A Numerical Study on the Seismic Behavior of Composite Steel Plate Shear Walls with Openings Soheil Kordbegli 1 and Farhang Farahbod 2 * 1 MSc in civil engineering structures, Department of Civil Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran. 2 PhD, 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 F y Specified minimum yield stress of the plate F u Specified minimum tensile strength µ Ductility coefficient D Ductility ratio E Modulus of elasticity E Absorbed energy K e Elastic stiffness P u Failure load K eff Effective or secant stiffness P peak Maximum absolute value of load resisted by the wall e Displacement at 0.4P peak Δ u Ultimate displacement Yield Displacement Δ yield 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. 6890
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) 1.2e Steel plate 200000 0.3 240 360 3 0.2 Columns and beams 200000 0.3 380 520 3 1.9e 0.2 Figure 1: Experimental model tested by [1] Bolt 200000 0.3 600 720 3 3e 0.2 Figure 2: Loading Sequenced Applied to the experimental model by [1] 6891
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 setup 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 C ABI / R 0.135. Now, the base shear force can be calculated as: V C W 0.135 12600 1700KN. 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 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.. Figure 3: Framing plan of the test set-up (a) 6892
Figure 6: Idealization of nonlinear response according to [11] (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 loaddisplacement curve idealized in Figure 6: i. Elastic stiffness (K e ): it can be expressed as a slope measured by the ratio of the resisted shear load to the corresponding displacement : K e = 0.4P peak e (1) 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). ii. iii. Effective or secant stiffness (k eff): which is the value of lateral force divided by the lateral displacement on force-displacement curve; Failure load (P u ): which is the load corresponding to the failure limit state on the envelope curve(fig. 4). it can be obtained as: P u = 0.8P peak (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 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 6893
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. 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 loaddisplacement 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 Figure 8: K-drift diagram 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 6894
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. REFERENCES [1]. Astaneh-Asl, A. 2001. Seismic Behavior and Design of Steel Shear Walls-SEONC Seminar". In: 2001 SEOANC Seminar on Structural Engineers Assoc. of Northern California, November 7, 2001, San Francisco, US. [2]. Zhao Q Zhao and Astane-Asl A. 2004. Experimental and analytical studies of cyclic behavior of steel and composite shear wall system. 6895
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