# Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra
## 3 Analysis Model and Input Ground Motions  
The structure model was simplified to a 5-story lumped mass stick model to see the variability of the ISRS, as shown Figure 6, and modeling and analysis were performed using SAP2000 software [33]. Because the purpose was to understand the characteristics of the ISRS, a simple model was used rather than a detailed finite element model. Although analyzing with a detailed finite element model is an accurate method, modeling takes a lot of time and cost, so we tried to first identify the ISRS variability with a simple model. In addition, to identify the various effects being considered, it was decided that using a simple model would be easier and sufficient to clearly analyze the results. Because the isolated structure is dominated by nonlinear behavior, there is a concern that lumped mass models may not accurately capture the nonlinear response. However, because the nonlinear behavior of the isolator is the main dynamic characteristic, the superstructure may be able to capture the seismic response even with a simplified model. [PERSON] [8] performed analyses on a finite element model as well as a lumped mass model of NPPs and confirmed that the responses of the two models were similar. If the natural frequencies obtained from the detailed finite element model and the simple beam-stick model are the same, the ISRS will be evaluated similarly from a structural dynamic perspective. Therefore, an arbitrary mass and stiffness of the structure model were set so that the natural frequency was 8 Hz, targeting the auxiliary building of NPPs that the evaluation of the ISRS is important. The basemat mass was set to correspond to 30% of the structure mass, and the isolator was applied below the basemat. The isolator used a bilinear model, and the mechanical properties were assumed based on the research conducted in the MCEER report [34], which was about the uncertainty quantification of the isolation response for NPPs. This report evaluated the displacement and shear force distributions of the LRB at the DBE and 150% DBE. The most important properties in isolation hysteresis behavior are the characteristic strength and the secondary stiffness. The characteristic strength is determined by the yield strength of the lead core and contributes to the energy dissipation. The secondary stiffness contributes to determining the isolation frequency, and this report selected the best-estimated model for the two properties. The best-estimate models were used by referring to the variability addressed in [PERSON] et al. [35], AASHTO [36], FEMA [37]. A total of nine design models were analyzed by combining characteristic strengths corresponding to 3, 6, and 9% of the weight of the supporting superstructure and secondary stiffness with isolation periods of 2, 3, and 4 s. Seismic analyses were performed on nine design models with the variability of bearing properties (\(\pm\)10% or \(\pm\)20%) to compare the statistical characteristics of displacement and shear force for the DBE and 150% DBE. Since the dynamic frequency characteristics of NPPs are almost the same, the seismic isolation properties were determined within the range used in this report. From this report, the secondary stiffness of the isolator was determined so that the frequency was 0.5 Hz (a period of 2 s), the characteristic strength was determined as the ratio of the weight of the superstructure, and the characteristic strength of the isolator was set to 0.06. The stiffness ratio that determines the initial stiffness was selected as 0.01 to 0.12 to include the recommended range and the stiffness ratio used in various studies. To confirm the tendency in extreme situations, 0.01 was also applied, and for heavy structures, such as NPPs, values close to 0.01 are used [9]. To clearly identify the ISRS change within this range of the stiffness ratio values, the values for the analysis were selected as shown in Table 1. These values were determined as a value at which the ISRS change was clearly confirmed without using an equal interval.