## 3 Numerical Analysis Overview  
### Verification of Numerical Model  
The electrical cabinet model was fabricated using rectangular hollow sections made of SRT275, following KS D 3568. Table 3 lists the material properties applied in the numerical model. The nonlinear material behavior was modeled using a bi-linear kinematic hardening model, referring to tensile test results from previous studies, as illustrated in Figure 9[48,49]. The dimensions of the rectangular hollow sections used for the main members of the electrical cabinet model differed from the nominal values specified in KS D 3568 due to discrepancies in actual production. Accordingly, the fabricated specimen was physically measured, and the corresponding dimensions in the preliminary numerical model were updated to reflect these measurements. The electrical cabinet model's frame--constructed by welding columns, beams, and braces--was partitioned and merged into a single part. The connections between the frame and the plates were modeled using tie constraints. Dummy masses, bolted onto the plates at each floor, were defined as nonstructural mass and applied directly to the plates. All parts were modeled using solid elements with hexahedral meshing (C3D8R), which employ linear reduced integration. The mesh size of the numerical model was set to 20 mm, which was sufficiently small to ensure convergence without significant differences in the analysis results. The final numerical model comprised 52,071 elements and 94,384 nodes, as detailed in Figure 10. A 3% damping ratio was defined in accordance with NUREG/CR-6919 and implemented using Rayleigh damping[50]. The applied Rayleigh damping coefficients were \(\alpha\) = 3.022 and \(\beta\) = 0.000297. The anchorage boundary condition was modeled as a fixed support, constraining displacements in tri-axial directions. The mesh in the anchor bolt connection region was locally refined to optimize the numerical model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Density** **(ton/mm\({}^{3}\))**} & **Young’s** **Modulus** **(MPa)** & **Poisson’s** **Ratio** & **Yield Stress** **(MPa)** & **Plastic Strain** \\ \hline \multirow{2}{*}{7.85 \(\times\) 10\({}^{-9}\)} & \multirow{2}{*}{210,000} & \multirow{2}{*}{0.3} & 395.69 & 0 \\  & & & 467.00 & 0.198 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties (SRT275). Figure 9: Bi-linear kinematic hardening model [48,49]. An eigenvalue analysis was performed to validate the optimized numerical model's accuracy. The resulting mode shapes are presented in Figure 11, with the corresponding translational and rotational participation factors for each mode summarized in Table 4. The natural frequencies of the first and second modes were found to be 15.18 Hz and 16.99 Hz, respectively. For the first mode, the participation factors were 0.855 (Y-direction translation) and 0.969 (X-direction rotation); for the second mode, they were 0.951 (X-direction translation) and 0.970 (Y-direction rotation), with rotational components dominating. This result aligns with the shaking table test findings, confirming that the dominant global modes of the cabinet are characterized by bending behavior in the two horizontal directions [23; 24]. As shown in Table 5, the numerical model weighed 410.73 kg, closely matching the specimen's 410.00 kg (0.18% difference). Natural frequencies varied by 2.12% and 1.43% from experimental results. The percentage difference (PD) used was calculated using Equation (2), with \(V_{1}\) and \(V_{2}\) representing the values obtained from the specimen and the numerical model, respectively, for calculating the percentage difference between experimental and numerical results. The natural frequency differences remained within 1-2%, and the weight difference was under 1%, confirming the developed numerical model's accuracy in simulating the specimen.