al were designed at a reduced scale of 1 2 esectional dimensions of each member are shown in Table 1e sectional plastic modulus ratio of the beams and col-umns was 143 which meets the design requirements ofstrong columns and weak beams of the ldquoCode for SeismicDesign of Buildingsrdquo (2016 Edition) (GB50011-2010) [20]e specimen loading device is shown in Figure 1

e comparison curve of the bending moment anglebetween the finite element analysis and the experiment isshown in Figure 2 and the comparison of the typical failuremodes is shown in Figure 3 It can be seen that it is feasible tosimulate the mechanical properties of semirigid joints byusing the established finite element model

3 Comparison of the Mechanical Behavior ofSemirigid Joints

31 Details of the Connections is paper selected threekinds of common semirigid joints including the top-seatangle connection with web and ear plate (J-1) the extendedendplate connection (J-2) and the T-section steel connec-tion (J-3) to establish finite element models to contrast andanalyze their mechanical properties e joint structures areshown in Figure 4 e sectional dimensions and specifi-cations of each member of the joint are shown in Table 2

32 Establishment of the Finite Element Model e consti-tutive relationship of the steel used the simplified classic

three-straight-line model and the parameters were de-termined according to the material property test of thesubject and Poissonrsquos ratio is taken as 03 e constitutiverelationship of the high-strength bolts was determinedaccording to the literature [21] e stress-strain curves ofthe steel and the bolts are shown in Figure 5

e surfaces for building the contact relation include thecontact between the bolts and the ear plates the steel anglesthe end-plates the T-section steels the beam flanges thebeam webs and the column flanges the contact between thesteel angles with column flanges and beam flanges thecontact between the steel angles with the column flanges andthe beam flanges the contact between the ear plates and thebeam webs the contact between the end plates and thecolumn flanges the contact between the T-section steels andthe column flange and the beam flange and the contactbetween the bar bolts and the bolt holes e contact typewas surface-to-surface contact and the tangential Coulombfriction was set on the contact surface with a friction co-efficient of 035

According to the actual stress condition of the joint theboundary condition of the finite element model was set as apinned base column joint and the top column limited thedisplacement in the translational direction of X and Y andthe rotation direction around Z axis In order to prevent thelateral torsional-flexural buckling of the beam its out-of-plane freedom (UY) was restrained at the end of the beamjoints e loads applied to the joint model included axialcolumn forces beam end loads and bolt pretighteningforces e loads were applied in three stages in the firststage a bolt pretightening force was applied to the middlesurface of the bolt using bolt load and the bolt pretighteningforce was considered to be 100 kN in the second stage axialpressure was applied to the column top in the manner of aconcentrated force and the axial pressure ratio for thecolumn was 02 in the third stage a beam end load wasapplied in the manner of displacement increment controland the loading device and the loading systems are shown inFigures 6 and 7e overall finite element models of the jointare shown in Figure 8

33 ComparisonofMechanical Behavior e analysis resultsof the load bearing capacity of the joints are shown in Table 3and Figures 9 and 10 It can be seen that the maximumbending moments of the three kinds of joints were7758 kNmiddotm 7856 kNmiddotm and 8442 kNmiddotm respectivelywhich were all greater than twice the total sectional plasticmoment of the beam (3568 kNmiddotm) and met the re-quirements for ldquostrong joint and weak memberrdquo e plastic

Table 1 Specification and material of the specimen

Parts Specification (mm) MaterialColumn H180times180times 8times10

Q235Beam H200times150times 6times 8Column stiffener 160times 86times 8End plate 380times150times16Bolt 8M20 level 109


500 50027

018

060

040

0

P

Displacementsensor

Anchor bolt

Column

BeamJack


(a) (b)


0 002 004 006 008 010 012 0140

20

40

60

80

100


M (k

Nmiddotm

)

θ (rad)


(a) (b)






2525

3555

35

50 405515

5050

5050

24 42 2455 55

6M16

4M16Column

Beam8

Angle steel

Ear plate

Joint region

(a)

4545

846

6746

845

45

35 75 3528 28

End plate

8M16Column

BeamJoint region

(b)

4050

4540

740

4550

40

25 40 2555 55

70 65 40

T-stub

8M16

8M16

Column

Joint region Beam

(c)




Q235


0025 0050 0075 0100 0125 0150 0175 02000

200

400

600

800

1000

1400

Q235 steel

Bolt

263

467

1130

σ (M

Pa)

ε

940

1200





1000

1000

200

200

1212

8

8

5

8

90

175

Axial force

Column

Beam


5∆y

ndash5∆y

t

6∆y5∆y4∆y

3∆y

∆y2∆y

075∆y

ndash05∆y



ndash2∆y

∆y

ndash∆y

δ (m

m)

ndash∆y


(a) (b) (c)





E S(ABC+CDA)

S(OBE+ODF)

(1)





λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)








J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3


0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3







020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


500 50027

018

060

040

0

P

Displacementsensor

Anchor bolt

Column

BeamJack


(a) (b)


0 002 004 006 008 010 012 0140

20

40

60

80

100


M (k

Nmiddotm

)

θ (rad)


(a) (b)






2525

3555

35

50 405515

5050

5050

24 42 2455 55

6M16

4M16Column

Beam8

Angle steel

Ear plate

Joint region

(a)

4545

846

6746

845

45

35 75 3528 28

End plate

8M16Column

BeamJoint region

(b)

4050

4540

740

4550

40

25 40 2555 55

70 65 40

T-stub

8M16

8M16

Column

Joint region Beam

(c)




Q235


0025 0050 0075 0100 0125 0150 0175 02000

200

400

600

800

1000

1400

Q235 steel

Bolt

263

467

1130

σ (M

Pa)

ε

940

1200





1000

1000

200

200

1212

8

8

5

8

90

175

Axial force

Column

Beam


5∆y

ndash5∆y

t

6∆y5∆y4∆y

3∆y

∆y2∆y

075∆y

ndash05∆y



ndash2∆y

∆y

ndash∆y

δ (m

m)

ndash∆y


(a) (b) (c)





E S(ABC+CDA)

S(OBE+ODF)

(1)





λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)








J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3


0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3







020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





2525

3555

35

50 405515

5050

5050

24 42 2455 55

6M16

4M16Column

Beam8

Angle steel

Ear plate

Joint region

(a)

4545

846

6746

845

45

35 75 3528 28

End plate

8M16Column

BeamJoint region

(b)

4050

4540

740

4550

40

25 40 2555 55

70 65 40

T-stub

8M16

8M16

Column

Joint region Beam

(c)




Q235


0025 0050 0075 0100 0125 0150 0175 02000

200

400

600

800

1000

1400

Q235 steel

Bolt

263

467

1130

σ (M

Pa)

ε

940

1200





1000

1000

200

200

1212

8

8

5

8

90

175

Axial force

Column

Beam


5∆y

ndash5∆y

t

6∆y5∆y4∆y

3∆y

∆y2∆y

075∆y

ndash05∆y



ndash2∆y

∆y

ndash∆y

δ (m

m)

ndash∆y


(a) (b) (c)





E S(ABC+CDA)

S(OBE+ODF)

(1)





λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)








J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3


0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3







020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




1000

1000

200

200

1212

8

8

5

8

90

175

Axial force

Column

Beam


5∆y

ndash5∆y

t

6∆y5∆y4∆y

3∆y

∆y2∆y

075∆y

ndash05∆y



ndash2∆y

∆y

ndash∆y

δ (m

m)

ndash∆y


(a) (b) (c)





E S(ABC+CDA)

S(OBE+ODF)

(1)





λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)








J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3


0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3







020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




E S(ABC+CDA)

S(OBE+ODF)

(1)





λj Fi+1

j

Fij

(2)

Ki +Fi

11138681113868111386811138681113868111386811138681113868 + minusFi

11138681113868111386811138681113868111386811138681113868

+Xi

11138681113868111386811138681113868111386811138681113868 + minusXi

11138681113868111386811138681113868111386811138681113868 (3)








J-1 4675 10344 1014955J-2 5561 10475 1207566J-3 5657 11257 1228612

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

P (k

N)

δ (mm)

J-1J-2J-3


0000 0015 0030 0045 0060 0075 0090 0105 0120 0135 01500

10

20

30

40

50

60

70

80

90

100

M (k

N)

θ (mm)

J-1J-2J-3







020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






020406080

100120

P (k

N)

δ (mm)


(a)



120100

80604020

0

δ (mm)

P (k

N)


(b)



020406080

100120

P (k

N)

δ (mm)


(c)


P (k

N)



020406080

100120

δ (mm)

J-2J-3

J-1


COF

D

AE

B

P

δ







4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






4 Conclusions





0 10 20 30 40 50 60 70 8000

05

10

15

20

25

30

E

δ (mm)

J-2J-3

J-1



λ j

δ (mm)

J-3

J-1J-2





0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 5 10 15 20 25 30 3500

01

02

03

04

05

06

07

08

09

10

Stiff

ness

ratio

Number of cycles

J-1J-2J-3


S Mises(Avg 75)


(a)

S Mises(Avg 75)

+2343e + 00+6187e + 01+1214e + 02+1809e + 02+2405e + 02+3000e + 02+3595e + 02+4190e + 02+4786e + 02+5381e + 02+5976e + 02+6571e + 02+7167e + 02

(b)

S Mises(Avg 75)


(c)





Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




References














(a) (b)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

AnalysisoftheMechanicalBehaviorofBoltedBeam-Column … · 2018. 11. 7. · beam webs, the contact between the end plates and the columnﬂanges,thecontactbetweentheT-sectionsteelsand