## 4 Discussion
### Seismic Response of the PSC Grider Bridge According to Seismic Properties  
In the FE model of the bridge considered in this study, the seismic load in Figure 6a was acting on the x-translation of the bridge, and the acceleration response at the deck of the bridge was evaluated. In addition, the response spectrum was calculated using the seismic load acting on the bridge and the acceleration response on the deck of bridge generated by the corresponding seismic load. Figure 12 shows the response spectrum generated by the seismic load acting on the bottom of the foundation, as well as the acceleration response generated at the deck of the bridge. It can be seen that the response spectrum generated by the acceleration response of the deck of the bridge is amplified at 3.215 Hz, 5.428 Hz, and 11.995 Hz, which are the natural frequencies of the 1 st, 2 nd, and 3 rd modes in the x-direction of the bridge, respectively. This is because the response acceleration of the bridge is amplified by resonance in the natural frequency in the x-direction of the structure. The response of acceleration and the maximum bending moment at the ground and deck of the bridge are shown in Figure 13 and Tables 4 and 5 for when Seismic Load 1, Seismic Load 2, Seismic Load 3, and Seismic Load 4 are acting on the PSC I-girder bridge. The peak acceleration of each seismic load was 0.357 g for Seismic Load 1, 0.300 g for Seismic Loads 2 and 3, and 0.406 g for Seismic Loads 4. The maximum bending moments  
Figure 12: Time–history and response spectrum: (**a**) modified time–history with soil properties; (**b**) response spectrum using time–history with soil properties; (**c**) response time-history at the deck of the bridge. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode No.**} & \multirow{2}{*}{**Natural Frequency (Hz)**} & \multicolumn{3}{c}{**Mass Participation (\%)**} \\ \cline{3-5}  & & **X-Translation** & **Y-Translation** & **Z-Translation** \\ \hline
1 & 1.784 & 0.000 & 13.000 & 0.000 \\
2 & 2.463 & 0.000 & 65.250 & 0.000 \\
3 & 2.484 & 0.000 & 0.000 & 0.000 \\
4 & 3.215 & 69.810 & 0.000 & 0.000 \\
5 & 3.881 & 0.000 & 0.000 & 6.050 \\
6 & 4.709 & 0.000 & 1.670 & 0.020 \\
7 & 5.138 & 0.000 & 0.000 & 51.500 \\
8 & 5.428 & 22.910 & 0.000 & 0.000 \\
9 & 6.651 & 0.450 & 0.000 & 0.000 \\
10 & 7.773 & 0.000 & 10.070 & 0.000 \\
11 & 11.995 & 3.880 & 0.000 & 0.000 \\
12 & 20.389 & 0.000 & 0.020 & 23.590 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Natural frequency and mass participation. of the bridge under Seismic Loads 2 and 3, with the same peak acceleration of 0.300 g, were 2308.36 kN\(\cdot\)m and 3223.90 kN\(\cdot\)m, respectively, showing a difference of \(\sim\)139%. It was confirmed that different member forces can be calculated according to the response spectrum acceleration of the natural frequency of the bridge under the seismic load of the same peak acceleration. Therefore, it was observed that even with identical acceleration for the seismic load, member forces depend on the seismic load and the natural frequency of the bridge. The response acceleration of the bridge was compared when Seismic Loads 1 and 3 were applied. From the results, Seismic Load 1 had a \(\sim\)119% higher maximum response acceleration than Seismic Load 3, but the latter had a \(\sim\)120% higher maximum bending moment than Seismic Load 1. This phenomenon might take place because, as mentioned above, the seismic load and natural frequency of the bridge affect the results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Seismic Load**} & \multirow{2}{*}{
\begin{tabular}{c} **Peaked** \\ **Acceleration** \\ \end{tabular} } & \multicolumn{3}{c}{**Spectral Acceleration**} \\ \cline{3-5}  & & **1 st Mode** & **2 nd Mode** & **3 rd Mode** \\ \hline El Centro & 0.357 & 0.732 & 0.739 & 0.561 \\ Initial Artificial Time–History & 0.300 & 0.670 & 0.823 & 0.581 \\ Considering U.S. NRC & 0.300 & 0.867 & 0.868 & 0.655 \\ Applied Soil & 0.406 & 1.009 & 0.728 & 0.464 \\ \hline \hline \end{tabular}
\end{table}