## 2 Design of Seismic Test Mockup
### Analysis Model and Dynamic Characteristics of Test Mockup  
To derive an appropriate plastic strain in the nozzle part, enough to validate the inelastic seismic analysis method, the test mockup is designed to have dominant dynamic characteristics resonant in the peak spectral frequency band of the seismic input motions. Figure 2 presents the target required response spectrum, representing those at the elevation of 136 ft in the in-structure building (ISB) of NSSS. As shown in the figure, the peak spectral frequency band is 9 to 12 Hz for the EW (east-west) direction, 5 to 20 Hz for the NS (north-south) direction, and 15 to 21 Hz for the V (vertical) direction. The dynamic characteristics of the test mockup are investigated by the modal analysis by using the ANSYS [16] commercial finite element program. Figure 3 shows the finite \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Parameters** & **Design Value** \\ \hline Pipe Outer Diameter (mm) & 89.1 \\ Pipe Thickness (mm) & 7.6 \\ Vertical Pipe Length (mm) & 850 \\ Horizontal Pipe Length (mm) & 550 \\ Elbow Curvature (mm) & 114.3 \\ Added Mass-1 (kg) & 80 \\ Added Mass-2 (kg) & 40 \\ Total Height of Nozzle (mm) & 167.35 \\ Nozzle Outer Diameter (mm) & 133.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of test mockup design parameters. Figure 1: Overall configuration of the test mockup and seismic directional axis. element seismic analysis model of the test mockup. As shown in the model, the element type of the nozzle is a three-dimensional solid element of SOLID185. For the piping system, the three-dimensional pipe elements of PIPE289 and ELBOW290 are used for the straight run section and for the elbow, respectively. To rigidly couple the solid element of the nozzle and the line element of the pipe, the element type of MPC184 is used. The added masses in the test mockup are modeled with a structural mass element of MASS21, including the effects of the rotary moments of inertia. Related to the boundary conditions, it is assumed that the seismic input motions are applied to the nozzle bottom surface as the design response spectrum is specified at the hot-leg piping system. Then, the modal analysis is carried out with the fixed condition of the nozzle bottom surface. Table 2 presents the summary results of the modal analysis. For the horizontal directions, the dominant fundamental frequency is 11.74 Hz for the NS direction and 11.99 Hz for the EW direction. Additionally, the dominant natural frequency in the vertical direction is 27.63 Hz, slightly apart from the vertical target peak response frequency band. From the modal analysis, it is confirmed that the dynamic characteristics of the test mockup will meet the intended design goal, deriving the sufficiently inelastic strains at the nozzle. Figure 4 presents the results of the mode shapes for dominant natural frequencies. From the results, it is expected that Mode 1 and Mode 3 will contribute to the torsional seismic response at the nozzle, and Mode 2, Mode 4, and Mode 5 will contribute to the bending seismic responses at the nozzle. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode No.**} & **Frequencies** & \multicolumn{3}{c}{**Modal Participation Factors**} & \multicolumn{3}{c}{**Effective Mass**} \\ \cline{2-9}  & **(Hz)** & **EW** & **NS** & **V** & **EW** & **NS** & **V** \\ \hline
1 & 11.74 & 0.00 & 10.07 & 0.00 & 0.00 & 101.46 & 0.00 \\
2 & 11.99 & \(-\)8.74 & 0.00 & 4.35 & 76.30 & 0.00 & 18.96 \\
3 & 25.89 & 0.00 & 5.47 & 0.00 & 0.00 & 29.94 & 0.00 \\
4 & 27.63 & 7.74 & 0.00 & 5.05 & 59.84 & 0.00 & 25.54 \\
5 & 101.61 & 0.00 & 0.07 & 0.00 & 0.00 & 5.81 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summaries of modal analysis. Figure 3: Finite element analysis model: (**a**) total model; (**b**) zoomed nozzle model. The deadweight effect of the added masses attached to the pipe was examined and included in the modal analysis, but it was found that it has minimal effects on the dynamic characteristics of the test mockup.