## 4 Numerical Analysis of Prototype Structure
### Nonlinear Time-History Analysis  
In this section, nonlinear dynamic time-history analyses were carried out on the FE model of prototype structure. As introduced in Section 2, the prototype structure was located in 8-degree seismic precautionary intensity region. According to the China seismic design code [22], when conducting the time-history analysis, the peak acceleration of input ground motion should be respectively scaled to 0.70, 0.20 and 0.40 g to reflect the three seismic hazard levels (frequent, basic and rare earthquakes) corresponding to the 8-degree seismic intensity. In this study, EL-Centro (NS) wave was selected as the input ground motion. The duration is 30 s and the time interval is 0.02 s. In addition, considering the importance of the lifeline engineering, the ground motion with the PGA of 0.62 g was added to further investigate the seismic performance of this hybrid structure under more severe earthquakes, which is in accordance with the rare earthquake hazard level corresponding to 9-degree seismic intensity recommended by the China seismic design code [22]. Furthermore, it also could be regarded as the very rare earthquake hazard level corresponding to 8-degree seismic intensity with \(10^{-4}\) probability of exceedance in one year. Because the peak acceleration of ground motion for the very rare earthquake \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mode Number**} & \multirow{2}{*}{**Period (s)**} & \multirow{2}{*}{**Vibration Mode**} & \multicolumn{4}{c}{**Participating Mass Coefficient**} \\ \cline{3-6}  & & & **X Direction** & **Y Direction** & **RZ Direction** \\ \hline
1 & 1.216 & Torsion & 0.023 & 0.000 & 0.964 \\
2 & 1.194 & Y-direction & & 0.950 & 0.000 & 0.026 \\  & & translation & & & \\
3 & 1.185 & X-direction & & 0.001 (0.974) & 1.000 (1.000) & 0.000 (0.990) \\ \hline \hline \end{tabular} Note: The value in the bracket is the accumulated participating mass coefficient.  
\end{table} 
Table 6: Numerical results of dynamic characteristics. Figure 14: Vibration mode shapes: (**a**) First mode (torsional vibration); (**b**) Second mode (vibration direction is perpendicular to the A-shaped frame direction); (**c**) Third mode (vibration direction is along the A-shaped frame direction). could be taken as the 2.7-3.2 times of the PGA corresponding to the basic earthquake recommended by the seismic ground motion parameters zonation map of China [23], equals to 5.4-0.64 g.  
Figure 15a,b show the time-history base shear force curves and roof lateral displacement curves subjected to different seismic hazard levels. Table 7 summarizes the maximum base shear forces and shear-weight ratios. The shear-weight ratio \(\lambda\) of the structure was calculated by the following formula [22]:  
\[\lambda=\frac{V_{\text{EK}}}{G} \tag{15}\]  
where \(V_{\text{EK}}\) is the maximum base shear force; \(G\) is the representative value of gravity load. Both time-history base shear force and displacement curves showed that the occurring moment of peak responses were delayed with increase of PGA, due to the accumulation of the structural damage. In addition, according to the China technical specification for concrete structures of tall building [31], the floor shear-weight ratio of structures under the frequent earthquake should be no less than 0.032 for those structures with significant torsion effects or whose fundamental periods are less than 3.5 s. The calculated results showed that the shear-weight ratio of this hybrid structure was 0.058, which was larger than 0.032. This indicated that the shear force distribution of this hybrid structure meets the requirements of the design code. Figure 16 shows the displacement nephograms of RC tubular columns and the steel truss under the rare earthquake with PGA of 0.40 g at the moment when the displacements reached the maximum values. Figure 17 shows the maximum lateral displacement versus height curves under different hazard levels. It can be found that the lateral deformation pattern of this hybrid structure was shear mode.