lateral stiffness of steel plate shear wall

7/27/2019 lateral stiffness of steel plate shear wall

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SCIENCE CHINA

Technological Sciences

Science China Press and Springer-Verlag Berlin Heidelberg 2013 tech.scichina.com link.springer.com

*Corresponding author (email: [email protected])

Article January 2014 Vol.57 No.1: 151162doi: 10.1007/s11431-013-5411-2

Lateral stiffness of steel plate shear walls

NIE JianGuo & ZHU Li*

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Received July 2, 2013; accepted October 9, 2013; published online December 23, 2013

The steel plate shear wall system has been used in a number of buildings as an innovative lateral force resistant system. Open-ings often exist in the steel plate shear walls due to the various functional requirements of structures. These openings may neg-

atively impact the lateral stiffness of steel plate shear walls. Therefore, an experimental research was instituted to investigate

the seismic behavior of steel plate shear walls, with and without openings. The experimental results showed that steel plate

shear walls have the satisfying seismic behavior, and, as expected, the strength and stiffness characteristics of the walls were

reduced due to openings. Then a single-story wall panel FE model and an analytical deep beam model are developed in order

to find the critical factors dominating the thickness reduction coefficient of wall panels with the opening. Furthermore, exten-

sive parametric analysis is conducted to derive a simplified formula for the determination of the thickness reduction coefficient

of wall panels with the opening for substituting solid wall panels with reduced thickness for actual wall panels with the open-

ing. Finally, the design method for calculating the lateral stiffness is verified by some experimental programs and recom-

mended for the routine practice of steel plate shear walls.

steel plate shear walls, wall panels with the opening, thickness reduction coefficient, lateral stiffness, design method,

analytical deep beam model

Citation: Nie J G, Zhu L. Lateral stiffness of steel plate shear walls. Sci China Tech Sci, 2014, 57: 151162, doi: 10.1007/s11431-013-5411-2

1 Introduction

The steel plate shear wall system has been used in a number

of buildings in North America and Japan as an innovative

lateral force resistant system. In earlier days, the steel plate

shear wall was treated like vertically oriented plate girder

and the design procedures tended to be overly conservative[1, 2]. The buckling of steel plates has been prevented by

selecting an appropriately thick plate, until more infor-

mation became available on the post-buckling behavior of

thin steel plates.

Due to the great steel consumption and high cost, thick

steel plate shear walls have been gradually replaced by thin

steel plate shear walls. Thin steel plate shear walls have

been studied by many researchers [38]. These research

works included model tests and nonlinear finite element

analysis, while some analytical models were presented and

design suggestions were also provided. It was found that

tremendous post-buckling strength can be achieved in a thin

plate when a tension field is developed only if boundary

columns are designed strong enough to resist the member

forces developed by the tension field action of the thin steelplate, and thin steel plate shear walls show high strength

and good ductility. Meanwhile, In addition to this research,

Strip Model has been proposed [9, 10] and then employed

[6, 8, 1113] to calculate the strength of thin steel plate

shear walls, and finally formulated the basis of the design

method adopted in Canadian design code (CAN/CSA 2001)

[14], FEMA 450 (FEMA 2003) [15] and AISC seismic de-

sign guidelines (AISC 2010) [16].

In addition, steel plate shear walls with openings for sat-

isfying the function requirements of structures have gradu-


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152 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1

ally been paid more and more attention in recent years.

Three kinds of opening forms of steel plate shear walls have

been reported in the literature, as shown in Figures 1(a), (b)

and (c), respectively. Perforated steel plate shear walls were

firstly proposed and experimentally studied by Roberts and

Sabouri-Ghomi [17]. The researchers have performed a se-

ries of quasistatic cyclic loading tests on steel plate shear

walls with centrally placed circular openings and recom-

mended that the ultimate strength and stiffness of a perfo-

rated panel can be conservatively approximated by applying

a linear reduction factor to the strength and stiffness of a

similar solid panel. Vian and Bruneau [18] have conducted

analytical and experimental work on perforated steel plate

shear walls shown in Figure 1(a). Purba and Bruneau [19]

have carried on the further numerical analysis based on the

experimental results and proposed a more accurate reduc-

tion factor compared with that proposed by Roberts and

Sabouri-Ghomi [17] for calculating the strength of a perfo-

rated panel and some design recommendations and consid-erations on the perforation ratio of a panel. Figure 1(b)

shows steel plate shear walls with full openings, essentially,

the interior column of which connects the steel frame and

the steel plate shear wall without openings. Li [20] has

conducted the experimental and numerical studies to inves-

tigate preliminarily the lateral force resistant behavior of

this kind of steel plate shear walls with openings. Choi and

Park [8] have conducted the experimental and theoretical

research on steel plate shear walls including a coupled wall

specimen shown in Figure 1(c) to determine the failure

mechanism and proposed the methodology of lateral re-

sistance capacity analysis of steel plate shear walls. Figure1(d) represents steel plate shear walls with partial openings

studied in this paper, which are used in Tianjin International

Financial Conference Hotel in Tianjin in China. Stiffeners

are provided to prevent the premature buckling of wall pan-

els and reinforce the openings.

For the routine design conception, the structural system

is designed based on the elastic properties, while the me-

chanical behavior of structure system in the plastic phrase is

only checked and not taken into account in the structural

design. Therefore, the response of load versus deformation

that depends on the stiffness of structural system is a domi-

nant factor for the structural elastic design. The paper

mainly presents the research on elastic lateral stiffness of

steel plate shear walls for the routine design practice. Since

the randomness of size and position of the opening increas-

es the model complexity and costs too much computation,

the methodology of substituting solid wall panels with re-

duced thickness for those with the opening is conceived and

the simplified formula for calculating the thickness reduc-

tion coefficient of wall panels with the opening is proposed.

Finally, some experimental programs of steel plate shear

walls are selected to validate the design method for calcu-

lating the lateral stiffness of the steel plate shear wall based

on the deep beam theory [21].

Moreover, two following viewpoints are used in the pre-

sent study. First, vertical loads applied to boundary columns

have little influence on the elastic mechanical behavior of

the steel plate shear wall, thus, the conclusion drawn in this

research is adapted for whether vertical loads are applied or

not. Secondly, stiffeners often provide local reinforcement

but have no significant effect on the global behavior of thestructural member. As a result, the lateral stiffness of the

steel plate shear wall is investigated without consideration

of the influence of stiffeners.

2 Experimental research

2.1 Experimental program

The prototype structure of test units is located at 3 stories of

Tianjin International Financial Conference Hotel in Tianjin

in China. Three representative steel plate shear walls wereselected for the 1/5 scale model tests. One specimen with

wall panels with the opening was designated as SPSW-1,

the other one with wall panels without the opening was

designated as SPSW-2, and a third one with an interior

column and wall panels with the opening was designated as

SPSW-3. The thickness of the wall panel was 4 mm and the

boundary columns and interior columns were selected as

CFST columns. The dimension of SPSW-1, similar to that

of SPSW-2 and SPSW-3, is shown in Figure 2. The half

level wall panel at the bottom was designed to simulate the

actual boundary condition for routine design practices. The

positions and dimensions of openings are shown in Figure 3.

Figure 1 Opening forms of steel plate shear walls.


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Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1 153

Figure 2 Dimension of SPSW-1 (unit: mm).

Figure 3 Positions and dimensions of openings of specimens (unit: mm).

Also, a heavy steel beam was placed on the top of the 4th

level to avoid the local crippling of the loading end and to

transfer the load to wall panels and columns uniformly. Test

units were connected with the rigid base that was anchored

on the ground. Moreover, some stiffeners were welded on

wall panels to prevent the premature local buckling of wall

panels and reinforce the openings. Constructional details of

specimens are shown in Figure 4.

The measured properties of steel plates and concrete

blocks of specimens are shown in Table 1.

The study conducted by Behbahanifard [22] has revealed

that the magnitude of initial geometric imperfection affects

the lateral stiffness of steel plate shear walls to some extent

and proposed the dimensionless parameter to reflect the

influence of initial geometric imperfection:

imp/ ,bh (1)

where imp is the magnitude of initial out-of-plane defor-mation, b is the wall panel width, and h is the wall panel

height. Figure 5 shows the distribution of initial out-of-

plane deformation for the bottom, 1stand 2ndlevel wall pan-

els and beams of three specimens, where the southward

out-of-plane deformation is positive and the southward

out-of-plane deformation is negative. The magnitude of the

initial geometric imperfection of wall panels are 16mm, 12

mm and 9 mm, and those of steel beams are 18 mm, 9 mm

and 11 mm for three specimens, respectively.

Figure 4 Constructional details of specimens.

Figure 5 Initial out-of-plane deformation of specimens.


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Table 1 Material properties of specimens

Steel

GradeThickness

(mm)

Yield strengthfy

(MPa)

Ultimate strengthfu

(MPa)

Elongation at ruptureA

(%)

Ratio of ultimate to

yield strength

Q345B 3 428 560 23.0 1.31

Q345B 4 365 537 31.0 1.47

Q345B 6 335 495 32.5 1.48

Concrete

Specimen Grade 150 mm cubic compressive strengthfcu (MPa)

SPSW-1 C50 44.1

SPSW-2 C50 45.3

SPSW-3 C50 49.9

Each test specimen was situated with the panel parallel to

the east-west axis, stood on the north side of the panel and

faced south. The vertical loads were firstly applied at the

top of CFST columns by two vertical hydraulic jacks for

three specimens, representing the action of gravity loads.

For SPSW-1 and SPSW-2, both of the values of two vertical

loads were 500 kN, whereas for SPSW-3, the loads provid-ed by the western and eastern hydraulic jacks were 400 and

800 kN, respectively, and a girder of large stiffness was

placed at the top of the interior column and the eastern

column in order to make the vertical load provided by the

eastern hydraulic jack equally applied to the interior column

and the eastern column. Horizontal loads representing the

action of an idealized earthquake were then applied by two

actuators that were connected to the top beam on one hand

and to the reaction wall on the other hand. Two triangular

supports were designed as the lateral support devices to

prevent the global out-of-plane deformation of specimens.

The specimens were anchored to the laboratory ground

through a rigid base, thus, the specimens can be seen fixed

at the bottom. The test setup is shown in Figure 6.

The horizontal loads were imposed using load-control

scheme and then displacement-control scheme. The detailed

loading procedure was described as follows: 1) The hori-

zontal loads were applied in three levels using load-control

scheme before the specimens yielded and repeated only

once at each control point; 2) the horizontal loads were

Figure 6 Test setup.

imposed using displacement-control scheme after the yield-

ing of specimens, which can be observed when an inflection

appeared for lateral load versus top displacement responses.

Meanwhile, the loads imposed using displacement-control

scheme were repeated twice at each control point. Notably,

the westward loading direction was designated as +, where-

as the eastward one was designated as .

2.2 Experimental results

Figure 7 shows global failure modes of specimens. It can be

observed that for SPSW-2, the buckles extended diagonally

over the entire height of the specimen; for SPSW-1, since

the openings enhanced by stiffeners inhibited the expansion

of buckles, the action of global buckling of SPSW-1 was

less significant than that of SPSW-2; and for SPSW-3, the

interior column prevented the development of buckling

more effectively than openings enhanced by stiffeners, thus,

only the local buckling appeared in stories.Figure 8 gives the typical failure features of specimens.

The steel plates at the opening in Level 1 fractured for

SPSW-1 and SPSW-3. The out-of-plane deflection of the

western column was observed in the later phase of loading,

and steel plates at the junction of tension fields fractured for

SPSW-2.

Lateral load versus top displacement responses and lat-

eral load-top displacement skeleton curves are shown in

Figures 9 and 10, respectively. It can be observed that 1) the

satisfying seismic behavior of steel plate shear walls was

verified by test results; 2) the lateral resistance capacity and

the lateral stiffness of SPSW-1 were smaller than those of

SPSW-2 and SPSW-3 respectively, demanding that the lat-

eral resistance capacity and lateral stiffness can be reduced

due to openings and increased by the interior column; 3) the

pinch effect of hysteretic loops of SPSW-3 was less signifi-

cant than that of SPSW-1, demonstrating the interior col-

umn may improve the stability, resulting in the increased

energy-dissipating capacity.

According to the method illustrated in Figure 11, the

yield and ultimate points are determined from the lateral

load versus top displacement skeleton curves shown in Fig-

ure 10. Table 2 lists the measured characteristic loads and

displacements for each of the test specimens. The ductility


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Figure 7 Global failure modes of specimens.

Figure 8 Typical failure features of specimens.

Figure 9 Lateral load versus top displacement responses of specimens.

Table 2 Measured characteristic loads and displacements of specimens

SpecimenLoading

direction

Yield load

Py(kN)

Yield

displacement

y(mm)

Yield

drift

angle

Peak

load Pm

(kN)

Displacement

at peak load

m(mm)

Drift

angle at

peak load

Ultimate

displacement

u(mm)

Ultimate

drift

angle

Ductility

factor

SPSW-1Westward 631.4 18.0 1/188 752.8 33.4 1/101 52.9 1/64 2.9

Eastward 644.6 16.7 1/203 744.0 24.4 1/139 39.4 1/86 2.4

SPSW-2Westward 931.2 18.7 1/181 1076.3 38.3 1/89 54.3 1/62 2.9

Eastward 926.3 18.5 1/183 1045 38.5 1/88 53.6 1/63 2.9

SPSW-3Westward 929.2 20.6 1/164 1063.9 41.9 1/81 61.9 1/55 3.0

Eastward 1000.0 22.0 1/154 1139.8 42.2 1/80 46.3 1/73 2.1


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Figure 10 Lateral load-top displacement skeleton curves of specimens.

Figure 11 Determination of the yield and ultimate points.

factor is expressed as the ratio of the ultimate displace-

ment u to yield displacement y and is also shown in

Table 2.

3 Thickness reduction coefficient of wall panels

with the opening

3.1 Numerical and analytical model

Lateral stiffness of the steel plate shear wall is investigatedby Topkaya and Atasoy [23] based on an equivalent simpli-

fied model of the cantilever deep beam instead of the com-

plicated two-dimensional mechanical analytical model.

Therefore, in this research, the single-story wall panel FE

model and analytical deep beam model are developed in

order to derive the simplified formula of thickness reduction

coefficient of wall panels with the opening and achieve the

design objective of substituting solid wall panels with re-

duced thickness for those with the openings.

The flexural stiffness of the steel beam is much larger

than that of the wall panel for the actual steel plate shear

wall and the concrete slabs between stories provide a strong

constraint for the wall panel. As a result, the horizontal steel

beam is simplified as the boundary condition that the rota-

tional degrees of freedom of two ends of the boundary

column and wall panel are constrained. Figure 12 shows a

single-story wall panel with boundary columns selected as

the basic numerical example of FE analysis and also illus-

trates the shell-solid elaborate FE model of the basic nu-

merical example using the general FE package ANSYS 12.0

[24]. In this model, SOLID45 elements are used to simulate

the steel column and SHELL 181 elements to simulate the

wall panel. Elastic modulus Es=2.0105 and Poisson ratio

Figure 12 Parameters and the finite element model of the basic numerical example (unit: mm).


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vs=0.3 for the steel material are used throughout the analy-

sis.

On the basis of AISC341-10 [16], the range of geometric

characteristics on the wall panel and the boundary column

are selected as panel width to height ratio b/h=0.792.53and boundary column flexural stiffness IcIc,s=0.00307twh4/b.Also, the range of geometric characteristics on the opening

are selected as opening ratio=01 (the definition ofwill

be explained subsequently), opening width to height ratio

bo/ho=16, opening height to width ratio ho/bo=16 and ar-

bitrary for opening position.

The theory of deep beam can be employed to calculate

the lateral deformation of the wall panel without the open-

ing shown in Figure 13. In order to match the analytical

deep beam model, the FE model should have the following

characteristics: 1) An integral section of simplified beam

model is composed of sections of the wall panel and bound-

ary column; 2) the boundary condition and load pattern of

FE model coincide with those of the analytical model as

shown in Figure 13(a); 3) the shear load Vis discretized into

the shear stress with a distribution obtained from eq. (2)

applied on the top and bottom surfaces of wall panel and

columns in the FE model as shown in Figure 13(b); 4) the

lateral deformation of the centerline of the wall panel is

selected as the index for calculating the lateral stiffness.

The total lateral deformation is sum of the flexural de-

formation fand the shear deformation s, and is the sec-

tion shear factor. , f, sand can be calculated from eqs.

(3)(6), respectively.

w

,VQIb

(2)

f s, (3)

3

f,

12

Vh

EI (4)

s,

Vh

GA

(5)

d

2

2 2

w

,A

A QA

I b (6)

Figure 13 Analytical model for calculating lateral deformation of the

single-story wall panel.

whereIis the inertia moment of the integral section;A is the

area of the integral section; E is the elastic modulus; G is

the shear modulus; Qis the area moment at the certain point

of the integral section; and bw is the width at the certain

point of the integral section.

Figure 14 illustrates the research flow of the thickness

reduction coefficient of wall panels with the opening. The

analytical deep beam model is firstly verified as being relia-

ble and feasible. Good agreement can be observed from

Figure 15 for the results of analytical and numerical model

of wall panels without the opening. Then the lateral defor-

mation of the wall panel with the opening is calculated us-

ing the numerical model, the characteristics of which are

similar to those of the numerical model of the wall panel

without the opening. On the basis of the equivalence of lat-

eral stiffness, if the wall panel with the opening is replaced

with that without the opening, the thickness of the wall pan-

el without the opening can be reduced and derived reversely

in accordance with the analytical model. Finally, the thick-ness reduction coefficient wd is defined as the ratio of the

reduced thickness tw,rto the actual thickness tw:

w,r

d

w

.t

wt

(7)

3.2 Parametric analysis and simplified formula

The factors reflecting the influence of the opening include

Figure 14 Research flow of thickness reduction coefficient of wall pan-

els with the opening.

Figure 15 Comparison between results of lateral deformation from analyti-

cal and numerical models of single-story wall panel without the opening.


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opening area, panel width to height ratio, opening width to

height ratio, opening horizontal and vertical position and

flexural stiffness ratio of boundary column to wall panel.

The opening area is the core factor that affects the thickness

reduction coefficient and the influence of opening area can

be reflected using opening ratioas

o,A A (8)

where Ais the wall panel area, and Aois the opening area.

Then the influence of other five factors except the opening

area on the thickness reduction coefficient is shown in Fig-

ures 1620, respectively.

From above five figures, it can be concluded that the

main factors influencing the thickness reduction coefficient

include wall panel height to width ratio, opening width to

height ratio (opening height to width ratio) and opening

vertical position besides opening area, where rhis defined as

eq. (9) to reflect the influence of opening vertical position

on wd. Based on this conclusion, the simplified formula for

calculating the thickness reduction coefficient of wall pan-

els with the opening will be proposed.

h l.r h h (9)

The simplified formula for calculating wd should have

the following characteristics that 1) opening ratio is a

major variable, whereas other factors are minor variables;

and 2) wdshould tend to be 1 when tends to be 0, and wd

should tend to be 0 when tends to be 1. As a result, the

following formula is proposed to calculate the thickness

reduction coefficient wd:

d 1 ,w

(10)

3 2

1.16 7.12 13.4 10.29,b b b

h h h

(11)

o o

o o

o o

o o

1 0.05 , 1,

0.98 0.03 , 1.

b b

h h

h b

b h

(12)

2

h h0.678 0.678 0.8305. (13)

Figure 21 gives the variation of wd with the change of

opening ratio for different values of h/b, and the corre-

sponding verification is shown in Figure 22. Figure 23 gives

the variation of wdwith the change of opening ratio for

different values of bo/ho(ho/bo), and the corresponding veri-

fication is shown in Figure 24. It can be observed that

maximum of wdcan be reached when b/h=1.5 and bo/ho=1,

and wddecreases when b/hand bo/hochanges to both sides

of 1.5 and 1, respectively.

In order to sufficiently verify the accuracy of proposed

Figure 16 Influence of horizontal position of opening blon wd whenis about 10%.

Figure 17 Influence of flexural stiffness ratio of boundary column to wall panel on wdwhenis about 10% and bo/hois 1.


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Figure 18 Influence of wall panel width to height ratio b/hon wd when

is about 10%.

Figure 19 Influence of opening width to height ratio bo/ho or opening

height to width ratio ho/boon wdwhenis about 10%.

Figure 20 Influence of vertical position of opening hl on wd when is

about 10%.

formula, large amounts of numerical results are obtained by

the full combinations of various values of the four critical

parameters , b/h, bo/ho (ho/bo) and rh within the selected

parameter range. Comparison between these numerical re-

sults and formula predictions are carried out for each item

of eqs. (10)(13) as shown in Figures 22, 24 and 25, respec-

tively. Good correlations can be observed between numeri-

cal results and formula predictions. Furthermore, Figure 26

shows the comparison on lateral deformation of single-story

wall panel between predictions calculated using the simpli-

fied formula and numerical results, and the satisfying accu-

racy for the simplified formula can be observed.

Figure 21 Variation of wdwith the change of opening ratio for differ-

ent values of b/h.

Figure 22 Verification of the accuracy of the proposed formula for cal-

culating wdwithin the whole range of b/hand

4 Experimental verification of design method

for calculating the lateral stiffness

In this section, the design method for calculating the lateral

stiffness of the steel plate shear wall will be verified by ex-

perimental programs. Besides the experimental program in


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Figure 23 Variation of wdwith the change of opening ratio for different values of bo/hoand ho/bo.

Figure 24 Verification of the accuracy of the proposed formula for calculating wdwithin the whole range of h/b,bo/ho(ho/bo) and.

Figure 25 Verification of the accuracy of the proposed formula for cal-

culating wdwithin the whole range of h/b,bo/ho(ho/bo), rhand

this study, some others are selected for the verification of

the proposed design method. Since steel plate shear wall

specimens similar to cantilever beams are fixed at the bot-

tom and free at the top, the flexural deformation fshould

be calculated from eq. (14), where hsis the height from the

Figure 26 Comparison on lateral deformation of single-story wall panel

between formula predictions and numerical results.

loading point to the bottom.

3

s

f .3

Vh

EI (14)

For steel plate shear walls with openings presented in this


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study, the simplified formula of the thickness reduction co-

efficient of wall panels with the opening can be firstly used

in order to replace wall panels with the opening with those

without the opening. Then when the service load taken as

50% of the ultimate load is applied laterally to the steel

plate shear wall specimens, the boundary column on one

side is under compression and that on the other side under

tension. The filled concrete in the boundary steel tube col-

umn under tension is no longer in service due to cracking,

thus, the flexural stiffness of the filled concrete is neglected.

In addition, based on the equivalence of the shear stiffness

GA, the CFST column rectangular section is equivalent to

the steel column rectangular section with the constant width

parallel to the wall panel and reduced width perpendicular

to the wall panel for calculating the shear factor of the

integral section. Finally, according to the study conducted

by Behbahanifard [22] and measurements of initial geomet-

ric imperfection shown in Figure 5, the reduction coefficient

of lateral stiffness can be calculated as 0.843, 0.912 and

0.936 for three specimens in this present study, respectively.

Table 3 gives the comparison on the lateral stiffness be-

tween the results calculated using the proposed design

method and experimental results. It can be observed that the

calculated values are in good agreement with the experi-

mental results.

5 Conclusions

Openings in the wall panel greatly affect the seismic be-

havior of steel plate shear walls, which have been used

more frequently as a lateral force resistant system in the

design and retrofit of multistory and high-rise buildings.This paper focuses on the influence of opening on the lateral

stiffness of steel plate shear walls. The experimental re-

search of three steel plate shear walls under low-cycle re-

verse load was firstly presented. The satisfying seismic be-

havior of steel plate shear walls was verified by the test re-

sults, and the strength and stiffness of the steel plate shear

walls were obviously reduced due to openings. Then the

design objective of substituting solid wall panels with re-

duced thickness for wall panels with the openings is con-

ceived in order to avoid the model complexity and compu-

tation consumption due to the randomness of size and posi-

tion of openings. The single-story wall panel FE model and

analytical deep beam model are developed to find the criti-

cal factors dominating the thickness reduction coefficient of

wall panels with the opening. Furthermore, extensive nu-

merical calculation and parametric analysis are conducted to

derive the simplified formula of the thickness reduction

coefficient of wall panels with the opening. A good correla-

tion between the numerical results and the predictions

Table 3 Experimental verification of the proposed design method for calculating the lateral stiffness

Specimen Story Vertical loadExperimental (kN/mm) Analytical

(kN/mm)

Analytical/Experimental

()(+)

()(+)

Park et al. [68]

SC2T 3 No 79.13 67.21 78.08 0.99 1.16

SC4T 3 No 125.89 115.21 118.09 0.94 1.02

SC6T 3 No 127.64 122.17 146.00 1.14 1.20

WC4T 3 No 93.57 109.01 90.26 0.96 0.83

WC6T 3 No 104.89 100.74 107.54 1.03 1.07

FSPW1 3 No 76.44 73.13 87.13 1.14 1.19

FSPW2 3 No 135.29 133.34 142.01 1.05 1.06

FSPW3 3 No 129.51 110.75 133.56 1.03 1.21

FSPW4 3 No 124.79 126.39 142.01 1.14 1.12

BSPW1 3 No 117.78 117.38 142.01 1.21 1.21

BSPW2 3 No 113.48 113.60 142.01 1.25 1.25

Driver et al. (multistory) [4] 4 Yes 422.66 417.09 483.25 1.14 1.16

Dong et al. [2527]

H-1 1 No 125.96 149.63 166.57 1.32 1.11

H-2 1 No 153.19 142.00 166.57 1.09 1.17

HS1-1 1 No 131.29 166.57 1.27

HS1-2 1 No 146.74 166.57 1.14

HS2-1 1 No 172.95 161.12 166.81 0.96 1.04

HS2-2 1 No 161.88 148.02 166.81 1.03 1.13

This study

SPSW-1 4 Yes 51.91 54.96 57.65 1.11 1.05

SPSW-2 4 Yes 67.53 72.66 79.01 1.17 1.09

SPSW-3 4 Yes 67.56 63.54 72.19 1.07 1.14

Average 1.11

Standard deviation 0.098


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obtained using the proposed simplified formula for the

thickness reduction coefficient is observed with the relative

errors within the range of 10%. Finally, the design method

for calculating the lateral stiffness of the steel plate shear

wall is verified by some experimental programs and rec-

ommended for the routine practice.

This work was supported by the National Key Technology R&D Program

of China (Grant No. 2011BAJ09B01), the National Natural Science Foun-

dation of China (Grant Nos. 51178246, 51222810) and Tsinghua Univer-

sity Initiative Scientific Research Program (Grant No. 20101081766).

1 Tromposch E W, Kulak G L. Cyclic and static behavior of thin panel

steel plate shear walls. Struct Eng Rep, No. 145, Univ of Alberta,

Edmonton, Alberta, Canada, 1987

2 Astaneh-Asl A. Seismic behavior and design of steel shear walls.

Steel TIPS Rep, Structural Steel Education Council, Moraga, Calif,

2001

3 Caccese V, Elgaaly M, Chen R. Experimental study of thin

steel-plate shear walls under cyclic load. J Struct Eng, 1993, 119:

573587

4 Driver R G, Kulak G L, Kennedy D J, et al. Cyclic test of four-story

steel plate shear wall. J Struct Eng, 1998, 124: 112120

5 Lubell A S, Prion G L, Ventura C E, et al. Unstiffened steel plate

shear wall performance under cyclic loading. J Struct Eng, 2000, 126:

453460

6 Park H, Kwack J, Jeon S, et al. Framed steel plate wall behavior un-

der cyclic lateral loading. J Struct Eng, 2007, 133: 378388

7 Choi I, Park H. Ductilitys and energy dissipation capacity of

shear-dominated steel plate walls. J Struct Eng, 2008, 134:

14951507

8 Choi I, Park H. Steel plate shear walls with various infill plate de-

signs. J Struct Eng, 2009, 135: 785796

9 Thorburn L J, Kulak G L, Montgomery C J. Analysis of steel plateshear walls. Struct Eng Rep, No. 107, Univ of Alberta, Edmonton,

Alberta, Canada, 1983

10 Timler P A, Kulak G L. Experimental study of steel plate shear walls.

Struct Eng Rep, No. 114, Univ of Alberta, Edmonton, Alberta, Can-

ada, 1983

11 Berman J, Bruneau M. Plastic analysis and design of steel plate shear

walls. J Struct Eng, 2003, 129: 14481456

12 Liu Y, Elgaaly M. Analysis of thin-steel-plate shear walls. J Struct

Eng, 1997, 123: 14871496

13 Shishkin J J, Driver R G, Grondin G Y. Analysis of steel plate shear

walls using the modified strip model. J Struct Eng, 2009, 135: 1357

1366

14 CAN/CSA. Limit states design of steel structures. S16-01, Canada

Standards Association, Mississauga, Ontario, Canada, 2001

15 FEMA. NEHRP recommended provisions for seismic regulations fornew buildings and other structures. FEMA 450, Washington, DC, 2003

16 AISC. Seismic provisions for structural steel buildings. ANSI/AISC

341-10, American Institute of Steel Construction, Inc., Chicago, 2010

17 Roberts T, Sabouri-Ghomi S. Hysteretic characteristics of unstiffened

perforated steel plate shear panels. Thin-Walled Struct, 1992, 14:

139151

18 Vian D, Bruneau M. Steel plate shear walls for seismic design and

retrofit of building structures. Tech Rep, No. MCEER-05-0010, Mul-

tidisciplinary Center for Earthquake Engineering Research, State

Univ of New York at Buffalo, Buffalo, NY, 2005

19 Purba R, Bruneau M. Finite-element investigation and design rec-

ommendations for perforated steel plate shear walls. J Struct Eng,

2009, 135: 13671376

20 Li G. Experimental and theoretical study on thin steel plate shearwalls with opening under cyclic loading (in Chinese). Dissertation of

Masteral Degree. Xian: Xian University of Architecture & Tech-

nology, 2008

21 Timoshenko S. Strength of Materials. Princeton: D. Van Nostrand

Company, 1955

22 Behbahanifard M R. Cyclic behaviour of unstiffened steel plate shear

walls. Dissertation of Doctoral Degree. Edmonton: Univ of Albearta,

2003

23 Topkaya C, Atasoy M. Lateral stiffness of steel plate shear wall sys-

tems. Thin-walled Struct, 2009, 47: 827835

24 ANSYS version 12.0 (Computer software). Pittsburgh: ANSYS, Inc.,

2009

25 Dong Z. Experimental and theoretical studies of unstiffened steel

plate shear walls (in Chinese). Dissertation of Masteral Degree. Xian:

Xian University of Architecture & Technology, 2005

26 Hou L. Experimental and Theoretical Studies of Thin Vertical and

Lateral Stiffened Steel Plate Shear Walls (in Chinese). Dissertation of

Masteral. Xian: Xian University of Architecture & Technology,

2005

27 Li F, Li H, Li Z, et al. Cyclic test of diagonally stiffened steel plate

shear wall (in Chinese). J Xian Univ Arch Tech (Natural Science

Edition), 2007, 41: 5762

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