## 5 Strengthening for MD-RC Frame Structure  
### Metallic Energy Dissipator  
Soft steel damper (SSD) has high plastic deformation ability and low cycle fatigue resistance, which can enter the plastic energy dissipation stage earlier than structural members during an earthquake. Therefore, SSD could reduce the structural damage by dissipating part of the seismic input energy, and it has been widely used as the metallic energy dissipator (MED) for structural retrofitting [20; 55]. Generally, typical SSD is designed to shear yielding mode (e.g., shear link or slit damper), because shear yielding dampers could provide higher initial stiffness under small earthquakes and significant energy dissipation potential during large earthquakes by inelastic deformation [28; 30; 55]. In addition, some studies have adopted opening-hole (or window) shaped SSD [30; 55; 56; 57; 35] or combined shear-and-flexural [44] SSD in order to limit stress concentration and out-of-plane buckling of SSD. Accordingly, a combined strip-shaped shear-and-flexural SSD (CSSD) MED has been designed and improved in this research by drawing on the above MEDs. This CSSD device consists of a strip-shaped SSD [35; 55; 57] (shear) and two flange plates (flexure) on the end of the SSD. A displacement-based design procedure has been used in order to design the capacity of the CSSD. The similar design process of these properties and capacity of the CSSD can be referred to following literature works [35; 55; 57]. The same capacity of the CSSD (i.e., designed according to maximum story yielding force) is employed for all stories in order to simplify the calculation. Figure 6 illustrates the configuration information of the CSSD device used in this research. As shown in Figure 6, all SSDs with an overall size of 400 \(\times\) 400 mm\({}^{2}\) and 12 mm thickness (\(t_{\rm s}\)) has been used in this study. Two flange plates of 12 mm thickness (\(t_{\rm f}\)) are welded to both ends of the SSD. Table 6 shows the material properties used in the CSSD device.  
Figure 5: IDR distribution and damage limitation value under MS1 and MS2 mainshock excitation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multirow{2}{*}{**Intact Structure**} & \multicolumn{2}{c}{**After MS1**} & \multicolumn{2}{c}{**After MS2**} \\ \cline{3-6}  & & **DS1** & **DS2** & **DS1** & **DS2** \\ \hline \(1\) & 1.23 & 0.99 & 0.76 & 1.11 & 0.93 \\ \(2\) & 4.05 & 3.62 & 3.13 & 3.80 & 3.46 \\ \(3\) & 7.04 & 6.39 & 5.86 & 6.65 & 6.22 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Natural frequencies of the intact RC frame and MD-RC frame (Hz).  
Because the CSSD device has two kinds of steel materials and complex geometric shapes, it is difficult to obtain a simplified calculation formula for computing the yield displacement, yield, and ultimate force of the CSSD device [55]. To this end, elastoplastic pseudo-static numerical analysis of the CSSD device under cyclic loadings is conducted while using the ABAQUS program to obtain the capacity of the CSSD device. Figure 7 shows the hysteretic curves of the CSSD numerical model under cyclic loadings. From this figure, it is clearly that CSSD device has larger initial stiffness and the hysteresis loop has a plump shape, which means that the CSSD has a higher ductility and a better energy dissipation performance after yielding.