The deformed shape of the present finite 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 finite 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 definition 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 floor 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 configurations 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 infill 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 Eh = 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 finite 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 five 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 field 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 field 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 significant 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 infill USPSW or SSPSW.
Figure 9 d) shows a comparison between the hysteretic behavior of SHt5 and SPt5-HS, which have the same weight. 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 field 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 first cycle were extracted from the hysteretic curves in both directions to form the backbone curves (Zhao et al. 2017). The initial stiffness (K1), the second cyclic stiffness (K2), load-carrying capacity, yield points, and maximum points can be evaluated from backbone curves, as shown in Table 3. Here, the K1, K2 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 identified with the commonly used “Equivalent area method”. Where Δy is the yield displacement, Vy is the yielding force, Δm is the displacement at the maximum load-carrying capacity, and Vm 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 K2 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 load-carrying 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 influence 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 Ki, K2 stiffness, yield, and maximum points were extracted from backbone curves, as shown in Table 4, as discussed in the previous section.
From Figure10 e) and 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 K2 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.
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 load-carrying 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, five 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 significant 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 significant 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 field 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 insignificant 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 first 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 field 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 field action leading to the partially plate’s post-buckling load-carrying capacity. The forces generated by incomplete tension field 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 significant high-stress demands. Incomplete tension field 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 field 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 reflects plastic buckling, out-of-plane deformation of infill panel, local failure in columns, and the damage occurs in different models under the same lateral displacement. In this study, the strength degradation coefficient (η) can be defined as (the ratio between the second and the first cycle load-carrying capacity at the same drift ratio).
Figure 12 a) shows the lateral strength degradation coefficient (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 infill panel, which reduces the load-carrying capacity of the wall. The strength degradation coefficient (η) for CSPSW systems is higher than the USPSW system. This happens due to the efficient tension field action forms in opposite directions in the USPSW. Although the tension field action is formed in the corrugated panel, it is less effective due to the initial corrugation of the sheet.
The cyclic stiffness (Ki) describes the stiffness degradation for the different models. Ki can be calculated by the method described in (Nie et al. 2008) as below;
![](https://myfiles.space/user_files/58677_ec8811c6b4185256/58677_custom_files/img1618428854.png)
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 reflects 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.
Figure 13 c) shows the accumulated energy dissipation capacity for the walls with welding separation PS1, PS2, PS3, PS4, and PS5 during cyclic number N=16. It can be concluded that welding separation has a significant effect on the system's energy-dissipation capacity. The separation caused energy-dissipation degradation in the walls PS1, PS2, PS3, PS4, and PS5 by percentage values of 14, 21, 3.3, 2.9, and 9%. The cases of the full and middle beam separation have the maximum and minimum reduction values, respectively. The plate-beam corner separation has a slightly greater impact on system energy-dissipation capacity than middle separation.
COMPARISON BETWEEN SYSTEMS FAILURE MODES
Figures 14 and 15 show the different failure modes for the systems. From Figure 14, it can be seen that the different details can change the deformed shape and failure mode of the models. Due to the cyclic loading process, two-way tension strips appear, and obvious out-of-plane deformation occurs. For plane SPSW, i.e., SPt5, WPt5, and SPt6.75, clear two-way tension strips occur, and local buckling occurs at the top and bottom of boundary columns. For CSPSW with a horizontal corrugated sheet, i.e., SHt5, WHt5, no clear tension field strips form, and local buckling occurs at the bottom of columns. The maximum deformations occur at the vertical centerline. The maximum out-of-plane shear buckling for SVt5 and WVt5 occurs at the horizontal centerline. Using a vertical corrugated steel plate lessens the impact of shear deformation on the boundary columns. For SPt5-HS and WPt5-HS, local failure occurs at the bottom and top of columns. 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.