Experimental study on slender buckling-restrained knee braces with round steel bar cores

Abstract

This study aimed to investigate a novel slender buckling-restrained knee brace damper (BRKB) for welded and weld-free steel framing systems. The proposed BRKB adopts steel bar cores connected by a central coupler and restrained by tube buckling restrainers with a cover tube supporter. The advantages of the proposed damper include easy assembly compared to conventional buckling restrained braces, and high architectural flexibility for the retrofitting of large-span weld-free or welded steel moment-resisting systems. Specifically, by increasing the number of contraction allowances, undesirable failure mechanisms that are global instability and local buckling of the restrainer ends can be effectively suppressed because the more uniform plastic deformation of the core bar can be achieved longitudinally. In this study, displacement-controlled compression and cyclic loading tests were carried out to investigate the deformation capacities of the proposed BRKBs. Structural performance metrics associated with both loading tests, such as strength capacities, strains at the cover tubes and buckling restrainers, and hysteretic behaviors of the proposed damper under cyclic loads, were measured and discussed. Test results revealed that the geometrical characteristics of the cover tubes and adopted contraction allowances at the dampers play essential roles in their load-bearing capacities.

Graphical abstract

Keywords

weld-free beam-to-column connections / moment-resisting frame / cyclic and compression loading tests / buckling-restrained knee brace / cover tube

1 Introduction

As severe earthquakes can induce excessive inelastic deformation in steel building structures [1,2], various damage-control structures and fuse energy dissipaters have been proposed and investigated for many years [3]. Earthquake-induced damage mainly occurs in the vicinity of welded beam-to-column connections in moment-resistant frames (MRFs). In this regard, to eliminate seismic damage, several novel beam connections have been proposed, such as damage-tolerant steel frames with composite steel joints [4,5] and damage-avoiding connections [6,7]. In the meantime, a knee bracing (KB) system has been developed as a seismic resilience ductile fuse element to prevent the collapse of moment-resisting frames under lateral loads [8–11]. KB systems provide high architectural flexibility and significantly improve the lateral stiffness of MRFs.

In the early stages of their development, KB systems were used as the main ductile fuse element for conventional diagonal bracing systems. For example, in a 1986 study of the KB system by Aristizabal-Ochoa [12], the conventional bracing technique was composed of two structural elements: knee and diagonal braces. The knee element provides ductility, whereas the diagonal brace remains elastic when the test specimen is subjected to a lateral load. The study concluded that a system comprising a knee brace and diagonal braces was effective in rigid and semi-rigid beam-to-column connections. Henceforth, various configurations with a different ductile manner of conventional buckling [13–16] and buckling-restrained knee brace dampers (BRKBs) that meet the high architectural versatility requirements of the structures have been investigated for MRFs and weld-free connection frames, respectively [17–22]. The approach, referred to as the BRKB weld-free system or the simple shear beam-to-column connection, is becoming increasingly popular in Japan and other countries. Inoue et al. [17], and Tagawa and Kaneko [22], for example, proposed BRKBs that consist of two main parts, namely buckling-restrainers and core elements, in which the core elements are placed between two buckling-restraining plates. These studies adopted the pin beam-to-column joint to examine the damper deformation. Consequently, research has revealed that BRKBs with the proper configuration have demonstrated good hysteretic behavior under cyclic loads up to controlled story drifts. In these systems, the beams were fully elastic under the forces caused by the knee braces.

Furthermore, steel bar cores have also been utilized for various buckling-restrained braces [23–29], with the exception of adopting core plates in BRKBs. For instance, a study conducted by Fujii and Tagawa [27] revealed that the BRB with a bar core exhibits an adequate capability under cyclic loading if the number of construction allowances is controlled. In addition, our previous study [30] investigated the plasticity behavior of rigid beam-to-column connections under cyclic loads using a shorter BRKB with steel bar core dampers. The proposed BRKB adopted two contraction allowances and exhibited a high potential for decreasing the stress concentration near the beam-to-column connection.

During the 1995 Kobe earthquake, brittle fractures were observed in the shop welding connections in column-tree connection structures, even though shop welding was believed to result in better quality column-tree moment frames than the field-welded connection [31]. Other conventional moment-frame structures such as school buildings, gymnasium halls, and long-span structures experienced concealed connection damage after severe earthquakes [32–35]. It was challenging to retrofit these structures without damaging the interior non-structural elements and ensuring free passageway for their usage. Therefore, relatively economically inefficient long conventional knee braces were utilized for retrofitting these structures.

In this study, a novel slender BRKB damper, a cover-tubed buckling-restrained steel bar core damper, was developed, and experimental verification of its deformation capacity was performed. The advantages of the proposed damper are reduced weight compared to conventional knee braces or mortar-filled BRKBs and high architectural flexibility for the retrofitting of large-span welded steel moment-resisting systems. It was revealed that the proposed damper could also effectively improve the lateral stiffness of weld-free connection systems. Specifically, by increasing the number of contraction allowances, undesirable failure mechanisms that are global instability and local buckling of the restrainer ends can be effectively suppressed because a more uniform plastic deformation of the core bar can be achieved longitudinally. In other words, the adoption of several contraction allowance zones with proper design of the cover tubes for the proposed dampers significantly improves the performance of the proposed dampers. The study conducted compression loading tests on nine BRKBs and cyclic loading tests on three full-scale specimens with a weld-free beam-to-column connection. The test results are discussed with emphasis on the deformation capacities of the proposed dampers.

2 Outline of the proposed BRKB dampers

2.1 Structural configuration

Fig.1 presents possible configurations of the structural system with the proposed BRKB dampers. Fig.1(a) presents an application of the BRKB for either retrofitting or strengthening the column-tree connection. Likewise, the proposed damper can be applied to the pin-connection interior or external steel frames, as shown in Fig.1(b) and Fig.1(c), to dissipate the seismic input energy during ground motion. In this weld-free system (pin connection), the beams are connected to the column flanges only at the top flanges by T-stub members with bolts. The beams rotate about the ends of their top flanges. As a result of implementing the BRKB in a weld-free system, the damper can freely deform without causing significant damage to the beams, floor slab, and other non-structural members under excessively large story drifts. Therefore, a description of an experimental study in which only a weld-free connection is used with BRKBs is provided in Section 4 to reveal the cyclic response of the proposed dampers.

2.2 Details of the proposed BRKBs

The configuration of the proposed BRKB is shown in Fig.2. Fig.3 shows the details and exploded view of the proposed damper, where each element of the BRKB is numbered from 1 to 11. The roll-threaded ends of the steel bar cores and are connected by a central coupler and placed inside detached round steel tubes and (buckling restrainers). The coupler acts as a connector and transmits the force from one core bar to another. Buckling restrainer tubes with sufficient stiffness and strength are set outside the core bars to ensure the stability of the steel core bars. For ease of construction, one of the steel bar cores is threaded by right screws at its ends, and the other is threaded by right and left screws at its ends. The two opposing screws make available adjustment capabilities during the erection process. In addition, a sufficient-strength steel cover tube is placed at the center of the damper and locked by Allen bolts to ensure the damper remains stable under axial loading, as shown in Fig.2. The relative movement of the cover tube along the longitudinal direction of the damper is prevented by four pieces of the Allen bolts screwed through the central coupler. In this study, four contraction allowances, as indicated by the roman numbers I, II, III, and IV, are adopted in the proposed BRKB based on preceding experimental experience [27–29]. These contraction allowances provide high flexibility to the steel bar core during applied loading conditions. Two pieces of commercial springs and are inserted into the core bars at the lower construction allowance zones to hold the tube restrainer during the loading tests, as shown in Fig.2, in regions I and III. Finally, the left and right screw connectors and are attached to the assembled damper to achieve sufficient holding force during earthquakes. Fig.4 presents explanations of the step-by-step built-up processes of the proposed damper.

2.3 Design method for the proposed damper

Fig.5 presents the geometrical parameters of the proposed BRKBs. First, a superior stiff buckling restrainer for the base damper (L-BR) (Fig.5(a) and Fig.5(b)) was selected based on the theory discussed in previous studies [30,36,37]. For example, the flexural rigidity and yield strength of the restrainer were designed with a safety factor, SF, utilizing the design method described in reference [30].

The steel bar core was considered to be relatively flexible in the proposed damper. A sufficiently stiff restrainer is expected to restrain the buckling amplitude of the steel bar core under compression loads without rippling. The threaded sections of the steel bar core were inserted through the connector at a distance of 2d_s for both the compression and cyclic loading tests, where d_s represents the diameter of the threaded section. In contrast, the insertion length of the threaded sections in the buckling restrainer must satisfy the following condition: if the rotation angle of the connection reaches 0.03 radian, the shank part should not be exposed [6]. In this regard, the insertion lengths of the threaded parts into the buckling restrainer were designed with a dimension of 2d_s in the cyclic loading test, whereas only d_s could be adopted in the compression tests. Two contraction allowance zones were adopted for the base damper (L-BR specimen, discussed in Subsection 3.1.1), considering the expected axial deformation of the steel bar core under given loads.

Fig.5(b) and Fig.5(c) show the proposed cover-tubed BRKB. As the number of contraction allowance zones increased, the efficacy and performance of the damper were expected to improve [28]. Thus, the central coupler split the base damper into two parts. Four contraction allowance zones were employed. A detailed description of the proposed damper is presented in Subsection 2.2. To ensure stability of the proposed damper, a cover tube with an outer diameter D_ct and thickness t_ct was utilized, as shown in Fig.5(b). To obtain the optimal parameters of the cover tubes, the ratio of the section modulus corresponding to the buckling restrainer and cover tubes was considered. A cover tube with a larger elastic section modulus than the buckling restrainer can likely support a load that is capable of inducing flexural loads in the buckling restrainer that are then transferred to the cover tubes. This ratio can be determined by Eq. (1).

(1)R_{\text{ct}}=\frac{Z_{\text{ct}}}{Z_{\text{br}}},

where Z_ct and Z_br are the elastic section modulus of the cover and buckling restrainer tubes, respectively, which are defined by Eqs. (2) and (3), respectively:

(2)Z_{\text{ct}} =\frac{\text{π}\left(D_{\text{c}\text{t}}^4-d_{\text{c}\text{t}}^4\right)}{32D_{\text{ct}}},

(3)Z_{\text{br}} =\frac{\text{π}\left(D_{\text{b}\text{r}}^4-d^4\right)}{32D_{\text{br}}}.

D_ct and d_ct are the outer and inner diameters of the cover tube, respectively, and D_br and d are the outer and inner diameters of the buckling restrainer, respectively, as shown in the section views in Fig.5(b).

3 Compression tests

3.1 Test specimens

3.1.1 Detailed descriptions of the specimens

Compression tests were conducted on nine specimens, including the base damper (L-BR), to reveal the load-bearing capacities of the proposed BRKB. The proposed damper specimens differed in the geometrical parameters of their cover tubes, such as the insertion length, l_in, and cross sections. Fig.6 shows the geometrical dimensions of all the specimens, while Tab.1 summarizes the detailed characteristics of the specimens. In general, the specimens were categorized into three groups: reference, short cover tubes (SCT), and long cover tube specimens (LCT). The reference specimens were assumed to consist of only the core bar (N-BR), long buckling restrainer base damper (L-BR), and four contraction allowance zones with no cover tube specimen (S-BR), as shown in Fig.6(a)−Fig.6(c), respectively. The reference specimens were identified based on the length of the buckling restrainer (N for none, S for short buckling restrainer, and L for long buckling restrainer). In contrast, Fig.6(d) represents the proposed damper with the short cover tube specimens, while Fig.6(e) represents the LCT. For example, for SCT48-D, 48 indicates the outer diameter of the cover tubes, D_ct = 48. D indicates the insertion length, l_in, of the cover tube to the buckling restrainer. This compression loading test considered only two insertion lengths l_in: l_in= D_br and l_in = 2D_br. D_br is the diameter of the buckling restrainer. In addition, the material properties of the main damper components are listed in Tab.2. The predicted core bar yield strength N_y and the Euler buckling load of the buckling restrainer that correspond to the L-BR specimen were obtained based on these data; the predicted values were N_y = 83 kN and N_{\text{E}}^{\text{B}} = 230 kN, respectively.

3.1.2 Core bar and contraction allowances

In the compression test, double-threaded structural anchor bolts M20 were used for the steel bar cores, in which the non-threaded section had a diameter of 18.2 mm (ABR product specifications and JIS B1220 standard). As mentioned in Subsection 2.3, the core bar threaded sections were inserted through the buckling restrainer at a distance of 20 mm and screwed through the end connector with a dimension of 40 mm for each specimen.

For the common BRBs, a stopper is often attached to the middle part of the steel core to keep the buckling restrainer’s position by welding and widening the cross-sectional area. However, it is difficult for the steel core bar to mount the stopper in its middle because any processing, such as welding and widening, cannot be performed. Thus, in this study, an ultra-high deflection coil spring with a size of SWY30-35 was selected as the stopper for the lower contraction allowance zones, where 30 and 35 indicate the outer diameter and the initial length of the spring, respectively. The allowable deflection of the spring was 22.8 mm. As shown in Fig.6, a dimension of 30 mm was adopted in each contraction allowance zone. As presented in Fig.6(c), when a 35 mm length spring is attached to the lower contraction allowances in each part of the steel bar core, the allowable deflection of the spring should ensure that the planned 30 mm gap is maintained, owing to the gravity force of the buckling restrainer.

3.1.3 Buckling restrainer and cover tube

A round steel tube of 40 mm × 9 mm with a diameter D_br = 40 mm and thickness t = 9 mm was selected for the buckling restrainer in the base damper specimen L-BR. The same round steel tube section was then used for the other specimens, except for the N-BR specimen. The clearances were estimated as c_s = 2 mm and c_sh = 3.67 mm. The safety factor of the base damper was SF = 1.65. The yielding moment capacity of the buckling restrainer was calculated by equations used in previous research [30].

For the cover tube specimens, the section of the restrainers was the same as that of the base damper. By contrast, the size of the cover tubes was varied for comparison. Dimensions of 48.6 mm × 3.5 mm, 54 mm × 6 mm, and 57 mm × 8 mm were utilized for the SCT and LCT specimens, as shown in Tab.1, based on the R_ct assumptions in Subsection 2.3. In this compression test, three R_ct corresponding section modulus of the cover tubes were considered: R_{\text{ct}} = 0.9, R_{\text{ct}} = 1.7, and R_{\text{ct}} =2.3, as listed in Tab.3. Two cover tube insertion lengths, l_in, were considered: 40 and 80 mm. Finally, the performances under compression loading tests were classified into three satisfactory scales: highly satisfactory, satisfactory (acceptable), and unsatisfactory, as shown in Tab.3 and discussed in Subsection 3.3.1.

3.2 Testing setup and data measurement

To examine the behavior of the proposed BRKB damper, compression loading tests were performed using a UH-F1000 hydraulic universal test machine equipped with easy-to-see display measurement control, as shown in Fig.7. The test specimens were placed vertically in the loading machine, and a vertical load P was applied to the upper cylindrical connector. Cylindrical end supporters were utilized at each end of the damper in the compression loading test. In addition, a mobile loading cell was placed beneath the lower cylindrical end-supporter to measure the vertical load, P, as shown in Fig.7 (right side).

For the reference specimens, strains of the buckling restrainer tubes at position 1 of specimen L-BR, and positions 1 and 2 of specimen S-BR, are as shown in Fig.8(a) and Fig.8(b), respectively. For the specimens with cover tubes, the strains of the cover tube edges were measured at gauge positions 2 and 3, and the strains of the restrainers were measured at gauge positions 1 and 4, as shown in Fig.8(c). Fig.8(d) shows the strain gauge positions around the tube surface. In addition, displacement sensors d1 and d2, as shown in Fig.7, were utilized to measure the average vertical displacement of the specimens under loading conditions.

3.3 Compression loading test results

3.3.1 Load-displacement relationship

Fig.9 presents the load−displacement relationships of all the test specimens subjected to compression loads. The notation P_y indicates the predicted yield load of the steel bar core. The primary horizontal axis indicates an applied compressive displacement, D, at each specimen. In contrast, the secondary horizontal axis presents the applied compressive displacement normalized by the yield displacement, D_y. The value of D_y for specimens N-BR and L-BR is 1.47 mm and reflected in Fig.9(a), while for the specimens with four contraction allowance zones, the value of D_y is 1.32 mm and reflected in Fig.9(b) and Fig.9(c).

In the case of the specimens in group 1, compared to the N-BR specimen (only bar), the highest increase in the maximum load of up to 111.5 kN was attained in the base damper specimen (L-BR) with a displacement of 38.6 mm, as shown in Fig.9(a). The N-BR and S-BR specimens showed a similar trend in the elastic stage. It can be seen that, if the proposed BRKBs with four contraction allowance zones had no cover tube, the failure mode was the same as that of the bar specimen at a load of 38 kN.

For the specimens in group 2 (Fig.9(b)), the axial load capacities tended to increase slightly in SCT48-D with R_ct = 0.9 and SCT54-D with R_ct = 1.7, the first two cover tube specimens, with maximum loads of 40 and 52 kN, respectively. However, these two specimens no longer resisted any additional load owing to the failure of the cover tubes, as shown in the photographs in Subsection 3.3.3. It is noted here that the SCT48-D and SCT54-D specimens, including N-BR and S-BR, buckled before yielding of the steel bar core. In addition, as the section modulus of the cover tube increased to R_ct = 2.3 with a shorter insertion length l_in, the axial load capacity tended to increase after core bar yielding, as revealed by the results for specimen SCT57-D. The maximum load that was attained was 111 kN.

For the specimens in group 3, (Fig.9(c)), the load resistance capacity tended to increase as the insertion length of the cover tubes increased. In particular, specimen LCT57-2D possessed an axial load capacity that was more significant than those of the other two LCT specimens. The overstrength behavior, as shown in Fig.9(c), will be assessed by cyclic loading tests and discussed regarding the brace compression-to-tension ratio in Subsection 4.5.1.

In summary, when the R_ct was less than 1.0, the damper could not achieve the design purpose regardless of the cover tube insertion length. When the R_ct was 1.7, it was observed that the insertion length, l_in, was more influenceable for the load-bearing capacity of the proposed damper. For example, the specimen SCT54-D was unsatisfactory, while the specimen LCT54-2D was satisfactory. Moreover, when the R_ct was 2.3, the specimen SCT57-D was also satisfactory. In contrast, the specimen LCT57-2D was highly satisfactory, in which a continuous strength increment was observed, as shown in Fig.9(c).

3.3.2 Variation in the strains for the cover tube and buckling restrainer

Fig.10 to Fig.11 show the relationship between the axial load and strain of the buckling restrainer and cover tubes for each specimen. The vertical dashed lines illustrate the yield strain corresponding to the buckling restrainer and cover tubes of the proposed damper. By employing large contraction allowances for specimen L-BR, the strain values of the buckling restrainer increased significantly, as shown in Fig.10(a). In the case of specimen S-BR, the strain values at the buckling restrainers and the maximum axial load were lower than those of the other all specimens, as shown in Fig.10(b) and (c).

Overall, the test results reveal that the strain values at the buckling restrainers were lower than the yield strain for the specimens in all the groups under given loads, as shown in Fig.12(a) and Fig.12(c), Fig.13(a) and Fig.13(c), and Fig.11(a) and Fig.11(c). However, the strain values in the cover tubes for the specimens in group 2 exceeded the yield strain regardless of the tube thickness corresponding to the given loads, as shown in Fig.12(b), Fig.13(b), and Fig.11(b). In contrast, the strain values at the cover tubes for the specimens in group 3, as shown in Fig.13(d) and Fig.11(d), were remained below the yield strain, except for specimen LCT48-2D, as shown in Fig.12(d). It is important to note that when the ratio of the section modulus, as defined with Eq. (1), is less than 1, for example, R_ct = 0.9, the strain values of the cover tube were exceeded yield strain regardless of the cover tube length, as shown in Fig.12(b) and Fig.12(d). In contrast, when the ratio R_ct increased to 1.7 for the specimen LCT54-2D, the strain values of the cover tube were attained to remain below the yield strain, as shown in Fig.13(d).

Furthermore, specimen LCT57-2D with a ratio of the section modulus of R_ct = 2.3 achieved good performance, as shown in Fig.11(c) and Fig.11(d), until the final loading stage. Finally, it was revealed that these two parameters, l_in and R_ct, likely play essential roles in the design of our proposed BRKB.

3.3.3 Residual deformation after compression loading

Fig.14 illustrates the residual deformation for all the specimens in the final loading stages. Fig.14(a)–Fig.14(c), Fig.14(d)–Fig.14(f), and Fig.14(g)–Fig.14(i) represent the deformations of the specimens in groups 1, 2, and 3, respectively.

For specimen L-BR, slight bending was observed in the middle of the buckling restrainer owing to the axial force acting on the steel bar core being transferred to the BR prior to the core bar yielding, as shown in Fig.14(b). When the compressive load was increasingly applied to the steel bar core, it induced a plastic hinge at the exposed portion of the steel bar core in the upper contraction allowance after the core bar yielded. The maximum axial load was N_max = 111 kN. Moreover, it can be seen from specimen S-BR that, when the proposed damper had no cover tube, plastic hinges quickly occurred in the steel bar core, as shown in Fig.14 (c). The maximum load, which leads to core bar buckling in the earlier stage of the applied loading, was only N_max = 30 kN. The flexural buckling of the steel bar core on its exposed portion caused an excessive lateral deflection in specimen S-BR.

Furthermore, to improve the stability of the proposed damper, a cover tube insertion length of l_in = 40 mm was employed for the specimens in group 2. In the first two specimens, specimens SCT48-D and SCT54-D, with R_ct = 0.9 and 1.7, respectively, an excessive distortion was formed at the edge of the cover tube because of its insufficient insertion length as shown in Fig.14(d) and Fig.14(e). These local failure behaviors were caused by a maximum axial load equal to N_max = 40 kN. In specimen SCT57-D with an R_ct = 2.3, the edge failure of the cover tube was visibly small. In contrast, the buckling restrainer was slightly deformed near the upper edge of the cover tube under the given loads, as shown in Fig.14(f). The maximum axial load was measured at N_max = 100 kN.

Although the insertion length of the cover tube increased to l_in = 80 mm for specimen LCT48-2D, global buckling occurred owing to the specimen’s small R_ct of 0.9. Plasticity initiation was slightly delayed with N_max = 80 kN compared with specimen SCT48-D. It is noted here that the small thickness of the cover tube could not sustain the normal force acting on it from the buckling restrainer, as shown in Fig.14(g). Moreover, plasticity patterns, similar to those of specimen LCT48-2D, were observed in specimen LCT54-2D (Fig.14(h)). The maximum axial load was N_max = 117 kN.

Finally, as a result of the compression loading tests, specimen LCT57-2D showed sufficient strength and a very stable behavior. No significant failure was observed in this specimen except for the shortening of the steel core without failure of the buckling restrainer and cover tube, as shown in Fig.14(i). In addition, the compression loading tests revealed that the number of contraction allowances strongly influenced the load-bearing capacities of the proposed dampers under given axial loads. Nevertheless, extended cyclic loading tests were conducted on different parameters of the cover tube BRKBs to examine the cyclic response of the proposed dampers.

4 Cyclic loading tests

4.1 Test specimen

The compression loading tests revealed that the dampers LCT54-2D and SCT57-D with cover tubes with R_ct of 1.7 and 2.3, respectively, exhibited satisfactory design performance. In contrast, LCT57-2D with R_ct of 2.3 exhibited highly satisfactory. Considering the compatibility of the cross-sections between the buckling restrainer and cover tube, the effect of the cover-tube insertion lengths was examined for a fixed R_ct value, which was 1.4 in the cyclic loading test specimens, as listed later in Tab.4. Three dampers, SCT60-D, LCT60-2D, and LCT60-3D, were prepared and tested to investigate their cyclic responses. Fig.15 presents the basic dimensions of the three dampers and the sub-assemblage of the cyclic loading tests. As previously mentioned, cover tube insertion lengths l_in of 45, 90, and 135 mm were selected as the experimental study test parameters, as shown in Fig.15(a) to Fig.15(c). As noted here, these values imply that l_in = D_br, 2D_br, and 3D_br for each damper.

The geometric characteristics and material properties of the dampers are listed in Tab.5 and Tab.6, respectively. Their identifications were the same as those used in the compression loading tests. A round steel tube of 45 mm × 10 mm was used for the buckling restrainers, while another of 60.5 mm × 7 mm was used for the cover tubes. Tab.4 presents the section modulus of tubes. The steel-core-bar configuration based on the fabrication standards JIS B 1220 is the same as that described in Subsection 3.1.2. However, the diameters of the core bar were 22 and 20.2 mm at the thread and shank parts, respectively. The insertion length of the core bar threaded parts into the restrainer was 40 mm. The core bar was screwed through the end connector with 45 mm. Under these conditions, the shank part should not be exposed if the rotation angle of the beam reaches 0.02 radian. Four contraction allowance zones with a total distance of 70 mm were employed for all the dampers. The lower contraction allowance zones with the coil spring were marked green for each damper. In addition, the safety factor, SF, of the buckling restrainer was calculated, implying the theory introduced in the previous research [30]. According to the calculation, the safety factor was SF = 2. Fig.15(d) illustrates the sub-assemblage used for the cyclic loading test. In order to observe the cyclic behavior of the proposed damper, a strong column and a sufficient strength beam were selected in the sub-assemblage. A 1.4 m beam of the hot-rolled H-section with dimensions of H250 × 125 × 6 × 9 and a built-up section column with dimensions of H250 × 250 × 19 × 25 were utilized. The length of each member was taken based on the damper length in this study. In addition, the performances of specimens under cyclic loading tests were classified into three satisfactory scales: highly satisfactory, satisfactory (acceptable), and unsatisfactory, as shown in Tab.4 and discussed in Subsection 4.5.3.

4.2 Testing setup

Fig.16 illustrates the design of the general apparatus used for the cyclic loading tests. The out-of-plane displacements were entirely constrained, as shown in Fig.16(a). Four rollers attached to the beam ensured that the beam moved freely over the surface of the vertical constrainer without any direct beam-to-constrainer interaction. The sub-assemblage that included a beam, column, and the proposed BRKB was attached to the reaction frame fully fixed and loaded by a vertical jack at the beam tip. As illustrated in Fig.16(b) and Fig.16(c), a beam-to-column weld-free connection (pin connection) was adopted to reveal the energy dissipation capacity of the proposed damper. In this regard, the shape of the T-stub element was used for the connection, as shown in Fig.16(c). Thus, the beam and column behaviors can be regarded as entirely elastic. An assembled BRKB was connected by the right and left screw connector to the beam and column of the specimen at a 45° inclination, as shown in Fig.16(b). In addition, Fig.17 shows photographs of the actual test setup.

4.3 Data measurement of testing

Fig.18 presents the cyclic loading tests program. A hydraulic jack with a stroke of 500 mm and a maximum force of 1000 kN was applied at the beam tip. The downward direction of vertical load P was assigned a positive sign, as shown in Fig.18(a). The following data were measured: (1) vertical displacement of the beam tip, \delta, regarding vertical load, P; (2) rotation of the beam relative to the beam-to-column pin connection; and (3) strains of the buckling restrainer and cover tube for each specimen. 16 strain gauges were mounted at each specimen to record its strain behavior, as shown in Fig.18(d).

Displacement sensors d1 and d2 to d5 were utilized to measure the vertical displacement of the beam tip and the rotation of the beam, respectively. Finally, displacement sensors d6 and d7 were placed along the axis of the BRKBs to measure the elongation of the steel bar cores.

4.4 Global rotation angles and loading conditions

Displacement-controlled cyclic loading was used in the test. Fig.18(c) shows the global rotation of the reference beam and the global rotation angle of the test specimen were determined based on a pure cantilever beam (R = \delta /\phantom{\delta L}L).

The loading protocol is shown in Fig.18(b). The right vertical axis represented the beam tip displacement imposed on the controlled global rotation angle and the left vertical axis illustrated the global rotation angle. In the cyclic loading test, the initial displacement was calculated as \delta = 7 mm corresponding to R(\text{rad})= 0.5\mathrm{\%}. The loading was increased up to R(\text{rad} ) =4 \mathrm{\%} in increments of R(\text{rad} ) =0.5 \mathrm{\%}. Each increment consisted of two cyclic loading steps. The beam and column were considered fully elastic to observe the cyclic response of the proposed damper, as shown in the test setup design. After each loading cycle, the loading was stopped, and a visual inspection of the specimen, including dampers, was performed.

4.5 Cyclic loading test results

4.5.1 Load and global rotation angle relationship

This section discusses the effect of the test parameters on the cyclic responses of the three dampers and results are illustrated in Fig.19. The horizontal dashed lines marked as P_y in each graph indicated the predicted yielding load of the steel bar core.

The specimen with damper SCT60-D achieved a global rotation of R ( \text{rad})= \pm 3 \mathrm{\%}, which is 75% of the R(\text{rad} ) =\pm 4\mathrm{\%} expected for the test specimens. Following the R(\text{rad})= \pm 0.5\mathrm{\%} increment, which consisted of two loading steps, the BRKB remained in the elastic range. At this stage, no yielding was apparent for each member of the dampers, such as the buckling restrainers and cover tubes. Significant strength deterioration was initiated in the specimen with the SCT60-D damper at a global rotation of R ( \text{rad})= +1 \mathrm{\%} (point (i)) after the cover tube edge failed in the second cycle of R ( \text{rad})= +1 \mathrm{\%} (point (ii)). The failure continuously occurred upon the further increase in the global rotation, as shown in Fig.19(a). The maximum load at points (i) and (ii) was 50 kN on the brace compression side and slightly over 50 kN on the brace tension side.

The specimen with the LCT60-2D damper achieved a global rotation R ( \text{rad})= \pm 4 \mathrm{\%}. However, in the second cycle R(\text{rad})= + 4\mathrm{\%}, a sudden strength degradation occurred because of the buckling of the bottom restrainer tube, as shown in Fig.19(b) (point (iii)). At this stage, the maximum brace compressive load reached 124 kN. In contrast, the maximum tensile load reached 80 kN.

Finally, the specimen with the LCT60-3D damper exhibited sufficient ductile behavior until the steel bar core reached the rupture point corresponding to the second cycle R(\text{rad})= + 4\mathrm{\%}, as shown in Fig.19(c) (point (iv)). At this stage, the maximum load P reached 106 kN. In contrast, the maximum load, P, corresponding to the tensile side of the brace, reached 78 kN. In addition, the observed maximum load that led to bracing in the compression state of the specimen with the LCT60-2D damper was slightly larger than that of the specimen with the LCT60-3D damper.

For the proposed BRKBs, it was observed that the insertion length of the cover tube played an essential role in its cyclic loading responses. For example, when l_in = D_br = 45 mm (SCT60-D), the damper could not dissipate energy efficiently, whereas the other two dampers could. In addition, slight slippage was observed during the cyclic loading tests for each result. It is likely that the jack-to-beam or brace-to-beam connection bolts were affected for the above reason because of their rigidity.

Fig.19(d) presents the variation in the brace compression-to-tension ratio [29,36], defined as the ratio of the maximal compressive force to the maximal tensile force for each cycle. In Japan, the BCJ specification [38] permits \beta ⩽ 1.2, while the US standard AISC 341 [39] permits \beta ⩽ 1.3-1.5. The results of this study are based on the BCJ specifications. It can be observed that the specimen with the SCT60-D damper could not meet these criteria. Therefore, its results were neglected in this study. The specimen with the LCT60-2D damper met these criteria between global rotations R (rad) = 0.01−2 and R (rad) = 0.03−2, while the specimen with the LCT60-3D damper met these criteria between R (rad) = 0.01−1 and R (rad) = 0.035−1. Finally, it is concluded that the specimen with the LCT60-3D damper exhibited the most efficient energy dissipation capacity among the proposed dampers.

The performances of the cyclic loading tests are shown in Tab.4. The dampers with the varying lengths of the cover tube and constant R_ct were used to examine their structural performances in cyclic loading tests. Considering design performances, the specimens with the SCT60-D, LCT60-2D dampers, and LCT60-3D damper were unsatisfactory, satisfactory, and high satisfactory performances, respectively.

4.5.2 Strains for the cover tube and buckling restrainer

Fig.20–Fig.22 show the relationship between the axial load of the braces and the measured strains for BRKBs for each specimen. Considering beam-tip load, P, the axial load of the brace was obtained from moment equilibrium in the tested model. The vertical dashed lines indicate the yield strain, and the horizontal dashed lines represent the Euler buckling load of the buckling restrainer tube for base BRKB (L-BR). Fig.20(a) and Fig.20(b) illustrate the measured strains for the buckling restrainer tubes, while Fig.20(c) and Fig.20(d) present the results of the strains of the cover tubes for each specimen.

For the specimen with the SCT60-D damper, the strain values induced in the buckling restrainer were noticeably smaller than the values induced in the cover tube, as shown in Fig.20(a) and Fig.20(b). The strains on the buckling restrainer were symmetric among gauge positions 1 and 4. In contrast, an excessive asymmetric spreading of the strains was observed in gauge position 3, as shown in Fig.20(d). This behavior illustrates that the cyclic response of the damper with a l_in = D_br insertion length of the cover tube was not satisfactory.

For the specimen with the LCT60-2D damper, the buckling restrainer experienced dominant strains for the induced axial force, as shown in Fig.21(a) and Fig.21(b). The cover tube strains remained in the elastic range except those at gauge positions 2B and 3B, as shown in Fig.21(c) and Fig.21(d). As the load increased, the strain values at gauge positions 1B, 4B, and 4D for the buckling restrainer, and the cover tube strains at gauge positions 2B and 3B exceeded the yield strain simultaneously, as shown in Fig.21(a)–Fig.21(d).

For the specimen with the LCT60-3D damper, all the strain values for the buckling restrainer and cover tubes did not exceed the yield strain and met the Euler buckling criteria. The strain values for the cover tube and buckling restrainers were visibly lower than those of the other two specimens, as illustrated in Fig.22. This behavior indicates that no plastic deformation or buckling failure occurred during the cyclic loading test for the damper in the specimen with the LCT60-3D damper.

4.5.3 Residual deformation after cyclic loading

Fig.23 shows the tested specimens and the residual deformation of the proposed BRKBs after the cyclic loading tests. Fig.23(a) shows that the cover tube end of SCT60-D loses its stability owing to the insufficient insertion length for the given loads. Likewise, global buckling occurs in LCT60-2D when the cover tube insertion length increases by two times the insertion length in the damper in the specimen with the SCT60-D damper, as shown in Fig.23(b). Finally, the specimen with the LCT60-3D damper achieved superior performance when the system was carefully designed and detailed, as shown in Fig.23(c). These behaviors indicate that the damper stability capacity is strongly governed by the insertion length of the cover tube as long as the damper is designed to meet all the strength and stiffness requirements. Moreover, a detailed visual inspection of the disassembled BRKBs was conducted, and three failure patterns were observed for the buckling restrainers, cover tubes, and steel bar cores.

For the specimen with the SCT60-D damper, an undesirable plastic hinge at the upper edge of the cover tube began to occur at a low amplitude of cyclic loading and continuously developed up to the final loading stage. This failure mechanism leads to excessive plastic deformation at the edge of the cover tube and slight bending of the buckling restrainer and steel bar core, as shown in the right photo of Fig.23(a).

The specimen with the LCT60-2D damper was intended to be adequately involved in the plastic work for the given loads. However, it was revealed that the 2D_br insertion length of the cover tube was insufficient to resist the relatively higher amplitude of the cyclic loading responses. Spiral buckling behavior was observed at the upper steel bar core, while the lower buckling restrainer, including the steel bar core, was slightly bent, as shown in the right photo of Fig.23(b).

After completion of all the cyclic loading stages, no severe failures were observed in the buckling restrainer and cover tubes for the specimen with the LCT60-3D damper. Higher mode buckling and spiral buckling simultaneously occurred in the lower and upper steel bar cores until the global rotation angle R(\text{rad})= 4\mathrm{\%} was reached. This behavior indicates that the 3D_br insertion length of the cover tube in the BRKB is sufficient for plastic work. However, when the elongation of the steel bar core introduced in BRKBs exceeds the plastic limits at R ( \text{rad})=0.04- 2, (see point (iv) in Fig.19(c)), fractures occur at the screw part placed in the lower contraction allowance zone, as shown on the right photo of Fig.23(c).

The assessment of the R_ct for the cyclic loading tests against the compression loading tests is shown in Tab.4. The specimen with the LCT60-3D damper showed high satisfaction for design purposes without a global buckling. In contrast, the specimen with the LCT60-2D damper was considered acceptable because the brace compression-to-tension ratio was achieved for design purposes, as shown in Fig.19(d).

5 Conclusions

A preliminary study investigated the behavior of plasticity amplification on a rigid beam-to-column connection using a steel-core-bar round tube BRKB damper under cyclic loading tests [30]. The results showed that the proposed damper significantly decreased the stress concentration at the rigid beam-to-column connection. This study proposed and tested a novel long BRKB with a steel bar core damper using a round central coupler, tube restrainer, and a cover tube with weld-free beam-to-column connections. Overall, the experimental study was conducted in two stages.

In the first stage, compression loading tests were conducted on nine specimens, including the base damper, using a UH-F1000 pressure machine to evaluate the energy dissipation capacities upon the application of compression loads. In this stage, the insertion length, l_in, and the ratio of the section modulus of the cover tube against the buckling restrainer were examined.

In the second stage, based on the observations from the first stage, extensive cyclic loading tests were carried out on three additional specimens with the BRKBs to investigate the effect of their insertion lengths on the cover tubes. In these tests, l_in was selected as the test parameter, and was set equal to D_br, 2D_br, and 3D_br for each damper, where D_br denotes the outer diameter of the buckling restrainer.

As a result of both experimental studies, the following conclusions can be drawn.

1) The advantages of the proposed damper include easy assembly compared to conventional buckling restrained braces and high architectural flexibility for the retrofitting of large-span weld-free or welded steel moment-resisting systems.

2) By increasing the number of contraction allowances, undesirable failure mechanisms that are global instability and local buckling of the restrainer ends can be effectively suppressed because the more uniform plastic deformation of the core bar can be achieved longitudinally. In other words, the adoption of several contraction allowance zones with proper design of the cover tubes for the proposed dampers significantly improves the performance of the proposed dampers.

3) The study revealed that the damper stability capacity is governed by the insertion length of the cover tube, l_in, and ratio of the section modulus of the cover tube against the buckling restrainer, R_ct. For the compression responses of the proposed dampers, when the R_ct was less than 1.0, the damper could not achieve the design purpose regardless of the cover tube insertion length. When the R_ct was 1.7, it was observed that the specimen SCT54-D was unsatisfactory. In contrast, the specimen LCT54-2D was satisfactory for the design performance. Finally, when the R_ct was 2.3, the specimens SCT57-D and LCT57-2D exhibited satisfactory and highly satisfactory, respectively.

4) For the cyclic responses of the proposed dampers, the damper with the insertion length of l_in = 3D_br exhibited high satisfaction with the load-bearing capacity. An R_ct of 1.4 can be recommended when designing the proposed dampers if a sufficient insertion length is adopted for the proposed damper.

Overall, these experimental studies were conducted on a specific number of test specimens to investigate the compression and cyclic behaviors of the proposed dampers. Therefore, in future research, the behaviors of a large number of damper models should be examined using a finite element analysis.

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