Keywords

1 Introduction

Steel plate shear wall (SPSW) is composed of boundary elements and infill steel plates (panels). Compared with the traditional concrete shear wall, the SPSW has excellent performance with the lightweight, high strength, high ductility, good energy dissipation, and flexible installation. In recent years, the SPSWs have been widely used to resist lateral force in high-rise buildings.

The SPSWs emerged in developed countries such as the United States [1], Japan [2], etc., and have been rapidly developing in China [3,4,5,6,7] since the twenty-first century. In the early stage, the elastic buckling of the infill panel was typically taken as the limit state [8]. This led to the necessity of designing the SPSW as a thick steel plate shear wall to resist seismic forces by increasing the infill plate thickness or using stiffeners [9]. Since the 1980s, Thorburn et al. [10] had noted the post-buckling strength of SPSWs and firstly proposed the tensile strip model for the thin infill plate. Afterwards, using the post-buckling strength rather than the critical buckling strength of the thin infill plate to resist lateral force had already formed a broad consensus. To investigate the mechanical performance of SPSWs, a lot of related research has been done. Literatures [11, 12] firstly summarized the past typical experiments and detailed them numerically. Berman and Bruneau [13,14,15] put forward the plastic uniform yielding mechanism and developed the plastic design of SPSWs. In the past decade, Tsai et al. [16,17,18] conducted experimentally and numerically investigations of two-story SPSWs with reduced-beam-section (RBS) connections. Besides, Hao, et al. [3,4,5,6,7, 19] have done a lot of research about SPSWs with various panel treatments, beam-to-column connections, etc. Previous research and engineering practices have shown the good prospect of SPSW in lateral-force resistance.

It is noted that the SPSW subjected to cyclic or seismic load has excellent behavior showing a promising application in high-rise buildings but it is also easily affected by the configuration of panels and beam-to-column joints. In view of this, exploring suitable beam-column connections and infill plate configurations is becoming increasingly necessary. Weak-axis connections, as an inevitable type of beam-to-column connections in steel structures, have been reported in some literatures [20,21,22]. But there are limited reports about the application of beam-to-column weak-axis connections in SPSWs. In this paper, a 4-story 1/3 scaled weak-axis connected steel plate shear wall is designed and tested under cyclic loading for examining its cyclic behavior. Based on the cyclic test, an improved infill plate configuration that partially slotted on the infill plate is proposed. To further investigate the mechanical performance of weak-axis connected SPSWs, the FE models of the test specimen and the partially slotted SPSW are developed and conducted numerical analysis through the FE software Abaqus.

2 Experimental Work

2.1 Test Specimen and Test Setup

The 4-story scaled specimen denoted as S4RN was designed per related provisions [12], as shown in Fig. 1. It is made of Chinese Q235B steel with a nominal yield stress of 235 MPa mainly consisting of the infill plates (QB), horizontal beams (HL1, HL2) and vertical columns (WZ, NZ). The QB configuration is composed of the flat panels (QB), the angle steels (JG), cover plates (GB), and fishplates (YWB). The test setup for S4RN is shown in Fig. 2, in which the test specimen S4RN is pinched by bracing system and mounted on the floor beam through M30 bolts; the S4RN is loaded by the horizontal actuator and vertical Jack through the transfer beam and distribution beam, respectively.

Fig. 1
A close up of the test specimen and illustrations of it explaining the details of its various components.

Geometry and details of test specimen (units: mm)

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Fig. 2
A photograph of a test setup for S 4 R N with labels indicating the reaction beam, hydraulic jack, pressure sensor, actuator, and distribution, transfer, bracing, pressure beam, balance block, and floor beams.

Test setup for S4RN

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2.2 Loading Protocol and Measurement

The pseudo-static loading of the specimen is mainly divided into vertical loading and horizontal loading. First, the vertical load is applied to the specimen by the hydraulic Jack until the axial compression ratio is about 0.2 on each column. After checking the test setup is working well, the actuator supplies the horizontal load to the specimen by displacement control (Fig. 3) until the specimen happens failure or the lateral fore has dropped to 85% of the max peak lateral force. The horizontal cyclic loading history has thirteen drift levels, each with two cycles, including the drift levels of 0.1, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0%.

Fig. 3
A line graph plots roof drift and displacement versus cycles. The curve indicates an increasing fluctuating trend.

Cyclic loading history

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To monitor the concerned deformation of the specimen in real time, displacement meters and strain gauges are selected to place at the corresponding measuring points, as shown in Fig. 4. The displacement meters set on each floor are aimed to gain the specimen’s lateral displacement state. The strain rosettes and strain gauges glued on the infill plates, including the strain gauges attached to the ends of horizontal beams, are aimed to monitor the strain state. Besides, the columns’ flanges are also glued with vertical strain gauges to determine the yielding of the column’s edge.

Fig. 4
An illustration of the measuring points of the test specimen between the west and east direction. It has labels indicating strain rosettes, strain gauges, and displacement meters.

Layout of measuring points

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2.3 Cyclic Behavior of Test Specimen

During the horizontal loading of 0.1~0.25% drift levels, slight local buckling (Fig. 5a) and crisp sound occurred in the 2nd and 3rd story infill plates due to the initial defects and compression. In the 0.5% drift level, infill plates of the 2nd and 3rd stories appeared outside protrusions then the tension bands with the inclined angle of about 36o were observed. Afterward, similar out-of-plane deformation and buckling were observed in the 0.75% drift level.

Fig. 5
A set of 7 different close ups a to e of the S 4 R N test specimen.

Details of the S4RN during test: a the 1st 0.25% drift cycle; b the 1st 3.0% drift cycle; c corner tearing of the 3rd story infill plate (2.0% drift); d corner fracture and folds of the 2nd story infill plate (3.0% drift); e lower edge fracture of the 2nd story infill plate (3.5% drift); f flexural hinge of the 1st story west column after the end of test; g final failure state of the S4RN

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Until the 1.0% drift, creases and yielding first appeared at the corners of the 2nd story infill plate then developed in the 3rd story. During the 1.5% lateral-drift cycles, multiple local yielding and main tension bands were obvious, the cracks occurred continuously in the corners of the 2nd ~ 4th story infill plates. During the 2.0% drift cycles, secondary tension bands on both sides of the main tension bands along the diagonal direction (about 45°) increased, and X-shaped creases near the corners of the 2nd and 3rd story infill plates cracked slightly. At the end of 2.0% drift level, except for the corners in the 1st story infill plate, the others were found horizontal and longitudinal cracks torn, especially the 3rd story infill plate (Fig. 5c). The corner cracks of infill plates developed and extended constantly during the drift level of 2.5 ~ 3.0%, after the first cycle of 3.0% drift (Fig. 5b), serious fracture (the horizontal crack length was about 95 mm) and obvious folds (Fig. 5d) were observed in the lower-left corner of the 2nd story infill plate while the folds on the diagonal of the 3rd story appeared multiple cracks. At this 3.0% drift, the specimen hit the peak shear capacity of 643.57 kN.

During the 3.5% drift cycles, the shear capacity of the specimen began to decrease gradually. The horizontal and longitudinal cracks in the lower corners of the 2nd story infill plate rippled outward in the 1st cycle of 3.5% drift, furthermore, the horizontal cracks in the lower edge extended along the whole edge, and suddenly the whole fractured and lifted outward (Fig. 5e) in the 2nd cycle. In this cycle, bending over the 1st- and 2nd-floor beams was observed. In the 4.0% drift level, the specimen’s shear capacity dropped rapidly to less than 85% of the peak shear capacity. At the end of test, a pronounced curvature (Fig. 5f) of the 1st story west column was observed while no buckling or cracks were detected after the end of test (Fig. 5g).

2.4 Cyclic Behavior of Test Specimen

In the whole horizontal loading, the load-displacement state is analyzed based on the cyclic behavior in Sect. 2.3. The hysteretic and envelope curves are shown in Fig. 6. Considering the first cycle of each drift level largely reflects the maximum capacity of the specimen, therefore, the first cycle is used for the subsequent examination.

Fig. 6
A graph plots lateral force versus lateral drift. The graph plots hysteresis loops for S 4 R N with Q B buckling, Q B yielding, H L end yielding, Q B edge fracture, and W Z flexural hinge labels marked on them.

Hysteretic and envelope curves

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As Fig. 6 depicted, the envelope curve looks like an S-shape, the hysteresis loops are stable before 3.5% drift and start to open in the 1.0% drift level due to the QB yielding. The specimen has happened QB buckling during the 0.5% drift cycles, then found QB yielding during the 1.0% drift cycles. The lateral force hits the peak at 3.0% drift then begins to decline since the HL end yielding and QB edge fracture. Finally, the lateral force has dropped to less than 85% of the max peak lateral force at 4.0% drift. Moreover, the hysteretic curve shows a little pinch near the zero drift. Figure 7 presents the secant stiffness state of the test specimen. It is noted that the initial stiffness of the specimen is 15.55 kN/mm; the stiffness decline gradually in the whole loading, it is almost 50% of the initial stiffness at 1.5% drift and increasingly declines to 3.73 kN/mm at 3.5% drift.

Fig. 7
A column chart plots secant stiffness versus peak lateral drift. The bars indicate S 4 R N in decreasing trends with the maximum and minimum values at 15.55 and 3.73.

Peak secant stiffness state

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Based on Fig. 6, the characteristic points and ductility for the test specimen are summarized in Table 1. The equivalent viscous damping ratio (η) is presented in Fig. 8, but the η before 0.5% drift is neglected since the specimen is almost elastic. The yield point is obtained by the geometric method [23]. The limit displacement is determined by the limit state (i.e. lateral force drops to 85% of the peak load). Table 1 indicates that the specimen yields roughly at 1.2% drift with the lateral force of 534.92 kN, then hits the peak at 3.0% drift with the lateral force of 643.57 kN, finally reaches the limit state at approximately 3.8% drift. Moreover, the ductility of test specimen is about 3.05. As illustrated in Fig. 8, the 1.0% drift is clearly the line that divided the whole loading into elastic and plastic stages, respectively. In addition, the η is increasing and climbs to 23.94% at 3.5% drift.

Table 1 Characteristic points and ductility
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Fig. 8
A column chart plots equivalent viscous damp ratio versus peak lateral drift. The bars indicate S 4 R N in increasing trends with the minimum and maximum values at 3.75 and 23.94.

Equivalent viscous damping ratio (η)

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3 Numerical Analysis

3.1 Validation of FE Model

To further investigate the mechanical properties of the weak-axis connected SPSW, the finite element (FE) model of the test specimen has been developed and simulated by the FE software Abaqus, as shown in Fig. 9. The FE model was meshed by shell element (S4R) with a grid size of 50 mm, while the regions of beam-to-column connections and the perimeter of infill plates were refined with a grid size of approximately 25 mm. The steel materials used in the FE model are the same as the test specimen, and these steel properties are obtained from the tensile test. For simplicity, the stress–strain behavior of materials is considered as multi-linearity, provided that the materials are isotropic in the elastic stage while following the Von-Mises yield criterion and associated plastic flow law after yielding. Thus, a trilinear stress–strain curve with combined isotropic and kinematic hardening was used to simulate the FE model. This trilinear curve reflects an elastic modulus and 1% strain hardening up to the ultimate stress. The nominal yield and ultimate strength of the infill plate, beam and column are reported in Table 2. In addition, the mental ductile damage based on stress triaxiality [24] was considered in the infill plates to reflect the cyclic cumulative damage.

Fig. 9
An illustration of a finite element model and a contour plot, a close up, and a hysteretic graph for the test specimen. The model comprises labels explaining vertical and cyclic loading and lateral and rigid support.

Development and validation of FE model

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Table 2 Material property of tensile coupon test
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To make the loading and boundary conditions of the FE model consistent with the experiment, the lateral support that restrains out-of-plane deformation and the rigid support with encastre constraints were adopted, as shown in Fig. 9a. Also, the cyclic loading and vertical loading were applied on reference points RP-1 and RP-2, respectively. The RP-1 and RP-2 were coupling constrained with the center hole of the top beam and the top surface of the columns, respectively. To verify the validity of the FE model, an implicit method (quasi-static) is used for the nonlinear analysis of the FE model. The hysteretic curve and cyclic behavior compared with that of the test specimen are present in Fig. 9b. It can be seen that the hysteretic curves of the test specimen and FE model are in good agreement. Also, the FE model has well predicted the failure mode of the test specimen, which indicates that the FE model developed and the numerical analysis method are applicable and valid.

3.2 Partially Slotted Steel Plate Shear Wall

The experiment has shown that the designed test specimen (i.e. the SPSW with no slotted infill plates) can well develop the tension field of infill plates, but the infill plates in the middle story level may eventually tear severely along the whole edge, which leads to a rapid loss of lateral force while the beam would happen overall bending (Fig. 9b) due to the incomplete synchronization of the tearing at adjacent story infill plates. In terms of the above issues, a partially slotted infill plate was proposed. The original infill plates in the test specimen were only slotted in the middle region of each side, i.e. each infill plate was divided into four corner regions and one central region. As shown in Fig. 10a, the total width of inter-slot steel strips in each side is about 1/3 length of the edge, each steel strip was designed as a flexural member with the height-width ratio of six per Chinese code [25], which can fully perform its deformation and obstacle the tearing along the whole edge.

Fig. 10
An illustration of a partially slotted infill plate with dimensions marked on it. A contour plot for the test specimen and a hysteretic graph plotting lateral force versus lateral drift for S 4 R N f.

Modeling for partially slotted SPSW

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To verify the effectiveness of the partially slotted SPSW, a FE model for the partially slotted SPSW, denoted as S4RNf, was established and performed cyclic loading according to the numerical method discussed in Sect. 3.1. The FE model for the test specimen, denoted as S4RNm, was selected for comparison. The only difference between S4RNf to S4Rm is the infill plate with slots. Comparing Fig. 9b with Fig. 10, it is noted that the partially slotted SPSW exhibits a plump hysteretic curve, and the infill plate at each story level has fully played the primary and secondary tension band. Besides, neither tearing along the whole edge nor beam overall bending happened in S4RNf until 4% roof drift, meanwhile, the stress of the bottom columns is smaller than that of S4RNm.

3.3 Comparison of Mechanical Performance

To further assess the characteristics of the weak-axis connected SPSWs with no slotted and partially slotted infill plates, the mechanical properties including strength, stiffness, energy dissipation, ductility, etc. were analyzed. In addition, the comparison of mechanical performance between the S4RNm and S4RNf was made as follows. The Figs. 11, 12 and 13 illustrated the variation of hysteresis, strength and energy, respectively. As shown in Fig. 11, the partially slotted SPSW (S4RNf) exhibits a plumper hysteretic curve than that one without slots (S4RNm), and both of them almost yield and hit the peak at the same lateral drift but the S4RNm is damaged too early to get a larger limit displacement. Also, the S4RNf shows more stable strength variation with a strength ratio of greater than 0.95, while, the S4RNm exhibits a severe strength degradation after 3.0% drift and shows a faster stiffness degradation than the S4RNf after yielding, as shown in Fig. 12. In addition, the energy dissipated and equivalent viscous damping ratio have been assessed, as shown in Fig. 13. It can be seen that the energy dissipated and damping ratio of S4RNf is climbing increasingly and hitting the maximum damping ratio of approximately 30%, which indicates that the partially slotted SPSW has a better performance in energy dissipation than that non-slotted SPSW.

Fig. 11
2 graphs plot lateral force versus lateral drift. The first graph plots hysteresis curves for S 4 R N m and S 4 R N f. The second graph plots 2 curves for S 4 R N m and S 4 R N f in increasing fluctuating trends with yield, peak, and limit points.

Hysteresis and skeleton

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Fig. 12
2 line graphs plot strength ratio versus lateral drift and secant stiffness versus lateral drift. The 2 curves in each graph indicate S 4 R N f and S 4 R N m, in fluctuating trend in the first graph and decreasing trends in the second graph.

Strength and stiffness state

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Fig. 13
2 line graphs plot energy versus lateral drift and damping ratio versus lateral drift. The 2 curves in each graph indicate S 4 R N f and S 4 R N m in increasing trends.

Energy dissipation

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Based on Fig. 11, the characteristic points of S4RNm and S4RNf were summarized in Table 3. Besides, the lateral displacement and inter-story drift were illustrated in Fig. 14. As shown in Table 3, the S4Rm and S4Rf both yield at 0.76% drift and hit the peak at 3.0% drift. However, the partially slotted SPSW (S4RNf) has a greater overstrength factor of 1.34. Also its peak lateral force still accounts for 75.37% of the S4RNm, although the S4RNf has been weakened by the slots in the infill plates. Moreover, the S4RNf hits the limit state at 4.4% drift while the S4RNm at 3.8% drift. The ductility of the S4RNf is up to 5.79 but 4.95 the S4RNm, which obviously indicates that the partially slotted SPSW has excellent properties in deformation and ductility. Furthermore, the S4RNf and S4RNm both exhibit a similar lateral deformation pattern (i.e. the deformation transitioned from flexural mode to shear mode). But the S4RNf has a smaller lateral deformation than the S4RNm after 3.0% drift, as shown in Fig. 14a. The S4RNf demonstrates almost the same inter-story drift mode before the 4.0% drift, while the S4RNm obviously has a larger inter-story drift at the 2nd floor due to the severe tearing along the whole edge, as shown in Fig. 14b. Taking the limit displacement as criteria, the limit inter-story drift of S4RNf at the 3rd floor is up to 6.1% but 5.5% the S4RNm.

Table 3 Characteristic points and ductility for the S4RNm and S4RNf
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Fig. 14
2 graphs plot floor versus lateral displacement and floor versus inter story drift. The curves indicate values at 0.1, 0.5, 1, 2, 3, 4, and 4.5 percent and the plots indicate S 4 R N m and S 4 R N f in varying trends.

Lateral deformation state

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4 Conclusions

The ordinary SPSWs have been studied comprehensively. But limited studies on weak-axis connected SPSWs and partially slotted infill plates have been reported, which restrict the improvement and extension of SPSWs. Thus, a 1/3 scaled weak-axis connected SPSW was designed and constructed. After it was tested under cyclic loading, the corresponding nonlinear FE model was developed and validated by test results. Based on the test results and FE model, the partially slotted SPSW was proposed and established the FE model. Finally, the nonlinear FE analysis was performed to further investigate the mechanical performance of these SPSWs with non-slotted and partially slotted infill plates. It is can be drawn from the experimental work and numerical analysis that:

  1. 1.

    The weak-axis connected SPSWs with non-slotted and partially slotted infill plates have good properties in strength, ductility and energy dissipation. Both of them hit the peak lateral force at 3.0% drift and the ratio of peak load to yield load is roughly more than 1.2. Also, the ductility for them is greater than 3.0.

  2. 2.

    Comparing the weak-axis connected SPSW with non-slotted infill plates, the proposed partially slotted SPSW exhibits a plumper hysteretic curve without visible pinch phenomenon. Moreover, it has a more gentle stiffness degradation and stable strength variation with a strength ratio of more than 0.93.

  3. 3.

    Replacing traditional flat steel plates by introducing partially slotted infill plates in SPSWs, which can effectively improve the structural deformation, ductility and strength redundancy, i.e. the limit inter-story drift can be enhanced from 5.5 to 6.1% and the overstrength factor enhanced from approximately 1.2–1.34.

  4. 4.

    Although the partially slotted infill plate will weaken the lateral resistance, the partially slotted SPSW still accounts for 75% of that one without slots in lateral bearing capacity. Furthermore, the proposed partially slotted infill plate can fully play the tension field and effectively obstacle severe tearing along the whole edge then avoid beam’s in-span bending. In addition, the ductility of the partially slotted SPSW is up to 5.79, and its equivalent viscous damping ratio is up to 30%.

Although this work is focused on weak-axis connected SPSWs, it can be extended to coupled steel plate shear walls due to their similar characteristics. Besides, the partially slotted infill plates can be extended to other structures with infill panels to serve as energy-consuming elements, provided that a proper plastic mechanism and design method was proposed. This will be examined in our future work.