A Numerical Study on the Seismic Behavior of Composite ... elastic stiffness of two specimens showed...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 10 (2016) pp 6890-6896

© Research India Publications. http://www.ripublication.com

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A Numerical Study on the Seismic Behavior of Composite Steel Plate Shear

Walls with Openings

Soheil Kordbegli1 and Farhang Farahbod2* 1MSc in civil engineering structures, Department of Civil Engineering,

West Tehran Branch, Islamic Azad University, Tehran, Iran. 2PhD, Faculty Member, Department of Civil Engineering,

West Tehran Branch, Islamic Azad University, Tehran, Iran. corresponding author

Abstract

In recent years the use of composite steel plate shear walls, as

a lateral load resisting system, has been increasing. In this

paper our aim is to study the seismic behavior of these

composite shear walls with embedded openings by

introducing the size and position of openings as the variables

of the study. Numerical studies were carried out to evaluate

the effect of elastic stiffness, effective or secant stiffness,

failure load, absorbed energy, and ductility ratio on the

performance of these walls. The results of analysis of finite

element models in the wall with openings modeled in

ABAQUS software showed that the use of openings in the

center of these walls was favorable due to the reducing

negative effects of the studied parameters on the wall

performance, and their use in the corners of the composite

shear walls is not suggested. Major changes and value

reduction rate of the parameters in different areas were seen in

the openings wider than 1000 mm. We concluded that

embedding openings in the corners of the composite steel

plate shear walls, especially those with larger sizes should be

avoided.

Keywords: Composite steel plate shear walls, Seismic

behavior, Stiffness, Ductility, Numerical study

Notations

Fy Specified minimum yield stress of the plate

Fu Specified minimum tensile strength

µ Ductility coefficient

D Ductility ratio

E Modulus of elasticity

E Absorbed energy

Ke Elastic stiffness

Pu Failure load

Keff Effective or secant stiffness

𝑃𝑝𝑒𝑎𝑘 Maximum absolute value of load resisted by the wall

∆e Displacement at 0.4𝑃𝑝𝑒𝑎𝑘

Δu Ultimate displacement

Δyield Yield Displacement

INTRODUCTION

From the beginning of the study and design of building

structures, one of the main concerns of engineers has been the

design and implementation of appropriate lateral load resisting

systems. Recently, lateral load resisting systems have attracted

the attention of many engineers and researchers. One of

resistant elements against lateral loads is shear walls. Since

1970’s, a number of important structures using steel plate

shear walls have been designed and constructed in the United

States and Japan such as the 6-story Sylmar Hospital in

greater Los Angeles or The 35-story office building in Kobe,

Japan [1]. The first generation of shear walls is reinforced

concrete walls. These types of shear walls have little practical

application in the structures. The second generations of these

walls were steel plate shear walls (SPSW). In this type of

shear walls, the resistant core is of steel sheets instead of

reinforced concrete. These walls, in addition to having

sufficient stiffness, have high ductility. The third generations

of shear walls are called composite steel plate shear walls

(CSPSWs). In these walls the prefabricated reinforced

concrete walls or cast-in-place (CIP) concrete walls are

connected to the plate on one or both sides by studs. These

steel plates are effective in maximizing the steel plate capacity

and the delay in their buckling. In other words, the concrete

plate in these walls is an equivalent of stiffener in stiffened

SPSW. In many studies, CSPSW is known as steel sections

embedded in concrete along with reinforced concrete

connected to one another by shear connectors.

About CSPSWs with no openings many studies have been

conducted (e,g. [1, 2]). Rahai and Hatami [3] evaluated the

effects of shear studs spacing variation, middle beam rigidity

and the method of beam to column connection on the CSPSW

behavior. They found that increasing the shear studs spacing

reduces the slope of load–displacement curve and improves

ductility up to a specific studs’ spacing. Also, the effects of

middle beam rigidity and beam to column connections were

insignificant on the composite steel shear walls behavior.

Arabzade et al. [4] investigated the buckling load of a CSPSW

and suggested that the elastic buckling coefficients can be

used for determination of the number of bolts or the spacing

between the bolts. In another study, they stated that this

system has reliable behaviour if the columns have high

bending stiffness. Also bolts spacing to plate thickness ratio

has direct relationship with system ductility. However, plate

yield load has an inverse relationship with this ratio [5]. Dan

et al. [6] investigated maximum load capacity, stress and

strain distribution in structural components, interstory drifts,

cracking patterns, deformation and degradation capacity of

composite steel–concrete structural shear wall with steel

encased profiles. In the study of Hatami et al. [7], the effects

of fiber content/angle and panel width on the properties of

CSPSWs reinforced with carbon fibers were investigated.



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Results showed that wider panel widths enhance the behavior

of CSPSW. Higher fiber contents increase energy absorption,

stiffness, over-strength and capacity, but decrease ductility

values.

About CSPSWs with openings there are fewer studies that

necessitate the need to perform research in this area. For

example, Lin and Kuo [8] analyzed the ultimate strength of

shear wall with opening under lateral load. Their results

indicated that the shear strength contributed by diagonal

reinforcement around opening reached 40% of its yield

strength while the shear strength contributed by the

rectangular pattern reached 20% of its yield strength. Marius

[9] studied seismic behaviour of reinforced concrete shear

walls with regular and staggered openings after the strong

earthquakes between 2009 and 2011. Considering the low

amount of investigations in this area, in this paper our purpose

is to investigate the seismic behavior of a single CSPSW with

nine openings and different widths of 500, 1000, 1250, and

1500 mm. In this regard, effects of elastic stiffness, effective

stiffness, failure load, absorbed energy, and ductility ratio on

its performance were evaluated.

EXPERIMENTAL SPECIMEN

The specimen for the experiments was ½-scale three stories,

one bay CSPSW with steel moment frames with high and low

levels of mezzanine which was set up by [1]. We modeled it

in ABAQUS finite element software (see Fig. 1). They tested

the CSPSW system in two cases: system with a gap between

the concrete wall and the boundary columns and beams, and

the system with no gap. The height of the wall was 6197.6 m

and the span width was 2133.6 mm. Table 1 shows the

materials used for the system. The loading sequence applied

to both

Systems were cyclic shown in Figure 2. We used the

experimental results of this system for the verification of our

findings.

Table 1: Specifications of the test set-up

Components E (N/mm2) µ Fy Fu ∈ (𝒚) ∈ (𝒖)

Steel plate 200000 0.3 240 360 32.1 e 0.2

Columns and beams 200000 0.3 380 520 39.1 e 0.2

Bolt 200000 0.3 600 720 33 e 0.2

Figure 1: Experimental model tested by [1]

Figure 2: Loading Sequenced Applied to the experimental

model by [1]



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Test set-up

In this study a single span frame and a floor from a five-story

building were selected for the study. The five-story building

has CSPSW with installed openings symmetrically on all

sides. The span’s length is 3.50 meters and the ceiling height

in the lowest floor (test specimen) is higher than 3.50 m.

Figure 3 and 4 show the framing plan and the elevation of the

shear wall system. It was designed according to AISC-341

[10] standard. The properties of materials used in the test set-

up are the same as those used in the experimental model (table

1). The thickness of steel plate was 3 mm, the distance

between shear connectors (bolts) was 250 mm, and their

diameter was determined as 8 mm. With a total infrastructure

of 1700 square meters, the seismic load of the structure was

obtained as W= 12600 KN. According to Iranian seismic code

(No. 2800), since the building is of residential type (I=1.0)

located on soil type B, and Iran is considered to be located in

a high seismic risk region (i.e. base design acceleration

A=0.35) and also, the structure’s behavior coefficient with

respect to the CSPSW is as R=6.5, therefore, seismic

coefficient for the building was calculated as

135.0/ RABIC . Now, the base shear force can be

calculated as: KNWCV 170012600135.0 .

Due to the symmetry in plan and symmetrical seismic force

distribution, the contribution of each shear wall from the base

shear will be equal to 850 KN.

Figure 3: Framing plan of the test set-up

Figure 4: Shear wall system dimension

Numerical specimens

Two types of specimens in the set-up were a single CSPSW

with the designed specifications but with no openings shown

in Figure 5a which was modeled in ABAQUS software

(named as WOP) as specimen 1, and a single CSPSW with

nine openings embedded at different positions shown by

numbers 1 to 9 in Figure 5b as specimen 2. In the second

specimen, the width of the openings were 500, 1000, 1250,

and 1500 mm defined laterally and longitudinally as OP50-1

to OP50-9, OP100-1 to OP100-9, OP125-1 to OP125-9, and

OP150-1 to OP150-9..

(a)



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(b)

Figure 5: A view of test specimens (a) CSPSW with no

openings, and (b) CSPSW with installed openings

Numerical parameters

To study the nonlinear static seismic behavior of specimens,

we investigated following parameters according to ASTM E

2126-07 [11] standard and calculated as the actual load-

displacement curve idealized in Figure 6:

i. Elastic stiffness (Ke): it can be expressed as a slope

measured by the ratio of the resisted shear load to the

corresponding displacement :

𝐾𝑒 =0.4𝑃𝑝𝑒𝑎𝑘

∆e

(1)

ii. Effective or secant stiffness (keff): which is the value

of lateral force divided by the lateral displacement on

force-displacement curve;

iii. Failure load (𝑃𝑢): which is the load corresponding to

the failure limit state on the envelope curve(Fig. 4). it

can be obtained as:

𝑃𝑢 = 0.8𝑃𝑝𝑒𝑎𝑘

(2)

iv. Absorbed energy (E): it is the area under envelope

curve from zero to ultimate displacement;

v. Ductility ratio (D): which is the ratio of the ultimate

displacement and the yield displacement.

Figure 6: Idealization of nonlinear response according to [11]

In this regard first we drew the force-displacement curve for

the specimens and then, according to ASTM E 2126-07

standard and the pushover curve, we obtained the values of

studied parameters for them.

NUMERICAL RESULTS

Following, we presents the results of comparing seismic

behavior of two test specimens in terms the above mentioned

parameters. In final section we provide overall results of

comparison.

Elastic stiffness

Comparing elastic stiffness of two specimens showed that

composite steel plate shear wall with no openings had higher

elastic stiffness value. Among different size of openings,

those with the size of 500 mm had the highest elastic stiffness,

and the difference of elastic stiffness between 500 mm and

1000 mm openings was greater compared to other dimensions

(see Fig. 7).

Figure 7: Elastic stiffness changes in CSPSW with and

without openings

Among opening with different zones, the opening No. 5 had

the highest elastic stiffness value. In other words, if the

symmetry of the structure is adhered and the opening is



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installed in the middle of the wall, we will have minimal

stiffness loss in the openings with any dimensions.

Effective stiffness

To compare the effective stiffness of two specimens we draw

the curve of effective stiffness for each opening with different

dimensions (see Fig. 8). In each four dimensions, it was seen

that 50% secant stiffness or effective stiffness loss occurs in

drifts between 1 and 2%. In other words, secant stiffness in

the models is reduced to about half in 40 mm to 80 mm

displacement (total displacement is 200 mm), and in

subsequent drifts, stiffness reduction occurs with a more

gentle slope. With increasing the size of openings, difference

of secant stiffness between the two specimens also increases,

and this difference decreases with the increase of drift. We

also found out that the location of openings does not have a

significant impact in reducing secant stiffness and this is true

for all dimensions of openings.

Figure 8: K-drift diagram

Energy absorption

One of the accurate ways of measuring seismic performance

of a structure depends on energy dissipation. all analyzed

specimens was measured as the area enclosed by load-

displacement curve. Absorbed energy of small size opening

(500 mm) in all zones on the wall except zones number 1, 3,

7, and 9 was higher compared to the system that had no

openings (see Fig. 9). Depending on the type of load,

pushover, and the nature of the seismic load which is cyclic,

results should be generalized for similar regions of the walls.

For example, if the direction of seismic loading changes, the

current situation of zone 9 will occur on zone 7. Similar to

stiffness changes, a significant reduction in absorbed energy

in the specimen with the opening of 500 mm and others is

evident. With larger openings, energy absorption changes in

different areas of the CSPSW is reduced (see Fig. 9)

Figure 9: Energy absorption changes in CSPSWs with and

without openings

Ductility ratio

Results showed that the wall corners have dramatic effects in

reducing its ductility. In different dimensions, the opening No.

5 was most effective in improving the ductility than other

openings. With larger openings, the ductility ratio changes in

different areas of the shear wall are reduced (see Fig.10). By

changing the direction of seismic loading, these conditions

created for zones 1 to 4 should also be considered for zones of

6 to 9.

Figure 10: Ductility ratio changes in CSPSWs with and

without openings

Failure load

In the CSPSW with installed openings, results showed that

failure load of the opening with the size of 500 mm were

higher compared to other dimensions, and 1000-mimimeter



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size opening had the second highest failure load value.

Reduction of failure load compared to the CSPSW with no

opening was seen in the openings with the size 1250 and 1500

mm. In the CSPSW with installed openings, the most affected

areas were in the corners. Although, considering the behavior

of the seismic load which is cyclic, reduction of failure load

was also seen in other areas. For example, in the direct

loading, the zone 1 was critical and in reverse loading, the

zone 3 becomes more critical in terms of failure load. This is

true for areas 7 and 9 (see Fig. 11).

Figure 11: Failure load changes in CSPSWs with and without

openings

Table 2 presents a summary of the results related to all

parameters mentioned above. In this table, for each size of

openings, its best conditions compared to the specimen with

no openings have been identified with colors where red color

shows the openings with the weakest performance. As can be

seen, for the dimension of 500 mm, because of the effect of

direct loading, openings located in zones 2, 4, 6 and 8 can be

selected as those with best performance. In other dimensions,

they were in zone 5.

Table 2: A summary of the results for the parameters of the

specimen with openings

Openings K D Pu E Openings K D Pu E

OP50-1 0.92 0.93 1.20 0.93 OP125-1 0.40 0.66 0.90 0.76

OP50-2 0.97 1.10 1.21 1.04 OP125-2 0.42 0.62 0.99 0.81

OP50-3 0.84 0.87 1.19 0.89 OP125-3 0.44 0.66 1.02 0.83

OP50-4 0.95 1.10 1.23 1.06 OP125-4 0.39 0.57 1.10 0.83

OP50-5 0.87 1.10 1.25 1.06 OP125-5 0.47 0.77 0.99 0.83

OP50-6 0.91 1.10 1.23 1.06 OP125-6 0.42 0.66 0.99 0.82

OP50-7 0.86 1.00 1.21 1.05 OP125-7 0.41 0.60 1.04 0.85

OP50-8 0.95 1.10 1.24 1.07 OP125-8 0.38 0.60 0.99 0.82

OP50-9 0.91 1.04 0.94 0.98 OP125-9 0.36 0.60 0.89 0.76

OP100-1 0.48 0.69 1.00 0.83 OP150-1 0.36 0.62 0.81 0.69

OP100-2 0.52 0.77 1.03 0.86 OP150-2 0.34 0.57 0.90 0.74

OP100-3 0.52 0.66 1.10 0.89 OP150-3 0.37 0.62 0.96 0.78

OP100-4 0.45 0.62 1.06 0.88 OP150-4 0.33 0.55 0.96 0.75

OP100-5 0.64 0.87 1.08 0.91 OP150-5 0.36 0.66 0.96 0.74

OP100-6 0.44 0.69 1.04 0.86 OP150-6 0.33 0.57 0.96 0.74

OP100-7 0.51 0.69 1.11 0.91 OP150-7 0.33 0.53 0.96 0.79

OP100-8 0.48 0.66 1.05 0.88 OP150-8 0.30 0.50 0.96 0.74

OP100-9 0.43 0.66 0.98 0.83 OP150-9 0.31 0.55 0.96 0.68

CONCLUSION

In this study we investigated the seismic behavior of

composite steel plate shear walls having openings with four

500, 1000, 1250 and 1500 mm dimensions located in nine

different areas of the wall. For this purpose, five parameters of

elastic stiffness, effective or secant stiffness, failure load,

absorbed energy, and ductility ratio related to the system with

openings were evaluated and compared to the system which

had no installed openings. Results showed that the specimen

with no openings had highest elastic stiffness while in the

specimen with nine openings, the one with 500 mm size had

the highest elastic stiffness and reduction of elastic stiffness

between the 500 and 1000 mm size openings were 50%.

Installing the openings in the center of the composite steel

plate shear wall increase the elastic stiffness and the change in

the stiffness in larger openings and in different areas was

subtle.

In the specimen with installed openings, secant stiffness

changes in 1 to 2 % drifts was reduced by about 50%. In drifts

higher than 2-5%, secant stiffness was reduced. Also, its

changes in different openings size and installation location

were not impressive. The absorbed energy in the composite

steel plate shear wall with the openings embedded in the

corner showed a sharp decrease. By increasing the opening

size above 1000 mm, the rate of change in energy absorption

in different areas was reduced, and the central zone had the

largest energy absorption by about 10% compared to other

areas.

In the composite steel plate shear wall with the openings

embedded in the corner, a significant reduction in ductility

was seen by about 30%, and the lowest reduction was

observed in the center area. Also, with bigger openings,

ductility ratio was reduced. In this system, the reduction of

failure load was observed in openings larger than 1000 mm,

and the corners had the lowest base shear capacity. Overall,

we concluded that installing the openings in the center of wall

(Zone 5) will have less reducing effects on elastic stiffness,

effective or secant stiffness, failure load, absorbed energy, and

ductility ratio, and it should be avoided from embedding

openings in the corners of the composite shear wall as much

as possible, especially those with larger sizes.

ACKNOWLEDGMENTS

This paper was extracted from a MSc thesis in civil

engineering structure prepared by Soheil Kordbegli approved

in 2015 by Faculty of Engineering, Islamic Azad University

of West Tehran Branch in Iran.

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[2]. Zhao Q Zhao and Astane-Asl A. 2004.

“Experimental and analytical studies of cyclic

behavior of steel and composite shear wall system”.



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[8]. Lin C.Y., and Kuo C.L. 1988. “behaviour of shear

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