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Tests of Two Three-Story Ductile Steel Plate Shear Walls

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Structures 2008: Crossing Borders<br />

© 2008 ASCE<br />

<strong>Tests</strong> <strong>of</strong> <strong>Two</strong> <strong>Three</strong>-<strong>Story</strong> <strong>Ductile</strong> <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong><br />

Authors:<br />

Saied Sabouri-Ghomi, K.N.T. University <strong>of</strong> Technology, Tehran, Iran, sabouri@kntu.ac.ir<br />

Majid Gholhaki, Semnan University, Semnan, Iran, mgholhaki@semnan.ac.ir<br />

ABSTRACT<br />

<strong>Two</strong> three-story unstiffened ductile steel plate shear walls were tested under cyclic loading.<br />

The shear walls had two types <strong>of</strong> beam-to-column connections consisting <strong>of</strong> rigid (SPSW-R)<br />

and simple (SPSW-S). Low and high strengths steel were used in the plates <strong>of</strong> panels and<br />

boundary frames, respectively. Both specimens endured many cycles <strong>of</strong> loading most <strong>of</strong><br />

which were in the inelastic range. They showed excellent ductility and energy dissipation<br />

characteristics and exhibited stable behavior at very large deformations.<br />

KEY WORDS<br />

Thin <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> Wall, Low Strength <strong>Steel</strong>, Hysteretic Behavior, Beam-to-Column<br />

Connection.<br />

INTRODUCTION<br />

During the past 3 decades, interest has grown globally in the application <strong>of</strong> steel plate shear<br />

walls (SPSWs) as lateral load resisting system. The system consists <strong>of</strong> steel plates one story<br />

high and one bay wide connected to the adjacent beams and columns. The plates are installed<br />

in one or more bays for the full height <strong>of</strong> a building, thereby forming a stiff cantilever wall<br />

(e.g. Figure 1).<br />

FIGURE 1 - OVERALL SHAPE OF SPSW (COURTESY OF M. GILMORE)<br />

The beam-to-column connections may be rigid or simple in the surrounding steel frame,<br />

depending on the design philosophy. <strong>Steel</strong> plate shear walls are well-suited for either new<br />

construction or as a means for the seismic upgrading <strong>of</strong> existing steel and concrete structures.<br />

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SPSWs possess properties that are fundamentally beneficial to resisting seismically<br />

induced loads. As is demonstrated herein, these include superior ductility, robust resistance to<br />

degradation under cyclic loading, high initial stiffness, and inherent redundancy and<br />

significant energy dissipation.<br />

Until the 1980s, the design limit state for SPSW in North America was out-<strong>of</strong>-plane<br />

buckling <strong>of</strong> the infill plates. Although it has been shown that stiffening the panel heavily can<br />

increase the amount <strong>of</strong> energy dissipated under cyclic loading significantly [1], the cost<br />

involved is likely to be prohibitive in most markets. However, it has been known for a long<br />

time that buckling does not necessarily represent the limit <strong>of</strong> useful behavior and there is<br />

considerable post buckling strength in an unstiffened shear panel [2].<br />

At the point <strong>of</strong> critical elastic buckling, the load-resisting mechanism changes from inplane<br />

shear to an inclined tension field. Finally by yielding <strong>of</strong> the steel panel significant<br />

amount <strong>of</strong> energy dissipate in cyclic loading.<br />

In recent years, SPSWs have been used in a number <strong>of</strong> buildings as part <strong>of</strong> the lateral load<br />

resisting system, mainly in Japan and North America. One <strong>of</strong> the most significant buildings<br />

constructed with SPSWs, in a highly seismic area, is a 35-story high-rise building in Kobe,<br />

Japan (e.g. Figure 2).<br />

FIGURE 2 - 35-STORY KOBE BUILDING (COURTESY OF C.E. VENTURA)<br />

This structure was constructed in 1988 and performed very well during the 1995 Kobe<br />

earthquake, [3]. The 24-story U.S. Courthouse building in Seattle, Washington, and 6-story<br />

building in Saint Georges, Quebec, are prime examples <strong>of</strong> the application <strong>of</strong> this system in the<br />

United States and Canada, (e.g. Figures 3 and 4, respectively).<br />

PREVIOUS TESTING OF STEEL PLATE SHEAR WALLS<br />

The studies so far is limited to the topic <strong>of</strong> physical testing <strong>of</strong> unstiffened SPSWs. Timler and<br />

Kulak [4] tested a single-story SPSW to verify the analytical technique established by<br />

Thorburn et al. [5].<br />

Tromposch and Kulak [6] tested a shear wall similar to the test undertaken by Timler and<br />

Kulak [4]. However, important modifications were introduced, including the use <strong>of</strong> bolted<br />

simple connections in the frame, a thinner infill panel, and very stiff beam members.<br />

An experimental program conducted by Elgaaly and Caccese [7] investigated the behavior<br />

<strong>of</strong> ten one-quarter scale SPSW models subjected to cyclic loading. The specimens were three<br />

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Structures 2008: Crossing Borders<br />

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stories high and one bay wide. Parameters that varied were the panel thickness and the beamto-column<br />

connection in both rigid and simple types.<br />

FIGURE 3 - 24-STORY COURTHOUSE BUILDING, SEATTLE, WASHINGTON (COURTESY OF F.<br />

OOMS)<br />

FIGURE 4 - 6-STORY SPSW DURING CONSTRUCTION, QUEBEC, CANADA (COURTESY OF M.<br />

GILMORE)<br />

Sabouri-Ghomi and Roberts [8] and Roberts and Sabouri-Ghomi [9] conducted a series <strong>of</strong><br />

small scale quasi-static cyclic tests on slender unstiffened shear panels. Twelve different<br />

specimens with infill panel dimensions <strong>of</strong> 300 mm by 300 mm and 450 mm by 300 mm were<br />

tested. Infill plate thicknesses were 0.54 mm and 0.83 mm <strong>of</strong> steel and 1.23 mm <strong>of</strong> aluminum.<br />

Driver [10] tested a half-scaled four-story SPSW frame under quasi-static cyclic loading<br />

utilizing full rigid connections. The objective <strong>of</strong> this test was to study the performance <strong>of</strong> a<br />

multi-story SPSW under the effects <strong>of</strong> very sever cyclic loading.<br />

Lubell [11] conducted cyclic tests on two single panel specimens and one four-story<br />

specimen. Each specimen was tested under fully reversed quasi-static cyclic loading in both<br />

its elastic and inelastic response regions.<br />

Rezai [12] conducted a shake table test on a four-story steel plate shear wall specimen.<br />

The scale for the SPSW was a factor <strong>of</strong> 1 4 and the thickness <strong>of</strong> the infill steel panels was 1.5<br />

mm. The limited capacity <strong>of</strong> the shake table prevented a significant inelastic response from<br />

the specimen.<br />

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Structures 2008: Crossing Borders<br />

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Astaneh-Asl and Zhao [13] conducted two half-scale three-story SPSW tests under cyclic<br />

loading. The specimens were one-half <strong>of</strong> a coupled wall with concrete-filled hollow steel<br />

section as columns and had a total height <strong>of</strong> 6.2 m. The specimens showed good displacement<br />

ductility capacity and stable hysteresis behavior with desirable energy dissipation<br />

characteristics.<br />

Behbahani-Fard [14] conducted a large-scale test on a three-story SPSW specimen under<br />

lateral quasi-static cyclic loading in the presence <strong>of</strong> gravity loads. The specimen formed the<br />

upper part <strong>of</strong> a four-story SPSW that had been tested earlier by Driver [10]. Since the test<br />

specimen had gone through a history <strong>of</strong> plastic deformation from previous testing by Driver<br />

[10], evaluating the effect <strong>of</strong> the previous test on the overall performance <strong>of</strong> the specimen was<br />

one <strong>of</strong> the objectives.<br />

Vian and Bruneau [15] conducted three SPSW specimen tests made <strong>of</strong> low yield strength<br />

(LYS) steel infill panels and reduced beam sections (RBS) at the beam-ends, under cyclic<br />

loading. <strong>Two</strong> <strong>of</strong> the specimens had holes for allowing mechanical utilities to pass through.<br />

Multiple holes were designed in the steel plate <strong>of</strong> the panel used in the first specimen that<br />

reduced the overall strength compared to the panel without perforations. The second<br />

perforated SPSW specimen was designed with quarter-circle cut-outs in the panel corners<br />

which were reinforced to transfer panel forces to the adjacent frame.<br />

Kharrazi [16] conducted two SPSW specimen tests. The infill panels in these specimens<br />

were made <strong>of</strong> low yield strength and mild steel. They had the ratio <strong>of</strong> height to width more<br />

than one. The overall strength, elastic post-buckling stiffness and post-yield stiffness were<br />

very high.<br />

SPECIMENS DETAILS AND TESTS SETUP<br />

Figure 5 shows the schematic representation <strong>of</strong> two test specimens SPSW-R and SPSW-S that<br />

differ principally in type <strong>of</strong> beam-to-column connections, [17].<br />

FIGURE 5 - SCHEMATIC REPRESENTATION OF SPECIMENS SPSW-R AND SPSW-S<br />

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Figures 6 and 7 show the rigid and simple types <strong>of</strong> beam-to-column connections which<br />

were used for specimens SPSW-R and SPSW-S, respectively.<br />

The beam-to-column connections <strong>of</strong> top beams in both specimens SPSW-R and SPSW-S<br />

were rigid.<br />

FIGURE 6 - DETAILS OF RIGID BEAM-TO-COLUMN CONNECTION<br />

All beams were selected such that out-<strong>of</strong>-plane buckling would not occur, eliminating the<br />

need for intermediate lateral bracing. In order to preclude probability <strong>of</strong> out-<strong>of</strong>-plane buckling<br />

<strong>of</strong> wall, the lateral supporting system were used at each beam level. The lateral supporting<br />

system consisted <strong>of</strong> three double beams, with both ends connected to the main supporting<br />

frame system.<br />

Both specimens were designed by plate-frame-interaction (PFI) technique, developed by<br />

Sabouri-Ghomi and Roberts [8, 9, 18, and 19] for analysis and design <strong>of</strong> steel plate shear<br />

walls. In addition, all requirements <strong>of</strong> AISC code for frames were met.<br />

FIGURE 7 - DETAILS OF SIMPLE BEAM-TO-COLUMN CONNECTION<br />

The mean measured thickness and the panel aspect ratio (width/height) for all panels are<br />

0.7 mm and 1.0, respectively.<br />

Equal horizontal load was applied at the top <strong>of</strong> specimens. Because <strong>of</strong> the laboratory<br />

limitations, only two hydraulic pressure jacks were used at both sides <strong>of</strong> the top level in each<br />

specimen.<br />

For analysis and design <strong>of</strong> specimens in addition to the use <strong>of</strong> PFI technique [20,21,22]<br />

for analysis and design <strong>of</strong> specimens, preliminary finite elements analyses were also carried<br />

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out using the commercial general-purpose finite elements s<strong>of</strong>tware ANSYS. Because the<br />

computational demands on this system were high due to shear-buckling and localized<br />

instabilities in the infill plate, monotonic loading was used to estimate the envelope <strong>of</strong> loaddisplacement<br />

response.<br />

TEST PROCEDURES AND LOADING PROTOCOL<br />

Numerous load and deflection histories could be used to evaluate a structural component for<br />

seismic performance. Most slow cyclic tests that are intended to simulate earthquake loading<br />

employ a horizontal in-plane load history that uses gradually increasing loads or<br />

displacements in successive cycles.<br />

Based on ATC-24 [23] for specimen SPSW-R, the yield displacement ( y ) in panel 1 was<br />

determined during the early stages <strong>of</strong> the test as 2.44 mm. Prior to reaching this value, single<br />

loading cycles leading to shears in panel 1 <strong>of</strong> 10.3 kN, 12.8 kN and 15.2 kN and three<br />

cycles each with shears <strong>of</strong> 18.0 kN were conducted to explore the elastic and the initial<br />

inelastic behavior. These constituted cycles 1-6. After cycles 7, 8, and 9 with a displacement<br />

<strong>of</strong> y =2.44 mm, the displacement in the first story was increased by 2.44 mm in each<br />

subsequent deformation step. Following the guidelines <strong>of</strong> ATC-24, three cycles were<br />

conducted at each deformation setup to a deformation <strong>of</strong> 3 y (cycles 13-15) and two cycles at<br />

each deformation setup with incremental deformation <strong>of</strong> y thereafter.<br />

After testing SPSW-R, the loading strategy was changed for specimen SPSW-S. The yield<br />

displacement ( y ) in panel 1 <strong>of</strong> specimen SPSW-S, was determined during the early stages <strong>of</strong><br />

the test as 3.09 mm. Prior to reaching this value, six cycles similar to specimen SPSW-R and<br />

with the same amplitudes were conducted to explore the elastic and the initial inelastic<br />

behavior <strong>of</strong> specimen SPSW-S. After cycles 7, 8 and 9 with a displacement <strong>of</strong> y =3.09 mm,<br />

two cycles were conducted at each displacement set-up with incremental displacement <strong>of</strong> 2 y<br />

up to cycle 17. In cycles 18 and 19 the displacement reached 10 y and 11 y , respectively.<br />

BEHAVIOR OF SPECIMENS<br />

The behaviors <strong>of</strong> specimens during the tests were as follow:<br />

Specimen SPSW-R<br />

Specimen SPSW-R before the test is shown in Fig. 8. During the 6 initial cycles, an<br />

inspection <strong>of</strong> the thin infill panels and boundary members revealed that no yielding had<br />

occurred. In cycle 7 (the first cycle with y 2.44mm<br />

that y is the first yielding in<br />

specimen); the existing yield patterns became considerably more pronounced.<br />

In this cycle panels 2 and 3, buckled visibly at maximum displacement. In addition,<br />

several loud bangs first occurred in this cycle as the plate buckles popped out and reoriented<br />

themselves upon reversal <strong>of</strong> the loading direction. These noises continued to occur in all<br />

subsequent cycles.<br />

During the cycles 10-12, as loading continued, amplitude <strong>of</strong> the buckles in the second and<br />

third story panels increased. After unloading the forces, residual buckles were clearly visible<br />

in a complex surface geometry that did not favor the orientation that formed in either direction<br />

<strong>of</strong> loading. In cycle 13, the sign <strong>of</strong> beam yielding was observed in panel 2.<br />

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FIGURE 8 - OVERALL PANELS OF SPECIMEN SPSW-R<br />

The first tear was detected during cycle 21 in the east top corner <strong>of</strong> plate <strong>of</strong> panel 2 near<br />

the pins (e.g. Figure 9). This tear propagated during subsequent cycles. After, the transverse<br />

welding <strong>of</strong> the L shape which was used as fish plate conjunction near the second beam<br />

cracked.<br />

FIGURE 9 - FIRST TEARING OF SPSW-R IN CYCLE 21<br />

In cycle 26, the crack <strong>of</strong> beam-to-column connection <strong>of</strong> second beam was increased. In<br />

addition, transverse welding <strong>of</strong> horizontal and vertical L shape conjunction at top east corner<br />

in panel 1 and bottom corners <strong>of</strong> panels 2 and 3 were cracked. Also, during cycle 26, at a<br />

displacement <strong>of</strong> 9 y in panel 1, the maximum base shear <strong>of</strong> 153 kN was reached. The load-<br />

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carrying capacity <strong>of</strong> the test specimen declined very gradually during each <strong>of</strong> the remaining<br />

cycles <strong>of</strong> increasing deformations.<br />

In cycle 27, the amplitude <strong>of</strong> the buckles in all panels increased. For example, the<br />

amplitude <strong>of</strong> the buckle in panel 2 was estimated to be about 130 mm from the neutral<br />

position. In cycles 29 and 30, in top and east edges <strong>of</strong> panel 2 and in bottom and west edges <strong>of</strong><br />

panel 3 the tearing around pins began and increased. In these cycles because <strong>of</strong> weakness <strong>of</strong><br />

the plate action and consequently serious frame action, the weld <strong>of</strong> conjunction beam flanges<br />

to column flange in levels 1 and 2 were fractured and crack propagated and moved to the web<br />

<strong>of</strong> beams.<br />

Beginning at cycle 31, when the displacement <strong>of</strong> panel 1 reached 11 y , tears in the<br />

interior <strong>of</strong> the panels 2 and 3 near the L shape suddenly formed as a result <strong>of</strong> kinking <strong>of</strong> the<br />

stretched plate during load reversals. During the first loading history <strong>of</strong> cycle 31, and just<br />

prior to failure, the base shear reached 91% <strong>of</strong> the maximum base shear reached in cycle 26.<br />

The stiffness <strong>of</strong> the shear panel itself was declining in a very gradual and stable manner, and it<br />

maintained its integrity to the end <strong>of</strong> the test.<br />

Up to the end <strong>of</strong> the test all columns remained undamaged and there were no signs <strong>of</strong> local<br />

or global buckling in them. Also no tearing occurred in panel 1 and there were no fracture in<br />

the column s toe due to good performance <strong>of</strong> the toe stiffeners.<br />

Figure 10 shows the behavior <strong>of</strong> specimen SPSW-R during the test.<br />

FIGURE 10 - HYSTERETIC BEHAVIOR OF SPECIMEN SPSW-R<br />

Specimen SPSW-S<br />

During the 6 initial cycles, an inspection <strong>of</strong> the infill panels and boundary members revealed<br />

that no yielding had occurred. In cycle 7 (the first cycle with y 3.09mm<br />

that y is the<br />

first yielding in specimen), the existing yield patterns, became considerably more pronounced.<br />

Panels 2 and 3, buckled visibly at the maximum displacement. In addition, several load bangs<br />

first occurred in this cycle as the plate buckles popped out and oriented themselves upon<br />

reversal <strong>of</strong> the loading direction. These noises continued to occur in all subsequent cycles.<br />

In cycles 8 and 9, some flaking <strong>of</strong> the white-wash paint on the plates <strong>of</strong> panels, near the<br />

conjunction <strong>of</strong> horizontal and vertical L shape, used as fish plate <strong>of</strong> panels 1 and 2, were<br />

noted. Minor signs <strong>of</strong> yielding also occurred in plates <strong>of</strong> the corresponding panels. During<br />

cycles 10 and 11, as loading continued, amplitude <strong>of</strong> the buckles in the second and third<br />

panels increased. In addition, the yielded areas on the plates <strong>of</strong> all panels had grown larger. In<br />

cycles 12 and 13, flaking increased in top west <strong>of</strong> panel 2 and bottom west <strong>of</strong> panel 3 and in L<br />

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shape connected between beam web and column flange flaking <strong>of</strong> white-wash was started.<br />

The first tear was detected during cycle 14 in the east bottom corner <strong>of</strong> plate near the L shape<br />

in panel 2, (e.g. Figure 11).<br />

FIGURE 11 - FIRST TEARING OF SPSW-S IN CYCLE 14<br />

During the cycles 15, 16 and 17 the flaking <strong>of</strong> the white-wash paint propagated all over<br />

the panels 2, 3 and to some extent in panel 1. In cycle 18, at a displacement <strong>of</strong> 10 y in panel<br />

1, the maximum base shear <strong>of</strong> 121 kN was reached. The load-carrying capacity <strong>of</strong> the test<br />

specimen reached rapidly during the remaining cycles.<br />

Beginning at cycle 19, when the displacement <strong>of</strong> panel 1 reached 11 y first in the top<br />

edge and then in the east edge <strong>of</strong> plate in panel 2, tearing formed suddenly as a result <strong>of</strong><br />

kinking <strong>of</strong> the stretched plate during load reversals. During the second loading history <strong>of</strong><br />

cycle 19, and just prior to failure, the base shear reached 68% <strong>of</strong> the maximum base shear<br />

obtained in cycle 18. Because <strong>of</strong> the tearing <strong>of</strong> panel 2, the rotation <strong>of</strong> beams 1 and 2 reached<br />

maximum and so, the L shape pr<strong>of</strong>ile connected between web <strong>of</strong> beam and flange <strong>of</strong> column<br />

was yielded. At the end <strong>of</strong> cycle 19, tearing started at the top east corner <strong>of</strong> plate in panel 1.<br />

Like the test <strong>of</strong> SPSW-R, up to the end <strong>of</strong> the test, all columns remained undamaged and there<br />

were no signs <strong>of</strong> local or global buckling in them. Also, there was no fracture in the column s<br />

toe because <strong>of</strong> the good performance <strong>of</strong> the toe stiffeners.<br />

Figure 12 shows the behavior <strong>of</strong> specimen SPSW-S during the test.<br />

SUMMARY<br />

The hysteretic behaviors <strong>of</strong> both specimens indicated that the shear wall configurations tested<br />

possess an extremely high degree <strong>of</strong> ductility. The results showed that the ductility factor <strong>of</strong><br />

specimens SPSW-R and SPSW-S are 6.63 and 8.24, respectively.<br />

The results <strong>of</strong> the tested specimens showed that the steel plate shear walls, which are<br />

designed based on the PFI technique and low strength steel plates are used in their panels<br />

according to the general concept <strong>of</strong> easy-going steel in which the low strength plate absorbs<br />

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much more energy in smaller displacement compared to the high strength boundary steel<br />

frame, are more ductile. As it was observed from the tests, in such walls, the columns can be<br />

protected from any damage.<br />

FIGURE 12 - HYSTERETIC BEHAVIOR OF SPECIMEN SPSW-S<br />

The hysteresis curves <strong>of</strong> specimens showed that the effect <strong>of</strong> beam-to-column connection<br />

type on the initial stiffness <strong>of</strong> thin steel plate shear walls is negligible but it effects on<br />

specimens' strengths.<br />

The results showed that in specimen SPSW-R the amount <strong>of</strong> energy dissipated during the<br />

loading cycles was significantly greater than those in SPSW-S.<br />

The results showed that, in effect <strong>of</strong> the presence <strong>of</strong> infill plate, there is a reduction in<br />

reliance on the beam-to-column connection <strong>of</strong> the frame for resisting the story shears.<br />

Therefore, the joint panel zone would not generally be a critical element. It is likely that it<br />

could be designed to remain essentially elastic.<br />

REFRENCES<br />

[1] Takahashi, Y., Takemoto, Y., Takeda, T., and Takagi, M., Experimental Study on Thin <strong>Steel</strong> <strong>Shear</strong><br />

<strong>Walls</strong> and Particular Bracings under Alternative Horizontal Load , Preliminary Report, IABSE<br />

Symposium on Resistance and Ultimate Deformability <strong>of</strong> Structures Acted on Well-defined Repeated<br />

Loads, Lisbon, Portugal, 1973,185-191.<br />

[2] Wagner, H., Flat Sheet Metal Girders with Very Thin Webs, Part I-General Theories and Assumptions ,<br />

Tech. Memo., No. 604, National Advisory Committee for Aeronautics, Washington, D. C., 1931.<br />

[3] Astaneh-Asl, A., Seismic Behavior and Design <strong>of</strong> <strong>Steel</strong> <strong>Shear</strong> <strong>Walls</strong> , <strong>Steel</strong> Tips Report, Structural <strong>Steel</strong><br />

Educational Council, July, Moraga, CA., 2001.<br />

[4] Timler, P. A. and Kulak, G. L., Experimental Study <strong>of</strong> <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> , Structural Engineering<br />

Report No. 114, Dept. <strong>of</strong> Civil Engineering, University <strong>of</strong> Alberta, Edmonton, Alta., Canada, 1983.<br />

[5] Thorburn, L. J., Kulak, G. L., and Montgomery, C. J., Analysis <strong>of</strong> <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> , Structural<br />

Engineering Report No. 107, Dept. <strong>of</strong> Civil Engineering, University <strong>of</strong> Alberta, Edmonton, Alta., Canada,<br />

1983.<br />

[6] Tromposch, E. W. and Kulak, G. L., Cyclic and Static Behavior <strong>of</strong> Thin Panel <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> ,<br />

Structural Engineering Rep. No. 145, Dept. <strong>of</strong> Civil Engineering, University <strong>of</strong> Alberta, Edmonton, Alta.,<br />

Canada, 1987.<br />

[7] Elgaaly, M., and Caccese, V., <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> , Proceeding <strong>of</strong> AISC National <strong>Steel</strong> Construction<br />

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Conference, American Institute <strong>of</strong> <strong>Steel</strong> Construction (AISC), Inc., Chicago, 1990.<br />

[8] Sabouri-Ghomi, S., and Roberts, T.M., Nonlinear Dynamic Analysis <strong>of</strong> Thin <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> ,<br />

Computers and Structures, 39(1/2), 1991, 121 127.<br />

[9] Roberts, T. M., and Sabouri-Ghomi, S., Hysteretic Characteristics <strong>of</strong> Unstiffened <strong>Plate</strong> <strong>Shear</strong> Panels ,<br />

Thin-Walled Structures, 12, 1991, 145 162.<br />

[10] Driver, R. G., Seismic Behavior <strong>of</strong> <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> , Ph.D. Dissertation, Department <strong>of</strong> Civil<br />

and Environmental Engineering, University <strong>of</strong> Alberta, Edmonton, AB, 1997.<br />

[11] Lubell, A. S., Performance <strong>of</strong> Unstiffened <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> under Cyclic Quasi Static Loading ,<br />

M.A.Sc. Thesis, Department <strong>of</strong> Civil Engineering, University <strong>of</strong> British Columbia, Vancouver, BC,<br />

Canada, 1997.<br />

[12] Rezai, M., Seismic Behavior <strong>of</strong> <strong>Steel</strong> <strong>Plate</strong> <strong>Shear</strong> <strong>Walls</strong> by Shake Table Testing , Ph.D. Dissertation,<br />

Department <strong>of</strong> Civil Engineering, University <strong>of</strong> British Columbia, Vancouver, BC, Canada, 1999.<br />

[13] Astaneh-Asl, A. and Zhao, Q., Cyclic Behavior <strong>of</strong> <strong>Steel</strong> <strong>Shear</strong> Wall Systems , Proceedings <strong>of</strong> Annual<br />

Stability Conference, Structural Stability Research Council, Seattle, 2002.<br />

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