An innovative system of coupled steel plate shear wall with pin FUSE in link beam: Cyclic behavior and energy dissipation

Abstract

Coupled steel plate shear wall (C-SPSW) is one of the resisting systems with high ductility and energy absorption capacity. Energy dissipation in the C-SPSW system is accomplished by the bending and shear behavior of the link beams and SPSW. Energy dissipation and floor displacement control occur through link beams at low seismic levels, easily replaced after an earthquake. In this study, an innovative coupled steel plate shear wall with a yielding FUSE is presented. The system uses a high-ductility FUSE pin element instead of a link beam, which has good replaceability after the earthquake. In this study, four models of coupled steel plate shear walls were investigated with I-shaped link beam, I-shaped link beam with reduced beam section (RBS), box-link beam with RBS, and FUSE pin element under cyclic loading. The finite element method was used through ABAQUS software to develop the C-SPSW models. Two test specimens of coupled steel plate shear walls were validated to verify the finite element method results. Comparative results of the hysteresis curves obtained from the finite element analysis with the experimental curves indicated that the finite element model offered a good prediction of the hysteresis behavior of C-SPSW. It is demonstrated in this study that the FUSE pin can improve and increase the strength and energy dissipation of a C-SPSW system by 19% and 20%, respectively.

Keywords

Coupled steel plate shear wall (C-SPSW)FUSE energy dissipation finite element method

Introduction

Steel plate shear walls (SPSWs) with high ductility and high energy dissipation are used as a lateral-resistant structural system (Gorji Azandariani, et al., 2020). In SPSWs, they can characterize their high ductility, strength, initial hardness, stable behavior in cyclic loading, and energy absorption capacity. Figure 1 illustrates the types of common steel shear wall systems. Common SPSW systems include SPSW with simple connections beam-column, SPSW with a rigid beam-column connection, and SPSW with a coupling system. Many researchers have investigated the performance of the SPSW and the effect of various parameters affecting its behavior using numerical and experimental methods (Caccese et al., 1993; Driver et al., 1997; Edalati et al., 2014, 2015; Elgaaly et al., 1993; Lubell et al., 2000; Thorburn et al., 1983; Timler and Kulak, 1983; Yadollahi et al., 2015). The coupled steel plate shear wall (C-SPSW) system consists of two separate shear walls connected by link beams (Figure 1(c)). The C-SPSW system has high ductility with a very good performance. In the C-SPSW system, the lateral force is distributed across the floors based on the stiffness and strength of the steel infill wall, bending frame, and link beams. The resistance to lateral forces at the C-SPSW occurs through a combination of the flexural behavior of the steel frame and the shear behavior of the steel infill wall and link beams (Borello and Fahnestock, 2012, 2013; Li et al., 2011, 2012; Pavir and Shekastehband, 2017).

Figure 1.

Types of steel shear walls (SPSWs) system. (a) SPSW with simple beam-to-column connection, (b) SPSW with rigid beam-to-column connection, and (c) coupled steel plate shear walls (C-SPSW).

The energy dissipation systems are an excellent commonly applied energy dissipation system with low-cost construction and interchangeability (Mohammadi et al., 2019, 2020). The energy dissipation mechanism in metallic yielding dampers is through the yield of the damper element and entry into the plastic zone at the time of the earthquake. Dampers also operate as fuse elements that cause the delayed entrance of other structural elements into the plastic phase (Gorji Azandariani, Abdolmaleki, et al., 2020; Gorji Azandariani, Gorji Azandariani, et al., 2020). The link beam is used as a fuse for energy absorption capacity, and dissipation caused by the earthquake in eccentrically braced frames used EBF. Most of the numerical and experimental work done on the link beams has been performed through cyclic tests to estimate their rotational capacity (Hjelmstad and Popov, 1983; Ji et al., 2016, 2017; Malley and Popov, 1984; Mohebkhah and Azandariani, 2020; Okazaki et al., 2005; Popov, 1983; Popov and Engelhardt, 1988; Roeder and Popov, 1978). Details and design codes for link beams are provided in the AISC 314 (2016) based on the type of link beam behavior. According to the AISC-314 (2016), link beam behavior is subdivided into three zones: shear, flexural-shear, and flexural. Dubina and Dinu (2014), Dimakogianni et al. (2015), and Dougka et al. (2014) presented a new energy dissipation system to improve the seismic behavior of the moment frames. In the proposed system, the FUSE pin element was used for the link beams. The FUSE pin element was designed to be easily replaceable and repairable with hysteretic behavior and suitable energy dissipation (Dimakogianni et al., 2015; Dougka et al., 2014). An innovative C-SPSW with a FUSE pin element system has been presented to improve the behavior and performance of the C-SPSWs. The innovative system of coupled steel plate shear wall (C-SPSW) with FUSE pin in the link beam consists of C-SPSW in which the link beam of FUSE pin element presented by Dougka et al. (2014) is used (Figure 2). The proposed system C-SPSW with FUSE pin as a lateral load-resistant system at the low seismic level by yielding FUSE pin element provides protection against SPSW damage. Thus, at low seismic levels, the system allows the steel shear wall stiffness to limit the relative displacements of the floors where the yielding FUSE of link beams for energy dissipation is used. The advantages of using the FUSE pin element in coupled steel plate shear walls include stable hysterical behavior, high energy absorption capacity, and alternative fuse with an easy and economical repair.

Figure 2.

Types of link beams in C-SPSWs: (a) Coupled steel plate shear wall (C-SPSW) system, (b) I-link beam section, (c) Hollow RBS-link beam sections, (d) RBS-link beam section, and (e) FUSE pin-link beam.

Li et al. (2012) investigated the cyclic behavior of coupled steel shear walls by experimental work. In this study, a six-story C-SPSW was designed as a sample, and its first 2.5 floors at a 40% scale were selected as a test specimen. In the simultaneous lateral cycle loading, the gravity load from the upper floors is applied by jacks. The test results confirm the proposed method based on the capacity design of the column, which aims to limit the formation of the plastic joint in a quarter of the lower height of the column. Borello and Fahnestock (2012) designed several 6-story C-SPSWs. The coupling beam sizes were 100, 200, and 400% of each story beam. The models were analyzed using Opensees software. The results showed that the shear strength of models and the story drift at the lower story levels increase with coupling beam sizes. Borello and Fahnestock (2012) performed an analytical study on the mechanisms and behavior of C-SPSWs. They suggested some correlations for determining strength and coupling degree of the systems. Borello and Fahnestock (2013) also studied fourteen models of C-SPSW using the uniform-yielding mechanism. They concluded that acceptable results are obtained if the uniform-yielding mechanism is employed for modeling of SPSWs. Gholhaki and Ghadaksaz (2016) studied models with different story numbers and different lengths of coupling beams under time history analysis. Findings showed a reduction in the shear strength of the C-SPSWs as the beam length increases. Furthermore, the period and roof drift increase with increasing the beam length. Recent researches on C-SPSWs focused on the analytical and numerical studies using beam elements and the presentation of an appropriate mechanism for designing these systems. Beam elements could not model shear yielding. Therefore, in the current study, modeling of specimens by shell elements may present more realistic behavior of coupling beams having shear yielding. Gorji Azandariani et al. (2021) an innovative hybrid linked-column steel plate shear wall (HLCS) system presented, and its ultimate capacities were investigated using numerical and analytical approaches. The system proposed in this research consists of a steel sheet shear wall (SPSW) which is coupled to two adjacent columns using the link beams. The results show that the proposed system has a significant effect on reducing the weight of the structure, especially for taller structures, so that, in a 12-story structure, a reduction of 30% of the weight was observed.

In this study, the cyclic behavior of the coupled steel plate shear walls with FUSE pin in the link beam is investigated. For this purpose, a 12-story C-SPSW structure is designed according to AISC 314 (2016), and the last 3-floors are selected for the cyclic behavior analysis. The finite element method and ABAQUS software (2010) have been used to study the cyclic behavior of the models C-SPSW. Validation for the results of finite element models has been performed with test results. In the validation section, Dubina and Dinu’s (2014) experimental specimens were modeled and analyzed, and used to confirm finite element models. After validation, parametric models including coupled steel plate shear walls with I-shaped link beam, I-shaped link beam with reduced beam section (RBS), hollow-link beam with RBS, and FUSE pin-link beam have been developed. The geometry and configuration of the link beams of the parametric studies are shown in Figure 2. The results of finite element models include hysteresis diagrams, lateral stiffness, and damped energy. Finally, the results of finite element models present hysteresis curves, lateral stiffness, and energy dissipation.

Design of the C-SPSW structure

In this section, to investigate the cyclic behavior of the C-SPSW in following Figure 3, three layers of full-scale 12-story C-SPSW structures are selected. To this end, in this section, details of the design of the C-SPSW structure are presented. The structural coupled C-SPSWs, the plan, and the prototype with details of span and height dimensions are shown in Figure 3. As shown in Figure 3, for the frames adjacent to the C-SPSW, a simple weight-bearing frame system is used; thus, only the C-SPSW is considered a lateral load-resistant system. The perimeter gravity frame bays, 5.0 m long; the SPSW bay, 5.0 m long; and the link beam bay, 2.5 m long, are considered from the center to center of the columns. The 12 stories of the building are considered to have uniform heights of 4.0 m. C-SPSW was designed according to the recommendations given in AISC Seismic Provisions (2016) and AISC Design Guide 20 (2007).

Figure 3.

The C-SPSW structures: (a) Case study structure, (b) full-scale specimen, and (c) plan-designed structure.

The Canadian Standards Association (CAN/CSA S16-01/2001) (2009) and the AISC Seismic Provisions (2016) have adopted the SPSW as a lateral-resistant structural system. In the Canadian Standards Association (CAN/CSA S16-01/2001) (2009) and the AISC Seismic Provisions (2016), for the design of SPSWs, the initial design of beam sections, columns, and infill plates are performed similarly to a tensile brace. This equivalent bracing model has been developed by Thorburn et al. (1983) to simplify the iteration steps in steel plate shear wall design. In this model, the infill plate is modeled only by a diagonal tensile brace. Hence, instead of each steel infill plate, an equivalent tensile brace is considered. After determining the cross-sectional area of each tensile brace, the AISC Design Guide 20 (2007) recommends Equation (1) to calculate the thickness of the steel infill plate as follows

t = \frac{2 A_{b} \sin θ \sin 2 θ}{L \sin^{2} 2 α}

(1)

where θ is the angle between the brace and the column, L shows the width of the frame opening, A_b represents the cross-sectional area of the brace is equivalent, and α denotes the angle of formation of the diagonal tensile field in the steel infill plate. Thorburn et al. (1983) proposed a strip model for predicting the capacity of SPSWs with thin infill plates. They also calculated the angle of the tension field (α) in terms of the normal stiffness of the boundary members using the principle of minimum energy. Thorburn et al.’s (1983) equation developed by considering the flexural strength of the columns was modified by Timler and Kulak (1983) (Equation (1)). Equation (2) is obtained as follows

\tan^{4} α = \frac{1 + \frac{t_{w} L}{2 A_{c}}}{1 + t_{w} h (\frac{1}{A_{b}} + \frac{h^{3}}{360 I_{c} L})}

(2)

where A_c and I_c reflect the cross-section and moment of inertia of the side columns, h is the height of the floor, and A_b represents the cross-section of the beam. After determining the thickness of the plate, AISC Design Guide-20 (2007) is used for analysis and design. The cross-sectional area of each strip is obtained from Equation (3)

A_{s} = \frac{L \cos α + h \sin α}{n} \cdot t

(3)

where n the number of strips is equal to 10 diagonal strips for C-SPSW analysis; it also proposes AISC Design Guide 20 (2007) and Equation (4) to the stiffness of the columns for preventing column buckling under the influence of the diagonal tensile field.

I_{c} \geq \frac{0.00307 t h^{4}}{L}

(4)

The use of residential structures is assumed, and the gravity loading of the model, as well as the floor loader system, are assumed to be composite slabs weighing 500 kg/m². The live load of the floors is 200 kg/cm², and the live roof load was considered 150 kg/cm². The combination of live and dead loads in the form of DL+0.2LL is considered to be an effective mass. Accordingly, the seismic mass of the floors is equal to 5589.7 kN. The spectrum design is based on the Iranian seismic building code, and, according to this code, the building is located in a relatively high seismic zone and on type II soil. The design spectral acceleration (S_a) according to the Iranian Seismic Building Code (2014) used to design a 12-story structure is shown in Figure 4. The period time a 12-story structure is calculated 0.91 s, which is obtained design spectral acceleration (S_a) is 0.518 g. According to the Iranian Seismic Building Code (2014) and code ASCE7-10 (2010), the seismic base shear is equal to V_E = C_sW. The seismic base shear to a 12-story building was equal to V_E = 0.074 W, where W is the effective seismic weight and C_s = 0.070 is the seismic response coefficient. Load combinations were based on Regulations ASCE7-10 (2010) where a combination of 1.2D + 1.6L, 1.2D + 1.0L + 1.0E and 0.9D + 1.0E was considered. American W-sections were used for beam and column design sections. The sections designed for the coupled steel plate shear wall are presented in Table 1. The assumed materials for modeling and analysis were considered for beams and columns sections of S355 steel with 410 MPa yield stress and infill plate of S235 steel with 310 MPa yield stress (2014). Also, S_a (T₁,5%) has been selected as the spectral acceleration at the period time of the first mode shape, along with 5% damping at the structure design of C-SPSW.

Figure 4.

Design spectral acceleration (Sa).

Table 1.

Designed sections for the C-SPSW.

Story	Plate thickness (mm)	Internal column section	External column section	Beam section	Link beam section
1	8	C1: W 33 × 263	C1: W 33 × 263	B1: W 18 × 234	LB1: W 18 × 192
2	8	C1: W 33 × 263	C1: W 33 × 263	B1: W 18 × 234	LB1: W 18 × 192
3	7	C2: W 30 × 261	C2: W 30 × 261	B2: W 18 × 158	LB2: W 18 × 130
4	7	C2: W 30 × 261	C2: W 30 × 261	B2: W 18 × 158	LB2: W 18 × 130
5	6	C3: W 27 × 281	C3: W 27 × 281	B3: W 18 × 106	LB3: W 18 × 97
6	6	C3: W 27 × 281	C3: W 27 × 281	B3: W 18 × 106	LB3: W 18 × 97
7	5	C4: W 24 × 250	C4: W 24 × 250	B4: W 18 × 71	LB4: W 18 × 65
8	4	C5: W 24 × 229	C5: W 24 × 229	B4: W 18 × 71	LB4: W 18 × 65
9	4	C5: W 24 × 229	C5: W 24 × 229	B5: W 18 × 60	LB4: W 18 × 65
10	3	C6: W 24 ×131	C6: W 24 ×131	B5: W 18 × 60	LB5: W 18 × 60
11	3	C6: W 24 × 131	C6: W 24 × 131	B5: W 18 × 60	LB5: W 18 × 60
12	3	C6: W 24 × 131	C6: W 24 × 131	B6: W 27 × 194	LB5: W 18 × 60

Nonlinear finite element method

An efficient and accurate finite element method should be used to study the cyclic behavior of the C-SPSW system. In this section, a finite element model has been developed using the ABAQUS (2010) software to predict the cyclic behavior of the coupled steel plate shear wall and pin FUSE. The modeling sections described below include material properties, loading, boundary conditions, mesh, element type, and analysis methodology.

Meshing and geometry

ABAQUS (2010) finite element software was used to model the coupled steel plate shear wall experimental specimens and validation. 4-node shell element (S4R) (2010) was used for modeling beam, column, and infill plate sections. The pin FUSE elements were developed by a three-dimensional solid continuum element with a mesh type of 8-node isotropic 3D element with reduced integration (C3D8R). Each node of this element had six degrees of freedom: three degrees of translational freedom and three degrees of rotational freedom. It also had a 4-node shell element capable of simulating general and local buckling on shear wall infill plates. Figure 5 illustrates the geometry and meshing of the finite element models of experimental specimens of C-SPSW and pin FUSE in the studies by Dubina and Dinu (2014) and Castiglioni et al. (2013). In FE modeling, nonlinear geometry behavior, strain hardening effects, large deformation, and post-buckling behavior were considered for S4R elements (Gorji Azandariani, 2021). A nonlinear dynamic method (Explicit dynamic) was used to analyze finite element models (Wang et al., 2015).

Figure 5.

The geometry, meshing, and boundary conditions of finite element models: (a) C-SPSW and (b) pin FUSE.

Loading and support conditions

The boundary conditions, including the supports and the cyclic loading applied to the finite element models of the C-SPSW and pin FUSE, were considered based on the details used in the experimental specimens (Castiglioni et al., 2013; Dubina and Dinu, 2014). Load displacement type control and cyclic loading were applied to finite element models. Boundary and support conditions included rigid floor support and side supports to prevent the out-of-plane displacement frame. Figure 5(a) shows boundary conditions and the place of cyclic loading. As shown in Figure 5(a), all degrees of freedom at the base of piers' shear walls are closed. According to the general coordinates shown in Figure 5(a), a cyclic load is applied to the x-direction to the reference point (RP-1 and RP-2). Also, according to the boundary conditions of the experimental setup (Dubina and Dinu, 2014), to prevent the out-of-plane displacements, lateral supports in the panel zone were used (Figure 5(a)). Figure 5(b) shows boundary conditions and the place of cyclic loading. As shown in Figure 5(b), all degrees of freedom at the bottom plate are closed. According to the general coordinates shown in Figure 6(b), a cyclic load is applied to the x-direction to reference point (RP-1) at the top plate. The displacement type of loading was applied in a cyclic manner and according to the experimental (Dubina and Dinu, 2014) protocol of the specimens. In addition, a buckling analysis was performed for the buckling to form a diagonal tensile field in the shear wall plate with the buckling mode shapes employed to create the initial imperfection (Mohebkhah and Azandariani, 2015, 2016). The applied imperfection magnitude was considered to be l_P/1000, where l_P is the web plate width.

Figure 6.

Comparison of test (Dubina and Dinu, 2014) results and finite element model: (a) R-M-T2 and (b) R-C-T2.

Material and properties

Material properties modeling uses steel material J₂ for beam, columns, and infill plate members (Gorji Azandariani, 2021). For all models, the behavior of the materials was considered inelastic. The stress–strain curve was a bilinear model, and the plasticity model used was based on von Mises yield surface and associated flow rule. Plastic strain hardening was also considered using the nonlinear combination isotropic and kinematic hardening law (Gorji Azandariani, 2021). The combined isotropic and kinematic hardening model is available in ABAQUS software as a tool in the materials section, which is parameterized as Hardening: Combined and Data type: Stabilized model (Gorji Azandariani, 2021). The input parameters in this model are in the characteristics of stress–strain data obtained from the experimental coupon test so that the ideal multi-line stress–strain curve from the test is obtained and introduced to the software as strain–stress data (Gardner et al., 2019; Yun and Gardner, 2017). Based on this, the ideal multi-line stress–strain curve based on the tensile coupon test results reported by references (Castiglioni et al., 2013; Dubina and Dinu, 2014) has been obtained and used for modeling in the software. The properties of the test material of the steel coupons of the specimens tested by Dubina and Dinu (2014) and Castiglioni et al. (2013) employed in the finite element modeling for infill plates, beams, columns, and pin FUSE are reported in Table 2.

Table 2.

Material properties of the test (Castiglioni et al., 2013; Dubina and Dinu, 2014) specimens and used FE models.

			Material properties
Element	Steel grade	Thickness (mm)	Modulus of elasticity (GPa)	Yield stress (Mpa)	Ultimate stress (MPa)
HEB 240	S355	17	200	457	609
HEB 240	S355	10	200	458	609
HEB 180	S355	14	200	360	515
HEB 180	S355	8.5	200	408	540
HEA 180	S355	9.5	200	419	558
HEA 180	S355	6	200	415	542
Infill plate	S235	2	200	305	429
Pin FUSE	S235	-	200	220	460

Validation of finite element model

In this part of the research, the accuracy of the finite element modeling of coupled steel plate shear walls and pin FUSE were investigated using ABAQUS (2010) software. For this purpose, laboratory samples of the coupled steel plate shear walls of Dubina and Dinu (2014) and pin Fuse Castiglioni et al. (2013) were used for validation. During experiments, to investigate the behavior of thin steel plate shear walls, Dubina and Dinu (2014) tested two samples of two-story steel sheet shear walls with a scale of 1:2 under uniform and cyclic loading. As these experimental specimens have been tested on two floors, they were selected for modeling and validation. Two models were selected for C-SPSW modeling, the specifications of both test specimens being the same, while only the type of loading was different. The thickness of the infill plates was 2 mm, and the axis distance of the columns was 1400 mm. Table 3 presents the specifications of the Dubina and Dinu (2014) test specimens. The specifications of the test specimens tested by Dubina and Dinu (2014) and employed in the finite element modeling for infill plates, beams, and columns are reported in Table 3. The diameter of the pin in the middle region was 45 mm, and the diameter of the side regions was 60 mm. Also, the middle pin length was 90 mm, while the side pin length is 160 mm.

Table 3.

Specifications of the test specimens of Dubina and Dinu (2014).

Specimen	Plate thickness (mm)	Beam-to-column connection	Ext. column section	Int. column section	Beam section	Link beam section	Loading
R-M-T2	2	Rigid	HEB240	HEB180	HEA180	HEA180	Monotonic
R-C-T2	2	Rigid	HEB240	HEB180	HEA180	HEA180	Cyclic

Model R-M-T2

The analysis of the finite element model and the R-M-T2 test specimen are presented in Figure 6(a). A comparison of the numerical model results and test specimen uniform loading shows that the model can simulate the behavior of the laboratory model. The maximum displacement applied in the R-M-T2 test (Dubina and Dinu, 2014) specimen was 182 mm, and the maximum load was 1143 kN. The maximum force tolerated by the numerical model was 1155.7 kN, with the ratio of the results of the finite element model to the test being 1.01. Figure 7(a) illustrates the out-of-plane displacement measurements of the finite element model and the R-M-T2 test specimen. As indicated in Figures 6(a) and 7(a), the predictions of the load-displacement curve and out-of-plane displacement measurements of the finite element model are consistent with the test results.

Figure 7.

(a) Out-of-plane displacement measurements comparison of FEM and test (Dubina and Dinu, 2014) specimens of R-M-T2 and (b) Comparison of failure modes of test (Dubina and Dinu, 2014) results and finite element model R-C-T2.

Model R-C-T2

The results of the analysis of the R-C-T2 finite element model under cyclic loading are shown in Figure 6(b). A comparison of the results of the cyclic loading of the numerical model and the test specimen indicates that the model has been well able to simulate the hysteresis behavior of the laboratory model. The maximum displacement applied in the R-C-T2 test (Dubina and Dinu, 2014) specimen was 182 mm, and the maximum load was 1151 kN. The maximum force tolerated by the numerical model was 1144 kN, with the ratio of the results of the finite element model to the test being 0.99. Figure 7(b) illustrated the failure modes of the finite element models and the R-C-T2 test specimen. As shown in Figure 7(b), the finite element model simulates out-of-plane buckling and the tensile field yield on the web plates. Comparison of the finite element analysis results and the test results reveal that the hysteresis behavior has predicted the initial stiffness of the loading and unloading, the permanent out-of-plane deformation, the stiffness, and the pinching phenomenon at the cyclic loading.

Model Pin FUSE

The results of the analysis of the R-C-T2 finite element model under cyclic loading are shown in Figure 8. A comparison of the results of the cyclic loading of the numerical model and the test specimen indicates that the model has been well able to simulate the hysteresis behavior of the test specimen (Figure 8(a)). The maximum displacement applied in the pin FUSE test (Castiglioni et al., 2013) specimen was 45 mm, and the maximum load was 225 kN. The maximum force tolerated by the numerical model was 234 kN, with the ratio of the results of the finite element model to the test being 1.04. Figure 8(b) illustrated the failure modes of the finite element models and the pin FUSE test specimen. Figure 8(b) shows that the finite element model simulated plastic hinges on the pin FUSE.

Figure 8.

Comparison of test (Castiglioni et al., 2013) results and finite element model Pin FUSE: (a) hysteresis load-displacement and (b) failure modes.

Cyclic behavior of coupled steel plate shear wall (C-SPSW)

The finite element models studied

To study the cyclic behavior of the C-SPSW with FUSE pin, it was selected to represent the last three floors of the 12-story structure designed at Section 2. According to Figure 3, the perimeter gravity frame bays, 5.0 m long; the SPSW bay, 5.0 m long; and the link beam bay, 2.5 m long, were considered from the center to center of the columns. The floors had the same height of 4 m, and the frames were considered in two directions with five bays. The dimensions and sections used along with the plate thickness are presented in Table 4. The abbreviated names of finite element models are also presented in Table 4. Finite element models included coupled steel plate shear wall with I-shaped link beam, I-shaped link beam with reduced beam section (RBS), hollow-link beam with RBS, and FUSE pin-link beam, and the geometry of models is exhibited in Figure 9. Figure 9 displays the geometry of the link beams of the finite element models. For the I-shaped beam, a cross-section of W18×60 was used according to Figure 9(a). The dimensions of the reduced cross-section were calculated according to FEMA-350 (2000), with values of a = 100 mm, b = 320 mm, c = 40 mm, and R = 340 mm, respectively (Figure 9(b)). A hollow rectangular beam was selected to obtain a weight of section W18×60. For this purpose, the hollow section flange thickness was equal to W18×60, and the web thickness of each side of the hollow section was equal to half the web thickness of W18×60. The reduced cross-section was also used for the hollow section, as displayed in Figure 9(c). The FUSE pin-link beam shown in Figure 9(d) was selected according to reference (Dougka et al., 2014). For the yield zone to occur away from the pin-to-beam connection, the diameter of the pin-to-beam connection was greater than the middle region. The diameter of the pin in the middle region was 200 mm, and the diameter of the side regions was 300 mm. Also, the middle pin length was 700 mm, while the side pin length is 400 mm, as shown in Figure 9(d). The dimensions of the link beam with the yielding FUSE pin have been selected so that the weight is equal to the other modes of the link beam to make a fairer comparison between them.

Table 4

Geometric and material properties of FE models.

			Yielding stress (MPa)
Model	Type of link beam	Geometric property of models	Plate	Beam and link beam	Column	Length link beam (m)
C-S-I	I-section	Plate thickness: 3 mm	310	410	410	2.5
C-S-RBS	RBS-section	Column: W24×131	310	410	410	2.5
C-S-H	Hol. RBS-sections	Upper floors beam: W24×194	310	410	410	2.5
C-S-Fuse	Fuse	Middle floors beam: W18×60	310	310	410	1.5
		Link beams: W18×60
		Fuse: Circular pin D200 mm

Figure 9.

The geometry of parametric models: (a) C-S-I, (b) C-S-RBS, (c) C-S-H, and (d) C-S-Fuse.

The material properties of the beams were columns of S355 steel with 410 MPa yield stress, while for infill plate and circular pin fuse of S235 steel with 310 MPa yield stress (Dubina and Dinu, 2014), and Poisson coefficient 0.3 and modulus of elasticity 210 GPa were considered (Table 4). For the entire model, the behavior of the materials was inelastic, and the stress–strain curve was considered elastic–plastic perfect. The loading of the type displacement control and cyclic was applied at the top floor level. The ATC-24 (1992) protocol was used for cyclic loading in the finite element models.

The geometry and meshing of the C-S-Fuse model are shown in Figure 10(a). 4-node shell element (S4R) was used for modeling beam, column, and infill plate sections. Figure 10(a) illustrates the geometry and meshing of the finite element models of pin FUSE. The boundary conditions included the supports and the cyclic loading applied to the parametric models. Load displacement type control and cyclic loading were applied to parametric models. Boundary and support conditions included rigid floor support and side supports to prevent the out-of-plane displacement frame. Figure 10(b) shows boundary conditions and the place of cyclic loading. As shown in Figure 10(b), all degrees of freedom at the base of piers' shear walls are closed. According to the general coordinates shown in Figure 10(b), a cyclic load is applied to the x-direction to the reference point (RP-1 and RP-2). Also, lateral supports in the panel zone were used (Figure 10(b)). The Tie interaction element was used to connect the pin FUSE to the beams at floor level. In this interaction element, all degrees of two interconnected levels are bound.

Figure 10.

(a) The geometry and meshing of the C-S-Fuse model and (b) cyclic loading and boundary conditions of C-S-Fuse model.

Results of finite element models

The finite element models of the coupled steel plate shear wall have been subjected to a quasi-static analysis (explicit method) according to the ATC-24 (1992) protocol cyclic loading. The results of finite element models include hysteresis curves, lateral stiffness, and dissipation energy. The section presents the results of finite element models.

Finite element model C-S-I, a 3-span, and 3-story coupled steel plate shear wall was used in the mid-span of the W60×18 cross-sections for link beams. The lateral load-displacement hysteresis curve of model C-S-I is shown in Figure 11(a). Initial stiffness and maximum base shear strength were 113 kN/mm and 6682 kN, respectively. Figure 12(a) displays the stress distribution in the contour of von Mises model C-S-I. In Figure 12(a), the von Mises stress distribution of the link beams is revealed. In the C-S-I model, the formation of the diagonal tensile field of infill plates, yield of the web plate, the yield of the link beams, the formation of plastic hinges in the beams, and then in the columns are observed. In the C-S-I model, first, the yielding occurred in the web plate due to the formation of the tensile field, followed by the formation of flexural plastic hinges at the end of the link beams. The maximum von Mises stress that occurred in the link beams of this model is equal to 420 MPa, which occurs at both ends of the link beams at the connection with the inner columns of the pier walls. Areas of maximum stress occurred in the proximity of the beam-column connections.

Figure 11.

Hysteretic lateral shear load—Roof drift ratio for models: (a) C-S-I, (b) C-S-RBS, (c) C-S-H, and (d) C-S-Fuse.

Figure 12.

von Mises Stress distribution of FE model: (a) C-S-I, (b) C-S-RBS, (c) C-S-H, and (d) C-S-Fuse (units of the stress: MPa).

C-S-RBS finite element model, a 3-span, and 3-story coupled steel plate shear wall, was used in the mid-span of W60×18 with a reduced cross-section (RBS) for link beams. The lateral load-displacement hysteresis curve of model C-S-RBS is indicated in Figure 11(b). Initial stiffness and maximum base shear strength were 112 kN/mm and 6602 kN, respectively. Figure 12(b) demonstrates the stress distribution in the contour of von Mises model C-S-RBS. Figure 12(b) shows the von Mises stress distribution of the reduced cross-section link beams. Due to the stress distribution, the maximum stress occurred at the reduced cross-section of the link beams. In the C-S-RBS model, the formation of the diagonal tensile field of infill plates, yield of the web plate, the yield of the reduced cross-section of the link beams, the formation of plastic hinges in the beams, and then in the columns are observed. In the C-S-RBS model, first, the yielding occurred in the web plate due to the formation of the tensile field followed by the formation of flexural plastic hinges at the end of the link beams. The maximum von Mises stress that occurred in the link beams of this model is equal to 420 MPa, which occurs at both ends of the reduced cross-section of the link beams at the connection with the inner columns of the pier walls.

C-S-H finite element model, a 3-span, and 3-story coupled steel plate shear wall, was used in the mid-span of the hollow section with an RBS for link beams. The lateral load-displacement hysteresis curve of model C-S-H is shown in Figure 11(c). Initial stiffness and maximum base shear strength were 110 kN/mm and 6534 kN, respectively. Figure 12(c) indicates the stress distribution in the contour of von Mises model C-S-H. Figure 12(b) displays the von Mises stress distribution of the hollow section link beams. In the C-S-H model, the formation of the diagonal tensile field of infill plates, yield of the web-plate, the yield of the reduced cross-section and hollow web section of the link beams, the formation of plastic hinges in the beams, and then in the columns are observed. In the C-S-H model, first, the yielding occurred in the web plate due to the formation of the tensile field, followed by the formation of flexural plastic hinges at the end of the link beams. The maximum von Mises stress in the link beams of this model is equal to 420 MPa, which occurs at both ends of the reduced cross-section and hollow web section of the link.

C-S-Fuse finite element model, a 3-span, and 3-story coupled steel plate shear wall, was used in the mid-span of the FUSE pin for link beams. The load-displacement hysteresis curve of model C-S-Fuse is shown in Figure 11(d). Initial stiffness and maximum base shear strength were obtained at 135 kN/mm and 7966 kN. Figure 12(d) demonstrates the stress distribution in the contour of von Mises model C-S-Fuse. The von Mises stress distribution of the FUSE pin-link beams is exhibited in Figure 12(d). The von Mises stress distribution contour in Figure 12(d) shows that plastic hinges have been formed in the FUSE pins. According to von Mises stress distribution, finite element models the column foot yields on the inner columns as well as the local buckling and yields of the external columns due to the internal axial force in the external columns. Also, the formation of plastic hinges occurred near the beam-to-columns connections. Further, with the formation of a tensile field in the infill plates, the shear yield of the plates in the finite element models is observed. The maximum von Mises stress that occurred in the link beams of this model is equal to 310 MPa, which occurs at both ends of the reduced cross-section of the pin FUSE.

Comparison of finite element models

The envelope curves of all hysteresis curves are displayed in Figure 13(a) to compare the general behavior of finite element models. The maximum base shear of C-S-I, C-S-RBS, C-S-H, and C-S-Fuse models is 6682, 6602, 6534, and 7966 kN, respectively. A difference of 19% of the maximum base shear of the C-S-Fuse model with other types of coupled steel plate shear walls is observed. Among the finite element models studied, the maximum base shear occurred in the C-S-Fuse model. This difference in capacity is significant in the C-S-Fuse model. Given the use of the FUSEs pin instead of typical link beams, the stiffness and ultimate capacity of the coupled steel plate shear walls have increased. The C-S-Fuse model upper bound and the C-S-H model lower bound made up this curve considering the ultimate capacity. To investigate the ultimate capacity and impact of the FUSE pin in the finite element models of the coupled steel plate shear wall, the bar graph of Figure 13(b) reveals the maximum base shear and the maximum normalized base shear relative to the C-S-I model. Given the maximum normalized base shear values, the impact of I-shaped beams with reduced cross-section, the hollow section with reduced cross-section, and the FUSE pin were 0.99, 0.98, and 1.19, respectively. The results suggest that the coupled steel plate shear wall with the FUSE pin-link beam has had a 19% increase in base shear compared to the typical coupled steel plate shear wall.

Figure 13.

Base shear of FE models: (a) Envelope curves and (b) Maximum base shear.

The initial stiffness is one of the most fundamental parameters in the design of structures. The initial stiffness of C-S-I, C-S-RBS, C-S-H, and C-S-Fuse models is 113, 112, 110, and 135 kN/mm, respectively. A difference of 20% of the initial stiffness of the C-S-Fuse model with other types of coupled steel plate shear walls is observed. Figure 14(a) indicates the variations in the stiffness secant of the finite element models to the drift ratio of the roof. The stiffness secant of each cycle plotted the slope of the line between the origin and the peak point of the cycle. According to Figure 14(a), the rate of stiffness reduction is almost the same in all models. In all finite element models, up to 0.5% drift ratio, no dramatic variation has occurred in stiffness. Figure 14(b) demonstrates the bar graph of the initial stiffness and the normalized stiffness. The normalized stiffness of C-S-I, C-S-RBS, C-S-H, and C-S-Fuse models is 1.00, 0.99, 0.97, and 1.2, respectively. Due to the shear behavior of the FUSE pin-link beam compared to other models, it has increased the initial stiffness of the coupled steel plate shear wall compared to other models.

Figure 14.

Stiffness of FE models: (a) stiffness degradation and (b) initial stiffness.

The surface enclosed within hysteresis loops has been used to compare the amount of energy dissipated by finite element models under cyclic loading. In this study, the finite element models were calculated from the intra-loop surface hysteresis, with the cumulative dissipation energy values to the drift ratio being shown in Figure 15(a). According to the hysteresis shapes and loops of Figure 11, it is observed that the C-S-Fuse model has had more energy dissipation than the other finite element models. The cause of this behavior in the C-S-Fuse model is due to the shear behavior of the FUSE pin element and the flexural behavior of the other link beams. According to Figure 15(a), three C-SPSW models with C-S-I, C-S-RBS, and C-S-H reveal a similar energy-absorbing behavior. Figure 15(b) displays the bar graph of the total energy dissipation and the total normalized energy. The total energy dissipation of C-S-I, C-S-RBS, C-S-H, and C-S-Fuse models is 319, 313, 303, and 383 kN.m, respectively. The results indicate that the coupled steel plate shear wall with the FUSE pin-link beam has a 20% increase in total energy dissipation compared to the typical coupled steel plate shear wall.

Figure 15.

Energy dissipation of FE models: (a) cumulative energy dissipation and (b) total energy dissipation.

Response modification factor

Elastic analysis of the structures under earthquake can create base shear force and stresses that are noticeably bigger than real structural response. Overstrength in structures is related to the fact that the maximum lateral strength generally exceeds its design strength. Hence, seismic codes reduce design loads, taking advantage of the fact that structures possess overstrength and ductility. In fact, the response modification factor includes the inelastic performance of the structure and indicates overstrength and ductility. There exist several methods through which the response modification factor is calculated. The most notable method among them is the ductility factor developed by Richards and Uang (2005), where the actual nonlinear behavior is equivalent to a bilinear ideal curve (Idealized Response). To illustrate this, the hardness of the superalgebra section is approximated based on the approximate equilibrium of the surfaces with a line.

The V_y is the yielding force, and V_e is the maximum base shear when the behavior of the structure is assumed to be linear during an earthquake. According to Figure 16, Ve is reduced to V_y due to the ductility and nonlinear behavior of the structure.

Figure 16.

Nonlinear behavior and equivalent bilinear ideal load-displacement curve.

Response modification factor is applied to convert the linear force of the structure into design force. Thus, Equation (5) obtained response modification factor as follows (Richards and Uang, 2005)

R = \frac{V_{e}}{V_{s}} = \frac{V_{e}}{V_{y}} \frac{V_{y}}{V_{s}} = R_{μ} Ω

(5)

where R_μ is the force reduction factor and Ω is the overstrength factor. The overstrength factor is the base shear of mechanism formation (V_y) to base shear of the first hinge-formed structure (V_s) ratio. R_μ is a parameter that measures a structure’s global nonlinear response due to the hysteretic energy. The R_μ is equal to the ratio of maximum base shear considering elastic behavior (V_e) to maximum base shear in elastoplastic perfectly behavior (V_y).

According to Equation (5) and using the ideal bilinear curve plotted in Figure 16, the response modification factor, the force reduction factor, the overstrength factor, and the ductility coefficient have been calculated for numerical models and are presented in Table 5. Also, the uniform and ideal bilinear load-displacement curves for numerical models are shown in Figure 17.

Table 5.

The response modification factor, force reduction factor, overstrength factor, and the ductility coefficient of numerical models.

Models	V_e (kN)	V_u (kN)	V_y (kN)	V_s (kN)	Δ_y (%)	Δ_max. (%)	μ	Ω	R _μ	R
C-S-I	29,862	6682	6433	4099	57	400	7.02	1.57	4.64	7.29
C-S-RBS	32,431	6602	6366	4065	57	400	7.02	1.57	5.09	7.98
C-S-H	31,939	6534	6269	3999	57	400	7.02	1.57	5.09	7.99
C-S-Fuse	42,809	7966	7445	4880	55	400	7.25	1.53	5.75	8.77

Figure 17.

Uniform and bilinear ideal load-displacement curve: (a) C-S-I, (b) C-S-RBS, (c) C-S-H, and (d) C-S-Fuse.

According to the results presented in Table 5, the ductility parameter and the overstrength factor of finite element models are not significantly different. According to the values obtained for the response modification factor and comparison of the results show that the largest coefficient of behavior belongs to the C-S-Fuse model with a value of 8.77, which, compared to other models, has increased by 17%. According to Table 5, the response modification factor of the C-S-I, C-S-RBS, and C-S-H models are 7.29, 7.98, and 7.99, respectively. In the finite element models, C-S-RBS and C-S-H compared to the C-S-I model, an increase in the response modification factor is observed which is 8.84 and 8.85%, respectively.

Conclusion

In this research, an innovative system of coupled steel plate shear wall with FUSE pin was presented. Finite element method and cyclic analysis were performed to investigate the behavior of the innovative coupled steel plate shear wall with FUSE pin-link beam. To verify the finite element method results, two test specimens of two-story coupled steel plate shear wall and pin FUSE were modeled and analyzed. Comparison of the finite element analysis of coupled steel plate shear wall and pin FUSE shows that it has a good prediction of hysteresis behavior and failure mode at the cyclic loading. The finite element models include coupled steel plate shear wall with I-shaped link beam, I-shaped link beam with reduced beam section (RBS), and hollow-link beam with RBS and FUSE pin-link beam. According to the results, the reduced sections used in link beams did not affect the stiffness, energy dissipation, and ultimate capacity. The results revealed that the FUSE pin-link beam increased the base shear by 19% compared to other link beams. Due to the shear behavior of the FUSE pin-link beam compared to other models, it has enhanced the initial stiffness of the coupled steel plate shear wall. According to the hysteresis loops, the coupled steel plate shear wall with the FUSE pin-link beam had more energy dissipation than other finite element models. The rate of total energy dissipation in the model with the FUSE pin in the link beam was approximately 20% more compared to the other models. The cause of this behavior in the C-S-Fuse model over other finite element models is due to the shear behavior of the pin element and the flexural behavior of other link beams.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ahmad Maleki

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