## 4 Validation of Inelastic Seismic Analysis
### Results of Inelastic Seismic Analyses  
#### 4.2.1 Validation of Strain Time History Responses  
Figure 17 presents the inelastic seismic time history analysis results, representing the accumulated equivalent plastic strain distribution at the end time of PGA = 0.3 g in the nozzle. As shown in the results, we can see that the maximum seismic strain responses occur in the region of the nozzle's safe end, as expected in the test mockup design. This result is considered to be dominantly caused by the bending motions of the piping system. In addition, the frequencies of Mode 1 (11.74 Hz, torsional) and Mode 2 (11.99, bending) are in a closed mode. It is judged that these closed bending and torsional modes strongly influence the determination of the location where the maximum strain response occurs.  
If we look more closely in Figure 17b, which shows the inelastic strain distribution in the cross-section where the maximum strain occurs, the largest inelastic strain occurs along the (EW, NS) direction. From the sectional view, it is expected that the largest seismic responses will occur at the SG-5 location among the strain gauges in tests.  
Figure 18 presents the material hysteretic responses at the location of the maximum accumulated equivalent plastic strain in Figure 17.  
To compare the inelastic seismic analysis results with the test results, the maximum and minimum principal strains are calculated at each node, corresponding to the locations of the strain gauges, as shown in Figure 17b. Figures 19 and 20 present the analysis results of the principal strains for PGA = 0.3 and 0.6 g, respectively. As expected from the inelastic seismic analysis, the largest strain responses occur at SG-5.  
When compared, the seismic strain time history responses of Figures 19 and 20 with the test results of Figures 8 and 9, the overall strain wave shapes and amplitudes are similar. Specifically, we can see that the largest strain responses occur at the same location of SG-5 in the tests and analyses, as expected in Figure 17. In general, the maximum accumulated equivalent plastic strain, which can be a failure mode in strain-based seismic design criteria, occurs at the location where the maximum value of the time history response occurs, but this is not always the case.  
Table 10 presents the comparison results of the maximum principal strain values of the time history responses between the tests and inelastic seismic analyses for the case of PGA = 0.3 g and PGA = 0.6 g. As shown in the table, the results of the inelastic strain responses are in good agreement with the test results.  
Figure 17: Inelastic seismic analysis results of accumulated equivalent plastic strain distributions at the nozzle (PGA = 0.3 g): (**a**) isometric view; (**b**) sectional view at the maximum region and node points corresponding to locations of strain gauges attached in the tests.  
Figure 19: Inelastic seismic analysis results of principal strain time history responses for PGA = 0.3 g: (**a**) SG-1; (**b**) SG-2; (**c**) SG-3; (**d**) SG-4; (**e**) SG-5.  
Figure 18: Hysteretic behavior of the material at the location of the maximum accumulated equivalent plastic strain for PGA = 0.6 g: (**a**) EW (X); (**b**) NS (Z); (**c**) V (Y).