On braced trapezoidal corrugated steel shear panels: An experimental and numerical study

Abstract

In this study, a new system consisting of a combination of braces and steel infill panels called the braced corrugated steel shear panel (BCSSP) is presented. To obtain the hysteretic behavior of the proposed system, the quasi-static cyclic performances of two experimental specimens were first evaluated. The finite element modeling method was then verified based on the obtained experimental results. Additional numerical evaluations were carried out to investigate the effects of different parameters on the system. Subsequently, a relationship was established to estimate the buckling shear strength of the system without considering residual stresses. The results obtained from the parametric study indicate that the corrugated steel shear panel (CSSP) with the specifications of a = 30 mm, t = 2 mm, and θ = 90° had the highest energy dissipation capacity and ultimate strength while the CSSP with the specifications of a = 30 mm, t = 2 mm, and θ = 30° had the highest initial stiffness. It can thus be concluded that the latter CSSP has the best structural performance and that increasing the number of corrugations, corrugation angle, and plate thickness and decreasing the sub-panel width generally enhance the performance of CSSPs in terms of the stability of their hysteretic behaviors.

Graphical abstract

Keywords

trapezoidal corrugated plate / steel shear panel / braced steel shear panel / experimental study / buckling resistance.

1 Introduction

The widespread damage of steel structures in the 1994 Northridge and 1995 Kobe earthquakes has resulted in extensive research on improving the performance of steel structures through various means such as the use of easily replaceable steel elements, self-centering steel structures, rocking steel structures, and smart materials [1]. Steel plate shear walls (SPSW) are common structural systems with acceptable performance against lateral forces in earthquake-prone areas. An SPSW comprises a steel infill panel and horizontal and vertical boundary members (beams and columns). The system behaves as a cantilevered vertical plate girder in which the columns and beams act as plate girder flanges and web stiffeners, respectively. This system has high initial elastic stiffness and ductility and an adequate capacity for seismic energy dissipation under earthquake loads. The most popular types of SPSW systems are unstiffened (simple) SPSWs and stiffened SPSWs. The limit states of unstiffened and stiffened SPSWs are tension field action development and shear yielding, respectively. The addition of stiffeners to simple shear panels to improve their efficiency by enhancing their buckling resistance has been suggested. The stiffeners contribute to a wider area in the infill panel for dissipating seismic energy through shear yielding and thereby increase the buckling resistance and ductility of the steel panels [2,3]. However, these two common types of SPSWs suffer from specific issues such as pinching of the cyclic force–displacement curve due to early buckling of the infill panel, the failure of boundary elements that are subjected to large distributed forces in unstiffened SPSWs, and the high cost of erecting stiffeners and possible low-cycle fatigue in the welding areas in stiffened SPSWs. Various solutions to address these issues have been suggested such as the use of half-bay SPSWs that are separated from columns [4,5], intermittent welding of SPSWs to boundary elements [6], perforated SPSWs [7–14], low-yield point materials [15–18], SPSWs with vertical slits [19], SPSWs with tension bracing [20], braced steel shear panels [21–26], auxetic-shaped SPSWs [27] and optimized SPSWs [28].

One novel idea is the use of corrugated steel plate shear walls (CSPSWs), which were introduced by Berman [29]. Emami et al. [30] performed experimental studies on SPSWs with unstiffened and trapezoidal corrugated panels. The results show that the corrugated specimens had a higher seismic energy dissipation capacity, ductility ratio, and initial elastic stiffness than the unstiffened specimen. Yadollahi et al. [31] investigated the effects of various parameters on the structural performance of corrugated SPSWs. Hosseinpour et al. [32] studied the behavior of unstiffened and corrugated SPSWs with sinusoidal and trapezoidal patterns and demonstrated that trapezoidal plates had a higher capacity for seismic energy dissipation, ductility, and ultimate strength compared to sinusoidal plates. Farzampour et al. [33] conducted a parametric study on CSPSWs and unstiffened SPSWs with and without openings. They investigated the effects of critical parameters such as the plate thickness, corrugation angle, opening size, and opening placement and concluded that the lateral stiffness, seismic energy absorption, and ductility of trapezoidal CSPSWs were increased compared to those of unstiffened SPSWs. At the same time, the occurrence of ultimate strength was postponed but the ultimate strength was decreased. The structural performance of SPSWs with horizontal trapezoidal corrugations in which the center of the infill panel was perforated by square holes was investigated by Bahrebar et al. [34], who studied the effects of some plate parameters such as the corrugation angle, thickness, and opening size. The effects of various corrugation inclinations and their corresponding failure modes [35] along with different opening properties and infill panel thicknesses [36] on the seismic performance of CSPSWs were studied. Banazadeh and Maleki [37] investigated the behavior of SPSWs and demonstrated that the ductility and seismic energy absorption of corrugated systems were significantly increased compared with those of unstiffened systems. Dou et al. [38] studied the behavior of sinusoidal CSPSWs and presented an equation for estimating the shear buckling load with reasonable accuracy. Cao and Huang [39] numerically and experimentally investigated the hysteretic behavior of CSPSWs and concluded that appropriately designed CSPSW parameters can prevent elastic buckling and increase the initial elastic stiffness, strength, seismic energy absorption capacity, and ductility. Dou et al. [40] numerically studied the effects of initial geometrical imperfections and dimensions on the shear resistance of sinusoidally corrugated panels and proposed fitting relationships between the shear resistances of the panels and their normalized height-to-thickness ratios. Tong and Guo [41] numerically studied the shear strength of stiffened CSPSWs and concluded that out-of-plane deformations could be restrained by a stiffened plate and both the shear strength and ductility of stiffened CSPSWs could be enhanced. Feng et al. [42] used steel strips to stiffen CSPSWs and reduce the amount of out-of-plane deformation and proposed formulas for estimating their elastic buckling loads. A double CSPSW (DCSPSW) consisting of two bolted corrugated plates was proposed by Tong et al. [43–45]. They investigated its buckling behavior and concluded that this new type of CSPSW had more stable cyclic behavior compared to common CSPSWs. They also theoretically obtained the rigidity constants such as the flexural and torsional rigidities of the DCSPSWs. In addition, they presented validated equations for estimating the shear elastic buckling based on finite element (FE) analysis results and some design guidelines for designing DCPSWs. Ghodratian-Kashan and Maleki [46] conducted an experimental study on three half-scale DCSPSW specimens. The main results of this study were that detaching the infill panel from the columns reduced their axial forces and that specimens with attached or detached corrugated plates had similar structural performances. Bahrebar et al. [47] investigated the behavior of curved CSPSWs with centrally placed openings by using FE models to analyze the effects of geometrical parameters on the behavior of the models. The obtained results show that adequately designed curved CSPSWs with web perforations had desirable performance. Yu et al. [48] introduced a novel specially shaped CSPSW with composite elements. Based on the experimental observations, they concluded that this new system had high initial stiffness, ductility, and elastic shear strength.

In light of the acceptable structural performance of braced steel shear panels and CSPSWs that has been confirmed by various researchers, the aim of this study is to enhance the structural performance of braced steel shear panels by using corrugated steel shear panels (CSSPs) instead of stiffened and unstiffened panels. It should be mentioned that in braced shear panel systems, the shear panel is placed at the center of a story separately from the surrounding main beams and columns using the considered braces. This new system is expected to reduce the costs and other disadvantages of stiffened shear panels and address the pinching of the hysteretic curves of unstiffened shear panels. Two experimental specimens of this innovative type of SPSW, which is named the braced corrugated steel shear panel (BCSSP), were evaluated under the considered cyclic loading time history. After validating the accuracy of the considered FE modeling method with respect to the experimental results, a parametric study of the proposed system was performed to investigate the effects of some effective parameters such as the sub-panel width, corrugation angle, and panel thickness. Finally, a relationship to estimate the buckling shear strength of the system was established using surface regression.

2 Experimental study

2.1 Experimental setup and specimen details

In this study, two full-scale CSSP experimental specimens with the same sub-panel width (i.e., parameter a in Fig.1) and various geometrical properties such as the number of ridges and grooves (i.e., corrugation) and corrugation angle were prepared and subjected to the considered quasi-static cyclic loading time history. The geometric properties of the considered specimens and the profile of the corrugated plates are shown in Tab.1 and Fig.1, respectively. As depicted in Fig.1, the sub-panel width, corrugation angle, inclined part length, horizontal projection of the inclined part, corrugation height, and sub-panel width at the sides of the panel are denoted as a, θ, d, b, h, and c, respectively.

Fig.2(a) shows a schematic representation of a braced steel shear panel system in which the braces are connected to the boundary members using pinned connections. As shown in Fig.2(b), the considered CSSP specimens contained boundary members with a double back-to-back UNP80 profile (i.e., a channel section), which were connected using pin connections at both ends. Along the direction parallel to the panel ridges and grooves, the corrugated plate was clamped between the boundary members using slip-critical high-strength bolted connections with a bolt diameter of 8 mm (Fig.2(b) and 2(c)). The other two sides of the corrugated panels in the direction perpendicular to the panel ridges and grooves were connected to the surrounding members using L-shaped fish plates, welds, and rivets (Fig.2(b)). Rivets and welds (i.e., hybrid joints) were used simultaneously to increase the safety factor of the plate at the connection and to prevent failure in the connection. The number of rivets required was determined based on the tensile capacity of the plate. To prepare the corrugated shear panels, flat plates were bent using an automatic machine. Fig.2(d), 2(e), and 2(f) show the geometrical dimensions and experimental setup of the CSSP specimens on a universal testing machine (UTM). The corrugated shear panels were painted with hydrated lime to observe the yielding regions (Fig.2(g)).

2.2 Material properties

The material properties of the corrugated steel plate and steel UNP80 profiles were determined using the coupon tension test described in ASTM A370-22 [49]. The thicknesses of the tension coupon test specimens for the corrugated steel plate (Fig.3(a)) and UNP80 (Fig.3(b)) were t = 0.5 mm and t = 6 mm, respectively. Fig.3(c) and Tab.2 show the obtained stress–strain curves and mechanical properties of the considered steel materials, respectively. It should be noted that the material properties in Tab.2 were determined from the lowest obtained stress–strain curves.

2.3 Cyclic loading protocol

The UTM machine was used to apply a quasi-static cyclic loading protocol based on ATC-24 [50,51] in which the approximate estimated yield displacement for the considered specimens was 0.92 mm in the vertical direction. Because there is no prescribed limit on the amplitude of the two steps before yield displacement in ATC-24, two steps with six cycles and amplitudes of 25% and 50% of the calculated yield displacement were defined to ensure the recording of the specimen elastic behavior in this study. The increment in the subsequent steps was equal to the yield displacement and the number of cycles was decreased to two after the amplitude reached three times the yield displacement. Moreover, based on the results obtained from preliminary FE analyses of the specimens before the experimental test, it was anticipated that it was very unlikely that the specimens could undergo the displacements in the last three steps; therefore, the number of cycles in these steps was reduced to 1. It should be mentioned that during the test, when any significant event such as painting flaking, rivet loosening, or buckling occurred, an additional step with a half increment (i.e., Steps 8, 11, 14, and 16) was added to the loading protocol to record any possible important events. The experimental specimens were subjected to the loading protocol along the diagonal direction to simulate the effect of the braces in braced steel shear panel systems. As shown in Tab.3, this protocol involved 23 loading steps (i.e., 48 cycles) that began from an amplitude of 0.25 mm (i.e., drift of 0.056%) and ended at an amplitude of 15.75 mm (i.e., drift of 3.5%). Moreover, it should be noted that as shown in Fig.2(a), the system in this study was a braced steel shear panel with a corrugated infill panel in which the steel shear panel was located at the center of a building frame and connected to the frame using braces. In the study by Hamed and Mofid [25], it was concluded that the optimum vertical and horizontal geometrical dimensions of the shear panel were between 10% and 30% of the story height and span length and that the shear panel should be located at the mid-point of a story. Depending on the span length and story height of the building frame, the experimental specimens in this study, which had the dimensions of 450 mm × 450 mm, can be considered as full-scale specimens. It is therefore necessary for the early yielding of the steel shear panel to occur at very small drift ratios compared to that of the frame itself.

2.4 Discussion on experimental observations

2.4.1 Steel shear panel-A specimen

Fig.4 shows the evolution of the steel shear panel-A (SSP-A) specimen during different steps of the test. At a drift of 1% (i.e., displacement amplitude of 4.5 mm) shown in Fig.4(a), the fish plate denoted by a red circle and the plate ridges leading to it were slightly deformed under the applied shear force and one of the rivets was loosened. Moreover, the painting began to crack and flake around the fish plates and at the corners of the corrugated plate. As shown in Fig.4(b), the second rivet on the same fish plate was loosened at a drift of 1.4% (i.e., displacement amplitude of 6.28 mm), and painting flaking occurred around the lower fish plate. At a drift of 1.86% (i.e., displacement amplitude of 8.4 mm), the painting flaking spread to the central region of the corrugated panel (Fig.4(c)). The painting flaking continued to develop until the end of the test and, as depicted in Fig.4(d), began to intensify at a drift of 2.2% (i.e., displacement amplitude of 9.93 mm). At a drift of 2.44% (i.e., displacement amplitude of 11.01 mm), the amount of crumpling in the corrugated plate increased (Fig.4(e)). As depicted in Fig.4(f), owing to the fracture of two additional rivets, the test was stopped at a displacement amplitude of 11.51 mm (i.e., drift of 2.55%). The obtained hysteretic curve of SSP-A is shown in Fig.5. The curve exhibits pinching owing to the buckling of the infill panel and separation of the two fish plates.

2.4.2 Steel shear panel-B specimen

Fig.6 shows the evolution of the steel shear panel-B (SSP-B) specimen during different steps in the test. As shown in Fig.6(a), the first local buckling occurred at a drift of 1.02% (i.e., displacement amplitude of 4.6 mm). The painting began to crack and flake, and cracking and flaking were clearly observed at a drift value of 1.21% (i.e., displacement amplitude of 5.43 mm) (Fig.6(b)). At a drift value of 1.38% (i.e., displacement amplitude of 6.22 mm), another major crumpling occurred in the opposite direction (Fig.6(c)). An additional major crumpling of the plate occurred at a drift value of 1.97% (i.e., displacement amplitude of 8.90 mm) and one of the fish plates was torn, as shown in Fig.6(d). At the drift values of 2% and 2.07% (i.e., displacement amplitudes of 9.01 and 9.66 mm, respectively), the plate began to crumple and the painting flaking spread across the corrugated plate (Fig.6(e)). Because of the loosening of an additional fish plate and a small tearing in the buckled region of the infill panel (i.e., inside the red circle on the right side of Fig.6(f)), the test was stopped at a drift of 2.07% (Fig.6(f)). The obtained hysteretic curve of SSP-B shown in Fig.7 has a more stable cyclic behavior compared to that of SSP-A.

Tab.4 presents the values obtained for the initial stiffness, ultimate strength, and dissipated energy of the SSP-A and SSP-B experimental specimens. The initial stiffness was calculated using the ideal bilinear curve obtained from the hysteretic curves according to FEMA 356.

As a general comparative summary of the experimental observations, it can be concluded that the only factor that resulted in the different behaviors of the two tested specimens (i.e., SSP-A and SSP-B) was the corrugation angle, which in turn affected the number of ridges. Moreover, as shown in Tab.1, the other two parameters that influence the performance of the CSSPs (i.e., the sub-panel width and plate thickness) were kept constant in this experimental study. The obtained results imply that the limit state (i.e., failure mechanism) of CSSPs is a combination of tension field action development and shear yielding (Fig.4 and Fig.6). However, at small plate thicknesses (e.g., t = 0.5 mm) and corrugation angles, the tension field action limit state was dominant. As a result, SSP-A exhibited more buckling, which resulted in further pinching in its hysteretic curve (Fig.5). In addition, comparing the performance of the corrugations to that of the braces in the building frames, it can be seen from Tab.4 that as the corrugation angle increased, the degree of its effect on the lateral stiffness of the panels decreased, and as a result, the initial stiffness of SSP-B decreased. However, owing to its more stable hysteretic behavior (Fig.7), SSP-B had a higher ultimate strength and energy dissipation. Moreover, it is possible that the infill panel may be torn owing to stress concentration at sharp angles (e.g., corrugation angle of 90°) or the low-cycle fatigue of the infill panel at the intersection of the buckled regions as a result of periodic changes in the loading direction and subsequent frequent crumpling of the plate. In the specimens tested in this study, one of the SSP-B fish plates (Fig.6(d)) was torn and a very small tear was observed at the buckled region inside the red circle on the right side of Fig.6(f), which can probably be attributed to fatigue. Owing to the importance of fatigue in the cyclic behavior of CSSWs, this issue should be investigated in detail in future research.

3 Verification of finite element modeling

The FE model is presented in this section and its validity and accuracy evaluated. The FE models were fitted to the SSP-A and SSP-B specimens tested in this study to verify the FE modeling procedure. The S4R element (ABAQUS) was used for all the components of the models. The coupling interaction was used at the four corners of the shear panel model to simulate the pinned connection of the boundary elements such that all degrees of freedom, except for in-plane rotation, were constrained. The steel material properties were defined based on the stress–strain curves presented in Subsection 2.2 and kinematic hardening was assigned. The models were subjected to the considered quasistatic loading (Tab.3) using a general static analysis step. There is good agreement between the experimental and numerical hysteretic curves (Fig.8(a) and Fig.8(b)) and the final deformation shapes (Fig.8(c) and Fig.8(d)). The FE model and experimental values of the ultimate strength and dissipated energy are compared in Tab.5. The coincidence of the hysteretic curves and the proximity of the F_num/F_exp and E_num/E_exp values to 1 indicate the acceptable accuracy of the FE modeling where F_num, F_exp, E_num, and E_exp represent the ultimate strengths and dissipated energies in the FE models and experimental specimens, respectively. The agreement between the experimental data and numerical results indicates that the FE models can be confidently employed in the parametric study.

4 Parametric study

In this section, nonlinear static analyses are performed to assess the effects of the subpanel width (a), corrugation angle (θ), and panel thickness (t) on the CSSP performance. Tab.6 shows the specifications of the considered models, which were modeled using the verified modeling procedure and material properties described in Section 3 and Subsection 2.2, respectively.

4.1 Sub-panel width

The effect of the subpanel width was studied for three different sizes. As shown in Fig.9, the subpanel size had a notable effect on the postbuckling behavior of the panel. A sudden spike occurred in the shear force–displacement curves of the panels as the subpanel size increased. Moreover, from the presented values for the initial stiffness, ultimate strength, and energy dissipation capacity of the CSSPs, it is seen that as the sub-panel width increased, the probability of panel buckling increased, and the behavior of the CSSP tended to that of an unstiffened shear panel. The CSSP stiffness and strength therefore decreased (Tab.7).

4.2 Corrugation angle

Five different corrugation angles (15°, 30°, 45°, 60°, and 90°) were used in the parametric study. The shear force–displacement curves in Fig.10 show that the CSSP with a corrugation angle of 15° was ductile and exhibited no sudden reduction in its strength. However, increasing the corrugation angle caused a sudden reduction in the shear force. The results in Tab.8 show that as the corrugation angle increased, the ultimate strength and dissipated energy generally increased while the initial stiffness decreased. By comparing the performance of the inclined parts of subpanels to braces with different angles (e.g., concentrically braced frames), it can be concluded that the stiffness decreased as the angle increased to 90°. In addition, excessive reductions of the corrugation angle caused the shear wall behavior to become closer to that of unstiffened shear walls with lower stiffness. It is also noteworthy that strength recovery (i.e., restoration) occurred in the obtained shear force–displacement curves for the θ values of 15° and 30° but disappeared at higher values of θ. It should be mentioned that as the corrugation angle decreased, the behavior of the CSSP tended toward that of an unstiffened shear panel in which the postbuckling strength resulted from the development of the tension field action. This phenomenon was not observed for corrugation angles of 45° and above. This conclusion is confirmed by the experimental results obtained in this study (Fig.5 and Fig.7).

4.3 Plate thickness

The effects of the plate thickness on the performance of the CSSP are presented in this section. The plate thickness values of 0.5, 1.25, and 2 mm were considered for this purpose. From the obtained results (Fig.11 and Tab.9), it can be concluded that increasing the thickness of the panel increased its initial stiffness, dissipated energy capacity, and ultimate strength. In general, the results obtained for the corrugation angle sensitivity analysis in Subsection 4.2 and plate thickness parametric analysis in Subsection 4.3 indicate that plate buckling inevitably occurred at every corrugation angle in CSSPs with small plate thicknesses, even in the combined limit state (i.e., tension field action and shear yielding) that occurred at higher corrugation angles. Moreover, as the corrugation angle decreased, the CSSP performance tended to that of the unstiffened SPSWs, in which the governing limit state was tension field development. The CSSPs with medium and large plate thicknesses exhibited a decreased amount of buckling and were governed by the shear yielding limit state. Less buckling occurred as the corrugation angle increased. It is known that the complete development of tension field action or complete net shear yielding results in more ductile behavior; therefore, as shown in Fig.11, at small and large plate thicknesses, more ductile behavior was exhibited at the corrugation angles of 15° and 90°, respectively, and there was no sudden reduction in the strength of the panel. Moreover, the amount of crumpling on the panel decreased as the panel thickness increased.

4.4 Optimal corrugated steel shear panel model

The CSSP with the best performance among the 39 studied models in terms of the obtained hysteretic curves and parameters is selected in this section. From Fig.12, which shows the values of the calculated parameters for all the models, it is concluded that model J (i.e., a = 30 mm, t = 2 mm, θ = 90°) has the highest energy dissipation capacity and ultimate strength, whereas model D (i.e., a = 30 mm, t = 2 mm, θ = 30°) has the highest initial stiffness. Meanwhile, the results indicate that the models with t = 0.5 and 1.25 mm have a uniform energy dissipation capacity and ultimate strength.

5 Estimation of buckling shear strength

A closed-form equation for estimating the buckling shear strength of CSSPs from their geometrical parameters is presented in this section. The buckling shear strengths of all the considered models (Tab.6) were obtained through the following process.

1) Buckling analysis was performed to determine the critical buckling mode (Fig.13).

2) The time step of the buckled panel that matches the critical buckling mode was identified.

3) The equivalent displacement was determined from the time step of the buckled panel and the buckling load specified from the hysteretic curve.

4) The shear strength of the panel was calculated by applying a force along the diagonal direction of the panel using the projection of the buckling load to 45°.

This process was performed for all the studied models and the shear strengths for different parameters determined. Fig.14 shows the variation of the shear strength with the two parameters θ and t/a. The relationship between the shear strength and the considered parameters (Eq. (1)) was extracted using surface regression as

(1)\begin{array}{rl}{T}_{\mathrm{c}\mathrm{r}}=& 363.7+1.754\times {10}^6\left(\frac{t}{a}\right)+34.21\theta \\ & -1.378\times {10}^7{\left(\frac{t}{a}\right)}^2+1050\left(\frac{t}{a}\right)\theta ,\end{array}

where t, a, and θ are the plate thickness, subpanel width, and corrugation angle of the steel panel, respectively. The shear strengths obtained from the experimental and numerical CSSPs are presented in Tab.10 and compared with the values estimated using Eq. (1). It can be seen that the average percentage deviation is 15%, which is an acceptable accuracy.

6 Conclusions

In this study, the structural performance of CSSPs was investigated. For this purpose, two experimental specimens were constructed and their behavior was investigated using a quasi-static cyclic loading time history. After validating the FE modeling procedure, a parametric study was performed to investigate the effects of geometrical properties such as the corrugation angle, sub-panel width, and plate thickness on the CSSP performance. Finally, a closed-form relationship to estimate the buckling shear strength of the CSSPs without considering residual stresses was presented. It should be mentioned that the findings of a comparative study by the authors on the effects of the residual stresses generated during the forming process (i.e., pressing) of the steel panel will be presented in the near future. The main results of this study are as follows.

1) Increasing the number of ridges and grooves (i.e., corrugation) resulted in more stable hysteretic curves, which increased the energy dissipation capacity.

2) As the sub-panel width increased, the probability of panel buckling increased and the behavior of the CSSP tended toward that of the unstiffened shear panels. The CSSP stiffness and strength therefore decreased. In addition, the shear force–displacement curves of CSSPs with smaller sub-panel widths exhibited more stable behavior.

3) The ultimate strength and dissipated energy capacity of the CSSPs increased while the initial stiffness decreased as the corrugation angle of the panel increased from 15° to 90°.

4) Increasing the plate thickness increased the initial stiffness, dissipated energy capacity, and ultimate strength of the CSSPs.

5) The CSSP with a = 30 mm, t = 2 mm, and θ = 90° has the highest energy dissipation capacity and ultimate strength while the CSSP with a = 30 mm, t = 2 mm, and θ = 30° has the highest initial stiffness. It can be concluded that the latter CSSP has the best structural performance.

6) An equation to estimate the buckling shear strength of CSSPs was proposed.

7) It should be mentioned that buckling and pinching of the hysteretic curve are always observed in the cyclic behavior of SPSWs. Different solutions such as the use of stiffened SPSWs, ring-shaped SPSWs, SPSWs with buckling-restrained plates, auxetic-shaped SPSWs, and SPSWs with optimized configurations have been introduced to address the infill panel buckling issue and increase the stability of the obtained hysteretic curve. One solution is the use of corrugated SPSWs, which was discussed in this study. Although some of the previously proposed dampers have more stable hysteretic curves compared to that of the CSSP, the focus of this study is on investigating the cyclic performance of unstiffened SPSWs and providing a solution to enhance their cyclic performance so that the solution can be used as a safe and reliable alternative to unstiffened SPSWs. More stable hysteretic curves for unstiffened SPSWs were achieved in the considered experimental specimens, particularly for the SSP-B specimen. According to the results in this study and as mentioned in the previous sections, a combined limit state of tension field action development and shear yielding occurred in the CSSPs; hence, buckling occurred even in CSSPs, especially in CSSPs with smaller plate thicknesses. It can therefore be concluded that buckling is one of the limitations of this type of metallic yielding dampers and that future research should continue to focus on this issue.

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