## 7 Conclusions  
In this study, the design of a vertical seismic isolation device that can be integrally used combined with a lead-inserted small-sized laminated rubber bearing (LRB) was studied for three-dimensional seismic isolation of the nuclear power plant equipment. The overall study was based on the target equipment installed at 136 ft elevation of the typical nuclear power plant building, the input vertical seismic motions of Figure 3, and the rigid superstructure. From the results of this study, some valuable conclusions are obtained, as follows:  
1. The design VIF required for the design of the vertical seismic isolation device should be determined considering both seismic isolation performance and limitation of the vertical displacement of spring. In this study, the design VIF is recommended to be in the range of 2.5 Hz\(\sim\)3.0 Hz. 2. It is confirmed that the disc spring and the helical coil spring are useful for a stiffness design of the vertical seismic isolation device for equipment. The validation of the  
Figure 23: Results of vertical response spectrum for steel damper, SD3: (**a**) Design VIF = 2.5 Hz; (**b**) design VIF = 3.0 Hz. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Steel** \\ **Damper** \\ **ID** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\# of** \\ **Dampers** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Peak Vertical Seismic Disp.** \\ **Response (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **(\(D_{\text{sd}}-D_{\text{dw}}\)) (\({}^{\text{1}}\)**)** \\ **for Disc Spring (mm)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **(\(D_{\text{sd}}-D_{\text{dw}}\)) (\({}^{\text{1}}\)**)** \\ **for Helical Coil Spring** \\ **(mm)** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **(\(D_{\text{sd}}\)** **–** **\(D_{\text{dw}}\)) (\({}^{\text{1}}\)**)** \\ **for Helical Coil Spring** \\ **(mm)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Vertical Disp.** \\ **Limits (mm)** \\ \end{tabular} } \\ \cline{3-10}  & & **VIF = 2.5 Hz** & **VIF = 3.0 Hz** & **2.5 Hz** & **3.0 Hz** & **2.5 Hz** & **3.0 Hz** & **2.5 Hz** & **3.0 Hz** \\ \hline \multirow{4}{*}{SD1} & 1 & \(-\)63.6/+62.1 & \(-\)63.2/+63.7 & & & & & & \\  & 2 & \(-\)45.1/+41.8 & \(-\)44.3/+42.7 & & & & & & \\  & 3 & \(-\)30.9/+32.1 & \(-\)33.5/+33.6 & 86.5 & 59.9 & 37.5 & 32.0 & 40.5 (\({}^{\text{2}}\)) & 28.1 \\  & 4 & \(-\)29.8/+28.2 & \(-\)29.0/+30.5 & & & & & & \\  & 5 & \(-\)25.9/+25.7 & \(-\)26.1/+27.9 & & & & & & \\ \hline \multirow{4}{*}{SD2} & 1 & \(-\)57.8/+55.0 & \(-\)59.8/+59.7 & & & & & & & \\  & 2 & \(-\)37.2/+36.3 & \(-\)38.6/+33.6 & & & & & & & \\  & 3 & \(-\)30.2/+28.7 & \(-\)29.7/+30.6 & & & & & & & \\  & 4 & \(-\)25.8/+25.6 & \(-\)26.0/+27.8 & & & & & & & \\ \hline \multirow{4}{*}{SD3} & 1 & \(-\)28.0/+27.9 & \(-\)27.9/+28.3 & & & & & & & \\  & 2 & \(-\)18.9/+17.8 & \(-\)16.4/+18.7 & 86.5 & 59.9 & 37.5 & 32.0 & 40.5 (\({}^{\text{2}}\)) & 28.1 \\ \cline{1-1}  & 3 & \(-\)13.6/+9.9 & \(-\)13.3/+10.5 & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 13: Results of vertical seismic displacement responses of vertical isolation device. design values obtained from the equation of a force and displacement relationship are verified by tests. 3. With an appropriate steel damper design, the vertical displacement response can be limited to the design value. In this study, the vertical displacement response is limited to 40.5 mm (disc spring) and 37.5 mm (helical coil spring) for the design VIF = 2.5 Hz and 28.1 mm for the design VIF = 3.0 Hz, which are based on the static displacement by the design vertical load of 10 kN. 4. It is verified that the designed three shapes of the steel dampers, SD1, SD2, and SD3 reveal the seismic energy dissipation performance over 30% critical damping ratio by tests and analyses. 5.