Figure 1. A Typical 3 Storey SPSW System
Steel Plate Shear Walls (SPSW) can be used as an effective lateral load resisting system, both in new constructions as well as for retrofitting purpose in highly seismic zones. Many of the experimental and numerical investigations on SPSWs have supported the logic of using the post buckling strength with formation of tension fields, good ductility, and high energy dissipating capability when subjected to cyclic loading. In the present paper, Ritz modal analysis and linear dynamic analysis were performed using El Centro, Cape Mendocino & Northridge Earthquakes Ground motion data as inputs to FE Models of a series of perforated single-storey, double-storey & four-storey SPSW system with variation in perforation diameter and perforation patterns with two different types of stiffening conditions, i.e. highly stiffened and lightly stiffened at the floor beam levels. The seismic responses such as lateral stiffness, roof displacement, and base shear were compared and presented. It was observed that, with the increase in perforation diameters and number of perforations, the lateral stiffness of the SPSW system tend to be decreasing and the roof displacement increases for all the three ground motion data and in almost all the models. In the present cases, SAP2000 has been used as a modelling and analysis tool.
Since the last decade, Steel Plate Shear Walls (SPSW) have gained both interest and popularity as an effective Lateral Load Resisting system. Significant stiffness and strength being the key feature of SPSW systems, it makes them a viable alternate solution to the most practised massive RCC Shear walls. Being Lightweight, the SPSW provide higher gross footprint area and saving in construction time. During the past few years, researchers and structural engineers in various countries have studied the behaviour of the SPSW system especially to lateral loads. Their studies have proven that, the SPSW system possesses resilient cyclic behaviour and hence these can be considered as one of the most ductile earthquake resistant systems. The main function of a SPSW system is to resist shear forces and overturning moments due to lateral loads arising from Earthquake and wind forces. The system consists of steel plate panels connected at all four sides by a steel frame consisting of beams and columns which are mostly referred as the horizontal and vertical boundary elements respectively. Typically, the beams are positioned at all the floor levels and the column location is determined by architectural requirements. However, in some SPSW applications, the minimum available thickness of infill plate might be thicker than required by design. As per the capacity design methods [16], at development of the system's plastic mechanism, yielding of the SPSW infill plates induces relatively larger demands to the surrounding boundary elements and consequently increases the sizes of horizontal and vertical boundary members. A number of solutions have been proposed by the below researchers to attenuate this concern, either by changing properties of the infill plate by using thin light-gauge cold-rolled steel plate panels (Berman, and Bruneau, 2005), using low yield strength steel panels (Vian, and Bruneau, 2004), or introducing multiple regularly spaced perforations, also known as perforated SPSW (Vian, et al.,). The later solution appears to be viable and at the same time it can accommodate the need for utility systems to pass-through the infill plate, without unfavourable effects to the SPSW system.
Steel plate shear walls, have been used in various buildings as a resistance system against lateral load specially force of the earthquake since 1970. The first building that used in steel shear walls was a Twenty-storey Nippon Steel Building in Tokyo. In third, high building in Tokyo named Shinjuku Nomura, height of 211m, and 51 floors from ground level and a height of 27.5 m and 5 floors in underground, steel plate shear walls have been used in the central core (which is around elevators, stairs, facility risers), in order to avoid the use of the RCC shear wall. For a thousand-room hotel placed in Dallas, the designer used steel shear walls in order to resist lateral forces, especially wind. Steel shear walls act like vertical cantilevered Plate girders in which the columns act as flanges, the beams act as stiffeners and the steel infill panels act as the web of it. The system of steel plate shear walls had a good performance in experimental studies Northridge (1994), America and Kobe (1995), and Japan strong earthquakes. A 3-storey SPSW system is shown in Figure 1.
Figure 1. A Typical 3 Storey SPSW System
The SPSW system can be both stiffened and unstiffened. While using thicker plates, it induces large demands of the surrounding members, using thinner ones poses difficulties in fabrication. Hence, in the present paper, the behaviour of a combination of highly stiffened to lightly stiffen SPSW having different patterns of circular openings are studied.
Initially, the stiffness of a series of single storied frames with various perforation patterns and diameters were calculated by carrying out Modal Analysis in SAP2000. Modal analysis, or the mode-superposition method, is a linear dynamic-response procedure which evaluates and superimposes free-vibration mode shapes to characterize displacement patterns. Mode shapes describe the configurations into which a structure will naturally displace. Typically, lateral displacement patterns are of primary concern. Mode shapes of low-order mathematical expression tend to provide the greatest contribution to structural response. As orders increase, mode shapes contribute less, and are predicted less reliably. It is reasonable to truncate analysis when the number of mode shapes is sufficient. A structure with N degrees of freedom will have N corresponding mode shapes. Each mode shape is an independent and a normalized displacement pattern which may be amplified and superimposed to create a resultant displacement pattern. In this study forces in X directions are only concerned with, hence only 4 modes have been considered and the initial mode shape has been considered for the Time period output of the structure.
The Singles storey bay frames with and without the perforated SPSW frames with various perforation patterns and diameters have been studied under the Linear dynamic History of1992 Cape Mendocino earthquakes. A comparative study has been carried out between Highly stiffened and Lightly stiffened Perforated SPSW systems with various perforation patterns using various storey heights of steel building frames ranging from 2 stories to 4 stories under the Linear Dynamic History of 3 Earthquakes i.e. (i) El Centro Earthquake 1940 (ii) Cape Mendocino earthquakes (1992) and (iii) Northridge Earthquake 1994. The Earthquake responses have been compared and tabulated to study the important parameters for the behaviors of the system. Linear dynamic analysis is also called Time History Analysis, is a technique for determining the dynamic response of a structure subjected any general time dependent loads. This type of analysis is used to determine the time-varying displacements and stresses. It incorporates the real time earthquake ground motions and gives the true picture of the possible deformation and collapse mechanism in a structure. The acceleration time history data were collected from the PEERI Berkeley website [18] taken as the input for the dynamic loading.
Sabouri Ghomi and Roberts (1992) conducted a series of quasi-static cyclic loading tests on unstiffened steel shear panels with centrally placed circular openings and found that, all the tested panels exhibited adequate ductility and stable S-shaped hysteresis loops with the energy absorbed per cycle increasing with the maximum amplitude of the shear displacement [11].
A. Deylami & H. Daftari (2000) analyzed more than 50 models by non-linear FE program NISA-II to study the effect of geometrical parameters like plate thickness, opening aspect ratio and opening percentage. They proposed the optimized aspect ratio for opening and shown that, it depends mostly on the plate thickness rather than opening percentage & shown that, for a given opening parentage, the thinner plates attain their maximum shear capacity with smaller aspect ratio of the openings[19].
Hitaka & Matsui (2003) tested SPSW with vertical slits. Test results were presented for 42 wall plate specimens which were subjected to static monotonic and cyclic lateral loading and inferred that, the steel plate segments between the slits behave like series of flexural links, which provide a fairly ductile response without the need of any heavy stiffening of the wall [20].
D Vian & M Bruneau (2004 & 2009) compared Experimental and Analytical results from an investigation of specially detailed ductile perforated SPSWs which are low yield strength steel infill panels and had beams with reduced sections connection and recommended the design procedure [1,4].
Ricky Chan, et al. (2011) studied the stiffness and strength of perforated SPSW through nonlinear FE technique and found that under monotonic loading, perforations reduce strength and stiffness of the system, promote more uniform stress on panels and reduce deformation demand on surrounding frame elements. On this study basis, they proposed a simple linear reduction function [6].
H. Valizadeh, et al. (2011) tested 8 no's of 1:6 scaled specimens of SPSW with central circular openings to study the effect of opening dimensions and slenderness factors of plates under cyclic hysteretic loadings and found stable and desired hysteresis behavior of SPSW for large displacements of upto 6% drift [19].
M.A. Barkhordari, et al. (2014) studied the behavior of SPSWs with stiffened full height rectangular openings with a series of single and multistoried SPSWs of varying aspect ratios with different opening features and found that, the relative reduction in strength & initial stiffness due to the openings can be reasonably assessed based on the relative reduction in infill plate area [21].
M. Hajsadeghi, et al., (2015) carried out the Non-Linear buckling analysis of steel plate shear walls with trapezoidally corrugated and perforated infill plates [22].
A.K. Bhowmick, (2009) examined the behaviour of unstiffened steel plate shear walls with circular perforations in the infill. & developed a shear strength model based on a strip model, where all the strips with perforations are discounted. Eight perforation patterns in single storey steel plate shear walls of two different aspect ratios were analysed using a non-linear finite element model to assess the proposed shear strength model. The proposed shear strength model for perforated shear walls was applied for design of boundary columns of one 4-storey shear wall. The predicted design forces (axial forces and bending moments) in the boundary columns for the 4-storey perforated shear wall were compared to the forces obtained from nonlinear seismic analysis [2].
Erfan Alavi and Fariboiz, (2012), studied the seismic behavior of unstiffened and diagonally stiffened and centrally perforated SPSW system experimentally by subjecting them to cyclic quasi-static loading. The test results also shown that, the ductility ratio of the specially perforated specimen was about 14% greater than the unstiffened specimen. A formula was developed on the basis of the study and the shear strength was estimated for both type of panels [9]. Other than the above, many researchers [13, and 14], from various countries have studied the behavior of perforated SPSWs which have provided valuable inputs for this investigation.
Capacity Design Method being the main design procedure for SPSW system (AISC & CN/CSA Codes) [4, 5, 8, 17], especially for earthquake prone zones, many of the above authors have found the required parameters which govern the design, i.e. using either thin steel panels or thick panels with perforations. The location, size, shape or percentage of opening, however depends on the effect they have on the response of the structure to required loading conditions. However, this paper focuses on only the numerical simulation of different SPSW models with different perforation diameters and patterns. Their response to different earthquake situations have been compared and presented.
The main intention of the study is to analyze and compare the responses such as roof displacement and base shear of the perforated steel plate shear walls, when they are used in multistoried building frames subjected to seismic lateral loads.
The primary objectives of the study are as under:
1. To analyze the single storey steel frame with and without perforated steel infill plate having,
2. To analyze the Two & Four storey steel frames with and without steel infill plate having,
3. To Analyze Lightly Stiffened SPSW with different perforation patterns.
Step 1: Modelling the single storey, 2-storey & 4-storey steel, bay frames with and without perforated SPSW with different perforation patterns & different perforation diameters. Perforation locations were determined using the Tension strip method.
Step 2: Removal of one horizontal stiffener each of alternate floor levels for the 2 & 4 storey bay frames.
Step 3: Performing Modal Analysis uses SAP2000 for arriving at fundamental time period “T” using Ritz Method because for the same number of nodes, Ritz vectors provide a better participation factor which enables the analysis to run faster with the same level of accuracy as Eigen Vectors.
Step 4: Calculating the stiffness of the models manually using “T” (from step 3) as an input.
Step 5: Performing linear dynamic time history analysis using SAP2000 to get the maximum displacement & maximum base shear.
Step 6: Summarizing, tabulating & comparing the results.
For the current numerical study, the bay width, storey height, the frame sections & plate thickness have been considered from past literatures [5] and [8] as shown in Table 1. All materials conform to ASTM A992 Grade 50 and the elastic properties are shown in Table 2.
Table 1. Details of Plate Thicknesses and Member Sizes for Different SPSWs
Table 2. Details of Material Properties
Initially a single storey bare frame and a single storey SPSW both with plate and boundary elements were modelled in SAP2000 finite element package tool. The geometrical data are tabulated in Table 2. All the frames are conforming to AISC seismic provisions [10] & AISC Design guide [23]. For both types of above frames, different patterns of circular perforations have been considered. Total seven types of perforation patterns and their locations on the infill panels have been illustrated in Figure 2. Three types of diameters were chosen for each and every perforation patterns, i.e. 400 mm, 500 mm and 600 mm. 23 models for single storey steel frames were modelled using SAP2000 Finite element software tool using Automatic frame and area fine meshes. The steel plate was modelled as shell elements and the frames were modelled as beam elements for the FE Analysis. The perforation Patterns have been chosen using the criteria, i.e. D/ Sdiag≤ 60%, where D is the perforation diameter and Sdiag is the tension field strip width, i.e. the diagonal distance between each line of perforations. In this study, all displacements are restrained for the base beam.
Figure 2. Types of Perforation Patterns
Initially Modal analysis was carried out using Ritz method to get the Fundamental Natural Time period of the Frame. From the “T” value, Circular frequency “ω” was arrived and the stiffness of the whole structural frame were founded out using the following equation,
All the single storey frames with and without SPSW and SPSW with seven types of perforation patterns were subjected to a dynamic Time history data for the 1992 Cape Mendocino OR Petrolia Earthquake as shown in Figure 3.
Figure 3. Ground Motion Curves of Cape Mendocino Earthquake 1992
From the Modal analysis, the stiffness's of all types of single storey frames has been calculated, tabulated and compared. The Time history analysis was carried out for 60 seconds and time step as 0.02 sec. The top beam displacement, Base Shear in X-direction, has been noted, tabulated and compared for various models.
For the 2 storey and 4 storey building frames, similarly as the single storey, initially a bare frame has been modelled using the beam elements. Then SPSW of 3.18 mm thickness were introduced in the bare frame. The second study intends here to check the stiffnesses and various seismic responses of the frame with one stiffener, i.e. the horizontal boundary element removed from every alternate floors, as shown in Figures 4(a) & 4(b). The infill plate of the frame were modelled using shell element of 4-nodes. The boundary condition provided for the frame was fixed at the bottom end.
Figure 4(a) Fully Stiffened 2-Storey SPSW System, (b) Lightly Stiffened 2-Storey SPSW System
Modal Analysis was carried out on the 2 and 4 storey frames and the fundamental natural time period was arrived as an output. The time period “T” was used as an input to derive the circular frequency and hence the stiffness of the system using Equation (1). The results were tabulated and compared using graphs.
For the time history analysis, the loading was provided dynamically in order to produce a dynamic effect on the frame. In total, 3 numbers of Earthquake data, i.e. El Centro (1940), [Figure 5(a)] Northridge (1994) & [Figure 5(b)] Cape Mendocino (1992) earthquake ground-motion records in terms of acceleration vs. time history were taken as input dynamic loading. The duration of time were taken from one to 53.76 seconds, 60 seconds and 60 seconds for the three earthquakes respectively. The outputs such as maximum top beam displacement, maximum base shear was noted, tabulated and compared using graphs.
Figure 5(a) Ground Motion Curves of El Centro Earthquake 1940, (b) Ground Motion Curves of Northridge Earthquake 1995
Perforation Patterns of type 4, 5, 6 & 7 (as shown in Figure 2) of 500 mm diameter were introduced for the 2-storey and 4-storey lightly stiffened Steel Plate Shear wall system and modelled using SAP2000 finite element analysis tool as shown in Figure 6. This case study intends to check the stiffnesses and various seismic responses of the frame with one stiffener having perforated SPSWs of different patterns. The Plates were modelled using thin shell elements of 3.18 mm thickness and frames were modelled as beam elements using the SAP2000 Finite Element Tool. The boundary condition provided for the 2 & 4 storey frame was fixed at the bottom end.
Figure 6. FE Mesh of 2 and 4 Storey SPSW with Type 7 Perforations
Modal analysis was carried out to calculate the stiffness of the multistoried frames with perforated SPSW. For the time history analysis, the loading was provided as dynamic loads by using the Time history data of the Earthquakes taken from the Case (II) and the results for all the frames were noted, tabulated and compared.
During this numerical study, effects of solid and perforated steel infill plate on seismic behavior of single storey frames were investigated. The stiffness graph, (Figure 7) displacement graph, (Figure 8(a)) & the base shear graph (Figure 8(b)) were taken into account for the study. The effect on the stiffness of the frames were inferred from the modal analysis. Stiffness of the single storey frames are tabulated in Table 3. From the results it can be seen that, stiffness of the bare frame are increased enormously, i.e. by 250% when any type of perforated steel plate shear wall is introduced to the system. For all types of frames, the system attains maximum stiffness for the type 1, i.e. single central perforation. This is probably because of negligible amount of material loss for a single perforation and it hardly affects the structure's load resisting capability. For the pattern type 1, the stiffness is decreased by 1.10% & 2.33% when the diameter is increased by 100 mm, and 200 mm respectively. For the type 2 perforation pattern, i.e. two perforations in the horizontal direction at the top, i.e. below the top beam, the stiffness in decreased by 1.22% & 2.87% when the diameter is increased by 100 mm, and 200 mm respectively. For the type 3 perforation pattern, i.e. two perforations in the horizontal direction at the bottom, i.e. above the base beam, the stiffness in decreased by 1.87% & 4.05% when the diameter is increased by 100 mm and 200 mm respectively. For the type 4 perforation pattern, i.e. three perforations along the vertical bisector line of the plate, the stiffness in decreased by 2.93% & 6.63% when the diameter is increased by 100 mm and 200 mm respectively. For the type 5 perforation pattern, i.e. four number of perforations as shown in Figure 2, the stiffness in decreased by 8.30% & 7.83%, when the diameter is increased by 100 mm, and 200 mm respectively. For the type 6 perforation pattern, i.e. five number of perforations as shown in Figure 9, the stiffness in increased by 19.18% & 16.82%, when the diameter is increased by 100 mm, and 200 mm respectively. For the type 7 perforation pattern, i.e. nine regularly spaced number of perforations as shown in Figure 2, the stiffness in decreased by 11% & 20.84%, when the diameter is increased by 100 mm, and 200 mm respectively. It can be seen that, the stiffness in decreased with the increase in diameter and increase in number of perforations in all the cases except the type 6 perforations in which the stiffness in increasing with increase in diameter and number of perforations.
Table 3. Stiffness Results for the Single Storey Frames
Figure 7. Stiffness vs Perforation Patterns for the Single Storey Frames
Figure 8(a) Maximum Displacement vs. Perforation Patterns for the Single Storey Frames, (b) Base Shear vs. Perforation Patterns for the Single Storey Frames
Figure 9. Deformed Plate for Type 6 perforation Pattern for Single Storey Frame
The maximum displacement was noted at the time of 3.48 seconds for all types of frames for the Petrolia Earthquake. A similar behavior pattern is seen in case of maximum displacement of the structure as the stiffness behavior. The maximum displacement, i.e. the lateral displacement of the top storey of the frame at the time of 3.48 seconds seem to be decreased by almost 69% with the introduction of the perforated SPSW in the moment frame. With the increase in diameter, the lateral displacement is increased in all cases whereas, when the number of perforations is increased, the maximum displacement is increased in all cases except for type 7 and 400 mm diameter, where it is decreasing by 21%. The base shear is increased by 6.04% from bare frame to perforated SPSW of type 1 pattern, i.e. the single central perforation. For all types of patterns and with the increase in diameter, the changes seen in base shear are almost of negligible amount as shown in Table 4.
Table 4(a) Maximum Displacement vs Perforation Patterns for the Single Storey Frames, (b) Maximum Displacement vs Perforation Patterns for the Single Storey Frames
The linear time history analysis for 2 & 4-storey SPSW systems were performed for ground motion data of three earthquakes and the outputs, e.g. stiffness, maximum displacement & base shear are tabulated in Tables 5 to 7. The stiffness are increased enormously for both 2-storey & 4-storey frames with the introduction of steel plate shear walls. For the 2 storey frames, the percentage increase in stiffness from bare frame to SPSW is 570%, whereas for the 4 storey frames it is 740% (Figure 10). With the addition of 3.18 mm Steel plate, the system is becoming stiffer & hence the displacement in both the cases is decreased by significant amounts. For the 2-storey frame, when one horizontal member from each alternate floor was removed, the stiffness were decreased by 6.75%, whereas, for the 4- storey frame it was increased by 0.56% only.
Table 5. Stiffness for 2 & 4-Storey SPSW Systems
Table 6(a) Displacement for 2-Storey SPSW Systems, (b) Displacement for 4-Storey SPSW Systems
Table 7(a) Base Shear for 2-Storey Frames, (b) Base Shear for 4-Storey Frames
Figure 10. Stiffness for 2 & 4 Storey SPSW System
For fully stiffened, i.e. when there is a horizontal boundary member at each floor level, the percentage decrease in displacement from bare frame to frame with plate is 84.44%, 84.61% & 84.60% for the El Centro, Northridge & Petrolia Earthquake respectively. For lightly stiffened, i.e. when there is a horizontal boundary member at alternate floor level, the percentage decrease in displacement from bare frame to frame with plate is 85.11%, 85.36% & 85.26% for the El Centro, Northridge & Petrolia Earthquake respectively. For the 4-Storey fully stiffened solid SPSW systems, the percentage decrease in displacement from bare frame to frame with solid SPSW is 87.49%, 88.62% & 87.41% for the El Centro, Northridge & Petrolia Earthquake respectively, whereas for the lightly stiffened SPSW system, it is 88.29%, 89.34% & 88.21% respectively. In both the cases, i.e. in 2-storey & 4-storey frames, the displacement in lightly stiffened SPSW system are decreasing more than the fully stiffened case by 1% which is almost negligible, so for the perforation studies, the lightly stiffened SPSW system were chosen as it can save more material & hence the cost as compared to the fully stiffened solid SPSW Frames. In the 2-storey frames the base shear is increased by 7.62%, 6.86% & 6.87% in case of the fully stiffened SPSW system as compared to the bare frame, whereas for the lightly stiffened frame the base shear is decreased by 1.97%, 2.68% & 3.42% for the El Centro, Northridge & Petrolia Earthquakes respectively. In the 4-storey frames the base shear is increased by 5.96%, 2.15% & 5.91% in case of the fully stiffened SPSW system as compared to the bare frame, whereas for the lightly stiffened frame the base shear is decreased by 4.28%, 10.88% &4.37% for the El Centro, Northridge & Petrolia Earthquakes respectively, which justifies the reason of considering the lightly stiffened SPSW system for the perforation studies. Figure 11 shows the Maximum Displacement for 2-Storey SPSW Systems.
Figure 11. Maximum Displacement for 2-Storey SPSW Systems
The linear time history analysis for the lightly stiffenedperforated SPSW system was performed and the results such as stiffness, maximum displacement & maximum base shear are tabulated in Table 5 through 7 & Figures 12 through 14. From Table 5 it can be seen that, the stiffness are decreasing with the increase in no. of perforations which is quite justifiable to the fact of loss of material.
Figure 12. Maximum Displacement for 4-Storey SPSW Systems
Figure 13. Base Shear for 2-Storey Frames
Figure 14. Base Shear for 2-Storey Frames
For type 6 perforation pattern, the maximum decrease is seen in stiffness from the solid plate is 38.85% & 33.55% for the 2-Storey & 4-Storey frames respectively. The maximum increase in displacement is seen for type 6 pattern of perforation, where the percentage changes are 82.91%, 84.35% & 48.96% for the El Centro, Northridge & Petrolia earthquakes respectively for the 2-storey frames. In case of 4-storey frames, similar behavior was noticed for the type 6 pattern, where a maximum increase in displacement is seen for all the earthquakes, i.e. 64.94%, 66.12% & 65.82% respectively. The base shear in X-direction also shows the similar behavior as the displacement for both 2& 4 storey frames, i.e. maximum in case of type 6 perforations as compared to the lightly stiffened solid SPSW system.
For single storey frames, the stiffness increases by a significant amount when perforated steel plates are incorporated in the bare frame, the maximum percentage being 245%, which is seen in the case of the 400 mm DIA single central perforations. The lateral stiffness decreases steadily with the increase in no of perforations in all cases discussed till the type 5, i.e. 4 perforations after which, it decreases sharply by a notable amount for type 6, i.e. 5 perforations. With the increase in diameter also, the stiffness are seen to be decreased steadily for all the single storey cases discussed. Lateral displacement & Base shear responses for the single storey frames are showing similar behavior in line with lateral stiffness, i.e. with the incorporation of perforated plates, the displacement is seen to be decreased by a major amount. With the increase in number of perforations, the displacement is observed to be increased steadily for all diameters except for 400 mm dia type 6 (5 perforations), where it is decreasing and then increasing for type 7, i.e. 9 perforations. The lateral stiffness were observed to be reduced insignificantly by a percentage of 6.75% & 2% for the 2 & 4- storey frames respectively when one horizontal boundary member is removed from alternate floor level.
For all the earthquake inputs, with the increase in number of perforations, the displacement is seen to be increased steadily and decreased suddenly for type 7. However, the stiffness for the type 7 patterns remain minimum. This signifies the effect of perforation locations on the dynamic responses of the system. Percentage decrease in lateral displacement from bare frame to perforated SPSW is maximum in case of type 4 pattern (3 perforations) i.e. 83.5% & 87.7% for the 2 & 4-storey frames respectively. For all the perforated SPSW cases discussed under the three ground motion data, the lateral displacement is maximum for type 6 perforation pattern (5 perforations) & minimum for type 4 (3 perforations). The base shear is maximum in case of type 6 (5perforations) Patterned SPSWs for all cases and minimum for type 7 (9 perforations) & type 5 (4 perforations) pattern SPSWs for 2 & 4- storey frames respectively. Percentage decrease in base shear from bare frame to perforated SPSW is maximum in case of type 7 pattern (9 perforations), i.e. 2.40%.
As per FEMA 310 [16], the drift ratio of the steel moment frame shall be less than 0.015, i.e. maximum displacement upto 51 mm for the storey height of 3.4 m and it was checked for the present study, which satisfies the criteria for all the bare frames. A cutout on infill plate beyond a limit leads the system to an unstable phase. Beyond the numbers of perforations studied, no significant lateral stiffness was achieved and hence not much change is the seismic behavior has been noticed.
This paper presents a general comparative study for fully & lightly stiffened SPSW with various types of perforation patterns. To investigate more into the overall seismic behavior & other significant responses of the system, the heights of the frames may be increased to 6,8 & 10 stories with the simultaneous increase in plate thickness, so that, a detailed parametric study could be carried out and their effects could be arrived at.