## 5 In-Structure Response Spectra
### Validation of Decoupling Criteria Based on Two-Degree-of-Freedom System  
In this section, we examine whether the difference in responses between the coupled and decoupled analyses conforms to the three representative decoupling criteria for determining the necessity of the coupled analysis. Figure 19: Decoupling criteria of US NRC [22] and [PERSON] et al. [23]. First, the equipment locations and frequencies for applying the decoupling criteria were selected as the frequency at which the response difference between the decoupled and coupled analyses was significant, as shown in Figures 12-15. Essentially, the frequency at the peak of the decoupled ISRS was selected for the following conditions: H2-directional ISRS at equipment location 1, V-directional ISRS at equipment location 2, V-directional ISRS at equipment location 3, of which total mass ratio \(\mu_{T}\) are 1, 0.1, and 0.001%, respectively. The selected equipment frequencies and corresponding response reduction rates are shown in Figure 20, where \(f_{pA}\) and \(f_{PB}\) represent the frequency at the peak of ISRS using Models A and B, respectively. In addition, \(f_{ucA}\) and \(f_{ucB}\) represent the frequency where the coupled ISRS yielded an unconservative response compared to uncoupled ISRS using Models A and B, respectively, and located in a relatively flat part of the ISRS. The peaks of uncoupled ISRS at \(f_{pA}\) and \(f_{PB}\) decreased by 29.8-65.3% using the coupled analysis. Meanwhile, the spectral accelerations of uncoupled ISRS at \(f_{ucA}\) and \(f_{ucB}\) increased by 20.2-42.1% using the coupled analysis. In other words, the selected conditions include both conservatism and non-conservatism that can exist in the coupled analysis. Figure 20: _Cont._  
For the selected frequencies in Figure 20, combinations of the frequency ratio and modal mass ratio are plotted with the decoupling criteria expressed by Equations (27) and (29) in Figure 21, where \(f_{pA}\), \(f_{pb}\), \(f_{ucA}\) and \(f_{ucB}\) are marked in the corresponding figure in Figure 20. All 1783 vibration modes of the auxiliary building structure with a natural frequency from 3.4 to 75.9 Hz calculated in the eigenvalue analysis were included to plot Figure 20. However, in Figure 21c, the mass ratio was limited to those higher than \(1.0\times 10^{-4}\) to concentrate on major modes with relatively higher mass ratios. Except for equipment frequencies \(f_{pA}=f_{pb}\) and \(f_{ucA}\) in Figure 21b, all points are located inside the region U, where coupled analysis is not required. However, as shown in Figure 20, the response obtained by the coupled analysis is significantly different from that of the decoupled analysis using Models A or B. In particular, the spectral acceleration at a number of selected equipment frequencies obtained by coupled analysis was 20-42% higher than that obtained by decoupled analysis using Models A or B. Two additional decoupling criteria by US NRC and [PERSON] et al. were applied to the same combinations of the frequency ratio and modal mass ratio mentioned above and the results are plotted in Figure 22. Most selected equipment frequencies denoted by \(f_{pA}\), \(f_{pb}\), \(f_{ucA}\) and \(f_{ucB}\) in each figure are related to one or more modes of which frequency ratio and modal mass ratio are located inside regions requiring coupled analysis by both US NRC and [PERSON] et al. criteria. However, for the equipment frequency \(f_{pb}\) in Figure 22c, all points are outside the coupling-required region of the US NRC criteria, but two of those points are inside Region C of [PERSON] et al. criteria. Therefore, Fouquiau et al. criteria can distinguish coupling-required equipment conditions the most adequately among the three criteria in comparison.