Experimental Hysteretic Behavior and Application of an Assembled Self-Centering Buckling-Restrained Brace

Fig. 1 illustrates the proposed ASCBRB, where members can be divided into the energy-dissipating (ED) system and the SC system.

The ED system takes advantages of the stable metal yielding in the core plate, wherein no concrete is required for buckling restraint. The steel case for confinement is composed of the core–filler–shim–guide plate group. The core plate is designed having three parts: an elastic segment, a transfer segment, and a yielding segment. When properly designed, earthquake-induced damage only occurs at the core plate and the guide plates, which are replaceable. The slot holes in the elastic segment are used to connect the core plate to the steel angles that have been welded to the end plate I in the factory, and high-strength bolts are used to create sufficient friction. The guide and filler plates restrain the buckling behavior of the core plate along its thickness and width, respectively. Another group of prestressed high-strength bolts clamp the guide plates and the core plate together to further reduce the global buckling behavior (Chou and Chen 2010). Shim plates are installed between the guide and filler plates to separate the core plate from the guide plate and reduce friction. A gap exists between the core plate and the filler plates along their width direction to decrease the friction due to Poisson’s effect during compression.

The SC system is primarily composed of prestressed disk springs with link stoppers and the outer and inner members. The outer tube is composed of the cover plates, channel steels with stiffening ribs, and blocking members with bolts. The channel steels and cover plates are connected to form a hat-shaped element [Fig. 1(b)] that possesses a high section moment of inertia and significantly reduces buckling in the core plate. The inner member is composed of twin screws, the end plates, and blocking nuts. Four uniformly prestressed disk-spring groups are installed on the twin screws. Type A disk springs [refer to the guideline in Code for Disc Spring, GB/T 1972-2005 (General Administration of Quality Supervision, Inspection and Quarantine 2005)], which process near-linear force–displacement behavior, are employed in the braces. The blocking members of the inner screws and the outer tube would contact with the link stoppers in compression in the well-assembled brace. The blocking components in the inner and outer members can be adjusted according to the length of the prestressed disk-spring groups. Consequently, the negative effect of length tolerance (Chou et al. 2014; Erochko et al. 2015a; Xie et al. 2016) in ASCBRBs can be ignored. All the members are prefabricated and can be assembled using bolts onsite.

The assembly procedure is shown in Fig. 2.

The core–filler–shim–guide plate group was placed on the channel steel of the outer tube in the order shown in Fig. 1(a). The plates were aligned with the slot holes along the channel steel in favor of easy installation of the clamping bolts. Both sides of the core plate were oiled to reduce the friction effect between the core plates and the steel case. Thin-type hydraulic oil cylinders, which only require a small workspace, were employed for the prestressing procedure to improve the efficiency of assembly. Thus, the prestress values in the two-disk spring groups increased simultaneously, as shown in Fig. 2(b). High-strength bolts, whose torque values are given in the Bolting Specification table in the Code for Design of Steel Structure, GB 50017-2017 (Ministry of Housing and Urban-Rural Development of China 2017), were used to provide the clamping force in the guide plates to prevent premature buckling in the core plate, as shown in Fig. 2(c).

For postearthquake repairs, the damaged core and guide plates can be replaced after removing the high-strength bolts at the steel angles and the clamping bolts in the steel channels. Generally, the deformation capacity of the disk-spring groups is designed to be much higher than the interstory drift demand. Thus, no special repair work needs to be conducted on the SC system. Moreover, the length of each disk-spring group should be checked to ensure that the SC force and the blocking screw in the outer tube can be used to recompress the group without any further disassembly. Then, the elements can be reassembled as described in the previous paragraph.

Compared with existing SCBRBs (Miller et al. 2012; Eatherton et al. 2014a; Chou et al. 2016; Dong et al. 2017), the main benefits of the ASCBRB are as follows:

The ED and SC systems are installed in parallel. Therefore, the overall hysteretic behavior of the ASCBRB system can be calculated by adding the hysteretic responses of the two systems together.

In previous studies, the force–displacement relationship of SC systems with multiple disk-spring groups has been expressed using a bilinear model (Xu et al. 2017; Dong et al. 2017). In fact, the force-displacement relationship of the SC system can be simplified as a multilinear model where stiffness changes are related to the contact-departure behavior between the blocking members and the disk-spring groups. The friction between the disk springs is comparatively small and is not considered in this paper. The force-displacement relationship of the members in the SC system can be considered as linear elastic, except for the blocking members, which only carry compression loads. The disk-spring groups are symmetrically installed around the core plate and axial members in the SC system and can be separated into two identical segments.

The blocking members can be numbered in sequence, as shown in Fig. 3, where the subscript $o$ represents the outer tube, $i$ represents the inner twin screw, $d$ represents the disk spring, and $b$ represents the blocking members. In addition, $k_{d1}$ represents the stiffness of two identical disk-spring groups. To ensure the same compression and tension performances, the stiffness in the outer tube is equated to that of the inner screw ($k_{i1}=k_{o1}$). Generally, the stiffness of the outer tube and inner screws are much higher than that of the disk-spring group ($k_{o1}=k_{i1}\gg k_{\mathit{d}1}$). The blocking member $k_b$ is considered to be rigid ($k_b=k_{i1}\gg k_{o1}$).

Figs. 4–7 represent the working mechanics of the SC system, which can be divided into three phases based on the changes in stiffness. The states of the SC members at critical points are shown on the left side of the figures, wherein a negative value represents compression. The force-displacement relationships are shown on the right side of the figures and the circle represents the critical point in each phase. Once the brace is completely assembled, the prestress in each disk-spring group is $-T_0/2$, and the force states of the other elements are as shown in Fig. 4. Because $k_{o1}=k_{i1}$, the prestress is equally borne by the outer and inner members. The blocking members that contact the link stoppers of the disk springs have a uniform compression of $-T_0/2$.

In Phase I, when the tensile force applied on the SC system increases from zero to $T_0$, the blocking members No. 11 and No. 24 depart from the link stopper, reducing the compression force to zero, as shown in Fig. 5. Because $k_{i1}=k_{o1}\gg k_{d1}$, the deformation in the outer and inner members has a negligible influence on the prestress in the disk-spring group, and the prestress remains $-T_0$. As the stress in the disk-spring group remains constant, the compression in blocking members No. 21 and No. 14 increases from $-T_0/2$ to $-T_0$. The compression in the other blocking members remains $-T_0/2$, as shown in Fig. 5. In each segment, the outer tube, inner screw, and disk-spring group are in parallel, with the same elongation during Phase I. The two segments of the SC system are in series, and the initial stiffness during Phase I is

During Phase II, as the tension force increases from $T_0$ to $2T_0$, the blocking members No. 13 and No. 22 also depart from the link stopper, whereas the compression in blocking members No. 12 and No. 23 increases from $-T_0/2$ to $-T_0$, as shown in Fig. 6. The stress in each disk-spring group is maintained at the initial prestress value of $-T_0$. In Segment 1, the tensile stress of the outer tube increases from $T_0$ to $2T_0$, and the tensile stress of the inner screw remains constant at $T_0$. However, this is reversed in Segment 2. During Phase II, the two segments in the brace are still in series, and the overall stiffness is

During Phase III, the tension force increases as $P>2T_0$, as shown in Fig. 7. The outer tube, inner screw, and disk-spring groups are in series, whereas the two segments are in parallel. The link stoppers move freely along the inner screw, and the disk-spring groups are compressed further. Because $k_{i1}=k_{o1}\gg k_{d1}$, the deformation in the disk-spring groups can be assumed to be the total elongation in the brace. The stiffness during Phase III is given by Eq. (3). Because the outer tube and inner screw have identical stiffness values, the stiffness change during compression is the same as that during tension

A bilinear elastoplastic model is proposed herein to represent the hysteretic behavior of the core plate considering the strain-hardening effect, as shown in Fig. 8. Because the friction between the core plate and the steel case is relatively small, it is not considered in the system mechanism.

The stiffness of the ED system is determined by the length and cross section of different segments in the core plate. The hysteretic relationship of the entire brace is shown Fig. 8, where, $f_{sc}$ is the prestress sum in the disk-spring groups, $f_{sy}$ is the yield force in the core plate, ${\mathrm{\Delta }}_{\mathit{sc}}$ is the activated displacement when all the departure behaviors occur, and ${\mathrm{\Delta }}_{sy}$ is the yield displacement which is related to the length of the different segments in the core plate. The energy-dissipation and resilience capacities are determined by the ED ratio $\eta =(f_{sc}+f_{sy})/2f_{sy}$.

To verify the seismic performance of the ASCBRBs, four specimens with different energy-dissipation ratios were tested under cyclic loading. The specimens had the same dimensions but different arrangements of the prestressed disk-spring groups and core plates. The layouts of the assembled BRB (ABRB), the assembled SC brace (ASCB), and two ASCBRBs that were tested herein are shown in Fig. 9.

The braces were identical in length (2,380 mm), and the gap between the outer tube and the inner twin screws, which determined the deformation capacity during the test, was 60 mm. End plate I was $190\times 520\mathrm{mm}$, and the thickness of the plate was 40 mm. End plate II was $650\times 650\mathrm{mm}$, and the thickness of the plate, which prevented the relative displacement between the two End plates I, was 50 mm. Two $180\times 16\text{-}\mathrm{mm}$ steel angles with bolt holes were welded onto End plates I to enable the installation of the core plate. The channel steel in the outer tube was Type 14a made of Q345 steel, which was also used for the stiffening ribs that were welded to it. The M16 blocking screws in the outer tube were made of high-strength steel (M8.8) and fixed using double nuts.

The guide and cover plates had the same cross section ($340\times 8\mathrm{mm}$) and were also made of Q345 steel. The disk springs were made of $60{\mathrm{Si}}_2\mathrm{MnA}$ steel, and the twin screw was made of high-strength steel (M8.8). Extra hardening treatment was conducted on the twin screw to prevent partial crush failure due to the movement of the disk springs. The inner twin screws were M48 and the blocking members of the inner screw were nuts with identical dimensions.

The core plates were made using Q235 steel, whose yield stress was 242 MPa, with an ultimate elongation ratio $\delta =18\%$. The lengths of the elastic, transfer, and yielding segments were 445 mm (495 mm), 275 mm, and 675 mm, respectively. The segment lengths of the core plates in the BRB, ASCBRB_1, and ASCBRB_2 specimens were identical. The cross section of the elastic segment of all the core plates was $22\times 8\mathrm{mm}$. The cross section of the yielding segment in the ABRB and ASCBRB_2 was $130\times 8\mathrm{mm}$, and that in the ASCBRB_2 was $90\times 8\mathrm{mm}$.

The filler and guide plates, which prevent the buckling of the core plate in the width and thickness directions, were made of Q345 steel. The shim plates (1-mm in thickness), which separate the core plate from the guide plates and eliminate the effects of friction, were made of stainless steel. The guide, shim, and filler plates are assumed to have no contribution to the stiffness of the energy-dissipation system.

The working diagram of the braced frame is shown in Fig. 10. According to the Chinese seismic design code [Code for Seismic Design of Building, GB 50011-2010 (Ministry of Housing and Urban-Rural Development of China 2010)], the maximum drift ratio of the frame during a rare earthquake is 2%. The axial deformation demand of the brace, which is related to the installed angle $\theta$ to the floor has a maximum value of 1% when $\theta =45°$ [Eq. (4)]. The axial deformation of the belt column is disregarded herein. The design deformation demand of the brace was ${\mathrm{\Delta }}_d=1\%\times \mathrm{2,380}=23.8\mathrm{mm}$. The axial deformation capacity of the ASCBRB was decided by the arrangement and prestress of the disk-spring group. Fig. 11 illustrates a single disk spring and the disk-spring group adopted herein. The disk spring had an outer diameter of $D=100\mathrm{mm}$, an inner diameter of $d=49\mathrm{mm}$, a thickness of $t=7\mathrm{mm}$, and a height of $H=9.2\mathrm{mm}$. For $(H-t)/t=0.314<0.4$, the force-displacement relationship of the disk-spring group can be simplified as a linear relationship with a stiffness $k_1=46.7\mathrm{kN}/\mathrm{mm}$ for a single piece, in accordance with the Chinese code (Code for Disc Spring, GB/T 1992-2005). When two disk springs are placed in the same direction, the load-carrying capacity $F_d$ doubles. When two disk springs are placed in opposite directions, the deformation capacity $f$ doubles (Fig. 11).

The prestress in each group was $T_0/2=50.8\mathrm{kN}$ with an initial deformation of 0.55 mm in each disk spring. The elastic deformation range of each disk spring was ${\mathrm{\Delta }}_1=0.75\times (H-t)=1.65\mathrm{mm}$. The deformation capacity of each prestressed disk-spring group was ${\mathrm{\Delta }}_c=({\mathrm{\Delta }}_1-0.55)\times 36=39.6\mathrm{mm}>{\mathrm{\Delta }}_d$. The stiffness of each prestressed disk-spring group was $0.5k_d=k_1\times 2/36=2.59\mathrm{kN}/\mathrm{mm}$. The SC system consists of four identical prestressed disk-spring groups that provide a SC force of $2T_0=203\mathrm{kN}$

The SC ratio ${\alpha }_{\mathrm{SC}}$, proposed by Eatherton et al. (2014b) (Qiu and Zhu 2016), is defined as the ratio of the resilient force divided by the strain-hardened BRB strengthwhere $\beta$ = compression strength adjustment factor; and $\omega$ = strain-hardening adjustment factor for the buckling-restrained core plate, where $\beta =1.2$ and $\omega =1.6$ (Bruneau et al. 2011). The SC ratios of the specimens are listed in Table 1. A lower value of ${\alpha }_{\mathrm{SC}}$ indicates a higher energy-dissipation capacity and a poorer resilience.

The experiment was conducted at the State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University. The load-carrying capacity of the servohydraulic actuator was 2,000 kN with a deformation capacity of $\pm 200\mathrm{mm}$. To prevent the brace from moving in directions other than the axial direction, the specimen was placed on a steel platform that only permitted axial deformation, as shown in Fig. 12.

Considering the conditions of the loading devices, pin connections were adopted for both ends of the novel brace in the test. High machining accuracy is required for pin connections to avoid uneven stress in the gusset plate. Generally, welding of the ribs and removal of the beam ends from the rigid region are necessary when the novel braces are used in buildings. In the absence of a loading rate in the code, we formulated a low-speed loading protocol to demonstrate the hysteretic behavior while disregarding the influence of damping for the displacement-dependent ASCBRB. The loading protocols for different specimens are shown in Fig. 13.

The loading protocol in the Chinese code recommends that the loading displacement for each level be a multiple of the yield displacement ${\mathrm{\Delta }}_{\mathrm{y}}$. However, Erochko et al. (2015a) reported that the connection at the ends of the brace and length tolerance influence the brace stiffness as well as the yield displacement ${\mathrm{\Delta }}_{\mathrm{y}}$. The ASCBRB mechanism described in the “Mechanical Properties” section does not yield a precise estimation of the stiffness, and a detailed model is required for further study. The same loading protocol was employed for the specimens, and the results were used to calibrate the detailed model.

The Chinese code loading protocol was followed for the full-length braces after the ASCBRB mechanism had been thoroughly studied. The connections, torsion mode of the core plate, and out-of-plane deformation have been observed to influence the stability of full-length BRBs (Black et al. 2004; Palmer et al. 2013). With regard to the loading condition of the devices, the specimens were considerably shorter than actual braces used in buildings, and only axial deformation was considered in this study.

The hysteretic curves of the specimens are shown in Fig. 14.

The ABRB specimen had satisfactory energy-dissipating capacity, but its ultimate ductility ($\mu ={\mathrm{\Delta }}_u/{\mathrm{\Delta }}_y=6.2$) can be improved. The yield force of the ABRB specimen ($f_{sy}=250\mathrm{kN}$) was close to the value calculated based on the section and the material test result ($f_{sy}=\mathrm{1,040}\times 0.242=251.7\mathrm{kN}$). The initial stiffness of the brace based on the test result was $96\mathrm{kN}/\mathrm{mm}$, which was 10% lower than the calculated stiffness ($128.3\mathrm{kN}/\mathrm{mm}$). This discrepancy is probably on account of the connections at both ends, which were in series with the brace members. The obvious decline in the restoring force of the ABRB indicated that the core plate ruptured during the 12th cycle of the tension test, as shown in Fig. 14(a). The maximum displacement of the specimen was ${\mathrm{\Delta }}_m=16.2\mathrm{mm}$, and the residual displacement was ${\mathrm{\Delta }}_r=12.7\mathrm{mm}$ after the 11th cycle. The residual displacement ratio was ${\mathrm{\Delta }}_r/{\mathrm{\Delta }}_m=78.4\%$, which indicates that residual interstory drift in the ABRB frame is inevitable after a severe earthquake.

Fig. 14(b) indicates that the ASCB possesses fairly good resilience and relatively low energy-dissipating capacity. The restoring force of the ASCB at the end of Phase II (230 kN) was higher than the designed prestress value (203 kN) obtained from the theoretical model owing to the friction between the twin screws and the disk springs. The residual displacement after the brace reached the peak displacement of ${\mathrm{\Delta }}_m=31.1\mathrm{mm}$ was ${\mathrm{\Delta }}_r=0.3\mathrm{mm}$; the residual displacement ratio was ${\mathrm{\Delta }}_r/{\mathrm{\Delta }}_m=0.96\%$. Furthermore, the restoring force did not reduce even after 17 cycles, and the deformation capacity of the ASCB was significantly higher than that of the ABRB. The initial stiffness of the ASCB was $347\mathrm{kN}/\mathrm{mm}$, which is higher than that of the ABRB owing to the contribution of the outer and inner members.

The hysteretic curves and the theoretical models of ASCBRB_1 and ASCBRB_2 [Figs. 14(c and d), respectively] fitted well. The experimental yield forces of ASCBRB_1 and ASCBRB_2 were 400 and 475 kN, respectively. The core plate in ASCBRB_2 was identical with that in ABRB (theoretical $f_{sy}=251.7\mathrm{kN}$) and its theoretical yield force in ASCBRB_2 was $f_{sy}=174.2\mathrm{kN}$.

The prestressed disk-spring groups in ASCBRB_1 and ASCBRB_2 were identical with the arrangement used in the ASCB specimen (theoretical $f_{sc}=203\mathrm{kN}$). The experimental yield force of the core plate $f_{sy}$ and the experimental activation force of the SC system $f_{sc}$ were recognized from the test result and marked in Figs. 14(c and d). The initial stiffness did not change significantly from one cycle to the next, and the restoring force reduced when the core plate ruptured during the 12th cycle. The ductility of ASCBRB_1 and ASCBRB_2 was the same as that of ABRB. The residual displacements of the two specimens were ${\mathrm{\Delta }}_r=0.61\mathrm{mm}({\mathrm{\Delta }}_m=17.1\mathrm{mm})$ and ${\mathrm{\Delta }}_r=0.75\mathrm{mm}({\mathrm{\Delta }}_m=17.5\mathrm{mm})$, which indicates that the braces had fairly good resilience (${\mathrm{\Delta }}_r/{\mathrm{\Delta }}_m=3.6\%$ for ASCBRB_1, and ${\mathrm{\Delta }}_r/{\mathrm{\Delta }}_m=4.3\%$ for ASCBRB_2) compared with the ABRB specimen.

The calculated initial stiffness of the ED system was $105.5\mathrm{kN}/\mathrm{mm}$, and the initial stiffness of the entire brace was $431\mathrm{kN}/\mathrm{mm}$. For specimen ASCBRB_2, the initial stiffness of the ED system was $128.3\mathrm{kN}/\mathrm{mm}$, and initial stiffness of the brace was $360\mathrm{kN}/\mathrm{mm}$. The test results indicate that the novel SCB can reduce the residual displacement by 73% at the same peak displacement. The initial stiffness of the two novel braces also improved by 180%–300% compared with the stiffness of the ED system.

Rupturing and local buckling were observed at the free end of the core plate when the specimens were disassembled after the experiment, as shown in Fig. 15(a). Local buckling was observed in the core plate at the free end; this was caused by the straight-line laser-cut shape of the core plate, which may have resulted from a manufacturing fault.

Permanent deformation was also observed in the guide plates near the free end, as shown in Fig. 15(b); this indicates that the thickness of the guide plate near the free end should be increased. Plastic torsional buckling was observed in the cruciform-section BRB ends, which extended out of the confinement tube (Black et al. 2004). However, the thick L-shaped steel and bolt groups at the free end prevented torsional buckling at the free end of the ASCBRB. At the fixed end, because of the clamping bolts, the core plates were protected from damage. For all the tested specimens, there were no buckling failures in the outer tube, blocking members, twin screws, or cover plates, which indicates that these elements can be reused.

To provide resilience, unlike existing ASCBRBs, the proposed ASCBRBs use parallel disk-spring groups, which are less expensive and are commercially available. Unlike in previous studies (Miller et al. 2012; Eatherton et al. 2014a), in this study, the damage to the proposed ASCBRBs was concentrated at the core plate; this enables replacement of the ASCBRB components. Moreover, complete bolt connections also allow for easy assembly and maintenance of ASCBRBs. Notably, the bolts were adopted in the blocking members and connections for both ends. Moreover, out-of-plane deformation is unlikely to occur in shortened specimens, which is limited by the condition of the loading device. Moreover, manufacturing imperfections in the core plate would also result in premature failure of the ASCBRB. These factors may negatively affect the repeatability of the tests conducted on the proposed brace. Thus, tests involving multiple cycles should be conducted on full-length specimens in future studies.

The seismic performance of the braced frames was analyzed using a 6-story office building that was developed in a previous study (Kammula et al. 2014). The steel frame is located on stiff soil (Site class D) in Los Angeles, California, an area with high seismicity. There are three bays in the north–south (N–S) direction and five bays in the east–west (E–W) direction, with a single span of 9.144 m, as shown in Fig. 16(a). The building is 21.95 m in height, and each story has a height of 3.658 m. The weight of the building is 32,100 kN, and the seismic force is equally assigned to the four braced frames in the N–S direction ($W=\mathrm{32,100}\times 0.25=8025\mathrm{kN}$) and the two special moment-resisting frames (SMRFs) in the E–W direction (not discussed herein), as shown in Fig. 16(a).

For frames braced in the N–S direction, the bent columns are pinned to the foundation, and splices for the column segments occur at the third and fifth floors, as shown in Fig. 16(b). The moment-resisting capacity of the girders in the braced frames is neglected, and the girder is pinned to the bent column with a uniform section along its height.

The braced frame in the N–S direction is studied herein to determine the seismic control effect and residual drift after an earthquake. Because the prototype building is an office building, the occupancy category according to ASCE 7-05 (ASCE 2005) is II, and the importance factor $I=1.0$. Previous studies have suggested that the seismic response of SCED-braced frames is comparable to that of BRBFs in terms of the story drift and floor acceleration. The seismic design parameters of the response modification coefficients $R=5.0$, deflection amplification factor $C_d=5.0$, and overstrength factor ${\mathrm{\Omega }}_0=2.0$ were applied to the SCED-braced frames and the BRBFs [ASCE 7-05 (ASCE 2005)], considering the ductility of the specimens used in the experiment. The effective brace stiffness is amplified by the factor $C_b=1.45$, considering the actual working length apart from the rigid gussets and the elastic/transfer segments in the core plate, as shown in Eq. (6)where $E_{\mathrm{s}}$ = Young’s modulus of steel; $A_{\mathrm{syc}}$ = section area of the yielding segment in the core plate; and $L_b$ = full length of the brace in the model including the gusset plates. Eq. (7) governs the design of the bent columns/graders, and the section properties are listed in Table 2. Compression and tension in braces produce fluctuations in the axial load in bent columns and influence the section design (Erochko 2013). The demand is slightly higher in the BRB-braced frame, and the same sections were also adopted in the ASCBRB-braced frame

The lateral force–resisting systems were designed using the Equivalent Lateral Force method prescribed in ASCE 7. The braces are the only elements that resist the seismic load, with the in-plane torsion omitted for simplicity. In the braced frame direction $(\mathrm{N}–\mathrm{S})$, the initial design period $T$ was calculated to be $0.74\mathrm{s}$ ($T=C_u{T}_a$, $C_u=1.4$, and $T_a{=0.0488\times 11.887}^{0.75}$). After several iterations, the final design period $T$ and the base shear $V_0$ of the BRBF were obtained as 0.77 s and 1,682 kN, respectively. The sections of the columns and beams, the area of the core plate, and the initial axial stiffness of the BRB are listed in Table 2. In the gravity system, the leaning columns, which belong to two braced frames, are delineated in Fig. 16(a).

The axial deflection in leaning columns is negligible compared with the deformation in the bent column, which is directly connected to the braces during earthquakes. A similar situation was also observed in the connecting beams. LY225, a kind of low-yield-point steel with good ductility, has been widely used to design BRBs and is considered herein. Because the disk-spring possesses a high axial deformation capacity, surplus deformation capacity is available in the disk-spring groups in which the pieces are installed in series. Second, because manufacturing defects may be present in some pieces, the entire disk-spring group can exhibit severe damage after the elastic deformation phase is exceeded. Thus, the disk springs should be designed to remain elastic at earthquake strengths beyond the maximum strength considered.

In the assembled SC buckling-restrained braced frame (ASCBRBF), the low stiffness at the point when the core plate yields was considered during the design phase, and $V_0=\mathrm{1,682}\mathrm{kN}$, which is identical with the value used in the BRBF. The arrangements of the disk springs were determined based on the design frame drift ${\mathrm{\Delta }}_d=2\%$ and the installation angle $\theta =21.8°$. The initial stiffness of the ASCBRBs is related to the sections of the outer tube, inner screws, and reduction effect of the in-series connections. According to the results obtained from the quasi-static experiment, the initial stiffness of the SC system is 1.8–3.0 times higher than that of the ED system. This implies that the stiffness of the SC system during Phase I is 2.0 times higher than the initial stiffness of the core plate, whereas the stiffness during Phase II is half of that during Phase I. The postactivation stiffness ratio is 0.015. The activation force $2T_0$ of the SC system, area of the core plate used in each floor, and stiffness values of the core plate and SC system are listed in Table 3. The sections of the columns and beams are the same as that of the BRBF. The area of the core plate in the ASCBRBs are only 70% of that in the BRBs for the same design shear force, except for the brace in topmost floor considering the high-order mode effect.

A two-dimensional numerical model was built using OpenSees version 3.2.2 (McKenna et al. 2013) as shown in Fig. 17. The mass of the frame ($M=W/\mathrm{g}=818\mathrm{t}$) was lumped at the closest nodes, denoted by an asterisk. The truss element was employed to simulate the ASCBRBs and BRBs. The material Steel01 was adopted for the BRBs and energy-dissipation system in the ASCBRBs. The material ElasticMultiLinear, which possesses key parameters including activation load, initial stiffness, and postactivation stiffness ratio, was adopted for the SC system in the ASCBRBs. With regard to the installation space in actual cases, the practical length of the truss element is $0.8L$ considering the connections at both ends, where $L$ is the distance between the central points of the panel zones. The ElasticMultiLinear element with a rigid section is used to simulate the reliable connections at the ends of the braces. The ZeroLength element with a weak rotation capacity is employed to solve the problem that the truss and ElasticBeamColumn elements have differently constrained degrees of freedom. The element PanelZone2D was used to represent the shear deformation at the beam–column joints, as shown in Fig. 17.

The columns and beams were modeled using different elements that were connected in series. Vertical and horizontal rigid end offsets were assigned to the ends of columns and beams to simulate the physical dimensions of the gusset plates in the corners. For columns, the center ElasticBeamColumn element was used to represent the column member, with zero-length hinges at either end, and the modified Ibarra–Medina–Krawinkler (IMK) deterioration model was adopted as the material. Because the replacement of an ASCBRB is impossible once the rigid region has been severely damaged, the deterioration parameters are set as 1,000, as recommended on the OpenSees website (OpenSees 2020), which represents that no stiffness deterioration occurs. A zero-length hinge with weak rotation was built at the bottom of the first-story column because the bent columns are pinned to the ground. In addition, zero-length hinges were built at the third and fifth stories to represent the column segment splices. The zero-length hinges at either end of the beams in the tested frame had weak rotational stiffness.

The dynamic characteristics of the BRBFs and ASCBRBFs that were obtained from an eigenvalues analysis of the numerical models built using OpenSees, including the modal information and periods, are given in Tables 4 and 5, respectively. The results of the analysis indicate that the BRBF ($T=0.77\mathrm{s}$) was considerably more flexible than the ASCBRBF ($T=0.65\mathrm{s}$). The stiffness of the BRB was calculated based on the brace length and cross section of the core plate. The concrete and outer tube of the buckling restraint made no contribution to the axial stiffness of the BRB. However, the outer tube and inner screw of the ASCBRB improved the axial stiffness of the brace while still favoring the buckling-restraining effect.

The earthquake motions used herein were originally developed as part of the SAC Steel Project (Somerville et al. 1997). In this project, 20 ground acceleration records were collected and scaled to match the design response spectrum for Los Angeles (location of the object structures). The ground motions correspond to Site class D according to ASCE 7-05 (ASCE 2005). In this study, the records were scaled based on the first period of the braced frame to represent the maximum considered earthquake (MCE) level that has an exceedance probability of 2% in 50 years. The code spectrum and applied earthquake spectra are shown in Fig. 18.

The results of the nonlinear analysis are illustrated in Fig. 19, including the peak/residual drifts under the effect of the 20 seismic waves considering the height and the ductility demand of the braces. The mean value of the peak drift is shown in Fig. 19(a). The average peak interstory drifts along the height of the building were similar for both braced frames (1.75% for ASCBRBF and 1.76% for BRBF). The peak drift (2.04% at the first floor) in the BRBF was a little higher than that in the ASCBRBF (1.9% at the fifth floor). The ASCBRBs provided a higher initial stiffness owing to the contribution of the outer tube and inner screw, which improved the displacement control compared with the BRBF.

The numerical result indicates that the ASCBRBF has comparable seismic performance to the BRBF for the same design parameters. Although the energy-dissipation capacity of the ASCBRB was higher than the recommended value (Macrae and Kawashima 2015), the resilience performance of the braced frame was fairly good, and the residual drift reduced significantly (under 0.1%), as shown in Fig. 19(b). The residual drift values of the stories with the BRBF exceeded 0.5% and the maximum residual drift occurred at the first floor (0.7%), which increases the cost and difficulty in retrofitting (McCormick et al. 2008). Moreover, the ductility demand in the ASCBRBs was less than 8.0 for all the stories, as shown in Fig. 19(c). This difference was more obvious at the first floor (7.6 for BRB and 9.1 for ASCBRB), which indicates that the reduced ductility demand with the ASCBRBs can increase the amount of material saved.

The time histories of the response at first floor and the roof in two braced frames subjected to LA32 are shown in Figs. 20 and 21. The peak drift with the two braced frames occurred at a similar time, as shown in Fig. 20. The peak drift of the first story with the BRBF (2.65%) was a little larger than that of the ASCBRBF (2.16%), as shown in Fig. 20(a). The residual drift of the first story with the ASCBRBF was significantly lower than that of the BRBF (1.4%), as shown in Fig. 21(a), allowing for quick occupancy after an earthquake. In Fig. 20(b), Drift Roof is defined as the ratio of the displacement at the roof to the total building height. Although the residual drift in the BRB frame at the first floor was severe, it was mitigated by the residual Drift Roof (0.56%).

The spectral accelerations on the roof in different frames are shown in Fig. 20(c). The first natural periods of the ASCBRB and the BRB braced frames are 0.65 and 0.77 s, as indicated in in Tables 4 and 5, respectively. The peak responses occur near 0.62 s, with similar peak values. The second-mode periods of the ASCBRB and the BRB braced frames are 0.23 and 0.29 s, as indicated in Tables 4 and 5, respectively. The peak responses also occur near 0.3 s; however, the equipment in the ASCBRB braced frame may experience more severe damage, as shown in Fig. 20(c). Qiu and Zhu (2016) reported that the use of braces possessing flag-shaped hysteretic behavior may result in more prominent high-mode effects in steel frames. The hysteretic curves of the braces in the first and sixth floors are shown in Fig. 21, with closed yield forces in the braces on each floor.

The results show that the prestress in the disk springs can efficiently reduce the final residual drift. The ASCBRBFs reduced the residual drift by over 90% compared with the BRBFs at the first and sixth floors. For the BRBF, the final residual drift was over 40% lower than the residual drift directly caused by the peak drift as shown in Fig. 21, both in the bottom and the top story, which is related to the shakedown effect (Macrae and Kawashima 2015). The shakedown effect was more obvious in the ASCBRBF, with a 95% reduction in the final result of both floors, which is the typical characteristic of flag-shaped hysteretic behavior. Although the peak drifts at the first floor are close for both braced frames, the hysteretic behavior is more symmetrical around the initial position in the ASCBRBF owing to the SC force provided by the prestressed disk springs. The hysteretic behaviors of the two frames are symmetrical for the sixth floor.

The design information in Tables 2 and 3 indicates that the section area in the ASCBRB is about 70% of that in the BRB. The ASCBRBs with flag-shaped hysteresis have lower energy-dissipating capacities in a single cycle than the BRBs with bilinear elastoplastic hysteresis behavior do. The braces that dissipate energy are the most critical parts in both frames; the relevant information is listed in Table 6. The total brace energy is listed in the last column. The results show that ASCBRBs may experience more cycles during the vibration to reach the total energy attained by the BRBs. For the bottom floors (Floors 1–3), the energy is directly related to the yielding forces of the braces. However, the most effective energy-dissipating brace, with the lowest yielding forces, is located at the top floor. This phenomenon is related to the interaction between adjacent stories and the high-mode effect.

The proposed assembled brace exploits the material of the outer tube to achieve a high initial stress. Further, the first period of the frame with the novel brace is lower that of the BRB braced frame, which possesses only a core plate. The results of nonlinear time-history analysis reveal that the drift response of the ASCBRB braced frame is close to that of the BRB braced frame assuming the same design parameters. However, the residual drifts of all stories are under 0.1%, which are significantly reduced compared with that of the BRB frame structure. This merit of the proposed devices is expected to largely reduce the retrofitting or rebuilding cost for seismic damage and has great application perspective in earthquake-prone areas.