## 4 Seismic Performance of Isolation Systems Equipped with SLDTFPB and SLDRFPB
### Seismic Response of Superstructures Equipped with SLDRFPB and SLDTFPB  
Inter-story drift ratios of isolation structures equipped with SLDTFPB or SLDRFFPB are outlined in Figure 14. It can be seen that inter-story drift ratio of each model is no more than 0.1% when the structure is subjected to frequent earthquakes. Some plastic damage (i.e., inter-story drift ratio is much larger than 0.1%) can be observed in the frame structure without isolation bearing subjected to earthquakes whose PGA is 2.2 m/s\({}^{2}\). It is no wonder that the frame structure without isolation bearing finds it hard to survive rare earthquakes. Structures with SLDTFPB or SLDRFFPB can withstand the seismic load whose PGA is up to 6.2 m/s\({}^{2}\), and in this case, maintain approximate elasticity, so that SLDRFPB and SPDTFPB have superior sufficient isolation effects under rare or very-rare earthquakes. This is because a large equivalent radius leads to small horizontal stiffness and thus brings a good isolation effect. In addition, inter-story drift ratio of frame structure increases linearly with earthquake intensity in completely elastic analysis. Inter-story drift ratios of three isolation structures increase \begin{table}
\begin{tabular}{c c c c c} \hline  & **Earthquake Event** & **Mw** & **Station** & **Component** \\ \hline Ground Motion 1 & Chi-Chi-Taiwan, 1999 & 7.62 & HWA043 & CHICHI/HWA043-FN \\ Ground Motion 2 & Chi-Chi-Taiwan, 1999 & 7.62 & TCU038 & CHICHI/TCU038-FP \\ Ground Motion 3 & Kocaeli-Turkey, 1999 & 7.51 & Ataky & KocaELI/ATK-FP \\ Ground Motion 4 & Loma Prieta, 1989 & 6.93 & Salinas–John and & & LOMAP/SJW-FP \\ Ground Motion 5 & Loma Prieta, 1989 & 6.93 & Agnews State Hospital & LOMAP/AGW-FP \\ \hline \end{tabular}
\end{table} 
Table 1: Five natural ground motions used in the time-history analysis. nonlinearly with PGA. This is because an isolation layer subjected to stronger earthquakes can avoid a stick pattern of the isolation layer induced by friction force. Moreover, inter-story drift ratio of SLDTFFB with a different equivalent radius is similar, and inter-story drift ratios of SLDTFFB and SLDRFPB with similar equivalent radius but different equivalent friction coefficient are different. This is validated by a similar isolation effect of isolation systems with different super-low frequency according to the change of the response spectrum in long periods. It also illustrates that the isolation effect of super-large displacement friction pendulum bearing is mainly determined by the equivalent friction coefficient. Figure 15 shows the relations between maximum vertical displacements of superstructures and PGA. In particular, the edge of the frame with SLDRFPB vibrates most violently in the vertical direction, and different parts of the frame with SLDTFFB behave identically to vertical vibration. It helps to understand the difference of vertical influence between rolling motion form and translation motion form along the arc. As shown in Figure 15, although the curve of SLDRFPB is much higher than those of SLDTFFBs, vertical displacements of the superstructure equipped with both SLDRFFB and SLDTFFB are small even when subjected to rare and very-rare earthquakes, thereby destruction of the superstructure from inclination of each story could not occur. Safety of both SLDRFPB and SLDTFFB can be achieved. Moreover, it can be concluded that the ratio between the response of the edge of each story and the response of the center of each story in the structure with SLDRFPB is approximately equal to \(1+\frac{L}{2|x_{0}|}\). Figure 16 shows the relations between vertical accelerations of the center of superstructures equipped with SLDTFFB or SLDRFPB and PGA. Maximum vertical acceleration of the superstructure is also inconspicuous. A strong sense of weightless or overweight in the structure could not occur even when subjected to very-rare earthquakes, so that the comfort of both SLDRFPB and SLDTFFB can be satisfied.