## 2 Bolted Gusset Connection
### Design of Bolted Gusset Connection  
The maximum axial force \(P_{\mathrm{max}}\) of the BRB is used as the force demand for the design of the BRB-RCB, which can be calculated as follows:  
\[P_{\mathrm{max}}=\beta R_{\mathrm{y}}\omega_{\mathrm{y}}f_{\mathrm{y}}A_{ \mathrm{c}} \tag{1}\]  
where \(\beta\) is the compression strength adjustment factor; \(R_{\mathrm{y}},f_{\mathrm{y}}\) and \(\omega_{\mathrm{y}}\) are the material overstrength, nominal yield stress and strain hardening factor of the inner core, respectively; \(A_{\mathrm{c}}\) is the cross-sectional area of the core yielding segment. The generalized uniform force method (GURM) [24] is adopted to obtain the dimension of the gusset plate in this study, in which there is more freedom in selecting the dimensions of the gusset plate for the designers. For the aim of achieving moment equilibrium, GURM assumes that the force components on the gusset resulting from \(P_{\mathrm{max}}\) are concentrated on the midpoint of both the gusset-to-beam and gusset-to-column interfaces. The extension lines of force components pass through the 'beam control point' and the 'column control point' and meet the brace force at the 'gusset control point' as shown in Figure 3. According  
Figure 2: Configuration of the bolted gusset connection. to the force equilibrium requirement for the gusset plate, the gusset-to-column and gusset-to-beam interface forces can be obtained as follows:  
\[H_{\text{uc}}=\frac{h_{\text{c}}\sin\varphi}{h_{\text{c}}+L_{\text{v}}}P_{\text {max}} \tag{2}\]  
\[V_{\text{ub}}=\frac{h_{\text{b}}[(h_{\text{b}}+L_{\text{v}})\cos\varphi-h_{ \text{c}}\sin\varphi]}{L_{\text{h}}(h_{\text{b}}+L_{\text{v}})}P_{\text{max}} \tag{3}\]  
\[H_{\text{ub}}=P_{\text{max}}\cos\varphi-H_{\text{uc}} \tag{4}\]  
\[V_{\text{uc}}=P_{\text{max}}\sin\varphi-V_{\text{ub}} \tag{5}\]  
where \(H_{\text{ub}}\), \(V_{\text{ub}}\), \(H_{\text{uc}}\) and \(V_{\text{uc}}\) are the horizontal and vertical forces on the gusset-to-beam and gusset-to-column interfaces, respectively; \(L_{\text{h}}\) and \(L_{\text{v}}\) are the gusset length and height, respectively; \(h_{\text{b}}\) and \(h_{\text{c}}\) are the beam depth and the column depth, respectively; \(\varphi\) is the BRB incline angle. As shown in Figure 4, [PERSON] suggested using a column strip with a unit width within the effective width [25] to obtain the gusset thickness \(t_{\text{g}}\). The peak stress \(\sigma_{\text{c}}\) within the effective width \(b_{\text{e}}\), which is expressed as Equation (2), should be less than the yield strength \(f\) of the gusset material. \[\sigma_{\text{c}}=\frac{P_{\text{max}}}{b_{\text{e}}t_{\text{g}}}<f \tag{6}\]  
Figure 4: Effective width method [25]. Figure 3: GUFM [24]. The compressive strength, \(P_{\rm cr}\), must meet the requirement specified in the Specification for Structural Steel Buildings [26] as follows:  
Figure 3.0  
Figure 3.1  
Figure 3.2  
where \(E\) is the elastic modulus of the gusset and \(r\) is the radius of gyration of the Whitmore section [25]. The buckling coefficient \(k\) = 0.65 when the gusset plate is restrained by free-edge stiffeners, and \(k\) = 2 or 1.2 when the gusset plate is susceptible to out-of-plane movement and side-sway buckling. The length of the column strip, \(L_{\rm c}\), is either the average of the lengths \(L_{1}\), \(L_{2}\) or \(L_{3}\), as presented in Figure 3.3  
According to the standard for the design of steel structures [28], the design shear capacity \(N_{\rm v}\)b for the high-strength bolt can be computed as follows:  
Figure 3.4  
where \(k\) = 0.7 for the contact force perpendicular to the slot direction; \(n_{\rm f}\) is the number of friction surfaces; \(\mu\) is the friction coefficient; \(P\) is the design value of pre-tensile force of the bolt.