Performance of reinforced concrete shear walls with steel reinforced concrete boundary columns
Fei-Yu Liao a ,Lin-Hai Han b ,⇑,Zhong Tao c
a
College of Transportation,Fujian Agriculture and Forestry University,Fuzhou 350002,PR China b
Department of Civil Engineering,Tsinghua University,Beijing 100084,PR China c
Institute for Infrastructure Engineering,University of Western Sydney,Penrith,NSW 2751,Australia
a r t i c l e i n f o Article history:
Received 11October 2010Revid 19May 2012Accepted 23May 2012
Available online 7July 2012Keywords:RC shear wall
SRC boundary column Finite element analysis Experimental investigation Load transfer mechanism Parametric study
a b s t r a c t
This paper reports an investigation into the behaviour of reinforced concrete (RC)shear walls with steel reinforced concrete (SRC)boundary columns.A finite element (FE)model is developed and ud to sim-ulate the composite shear walls under constant axial load and lateral loading.A ries of tests,including six shear wall specimens,were conducted to investigate the strength,ductility and energy dissipation of the tested models,as well as to verify the FE model.It is found that the FE model can predict the behav-iour of the composite shear walls with reasonable precision.Stress and strain analysis is then conducted using this FE model to investigate the load transfer mechanism of the composite shear walls.Parametric studies are also carried out to study the influence of different parameters on the performance of the RC shear wall with SRC boundary columns.
Ó2012Elvier Ltd.All rights rerved.
汽车报废年限是多少1.Introduction
In the past veral years,composite frames,using concrete-filled steel tubular (CFST)columns and steel beams,or steel reinforced concrete (SRC)columns and SRC beams,have been increasingly ud in the mainland of China.In structural design,composite frames are often ud in combination with reinforced concrete (RC)shear walls to form a high-ri building system to re-sist both the vertical and lateral loads efficiently,as shown in Fig.1[1].Such a structure can be named as composite-frame and RC-wall mixed system,which is usually characterid by fast construc-tion due to the fact that the adjacent composite frame and the inner RC shear wall can be constructed at the same time.
In a composite-frame and RC-wall mixed system,the ductility of the conventional RC shear wall may be improved by using com-posite boundary columns (e.g.CFST or SRC columns)due to the fact that the boundary columns can suppress the development of cracks on the RC wall.In addition,if the adjacent frames consist of SRC beams,using SRC boundary columns instead of using RC boundary columns in the RC shear wall can make the beam-to-wall connections more reliable and easier to co
nstruct.In this ca,the I-shaped steel embedded in the frame beam can be anchored into the shear wall by welding it to the I-shaped steel in the SRC boundary column.For the above reasons,RC shear walls with SRC boundary columns (designated as ‘‘SRC–RC wall’’hereafter)are increasingly ud in high-ri buildings in China recently.
Previous rearches,conducted by Yamada et al.[2],Mau and Hsu [3]and Gao [4],have shown that RC shear walls with RC boundary columns (designated as ‘‘RC–RC walls’’hereafter)may provide superior strength,stiffness,energy dissipation,and repara-bility characteristics compared with the pure cantilever RC shear walls.Some tests have also been carried out by Tong et al.[5]and Cho et al.[6]to investigate the ismic behaviour of S–RC walls (RC walls framed with I-shaped steel boundary columns).Tests conducted by the authors previously indicated that CFST–RC walls (RC walls framed with CFST boundary columns)can provide strong confinement to the RC wall panels and thus enable the shear wall system to achieve a higher ductile manner [7].Esaki and Ono [8]compared the mechanical behaviour of SRC–RC walls under two different loading 0.01cm/s for the static loading and 1cm/s for the dynamic loading.The test results indicated that the RC wall panel of the specimens shows a sliding shear failure mode,and the initial lateral stiffness and load-carrying capacity of the SRC–RC wall subjected to the dynamic loading are around 10%higher than tho of t
he specimen subjected to the static load-ing.Dan et al.[9]reported the test results of the RC shear wall with vertical steel encad profiles.Mostofinejad and Anaei [10]inves-tigated the effect of confinement of boundary elements for the RC shear wall by FRP composites.
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Corresponding author.Tel./fax:+861062797067.
E-mail address:lhhan@ , (L.-H.Han).
From the above literature review,it can be concluded that, though some studies have been carried out on RC walls with differ-ent types of boundary columns,the rearch on performance of the SRC–RC walls under constant axial load and lateral loading is still not sufficient.Meanwhile,though different analytical models were introduced to predict the nonlinear behaviour of RC shear wall [3,11–13],little effort has been devoted to analy the stress and strain distributions of SRC–RC walls by usingfinite element meth-od,which can be recognid as a basis for developing a reasonable simplified model.Since the‘‘composite action’’of different compo-nents in a SRC column differs from that in a RC column or a CFST column,the behaviour of SRC–RC wall is also suppod t
o be differ-ent from that of RC–RC wall or CFST–RC wall.
Bad on the above discussion,this paper aims to carry out an investigation into the performance of SRC–RC walls.A one-bay, one storey SRC–RC wall is lected as the analytical and testing model,as shown in Fig.2.According to Tomii[14]and Gao[4], as a part of the overall frame system,the framed shear wall is ex-pected to carry a larger portion of the horizontal load due to its high stiffness.Thus unlike the cantilever shear wall which is con-sidered to carry a large overturning moment,the framed shear wall is predominated by the shear action under earthquake[4,14].Afi-nite element(FE)model is developed to simulate the behaviour of SRC–RC walls under constant axial load and lateral loading.A r-ies of tests,including six shear wall specimens,were conducted under cyclic loading condition to investigate the strength,ductility and energy dissipation of them,as well as to verify the FE model. This FE model is then ud to investigate the load transfer mecha-nism and to carry out a parametric analysis for SRC–RC walls.
2.FE model and verification
2.1.FE model
ABAQUS software package[15]was employed throughout the finite element analysis.The I-shaped st
eel and the concrete were simulated by using4-node shell elements and8-node brick ele-ments,respectively.The steel bars were simulated by using2-node truss elements,with three translation degrees of freedom at each node.A mesh convergence study was performed to identify an appropriate mesh density to achieve reliable results with reason-able computation time.
2.1.1.Material modelling
The steel was simulated by an elastic–plastic mode.Afive-stage stress–strain model propod by Pan[16]was ud,and the de-tailed expressions can be found in Han et al.[17].The elastic modulus(E s)and the Poisson0s ratio(m s)of steel were taken as 206,000N/mm2and0.3,respectively.
In the current FE model,the damage plasticity model provided in the ABAQUS library was ud for modelling concrete material [15].This model assumes non-associated potentialflow rule and adopts a yield surface propod by Lubliner et al.[18]and Lee and Fenves[19]to account for the different evolution of strength under tension and compression.The description of the plastic behaviour comes from the equivalent stress–strain relationship of the concrete.The modulus of elasticityðE cÞof concrete was ta-ken as4730
ffiffiffiffi
f0
c
p
according to ACI318[20],where f0
c
is the cylinder compression strength of concrete,in N/mm2.The Poisson’s ratio ðm cÞwas taken as0.2.In order to simulate the plastic behaviour of the concrete under compression,an equivalent stress–strain model propod by Attard and Setunge[21]was adopted,and the expressions are as follows:
Y¼
AXþBX2
1þCXþDX
ð1Þ
where Y¼r c=f0c,X¼e c=e co;r c and e c are stress and strain of con-crete respectively;and e co,A,B,C and D are parameters for which expressions can be found in Attard and Setunge[21].
For concrete in tension,the cracking strength of concrete(r t) was determined by using the equation given by Shen et al.[22], which is expresd as r t¼0:26Áð1:25f0cÞ23.It is a common fact that the significant drop of the tensile strength after cracking makes it difficult to achieve convergence for normal concrete in FE analysis. In this regard,a fracture energy model suggested by Hillerborg et al.[23]was ud to simulate the tensile softening behaviour
Notations
b width of the RC shear wall
B width of the boundary column
E total total dissipated energy during the whole testing process E c concrete modulus of elasticity
E s steel modulus of elasticity
f0 c concrete cylinder compressive strength
f cu concrete cube compressive strength
f y yield strength of steel
f u ultimate strength of steel
F lateral load
F u ultimate lateral load capacity
h height of the RC shear wall
双合汤
K j lateral stiffness
n axial load level of the boundary column N0axial load applied to the boundary column
N u compressive capacity of the boundary column
t w thickness of the RC shear wall
a steel ratio of the SRC column
e strain
h rotation
h y yield rotation
h u ultimate rotation
m s Poisson’s ratio of steel
D lateral displacement
D shear shear deformation
Dflexureflexural deformation
l displacement ductility coefficient
Composite columns
RC shear wall
Fig.1.Composite-frame and RC-wall mixed high-ri building.
F.-Y.Liao et al./Engineering Structures44(2012)186–209187
of concrete[15].The fracture energy(G f)was assumed as0.04kN/ mm and0.12kN/mm respectively for the concrete with a compres-sive strength of20MPa and40MPa as recommended in[15].
2.1.2.Interfaces
A surface-bad interaction was ud to simulate the surface between the I-shaped steel and concrete.In the normal direction, the‘‘Hard’’contact was applied that allows the two contact sur-faces parating but not penetrating,and a‘‘Mohr–Coulomb’’fric-tion model was adopted in the tangential direction by taking the frictional coefficient of0.6.In the numerical model,the possible minimal slippage between concrete and the hoops in the boundary column or beam was neglected.In this regarding,the‘‘embed’’contact was lected to describe the interface behaviour between the hoops and their surrounding concrete.The‘‘spring’’elements were employed to simulate the tangential slipping behaviour be-tween the longitudinal steel reinforcing bars and concrete.The model propod
by Houde and Mirza[24]was lected to define the stiffness of spring elements,which is expresd as:
s¼5:3Â102s sÀ2:52Â104s2
s þ5:86Â105s3
s
À5:47
Â106s4
s ffiffiffiffiffiffiffiffiffiffif0
c
40:7
r
ð2Þ
where s is the shear stress,in N/mm2.And,s s is the relative slippage between the longitudinal steel bars and concrete,in mm.
2.1.
3.Boundary conditions
The bottom of the shear wall was restrained in all degrees of freedom.The initially constant axial loads on the top of boundary columns were applied in thefirst step,and then the lateral load at the beam end was applied in an appointed displacement by using boundary condition.The modulus of elasticity and Poisson’s ratio of the rigid plate were taken as1012N/mm2and0.0001, respectively,to eliminate its deformation during loading.A typical FE model of SRC–RC wall is shown in Fig.3,which includes15,676 elements and19,619nodes.Due to the nonlinear nature of the modelling ud,the well-known Newton–Raphson incremental-iterative solution method was ud in the analysis.
2.2.Verification of the FE model
The FE model described above was ud to simulate the RC columns,SRC beams and RC shear walls for the purpo of verification.The comparisons with test results reported by Tao and Yu[25],Zh
eng[26]and Cao et al.[27]are shown in Fig.4.It can be en that a good agreement was achieved between the pre-dictions and the test results in terms of load versus deflection curves and cracking pattern of concrete.
Besides that,a ries of tests were conducted by the authors to experimentally investigate the behaviour of SRC–RC walls,as well as to further verify the FE model.The comparisons of the failure modes and the lateral load(F)–lateral displacement(D)curves be-tween the predicted results and the tested results will be pre-nted in the following ctions.
3.Experimental investigation
3.1.Specimen preparation and material properties
Six shear wall specimens,including three SRC–RC walls and three counterparts of RC–RC walls,were tested.Owing to the load-ing limitation of the test machine,the specimen size was designed as approximately one-third scale of the prototype structure.The testing parameters are as follows:(1)the type of boundary column (SRC or RC column);(2)the height–width ratio of RC wall(h/ b=0.62and0.95),where h and b are the overall height and width of the RC wall respectively,as shown in Fig.2;(3)the axial load le-vel of boundary column(n=0.26and0.52,which is defined as n=N0/N u,wh
ere N0is the axial load applied on the column,and N u is the axial compressive capacity of the column,which was determined according to the Chine codes JGJ138-2001[28]and GB50010-2002[29]for the design of SRC columns and RC col-umns,respectively).
More details of the test specimens are given in Table1.The RC wall panels of all specimens have a height(h)of820mm and a thickness(t w)of85mm.The reinforcements of the RC wall panel were determined to have the same reinforcement ratio as that in the prototype structure.Both horizontal and vertical reinforcing steel bars of a wall panel consist of two layers of6mm diameter bars spaced at120mm,which makes the wall panel having a rein-forcement ratio of0.55%in both directions.The shear strength of the SRC–RC wall was determined according to the Chine code JGJ138-2001[28]:
V¼
1
kÀ0:5
0:05b r f ck t w b0þ0:13N0
A w
A
þf yh
A sh
s
b0
þ
0:4
f ya A að3Þ
Reinforcing
steel bars
SRC beam
Reinforcing
steel bars
b RC wall
SRC column RC wall
I-shaped steel
188 F.-Y.Liao et al./Engineering Structures44(2012)186–209
where k ¼H
六年级绘画作品
b 0
ð1:56k 62:2Þ,in which H is the height of the speci-men and can be obtained as H =h +h b /2(h and h b are the heights of the RC wall panel and boundary beam respectively),and b 0¼ðb þ1:5B Þis the effective width of wall panel (B is the width of boundary column);b r ð¼1:2Þis a factor to consider the
confine-ment effect of wall concrete by the boundary columns;f ck is the characteristic strength of the concrete and equals to 0.67f cu for nor-mal strength concrete;and f cu the cube strength of the concrete;t w is the thickness of wall panel;A w and A are the ctional areas of the wall panel and the whole specimen,respectively;f yh and f ya are the yield strengths of the horizontal reinforcing bars in the wall and I-shaped steel of the column,respectively;A a is the ctional area of the I-shaped steel;A yh is the total ctional area of all horizontal bars in the wall at the same height;and s is the space of the horizontal bars.
The flexural capacity of the SRC–RC wall was determined by the following equation [28]:
M ¼f ck n ð1À0:5n Þt w b 2
þB ðB Àt w Þb 0À
B
2
þf yc A sc b 0ÀB 2 þf a A a b 0ÀB
2
þM sw
ð4Þ
where n ¼x n
,and x n is the depth of the flexural compression zone which can be determined by the ctional analysis for the stage when the extreme fibre of concrete reaches its ultimate compres-
sive strain;f yc and A sc are the yield strength and total ctional area of the longitudinal steel bars in a boundary column,respectively;
and M sw ¼½0:5Àðn À0:80:8x
Þ2
Áf yv ÁA sv Áb ,in which x ¼b b 0,f yv and A sv
are the yield strength and total ctional area of the vertical reinforcing bars in the wall,respectively.
The calculated lateral load-carrying capacities at shear failure are 329kN,506kN and 574kN for the S
RC-S-1,SRC-L-1and SRC-L-2,respectively,which are much less than the calculated ones determined by flexural failure.It should be note that,the design approach of Chine code for the cantilever shear wall is generally bad on the well-known concept,that the shear reinforcement is designed to make the shear wall reach flexural failure prior to shear failure for the purpo of achieving a ductile manner.How-ever,in the ca of RC shear wall framed with boundary elements,it is usually predominated by the shear action under earthquake [4,14],and its RC wall panel tends to show shear failure character-istic if the boundary columns are sufficiently strong and properly reinforced.This shear failure is allowable since the boundary columns can sustain the vertical load after the wall panel fails and hence the collap of the building is prevented.Therefore,the SRC–RC wall specimens in current tests are designed to form a similar failure mode.
Fig.5a shows the detailed specimen configurations of the SRC–RC wall.The SRC boundary columns have a ctional dimen-sion of 160Â160mm and are reinforced by 8mm diameter hoops spaced at 100mm.Due to the relatively small dimension of the test
(a) Boundary conditions (b) Inner components
SRC beam
Axial load (N )Lateral load (F )
Rigid plate Rigid plate
Rigid plate SRC column底纹样式
SRC column
RC wall
Fixed boundary condition
1
3
2
鹞子是什么鸟
Axial load (I-shaped steel Longitudinal bars
Reinforcing bars
Hoops
Hoops I-shaped steel Longitudinal bars
Fig.3.A general view of FE model.
F.-Y.Liao et al./Engineering Structures 44(2012)186–209189
防震减灾图片specimens compared with the prototype structure,only four longitudinal bars with a diameter of 14mm are arranged at four corners of the column ction to avoid the difficulties of the specimen fabrication.Therefore,the reinforcement ratio of the SRC boundary column achieved is 2.4%.The clear concrete cover of both wall panel and boundary beam is 15mm,and tho of the boundary column and foundation are 20mm and 25mm,respectively.All the horizontal reinforcing steel bars of the RC
wall
阻燃标准
Table 1
Summary of specimen information.Specimen label b (mm)h /b N 0(kN)n F ue (kN)h y (10À2rad)h u (10À2rad)l
位图图片E total (kN m)
F uc (kN)F uc /F ue SRC-S-18600.953000.266220.39 1.47 3.835.4635 1.02RC-S-18600.953000.266940.39 1.29 3.429.76360.92SRC-L-113200.623000.268910.330.88 2.828.28400.94RC-L-113200.623000.269310.300.79 2.625.88520.92SRC-L-213200.626000.5211360.310.83 2.727.19660.85RC-L-2
1320
0.62
600
0.52
1158
0.29
0.75
2.6
25.9
951
0.82
190 F.-Y.Liao et al./Engineering Structures 44(2012)186–209
