## 2 Design Procedure of DBDM  
(Step 1) The flow chart in Figure 1 explains the procedure of the DBDM. The methodology starts with preparing structural prototypes. In this study, the structural system is classified as a structural wall system, where two shear walls are interconnected by coupling beams. Energy dissipation dampers are installed on these coupling beams. (Step 2) As schematically shown in Figures 2 and 3, the step-by-step results of nonlinear push-over analysis are used to obtain the capacity curve of the equivalent SDOF system using Equation (1). The design target story drift is assumed to be \(1/250\). Figure 1: Displacement-based design method flowchart. Figure 2: Pushover analysis to obtain equivalent SDOF. \[S_{d}=\frac{\sum{m_{i}\Delta_{i}}^{2}}{\sum{m_{i}\Delta_{i}}}\,\ S_{a}=\frac{\sum{m_{i}\Delta_{i}}^{2}}{ \left(\sum{m_{i}\Delta_{i}}\right)^{2}}Q_{d}=\frac{\Delta_{eff}}{\sum{m_{i} \Delta_{i}}}Q_{d} \tag{1}\]  
Design target story drift : \(\dfrac{1}{250}\times\) inter-story height (2)  
where  
\(S_{d}\): displacement spectrum;  
\(S_{a}\): acceleration spectrum;  
\(Q_{d}\): based shear force. (Step 3) The effective damping factor for each member at the target drift is determined using the following formula based on the ductility factors [13]. \[\text{Damping of RC wall}:\ \bar{\xi}_{e,wi}=0.05+0.444((\mu-1)/\mu\pi) \tag{3}\]  
\[\text{Damping of metallic damper}:\ \bar{\xi}_{M}=(0.8)2/\pi[(1-1/\mu)]\ [(1- \text{a})/(1+\text{a}(\mu-1))] \tag{4}\]  
\[\text{Damping of viscoelastic damper}:\ \bar{\xi}_{VE}=(G_{c}\omega)/(2G_{E}) \tag{5}\]  
where  
\(\bar{\xi}_{e,Wi}\): effective damping for RC shear wall;  
\(\bar{\xi}_{M}\): effective damping for metallic damper;  
\(\bar{\xi}_{VE}\): effective damping for viscoelastic damper;  
\(\mu\): ductility factor;  
a: stiffness ratio of metallic damper;  
\(G_{c}\): shear storage modulus of viscoelastic material;  
\(\omega\): the circular frequency of the structure;  
\(G_{E}\): shear loss modules of viscoelastic material. (Step 4) The damping factor of the entire structure is derived from the energy average  
\[\bar{\xi}_{e}=\frac{\sum{E_{wi}}\bar{\xi}_{e,wi}+\sum{E_{tb}}\bar{\xi}_{c,bi}}{ \sum{E_{twl}}+\sum{E_{bi}}} \tag{6}\]  
where  
\(\bar{\xi}_{e}\): effective damping factor of structural system;  
\(\bar{\xi}_{e,bi}\): effective damping factor of coupling beam  
(=\(\bar{\xi}_{M}\) for metallic damper, = \(\bar{\xi}_{VE}\) for viscoelastic damper);  
\(E_{Wi}\): potential energy of wall;  
\(E_{bi}\): potential energy of coupling beam  
(= \(E_{M}\) for metallic damper, = \(E_{VE}\) for viscoelastic damper). (Step 5) The effective displacement of the SDOF system is determined based on the displacement distribution corresponding to the target displacement, as follows:  
Figure 3: Displacement-based design method performance graph. \[\Delta_{eff}=\frac{\sum m_{i}\Delta_{i}{}^{2}}{\sum m_{i}\Delta_{i}} \tag{7}\]  
where  
\(\Delta_{eff}\): effective displacement;  
\(m_{i}\): story mass;  
\(\Delta_{i}\): story displacement at the target story drift. (Step 6) Based on the target deformation and the effective damping factor, the effective period \(T_{eff}\) is derived from the displacement response spectrum, and the spectrum reduction factor \(F_{h}\) is calculated using the following formula:  
\[F_{h}=\frac{1.5}{(1+10(\xi_{e}))} \tag{8}\]  
(Step 7) Evaluate the effective stiffness, \(K_{eff}\). Figure 2:0  
where  
\(m_{eff}\): effective mass;  
\(T_{eff}\): effective period. (Step 8) Identify the shear force \(Q_{d}\) of the equivalent SDOF system based on effective stiffness and effective displacement. Figure 2:1  
Figure 3 shows the target line of the equivalent linear system. (Step 9) Design adequacy is evaluated based on whether the target line touches the capacity curve line, as shown in Figure 2:2 Additionally, if the target line surpasses the capacity curve, the design is considered under-designed. Meanwhile, if the target line is drawn below the capacity curve, it is considered as over-designed.