## 6 Evaluations of Vertical Seismic Isolation Performance  
To investigate the seismic energy dissipation performance and find the adequate number of steel dampers required for the vertical displacement limits, the vertical seismic isolation performance evaluations are carried out for the chosen design VIF of 2.5 Hz and 3.0 Hz with three designed steel dampers of SD1, SD2, and SD3. The used finite element seismic analysis model is shown in Figure 4, and the steel damper is modeled by the bilinear stiffness, as identified in Table 11.  
Figures 21-23 present the calculation results of the floor response spectrum according to the used number of steel dampers. As shown in Figure 21, in the case of the relatively flexible steel damper SD1, the variation of the actual VIF is not sensitive to the used number of steel dampers. However, in order to obtain effective vertical seismic isolation performance, it was found that two or more SD1 dampers should be used when VIF is 2.5 Hz, and three or more when design VIF is 3.0 Hz. From the results of Figure 22, it can be seen that the steel damper SD2 shows almost similar vertical seismic isolation performance characteristics to that of the steel damper SD1.  
Figure 19: Comparison results of hysteretic behavior between tests and analyses for steel damper, SD2: (**a**) for \(\pm\)24 mm stroke; (**b**) for \(\pm\)30 mm stroke.  
Figure 20: Comparison results of hysteretic behavior between tests and analyses for steel damper, SD3: (**a**) for \(\pm\)24 mm stroke; (**b**) for \(\pm\)30 mm stroke.  
In the case of the SD3 steel damper, which has relatively strong rigidity, as the used number of steel dampers increases, the actual VIF significantly increases, and the effective frequency range in which the seismic isolation effects can be obtained is greatly reduced, especially at lower frequency less than 10 Hz as shown in Figure 23. However, in case of vertical seismic isolation design for nuclear power plant equipment designed with a vertical natural frequency of 10 Hz or higher, it can be seen that an effective vertical seismic isolating effect can be obtained even if three steel dampers are used.  
To check the vertical displacement limits, as discussed in Section 2.2 above, the seismic displacement responses were investigated for each case of the disc spring and helical coil spring. Table 13 presents the summary analysis results of the maximum vertical seismic displacement response of the vertical seismic isolation device according to the used number of steel dampers. In the table, the values of column 4 and column 5 represent the accommodatable vertical seismic displacement by extracting the static displacement from the shut displacement. As shown in the table, when the steel damper SD1 is used, five or more steel dampers must be used to satisfy the vertical displacement limits, and four or more steel dampers are required for SD2 and one or more steel dampers for SD3.  
Figure 21: Results of vertical response spectrum for steel damper, SD1: (**a**) Design VIF = 2.5 Hz; (**b**) design VIF = 3.0 Hz.  
Figure 22: Results of vertical response spectrum for steel damper, SD2: (**a**) Design VIF = 2.5 Hz; (**b**) design VIF = 3.0 Hz.