## 6 Conclusions and Discussion  
This study employed EQSignal software to synthesize three ground motions, each with unique characteristic periods, to assess their effects on the displacement and shear stress behaviour of tall bridge pier subjected to multidimensional seismic loading. This research specifically considered the influence of damping ratios, pulse ground motion characteristics, and multidimensional seismic actions. The analysis focused on the factors that interact to affect the structural behaviour of the bridge pier. The results revealed several key findings regarding the combined impact of the variables on the displacement and shear stress distributions within the pier:  
1. Compared with those under non-pulse ground motion, the displacement and shear stress behaviour of a tall bridge pier under pulse ground motion are significantly greater. In the time range of 0-5 s, the displacement and shear stress time histories exhibit more intricate variations when the ground motion is in the form of pulse ground motion. This is particularly evident in the case of tall bridge pier. 2. When under pulse ground motion, the peak displacement and shear stress errors of tall bridge pier structures, incorporating three different damping ratios, are notably smaller than those under non-pulse ground motion conditions. When the time t on the displacement and shear stress time history curves exceeds 18 s, the influence of pulse ground motion on the variations in the curves becomes more significant than the impact of the damping ratio itself. In contrast, for non-pulse ground motion, the influence of the damping ratio on the changes in the displacement and shear stress time histories is more pronounced than that of the ground motion. \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}{**Shear Stress (MPa)**} \\ \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 & \(3.0518\times 10^{-11}\) & 0.3232 & 0.3225 & \(2.2880\times 10^{-11}\) & 0.3162 & 0.3153 & \(1.5259\times 10^{-11}\) & 0.3054 & 0.3050 \\
10 & \(3.0518\times 10^{-11}\) & 0.2956 & 0.2952 & \(1.5259\times 10^{-11}\) & 0.2908 & 0.2900 & \(1.1444\times 10^{-11}\) & 0.2826 & 0.2821 \\
15 & \(1.9074\times 10^{-11}\) & 0.2751 & 0.2747 & \(1.5259\times 10^{-11}\) & 0.2672 & 0.2667 & \(1.5259\times 10^{-11}\) & 0.2624 & 0.2620 \\
20 & \(1.9074\times 10^{-11}\) & 0.2499 & 0.2496 & \(1.5259\times 10^{-11}\) & 0.2470 & 0.2468 & \(1.1444\times 10^{-11}\) & 0.2412 & 0.2412 \\
25 & \(1.7166\times 10^{-11}\) & 0.2311 & 0.2310 & \(1.5259\times 10^{-11}\) & 0.2243 & 0.2240 & \(1.5259\times 10^{-11}\) & 0.2178 & 0.2176 \\
30 & \(1.5259\times 10^{-11}\) & 0.2232 & 0.2231 & \(1.5259\times 10^{-11}\) & 0.1978 & 0.1975 & \(9.5367\times 10^{-12}\) & 0.1917 & 0.1914 \\
35 & \(1.4305\times 10^{-11}\) & 0.2017 & 0.2009 & \(1.3351\times 10^{-11}\) & 0.1726 & 0.1722 & \(9.5367\times 10^{-12}\) & 0.1601 & 0.1599 \\
39.75 & \(7.8125\times 10^{-9}\) & 4.6484 & \(4.6849\) & \(7.8125\times 10^{-9}\) & 4.4148 & \(4.1414\) & \(7.8125\times 10^{-9}\) & 3.3451 & 2.8067 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Peak shear stress of the XY section of tall bridge pier with varying damping ratios under multidimensional pulse ground motion. 3. When subjected to two-dimensional and three-dimensional non-pulse ground motions, the displacement at the Z section and the shear stress at the YZ section of a tall bridge pier are found to be smaller than those under one-dimensional ground motion.