Seismic performance of steel–concrete composite structural walls with internal bracings

Seismic performance of steel–concrete composite structural walls withinternal bracings

Wenwu Lan a,b, Jiaxing Ma c, Bing Li c,⁎a College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, PR Chinab Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Guangxi University, Nanning 530004, PR Chinac School of Civil and Environmental Engineering, Nanyang Technological University, Singapore

a b s t r a c ta r t i c l e i n f o

Article history:Received 20 June 2014Accepted 26 February 2015Available online xxxx

Keywords:Steel–concrete compositeBracingMaterial nonlinearityCyclic loadingFinite elementHysteresis loops

This paper presents experimental and analytical investigations of steel–concrete composite structural walls withinternal bracings. In the experimental study, four full-scale wall specimens were tested under cyclic load rever-sals. The performance of the wall specimens in terms of load–deformation response and cracking patterns is de-scribed. However, due to the inherent complexity of shear walls and unique features of the embedded diagonalbracing, the experimental investigation was not sufficient to fully explain the influence of several parameters.Therefore, an analytical investigation based on the FE models using DIANA is presented. Validation of the FEmodels against the experimental results has shown a good agreement. Critical parameters influencing theshear wall's behavior such as shear span ratio, axial load, the size and thickness of shaped steel are varied, andtheir effects on the walls' seismic behavior are discussed.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Owing to the combination of advantages of reinforced concrete andsteel plates, steel–concrete composite structural walls have demon-strated superiorities in strength stiffness and ductility [5], which makethem favorable worldwide, especially in the high seismic regions suchas China and Japan. From the study of Synge [13], it is also noticeablethat diagonal bracings can be introduced in shear walls as an effectiveapproach to withstand shear force and improve the energy dissipationcapacity. By adding inclined bracings in the steel–concrete compositestructural walls, steel buckling, crushing and spalling of concrete andtensile cracks can be effectively reduced according to the experimentconducted by Astaneh and Zhao [1].

In spite of thewide application of steel–concrete composite structur-al walls, the complexity of the combination of steel and concrete makesit difficult to understand their behaviors. Scholars have done quite anumber of experiments in this area. Emori [5] conducted compressionand shear test 1/4 scale specimens on concrete filled steel box walls,concluding that the resisting effect of concrete on the local buckling ofthe steel plates as well as the confinement effect of steel plates on con-crete gave the composite structure high strength and sufficient ductility.In an attempt to simulate the behavior of composite concrete–steelplate walls, Link [10] developed a series of FE analyses, finding that

the strength degradation was effectively inhibited by introducing twolayers of steel plates, making the walls more ductile. As an effort tostudy the energy dissipation behavior of shear panels, Nakashima [11]tested six full-scale shear panels, showing that horizontal and verticalshear panels exhibited stable hysteresis and large energy dissipationcapacity. Brando [2] later specifically investigated the effect of bucklinginhibition of shear panels, and explained the mechanism of their betterperformance in terms of dissipated energy. In order to further explorethe seismic behavior of steel plate, Driver [4] and Abolhassan [1] con-ducted their own cyclic tests on the steel plate shear wall system.Their test specimens demonstrated excellent ductility and energy dissi-pation characteristics, exhibiting stable behavior at very large deforma-tions even after many load cycles. However, there were hardly anyexperiments on steel–concrete composite structural walls with brac-ings. Furthermore, most of research in the literature just gave generalcomments on the performance of steel composite shear walls, withoutdeeper explorations about the effect of individual parameters.

In order to supplement the insufficient ongoing research on steel–concrete composite structural walls with bracings, especially that oninelastic behavior under reversed cyclic loadings, Guangxi Universitydeveloped and tested four specimens consisting of one steel–concretecomposite structural walls for control and other three ones with brac-ings. This paper covers a comprehensive research involving experimen-tal and FE numerical investigations. First, the test program is introducedand then the observations of experiments are described in detail. Aseries of FE analyses including 54 cases is presented using a proven re-liable tool DIANA [3] in terms of load–displacement relationship, secant

Journal of Constructional Steel Research 110 (2015) 76–89

⁎ Corresponding author. Tel.: +65 67905090.E-mail address: [email protected] (B. Li).

http://dx.doi.org/10.1016/j.jcsr.2015.02.0150143-974X/© 2015 Elsevier Ltd. All rights reserved.

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Journal of Constructional Steel Research

stiffness and the energy dissipation capacity. Key parameters studiedhere are the shear span ratio, thickness of shaped steel and axial loadratio.

2. Test program

2.1. Details of specimens

The experimental program included a total of four specimens namedSW-1, SW-2, SW-3 and SW-4, which represented a series of half-scaleshort-pier shearwalls of commonbuilding. All specimenshad the exact-ly same dimension as illustrated in Fig. 1. The specimen was designedand constructed following the code provisions of Chinese code GB50010-2002. A size of 720 mm × 120 mm × 1300 mm was adoptedfor the wall, which was connected to a concrete head with the dimen-sion of 920 mm × 400 mm × 400 mm. Four reinforcing bars with a di-ameter of 12 mm were used as vertical reinforcement, while thehorizontal reinforcementwas provided by reinforcing barswith a diam-eter of 6mm at a spacing of 100mm. There were embedded columns attwo ends of walls whichwere reinforced with channel shaped steel andangle shaped steel. The reinforcement layout is shown in Fig. 2. The dif-ferences between each specimenwere about flat shaped steel served astransverse reinforcement of the embedded columnand “X” shaped steelbracings, which is demonstrated in Fig. 3. The control specimen SW-1was constructed using flat shaped steel at a spacing of 200 mm in theembedded column but with no steel bracing. Specimens SW-2 andSW-3 differed with SW-1 in steel bracing, which had three and fourlayers of “X” shaped steel bracings in the wall respectively. SpecimenSW4 had the same layers of steel bracing with SW-2 but the spacingof flat shaped steel in the embedded column was adjusted to 100 mm.The details of specimens were summarized in Table 1 and the compar-ison of reinforcement ratios of specimens were listed in Table 2.

2.2. Material properties

The concrete used for all specimens was of C35 with the averagecompressive strength calculated using the cube samples of 33.5 MPa.The longitudinal reinforcement used in the wall was 12 mm diameterdeformed bars of HRB335, while the horizontal reinforcementemployed was 6 mm diameter deformed bars of HPB300. Test resultsobtained from samples of 12 mm and 6 mm diameter bars indicatedan average yield stress of 335MPa and 326MPa respectively. Three dif-ferent kinds of shaped steel were adopted in this experiment, namely8# channel steel, 30 × 3 angle steel and 25 × 3 flat steel. The relevantproperties of concrete, reinforcing bars and shaped steel are listedbelow in Table 3.

2.3. Instrumentation

A sufficient number of measuring devices were used in the experi-mental tests to record the strains and deformations. Strain gaugeswere placed on both shaped steel and longitudinal reinforcements atselected locations within the walls. The lateral displacements of thetop head were measured using displacement transducers, while arange of LVDTs was installed at the surface of walls to measure theflexural and shear deformations.

2.4. Test setup

Each of the test specimens was subjected to axial loads and quasi-static load reversals to simulate an earthquake scenario. A constantaxial load of 721 kN (0.3Agfc′) will be applied by one hydraulic jack of1000 kN loading capacity with its end connecting to the concrete head.A load cell will be attached to the jack to measure reaction force. Theload transfer system consists of a steel beam, a steel spreader plate of50 mm and several steel rollers, which can be seen from Fig. 4. Thissetup is designed to ensure uniform axial load distribution on the wallcross section area, andmore importantly, to accommodate the horizon-tal movement of wall specimens due to lateral displacements.

A reversible horizontal load was applied to the concrete head by adouble acting 2000 kN capacity electro hydraulic actuator. The loadinghistory with applied cycles versus the displacement is shown in Fig. 5,which includes three stages: two before yielding and one after yielding.The first stage aiming to find the cracking displacementΔcr increases bythe step of 2 mm. After cracking happening in both directions, the cyclecontinues by the same size of step until the yielding of steel is moni-tored. The post-yielding part of loading history has an increase of oneyield displacement Δy every three cycles, and will be terminated whenthe specimen is deemed to have failed.

The bottom of the wall was connected to laboratory strong floorby prestressing rods, which aimed to prevent horizontal movementbetween wall base and the strong floor as well as the overturningFig. 1. Specimen dimension.

Fig. 2. Reinforcement layout.

77W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

movement. One end of actuatorwasfixed to the reactionwalls of lab. Allspecimens share the same loading apparatus.

3. Experimental observations and results

3.1. Load–deformation response

Fig. 6a shows the shear force versus lateral displacement of hystere-sis loops of specimen SW-1. The elastic behavior dominated in initialcycles with no evident pinching in hysteretic hoops. With the increase

in the loading runs, the specimen attained the first yield at the displace-ment of 3.6mm corresponding to a shear force of 221 kN. In positive di-rection, a maximum load of 359 kN was recorded at a correspondingdisplacement of 12.53 mm, and a load of −393 at a displacement of−12.4 mm was attained in the negative direction. Concrete crushingat the wall corner led the failure of the specimen, while the bulking ofshaped steel was not observed at this point. Compared with the rest ofthe specimens, the pinching effect was more evident in SW-1, whichhas less energy dissipating capacity. This can be attributed to the “X”shaped steel bracings which were able to bear some shear force, inhibit

Fig. 3. Steel structure of specimens.

Table 1Details of specimens.

Specimen SW-1 SW-2 SW-3 SW-4

Length (mm) × width (mm) × height (mm) 720 × 120 × 1300 720 × 120 × 1300 720 × 120 × 1300 720 × 120 × 1300Horizontal reinforcement of the wall ϕ6@100 ϕ6@100 ϕ6@100 ϕ6@100Vertical reinforcement of the wall 4ϕ12 4ϕ12 4ϕ12 4ϕ12Spacing of flat steel in embedded column (mm) 200 200 200 100Layers of “X” shaped bracing in the wall None 3 4 3

78 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

the expansion and extension of diagonal cracks, and reduce the slipbetween shaped steel.

Fig. 6b illustrates the shear force versus lateral displacement ofhysteresis loops of specimen SW-2. In the positive loading direction,the first yield occurred in the left embedded column at a displacementof 5.4 mm, with a corresponding shear of 290 kN. In the subsequentloading cycles, the specimen reached amaximumshear force of approx-imately 404 kN, in the positive loading direction and −395 kN, in thenegative loading direction. The corresponding displacements were17.34 mm and −14.99 mm respectively. The specimen failed at thecycle of 7.0 ductility factor, when severe spalling of concrete occurred500 mm above the ground. Moreover, the concrete at the corner ofwall also crushed and shaped steel in embedded columns as well asbracings bulked. As a result, SW-2 demonstrated better energy dissipa-tion than SW-1.

The shear force versus lateral displacement relationship of SW-3 ispresented in Fig. 6c. In the positive loading direction, the first yieldoccurred at a displacement of 13.8 mm corresponding to a DF of 0.82.Themaximumcapacities, 382 kN in the positive and−395 kN in the neg-ative loading directions, were reached at displacements of 11.6 mm and−17 mm, respectively. In the positive direction, when compared withspecimen SW-1 the maximum capacity of Specimen SW-3 was 12.5%

higher, while in the negative direction, it was around 6.3% greater. Thisindicated the fact that “X” shaped steel bracings improved the perfor-mance marginally with respect to shear capacity. This specimen shareda similar failure phenomenon with SW-2 but the secant stiffness afterreaching the peak shear force was slightly higher than SW-2, indicatingthat the increase of “X” shaped steel bracings brought improvement re-garding stiffness degradation.

Fig. 6d shows the shear force versus lateral displacement relation-ship of SW-4. At a displacement of 5.2 mm, the specimen attained thefirst yield with a reaction shear force of 282.83 kN. With the enhance-ment in the loading cycles, the maximum load and the correspondingdisplacement in the positive direction were 392 kN and 13.4 mm,respectively, and−392 kN and−13mm for the negative loading direc-tion. Although the difference of stiffness at the same displacement ofeach specimen was negligible in the initial stage, specimens SW-2,SW-3 and SW-4 obviously had higher stiffness as loading increased,which indicated that “X” shaped steel bracings can effectively reducethe speed of stiffness degradation. Furthermore, like SW-3, SW-4 hadslight higher secant stiffness compared with SW-2, which revealedthat the increase of flat shaped steel has a beneficial effect on stiffnessdegradation.

3.2. Cracking pattern

Fig. 7a illustrates the final cracking pattern of all specimens. For SW-1, cracks initiated at wall corner 270 mm above the ground whenthe horizontal displacement increased to 1.4 mm (Fig. 7b). With the in-crease in the loading runs, the cracks further propagated to other areas.Few diagonal cracks appeared at the displacement of 7mm, andmost ofthem propagated 45° from the wall ends (Fig. 7c). As the displacementwas further increased from 7 mm to 17.5 mm, more diagonal cracksformed and the concrete cover began to crush forming an obviousdiagonal compression strut (Fig. 7d). The specimen failed when the dis-placement reached 24.5 mm, with concrete at corners of wall crushingand two evident vertical cracks located at the connection of concreteand shaped steel forming. The main reason behind the failure of speci-men was that the connection between concrete and shaped steel wasimpaired due to propagation and development of the diagonal cracksas horizontal displacement increased, whereas the shaped steel wasnot buckled in the whole process of cyclic loadings. Hence specimenSW-1 experienced flexure-shear failure.

In SW-2, firstly, a horizontal crack appeared 280 mm above theground at the displacement of 1.6 mm (Fig. 8a). As displacement in-creased, a few horizontal cracks occurred at the area of wall bottom(Fig. 8b), but no diagonal cracks were observed until the displacementreached 7 mm. As the loading run was increased to the displacement

Table 3Steel properties.

Material Es(N/mm2)

fy(N/mm2)

fu(N/mm2)

εy εsh

8# channelsteel

1.97 × 105 385 513 1.954 × 10−3 1.954 × 10−2

30 × 3 anglesteel

2.03 × 105 332 453 1.635 × 10−3 1.635 × 10−2

25 × 3 flatsteel

1.87 × 105 356 458 1.904 × 10−3 1.904 × 10−2

ϕ6 bars 1.95 × 105 326 438 1.672 × 10−3 1.672 × 10−2

Fig. 4. Test setup [8].

Table 2Reinforcement ratios of specimens.

Specimen SW-1 SW-2 SW-3 SW-4

Horizontal reinforcement ratio of wall (%) 3.02 3.02 3.02 3.02Vertical reinforcement ratio of wall (%) 0.523 0.523 0.523 0.523Vertical reinforcement ratio of embeddedcolumn (%)

0.625 0.625 0.625 1.25

Horizontal reinforcement ratio of embeddedcolumn (%)

0.471 0.471 0.471 0.471

79W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

of 14 mm, more additional diagonal cracks appeared and they furtherpropagated showing a “V” shape of distribution (Fig. 8c). Besides, thespecimen also experienced some vertical cracks, while spalling ofconcrete began simultaneously. A primary horizontal crack at the leftside of wall was formed 250 mm above the bottom at the displacementof 17.5 mm. The specimen failed at the displacement of 24.5 mm due tothe crushing of concrete atwall corners aswell as the spalling of concreteof the primary horizontal crack (Fig. 8d). Besides, shaped steel, “X”

shaped steel bracings and longitudinal reinforcement also buckled inthis stage. The major difference between SW-1 and SW-2 was theappearance of the primary horizontal crack, with no vertical cracks atthe connection of concrete and shaped steel forming, which means thatfailuremode has transferred fromflexural-shear failure toflexural failure.

Specimens SW-3 and SW-4 had a similar crack pattern formation asSW-2 as shown by Fig. 9a and b, thereby generating quite analogousfailuremodes. “X” shaped steel bracings and longitudinal reinforcement

Fig. 5. Loading history.

a) Specimen SW-1 b) Specimen SW-2

c) Specimen SW-3 d) Specimen SW-4

Fig. 6. Comparison of analyzed and experimental hysteresis loops.

80 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

were found buckled at the final stage, and crushing of concrete at wallcorners together with the spalling of concrete of the primary horizontalcrack also happened. The minor differences between them were thetime of crack formation and the location of the primary horizontal crack.

4. Finite element analysis

In order to better the understanding of seismic behavior of steel–concrete composite structural walls, it is highly necessary to thoroughlystudy the impact of some crucial parameters such as shear span ratio,reinforcement ratios and axial load ratio. Due to the cost and time ofexperimental studies, it is more efficient to utilize finite element toolsfor analysis. In this study, the specimens were analyzed using aproved-reliable finite element software DIANA [3]. Three-dimensional(3D) twenty-node isoparametric solid brick elementswere used to sim-ulate the concrete, which is based on quadratic interpolation and Gaussintegration; while reinforcing bars were modeled by the embeddedreinforcement technique. The shaped steel and bracing, with specialcare, were modeled by 2D curved shell elements. In material modeling,the concrete models were based on nonlinear fracture mechanics to

account for cracking, and plasticity models were used for the concretein compression and steel reinforcement.

4.1. Modeling of concrete

The analysis used the total strain rotating crackmodel for themodel-ing of concrete. In this model, when the principal tensile stress in the el-ement exceeds a certain limiting value, cracks initiate in a directionperpendicular to it. The most significant difference between thismodel and its counterpart — the fixed crack model, is that the formerassumes that the crack direction is aligned orthogonal to the principaltensile stresses, whereas the latter considers that the crack is fixedonce it is generated. Although the fixed crack model fits the nature ofshear effect such as aggregate interlock, it can also complicate the anal-ysis because of the uncontrollable rotation of axes of principle stress,which ceases to coincide with the axes of principle strain. Moreover, ashear stress parallel to the crack direction should be introduced in thefixed crack model when the direction of principal stress changes whilethis kind shear transfer mechanism is not necessary in a rotating crackmodel. The rotating crack model was selected here in consideration ofits simplicity and reasonable accuracy. More information regarding

Fig. 7. Cracking patterns of specimen SW-1.

81W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

the crack formation, orientation, angle limitation, etc. can be referredfrom Hajime and Kohichi's book [7].

Threemajor aspects involved in the total strain rotating crackmodelare compressive behavior, tensile behavior and shear behavior. The firsttwo are represented by some predefined nonlinear functions betweenthe stress and the strain in DIANA. In this study, the parabolic curve(Fig. 10) proved reliable in previous wall analysis [9,15] was selectedfor the compressive behavior of concrete. The strain αc/3, at whichone-third of the maximum compressive strength fc is reached, is

αc=3 ¼ −13f cE

:

The strain αc, at which the maximum compressive strength isreached, is

αc ¼ −53f cE

¼ 5αc=3:

The ultimate strain αu, at which the material is completely softenedin compression, is

αu ¼ αc−32GC

hf c:

The total compressive fracture energy GC found by Feenstra [6]ranges from 10 to 25 Nmm/mm2. Hence he parabolic compressioncurve in DIANA is now described by

f ¼

− f c13

α j

αc=3if αc=3bα j≤0

− f c13

1þ 4α j−αc=3

αc−αc=3

!−2

α j−αc=3

αc−αc=3

!2 !i f αcbα j≤αc=3

− f c 1−α j−αc

αu−αc

! "2! "if αubα j≤αc

8>>>>>>>><

>>>>>>>>:

:

With regard to the tensile behavior, there are seven predefinedstress–strain curves in Diana, which can been seen in Fig. 11. The linearcurvewas chosen in this study due to its relative accuracy and efficiencyin analysis. The uniaxial tensile strength of concrete ft was calculatedfrom the compressive strength fc according to CEB-FIP Model code[14]. 0.0015 was used as the value of the ultimate tensile strain εu. Itwas based on the assumption that the stress decreases linearly to zeroat a total strain of about 10 times the strain at concrete failure in tension,which was taken as 0.00015 based on authors' parametric studies.

As mentioned above, the modeling of shear behavior is only neces-sary in the fixed crack concept where the shear stiffness is usuallyreduced after cracking. Hence in this analysis, the shear retention factor

Fig. 8. Cracking patterns of specimen SW-2.

82 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

was assumed to be one, which means that shear modulus is constantbefore and after cracking.

As for the lateral influence to concrete, Vecchio & Collins' model [12]was adopted here to explain the reduction of compressive strength ofconcrete due to the cracks caused by tensile strain aswell as the increaseof strength and deformability of concrete due to lateral confinement.

4.2. Modeling of reinforcement and shaped steel

DIANAhas twomethods for themodeling of reinforcement bars. Thefirst one is embedded reinforcement. In this method, reinforcement isembedded in structural elements, the so-called “mother elements”and do not have degrees of freedom of their own. Hence reinforcementstrains are by default calculated from the displacement field of themother elements, which means that a perfect bond between thereinforcement and the surrounding materials is assumed. The secondtechnique uses separate element to model reinforcement, in whichtruss and beam elements are often applied. This method is superiorbecause the bond-slip behavior can be investigated by adding interfaceelements between the concrete and the reinforcement. However, sincethe behavior of reinforcement bars was beyond the aim of this study,the embedded reinforcement technique was chosen which allowedfor less computation and easier modeling.

The shaped steel was modeled with 2D curved shell elements andwas assigned the material properties of steel. The constitutive behaviorof curved shell elements was modeled with von Mises yield criterionwith isotropic strain hardening and an associated flow rule. The thick-ness of the shell element was assigned related values to represent thethickness of shaped steel.

4.3. Solution algorithm

The regular Newton–Raphson method was chosen to solve thenonlinear equations. Compared with the modified Newton–Raphsonmethod, it could yield more accurate results within identical numberof iterations. The line search method was adopted at the same time tostabilize the convergence behavior or increase the convergence speed.It is necessary to decide upon a suitable convergence or divergencecriterion when the equilibrium position is accepted as converged stateor need to be modified due to divergence. A maximum limit of 100iterations was used for the convergence and the tolerance was taken

as 0.001. From the analyses it was observed that the convergencegenerally occurred in less than 50 iterations. All the specimens wereapplied with quasi-static simulated seismic loading as displacement-controlled part in Fig. 5.

5. Verification of finite element model

5.1. Specimen modeling

Beforemodeling approaches are practiced in the parametric study, itis necessary to utilize these techniques to simulate experiments forvalidation. In this finite element analysis, the numbers of nodes ofSW-1, SW-2, SW-3 and SW-4 are 4380, 4636, 4777 and 7480 respective-ly, and the numbers of elements are 1200, 1262, 1286 and 2070 respec-tively. The model of SW-2 can be seen in Fig. 12.

Apart from the material models discussed in previous chapter forboth concrete and reinforcement, it is also significant to correctly simu-late the test setup, i.e., boundary conditions and loadings. As illustratedin Fig. 12, the upper part where the bracings are not extended to ismodeled as the transfer beam,which is connected to thewall by sharingsame nodes and element, thereby ensuring evenly distributed horizon-tal displacement along the top of wall. The bottom of wall was fixed to

Fig. 9. Cracking patterns of specimens SW-3 and SW-4.

Fig. 10. Parabolic compression curve [3].

83W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

simulate the connection between wall and laboratory strong floor.Moreover, a uniformly distributed axial stress of 0.3Agfc′ and a displace-ment identical to the actual test are imposed to simulate loadings inexperiments.

5.2. Analysis results

Global behavior is reflected in terms of hysteretic loops. Fig. 6 showsthe comparison of results between the experimental and analytical lat-eral load–top displacement relationships. In general, analytical resultsshowed a good correlation with the experimental ones in terms ofstrength capacity, deformation characteristics and energy dissipationfor the specimen. As reflected in Fig. 6b, a good energy dissipating ca-pacity was observed in both the loops beginning from the initial cycles.Also, the initial stiffness of numerical and the experimental resultsshowed a very good agreement. As the drift ratio increased, both loopsyielded the same value of peak shear stress (480 kN) at a displacementof around 20 mm.

However, there were still some discrepancies, especially in last fewcycles. In numeric simulations, all models were considered failed slight-ly earlier than the related experiment. Fig. 6a shows comparison of theFE numerical and the experimental results of SW-1. The model wasdeemed to be failed and cycles of displacements were terminated atthe lateral displacement of 22 mm, whereas SW-1 in the lab survivedat this level of lateral drift and failed at displacement of 25 mm. Asshown in Fig. 6c, the FEnumerical of SW-3demonstrated high similaritywith the experiment result in the initial cycles, where both of themreached the peak value of shear strength at a displacement of 22 mm.However, similar to SW-1, the last few cycles showed a bit of deviation.

Fig. 11. Predefined stress–strain curves for concrete in tension [3].

Fig. 12.Model of SW-2.

Table 4Summary of parameters.

Specimen Shear span ratio Thickness of shapedsteel

Axial Load Ratio

Name Name Properties Name Properties Name Properties

SW2 L 1.81 T3 3 mm P0 0%SW4 M 1.25 T4 4 mm P1 15%

S 0.69 T5 5 mm P3 30%

84 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

Fig. 13. Effect of shear span ratio on each analytical case.

85W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

This phenomenon may be attributed to the simplicity of strain–stresscurves of reinforcements.

From the aforementioned observations and predictions of seismicbehaviors using the FE analysis, it is justified to conclude that FEmodel-ing techniques can be further extended to study the effects of differentparameters.

6. Parametric studies

In order to enhance the understanding of the seismic behaviors ofsteel–concrete composite structural walls with bracings, the FE model-ing approach was applied by varying three critical influencing parame-ters: shear span ratio, thickness of shaped steel and axial load ratio.Specimens SW-2 and SW-4 which only differed in the amount of flatshaped steel in embedded column were selected here and totally 54cases were studied (Table 4). The following sections present the inves-tigations and possible implications of these parameters.

6.1. Effect of shear span ratio

In general, the strength of walls gradually decreased as the shearspan ratio increased. The peak strength of wall SW4_S with 3 mmshaped steel under zero axial load was 499 KN, which was 157% and188% of its counterparts SW4_M and SW4_L. Also needed to behighlighted was the impact shear span ratio has on ductility of walls.As illustrated in Fig. 13, walls with the smallest shear span ratio (0.7)always failed before lateral displacement arrived 10 mm, while wallswith the largest shear span ratio (1.8) could reach a displacementnear 30 mm. As for the impact of flat steel in embedded column, itwas found that after reaching the peak force, SW2 walls with thesmallest shear span ratio decreased faster than their counterparts there-by creating the gap of strength. However, the decline of shear span ratiohad a tendency to reduce this gap, and such discrepancy did not exist inthe smallest shear span ratio.

Fig. 13 also reveals the variation of secant stiffness of all walls withvarious thicknesses of shaped steel under different axial load. It wasevident that a shorter shear span ratio brought a significant increaseon overall secant stiffness. The differential gap was most obvious inthe initial drift ratio and narrowed down in the increment of driftratio. When imposed 30% axial load, for example, the SW2_S_T5 wallhad a secant stiffness of 411 KN/mm while the SW2_L_T5 only had asecant stiffness of 71.2 KN/mm at drift ratio of 1.9%, which means thatthe former is asmuch as 577%of the latter. However, the gapdiminishedto 153% as drift ratio increases. Furthermore, SW4 wall series appearedto have larger secant stiffness than SW2wall series, whichwasmost ev-ident as drift ratio proceeds after 1%. However, a larger shear span ratiohad a counter effect on the gap between thesewall series, and therewashardly any difference when the shear span ratio rises to 1.8.

With regard to energy dissipation capacity, it appears that mediumshear span ratio walls always perform best. Imposed with zero axialloading, wall SW2_M_T3 had a hysteretic damping ratio of 55% at thedrift ratio of 1.9%,whilewall SW2_L_T3 only had 18%. This phenomenonhowever was inconsistent with other studies [9, 15] regarding shearwalls, which showed energy dissipation capacity increases with thehigher shear span ratios. Compared with SW4 walls, SW2 walls withmedium (1.25) and small (0.69) shear span ratios seemed to have largerenergy dissipation capacity between each level of shear span ratio,while the opposite was true for walls with a large shear span ratio(1.81).

6.2. Effect of thickness of shaped steel

Fig. 14 demonstrates the effect of thickness of shaped steel on thebackbone curves of load–displacement loops. It was noticeable thatthe wall strength capacity increased with the augment of thickness ofshaped steel. Compared with the same effect brought by lowering the

shear span ratio, however, this augmentwas insignificant. The enhance-ment of peak strength of SW2_S_P1 was only 7.13%when the thicknessof shaped steel was changed from 3mm to 5 mm, while the number byraising the shear span ratio from1.8 to 0.7 could be as large as 69% in thesame wall.

With regard to secant stiffness, Fig. 14 demonstrates that the stiff-ness increased slightly as the shaped steel became thicker along alldrift ratios. At the drift ratio of 1.9%, for instance, the secant stiffness ofSW2_S _P1 with 5 mm thickness of shaped steel was 358.5 KN/mm.Compared with the same wall with 3 and 4 mm thickness of shapedsteel, the improvements were only 2.1% and 4.1% respectively.

As for the energy dissipation capacity, some cases showed that thehysteretic damping ratio increased a bit as the thickness of the shapedsteel was raised from 3 mm to 5 mm. However, inconsistency of thistrend existed which made it difficult to draw a definite conclusion.

6.3. Effect of axial load ratio

As demonstrated in Fig. 15, basically, the strength aswell as the stiff-ness of these walls increased gradually as the level of axial loading rose.SW2_S_T3, for instance, obtained a peak force of 559 kN under the axialratio of 30%, which was 28% larger than the same value with no axialload. Moreover, it was evident that walls with higher axial load alwaysreached their peak strengths in relatively large displacement, whichmeans that the existence of axial load had a beneficial effect on theductility of walls.

The change of secant stiffness for steel–concrete composite structur-al walls with bracings under cyclic loading is shown in Fig. 15. In gener-al, wall secant stiffness degraded significantly as drift ratio increased. Aspreviously stated, the existence of axial loading increased the stiffness ofa wall which might become stiffer when a higher axial loading wasapplied, the effect ofwhichwas greater than that of increasing the thick-ness of shaped steel. Nevertheless, this effect reduced with the increaseof top displacement. For instance, when drift ratio was 0.3%, the secantstiffness of wall SW2_L_T3 under axial load ratio of 30%was 69 kN/mm,which was almost 144% of the stiffness 48 kN/mm obtained whenimposing none axial load on the same wall. However, as drift ratioincreased to 1.9%, the two figures were 14 kN/mm and 11 kN/mm re-spectively, which showed narrowed gap between different axial loads.

From the results, the energy dissipation capacity generally increasedas drift ratio rose for walls under all levels of axial loads. Some research[9] conducted on RC squat walls showed that at lower drift ratios, thelower hysteretic damping was obtained under higher axial loads, athigher drift ratios, the higher hysteretic damping was observed whenhigher axial loads were applied. However, in this study, inconsistencywas noticed and no evident relationship can be summarized.

7. Conclusions

The seismic behavior of steel–concrete composite structural wallswith diagonal bracings was investigated using the experimental andthe FE numerical models. Based on the observations and results fromthese studies, the following conclusions can be drawn.

Experimental observations showed that the “X” shaped steel brac-ings had a beneficial effect on the shear capacity, stiffness degradationand energy dissipating capacity of steel–concrete composite structuralwalls.

By adding more “X” shaped steel bracings and flat shaped steel,steel–concrete composite structural walls was able to withstand moreshear force under cyclic loading, thereby trending the failure modetowards flexural failure.

Experimental and FE numerical investigations showed that theincrease of flat shaped steel in embedded columns could evidentlyimprove the performance concerning stiffness degradation of steel–concrete composite structural walls with a large shear span ratio (1.8).Moreover, flat shaped steel was found useful for walls to have higher

86 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

Fig. 14. Effect of thickness of shaped steel on each analytical case.

87W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

Fig. 15. Effect of axial load ratio on each analytical case.

88 W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89

secant stiffness along all drift ratios, especially in the small shear spanratio (0.7) group. With respect to energy dissipation, augment of flatshaped steel in walls with a large shear span ratio (1.8) resulted inbetter capacity, while the opposite was true for walls with a smallershear span ratio.

FE numerical results demonstrated that the wall strength capacitydecreasedwith the augment ofwall shear span ratio. Moreover, a small-er shear span ratio always led to a decrease in ductility of walls. As forsecant stiffness, it was highly noticeable that a shorter shear span ratiobrings a significant increase on the overall secant stiffness, which wasmost obvious at the initial drift ratio. Unlike the results from someresearch [9, 15] conducted on RC squat walls, the medium shear spanratio always brought the shaped steel concrete short-pier shear withbracings best performance regarding energy dissipation capacity.

The FE analyses indicated that the wall strength capacity increasedwith the augment of thickness of shaped steel. Nonetheless, this en-hancement was insignificant compared with the same effect broughtby lowering the shear span ratio. Similarly the secant stiffness only in-creased slightly as the shaped steel becomes thicker along all drift ratios.With regard to energy dissipation capacity, some cases showed that thehysteretic damping ratio increased a bit with the thickening of theshaped steel while others revealed different relations, which made itdifficult to draw a definite conclusion.

FE numerical simulations revealed that the presence of axial loadsincreased the wall strength as well as the stiffness. Moreover, it wasevident that the existence of axial load had a beneficial effect on theductility of shaped steel concrete short-pier shear with bracings. Thesecant stiffness of walls at the same drift ratio increased with theadded axial load, however, this effect reduced with the increase of topdrift. Unlike the relationship [9] between axial load ratios and energydissipation capacities found in the literature, inconsistency was con-stantly found and no evident relationship could be summarized in thisstudy.

NomenclatureAg the gross area of wallsΔcr the cracking displacementΔy the yield displacementαc/3 the strain at which one-third of the maximum compressive

strength is reachedαc the strain at which the maximum compressive strength is

reached

αu the ultimate strain at which the material is completely soft-ened in compression

fc the maximum compressive strengthE Young's modulusGC the total compressive fracture energyGF the total tensile fracture energyh the characteristic element length

Acknowledgements

This work was financially supported by the NSFC program (No.51308135) of China, and by the Systematic Project of Guangxi Key Lab-oratory of Disaster Prevention and Structural Safety (No. 2014ZDX04).The authors wish to express their gratitude for the financial support.

References

[1] Abolhassan Astaneh-Ash, Zao Q. Cyclic behavior of steel shear wall systems. AnnualStability Conference, Seattle; 2002.

[2] Brando G, D'Agostino F, DeMatteis G. Experimental tests of a new hysteretic dampermade of buckling inhibited shear panels. Mater Struct 2013;46(12):2121–33.

[3] DIANA 9.4.4. Delft. The Netherlands: TNO DIANA BV; 2012.[4] Driver RG, Kulak GL, Kennedy DL, Elwi AE. Cyclic test of four-story steel plate shear

wall. J Struct Eng 1998;124(2):112–20.[5] Emori K. Compressive and shear strength of concrete filled steel box wall. Steel

Struct 2002;68(2):29–40.[6] Feenstra PH. Computational aspects of biaxial stress in plain and reinforced concrete.

PhD Thesis Delft University of Technology; 1993.[7] Hajime O, Kohichi M. Nonlinear analysis and constitutive models of reinforced

concrete. Tokyo: Gihodo; 1991.[8] Lei L. The experimental studies on the antiseismic behavior of short-shear wall

which adopts prestressed concrete and shape steel concrete. Master Thesis GuangxiUniversity; 2009.

[9] Li B, Hui W. Design of reinforced concrete walls with openings — strut-and-tieapproach; 2005[PhD Thesis].

[10] Link R, Elwi A. Composite concrete–steel plate walls: analysis and behavior. J StructEng 1995;121(2):260–71.

[11] Nakashima M, Iwai S, Iwata M, Takeuchi T, Konomi S, Akazawa T, et al. Energydissipation behaviour of shear panels made of low yield steel. Earthq Eng StructDyn 1994;23(12):1299–313.

[12] Palermo D, Vecchio FJ. Compression field modeling of reinforced concrete subjectedto reversed loading: formulation. ACI Struct J 2003;100(5).

[13] Paulay T, Priestley M, Synge A. Ductility in earthquake resisting squat shearwalls. ACIJournal ProceedingsACI; 1982.

[14] Comité euro-international du béton. CEB-FIP model code-1990. Lausanne, Switzer-land: Technology & Engineering, Thomas Telford; 1993 pp. 437.

[15] Xiang W. Seismic performance of RC structural squat walls with limited transversereinforcement; 2009[PhD Thesis].

89W. Lan et al. / Journal of Constructional Steel Research 110 (2015) 76–89