# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 2 Consideration When Developing ISRS of Fixed and Isolated Structures  
### Developing the ISRS of Fixed Structures  
Many studies have been conducted on how to develop the ISRS for building structures, and methodologies related to floor response prediction have also been presented [18, 19, 20, 21, 22, 23]. ISRS can be generated using two methods: time history analysis and direct spectrum-to-spectrum method, and methodologies for numerically calculating the ISRS using prediction equations using the response of each floor due to the input ground have been studied [18,19]. When comparing the ISRS prediction model with time history analysis results, it was generally accurate. However, there were cases where it was inaccurate at certain frequencies, and it was also difficult to predict for complex structures. To supplement these limitations, research was conducted to predict the ISRS for various structures, such as low-rise and high-rise reinforced concrete structures [20,21], structures for equipment-structure resonance [22], and irregular structures that can cause torsion [23]. Due to numerous studies on the ISRS, criteria for the development of the ISRS for fixed structures have been established to enable accurate prediction of the ISRS even for complex structures. The criteria for developing the design ISRS are presented in Reg. Guide 1.122 [1], and these criteria were proposed to be broadened by \(\pm 15\%\) from the peak frequency and smoothed in consideration of frequency variability due to uncertainties such as material properties of structures and soil, numerical errors in modeling techniques used in seismic analysis, and soil-structure interaction (SSI). EUROCODE 8 [24] provides input values related to the ground response spectrum, structural dynamic analysis principles, nonlinear behavior evaluation, seismic load, and SSI. It provides an analysis method for deriving the ISRS from these inputs but does not present a specific methodology for developing the design ISRS. In addition, because the target structure was a very important facility in this study, the design ISRS criteria of nuclear power facility presented in ASCE were referenced.  
ASCE 4-16 [2] describes the design ISRS generation methods for the seismic design and performance evaluation of systems and equipment in NPPs. Figure 1 shows an example of the ISRS derived from analysis and the design ISRS with the broadened peak frequency according to ASCE. For the damping of equipment with less than 10%, if the bandwidth-to-central-frequency ratio, \(B\), which is determined according to the frequency with an amplitude exceeding 80% of the peak spectral amplitude, does not exceed 0.30, a 15% reduction in the narrow frequency peak amplitude is permissible. These criteria were presented based on the assumption that non-structural elements and structures behave linearly and that interactions between two different systems are ignored. This is because when the seismic intensity increases, the response also increases linearly, making predictions possible in the linear range. However, in the case of an isolated structure, it is difficult to apply the same assumptions because isolators behave nonlinearly. Because the ISRS variability of isolated structures can be higher due to the uncertainty of the mechanical characteristics of isolators, hysteresis behavior, and ground motion characteristics, it is important to determine how to include this variability in the design ISRS.