## 6 Analysis of Retrofit Effect of SSDB Systems
### Interstory Drift Ratio (IDR)  
IDR is one of the macroscopic parameters reflecting the structural story deformation and stiffness, and it is also one of the important indicators for judging the structural damage levels in engineering, as was mentioned previously. To this end, Figures 12 and 13 shows the IDR distribution along with the height of MS1 and MS2 MD-RC frame with minor (DS1) and moderate (DS2) damage state before and after retrofitting under aftershocks excitations, respectively. From these figures, it can be initially observed that, in the case of LS-1, the maximum IDR reduction rate is up to 97.7% (first story) when compared with un-retrofitted MD-RC frame. LS-1 has a better performance in reducing the IDR of the first story of MD-RC frame structure as compared with other retrofitting schemes. However, the IDR reduction rate of second and third story of MD-RC frame is lower than other schemes. Especially for the non-pulse-like aftershocks scenarios, in some MD-RC frames retrofitted while using LS-1, the IDRs of second and third story even exceed those of un-retrofitted structure. The maximum IDR is 276.6% (third story) as large as the un-retrofitted case. It further illustrates that the LS-1 retrofitting scheme is not suitable for the retrofitting of MD-RC frame in this study. For the LS-2 retrofitting scheme, it is evident that the IDRs are lower than un-retrofitted MD-RC frame, except for the top story. Especially for the LS-3 retrofitting scheme, the IDR of each story of MD-RC frame are significantly reduced no matter the damage state. More specifically, the lowest reduction rate of IDR is 18.6%, and the highest reduction rate of IDR is up to 87.9%, which indicates that LS-3 plays a more positive effect on the seismic performance of MD-RC frame as compared with other retrofitting schemes. Moreover, when comparing the results of LS-2 and LS-3, although LS-2 does not reinforce the top story of MD-RC frame, the maximum IDR of the first and second story are relatively close under LS-2 and LS-3 schemes. Although the IDR of the top story under the LS-2 retrofitting scheme exceeds other stories, the maximum IDRs are significantly lower than the un-retrofitted case. Therefore, with the comprehensive consideration of economy and installation portability, the engineering applicability of LS-2 scheme is better than LS-3 scheme. In addition, to quantitatively analyze the retrofit effect of these CSSDB systems on MD-RC frame, in this study the shock absorption rate (SAR) index is used and it is defined as,  
\[SAR=\frac{MIDR_{ur}-MIDR_{r}}{MIDR_{ur}}\times 100\% \tag{4}\]  
where, \(MIDR_{ur}\) and \(MIDR_{r}\) are the maximum IDR (MIDR) of un-retrofitted and retrofitted MD-RC frame, respectively. Table 8 summarizes the MIDR and SAR values of MD-RC frame before and after retrofitting under different LSs. From this table, it is evident that the MIDR of retrofitted MD-RC frame has dropped significantly for LS-2 and LS-3 schemes, the maximum drop is nearly 5.6 times. However, for the LS-1 scheme, similar to the previous observations, the MIDRs of some retrofitted MD-RC frames even exceed that of un-retrofitted structures, especially under non-pulse-like aftershocks. More specifically, for the minor damage MD-RC frame, the MIDR under LS-1 scheme is usually 2.0-4.0 times as large as that of LS-2 and LS-3 schemes; for the moderate damage MD-RC frame, the MIDR under LS-1 scheme is usually 1.4-2.2 times as large as that of LS-2 and LS-3 schemes. In terms of SAR; it is evident that the SAR under LS-1 is usually the lowest and even negative under non-pulse-like aftershocks, with a maximum SAR of \(-\)74.1%. Obviously, it is not sufficient to carry out only retrofit on structural bottom story for MD-RC frame due to the randomness and uncertainty of ground motion.