## 2 Materials and Methods
### The BRBF  
The geometrical properties of BRB used in the BRBF specimen were identical to those of BRB4, which was tested by [PERSON] et al. [2]. As can be seen in Figure 4, the CM with a concrete compressive cylinder strength of 25 MPa consisted of an SHS 250X6. The CP was made of a 15 mm thick steel plate wrapped with 4 mm thick rubber (see Figure 4). The additional end restrainers were provided with steel plates welded to each other to prevent local deformation at both ends of the BRB (see Figure 4). The yield stress of CP and members of the steel frame were determined to be 270 MPa and 330 MPa, respectively, from the tensile coupon tests. All connections in the BRBF were designed to allow for rotation so that all demands were withstood by the BRB. The boundary conditions were considered to be pinned connections, which allow for rotation. They were provided with high-strength transmission miles. The support plates were installed first. This was followed by the steel columns being assembled with support plates by using high-strength transmission miles. The details of connection with the transmission mile are given in Figure 3. The steel beams and steel columns were then connected to each other with high-strength 10.9 M16 bolts. The details of the connection between the steel column and beam are given in Figure 3. The BRB was lastly attached to the steel frame with high-strength 10.9 M24 bolts (see Figure 4) and the LVDTs with a 200 mm measuring capacity were placed to measure the displacements in the BRBF. The yield and the tensile strengths were 900 MPa and 1000 MPa, respectively, for all high-strength 10.9 bolts with respect to TSC [43]. The bolted connection with slotted holes between the BRB and gusset plate was used to ensure easy installation of the BRB. In order to prevent the slip in these connections, they were designed according to the slip-critical connection design provisions in the TSC [43]. The gusset plate was designed with respect to the Uniform Force Method (UFM) given in the American Institute of Steel Construction (AASC) [44]. The size of the gusset plate was determined by solving equilibrium equations about the working point, which is the intersection point of axes of the beam, column, and brace members (see Figure 5). Figure 3: Details of steel frame. Figure 4: Test setup and BRBF. The buckling capacity of the gusset plate was predicted with Thornton's Method [45]. According to this method, the equivalent width (\(\rm b_{w}\)) is determined by using 30-degree extrapolation (see Figure 5). The buckling length (\(\rm l_{t}\)) is determined by Equation (1) [45]. \(\rm l_{1}\), \(\rm l_{2}\), and \(\rm l_{3}\) are given in Figure 5.  
\[l_{t}=min\left(l_{2},\frac{(l_{1},l_{2},l_{3})}{3}\right) \tag{1}\]  
Figure 5: Detail of gusset plate. It is then used to calculate a buckling coefficient (\(\lambda_{\mathrm{t}}\)). The \(\lambda_{\mathrm{t}}\) is calculated by Equation (2) [43], where \(\mathrm{i}_{y}\) is the radius of gyration and the effective length factor (k) is taken as 0.5 for square gusset plates and 0.65 for tapered gusset plates [44]. However, k was taken to be 1 in this study. \[\lambda_{t}=\frac{k\times l_{t}}{i_{y}} \tag{2}\]  
The critical buckling capacity of the gusset plate was determined to be 1841 kN with respect to Equations (3)-(5) given in TSC [43], where \(\mathrm{F}_{\mathrm{e}}\) is the elastic buckling stress, \(\mathrm{E}\) is the elastic modulus, \(\mathrm{F}_{\mathrm{y}}\) is yield stress, \(\mathrm{P}_{\mathrm{n}}\) is the buckling capacity, \(\mathrm{F}_{\mathrm{cr}}\) is the critical buckling stress, and A is the cross-section area.