Effect of Different Inll Types and Welding Separation on the Cyclic Behavior of Steel Shear Walls

Currently, the steel plate shear wall (SPSW) is commonly used in high-rise steel buildings as a lateral load resisting system. The SPSW consists of the boundary frame and inll plate. The objectives of this work are to study the effect of same weight different inll plate types, the effect of boundary frame characteristics, and the effect of inll plate weld separation on the seismic behavior of the SPSWs. A numerical method was proposed to have a comprehensive comparison of seismic behaviors of different types of SPSWs, having the same weight. The model was validated by using previously published numerical and experimental works. The study covers unstiffened (USPSW), stiffened (SSPSW), and corrugated steel plate shear wall (CSPSW). Similarly, the effect of boundary frame stiffness and welding separation characteristics between the plate and boundary frame will be studied, and key issues, such as load-carrying capacity, stiffness, and energy-dissipation capacity were discussed deeply. It was found that the SSPSW has better seismic behavior than USPSW and CSPSW. SSPSW has a higher load-carrying capacity than USPSW, and CSPSW by about 14, 24%, respectively. USPSW is more sensitive to the stiffness of the boundary frame than CSPSW. The plate welding separation has a greater impact on the initial stiffness than load-carrying capacity. When plate-column welding separation occurs, the initial stiffness, and the energy dissipation capacity reduces by about 21%, and 14%. Whereas, when the plate-beam separation occurs, the initial stiffness and energy dissipation capacity reduce by about 36%, and 20.5%. type, frame welding separation characteristics for and which same weight, under cyclic loading test The cyclic nonlinear behavior of CSPSWs and SPSWs was studied. Finite element models were developed by using ABAQUS software. Experimental and numerical works from the literature were used to validate the nite element model. Different seismic behavior, load-carrying mechanism, load-carrying capacity, hysteretic behavior, and energy dissipation capacity were analyzed and compared for different parameters. Two main topics were focused on this paper; the rst topic is the seismic behavior of different kinds of SPSWs, having the same weight. The second topic is the effect of welding separation between the inll plate and the boundary frame.


Introduction
The steel plate shear wall consists of a boundary frame, sh plate, and in ll panel, as shown in Fig. 1a).
The steel plate shear wall is commonly used in high-rise steel buildings as a lateral load resisting system. Steel plate shear walls (SPSW) are preferred by designers due to many advantages such as lightweight, easy construction, and reduced structure reactions. SPSW is a lateral load resisting system with high lateral strength, initial stiffness (K 1 ), and shear performance, (Youssef et al. 2010;Yousuf and Bagchi 2010).
The SPSWs can be classi ed as follows: Unstiffened steel plate shear wall (USPSWs).
The CSPSWs can be classi ed according to the corrugation direction as follows: Horizontal corrugated steel plate shear wall (HCSPSWs).
Vertical corrugated steel plate shear wall (VCSPSWs). Some works focused on the seismic performance of USPSW. It was found that thin USPSW can achieve high post-buckling strength and good seismic behavior, which can be attributed to tension eld action. Using thin USPSW instead of thick USPSW produces early tension eld action that can dissipate more energy by acting as a plastic hinge (Thorburn et al. 1983). Single-span three-story USPSW was experimentally studied (Caccese et al. 1993). It was found that the thickness of the in ll panel has a great in uence on seismic behavior (Caccese et al. 1993). A cyclic test of four-story thin USPSW was conducted (Driver et al. 1998); the results showed good seismic performance, as story drift reached 4% before reached to failure and high energy dissipation capacity. Other works focused on the in ll plate interconnection with the boundary frame. The in ll plate interconnection effects on the structural behavior of steel plate shear walls were numerically studied (Paslar et al. 2020). The behavior of the partially connected plates with different interconnections types was compared to the fully connected in ll plate. It was found that a system with an 80% connection between in ll plate with boundary elements has a lower load-carrying capacity, stiffness, ductility, and energy-dissipation capacity than a fully-connection system. Although partially connected plates showed effects on the wall performance, the simulation of actual separation due to cracks was not involved in that study. A lot of studies focused on using SSPSW to improve seismic behavior (Hitaka and Matsui 2003b;Alinia and Dastfan 2007;Cao et al. 2008;Li et al. 2009;Alavi and Nateghi 2013b;Guo et al. 2017). Due to the favorable performance of the corrugated webs in the analysis and design of bridge plate girders, researchers started to utilize them in the SPSW as an in ll plate. The application of corrugated plates as the web of steel coupling beams was investigated (Shahmohammadi et al. 2013). It was found that using the corrugated web could achieve more rotation capacity than common steel coupling beams.
An equivalent classical plate model of corrugated structures was proposed and studied (Ye et al. 2014). Other studies were conducted on shear buckling and buckling tendency (Yi et al. 2008;Moon et al. 2009;Ye et al. 2014).
Due to its construction and structural performance advantages over the USPSW, many researchers moved toward studying the performance of CSPSW (Emami and Mo d 2014;Bahrebar et al. 2016;Dou et al. 2016;Shon et al. 2017). It was found that the energy dissipation capacity, ductility ratio, and the initial stiffness of the CSPSW are approximately 52%, 40%, and 20% greater than USPSW (Emami and Mo d 2014;Vigh et al. 2014). Shear buckling deformation of corrugated metal was studied, and an equation to calculate the global shear buckling of corrugated metal was proposed (Easley and McFarland 1969). An experimental study on the shear hysteresis behavior of CSPSWs was conducted (Shon et al. 2017). It was found that CSPSWs have good seismic behavior, high carrying moment capacity, energy dissipation capacity, and high initial stiffness. In addition to experimental results, numerical methods were used in the analysis of SPSW (Dou et al. 2016). Results showed that repeating the number of corrugations has a great effect on lateral strength. Comparative studies were conducted on the shear buckling behavior of trapezoidal and sinusoidal corrugated steel plates (Zhao et al. 2017). It was found that sinusoidal corrugation has slightly greater lateral strength than trapezoidal corrugation with the same fold length. Although a lot of research works focus on the behavior of the USPSWs. This paper has two main purposes; The rst purpose is to perform a comparative study to investigate the different behaviors of the Problem Description A typical two groups of thin USPSW, SSPSW, and CSPSW systems were modeled using ABAQUS software. The rst group represents the strong boundary frame case (denoted as S), and the second group represents the weak boundary frame case (denoted as W). The parametric study includes the effect of panel type, stiffness of boundary elements, and welding separation characteristics. Panel type can be plane (P), stiffened, or sinusoidal corrugated panel. The sinusoidal corrugation direction can be horizontal (H) or vertical (V). In this study, for the case of stiffened panels, only horizontal stiffeners case (HS) will be studied.
The samples were as following: SPt5, SPt6.75 represent the strong cases of the plane with thickness 5, 6.75 mm, respectively. SHt5, SVt5 represents the strong cases of the horizontal and vertical corrugated panel.
SPt5-HS represents the strong cases of the stiffened plane steel shear wall.
The models of SPt6.75, SHt5, SVt5, and SPt5-HS have the same weight per unit area. Figure 3 shows the geometry of the strong case SPt5 & SPt6.75,SHt5,SVt5, In the weak case, the boundary frame was 40% lower bending stiffness than the strong case. The beam section was HM400×300×10×16 equivalent to W16×67 and the column section was HW350×350×12×19 equivalent to W14×90. Wall panels had a height of 3000 mm, a span of 3000 mm, and a thickness of 5 mm.
The samples were as following: wall with in ll plates that have different types and the same weight per unit area. The second purpose of this study is to investigate the effect of welding separation that can happen due to aging, cyclic load due to wind or fabrication de ciency, and its effect on the hysteretic and other behaviors will be investigated. This paper studied more parameters such as in ll plate type, boundary frame stiffness, and welding separation characteristics for USPSWs, CSPSWs, and SSPSW, which have the same weight, under cyclic loading test Fig. 1.c. The cyclic nonlinear behavior of CSPSWs and SPSWs was studied. Finite element models were developed by using ABAQUS software. Experimental and numerical works from the literature were used to validate the nite element model. Different seismic behavior, load-carrying mechanism, loadcarrying capacity, hysteretic behavior, and energy dissipation capacity were analyzed and compared for different parameters. Two main topics were focused on this paper; the rst topic is the seismic behavior of different kinds of SPSWs, having the same weight. The second topic is the effect of welding separation between the in ll plate and the boundary frame.
WPt5 represents the weak cases of the plane wall.
WHt5, WVt5 represent the weak cases of the horizontal, vertical corrugation walls, respectively.
WPt5-HS represents the weak cases of the stiffened plane steel shear wall.
All the models of WHt5, WVt5, and WPt5-HS have the same weight per unit area. Figure 1d) shows the section of stiffeners used in SPt5-HS and WPt5-HS. The height of the stiffeners was 120 mm. The stiffener ange was 60 mm, and the thickness of the stiffeners was 5 mm. Figure 4 shows the geometry of weak case WPt5, WHt5, WVt5, and WPt5-HS.
Additional models were created to study the effect of welding crack/separation. The Models were as following: PS1 and PS2 represent the plate welding separation with one column and beam, respectively. The separation length was 3000 mm (whole length).
PS3 represents corner beam separation with a length of 1000 mm.
PS4 represents middle beam separation with a length of 1000 mm.
PS5 represents corner beam separation with a length of 2000 mm. The location weld separation can happen randomly due to the effect of aging deterioration. The separation due to the vertical and horizontal load happens at the location of stress concentrations. A preliminary study was done to investigate the separation length that can provide a signi cant effect on the wall behavior. The model PS1, PS2 studied the effect of plate Colum, and Beam full separation to know which element separation has more effect on the USPSW seismic behavior. It was observed that USPSW is more sensitive to beam welding separation than column welding separation, so the effect of plate-beam welding separation was studied deeply in the models PS3, PS4, and PS5. The models PS3, PS4 studied the effect of beam separation location to know which location has an obvious effect on the seismic behavior. The model PS3 studied the plate corner separation, where tension elds start to form. The model PS4 studied the plate middle separation as the maximum out-of-plane deformation occurs at the plate center. The separation length was one-third of the plate width. The model PS5 represents a combination of plate corner and middle separation.
All walls have the same width and height and the same aspect ratio (Ratio) of one. The wavelength of the corrugation is 300 mm, with a 60 mm amplitude, as shown in Fig. 1b). The VCSPSWs and HCSPSWs have the same wavelength, amplitude, and corrugation with different directions of the corrugated panel, i.e., H or V. The USPSW with stiffeners had the same weight as the CSPSW. The difference between the fold length (the original length of the corrugated panel before corrugation) and panel length determines the stiffener's size. The parametric case study is shown in Table 1.

FINITE ELEMENT MODELING
To study the nonlinear behaviors of USPSW, SSPSW, and CSPSW, accurate nite element analysis should be conducted. The boundary frame and in ll panel were modeled using quadrilateral shell elements (S4R), to avoid shear locking phenomena (Tessler and Spiridigliozzi 1988;Abaqus et al. 2013). Shear locking phenomena can be de ned as the unintentional generation of shearing deformation rather than the desired bending deformation. Therefore, the element becomes too stiff and the overall de ections are lesser. This phenomenon could have happened mainly with fully integrated, rst order, solid linear elements subjected to bending loads. It can be avoided by using higher-order elements like quadratic elements and do not use the linear elements if there is a bending load. Therefore, quadrilateral shell elements with reduced-integration (S4R) were used (Abaqus et al. 2013).
Structural modeling, mechanical properties of materials, the boundary condition of models, and time history of loading and initial defect are presented in detail as follows.

Mechanical Properties of Steel Materials
For the parametric study, the boundary frame steel and the in ll panel materials have a yielding strength of 345 MPA and 235 MPA, respectively. The materials elastic modulus E = 206000 MPA, Poisson's ratio ν = 0.3 and hardening modulus E h = E/100. The four-node shell element S4R with reduced integration was used for the modeling of all members. Material and geometric nonlinearity was taken into consideration in the analysis. After the material reaches to yield point, the response of the system becomes nonlinear and irreversible. Moreover, the response of the material under cyclic and monotonic loading is different; therefore, material nonlinearity should be taken into consideration (Shi et al. 2011). Due to changes in geometric out-of-plane deformation of the system during the loading process, reciprocating two-way tension elds snapped through the shape of the corrugated panel and zero or negative stiffness phenomena, the geometric nonlinearity should be taken into consideration. The isotropic hardening behavior was considered (Abaqus et al. 2013).

Modal Analysis and Initial Defect
The initial defect of out-of-plane or out-of-plane initial imperfection, which may occur due to the manufacturing process, storage, and installation process, should be taken into consideration in the cyclic analysis as it might affect the plate strength. Initial imperfection was set as 1/1000 of the plate length in the previous researches of the thin USPSW. Due to the higher out-of-plane stiffness of CSPSW, initial imperfection was set as 1/750 of panel height in this study (Nie et al. 2013b). ABAQUS command "Imperfection" was used to modify the coordinates of plate nodes using major buckling modes The eigenvalue buckling analysis was used to evaluate the imperfection distribution over the panel by multiplying the rst buckling mode by the scale factor.

Boundary Conditions and History Loading
The nonlinear cyclic analysis was conducted on groups of thin USPSW (e.g. SPt6.75, SPt5, WPt5, PS1, PS2, PS3, PS4, and PS5), CSPSW (e.g. SHt5, SVt5, WHt5, and WVt5), and SSPSW (e.g. SPt5-HS, and WPt5-HS). The lateral displacement was applied on the exterior column ange on the top right panel zone. The lateral displacement was increased gradually to produce drift ratios of 0.25%, 0.5%, 1%, 1.5%, 2%, 2.5%, 3% and 4%. Each amplitude was repeated twice, as shown in Fig. 1c). The column base region had a xed boundary condition, in which all these nodes were restrained in all the six degrees of freedom. To prevent the out-of-plane buckling of the whole system, the out-of-plane displacement for the nodes of the beam centerline and all nodes of the column and beam connections were constrained. These constraints consider the out-of-plane bracing provided by the oor system.

Experimental Work Details and Numerical Model Validation
To verify the accuracy of numerical simulation, previously published quasi-static test results were used (Park et al. 2007;Zhao et al. 2017). Finite element models were created, and the hysteretic curves were compared to the experimental results.

Tested Specimens
Five USPSW specimens with a single bay and three stories were tested where the specimen SC4T was selected for validation in this study (Park et al. 2007). The height, width, and thickness of the plates were 1000 mm, 1500 mm, and 5 mm, respectively. The section of the internal beams was H200×200×16×16 mm, and the top beam and the columns sections were H400×200×16×16 and H250×250×20×20, respectively. The detailed dimensions of the specimen are shown in Fig. 6a).

Numerical simulation
The material of in ll panels and boundary elements was steel SM490 with yield stress F y = 330 MPa. The Chaboche constitutive model (Chaboche 1986(Chaboche , 1989) is adopted; therefore, the combined hardening behavior was considered (Abaqus et al. 2013). This rule should be determined to perform a cyclic analysis and predict deformation behavior. A combined hardening model includes isotropic and nonlinear kinematic hardening rules. This model was rstly summarized by (Chaboche et al.). In the model, two parameters for isotropic hardening (i.e.Q ∞ and b), and eight parameters for nonlinear kinematic hardening containing four back stresses (i.e. C 1 , γ 1 , C 2 , γ 2 , C 3 , γ 3, C 4 , γ 4 ). Cyclic stress versus strain curve should be required to determine the isotropic hardening parameters Q ∞ and b. Therefore, Q ∞ can be determined from the difference between cyclic and monotonic stress versus strain curves. The value of b can be determined from the tting of peak stresses for each cycle. Whereas the parameters of nonlinear kinematic hardening model can be determined from hysteretic loop dada from strain-controlled roud bar tensile tests (Ryu et al. 2018). Several cyclic hardening parameters of the material should be assigned such as the kinematic hardening modulus (C), the rate at which hardening modulus decreases with the plastic strain (γ), the maximum change in the size of the yield surface (Q ∞), and is the rate at which initial yield stress change with the plastic strain (b) (Abaqus et al. 2013). The cyclic hardening parameters of the material are shown in Table 2. S4R elements were used to simulate the boundary frame and in ll panel. The bottom of the model had a xed boundary condition, and the initial out-of-plane defect was selected 1/1000 of the steel plate height. The cyclic loading process is shown in Fig. 2a) where the loading test was applied using the reference point in the middle of the upper beam until the system is destroyed completely.

Results And Discussion
The deformed shape of the present nite element model for the sample SC4T is found in Figure 6 b). Besides, the load-displacement curves for the experiment test, previous and present FEM results can be seen in Figure 6 c) (Zhao et al. 2017). The previous nite element modeling shows differences in the maximum lateral capacities of about 7% and 9% in the positive and negative direction and some differences in hysteretic behavior. However, the present numerical simulation shows hysteretic behavior similar to the experimental results with a difference in the load-carrying capacity of 4%. The reason for the bigger difference between previous simulation and experimental results was the absence of a cyclic hardening parameter in the de nition of material. It can be concluded that the current numerical simulation technique can be used to predict the nonlinear behavior of SPSWs.

Numerical Work Validation
Another validation for this modeling technique was performed by using a previously published numerical study (Zhao et al. 2017). In that study, eight USPSW models with single-bay and one oor were studied (Zhao et al. 2017). The models SC-PW and SC-HSW were selected for the validation of the current FEM. The FEMs geometry and con gurations are shown in Figure7 a) and b). The wall dimensions were 3000×3000×5 mm, the length of the corrugation wave was 300 mm, and the amplitude was 60 mm. The boundary column's section was HW400×400×13×21 mm, and the top beam's section was HM500×300×11×15 mm. The material of the in ll panel has a yield strength of 235 MPa, while the boundary frame material has a yield strength of 345 MPa, with an elastic modulus E= 2.06 GPa, a Poisson's ratio ν = 0.3, and hardening modulus E h = 1/100E. For SC-PW, the present FEM had initial stiffness greater than the previous FEA by about 3% and by about 4.4% higher load-carrying capacity, as shown in Figure 7 c). For SC-HSW, the present simulation had less initial stiffness than the previous simulation by about 0.7% and by about 3.7% less load-carrying capacity, as shown in Figure 7 d). The current nite element modeling results have good agreement with the previously published works.

EFFECT OF PANEL TYPE AND DIRECTION OF CORRUGATION
To show the effect of panel type and direction of corrugation on the seismic behavior, the results of models SPt5, SHt5, SVt5, SPt5-HS, and SPt6.75 will be compared and discussed. Models SHt5, SVt5, SPt5-HS, and SPt6.75 have the same weight for comparison reasons. The nonlinear cyclic analysis was conducted on the ve models, and the hysteretic behavior was recorded.
Hysteretic behavior of strong SPSW walls SPt5, SVt5, SHt5, SPt5-HS, and SPt6.75 are shown in Figure 9, in which the drift ratio is presented on the x-axis (%) and load-carrying capacity is presented on the y-axis (kN). The hysteretic curves show that panel type and corrugation direction have an obvious effect on hysteretic behavior. From Figure 9 a), it is clear that SHt5 has a higher load-carrying capacity than SPt5 in the early stages up to ±1.5% drift. After SHt5 reached peak lateral strength, plastic buckling occurred.
Therefore, the load-carrying capacity of SHt5 is degraded faster than the case of SPt5, which uses tension eld action to have high post-buckling lateral strength. Also, Figure 9 a) shows the reduction of reloading stiffness, which can be attributed to the plastic deformation caused by the loading, unloading, and reloading in the opposite direction. Figure 9 b) shows that both SPt5-HS and SPt5 have the same lateral strength mechanism, which depends on tension eld action; this action produces post-buckling load capacity. The results show that SPt5-HS achieves plumper hysteresis behaviors and stiffness than SPt5. Figure 9 c) indicates that when the span-to-height ratio, panel thickness, and the boundary frame remain the same, corrugation direction has a signi cant effect on load-carrying capacity. SHt5 has a higher load-carrying capacity than SVt5 in the early stages. This might be attributed to the accordion effect, which means that the horizontal corrugations represent horizontal ribs, which resist lateral displacement. After SHt5 reached the yield, plastic buckling occurred in the panel; therefore, the load-carrying capacity of SHt5 became the same as SVt5. In general, Figure 9 a), d), and e) indicate that with the same weight, CSPSW has different lateral strength mechanisms than plane in ll USPSW or SSPSW.  Figure 9 d) shows that SPt5-HS has better seismic behavior than SHt5, hence after SHt5 reached peak load-carrying capacity, at lateral story drift ±1%, plastic deformations, and local buckling occur in the system. SHt5 load-carrying capacity starts to degrade faster, while SPt5-HS load-carrying capacity increases depending on tension eld action. Figure 9 e) shows a comparison between the hysteretic behaviors of SHt5 and SPt6.75, where both of them have the same weight. Figure 9 e) shows that SPt6.75 has better seismic behavior than SHt5. As, SHt5's load-carrying capacity decreases after reaches to the peak capacity at lateral drifts ±1%, while SPt6.75's lateral load capacity increases up to lateral drifts ±4%.
The backbones curves can be obtained from the hysteretic curve in both pull and push directions, as shown in Figure 9 f). For each drift, the highest load-carrying capacities for the rst cycle were extracted from the hysteretic curves in both directions to form the backbone curves (Zhao et al. 2017). The initial stiffness (K 1 ), the second cyclic stiffness (K 2 ), load-carrying capacity, yield points, and maximum points can be evaluated from backbone curves, as shown in Table 3. Here, the K 1 , K 2 stiffness is the system stiffness at drifts of 0.25, 0.5%, respectively. It can be calculated by Eq. (1) (Nie et al. 2008). The yield point Y is a point at which local buckling and plastic deformations appear in the system, which can be identi ed with the commonly used "Equivalent area method". Where Δ y is the yield displacement, V y is the yielding force, Δ m is the displacement at the maximum load-carrying capacity, and V m is the maximum load-carrying capacity.
From Figure 9 f) and Table 3, at the 0.5% drift in the push direction, it can be observed that the walls SHt5, SVt5, SPt5-HS, and SPt6.75 have higher K 2 stiffness than SPt5 by percentage values of 14.6, 15.6, 9, and 22.8%, respectively.
At story drifts of ±4%, SPt5 gives approximately the same load-carrying capacity of SHt5 and SVt5 which occurs at ±1% lateral drifts. At the 4% drift in the push direction, SPt5-HS, and SPt6.75 have a higher loadcarrying capacity than SPt5 by about 23, and 7.5%, respectively. The case of SPt5-HS has the maximum increasing percentage value. Therefore, the horizontal stiffened wall has better seismic behavior than a horizontal corrugated wall, which has the same weight.

EFFECT OF BOUNDARY FRAME STIFFNESS
In this section, the in uence of boundary element stiffness on the seismic behavior of USPSWs, SSPSWs, and CSPSWs will be studied deeply.
In this section, the hysteretic behaviors of corrugated steel plate wall, USPSW, and SSPSW with the weak case were compared with the strong case, as shown in Figure 10 a-d). It can be found that a system with weak stiffness boundary elements has a 40% lower stiffness than the strong systems. The same cyclic behavior with lower lateral strength and lower initial stiffness was observed. USPSW and SSPSW showed more sensitivity for weak boundary elements. The effect of weak boundary elements on lateral strength is more obvious for the horizontal HCSPSW systems SHt5 and WHt5 than the VCSPSW systems SVt5 and WVt5.
Backbone curves were extracted from hysteretic curves in pull and push direction for different models, as shown in Figure10 e). The K i , K 2 stiffness, yield, and maximum points were extracted from backbone curves, as shown in Table 4, as discussed in the previous section. Table 4, at the 0.5% drift in the push direction, it can be seen that reducing the boundary frame stiffness by about 40% causes K 2 stiffness degradation in the walls WPt5, WHt5 and WVt5, and WPt5-HS by percentage values of 16, 7, and 8%, respectively. It can be concluded that USPSWs (i.e. WPt5) and CSPSWs (i.e. WHt5 and WVt5) have the maximum and minimum reduction values, respectively.

From Figure10 e) and
At the 4% drift in the push direction, it can be observed that reducing the boundary frame stiffness causes load-carrying capacity degradation in the walls WPt5, WHt5, WVt5, and WPt5-HS by percentage values of 18, 12, 11, and 16%, respectively.
It can be concluded that the stiffness reduction of boundary members has a greater impact on loadcarrying capacity than the stiffness of the system. Plane steel plate walls and stiffened steel plane walls are more sensitive to the effect of boundary frame stiffness reduction. VCSPSW is less sensitive to boundary frame stiffness reduction. This might be attributed to the that the vertical corrugations represent vertical ribs, which resist the frame action.

EFFECT OF WELDING SEPARATION CHARACTERISTICS
To study the impact of welding separation/crack on the lateral strength, energy dissipation capacity, and cyclic behavior, ve FEMs with different welding separation characteristics were developed. As the plane wall, such as USPSW, was more sensitive to the boundary frame stiffness, the welding separation of the plane plate with the boundary frame was studied. The thicknesses of the plate and boundary frame elements remain the same as SPt5 for comparison reasons. Figure 5 shows the details of welding separation models PS1, PS2, PS3, PS4, and PS5, including the location and length of the separation.

Hysteretic Behavior and Backbone Curves of Systems with Welding Separation
The hysteretic curves of SPt5, PS1, PS2, PS3, PS4, and PS5 were presented and compared in this section, as shown in Figure 11 a-e). Figure 11 a-b) compares the hysteretic curve of wall SPt5 to the column welding separation case PS1, and beam welding separation case PS2. It can be observed that the weld separation causes a reduction in the load-carrying capacity values for the cases PS1 and PS2 through the hysteretic relation. Also, the beam welding separation has a more signi cant effect on reducing the base shear than the column welding separation case. At 0.25% drift, the reduction percents for the case of PS1 and PS2 are 21% and 36% in push direction, respectively; similar behavior was observed in the pull direction. At the 4% drift in push direction, similar behavior was observed with reduction percentage values of 13% and 16% for PS1 and PS2, respectively. It can be concluded that USPSW is more sensitive to beam welding separation than column welding separation, so the effect of plate-beam welding separation will be studied deeply.
Hysteretic curves of plate-beam welding separation models with different separation lengths, and locations PS2, PS3, PS4, and PS5 were shown in Figure 11 c-e). At 0.25% drift in push direction, the welding separation in cases PS3, PS4, and PS5 caused a reduction in the load-carrying capacity by 20%, 20%, and 10% and at 4% drift, this reduction was 3%, 0%, and 4%, respectively. It can be concluded that, in the early stages of cyclic loading, the separation has a signi cant effect on the load-carrying capacity, and the effect is decayed by increasing the drift. At low values of drift, the wall mostly resists the shear force by the contact between the plate and the frame element, which makes the contact separation more effective. For high drift value, the tension eld action starts at the non-separated part, and the dependency on the contact decreases. Besides, at the same separation length, the effect of separation is insigni cant regardless of the location of the separation.
Backbone curves of PS1, PS2, PS3, PS4, and PS5 were extracted from the hysteretic curves, as shown in Figure 11 f). Seismic behavior for different welding separation characteristics was evaluated using the loading function of Fig. 1.c and compared with the system without welding separation. Feature points were summarized from backbone curves, as shown in Table 5, using the method discussed in the rst section. At the push direction, it can be found that welding separation affects the initial stiffness of the walls. The separation caused stiffness degradation in the walls PS1, PS2, PS3, PS4, and PS5 by percent values of 21, 36, 20, 22, and 10%. The cases of full-beam separation and 2000 mm corner separation have the maximum and minimum reduction values. Both the case of 1000 mm separation in corner and middle approximately has the same reduction value. For the pull directions the reduction ratios were 21, 18, 18, 18, and 10% respectively and the second cycle stiffness reduction ratios were 30% 30% 6% 7% and 15%, respectively. It seems that the plate welding separation has more effect on the system stiffness than the load-carrying capacity (base shear). The USPSW system is more sensitive to plate-beam welding separation than plate-column. The plate-beam corner separation has a slightly greater impact on system strength than plate-beam middle separation, which reaches the same lateral strength at the drift ratio of 4%.
By comparing PS1, and SPt5 backbone curves shown in Figure 11 f) considering Von-Mises stress distribution shown in Figure 14, 15, it can be observed that the right portion of the plate that is separated from the column does not undergo high-stress demands. The plate-column separation leads to fewer demand forces generated by tension eld action on the column. As a result, a smaller column section is required. It can be observed a large stress concentration at the beam-column joint areas in the left portion of the plate that is connected to the boundary column, which should be designed for.
For the PS2 model, it can be seen that the concentration of the stress in plate-boundary connection areas. This might be attributed to incomplete tension eld action leading to the partially plate's postbuckling load-carrying capacity. The forces generated by incomplete tension eld action and gravity loads are concentrated at the columns, producing large demand forces, which the boundary columns should be designed for. While, the top portion of the plate, which is separated from the top beam, does not undergo high-stress concentration. As a result, a smaller top beam section is required.
For partially plate-beam separation (i.e. PS3, PS4, and PS5), it can be observed that the separated portion does not undergo signi cant high-stress demands. Incomplete tension eld action was observed, which leads to the partial plate's post-buckling load-carrying capacity.
In general, the partially plate-beam separation (PS4, PS5) could negatively increase the stresses at the connected column-beam joint areas leading to higher possibilities of early failure under seismic load.
High demands due to diagonal tension eld action at connected joint, which should be designed for. Increasing the separation length leads to a large increase in stress concentrations at the connecting portions.

Properties Degradation and Energy Dissipation Capacity
Lateral strength degradation re ects plastic buckling, out-of-plane deformation of in ll panel, local failure in columns, and the damage occurs in different models under the same lateral displacement. In this study, the strength degradation coe cient (η) can be de ned as (the ratio between the second and the rst cycle load-carrying capacity at the same drift ratio).
Figure 12 a) shows the lateral strength degradation coe cient (η) for USPSWs (i.e. SPt6.75, SPt5), CSPSWs (i.e. SHt5, SVt5), SSPSWs (i.e. SPt5-HS); it can be found that the η are varying between 0.85 and 1.0 except the second cycle of SPt5 and SPt6.75, where the lateral strength degradation is about 0.8. This happens due to the initial yielding of the plane in ll panel, which reduces the load-carrying capacity of the wall. The strength degradation coe cient (η) for CSPSW systems is higher than the USPSW system. This happens due to the e cient tension eld action forms in opposite directions in the USPSW. Although the tension eld action is formed in the corrugated panel, it is less effective due to the initial corrugation of the sheet.
The cyclic stiffness (K i ) describes the stiffness degradation for the different models. K i can be calculated by the method described in (Nie et al. 2008) as below; Figure 12 b) shows the stiffness degradation for USPSW, SSPSW, and CSPSW. It can be seen that stiffness degradation decreases steadily during the cyclic loading process. SPt6.75 sample has higher initial stiffness than other samples. After the drift of ±1%, the stiffness decreases below the SSPSW case.
On the other hand, SPt5 has the least cycle stiffness than other models.
Energy dissipation capacity re ects the seismic performance of the lateral resisting system. The energy dissipation capacity for each cycle is equal to the enclosed area of each hysteretic curve. The system with a plumper hysteretic curve has more energy-dissipation capacity. Figure 13 a) shows the accumulated energy dissipation capacity for different panel types with the strong case during cyclic number N=12. From Figure 13 a), it is clear that the energy-dissipation capacities of SPt6.75, SHt5, SVt5, and SPt5-HS are higher than the case of SPt5 by 14%, 29%, 32%, and 50%, respectively. SVt5 has slightly greater energy dissipation than SHt5. The cases of SPt5-HS and SPt6.75 have the maximum and minimum increasing values, respectively.
Figure 13 b) shows the accumulated energy dissipation capacity for USPSW, CSPSW, and SSPSW with different frames during cyclic number N=12. Similar to the strong case, SSPSW, and CSPSW still have more energy-dissipation capacity than USPSW with the weak case. From Figure 13 b), it can be concluded that reducing boundary frame stiffness by about 40% causes energy-dissipation capacity degradation in the walls WPt5, WHt5, WVt5, and WPt5-HS by percentage values of 18, 15, 12, and 12%, respectively. This means that the accumulated energy dissipation of USPSW is more sensitive to the frame stiffness than CSPSW, and the VCSPSW is less sensitive to the frame stiffness than HCSPSW. The out-of-plane deformation was effectively restrained by stiffeners. When plate-column welding separation occurs at PS1, local failure was not observed at the top of the column, whose welding was separated, Figure 15. It can be concluded that plate-column separation lessens the impact of tension strips on the column. The plate-beam welding separation model PS2 has local buckling at the top and the bottom of the columns. The top beam did not provide an anchor for tension strips, due to welding separation. High out-of-plane deformations were observed at the top of the plate. The models with partially plate-beam welding separation, i.e., PS3, PS4, and PS5, showed local buckling at the top and bottom of the columns. Welding separation progress was observed, as shown in Figure 15.

Conclusion
In this paper, nonlinear cyclic analyses were conducted using numerical simulation for USPSW, SSPSW, and CSPSW. The effects of panel type, the direction of corrugation, boundary frame stiffness, and welding separation on initial stiffness, load carrying, energy, and dissipation capacities were investigated.
Two main topics were focused on this paper; the rst topic is the seismic behavior under different kinds of in ll walls with the same unit weight. The second topic is the effect of welding separation between the in ll plate and the boundary frame.
Finite element models were created and validated with published experimental and numerical works.
The models were able to predict the previous results with a percentage error of 4%. It was found that HCSPSW has 15% and 11% higher stiffness at a drift ratio of 0.5% in the push and pull directions, respectively, and 29% higher energy dissipation than USPSW. It also has a higher lateral loadcarrying capacity than vertical corrugation by about 4.3% in the pull direction. VCSPSW has a higher energy dissipation capacity than USPSW by about 32%.
At the lateral story drift of 0.5%, The stiffness of SSPSW with U120 stiffeners is higher than the USPSW with about 9.2%. SSPSWalso has 23% and 24.5% higher lateral strength than SPSW and 34.6% and 23.7% higher than horizontal CSPSW in the push and pulls directions, respectively. It also has higher energy dissipation energy than USPSW by about 50%. USPSW is more sensitive to boundary element stiffness than CSPSW, and VCSPSW is less sensitive to weaker frames than HCSPSW.
The reduction of the boundary frame stiffness has a greater impact on load-carrying capacity than the initial stiffness, while the plate welding separation has more in uence on the system stiffness than the lateral strength. The separation has a signi cant effect on seismic behavior in the early stages of cyclic loading, as the walls mostly resist the shear force by plate-boundary frame contact before tension elds start at the non-separated part. When the plate-column welding separation occurs, the initial stiffness, lateral strength, and energy dissipation capacity reduce by about 21%, 13%, and 14%, respectively. While, the system with the plate-beam separation has lower initial stiffness, base shear capacity, and energy dissipation capacity than the system without separation by about 36%, 16%, and 20.5%, respectively. The USPSWs system is more sensitive to the plate-beam separation than the plate-column, especially the corner plate-beam separation.
At the same in ll plate weight per unit area, SSPSW has better seismic behavior than USPSW and CSPSW. SSPSW has a higher load-carrying capacity than USPSW, and CSPSW by about 14, 24%, respectively. It is recommended to use the SSPSWs system instead of USPSWs, and CSPSWs to improve the seismic behavior of the buildings.
For engineering applications, during low cyclic drift ratio levels up to 0.5%, USPSW would be better to use, CSPSW would be preferred to use during medium cyclic drift ratio levels (0.5-1%). During high cyclic drift ratio levels, SSPSW would be preferred to use.

Declarations
Funding Not applicable  Where, C is the kinematic hardening modulus, γ is the rate at which hardening modulus decreases with the plastic strain, Q∞ is the maximum change in the size of the yield surface, and b is the rate at which initial yield stress change with the plastic strain. Where K i is the initial stiffness, K 2 is the second cyclic stiffness, Δ y represents yield displacement, V y represents yield force, Δ m represents displacement at maximum lateral capacity, and V m represents maximum lateral strength capacity. Where K i is the initial stiffness, K 2 is the second cyclic stiffness, Δ y represents yield displacement, V y represents yield force, Δ m represents displacement at maximum lateral capacity, and V m represents maximum lateral strength capacity. Where K i is the initial stiffness, K 2 is the second cyclic stiffness, Δ y represents yield displacement, V y represents yield force, Δ m represents displacement at maximum lateral capacity, and V m represents maximum lateral strength capacity. Figure 1