## 4 DBDM of Coupled Shear Wall Structures with Metallic Dampers  
The working mechanism of metallic dampers involves the dissipation of input energy through the plastic yielding of the metal. As illustrated in Figure 8, a metallic damper is positioned at the center of the coupling steel beam connecting two RC shear walls. The metallic damper was designed with an hourglass-shaped geometry, allowing the central section of the plate to undergo yielding and effectively dissipate energy. Figure 9 illustrates the hysteresis loop of the metallic damper. The shape of the hysteresis loop is represented by the bilinear model. The symbols of elastic stiffness, yield force, and post-yield stiffness are defined as \(K_{d}\), \(F_{y}\), and \(K_{dd}\). The properties of the metallic dampers are presented in Table 2. The maximum shear capacity (100%) of the damper was assumed to be 500 kN for 6-story CSW, 600 kN for 12-story CSW, and 700 kN for 18-story CSW. To determine the optimum amount of damper to achieve the target displacement, the analysis was performed by varying the damper capacity to 75%, 50%, and 25%. This ratio is referred to as damping force reduction (DFR) in this paper. \begin{table}
\begin{tabular}{c c c c c} \hline
**Structural Member** & **Size (mm)** & **Concrete Strength (MPa)** & **Steel Strength (MPa)** & **Rebar Size** \\ \hline \multicolumn{5}{c}{6 Stories} \\ \hline Column & 500 \(\times\) 500 & 40 & - & D25 \\ \hline Shear wall & 5000 \(\times\) 250 & 40 & - & D10 \\ \hline Steel beam & I-600 \(\times\) 300 \(\times\) 10 \(\times\) 10 & - & 325 & - \\ \hline \multicolumn{5}{c}{12 Stories} \\ \hline Column & 700 \(\times\) 700 & 40 & - & D29 \\ \hline Shear wall & 5000 \(\times\) 300 & 40 & - & D10 \\ \hline Steel beam & I-600 \(\times\) 300 \(\times\) 10 \(\times\) 10 & - & 325 & - \\ \hline \multicolumn{5}{c}{18 Stories} \\ \hline Column & 900 \(\times\) 900 & 40 & - & D35 \\ \hline Shear wall & 5000 \(\times\) 500 & 40 & - & D10 \\ \hline Steel beam & I-600 \(\times\) 300 \(\times\) 10 \(\times\) 10 & - & 325 & - \\ \hline \end{tabular}
\end{table} 
Table 1: Structural member properties. Figure 8: Metallic damper details. Following the procedure of the DBDM outlined in Section 2, the capacity curves and target lines are compared, where the equivalent damping factor of the metallic damper is obtained using Equation (4). Figure 10 illustrates the DBDM performance of the 6-story CSW system with metallic dampers with different DFRs. Figure 10a,b indicates that the 25% DFR and 50% DFR designs fail to meet the required design capacity, as evidenced by the target line surpassing the capacity curve line. Figure 10d illustrates the target line positioned below the capacity curve, indicating that the 100% DFR design is over-designed. On the other hand, as shown in Figure 10c, 75% DFR design meets the design requirements. The accuracy of the DBDM is verified by comparing the story drift obtained from the THA with the target story drift of 1/250 under three artificial ground motions as shown in Figure 11. In all cases, the maximum story drift for 75% DFR design is in good agreement with the target story drift, while the maximum story drifts for 50% DFR and 25% DFR exceed the threshold. This means that the accuracy of 75% DFR design, which was considered optimal in the DBDM, was confirmed.