## 4 Numerical Analysis of Prototype Structure
### Nonlinear Time-History Analysis
The deformation of steel truss could be recognized as the global translation, because the in-plane deformation of steel truss was very small, as shown in Figure 16b, the difference between the maximum and minimum displacements was only 22 mm. This was due to the rigid-upper-flexible-bottom \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Hazard Level** & \multicolumn{2}{c}{**Frequent Earthquake**} & \multicolumn{2}{c}{**Basic Earthquake**} & \multicolumn{2}{c}{**Rare Earthquake**} & \multicolumn{2}{c}{**Very Rare Earthquake**} \\ \multicolumn{2}{c}{**(PGA)**} & \multicolumn{2}{c}{**(0.07 g)**} & \multicolumn{2}{c}{**(0.20 g)**} & \multicolumn{2}{c}{**(0.40 g)**} & \multicolumn{2}{c}{**(0.62 g)**} \\ \hline Loading & Positive & Negative & Positive & Negative & Positive & Negative & Positive & Negative \\ direction & (+) & (\(-\)) & (+) & (\(-\)) & (+) & (\(-\)) & (+) & (\(-\)) \\ \hline Base shear force & \multirow{2}{*}{19,823} & \multirow{2}{*}{17,730} & \multirow{2}{*}{32,253} & \multirow{2}{*}{35,736} & \multirow{2}{*}{43,745} & \multirow{2}{*}{43,732} & \multirow{2}{*}{60,916} & \multirow{2}{*}{63,447} \\ (kN) & & & & & & & & \\ \hline Shear-weight & \multirow{2}{*}{0.065} & \multirow{2}{*}{0.058} & \multirow{2}{*}{0.105} & \multirow{2}{*}{0.117} & \multirow{2}{*}{0.143} & \multirow{2}{*}{0.143} & \multirow{2}{*}{0.143} & \multirow{2}{*}{0.199} & \multirow{2}{*}{0.207} \\ ratio & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Base shear forces and shear-weight ratios under different earthquake intensity levels. Figure 15: Time-history response curves subjected to different PGAs: (**a**) Base shear force; (**b**) Roof lateral displacement. characteristics of the stiffness distribution along the vertical direction for this kind of hybrid structure. The plastic deformation of this hybrid structure mainly occurred in the RC tubular columns. Therefore, RC tubular columns are the main energy dissipating components for this kind of hybrid structure. Table 8 summarizes the maximum lateral displacements and drift ratios. The numerical results showed that the maximum roof drift ratios were respectively 0.06%, 0.13%, 0.22% and 0.40% under the frequent earthquake, basic earthquake, rare earthquake and very rare earthquake. Figure 18 shows the maximum stress of steel components, i.e., A-shaped steel frames, steel diagonal braces and steel truss, subjected to different hazard levels of earthquakes. The results indicated that the steel components did  
Figure 16: Displacement nephograms of RC tubular columns and the steel truss under the rare earthquake at the moment when the displacements reached the maximum values (unit: m; the deformation scale factor is 100): (**a**) Columns; (**b**) Truss. Figure 17: Maximum lateral displacements versus height curves subjected to different hazard levels. not yield, which were in accordance with the PDT results of the model structure. Figure 19 shows the relative stiffness ratios and damage indexes of the structure. It can be found that the lateral stiffness of the structure decreased with the increase of PGA, however, it was still 36% of the initial stiffness under the very rare earthquake. With the increase of PGA, the damage gradually generated and accumulated. When the PGA equaled to 0.62 g which referred to the very rare earthquake having \(10^{-4}\) probability of exceedance in one year, the maximum tensile damage index was 0.95, indicating that the structure damaged severely but still not collapse. Actually, it is not feasible to evaluate its performance states for this peculiar hybrid structure by reference to general buildings (e.g., frame structures, shear structures) due to lack of the specified allowable limits of maximum drift ratios for this kind of hybrid structure recommended by the seismic design code [22].