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7/27/2019 lateral stiffness of steel plate shear wall
1/12
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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154 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1
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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Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1 155
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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156 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1
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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Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1 157
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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158 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1
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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Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1 159
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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160 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1
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
7/27/2019 lateral stiffness of steel plate shear wall
12/12
162 Nie J G,et al. Sci China Tech Sci January (2014) Vol.57 No.1
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).
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