Investigation on the Structural Behavior of Shear Walls

Investigation on the Structural Behavior of Shear Walls with Steel Truss Coupling Beamsunder Seismic Loading

Deng Zhiheng Xu Changchun Hu Qiang Zeng Jian Xiang Ping

Published inAdvances in Materials Science and Engineering

Published 01012018

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Publication detailsDeng Z Xu C Hu Q Zeng J amp Xiang P (2018) Investigation on the Structural Behavior of Shear Wallswith Steel Truss Coupling Beams under Seismic Loading Advances in Materials Science and Engineering2018 [5602348] httpsdoiorg10115520185602348

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Research ArticleInvestigation on the Structural Behavior of ShearWalls with SteelTruss Coupling Beams under Seismic Loading

Zhiheng Deng1 Changchun Xu12 Qiang Hu13 Jian Zeng12 and Ping Xiang 456

1College of Civil and Architectural Engineering Guangxi University Nanning 530004 China2Hualan Design amp Consulting Group Nanning 530011 China3Department of Civil and Architectural Engineering Guangxi University of Science and Technology Liuzhou 545006 China4School of Civil Engineering Central South University Changsha 410075 Hunan China5National Engineering Laboratory for High-Speed Railway Construction Changsha China6Department of Architecture and Civil Engineering City University of Hong Kong Kowloon Hong Kong

Correspondence should be addressed to Ping Xiang pxiang2-cmycityueduhk

Received 23 March 2017 Revised 16 October 2017 Accepted 19 October 2017 Published 25 March 2018

Academic Editor Carlos Garcia-Mateo

Copyright copy 2018 Zhiheng Deng et alis 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

Based on existing experimental results the finite element analyses were carried out on shear wall structures with steel trusscoupling beams is work studied the seismic behaviors and the working mechanism of the steel truss coupling beam at theultimate state and put forward two parameters the area ratio of web member to chord and the stiffness ratio of coupling beam toshear wall e seismic optimum design method of the coupling beam was also proposed Afterwards a comparative analysis wasimplemented on the three-dimensional shear wall model with steel truss coupling beams designed by the proposed designmethode results show that the structures designed by the proposed method have excellent seismic behaviors the steel truss couplingbeams have enough stiffness to connect shear walls effectively and its web members have appropriate cross sections to dissipateseismic energy

1 Introduction

Coupling beams (CBs) are important structural componentsto shear wall structures as they provide effective connectionsbetween shear wall limbs and increase global lateral stiffnesse seismic performance of shear wall structure is largelydependent on the behaviors of CBs e steel CB has a lot ofadvantages such as light weight good ductility force clear andeasy to be replaced after the earthquake Ever since the be-ginning of research on the steel CBs in the 1990s the structuralbehaviors of steel CBs have been investigated by experimentsand theoretical analysis [1ndash3] the research pointed out thatsteel CB structure has sufficient rigidity strength toughnessand a good seismic performance the plastic deformation of theweb after yielding helps to dissipate seismic energy thussignificantly improves the seismic performance of CBsNonlinear seismic response of walls coupled with steel andconcrete beams was also investigated [4ndash6] the researchdemonstrated the advantages of using steel beams to couple

reinforced concrete walls Experiments and simulations havebeen conducted on the joints of steel CBs and shear walls[7ndash11] and the results demonstrated that the anchorage hasimportant impacts on the stiffness degradation the shear yieldstyle steel CB has excellent ductility performance and energyperformance construction convenient and easy maintenanceand replacement and especially the maintenance can be easilyreplaced after the earthquake Wu [12] investigated the steelCB and concrete shear wall joints by employing experimentsand finite element analysis the failure mode of joints straindistribution bearing capacity CB size concrete strengthductility and hysteretic behaviors were studied

In recent decades composite structures [13ndash16] developquickly and have been investigated in researches [17ndash23] andused in various kinds of structures [24ndash32] and infrastructures[33ndash42] e steel truss CB is a special kind of steel CB thatsatisfies flexible layout clear loading path and adaptable ar-chitectural features however investigations on steel truss CBshear wall structures are scarce Experimental researches have

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 5602348 16 pageshttpsdoiorg10115520185602348

been employed to investigate seismic behaviors and energydissipation mechanism of steel truss CBs under low-cyclicreversed loading [43ndash45] ey also proposed a novel jointdesign style for steel-reinforced concrete T-shaped columnsconducted experiments on joint samples under low-cyclicreversed loading [46] and further studied on hysteresis be-haviors and the bond-slip curves [47] Finite element analysesand pseudostatic tests were adopted for studies on steel trussCBs [48ndash50] it is proved that the steel truss CB has excellentductility and energy dissipation properties ey also pointedout that the appropriate design of steel truss will result in theenhancement of structural bearing capacities and the ductilityhowever simply increasing the size of chord or websmay causeuncoordinated force distribution in structures A series ofworks has been reported by employing cyclic and biaxialloading tests in which the instability fatigue strength andhysteretic behaviors were investigated [51ndash55] Condition as-sessment and energy dissipation of steel shear walls with ta-pered links under various loadings were investigated usinga baseline incremental two-cycle loading protocol [56] A ra-tional method was proposed for determining the chord yieldrotation of RC coupling beams [57] in which several recentlydeveloped coupling beam models were also reviewed oughefforts have been made to investigate the seismic performancesof steel truss CBs further efforts on the design methods of steeltruss elements revealing the energy dissipating mechanismstress-strain status and how to actualize excellent mechanicalperformances are still in demand

Given the above reasons this work presents a finite elementstudy on the seismic behaviors of steel truss CBs simulationresults are compared with available test results Seismic be-haviors and mechanical performances under limit states arefurther discussed Based on the working mechanism analysis

the area ratio of web member to chord and the stiffness ratio ofcoupling beam to shear wall are proposed for the evaluation ofseismic performances of steel truss CBs

is paper is structured as follows In Section 2 thestructural characteristics of the steel truss CBs are pointed outIn Section 3 the seismic behaviors and energy dissipationproperties of steel truss CB shear wall structures are investigatedshear wall models stiffness ratio and load-displacement re-lationships are presented Section 4 presents a study on themechanism of steel truss CB structures under limit state InSection 5 the design methods and optimization suggestion ofsteel truss CBs are proposed including the evaluation of sectionsizes and bearing capacities Further Section 6 presents a three-dimensional analysis of seismic performances of the steel trussCB structures a series of parameters are adopted for theevaluation of overall seismic performances of three-dimensionalsteel truss CBs structures Conclusions and discussions aredrawn in Section 7

2 Characteristics of Steel Truss CBs

Steel truss CBs are specific steel trusses with small span-depth ratio which can effectively connect shear wall limbsunder seismic actions dissipate seismic energy and reducedamage during earthquakes e differences between thesteel truss CB and conventional steel truss lie in the fol-lowing (1) diagonal webmembers can be utilized to dissipateseismic energy and (2) steel chords are presented as aneffective connection between shear walls chord memberswill remain in elastic stage during working without pro-ducing plastic hinges at the ends

Taking into consideration the structural characteristicsthe steel truss CB and steel truss will have similarities to some

d

2l

αid

αi

αid

β

3icαil

Nc

Nf Nf

3ic αi

Figure 1 Deformation mode and internal force of steel truss CBs

2 Advances in Materials Science and Engineering

extent in the working mechanism us the area ratio of webmember to chord ρA and the stiffness ratio of coupling beamto shear wall ρK can be proposed to evaluate the mechanicaland seismic performances of the steel truss CBs

3 Seismic Behaviors of Shear Wall Structureswith Steel Truss CBs

31 CB-Shear Wall Compatible Deformation and the StiffnessRatio e shear wall limb deforms horizontally and inclinesunder horizontal seismic actions Because of the globaldeformation of shear wall limb the deformation of steeltruss CB will include rigid body motion the rotation at theend of CB chords and relative displacements of top andbottom chord membersus as shown in Figure 1 it can beconsidered that the rotation at the ends of CB chords is thesame as the interstorey displacement angle of the shear walls

It is assumed that the shear force at level i is Vi thestorey drift and interstorey displacement angle are re-spectively Δi and αi the storey height CB depth andsegment length of the CB are hi d and l respectively elength and angle of diagonal web member are lf and βrespectively As shown in Figure 1 the stretch of web

member is obtained as the product of cos β and the relativedeformation of top and bottom chords

Δlf asymp Δi

d

hi

cos β Δi

d

hi

l

lf (1)

then the axial force of diagonal web member can be cal-culated as

σf Efεf

Ef

Δlflf

εle εy

εy + κΔlflfminus εy1113888 11138891113890 1113891Ef εgt εy

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

By substituting (1) into (2) and considering κ 1 whenεle εy it can be obtained that

Nf EfAf

κΔidl

hil2f

+(1minus κ)εy⎡⎢⎣ ⎤⎥⎦ (3)

where Ef is the elastic modulus of web members κ and εy

are respectively the hardening coefficient and yield strain ofthe steel used for web members

450 450 450

200

210

300

300

700

300

800

500

400

400

410 2350

1 1

2 2

(a)

110

450

10ϕ8ϕ4

50

ϕ6

125

1-1

(b)

110

450

14ϕ8

2-2

ϕ4

50

ϕ6

60

(c)

200 450 200300

5050

300

(d)

Figure 2 Shear wall specimens with steel truss CBs (a) elevation (b) reinforcement details of shear wall on the second floor (c) re-inforcement details of shear wall on the first floor (d) dimensions of CBs

Advances in Materials Science and Engineering 3

Total shear force at the CB ends is composed of verticalforce component of web member and the shear forces ofchords As the shear force of chords is generated fromrotation at joints which can be considered as the inter-storey displacement angle αi the CB shear force can beexpressed as

Vb 2Δi

hi

ψEfAf

κd2l

lfminus3icl

1113888 1113889 + 2(1minus κ)ψdEfAfεylf

(4)

where ic is the linear stiffness of chords calculated asic EcIcl Ec and Ic are respectively the elastic modulusand moment of inertia of chord section and

ψ 1

lf + Δidl1113902hilf1113872 1113873 lf minusΔidl1113902hilf1113872 1113873 (5)

Before the web member reaches the plastic stage theshear stiffness of CB can be derived based on interstoreyshear deformation as

Kb limΔi0

Vb

Δi

11138681113868111386811138681113868111386811138681113868κ1

2hi

EfAfd2l

l3fminus3EcIc

l2⎛⎝ ⎞⎠ (6)

e lateral stiffness of shear wall can be obtained asKw 12EwIw0h

3i where Ew is the elastic modulus of shear

wall concrete and Iw0 is the moment of inertia of transformedconcrete shear wall section in which steel has been trans-formed to concrete based on equal contribution to thestiffnessen the stiffness ratio of shear wall to steel truss CBcan be calculated as

ρK Kb

Kw

(7)

32 ShearWallModel e finite element model of shear wallsteel truss CBs as shown in Figure 2 is built on the basis of theexperimental specimens in [5] as shown in Figure 3 eelements T3D2 C3D8R and S4R in ABAQUS are used forreinforcements shear walls and CBs respectively e stress-strain models of concrete under monotonic and cyclic loadsconform to Chinese code for design of concrete structures GB50010-2010 [58] which is determined by the characteristicvalue of axial compressive strength fck measured in the ma-terial tests e stress-strain curve of concrete and steel isrespectively presented in Figures 4 and 5 e material pa-rameters of specimens are listed in Table 1

Since specimens were loaded under pseudodynamic teststhe positive and negative skeleton curves are found not strictlysymmetrical because of the certain damage existed in speci-mens As shown in Figure 6 the positive skeleton curves ofexperiment values and modeling results match well with eachother only small discrepancy exists in the negative skeletoncurve However the material property nonuniformity fabri-cation error and eccentricity are not considered in the finiteelement analysis which may result in an overestimation of theinitial stiffness in comparison with the test resultse positivehysteresis curve derived from experiments and modelingresults match well with each other as shown in Figure 7 It canbe seen in Table 2 that the predicted ultimate load is con-sidered alongside with experiments In order to investigate theeffects of CB size beams on the seismic performance of thestructure a series of results are obtained by changing sizes andthickness of web members as shown in Table 3 Displacementloading is applied in the calculation and the controlled dis-placement between test and analysis is different Because thespecimen was initially loaded before the low cyclic reversedloading tests and the damage displacement in the test is2866mm we adopt a maximum displacement loading of

(a) (b)

Figure 3 e finite element model (a) shear wall structure (b) CBs


30mm in the simulation which is slightly larger than themeasured value (2866mm) in the tests

33 Load-Displacement Curve Several load-displacementcurves of specimens are obtained and plotted in Figure 8It can be seen that the shear force increases with the increaseof web member sizes however the peak value of shear forcedecreases with the web member size increased beyonda certain degree is goes to show that the diagonal webmembers and chords should have compatible sizes to ensurethat all the members can cooperate well with each other anddemonstrate a significant impact

34 Energy Dissipation Behaviors Reversed displacementloadings have been applied on specimens with web membersof L30 angle steel hysteretic curve is shown in Figure 9 eviscous damping coefficients (he) of the specimens arepresented in Table 4 and Figure 10

As shown in Figure 9 pinching behaviors are observed inall specimens e hysteresis curve of structure with smallsize web members is fatter than the structure with big webmembers However the structure with big size webmemberswill have higher peak strength e strength degradation isobvious for specimens with thick web members after severaltimes of reserved loadings at is because plastic hinges

formed at the end of chords and finally result in large plasticdeformation and significant stiffness degradation

Equivalent viscous damping coefficients of specimens arecalculated and plotted in Figure 10 e experimental resultcurve (marked with small squares) is schematically comparedwith a series of numerical simulation results It can be seenthat the viscous damping coefficient value is small forspecimens with thin web members With the increase of webthickness the viscous damping coefficients decrease and tendto stabilize erefore it is important to determine an ap-propriate CB stiffness to achieve a larger carrying capacity andgood energy dissipation performance of steel truss CBs

4 Working Mechanism under the Limit State

In order to study the deformation styles of steel truss CBsunder limit state the deformation of specimens can bedivided into three major types as shown in Figure 11

Type I steel truss chords keep in elastic stage and thedeformation is small overall bending deformationoccurs in diagonal web members with ρA le 04 andρK lt 015Type II steel truss chords deform to some extent di-agonal web members buckle locally it is likely thatchord members will enter the plastic stage but withina limited degree with 04lt ρA le 065 or 015le ρK le 02

0 0002 0004 ε

0

30

20

10

σ (M

Pa)

Figure 4 Concrete stress-strain curve

0

σy

σu

0 εy 03 ε

σ

κE

E

Figure 5 Constitutive relations of steel

Table 1 Mechanical behavior of samples

Steel grade Position Diameter (mm) Standard value of compressionstrength (Nmm2) Ultimate strength (Nmm2) Elastic modulus (Nmm2)

HPB235 Stirrup 6 2297 5830 245times105

HPB235 Longitudinal bar 8 3181 4573 186times105

I10 Chord member Web 3426 4005 187times105

Flange 30769 3875 192times105

L30times 3 Web member mdash 4638 5217 182times105

Concrete Base mdash 4898 mdash 345times104


Type III wave style buckling and plastic deformationoccur on chord members wavy deformation occursenter more plasticity however diagonal web membersremain straight without bending deformation withρA gt 065 and ρK gt 02

In the deformation type I deformation of CB chord issmall chord members are in elastic stage globallybending deformation occurs on diagonal web membersIn the deformation type II CB chord members deform toelastoplastic state local buckling occurs on diagonal webmembers which will have certain impact on the energydissipation performances of steel truss CBs In the de-formation type III the deformation of web members issmall because of the big sizes of web members howeverlarge plastic deformation occurs on chords In this caseseismic energy is majorly dissipated by the plastic de-formation and plastic hinges occurred on chord memberswhich may result in a decrease of bearing capacity of steeltruss CBs e connection between shear wall limbs willalso be reduced erefore the deformation types I and IIcan satisfy the requirement of steel truss CBs however thedeformation characteristics and energy dissipation per-formances of the type III are not satisfactory

Taking into consideration the bearing capacity and energydissipation performance analysis results the reasonable arearatio and stiffness ratio of steel truss CBs can be obtained as thethreshold value between the deformation types I and II namely

ρA 04

ρK 015(8)

In order to ensure that the steel CBs will deform as thestyle I and II it is suggested that the area ratio and stiffnessratio of steel truss CBs should not exceed 05

5 Seismic Design Optimization of Steel TrussCBs

e main function of steel truss CBs lies in an effectiveconnection between shear wall limbs and energy dissipation

under seismic actions through the plastic deformation ofCB web members Since the CB web member will defi-nitely reach plastic deformation stage under heavy seis-mic actions no specific provision could be found relatedto this situation erefore it is not practical to design thesteel truss CBs based on the ultimate limit state designmethod specified in current codes code of practice forbuilding design is research proposes steel truss CBdesign methods based on the foregoing characteristicse proposed design method is to achieve certain seismicperformances by appropriately designed stiffness ratioand area ratio of steel truss CBs Specifically reasonabledesigned area ratio will be used to ensure energy dissi-pation performances of web members and the stiffnessratio will be utilized to provide an effective connectionbetween shear wall limbs

P (k

N)

10 20 30minus10 minus50

0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30

e proposed methodTest results

∆ (mm)

Figure 6 Skeleton curves on top floor of the specimen

P (k

N)

∆ (mm)

minus30 minus20 minus10 0 10 20 30

minus150

minus100

0

0

50

100

150

Test resultse supposed method

Figure 7 Hysteretic curves on top floor of the specimen

Table 2 Comparison of the calculation results

Yield load Py (kN) Ultimate load Pu (kN)Test value FEM Error () Test value FEM Error ()6944 6336 875 11618 11558 052

Table 3 Specimens details

Span (m) Depth (m) Chord membersize (mm)

Web angle steelproperties (mm)

Limb width ickness045 03 Half-I10 30 3ndash7045 03 Half-I10 40 3ndash5045 03 Half-I10 45 4ndash6045 03 Half-I10 50 4ndash6045 03 Half-I10 56 458045 03 Half-I10 63 4ndash6 8 10


51 Estimation of Cross-Section Dimensions e effectivelength of chord member under compression is defined aslx0 l and allowable slenderness ratio is λ By defining ix

lx0[λ] and then Ic i2xAc l2Ac[λ]2 substituting into (6)it has

Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)

By substituting ρA AfAc and (9) into (7) the cross-sectional area of web member can be estimated as

Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)

52 Calculation of Bearing Capacity e bearing capac-ity of the steel truss CB is evaluated by considering twocases

(1) Under small earthquakes diagonal web membersyield and the steel truss CBs reach the bearing ca-pacity then interstorey displacement can be calcu-lated as

ΔNiy

hilf

dl

fy

Ef

(11)

At this time diagonal web members reach bucklingforces therefore the carrying capacities provided byweb members under tension are only considereden the bearing capacity of steel truss CBs can beobtained by considering κ 1 and substituting (11)into (4) which is expressed as

VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)

where ψ 1 lf + lffyEf1113872 1113873 lf minus lffyEf1113872 1113873(2) Under heavy earthquakes in order to avoid shear

failure of steel truss CBs the bearing capacity can becalculated when the chord member yields At thistime the interstorey displacement is

ΔViu

twl2hi

3EcSc

fv (13)

By substituting (13) into (4) and considering the bucklingof diagonal web members under compressive force the shearcapacity of steel truss CBs can be derived as

Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc

minus 11113888 1113889 + 2ψ1(1minus κ)dEfAfεyfy

(14)

where ψ1 1(lf + dtwl33lfEcSc fv)(lf minus dtwl33lfEcSc fv)

andfv is the shear yield strength of steel used for chordmembersTable 4 shows the bearing capacity at CB ends by

considering the proposed two cases It can be seen that theshear capacities derived from modeling results are in goodagreement with experimental values in the case It meansthat the proposed design method is effective for the caseunder small earthquakes However for the case under heavyearthquakes discrepancies exist between finite elementmodeling results and the simulation results derived based onthe proposed methodsat is because the proposed methoddoes not consider the plasticity of chord members ough

0

110

220

0 10 20 30Top displacement (mm)

Base

shea

r (kN

)

L40 times 4L40 times 5L40 times 6

(a)Ba

se sh

ear (

kN)

Top displacement (mm)

0

110

220

0 10 20 30

L40 times 4L45 times 4

L30 times 4 L50 times 4L56 times 4L63 times 4

(b)

Figure 8 Base shear-displacement curves of the specimen


small discrepancies are found in values of the predictedbearing capacities the impact is limited and the deformationmodel and intrinsic working mechanism are fully unveiled

6 Three-Dimensional Seismic PerformanceAnalyses of Shear Walls

61 Model Establishment In order to study the three-dimensional behaviors of the steel truss CBs and shear walllimbs a six-storey three-dimensional shear wall model with

steel truss CBs is established for numerical studies as shownin Figures 12 and 13 Details of the specimens are presented inTable 5 Displacement loading with the maximum dis-placement value of 03m is applied at the top level

62 Carrying Capacity Bottom shear force versus top dis-placement (FvminusΔ) curves are presented in Figure 14 It isfound that the three FvminusΔ curves shown in Figure 14 arequite different e initial stiffnesses of the three specimensare almost the same However it can be seen that as the area

minus40 40minus200

minus100

0

100

200

Displacement (mm)minus20 200

Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)

Displacement (mm)minus20 0 20

(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)

Figure 9 Load-displacement hysteresis curves of specimens (a) L30times 3 (b) L30times 5 (c) L30times 7

Table 4 Bearing capacities of the specimens

Diagonal web member styleCase 1 diagonal web member yielding Case 2 ultimate state

Test value Result from this work FEM Test value Result from this work FEML30times 3 6944 6879 6336 11618 9728 11558L30times 4 mdash 8733 9578 mdash 11567 10143L40times 3 mdash 8978 8496 mdash 11810 10447L40times 4 mdash 11531 11511 mdash 14343 14287L40times 5 mdash 14015 13746 mdash 16806 15993


ratio and stiffness ratio increase the initial stiffness of thecurve increases slightly e stiffness ratio and area ratio ofspecimenWALL1 are small and the yield load and peak loadare relatively lower than those of the other two specimensis is due to that the area ratio and stiffness ratio arerelatively small and the stiffness of the CB is also smallusthe constraints of the shear wall are weak and the horizontalload is mainly taken by the shear wall Consequently the

bearing capacity reaches the peak load quickly With theincrease of the stiffness ratio and area ratio the stiffness andthe peak load of specimen WALL2 are also increasedMeanwhile the area ratio is close to the reasonable valueand the CB provides enough restraint on the shear wall ehorizontal load is supported by the combined effect ofthe CB and the shear wall so the bearing capacity is high andthe ductility is also good e stiffness ratio and area ratio of

0 300

005

010

015

020

he

Δ (mm)10 20

L30 times 3L30 times 4L30 times 5L30 times 6


Test results L30 times 7

Figure 10 Equivalent viscous damping coefficient he

(a) (b)

(c)

Figure 11 Deformationmodes of the coupling beams (a) type I ρA le 04 and ρK lt 015 (b) type II 04lt ρA le 065 or 015lt ρK lt 02 (c) typeIII ρA gt 065 and ρK gt 02


the specimen WALL3 are even larger which result in thehighest peak load among the three specimens At this timethe constraint of the CB on the shear wall is obviously in-creased and it seems that the bearing capacity of the shearwall structure can be increased However plastic defor-mation develops at the end of the chord due to the large arearatio and the plastic hinge will finally weaken the constraintsof the shear wall erefore the loading capacity decreasedrapidly and the bearing capacity degradations are moresignificant than those of WALL1 and WALL2

63 Energy Dissipation Behaviors In order to evaluate theenergy dissipation behaviors of the steel truss CB structurebottom shear force versus top displacement hysteresis curvesare plotted in Figure 15 It can be seen from the three plotsthat the hysteresis curve is relatively fat for the specimenWALL1 with small stiffness ratio and area ratio e hys-teresis curves are getting thinner with the increase of thestiffness ratio and area ratio which means the energy dis-sipation capacities are decreasing High stiffness ratio andarea ratio will definitely result in a significantly droppedenergy dissipation performance

Equivalent viscous damping coefficients are calculatedand presented in Figure 16 It is analyzed that (1) the viscousdamping coefficient of specimen WALL1 increases with theincrease of displacement load Because the web member is

110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700

Figure 12 Multilevel shear wall model with steel truss couplingbeam

Figure 13 Multilevel three-dimensional finite element shear wallmodel with steel truss CBs

Table 5 Specimen details of steel truss CB shear wall structure

Specimen Chord membertype

Web membertype

Arearatio

Stiffnessratio

WALL1 Half-I10 L30times 3 02448 00765WALL2 Half-I10 L40times 4 04321 01435WALL3 Half-I10 L56times 5 0758 026


relatively small in the specimen WALL1 diagonal webmembers can participate in energy dissipation and graduallytake major role in dissipating seismic energy us theviscous damping coefficient is always increasing with theincrease of the displacement load but the peak value issmall (2) the viscous damping coefficient curves of thespecimens WALL2 and WALL3 could be generally dividedinto three segments with specific characteristics in eachsegment e three segments are respectively upwarddescent and peak (3) the viscous damping coefficientcurve and peak value of the specimen WALL2 are thehighest among the three specimens Because the webmember size is relatively large the web members playa major role in the energy dissipation during reversedloading procedure us the viscous damping coefficientincreases with the increase of displacement load Howeverthe viscous damping coefficient decreases in the last stagebecause of the yielding and plastic deformation of webmembers (4) the web member size of the specimenWALL4is the largest therefore the deformation of web members isvery small the web will not participate effectively in theenergy dissipation under seismic actions In this case theseismic energy is dissipated only by the plastic deformationof chord members us the viscous damping coefficientsof WALL3 are small peak value occurs in an early stageFurthermore the viscous damping coefficients decreasesignificantly in the last loading stage because of the failureof chord members

64 Deformation Characteristics Judging from the de-formation and stress states of the concrete shear wall limbsand steel truss CBs the deformation and stress are large inthe lower storey and relatively small in the upper storey Inorder to investigate the failure deformation and charac-teristics the shear wall deformation and Mises stress

obtained under the largest deformation load are presentedin Figure 17 e deformed shapes of shear wall limb of thethree specimens are comparable Generally the stresses inshear wall limbs increase with the increase of the area ratio

minus600

minus400

minus200

0

200

400

600

minus350 minus280 minus210 minus140 140 210 280 350

Base

shea

r (kN

)

Top displacement (mm)0minus70 70

Wall1Wall2Wall3

Figure 14 Base shear force-top displacement curves of thespecimens

minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)

Figure 15 Hysteretic curves of bottom shear force versus topdisplacement (a) WALL1 (b) WALL2 (c) WALL3


and stiness ratio especially the shear wall stress state ofthe specimen WALL1 is comparable to the stress state inthe shear wall of the specimenWALL2 However the stressstate of the specimen WALL3 is even larger which dem-onstrates that the steel truss CBs in WALL1 and WALL2can eectively dissipate seismic energy and thereby help toreduce the damage to shear wall limbs

e deformation shape and Mises stress state of steeltruss CBs under the largest displacement load are pre-sented in Figure 18 It is found that the deformation modelof all three specimens has common characteristics especimens WALL1 and WALL2 deform globally as anintegral the deformations of web members are majorlytorsion However wavy deformation style and plastic

deformation occurs in the specimen WALL3 because ofthe large stiness of diagonal web members e peakMises stress in the specimenWALL2 is the smallest amongall three specimens the whole web section of the specimenWALL2 is completely yielding in compression the stressdistributes evenly along the whole cross section oughthe diagonal web members of the other two specimens arealso developed to plastic stage the stress distributions inthe cross section are inhomogeneous and stress con-centration occurs at the end of web members

From the above analysis it is understood that thestiness ratio and area ratio of steel truss CBs have a sig-nicant impact on the shear wall rigidities energy dissi-pation properties stress distribution and deformation

00

012

016

024

028

he


020

150 100 50 200

Wall1 L30lowast3Wall2 L40lowast4Wall3 L56lowast6

Figure 16 Equivalent viscous damping coecient he

S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)

Figure 17 Deformation andMises stress (unit Nm2) of the shear walls (a) specimenWALL1 (b) specimenWALL2 (c) specimenWALL3


S MisesSNEG (fraction = minus10)(Avg 75)

+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)

Figure 18 Deformation andMises stress (unit Nm2) of the steel truss CBs on the 1st oor (a) specimenWALL1 (b) specimenWALL2 (c)specimen WALL2


model under seismic actions Reasonable stiffness ratio andarea ratio will result in better shear wall structures withexcellent deformation properties and energy dissipationcapacities under earthquakes

7 Conclusion

is research investigates the mechanical properties andseismic performances of steel truss CBs e stiffness ratioand area ratio are proposed for effective evaluation anddesign of the steel truss CB Numerical simulations havebeen conducted to understand the structural and seismicperformances by employing different types of steel trussCBs Conclusions are made as follows

(1) Steel truss CB structures can achieve good seismicperformances by the appropriate design of web andchord members Steel members work cooperativelyto satisfy strength and seismic capabilities requiredunder seismic actions

(2) ree major deformation patterns of steel truss CBswith specific threshold values of stiffness ratios andarea ratios are proposed for the classification of steeltruss CB structures under heavy seismic action It issuggested that the bearing capacities and seismicenergy dissipation properties of the pattern II is thebest which can be further adopted in practical design

(3) e area ratio reflects the compatibility among steeltruss members reasonable area ratio will definitelyresult in good energy dissipation performances ofsteel truss CBs

(4) e stiffness ratio demonstrates relative rigiditiesbetween the steel truss CBs and shear walls as majorconnections between shear wall limbs reasonablestiffness ratio can ensure an effective combinationbetween neighboring limbs

(5) e proposed seismic design methods based on thestiffness ratio and area ratio will provide efficient andeffective seismic design of shear wall structures withsteel truss CBs it also helps to avoid compatibilityproblems among trussmembers in the structure design

(6) e steel truss CB shear wall structure with reasonablestiffness ratio and area ratio will have good deformationproperties and energy dissipation capacities mean-while reasonable stiffness ratio ensures effective con-nections between shear wall limbs erefore it isunderstood that the proposed steel truss CB structurewill perform satisfactorily during earthquakes

Conflicts of Interest

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

Authorsrsquo Contributions

Zhiheng Deng was the project leader Changchun Xu isa PhD candidate who built the model and conducted the

numerical simulation Qiang Hu supervised the work JianZeng helped to organize data and draw pictures Ping Xianganalyzed the data and wrote the paper All authors con-tributed to discussion of the results

Acknowledgments

e work described in this paper was supported by grantsfrom the National Natural Science Foundation of China(Grant no 51268005) Guangxi Natural Science Foundation(Grant no 2013GXNSFAA019311) and startup research fundingfrom Central South University (Grant no 502045006)

References

[1] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams II subassembly testing and design verifi-cationrdquo Journal of Structural Engineering vol 127 no 6pp 632ndash638 2001

[2] B Gong and B M Shahrooz ldquoConcrete-steel compositecoupling beams I component testingrdquo Journal of StructuralEngineering vol 127 no 6 pp 625ndash631 2001

[3] B G Gong and B M Shahrooz ldquoSteel-concrete compositecoupling beamsmdashbehavior and designrdquo Engineering Struc-tures vol 23 no 11 pp 1480ndash1490 2001

[4] K A Harries D Mitchell R G Redwood and W D CookldquoNonlinear seismic response predictions of walls coupled withsteel and concrete beamsrdquo Canadian Journal of Civil Engi-neering vol 25 no 5 pp 803ndash818 1998

[5] K A Harries D Mitchell W D Cook and R G RedwoodldquoSeismic response of steel beams coupling concretewallsrdquo Journalof Structural Engineering vol 119 no 12 pp 3611ndash3629 1993

[6] K A Harries W D Cook R G Redwood and D MitchellldquoConcrete walls coupled by ductile steel link beamsrdquo in Pro-ceedings of the Tenth World Conference on Earthquake Engi-neering vol 1ndash10 pp 3205ndash3210 Madrid Spain July 1992

[7] W S Park H D Yun S K Hwang B C Han and I S YangldquoShear strength of the connection between a steel couplingbeam and a reinforced concrete shear wall in a hybrid wallsystemrdquo Journal of Constructional Steel Research vol 61 no 7pp 912ndash941 2005

[8] W S Park and H D Yun ldquoSeismic behaviour of steelcoupling beams linking reinforced concrete shear wallsrdquoEngineering Structures vol 27 no 7 pp 1024ndash1039 2005

[9] W S Park andH D Yun ldquoSeismic behaviour and design of steelcoupling beams in a hybrid coupled shear wall systemsrdquoNuclearEngineering and Design vol 236 no 23 pp 2474ndash2484 2006

[10] W S Park and H D Yun ldquoBearing strength of steel couplingbeam connections embedded reinforced concrete shear wallsrdquoEngineering Structures vol 28 no 9 pp 1319ndash1334 2006

[11] F J Molina P Pegon and P Labbe ldquoStiffness-displacementcorrelation from the RC shear wall tests of the SAFE programderivation of a capacity linemodelrdquoAdvances inMaterials Scienceand Engineering vol 2016 Article ID 5750672 21 pages 2016

[12] J H Wu Nonlinear Finite Element Analysis on Seismic Be-havior for Coupled ShearWalls Structure with Steel Beam PhDthesis Central South University Changsha China 2010

[13] Z P Lai L Z Jiang W B Zhou and X L Chai ldquoImprovedfinite beam elementmethod to analyze the natural vibration ofsteel-concrete composite truss beamrdquo Shock and Vibrationvol 2017 Article ID 5323246 12 pages 2017

[14] W B Zhou and W J Yan ldquoRefined nonlinear finite elementmodelling towards ultimate bending moment calculation for


concrete composite beams under negative momentrdquo Cin-Walled Structures vol 116 pp 201ndash211 2017

[15] W B Zhou L Z Jiang and Z W Yu ldquoAnalysis of freevibration characteristic of steel-concrete composite box-girder considering shear lag and sliprdquo Journal of CentralSouth University vol 20 no 9 pp 2570ndash2577 2013

[16] L Z Jiang Z P Lai and W B Zhou ldquoImproved finite beamelement method for analyzing the flexural natural vibration ofthin-walled box girdersrdquo Advances in Mechanical Engineer-ing vol 9 no 8 Article ID 1687814017726292 2017

[17] W B Zhou S J Li Z Huang and L Z Jiang ldquoDistortionalbuckling of I-steel concrete composite beams in negative momentareardquo Steel andComposite Structures vol 20 no1 pp 57ndash70 2016

[18] W B Zhou L Z Jiang Z J Liu and X J Liu ldquoClosed-formsolution for shear lag effects of steel-concrete composite boxbeams considering shear deformation and sliprdquo Journal ofCentral South University vol 19 no 10 pp 2976ndash2982 2012

[19] W B Zhou L Z Jiang S J Li and F Kong ldquoElastic dis-tortional buckling analysis of I-steel concrete composite beamconsidering shear deformationrdquo International Journal ofStructural Stability and Dynamics vol 16 no 8 Article ID1550045 2016

[20] W B Zhou S J Li L Z Jiang and Z Huang ldquoDistortionalbuckling calculation method of steel-concrete composite boxbeam in negative moment areardquo Steel and Composite Struc-tures vol 19 no 5 pp 1203ndash1219 2015

[21] W B Zhou L Z Jiang Z Huang and S J Li ldquoFlexuralnatural vibration characteristics of composite beam consid-ering shear deformation and interface sliprdquo Steel and Com-posite Structures vol 20 no 5 pp 1023ndash1042 2016

[22] W B Zhou L Z Jiang J T Kang and M X Bao ldquoDis-tortional buckling analysis of steel-concrete composite girdersin negative moment areardquo Mathematical Problems in Engi-neering vol 2014 Article ID 635617 10 pages 2014

[23] W B Zhou S J Li L Z Jiang and S Q Qin ldquoVibrationanalysis of steel-concrete composite box beams consideringshear lag and sliprdquo Mathematical Problems in Engineeringvol 2015 Article ID 601757 8 pages 2015

[24] L Z Jiang J J Qi A Scanlon and L L Sun ldquoDistortionaland local buckling of steel-concrete composite box-beamrdquoSteel and Composite Structures vol 14 no 3 pp 243ndash2652013

[25] Q Q Liang B Uy M A Bradford and H R RonaghldquoStrength analysis of steel-concrete composite beams incombined bending and shearrdquo Journal of Structural Engi-neering vol 131 no 10 pp 1593ndash1600 2005

[26] L Y Zhou Z W Yu and L Z Jiang ldquoCoupled analysis of slipand deflection for continuous composite beams of steel andconcreterdquo Advances in Structural Engineering vol 7 no 3pp 257ndash269 2004

[27] Z H Deng Q Hu J Zeng and P Xiang ldquoStructural per-formance of steel-truss reinforced composite joints undercyclic loadingrdquo Proceedings of the Institution of CivilEngineers-Structures and Buildings pp 1ndash19 2017

[28] P Xiang and H P Wang ldquoOptical fiber based sensors fordistributed strain monitoring of asphalt pavementsrdquo In-ternational Journal of Pavement Engineering pp 1ndash9 2016

[29] P Xiang Z H Deng Y S Su H P Wang and Y F WanldquoExperimental investigation on joints between steel reinforcedconcrete T-shaped column and reinforced concrete beamunder bidirectional low-cyclic reversed loadingrdquo Advances inStructural Engineering vol 20 no 3 pp 446ndash460 2016

[30] H PWang and P Xiang ldquoeoretical analysis on strain transfererror of FBG sensors attached on steel structures subjected tofatigue loadrdquo Strain vol 52 no 6 pp 522ndash530 2016

[31] H PWang and P Xiang ldquoStrain transfer analysis of optical fiberbased sensors embedded in asphalt pavement structurerdquo Mea-surement Science and Technology vol 27 no 7 p 075106 2016

[32] X Yang Y Bai F J Luo X L Zhao and X H He ldquoFiber-reinforced polymer composite members with adhesivebonded sleeve joints for space frame structuresrdquo Journal ofMaterials in Civil Engineering vol 29 no 2 Article ID04016208 2017

[33] G A Yin F X Ding H B Wang Y Bai and X M LiuldquoConnection performance in steel-concrete composite trussbridge structuresrdquo Journal of Bridge Engineering vol 22 no 3Article ID 04016126 2017

[34] X H He H X QinW S Liu Y F Chen J P Zhai and L YuldquoDesign analysis and construction of a steel truss cable-stayedbridge for high-speed railway in Chinardquo Structural Engi-neering International vol 26 no 4 pp 381ndash388 2016

[35] C K Chen and W Zhang ldquoComparative experimental in-vestigation on steel staggered-truss constructed with differentjoints in firerdquo Journal of Constructional Steel Research vol 77pp 43ndash53 2012

[36] C K Chen D Zhang W Zhang and B Y Shen ldquoExperi-mental behaviors of steel staggered-truss system exposed tofire under lateral forcerdquo International Journal of SteelStructures vol 12 no 1 pp 59ndash70 2012

[37] L Y Zhou and G C He ldquoExperimental research on end jointof steel-concrete composite trussrdquo Baltic Journal of Road andBridge Engineering vol 7 no 4 pp 305ndash313 2012

[38] C K Chen and W Zhang ldquoExperimental study of the me-chanical behavior of steel staggered truss system under poolfire conditionsrdquo Cin-Walled Structures vol 49 no 11pp 1442ndash1451 2011

[39] J Liu F X Ding X M Liu and Z W Yu ldquoStudy on flexuralcapacity of simply supported steel-concrete composite beamrdquoSteel and Composite Structures vol 21 no 4 pp 829ndash847 2016

[40] F X Ding J Liu X M Liu F Q Guo and L Z JiangldquoFlexural stiffness of steel-concrete composite beam underpositive momentrdquo Steel and Composite Structures vol 20no 6 pp 1369ndash1389 2016

[41] Y Peng W Y Deng P Xu and S G Yao ldquoStudy on thecollision performance of a composite energy-absorbingstructure for subway vehiclesrdquo Cin-Walled Structuresvol 94 pp 663ndash672 2015

[42] S C Xie X F Liang and H Zhou ldquoDesign and analysis ofa composite energy-absorbing structure for use on railwayvehiclesrdquo Proceedings of the Institution of Mechanical Engi-neers Part F Journal of Rail and Rapid Transit vol 230 no 3pp 825ndash839 2016

[43] Q Hu Z H Deng Q Lin and D X Xu ldquoAnalysis of failuremode and ultimate bearing capacity of steel truss couplingbeamrdquo Advances in Industrial and Civil Engineeringvol 594ndash597 pp 824ndash827 2012

[44] Q A Lin Z H Deng and G X Tang ldquoExperimental study onseismic behavior of full-scale new steel truss coupling beamsrdquoAdvances in Structures vol 163ndash167 pp 2041ndash2046 2011

[45] Z H Deng Q Hu Q Lin and D X Xu ldquoExperimentalresearch of steel truss coupling beam on seismic behavior andenergy dissipation mechanismrdquo in Proceedings of ISISS prime2009Innovation amp Sustainability of Structures vol 1-2 pp 1500ndash1505 Guangzhou China November 2009

[46] Z H Deng G X Tang P Xiang and X Y Wang ldquoEx-perimental study on joints of steel reinforced concrete


T-shaped column under to direction low-cyclic reversedloadingrdquo in Proceedings of the Tenth International Symposiumon Structural Engineering for Young Experts vol 1-2pp 895ndash900 Changsha China October 2008

[47] H F Yang Z H Deng Y H Qin and L S Lv ldquoA study onthe bond behavior of corroded reinforced concrete containingrecycled aggregatesrdquo Advances in Materials Science and En-gineering vol 2015 Article ID 249301 9 pages 2015

[48] Z H Deng Q Lin Q Hu Z M Pan and D X Xu ldquoTest forseismic behaviors of new steel truss coupling beamsrdquo Journalof Vibration and Shock vol 31 pp 76ndash81 2004

[49] Q Lin Z H Deng and Q Z Liu ldquoExperimental study andnonlinear finite element analysis on the seismic performanceof full-scale steel truss coupling beamsrdquo Engineering Me-chanics vol 29 pp 256ndash263 2012

[50] Q Hu T J Liao and Z H Deng ldquoCyclic loading experimenton seismic behavior of shear wall with steel truss couplingbeamrdquo Journal of Earthquake Engineering and EngineeringVibration vol 34 pp 1ndash10 2014

[51] K Sugiura G C Lee E Watanabe and K C Chang ldquoIn-stability of steel short column under cyclic loadingsrdquo Stabilityand Ductility of Steel Structures under Cyclic Loadingpp 15ndash23 CRC Press Osaka Japan 1992

[52] K Sugiura K C Chang and G C Lee ldquoEvaluation of low-cycle fatigue-strength of structural metalsrdquo Journal of Engi-neering Mechanics vol 117 no 10 pp 2373ndash2383 1991

[53] K Sugiura G C Lee and K C Chang ldquoEndochronic theoryfor structural-steel under nonproportional loadingrdquo Journalof Engineering Mechanics vol 113 no 12 pp 1901ndash1917 1987

[54] E Watanabe K Sugiura M Kanou M Takao and S EmildquoHysteretic behavior of thin tubular beam-columns withround cornersrdquo Journal of Constructional Steel Researchvol 18 no 1 pp 55ndash69 1991

[55] E Watanabe K Sugiura and W O Oyawa ldquoElasto-plasticinstability of steel compression tubular members subjected tocyclically applied bi-directional horizontal loadsrdquo Cin-Walled Structures pp 809ndash816 1998

[56] L S He M Kurata and M Nakashima ldquoCondition assess-ment of steel shear walls with tapered links under variousloadingsrdquo Earthquakes and Structures vol 9 no 4pp 767ndash788 2015

[57] S Gwon M Shin B Pimentel and D Lee ldquoNonlinearmodeling parameters of RC coupling beams in a coupled wallsystemrdquo Earthquakes and Structures vol 7 no 5 pp 817ndash8422014

[58] GB50010-2002 Code for Design of Concrete Structures ChinaArchitecture and Building Press Beijing China 2002 (inChinese)


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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Journal of


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nom

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ria

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Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Research ArticleInvestigation on the Structural Behavior of ShearWalls with SteelTruss Coupling Beams under Seismic Loading

Zhiheng Deng1 Changchun Xu12 Qiang Hu13 Jian Zeng12 and Ping Xiang 456

1College of Civil and Architectural Engineering Guangxi University Nanning 530004 China2Hualan Design amp Consulting Group Nanning 530011 China3Department of Civil and Architectural Engineering Guangxi University of Science and Technology Liuzhou 545006 China4School of Civil Engineering Central South University Changsha 410075 Hunan China5National Engineering Laboratory for High-Speed Railway Construction Changsha China6Department of Architecture and Civil Engineering City University of Hong Kong Kowloon Hong Kong

Correspondence should be addressed to Ping Xiang pxiang2-cmycityueduhk

Received 23 March 2017 Revised 16 October 2017 Accepted 19 October 2017 Published 25 March 2018

Academic Editor Carlos Garcia-Mateo

Copyright copy 2018 Zhiheng Deng et alis 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

Based on existing experimental results the finite element analyses were carried out on shear wall structures with steel trusscoupling beams is work studied the seismic behaviors and the working mechanism of the steel truss coupling beam at theultimate state and put forward two parameters the area ratio of web member to chord and the stiffness ratio of coupling beam toshear wall e seismic optimum design method of the coupling beam was also proposed Afterwards a comparative analysis wasimplemented on the three-dimensional shear wall model with steel truss coupling beams designed by the proposed designmethode results show that the structures designed by the proposed method have excellent seismic behaviors the steel truss couplingbeams have enough stiffness to connect shear walls effectively and its web members have appropriate cross sections to dissipateseismic energy

1 Introduction

Coupling beams (CBs) are important structural componentsto shear wall structures as they provide effective connectionsbetween shear wall limbs and increase global lateral stiffnesse seismic performance of shear wall structure is largelydependent on the behaviors of CBs e steel CB has a lot ofadvantages such as light weight good ductility force clear andeasy to be replaced after the earthquake Ever since the be-ginning of research on the steel CBs in the 1990s the structuralbehaviors of steel CBs have been investigated by experimentsand theoretical analysis [1ndash3] the research pointed out thatsteel CB structure has sufficient rigidity strength toughnessand a good seismic performance the plastic deformation of theweb after yielding helps to dissipate seismic energy thussignificantly improves the seismic performance of CBsNonlinear seismic response of walls coupled with steel andconcrete beams was also investigated [4ndash6] the researchdemonstrated the advantages of using steel beams to couple

reinforced concrete walls Experiments and simulations havebeen conducted on the joints of steel CBs and shear walls[7ndash11] and the results demonstrated that the anchorage hasimportant impacts on the stiffness degradation the shear yieldstyle steel CB has excellent ductility performance and energyperformance construction convenient and easy maintenanceand replacement and especially the maintenance can be easilyreplaced after the earthquake Wu [12] investigated the steelCB and concrete shear wall joints by employing experimentsand finite element analysis the failure mode of joints straindistribution bearing capacity CB size concrete strengthductility and hysteretic behaviors were studied

In recent decades composite structures [13ndash16] developquickly and have been investigated in researches [17ndash23] andused in various kinds of structures [24ndash32] and infrastructures[33ndash42] e steel truss CB is a special kind of steel CB thatsatisfies flexible layout clear loading path and adaptable ar-chitectural features however investigations on steel truss CBshear wall structures are scarce Experimental researches have

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 5602348 16 pageshttpsdoiorg10115520185602348








d

2l

αid

αi

αid

β

3icαil

Nc

Nf Nf

3ic αi








Δlf asymp Δi

d

hi

cos β Δi

d

hi

l

lf (1)


σf Efεf

Ef

Δlflf

εle εy


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Nf EfAf

κΔidl

hil2f

+(1minus κ)εy⎡⎢⎣ ⎤⎥⎦ (3)



450 450 450

200

210

300

300

700

300

800

500

400

400

410 2350

1 1

2 2

(a)

110

450

10ϕ8ϕ4

50

ϕ6

125

1-1

(b)

110

450

14ϕ8

2-2

ϕ4

50

ϕ6

60

(c)

200 450 200300

5050

300

(d)




Vb 2Δi

hi

ψEfAf

κd2l

lfminus3icl


(4)


ψ 1



Kb limΔi0

Vb

Δi

11138681113868111386811138681113868111386811138681113868κ1

2hi

EfAfd2l

l3fminus3EcIc

l2⎛⎝ ⎞⎠ (6)




ρK Kb

Kw

(7)



(a) (b)












0 0002 0004 ε

0

30

20

10

σ (M

Pa)


0

σy

σu

0 εy 03 ε

σ

κE

E







Flange 30769 3875 192times105







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls











d

2l

αid

αi

αid

β

3icαil

Nc

Nf Nf

3ic αi








Δlf asymp Δi

d

hi

cos β Δi

d

hi

l

lf (1)


σf Efεf

Ef

Δlflf

εle εy


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Nf EfAf

κΔidl

hil2f

+(1minus κ)εy⎡⎢⎣ ⎤⎥⎦ (3)



450 450 450

200

210

300

300

700

300

800

500

400

400

410 2350

1 1

2 2

(a)

110

450

10ϕ8ϕ4

50

ϕ6

125

1-1

(b)

110

450

14ϕ8

2-2

ϕ4

50

ϕ6

60

(c)

200 450 200300

5050

300

(d)




Vb 2Δi

hi

ψEfAf

κd2l

lfminus3icl


(4)


ψ 1



Kb limΔi0

Vb

Δi

11138681113868111386811138681113868111386811138681113868κ1

2hi

EfAfd2l

l3fminus3EcIc

l2⎛⎝ ⎞⎠ (6)




ρK Kb

Kw

(7)



(a) (b)












0 0002 0004 ε

0

30

20

10

σ (M

Pa)


0

σy

σu

0 εy 03 ε

σ

κE

E







Flange 30769 3875 192times105







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









Δlf asymp Δi

d

hi

cos β Δi

d

hi

l

lf (1)


σf Efεf

Ef

Δlflf

εle εy


⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)


Nf EfAf

κΔidl

hil2f

+(1minus κ)εy⎡⎢⎣ ⎤⎥⎦ (3)



450 450 450

200

210

300

300

700

300

800

500

400

400

410 2350

1 1

2 2

(a)

110

450

10ϕ8ϕ4

50

ϕ6

125

1-1

(b)

110

450

14ϕ8

2-2

ϕ4

50

ϕ6

60

(c)

200 450 200300

5050

300

(d)




Vb 2Δi

hi

ψEfAf

κd2l

lfminus3icl


(4)


ψ 1



Kb limΔi0

Vb

Δi

11138681113868111386811138681113868111386811138681113868κ1

2hi

EfAfd2l

l3fminus3EcIc

l2⎛⎝ ⎞⎠ (6)




ρK Kb

Kw

(7)



(a) (b)












0 0002 0004 ε

0

30

20

10

σ (M

Pa)


0

σy

σu

0 εy 03 ε

σ

κE

E







Flange 30769 3875 192times105







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Vb 2Δi

hi

ψEfAf

κd2l

lfminus3icl


(4)


ψ 1



Kb limΔi0

Vb

Δi

11138681113868111386811138681113868111386811138681113868κ1

2hi

EfAfd2l

l3fminus3EcIc

l2⎛⎝ ⎞⎠ (6)




ρK Kb

Kw

(7)



(a) (b)












0 0002 0004 ε

0

30

20

10

σ (M

Pa)


0

σy

σu

0 εy 03 ε

σ

κE

E







Flange 30769 3875 192times105







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls













0 0002 0004 ε

0

30

20

10

σ (M

Pa)


0

σy

σu

0 εy 03 ε

σ

κE

E







Flange 30769 3875 192times105







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







ρA 04

ρK 015(8)





P (k

N)


0

0

50

minus100

100

minus150

150

minus200

200

minus20 minus30


∆ (mm)


P (k

N)

∆ (mm)


minus150

minus100

0

0

50

100

150












Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Kb 2Af

hi

Efld2

l3f+

3Ec

ρA[λ]2⎛⎝ ⎞⎠ (9)


Af ρKhi

2 Efld21113902l3f + 3Ec1113902ρA[λ]21113874 1113875

Kw(10)



ΔNiy

hilf

dl

fy

Ef

(11)


VNbu

2l2ffy

dlEf

ψEfAf

d2l

lfminus3ic

l1113888 1113889 (12)



ΔViu

twl2hi

3EcSc

fv (13)


Vbu 2Ictw

Sc

fv ψκEfAfd2l3

3lfEcIc


(14)




0

110

220


Base

shea

r (kN

)


(a)Ba

se sh

ear (

kN)


0

110

220

0 10 20 30



(b)








minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









minus40 40minus200

minus100

0

100

200


Load

(kN

)

(a)

minus40 40minus200

minus100

0

100

200

Load

(kN

)


(b)

minus40 40minus300

minus150

0

150

300


Load

(kN

)

(c)








0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






0 300

005

010

015

020

he

Δ (mm)10 20





(a) (b)

(c)






110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







110

410

410

830

410

410 450 450450450450

500

800

300

300

300

300

300

300

700

700

700

700

700





Web membertype

Arearatio

Stiffnessratio






minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







minus600

minus400

minus200

0

200

400

600


Base

shea

r (kN

)


Wall1Wall2Wall3


minus250 125 00 125 250minus350

0


Base

shea

r (kN

)

350

(a)

minus250 minus500

0

500


Base

shea

r (kN

)

200 minus200 minus100 0 100 300

(b)

minus600

0

600


Base

shea

r (kN

)

minus320 160 00 160 320

(c)







00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








00

012

016

024

028

he


020

150 100 50 200



S Mises(Avg 75)

+1887e + 07+1730e + 07+1572e + 07+1415e + 07+1258e + 07+1101e + 07+9407e + 06+7865e + 06+6294e + 06+4722e + 06+3150e + 06+1579e + 06+7213e + 06

(a)

S Mises(Avg 75)

+1942e + 07+1780e + 07+1618e + 07+1457e + 07+1295e + 07+1133e + 07+9714e + 06+8096e + 06+6479e + 06+4862e + 06+3244e + 06+1627e + 06+9242e + 06

(b)

S Mises(Avg 75)

+2272e + 07+2083e + 07+1894e + 07+1705e + 07+1516e + 07+1327e + 07+1139e + 07+9496e + 06+7607e + 06+5717e + 06+0020e + 06+1938e + 06+4905e + 06

(c)




+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





+4924e + 08+4924e + 08+4130e + 08+3733e + 08+3336e + 08+2939e + 08+2542e + 08+2145e + 08+1748e + 08+1350e + 08+9534e + 07+5563e + 07+1592e + 07

(a)


+4694e + 08+4312e + 08+3929e + 08+3547e + 08+3165e + 08+2783e + 08+2400e + 08+2018e + 08+1636e + 08+1254e + 08+8713e + 07+4890e + 07+1068e + 07

(b)


+4912e + 08+4511e + 08+4109e + 08+3708e + 08+3306e + 08+2905e + 08+2503e + 08+2102e + 08+1700e + 08+1299e + 08+8971e + 07+4956e + 07+9414e + 06

(c)




7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





7 Conclusion













Acknowledgments


References


































































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Documents

Investigation on the Structural Behavior of Shear Walls