## 2 Numerical Model of Containment Building
### Nonlinear Modeling  
The inelastic behavior of the containment building is modeled based on the methodology proposed by [PERSON] et al. (2006) [2; 3]. Plastic hinges were placed at the support and nodes between the beam elements to represent the inelastic flexural deformation. In addition, inelastic shear deformation springs were inserted at the midpoint of each beam-column. Inelastic modeling was limited only to cylindrical walls consisting of the lower part of the structure, and the upper dome was assumed to be elastic considering the seismic force distribution in the vertical cantilever-type structure. Table 2 summarizes the median values of the material properties applied to the inelastic model. In Table 2, \(F_{c}\), \(F_{y}\), and \(F_{yy}\) are the compressive and tensile strengths of concrete and the yield strengths of rebars and tendons, respectively, and \(\epsilon_{c}\) is the strain at the peak stress of concrete. \(E_{c}\), \(G\), \(E_{s}\), and \(E_{p}\) are the elastic and shear moduli (MPa) of concrete and the elastic moduli of rebars and tendons, respectively. Two adjacent elements were grouped as a single element group, to which the same plastic hinge property was assigned, and the load-deformation curves for the five beam element groups from the bottom are plotted in Figure 2.  
The load-deformation curves for the plastic hinge of beam elements have a tri-linear shape in accordance with the model proposed in JEAG 4604-1987 [24]. These curves for five elements are shown in Figure 2a. In the triangular load-deformation curve, \(M_{1}\) is the moment at the tensile crack of concrete, \(M_{2}\) is the moment corresponding to the first yielding of the outermost reinforcements, and \(M_{3}\) is the moment at the ultimate curvature suggested in JEAG 4604-1987 [24]. The three points defining the trilinear load-deformation curve were determined based on the inelastic bending moment-curvature relationship obtained through inelastic cross-sectional analysis. The material models of concrete and rebars proposed by [PERSON] [25] were adopted, and the increase in strength after yielding was due to strain hardening of the rebars. The degrading trilinear model [24] was adopted to represent the hysteretic behavior of the plastic hinge. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Natural Frequency (Hz)**} & \multicolumn{2}{c}{**Mass Participation Ratio (\%)**} \\ \cline{2-5}  & **LMS Model** & **FE Model** & **LMS Model** & **FE Model** \\ \hline
1 st & 3.65 & 3.43 & 76.9 & 70.5 \\
2 nd & 11.2 & 10.2 & 14.4 & 19.2 \\
3 rd & 20.0 & 18.4 & 3.85 & 3.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Modal characteristics of the median model. Figure 1: Numerical model of the containment building: (**a**) 3D finite element model; (**b**) Lumped mass stick model. The inelastic shear deformation of the cylindrical wall was modeled using a trilinear load-deformation curve, as shown in Figure 2b, for the same elements as in Figure 2a. The strengths of the two points corresponding to the cracking and yield strengths were calculated using Equations (1) and (2) with reference to JEAG 4604-1987 [24]. For the extreme strength defining the third point, Equation (3) for the ultimate strength of the prestressed cylindrical walls proposed by [PERSON] et al. (1981) was adopted [26]. \[\tau_{1}=\sqrt{0.313\sqrt{F_{c}}\Big{(}0.313\sqrt{F_{c}}+\sigma_{m}\Big{)}}\ ( \text{MPa}) \tag{1}\]  
\[\tau_{2}=1.5\times\tau_{1} \tag{2}\]  
\[\tau_{3}=0.664\sqrt{F_{c}}+\left(\rho F_{y}\right)_{AVER}\leq 1.75\sqrt{F_{c}} \ (\text{MPa}) \tag{3}\]  
where  
\[\left(\rho F_{y}\right)_{AVER}=\frac{\rho_{h}+\rho_{m}}{2}F_{y}+\frac{\rho_{ ph}+\rho_{pm}}{2}F_{py}-\frac{\sigma_{h}+\sigma_{m}}{2}\ (\text{MPa}) \tag{4}\]  
In the above equations, \(\rho_{h}\) and \(\rho_{m}\) denote the reinforcement ratios for the rebars in the circumferential and vertical directions, respectively.