Abstract
This article experimentally studies the seismic behavior of reinforced concrete frames with buckling-restrained steel plate shear walls. The buckling-restrained steel plate shear wall is connected to adjacent reinforced concrete beams alone by an embedded steel connector in the beams (two-side connection). This is to avoid the force transfer between the shear wall and adjacent columns with a four-side connection. Four specimens of two-story and one-bay reinforced concrete frames with buckling-restrained steel plate shear walls are designed and tested under monotonic and cyclic loads. Finite element analyses are also conducted to further investigate the advantages of buckling-restrained steel plate shear walls by comparing the behavior of reinforced concrete frames with and without buckling-restrained steel plate shear walls. The results show that the presence of buckling-restrained steel plate shear wall can not only enhance the stiffness and load-bearing capacity but also improve the ductility and energy dissipation capacity of reinforced concrete frame structures. It is found that the drift ratio of the specimens reaches 1/15 under monotonic loads and 1/30 under cyclic loads. The specimens have ductility coefficients greater than 10. Two failure modes are found for reinforced concrete frames with buckling-restrained steel plate shear walls. Damages may concentrate at the base of ground floor columns for a frame with strong connectors, while plastic hinges may form at the ends of beams and columns for frames with weak connectors.
Keywords
Introduction
Steel plate shear walls (SPSW), as a lateral load-resisting component, have been developed and applied since 1970s. It is composed of horizontal boundary elements, vertical boundary elements, and steel plates connected between them. The infill steel plate has good load-bearing capacity but always suffers from shear buckling, significantly decreasing its stiffness and energy dissipation performance.
SPSWs have been widely used in the steel-framed structures, and numerous experimental and numerical studies have been done (Astaneh-Asl, 2001; Caccese et al., 1993; Choi and Park, 2008; Driver et al., 1998). The cyclic behavior of thin and thick SPSWs is dominated by shear and flexure strength of the steel plate, respectively (Park et al., 2007). The SPSWs are also used in the frames with concrete-filled steel tubular columns (Nie et al., 2013) or steel–concrete composite structures (Rahai and Hatami, 2009). The application of SPSWs in reinforced concrete (RC) structures have attracted increasing interests, motivated by the improvement of energy dissipation capacity (Choi and Park, 2011; Su et al., 2002). It showed that the SPSW improved the strength, stiffness, and ductility of RC frames (Choi and Park, 2011). However, concrete cracking was observed at the middle height of beams and columns, which may decrease the load-bearing capacity of columns under vertical loads. Furthermore, the ductility of SPSW systems may be reduced due to the premature shear failure at the ends of beams (Su et al., 2002).
In general, the seismic behavior of SPSWs is limited by the buckling of the infill steel plate. Using restraining panels (concrete or steel) is one of the most popular methods to restrain the buckling of steel plates. Two panels are fixed on both sides of the steel plate but are not connected to the adjacent beams and columns thus providing no contribution to the stiffness and strength of frames. The behavior of buckling-restrained steel plate shear wall (BRSPSW) with four-side connections (connections to the adjacent beams and columns) have been well studied and understood (Amani et al., 2013; Guo and Dong, 2005; Guo et al., 2012; Jin et al., 2016; Wei et al., 2016). Compared to thin SPSWs, the BRSPSW has better load-bearing capacity and energy dissipation capacity (Guo et al., 2012). Furthermore, the four-side connected BRSPSW has good mechanical behavior since the whole steel plate is in shear. However, the connection of the shear wall to the adjacent columns in a four-side connection may transfer shear forces from the shear wall to the columns thus leading to the premature damage in concrete columns induced by the embedded connector. This would decrease the vertical load-resisting capacity of the adjacent columns. In addition, there always occur local buckling and fracture of the steel plate at the edges. It is also difficult to erect shear walls to columns with a large spacing. As an alternative, BRSPSW with connections to beams alone (i.e. two-side connection) is proposed (Lu et al., 2011; Sun et al., 2006). The BRSPSW with a two-side connection avoids the direct force transfer between the shear wall and columns, and also makes it feasible for a flexible arrangement of steel plates and opening for windows and doors. However, there is a lack of insight understanding of lateral stiffness, load-bearing capacity, energy dissipation capacity of two-side connected BRSPSWs.
This article proposes a novel type of X-shaped BRSPSW with a two-side connection. The BRSPSW is connected to the beams at its top and bottom (no connection to the columns), and restraining panels are fixed on both sides of the steel plate but not connected to the boundary members. Different from rectangular steel plates in which the yielding region occurs around the top and bottom edges, the yielding region of X-shaped steel plates occurs simultaneously at the middle part and top/bottom edges (Liu and Li, 2015). The larger yielding regions in X-shaped steel plates make them possess better energy dissipation capacity than rectangular steel plates with similar sizes and have lower PEEQ (Equivalent plastic strain, which is the cumulative result of plastic strain of the whole deformation process) peak values. The greater the PEEQ, the easier the fracture of steel plates. The performance of RC frames with the proposed BRSPSW were experimentally and numerically studied. Four specimens of two-story and one-bay RC frames with different dimensions of BRSPSWs and loading schemes were tested to investigate their stiffness, strength, ductility, and energy dissipation capacity. Numerical simulations were also conducted to further study the seismic behavior of the proposed BRSPSW.
Specimen design and test setup
Design of specimens
A total of four specimens of two-story and one-bay RC frames with BRSPSWs, labeled as CSW-1–CSW-4, were designed and tested, as shown in Table 1. All the frames are 2.6-m high and 1.8-m wide (scaling factor of 1:3), as shown in Figure 1. The specimens CSW-1 and CSW-2 had the same dimension of RC frames as CSW-3 and CSW-4 but different reinforcements. The specimens CSW-1 and CSW-2 were designed a bit stronger (larger diameter of reinforcements, ϕ25 and ϕ12) than the specimens CSW-3 and CSW-4 (ϕ22 and ϕ10), as shown in Table 1. The four specimens had different schemes of loading, arrangements of reinforcements in the RC beams and columns, and dimensions of SPSWs. The specimen CSW-1 was tested under monotonic loads, while the other three specimens were under cyclic loads.
Parameters of the tested specimens (all units in mm).

Dimension and reinforcements of CSW-3 and CSW-4: (a) dimensions of RC frame, (b) RC frame in the test, (c) RC beam, and (d) RC column.
The X-shaped BRSPSW proposed by the authors (Liu and Li, 2015) was used in this study. The shape and dimension of the steel plates for the four specimens are shown in Figure 2(a) and (b). The specimens CSW-1 and CSW-2 were first tested, and it was found that their load-bearing capacities were beyond the tensile capacity of the actuator. To reduce the load-bearing capacity, the dimension of the steel plate (Figure 2) and reinforcement layout of RC frame for CSW-3 and CSW-4 were reduced. The width of the middle region of CSW-3 and CSW-4 was reduced to 750 mm, compared to 1000 mm for CSW-1 and CSW-2. In addition, the width of the middle region of the steel plate was reduced to avoid the premature failure at the connection between the steel plate and RC beam, which is a main failure mode for a rectangular steel plate. Furthermore, there is very small stress in the middle region of the two sides of the plate which is removed to save material.

Dimension of steel plates and restraining panels: (a) steel plate in CSW-1 and CSW-2, (b) steel plate in CSW-3 and CSW-4, and (c) restraining panels.
Two restraining panels were used and fixed on the both sides of the inner thin steel plate to restrain its out-of-plane buckling, as shown in Figure 2(c). Each panel consists of two steel plates with longitudinal and transverse steel channels between them. For each panel, the thickness of the two steel plates was 10 mm with a spacing of 37 mm. The total thickness of the panel was 57 mm (10 mm + 37 mm + 10 mm). The panels can be seen clearly in Figure 5. The restraining cover panel was conservatively designed to be reused in the tests. In practice, the steel cover panel can be designed with less material and can also be replaced by concrete panels. The BRSPSW was connected to a steel connector embedded in the RC beam, as shown in Figure 3. There was no connection between the shear wall and RC columns. The connector is a H-shaped steel beam with holes in the web and fish plates at the top and bottom. The width of the holes was taken as 100 mm, the same as the spacing of the stirrups in the beam, to facilitate their arrangement. A solid web was used at the ends of the connector for the specimens CSW-1 and CSW-2 (Figure 3(a)). The stirrups can be arranged through the holes in the solid web. The width of holes at the end of the connector was reduced to 20 mm for CSW-3 and CSW-4 (Figure 3(b)). The BRSPSW was welded to the fish plate of the connector.

Steel connectors in the test: (a) the connector in CSW-1 and CSW-2 and (b) the connector in CSW-3 and CSW-4.
Properties of material
Tension tests were carried out to obtain the yield strength (fy) and ultimate strength (fu) of steel. The results for the four specimens are listed in Table 2. The compressive strength of concrete was 51 MPa for the specimens CSW-1 and CSW-2, and 43 MPa for CSW-3 and CSW-4. The Young’s modulus of steel was taken as 200 GPa.
Mechanical properties of steel for specimens.
t: thickness; d: diameter.
Scheme of loadings
A vertical force of 375 kN was first applied to each column (load ratio of 0.15), as shown in Figure 4(a). It is recognized that this load ratio may be smaller than that of columns in practical buildings. This is because, a large load in columns may impose large compressive forces in the BRSPSW, which is different from the reality that the wall is always erected after the construction of the frame and thus bears small vertical loads. A lateral load was then gradually imposed at the top of the frame. The displacement control was used by selecting target lateral displacements of h/600, h/300, h/150, h/100, h/75, h/50, h/40, and h/30 (h = 2.6 m). The cyclic loading was repeated three times for each target displacement after the first two target displacements.

Test setup and layout of measurements: (a) layout of displacements sensors (LVDT) and (b) layout of strain gauges.
Layout of measurements
The lateral displacements at each story (including the base) and vertical displacements at the bottom of the columns were measured, as shown in Figure 4(a). The rotation of the base can be calculated based on the vertical displacements. Strain gauges were also arranged on the key locations of the connector and reinforcements (Figure 4(b)).
Test results
Test phenomena
The specimens CSW-3 and CSW-4 showed similar behavior since they had the same test layout and loading process and therefore only the deformation of CSW-3 was shown in Figures 5 and 6. The difference between CSW-1 and CSW-2 was that cracks occurred on all the columns in CSW-2 because of cyclic loading. The detailed test results are presented as follows:
The tested RC frames with BRSPSWs showed large stiffness and load-bearing capacity, and good ductility. The ultimate capacities of the specimens CSW-1, CSW-2, CSW-3, and CSW-4 were 1758.4, 1590.4, 1336.7, and 1328.4 kN, respectively. The maximum drift ratios of these four specimens were 1/15, 1/19, 1/30, and 1/30, respectively. The maximum drift ratio was determined when the load reduced to 85% of its maximum value.
At the drift ratio of 1/50 (top displacement of 48 mm), there was no damage in the specimens except for cracks uniformly distributed in the columns (Figure 5). After that there was also no severe damage such as wide crack or fracture of the steel plate and reinforcements in the specimens until the occurrence of failure when the load began to decrease.
The damage of the specimens CSW-1 and CSW-2 concentrated at the base of the columns in large compression and shear (Figure 6(a) and (b)). When the load reached the ultimate capacity, there was a main crack at the column base on the compression side. For the specimens CSW-3 and CSW-4, the damage concentrated at the ends of beams and columns (Figure 6(c)), indicating that plastic hinges were fully developed at these locations. After the test, there were obvious crack and crush of concrete at the ends of beams and columns. There were lots of diagonal cracks at the beam-column joint on the first story, which were mainly induced by shear. The difference in the failure modes of the specimens may be due to the stiffness of the ends of the connector. The CSW-1 and CSW-2 had a stronger connector (a solid web at the ends), leading to the damage at the base of columns. The weaker connector in CSW-3 and CSW-4 led to the formation of plastic hinges at the ends of the beams, as well as the ends of columns. This indicates that the web of the connector can be weakened to form plastic hinges in beams since the formation of plastic hinges can further dissipate seismic energy.
The BRSPSW in the four specimens showed good mechanical performance. The restraining panels kept contact during the test and were effective in preventing the buckling of steel plate. In the specimens CSW-1 and CSW-2, there were local tearing of the bolt holes near the edge of the plate, as shown in Figure 7(a) and (b). This is due to the small distance between the hole and the edge of the plate. The tearing of the steel plate concentrated in the middle region for the specimens CSW-3 and CSW-4, as shown in Figure 7(c) and (d). The tearing developed along the diagonal direction due to the fact that the middle region of the steel plate was mainly in shear of which the principle stress was in a 45° angle. The tearing failure of middle region is the primary and favorable failure mode for BRSPSW. It is suggested to increase the distance of the corner holes from the edge to avoid its tearing and induced failure of the connection between the steel plate and RC beam. No failure was found in the welding between the shear wall and fish plate of the connector for all the four specimens, which guaranteed the strength of the steel plate–beam connection. The test results show that the application of the proposed X-shaped BRSPSW can effectively avoid the connection failure between the wall and beams. It made the plastic zone move and concentrate in the middle region with a reduced area, leading to a more uniform distribution of plastic strain and better ductility.
There was no damage in the embedded connector, thus effectively ensuring the force transfer between the BRSPSW and RC beams. Furthermore, the embedded connector greatly enhanced the shearing and bending capacity of the RC beams. The end of the connector was extended into the column which especially enhanced the shearing capacity of the beams.

Deformation of the specimens at 1/50 drift ratio: (a) CSW-1, (b) CSW-2, and (c) CSW-3.

Deformation of the specimens after test: (a) CSW-1, (b) CSW-2, and (c) CSW-3.

Failure modes of X-shaped steel plates: (a) CSW-1, (b) CSW-2, (c) CSW-3, and (d) CSW-4.
Load–displacement curves
Figure 8(a) shows the load–displacement curves of CSW-1. The frame stayed elastic at the beginning of loading. The stiffness started to reduce after the cracking of concrete at about 300 kN. The load-bearing capacity increased until reaching the ultimate load of 1758 kN. The two story had relatively uniform deformation until failure. Figure 8(b) to (d) show the hysteretic load–displacement curves of the specimens CSW-2–CSW-4. The figures show large load-bearing capacity, great initial stiffness, and good energy dissipation capacity of the frames with BRSPSWs. As the ultimate capacity of CSW-2 exceeded the tensile loading capacity of the actuator (1500 kN), the specimen was pushed to failure after a drift ratio of 1/40.

Load–displacement curves of the specimens: (a) CSW-1, (b) CSW-2, (c) CSW-3, and (d) CSW-4.
For CSW-1, CSW-2, CSW-3, and CSW-4, the yield loads were 1010, 1013, 823, and 827 kN corresponding to the yield displacements of 12.1, 10.5, 8.0, and 7.7 mm, respectively. The ultimate loads were 1758.4, 1590.4, 1336.7, and 1328.4 kN, and the ultimate displacements were 162, 129, 80.3, and 76.1 mm, respectively. The ultimate displacements of all the specimens were determined at 85% of the ultimate load. The ductility coefficients were 13.4, 12.3, 10.0, and 9.9, respectively, which showed good ductility.
Energy dissipation capacity
The energy dissipation capacity is an important index to estimate the seismic performance of structures. As the hysteretic curve of CSW-2 (Figure 8(b)) is incomplete due to the fact that its load-bearing capacity was beyond the tensile capacity of the actuator, only the energy dissipation capacities of CSW-3 and CSW-4 were discussed in this section. Figure 9 shows the cumulative energy dissipation of the frame and each story for the specimen CSW-3. The specimen CSW-4 had a similar trend. The cumulative energy dissipations at the first cycle of each target displacement were determined. As shown in Figure 9, the cumulative energy dissipation increased steadily with the increasing displacement, indicating that there was no weak story in the frame.

Cumulative energy dissipation curves of CSW-3.
Degradation of stiffness
With the increase in lateral displacements, the secant stiffness of the tested frame decreased gradually. The secant stiffness of the frame can be calculated as (JGJ101-96, 2008)
where Fi and −Fi are the peak load at each target displacement in the positive (push) direction and negative (pull) direction, respectively; Xi and −Xi are the displacements corresponding to Fi and −Fi, respectively.
Figure 10(a) shows that the secant stiffness of the frame decreased dramatically at the early stage of loading, which may be due to the cracking of concrete and yielding of BRSPSW. A smooth reduction of secant stiffness occurred at the middle and later stage. The degradation of stiffness was uniform and continuous, that is, no sudden change of stiffness.

Stiffness and load-bearing capacity degradation of CSW-3: (a) secant stiffness curves and (b) capacity degradation coefficients.
Degradation of load-bearing capacity
The load-bearing capacity of the specimens decreased as the number of loading cycles increased for the same target displacement. The magnitude of the capacity degradation can be represented by a capacity degradation coefficient λi which is defined as the ratio of the peak load in the current loading cycle to that in the previous cycle (JGJ101-96, 2008)
where
Figure 10(b) shows the variation of capacity degradation coefficients against lateral displacements. The coefficient λ2 represents the capacity degradation between the first and second cycles and λ3 for the second and third cycles. It can be seen that the capacity degradation coefficients varied in a range of 0.9–1.0, indicating a steady load-bearing capacity of the specimens and no occurrence of brittle failures.
In summary, the RC frame with BRSPSWs showed large stiffness, great load-bearing capacity, good energy dissipation and ductility. The lateral load was mainly resisted by the shear wall until its yielding, and the RC frame then shared an increasing contribution, leading to the formation of plastic hinges at the ends of the RC beams and columns. The presence of BRSPSW increased the redundancy of the frame and thus further increased the load-bearing capacity of the frame after the formation of plastic hinges.
Numerical simulation
Finite element model
The behavior of the specimens subjected to lateral loads was also simulated by finite element (FE) software ABAQUS and OpenSees. A detailed model was created in ABAQUS, while a reduced-order model was established in OpenSees. The solid element (C3D8R), shell element (S4R), and truss element (T3D2) were used to simulate concrete beams/columns, steel plates, and reinforcements, respectively, in ABAQUS (Figure 11(a) and (b)). The damaged plasticity material model was used for concrete (dilation angle = 30°, eccentricity = 0.1, fb0/fc0 = 1.16, Kc = 0.667, viscosity parameter = 0.0005). The reinforcement was set to be embedded in concrete and no slip between them was considered. Hard and friction contacts were set in the normal and tangential direction of the surface between the steel connector and concrete beam, respectively. A friction coefficient of 0.5 was used for the friction contact (Baltay and Gjelsvik, 1990; Qureshi et al., 2011). The restraining panels on both sides of the steel plate were not directly simulated, and the out-of-plane degree of freedom of the steel plate was restrained. The effect of initial imperfection was not considered in the FE models. Note that the initial imperfection of the steel plate affects its buckling behavior. The exclusion of initial imperfection will not affect the results as the steel plate may experience yielding in this case rather than buckling due to the strong restraint from the cover plates.

Finite element model of the tested specimens: (a) whole model in ABAQUS, (b) steel plate, connector, and reinforcements in ABAQUS, and (c) reduced-order model was created in OpenSees (units in mm).
In contrast, a reduced-order model was created in OpenSees, as shown in Figure 11(c). The RC beams and columns were simulated using nonlinear beam–column elements, and the BRSPSW was simulated by crossing braces using truss elements (Li et al., 2015). A fiber section was defined for beam–column elements where the reinforcement was simulated by a number of single fibers, and the effect of stirrups was simulated by defining confined concrete at the core of the member section. The BRSPSW was simulated by an equivalent bracing system. The cross section area of braces was determined according to an equivalent lateral stiffness to the BRSPSW, and the material strength of braces was determined based on an equivalent load-bearing capacity (Li et al., 2015). The material model Steel02 and Concrete02 in OpenSees was used for steel and concrete, respectively. The properties of steel and concrete were taken from Table 2. A strain-hardening ratio of 1% was used for steel. The bracing model in OpenSees was to simply detail the modeling approach and to save computation time. The reduced-order model using braces can be used when no shear wall elements are available.
Comparison between the test and numerical analysis
Figure 12 shows the distribution of plastic strains in the modeled RC frame with BRSPSWs. The maximum plastic strain occurred at the base of columns which is consistent with the obvious cracking of concrete at the column base in the test. The predicted strain distribution in the connector is in a reasonable agreement with the measured results.

Distribution of plastic strains in the concrete frame.
Figure 13 shows the comparison of measured and predicted load–displacement curves of the specimens. A reasonable agreement was achieved and thus the proposed FE model can be used to study the behavior of RC structures with BRSPSWs. The predicted load-bearing capacity of CSW-1 was a bit smaller than the test results (Figure 13(a)) which may be due to the friction or the strain-hardening effect of the steel. For the load–displacement curves of CSW-3 (Figure 13(b)), the monotonic loading was used for the numerical analysis and thus the predicted results were larger than the test results from cyclic loadings.

Comparison of measured and predicted load–displacement curves of the tested specimens: (a) CSW-1, (b) CSW-3, (c) hysteretic curves of CSW-2, and (d) hysteretic curves of CSW-3.
Comparison of RC frames with and without BRSPSW
To investigate the effect of BRSPSW on the behavior of RC frame structures, the RC frames with and without BRSPSW were modeled in OpenSees. Figure 14 shows the comparison of load–displacement curves for the frame with BRSPSWs (i.e. the specimens), concrete frame without BRSPSW (labeled as frame), and BRSPSW alone. It can be seen that the presence of BRSPSW greatly enhanced the stiffness and load-bearing capacity of RC frame structures. The drift ratio of the frame with BRSPSWs at yielding fell between those from the frame alone and BRSPSW alone, indicating that the proposed connector could effectively ensure the composite action between the BRSPSW and concrete frame.

Comparison of load–displacement curves between frame with BRSPSWs, frame alone, and BRSPSW alone: (a) CSW-1 and (b) CSW-3.
The energy dissipation capacity can also be estimated using energy dissipation coefficient E (JGJ101-96, 2008), which can be calculated according equation (3) and Figure 15(a)
where S is the area of corresponding zones.

A circle of hysteretic curves and comparison of energy dissipation coefficients between the specimens and frame alone: (a) a circle of hysteretic curves and (b) comparison of energy dissipation coefficients.
Figure 15(b) shows the comparison of energy dissipation coefficients calculated using the first cycle of the load–displacement curve at every target displacement for the specimens and RC frame alone. The energy dissipation coefficient of the specimens increased steadily, and the peak value was nearly 2.0, which was much larger than that of RC frame alone. Therefore, the presence of BRSPSW significantly increased the energy dissipation capacity of RC frame structures.
Conclusion
This article experimentally studied the behavior of RC frames with X-shaped BRSPSW under lateral loads. Numerical models were created to further investigate the effect of BRSPSW on the mechanical behavior of RC frames. The following conclusions can be drawn:
RC frame structures with BRSPSWs exhibited good seismic performance. The BRSPSW can not only greatly enhance the stiffness and load-bearing capacity but also improve the ductility and energy dissipation capacity of RC frame structures. The drift ratios of the specimens reached 1/15 under monotonic loads and 1/30 under cyclic loads. The four specimens had ductility coefficients over 10.
Two failure modes were found for the RC frames with BRSPSWs. The frame with a stronger steel connector embedded in RC beams failed due to the cracking and crushing of the bottom columns in compression and shear force. For the frame with a weaker connector, plastic hinges formed at the ends of beams and columns, leading to its failure as a mechanism similar to RC frame structures. It indicates that a reasonable failure mode can be obtained for structures with BRSPSWs by a proper design of steel connectors.
There occurred tearing of bolt holes in the steel plate (CSW-1 and CSW-2) because of stress concentration. It suggested to increase the distance of corner holes from the edge of the steel plate to avoid its tearing failure. It was found that the tearing of bolt holes would not affect the connection between the steel plate and beams since no failure in the wielding of the connection occurred. It showed that the application of the proposed X-shaped BRSPSW can effectively avoid the connection failure between the wall and beams. The plastic zone concentrated in the middle region with a reduced area and thus led to a more uniform distribution of plastic strain and better ductility.
The proposed connector between the BRSPSW and RC beam effectively ensured the composite action between them and thus greatly enhanced the bending and shearing capacity of RC beams. The application of connectors also guaranteed the shear strength of the beam-to-column connection which should be considered in the practical design to prevent the premature shear failure of the connection.
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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by National Natural Science Foundation of China (Grant No. 51608180) and Natural Science Foundation of Heilongjiang Province (Grant No. QC2016071).
