## 3 Analysis of Acceleration Response Results  
### Acceleration Response at the Top of the Piers  
Table 4 presents the acceleration response of each pier top to \(Z\)-direction excitation from the El Centro and Lanzhou seismic waves. The Z-direction excitation generated accelerations in both the X- and Y-directions. The peak values were different with the El Centro and Lanzhou waves. The weak values for the X-direction and Y-direction acceleration responses were because the center of gravity of the bridge structure was not consistent with the center of gravity of the stiffness. Piers 3 and 6 had somewhat stronger responses than the other piers; the most significant acceleration response belonged to pier 6, which had a Y-direction response that reached 0.532 \(g\). This could be attributed to the arrangement and support of pier 6, which was a side pier of the curved beam 3, so the excitation direction formed an angle with it. The final response was equivalent to the coupling of multidirectional excitation. A moveable support was set at the top of pier 6, which increased the transfer of seismic action while restraining the Y-direction displacement of beam 3 during vibration. The same held true for pier 3, but this was a side pier of the straight beam 2, so it had a more regular arrangement and, thus, a smaller response than pier 6. Figure 5 shows the acceleration response at the top of pier 1 subjected to tridirectional (X + Y + Z) El Centro and Lanzhou waves. Figure 6 shows the acceleration response at the top of pier 2. The El Centro and Lanzhou waves caused different structural responses. One reason may be the difference in the spectral distributions of the excitation waves. The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Waves**} & \multirow{2}{*}{**X**} & \multirow{2}{*}{**Y**} & \multirow{2}{*}{**X**} & \multirow{2}{*}{**Y**} & \multirow{2}{*}{**X**} & \multirow{2}{*}{**Y**} \\ \cline{3-3} \cline{5-7}  & & & & & **Pier 1** & & **Pier 2** & **Pier 3** \\ \hline El Centro & 0.241 & 0.250 & 0.106 & 0.15 & 0.342 & 0.293 \\ Lanzhou & 0.215 & 0.215 & 0.086 & 0.24 & 0.138 & 0.307 \\ \hline
**Waves** & \multicolumn{2}{c}{**Pier 4**} & \multicolumn{2}{c}{**Pier 5**} & \multicolumn{2}{c}{**Pier 6**} \\ \hline  & 0.096 & 0.121 & 0.169 & 0.223 & 0.352 & 0.523 \\ El Centro & 0.296 & 0.34 & 0.221 & 0.226 & 0.383 & 0.532 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Peak acceleration at the top of the piers (g). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & \multirow{2}{*}{**Waves**} & \multicolumn{4}{c}{**Peak Value/\(g\)**} & \multirow{2}{*}{**Seismic Wave**} \\ \cline{3-3} \cline{5-7}  & & **X-Direction** & **Y-Direction** & **Z-Direction** & **Excitation** \\ \hline \multicolumn{7}{c}{Scanning white noise} \\
1 & EI & / & / & 0.65 & Z \\ \multicolumn{7}{c}{Centro} \\
2 & EI & 1 & 0.85 & 0 & X + Y \\ \multicolumn{7}{c}{Centro} \\
3 & EI & 1 & 0.85 & 0.65 & X + Y + Z \\ \multicolumn{7}{c}{L} \\
4 & Imperial & / & / & 0.65 & Z \\ \multicolumn{7}{c}{Valley} \\
5 & \multicolumn{1}{c}{} \\ \multicolumn{7}{c}{Valley} \\
6 & \multicolumn{1}{c}{} \\ \multicolumn{7}{c}{L} \\
7 & Lanzhou & / & / & 0.65 & Z \\ \multicolumn{7}{c}{Lanzhou} \\
8 & Lanzhou & 1 & 0.85 & / & X + Y \\ \multicolumn{7}{c}{Sanning white noise} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test cases. peak accelerations of the excitation waves were the same, but the responses at the tops of the piers were obviously different. If the influence of the shaking-table equipment on the variability of the acceleration input was assumed negligible, then the multidirectional excitation resulted in a coupled structural response. Although the peak acceleration of the excitation waves was greater in the X-direction than in the Y-direction, the response at the top of the pier was greater in the Y-direction than in the X-direction.