International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 Some Studies on Behavior Of Steel Plate Shear Wall In Earthquake Prone Area: A Review Gajendra Kumar Verma*1 and Savita Maru2 1 PhD.Scholar, Civil Deptt.,Ujjain. Engineering College, Ujjain 2 Professor, Civil Deptt.,Ujjain. Engineering College, Ujjain Abstract - A steel plate shear wall (SPW) is a lateral-loadresisting system consisting of vertical steel plate infills connected to the surrounding beams and columns and installed in one or more bays along the full height of the structure to form a cantilevered wall. SPSW subjected to cyclic inelastic deformations exhibit high initial stiffness, behave in a very ductile manner, and dissipate significant amounts of energy. These characteristics make them suitable to resist seismic loading. The emergence of steel plate shear walls, both as a topic of research and in actual construction, began in the early 1970's. Most of the structures constmcted during this period that employed steel shear walls were built in Japan and the United States, and they were generally a substitute for conventional reinforced concrete shear walls. As a result, the earliest research came from Japan and the United States, the Japanese being the first to study the overall behaviour of steel plate shear walls [Takahashi et al., 19731. Prior to key research performed in the 1980s, the design approach used by the Japanese and Americans concentrated on preventing the steel plate shear panels from buckling prior to the attainment of shear yield. In Japan, this was achieved by reinforcing the thin panels with a relatively large number of longitudinal and transverse stiffeners and in the United States, this was achieved by using the thick steel plate shear walls. Both the solution had economic implications with respect to material cost and erection. However, several experimental and analytical studies using both quasistatic and dynamic loading showed that the postbuckling strength and ductility of thin unstiffened SPSW can be substantial and that is why The unstiffened steel plate shear wall is included as a “Basic Seismic Force Resisting System” in ASCE 7 and AISC 341. reinforced concrete. But now days Steel Plate Shear Wall (SPSW) is employed in several structures in USA, Japan, Canada and UK. Steel Plate Shear Wall system has relatively large energy dissipation capability, thus being very attractive for high risk earthquake zones.The post bucking strength and tension field action mechanism (as shown in Fig-1) has been recognized as early as in the 1930s in aerospace engineering (Wagner, 1931), and as early as in the 1960s in steel building construction, when it was incorporated in to the design process of plate girders ( Basler, 1961). The appropriateness of post-bucking stiffness and strength characteristics of SPSW to resist service lateral loads was analytically predicted by Thorburn in (1983) and experimentally confirmed by Timler and Kulak (1983). Research on unstiffened steel plate shear walls has investigated the effect of simple versus rigid beam-to-column connections on the overall behavior ( Caccese et al., 1993), the dynamic response of steel plate shear walls (Sabouri_Ghomi and Roberts, 1992; Rezai,1999), the effects of holes in the infill plates ( Roberts and Sabouri-Ghomi,1992; Vian and Bruneau, 2004), the use of low-yield-point steel and light-gauge steel (Vian and Bruneau, 2004; Berman and Bruneau, 2005), and infill connections (Elgaaly 1998; Schumacher et al.,1999). Furthermore, finite-element modeling of unstiffened steel plate shear walls has been Keywords : Steel plate shear walls (SPSW); steel building, strip modeling; aspect ratio; I. INTRODUCTION Recently there has been a considerable increase in the number of tall building, both residential and commercial and the modern trend is towards taller and more slender structure. Thus the effect of lateral loads like wind loads, earthquake forces and blast forces are attaining increasing importance and almost every designer is faced with the problem of providing adequate strength and stability against lateral loads. There are number of lateral load resisting system but shear wall system is commonly adopted in high-rise building. The shear wall systems have conventionally been built almost exclusively of ISSN: 2231-5381 FIG: .1 Idealized Tension Field in a SPSW investigated in some of the aforementioned papers, as well as by Elgaaly et al. (1993) and Driver et al.(1997). Takahashi et al. (1973)who is believed to have conducted the first extensive research programme on the behaviour of steel plate shear wall panels, found that under cyclic loads heavily stiffened steel http://www.ijettjournal.org Page 1392 International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 panels perform better in shear than unstiffened steel panels, although it is unlikely that they would be economical in most markets. The following sections describe the primary research developments related to unstiffened steel plate shear walls, with an emphasis on analytical techniques. II. LITERATURE REVIEW 1.Thorburn et al. (1983) The first comprehensive analytical investigations of conventional unstiffened steel plate shear walls were conducted at the University of Alberta. Thorburn et al. (1983) recognised that buckling of the infill plate due to lateral loads does not represent the ultimate capacity of steel plate shear walls and that the inclined tension field dominated the postbuckling behaviour of the infill plates. An analytical model— termed the strip model (as shown in Fig-2) was developed to simulate the tension field behaviour, wherein the infill plate is modelled as a series of tension–only strips oriented at the same angle of inclination, α, as the tension field. present. The strip model assumes that the boundary beams are infinitely stiff in order to reflect the presence of opposing tension fields above and below the modelled panel. diagonal brace represents the stiffness characteristics of the tension field in the infill plate, assuming rigid boundary elements. The equation for the area of the brace is as follows: = ∝. . where φ is the acute angle of the brace with respect to the column and all other parameters are as defined above. The equivalent brace model is considered as a preliminary design tool for steel plate shear walls. Thorburn et al. (1983) conducted a parametric study to assess the effect on the panel stiffness and strength of the plate thickness, the panel height, the panel width, and the column flexural stiffness. It was found that the parameters were closely interdependent with one another and their interaction complex. 2. Timler and Kulak (1983) To verify the analytical method developed by Thorburn et al. (1983), Timler and Kulak (1983) tested a full-scale specimen that represented two single–storey, one–bay steel plate shear wall elements. Due to the testing procedure implemented in this research, the columns were the horizontal elements while the beams were vertical. The specimen was loaded in an incremental manner to both service and ultimate levels. A cyclic load test up to the allowable deflection limit was also performed. The researchers recognized that the flexural stiffness of the columns affects the value of α. Thus, the equation for α, originally developed by Thorburn et al. (1983), was modified as follows: tan ∝ = FIG: 2. Strip Model of SPSW Thorburn et al. (1983) showed that ten strips per panel adequately represent the tension field action developed in the plate. Thorburn et al. (1983) derived an following equation for determining α: . tan ∝ = . ---------- (i) where t is the thickness of the infill plate, Ac and Ab are the cross-sectional areas of the column and beam, respectively,. In order to simplify the iterative process of designing a steel plate shear wall, Thorburn et al. (1983) developed a Pratt truss model, known as the equivalent brace model. The infill plate at a single storey is modelled as a single diagonal tension-only brace intersecting the working points of the frame. The ISSN: 2231-5381 --------------(ii) . --------- (iii) . . . where Ic is the moment of inertia of the column about an axis perpendicular to the panel and all other parameters were defined earlier. It was found that for the case of beams that have an infill plate on one side only, and are therefore free to bend, such as the beam at the top of a shear wall (or the edge of the test specimen), the flexural stiffness of the beam affects α. Thus, the equation for α was re-derived for the infill plate at the top of a steel plate shear wall and was presented as follows: tan ∝ = ( . . . . . . ) ----------(iv) where Ib is the moment of inertia of the beam about an axis perpendicular to the panel and all other parameters were defined previously. Timler and Kulak (1983) modeled their test specimen using the strip model. Since an elastic analysis program was utilised, inelastic behaviour was simulated in the boundary members by successive reductions in the cross-sectional properties of the entire length of the members and in the strips by limiting the stress to the static yield stress measured from tension coupons. Good correlation was found between predicted and actual values of the infill plate stresses, axial strains, and the load vs. deflection response. The discrepancies found in using the Thorburn et al. (1983) equation for α were minor. http://www.ijettjournal.org Page 1393 International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 However, it was recommended that the equation (iii) be used to describe more accurately the angle of the tension field. 3. Tromposch And Kulak (1987) Tromposch and Kulak (1987) performed a test on a large scale SPSW similar to that tested by Timler and Kulak (1983). The major differences between the two were the change in bay dimension, the use of bolted rather than welded beam to column connection, thinner plate (3.25 mm) and stiffer beams. In addition, the columns were pre-stressed before testing to simulate gravity loads on the structure. The main objectives of the tests were to examine the hysteretic behaviour of the specimen and to verify the analytical strip model proposed by Thorburn et al (1983). The specimen displayed ductile behaviour with severely pinched hysteresis curves due to the thin infill plate and flexible boundary frame. Tromposch and Kulak also showed that the strip model (Thorburn et al. 1983) gave conservative estimates of both initial stiffness and ultimate capacity of steel plate shear walls. Inelastic behaviour was accounted for in a similar manner to that used by Timler and Kulak (1983). Tromposch and Kulak (1987) also found that the eccentricity of the fish plate with respect to the centre of the boundary members had no noticeable effect on the performance of the steel plate shear wall specimen. 4.Elgaaly, Caccese, And Du (1993) Elgaaly et al (1993) used finite-element models, and models based on the revised multi-strip method proposed by Timler and Kulak (1983), to replicate results experimentally achieved by Caccese et al (1993). The finite element model used nonlinear material properties and geometry, a 6x6 mesh to represent the plates on each story and six beam elements for each frame member. The 0.075 in. and 0.106 in. (1.9 mm and 2.7 mm) plate thickness used in the finite-element models were identical to those from the experimental work. Momentresisting beam-to-column connections were assumed. Lateral load was monotonically applied until loss of stability developed due to column plastic hinging and flange local buckling .It was found that the wall with thicker plates was not significantly stronger because column yielding was the governing factor for both cases. The specimen using moment resisting beam-tocolumn connections and the 0.075 in. (1.9mm) thick plate was also modeled using the multi-strip method. Twelve strips were used to represent the plate at each story. The angle of inclinations of the strips was found to be 42.8 degree, which agreed well with the results of the finite element model that predicted the principal strains in the middle of the plates oriented between 40 and 50 degree with the vertical. Using an elastic perfectly plastic stress-strain curve for the strips, the model was found to produce results in reasonable agreement with the experimental results with respect to initial stiffness, ultimate strength, and displacement at the ultimate strength. An analytical model for predicting the hysteretic cyclic behavior of thin steel plate shear walls was also developed. This model was based on the strip model but ISSN: 2231-5381 incorporated strips in both directions (Figure -3), which is necessary to capture cyclic behavior. The hysteretic model involved the use of an empirically derived, hysteretic, stressstrain relationship for the strips, and good agreement with experimental results was reported. Fig:3. Cyclic Strip Model .5.Xue And Lu (1994) Xue and Lu (1994) performed an analytical study on a three bay, 12-story, moment-resisting frame structure, which had the middle bay infilled with a steel plate shear wall. The effect of beam-to-column and plate connections was the focus of this study. Four scenarios were considered: 1. Moment resisting beam-to-column connections and infill plates fully connected to the surrounding frame. 2. Moment-resisting beam-to-column connections and the infill plates attached to only the beams. 3. Simple beam-to-column connections and fully-connected infill plates. 4. Simple beam-to-column connections with infill plates connected only to the beams. Plate thicknesses were the same for each configuration but varied along the height Stories 1 to 4, 5 to 8, and 9 to 12, respectively, had 0.11-in., 0.094-in., and 0.087-in. (2.8-mm, 2.4-mm and 2.2-mm) thick plates. The exterior bays were 360 in. (9,144 mm) wide the interior ( infilled) bay was 144 in. (3,658 mm) wide, and all stories were 144 in ( 3,658 http://www.ijettjournal.org Page 1394 International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 mm) tall, except the first story, which was 180 in. (4,572 mm) tall. The finite-element analysis considered beams and columns modeled using elastic beam elements and plates modeled using elasto-plastic shell elements. Each model was subjected to pushover analysis with forces applied at each story. It was found that the type of beam-to-column connection in the infilled bay had an insignificant effect on the global force-displacement behavior of the system and that connecting the infill panels to the columns provided only a modest increase in the ultimate capacity of the system. Xue and Lu (1994) concluded that connecting the infill plates to only the beams and using simple beam-to-column connections in the interior bay was the optimal configuration because this drastically reduced the shear forces in the interior columns and helped avoid premature column failure. However, because the small number of cases considered does not allow generalization of this observation. This recommendation has not been implemented in the NEHRP Provisions or AISC 341. 6. Driver et al. (1997; 1998a, b) Driver et al. (1997; 1998a) tested a large–scale, four–storey, single bay steel plate shear wall specimen to identify the elastic stiffness, ductility and energy absorption capacity. The specimen had moment–resisting beam-to-column connections, fishplates welded connection was used to connect the infill plates. The Gravity loads were applied to the tops of the columns, and cyclic lateral loads of equal magnitude were applied at each floor level, as per the requirements of ATC-24 (Applied Technology Council 1992). The test behavior showed that a properly designed steel plate shear wall system is an excellent lateral load-resisting system for seismic loading. Driver et al. (1997; 1998b) also developed an finite element models to predict the structural behaviour of the steel plate shear wall specimen. This analysis was found to be in excellent agreement with the experimental data, but was unable to reach the full shear wall capacity. A full response analysis was also performed and provided an excellent prediction of ultimate strength but overestimated the initial stiffness by about 15%. 7. Elgaaly and Liu (1997) Elgaaly and Liu (1997) conducted an analytical investigation of steel plate shear walls. Based on test observations made by Caccese et al. (1993), it was found that the tension strains in the infill plate were not uniform throughout, but were higher near the boundary members. To reflect this observation, the researchers modified the trilinear material model (Elgaaly et al. 1993a) by incorporating square gusset plates at the ends of the tension strips. An angle of inclination of the tension strips was assumed 45° and an empirical plastic deformation factor was incorporated into the analysis to obtain good agreement between the analytical model and the quarter–scale test specimens of Cacceseet al. (1993). ISSN: 2231-5381 8. Lubell (1997) Lubell (1997) conducted experiments on two one–storey steel plate shear wall specimens and one four–storey specimen .In all specimens, the beams were connected to the columns using moment–resisting connections. Steel masses were placed at each storey of specimen to simulate gravity loading. Quasistatic cyclic testing was performed on all three specimens. Fifteen equally spaced tension–only inclined elements were used to represent the infill plate of each panel and were oriented, with respect to the column, at an angle of 37. Two types of strip models were created. The first used monotonic loading to describe the pushover envelope behaviour of the specimens. The second used reversed cyclic loading to describe the hysteretic behaviour of the models. In the second model, the tension–only strips were inclined in both directions, giving a total of thirty strips per panel. The results for the monotonic SPSW model were found to be inconsistent with the test results. The model predicted a higher initial stiffness and ultimate strength (10% above test ultimate strength). Overall behaviour of the cyclic model matched that of the test. However, a few minor localized differences were attributed to the numerical modeling simplifications used. It was found that neither could accurately describe the specimen pushover envelope behaviour completely. Lubell (1997) conducted a series of parametric studies, using the SPSW monotonic model, to investigate the sensitivity of certain model parameters. It was found that the initial stiffness was not overly sensitive to changes in infill plate thickness, t, but the ultimate strength was found to increase as t increased. It was also found that as α decreases, both the initial stiffness and the ultimate strength of the specimen decreased. 9. Timler et al. (1998) An analytical study were performed on design and cost feasibility of steel plate shear walls at Canada. Comprehensive designs of medium–sized office buildings with steel plate shear walls of varying ductility ratings for different locations across Canada were conducted and compared with alternative designs using reinforced concrete shear walls. It was found that for steel plate shear wall structures, the super- and substructure works were less expensive than traditional reinforced concrete shear wall forms. It was also found that a building with steel plate shear walls could be turned over to the owner substantially more quickly than a similar building with a reinforced concrete core. These factors both contribute to the economic feasibility of steel plate shear wall structures. 10. Rezai (1999) Rezai (1999) performed shake-table testing on a 1:4 scale, four–storey steel plate shear wall specimen nearly identical to the one tested by Lubell (1997) to study the dynamic behaviour. This was the first time a test of this kind was conducted on a steel plate shear wall specimen. The specimen was subjected to various site-recorded and synthetically generated ground motions at varying intensities. Due to limitations of the shake table, the test results remained mainly in the elastic range. Thus, the nonlinear behaviour of the steel plate shear wall specimen could not be explored in detail. http://www.ijettjournal.org Page 1395 International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 Rezai (1999) found that the first mode was the primary mode of vibration with very little contribution from higher modes. The top storeys exhibited behaviour that suggested that flexural behaviour dominated, while the bottom storey acted as a shear panel throughout the test sequence. Based on the load vs. deformation plots for all four storeys, it was shown that the first storey dissipated the majority of energy, while the top floors acted as a rigid body rotating about the first floor. Also, it was found that the flexural strains generated in the intermediate level beams could be considered negligible. Rezai (1999) also conducted sensitivity analyses to assess the effects of various structural properties on the value of the angle of inclination of the infill plate tension field, α. One structural property was changed while the remainder were kept constant. Five different test specimens were used.It was found that α did not vary significantly for any change in beam and column cross-sectional area and for infill plate thicknesses, t, of 6 mm and greater. 11. Astaneh-Asl (2001) An attempt at compiling a comprehensive document detailing the behaviour and design of steel plate shear walls was made by Astaneh-Asl (2001). Both stiffened and unstiffened panels were examined and it was recommended that unstiffened infill plates be used unless there are openings in the shear wall that require stiffening. A chart was prepared for checking each member in a steel plate shear wall system. Ductile failure modes are ranked as more desirable than brittle failure modes and are arranged first. 12. Kulak et al. (2001) Kulak et al. (2001) presented an overview of steel plate shear wall research conducted to date. A design example of a hypothetical eight-storey building in Vancouver, Canada, using steel plate shear walls as the lateral load resisting system, was also presented. The preliminary design was performed using the equivalent brace method and the detailed design was performed using the strip model (Thorburn et al. 1983). The inelastic static and dynamic response of the shear wall was also analyzed using a tension-compression strip model, which is an extension of the tension–only strip model and has inclined strips in both directions to resist lateral load in either direction. A nonlinear pushover analysis was conducted on the tension–compression strip model and it was found that the shear wall had an over strength of about two times with respect to the NBCC 1995 design shear. This over strength resulted largely from using a minimum infill plate thickness of 4.8 mm, which was considerably greater than what was required as determined during the preliminary design. A nonlinear dynamic time history analysis showed that the inter storey drifts were well within the NBCC 1995 seismic limits, which implies that both structural and nonstructural elements are protected from damage due to the stiffness of the steel plate shear wall. 13.Bruneau And Bhagwagar (2002) Bruneau and Bhagwagar conducted nonlinear inelastic dynamic analyses to investigate how structural ISSN: 2231-5381 behavior is affected when thin infills of steel, low-yield steel and other nonmetallic materials are used to seismically retrofit steel frames located in regions of low and high seismicity, namely, New York City and Memphis. A typical three-bay frame extracted from an actual 20- story hospital building in New York City was considered for this purpose. Fully rigid and perfectly flexible frame connection rigidities were considered to capture the extremes of frame behavior. Thin steel infill panels were found to reduce story drifts without significant increases in floor accelerations, and low-yield steel was found to lead to slightly better seismic behavior than A572 Grade 50 steel under extreme seismic conditions, but at the cost of some extra material. 14. Behbahanifard et al. (2003) Behbahanifard et al. (2003) conducted an experimental and numerical investigation of steel plate shear walls. The test specimen was taken directly from the one tested by Driver et al. (1998a), with the bottom panel removed due to the damage from the original test, thus creating a large–scale, three-storey, single–bay specimen. The loading sequence followed ATC-24 guidelines. Before the ultimate strength of the specimen was reached, the first–level beam ruptured at the top flange and web of the beam-to-column connection (after 50 cycles of load, including the original test). Since one of the objectives of the test was to observe the ultimate capacity of the wall and behaviour of the boundary members under extreme loading conditions, the fracture was repaired and testing continued. The specimen reached its ultimate capacity at a deflection of seven times the yield deflection, at which point the strength started to deteriorate gradually due to the formation of tears in the lower–storey infill plate. The specimen displayed high elastic stiffness, excellent ductility, the ability to dissipate high amounts of energy, stable hysteresis loops, and a high degree of redundancy. A finite element model was also developed for analysis of steel plate shear walls. Using this finite element model, a parametric study was conducted to identify parameters affecting the behaviour of a single panel steel plate shear wall. It was found that altering the aspect ratio of the infill plates within the range of 1.0 to 2.0 had a negligible effect on the behaviour of the shear wall panel. However, for aspect ratios less than 1.0, both stiffness and shear capacity of the panel increase. Increasing the ratio of the axial stiffness of the infill plate to that of the columns (tL/2Ac) led to an increase in the stiffness of the shear wall panel, but had a negligible effect on the shear capacity of the system. 15. Berman and Bruneau (2003) Using plastic analysis theory and the assumption of discrete strips to represent the infill plate, Berman and Bruneau (2003) derived equations to calculate the ultimate strength of singleand multi-storey steel plate shear walls with either simple or rigid beam-to column connections. For multi-storey shear walls, equations were developed based on two types of failure mechanisms that provide a rough range of ultimate strengths: soft storey failure and uniform yielding of the infill plates in all storeys simultaneously. To provide a lower bound estimate http://www.ijettjournal.org Page 1396 International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013 of capacity, the equation derived for single–storey steel plate shear walls with simple beam-to-column connections was used to predict the capacity of a variety of single- and multistorey steel plate shear wall specimens from the literature having either pinned or semi-rigid connections. This equation was found to underestimate the experimental capacities by an average of about 6%, although it overestimated the capacity of one case by about 9%. The equation derived for the soft storey mechanism was found to overestimate the capacity of multistorey test specimens with rigid connections by about 17%. This model provides only the ultimate capacity. The proposed equations do not describe the initial stiffness, the ductility, or the actual failure mechanism, nor do they provide a means of determining the frame forces for use in design. 16.Kharrazi, Ventura, Prion, And Sabouri-Ghomi (2004) Kharrazi et al.(2004) investigated the design of SPSW systems in terms of the separate shear and bending deformations occurring in a multi-story frame. They proposed a modified plate-frame interaction model for the analysis of shear and bending deformations and resulting forces in SPSW. The objective was to describe the interaction between those components and characterize the respective contributions to deformations and strength. The bending component of plate wall behavior was investigated. Equations for moment and displacement were derived for a single-story panel at the critical point at which panel bucking occurs, assuming a linear strain distribution across the wall cross-section. The procedure assumes that, after panel bucking, the neutral axis will move toward the column in tension, since compressive stresses in the web will be released, similar to the neutral axis migration in a reinforced concrete beam following section cracking on the tension side. Expressions were developed for behavior of the panel after this event. Equations for shear behavior and bending behavior are combined using interaction equations to complete the proposed method. III. CONCLUSIONS Thin unstiffened steel plate shear wall (SPSW) is rapidly gaining popularity as a very effective lateral load resisting system in highly seismic areas. A valuable research works have been performed on SPSW worldwide to evaluate the static and dynamic behavior of SPSW for the past three decades. A detailed summary of these research and development activities on various aspects of SPSW systems have been presented which might be useful for researcher and engineers in order to formulate efficient seismic design and analysis techniques. Design methods need to be developed for non-seismic loading, such as, wind, blast, fire, etc. In order to make the analysis and design methods for SPSW convenient for practical purposes new modeling techniques are also necessary. It is expected that actual use of this relatively new lateral load resisting system will greatly increase in the coming decade through an effective cooperation among researchers, code writers, practicing engineers and developers. ISSN: 2231-5381 ACKNOWLEDGMENT The authors acknowledge the authors, editors and publishers of all those articles, journals and books from where the literature of this article has been reviewed and discussed. REFERENCES 1.Thorburn, L.J., Kulak, G.L., and Montgomery, C.J. (1983). 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Structural Engineering ASCE, 6: 878-889. 18.Steel Plate Shear Wall Buildings: Design Requirements and Research by Michel Bruneau, P.E., Jeff Berman, Diego Lopez Garcia, and Darren Vian 19. A Closer Look at Steel Plate Shear Walls By Jason Ericksen, S.E., and rafael sabelli, S.E. Steel Solution centre ,January 2008,Modern Steel Construction. 20. Steel Plate Shear Walls: Practical Design and Construction By Ignasius F. Seilie, P.E. and John D. Hooper, P.E.(, Modern Steel Construction, April 2005)( 21.AISC Design Guide 20, Steel Plate Shear Walls -2007 22. Jonah J.Shishkin,Robert G. Driver and Gilbert Y.Grondin(2005). Analysis of steel plate shear Walls using modified stip model. Structural Engineering Report No. 261, Department of Civil Engineering, University of Alberta,Edmonton, Alberta, Canada. http://www.ijettjournal.org Page 1397