## 3 Two-Directional Coupled Dynamic Excitation Analysis Process
### Two-Directional Coupled Dynamic Excitation Analysis Steps  
Steps of the method of dismantling the components: firstly, calculate the static force for the intact structure and obtain the internal force of the component; then, dismantle the component and apply its reaction force to the remaining structure to make it in a static equivalent state; finally, the reaction force is removed instantaneously to simulate the instantaneous failure of the component, also known as the alternate load path method. This research method only considers the dynamic effect of the vertical unbalanced load after the component is removed, so this article added the horizontal seismic action, that is, it considered the vertical unbalanced load and the horizontal seismic action at the same time. The analysis process of bidirectional coupling excitation is shown in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Vertical Performance**} & **Compression Limit Strength** & **Datum Pressure** & **Vertical Stiffness** & **Tensile Limit Strength** \\  & **N/mm\({}^{2}\)** & **N/mm\({}^{2}\)** & **N/mm\({}^{2}\)** & **N/mm\({}^{2}\)** \\ \cline{2-5}  & **49** & **10** & **1802** & **1.5** \\ \hline \multirow{3}{*}{**Horizontal performance**} & Equivalent horizontal stiffness & Equivalent damping ratio\% & Secondary stiffness \\  & kN/m & & \(\mathrm{kN/m}\) \\  & 2312 & 33 & 949 \\ \hline \multirow{3}{*}{**Horizontal performance**} & Equivalent horizontal stiffness & Equivalent damping ratio\% & Stiffness before yielding & Stiffness after yielding & Yield forceN \\  & kN/m & & \(\mathrm{kN/m}\) & \(\mathrm{kN/m}\) \\  & 1480 & 27.2 & 5187 & 798 & 65.4 \\ \hline \multirow{3}{*}{**Horizontal performance**} & Equivalent horizontal stiffness & Equivalent damping ratio\% & Secondary stiffness & \\  & kN/m & ratio\% & \(\mathrm{kN/m}\) & \\ \cline{1-1} \cline{2-5}  & 907 & 18.4 & 635 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of LRB500 isolated bearing.  
Figure 8: Design steps of isolated structure. The LRB500 seismic isolation bearing was selected, and its design load was 1963 kN. Table 1 shows the parameters of the LRB500 seismic isolation support used in the seismic isolation structure model.  
The analysis steps are as follows:  
1. [label=(0)]
2. Act on the static load combination \(GL\) on the initial structure to solve the internal force F of the column (support bearing) to be dismantled \[GL=(1.0\ DL+0.25\ LL)\] (4) where \(DL\) is the dead load and \(LL\) is the live load.
3. Remove the target column (support bearing) from the initial structure and apply the internal force \(\mathbf{F_{0}}\) obtained in step (1) to the top of the column in reverse to maintain the static equivalent state.
4. Unload the internal force \(\mathbf{F_{0}}\) in a very short time \(\mathbf{t}\) to simulate the instantaneous failure of the support bearing (bottom column) under unexpected action, and input horizontal seismic waves to the structure at the same time, and the remaining structure bears the bidirectional dynamic coupling of the vertical unbalanced load and the horizontal seismic action. The equivalent load is shown in Figure 10.