## 5 Results Analysis
### Tall Bridge Pier Under Multidimensional Ground Motions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Pier** \\ **Heights** \\ **(m)** \\ \end{tabular} } & \multicolumn{6}{c}{**Displacement (m)**} \\ \cline{2-9}  & \multicolumn{3}{c}{**\(\boldsymbol{\zeta}\) = 3\%**} & \multicolumn{3}{c}{**\(\boldsymbol{\zeta}\) = 5\%**} & \multicolumn{3}{c}{**\(\boldsymbol{\zeta}\) = 10\%**} \\ \cline{2-9}  & **1D** & **2D** & **3D** & **1D** & **2D** & **3D** & **1D** & **2D** & **3D** \\ \hline
5 & 2.3783 \(\times\)\(10^{-13}\) & 0.0036 & 0.0036 & 1.8606 \(\times\)\(10^{-13}\) & 0.0032 & 0.0032 & 1.1612 \(\times\)\(10^{-13}\) & 0.0032 & 0.0032 \\
10 & 8.8947 \(\times\)\(10^{-13}\) & 0.0135 & 0.0135 & 6.9469 \(\times\)\(10^{-13}\) & 0.0117 & 0.0117 & 4.9610 \(\times\)\(10^{-13}\) & 0.0119 & 0.0118 \\
15 & 1.8826 \(\times\)\(10^{-12}\) & 0.0285 & 0.0284 & 1.4681 \(\times\)\(10^{-12}\) & 0.0248 & 0.0248 & 1.0479 \(\times\)\(10^{-12}\) & 0.0250 & 0.0250 \\
20 & 3.1468 \(\times\)\(10^{-12}\) & 0.0473 & 0.0472 & 2.4497 \(\times\)\(10^{-12}\) & 0.0416 & 0.0416 & 1.7494 \(\times\)\(10^{-12}\) & 0.0419 & 0.0419 \\
25 & 4.6151 \(\times\)\(10^{-12}\) & 0.0691 & 0.0690 & 3.5862 \(\times\)\(10^{-12}\) & 0.0612 & 0.0612 & 2.5625 \(\times\)\(10^{-12}\) & 0.0615 & 0.0615 \\
30 & 6.2258 \(\times\)\(10^{-12}\) & 0.0931 & 0.0929 & 4.8297 \(\times\)\(10^{-12}\) & 0.0828 & 0.0828 & 3.4522 \(\times\)\(10^{-12}\) & 0.0831 & 0.0831 \\
35 & 7.9231 \(\times\)\(10^{-12}\) & 0.1186 & 0.1183 & 6.1375 \(\times\)\(10^{-12}\) & 0.1057 & 0.1056 & 4.3875 \(\times\)\(10^{-12}\) & 0.1059 & 0.1059 \\
40 & 9.6923 \(\times\)\(10^{-12}\) & 0.1454 & 0.1451 & 7.4841 \(\times\)\(10^{-12}\) & 0.1301 & 0.1301 & 5.3736 \(\times\)\(10^{-12}\) & 0.1300 & 0.1300 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: X section peak displacement values of tall bridge pier with different damping ratios under multidimensional pulse ground motion. Figure 14: The variation trend of the XY section peak shear stress of tall bridge pier with different damping ratios under multidimensional pulse ground motion: (**a**) \(\bar{\zeta}\) = 3\%; (**b**) \(\bar{\zeta}\) = 5\%; and (**c**) \(\bar{\zeta}\) = 10\%. Figure 13: The variation trend of the X section peak displacement of tall bridge pier with different damping ratios under multidimensional pulse ground motion: (**a**) \(\bar{\zeta}\) = 3\%; (**b**) \(\bar{\zeta}\) = 5\%; and (**c**) \(\bar{\zeta}\) = 10\%. tional seismic effects in structural evaluations. In this study, torsional or biaxial bending effects in three-dimensional motion are not considered. According to the seismic design code, the load applied in the main load direction is large, and the structural symmetry makes the coupling effect negligible. As illustrated in Figure 14 and Table 5, the peak shear stress of the XY section of a tall bridge pier structure with different damping ratios under three-dimensional ground motion decreases as the tall bridge pier height increases. However, a sudden point is observed at the top of the tall bridge pier. The peak shear stress of the XY section of a tall bridge pier structure with different damping ratios under two-dimensional and three-dimensional earthquake action is markedly greater than that under one-dimensional earthquake action. This suggests that the effects of two-dimensional and three-dimensional earthquakes must be considered for the shear stress response of the XY section of a tall bridge pier.