# Progressive Collapse Analysis of SRC Frame-RC Core Tube Hybrid Structure
## 4 Progressive Collapse Analysis
### Nonlinear Dynamic Analysis  
#### 4.5.1 Case 1--Column C1 at Ground Floor Removed  
The nonlinear dynamic analysis is to simulate the structure under earthquake action with critical component removal. Under the influences of different seismic waves, the displacement-time curves of the top floor are shown in Figure 17, the inter-story displacement angles \(\theta\) of structure are shown in  
Figure 16: Displacement of structure in (**a**) case 2, (**b**) case 3, (**c**) case 4 and (**d**) case 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Beam** & \multirow{2}{*}{**Direction**} & **Bending** & \multirow{2}{*}{**Portion (\%)**} & **Average** & \multirow{2}{*}{**DCR**} \\  & **Number** & & & **Moment/kN-m** & & & **Value (\%)** & \\ \hline \multirow{4}{*}{3 (C3)} & B1 & Positive & 206.25 & 22.39 & \multirow{2}{*}{20.02} & 0.42 \\  & B1 & Negative & \(-\)88.75 & 17.66 & \multirow{2}{*}{32.21} & 0.18 \\  & & Positive & 313.75 & 34.06 & \multirow{2}{*}{32.21} & 0.64 \\  & B2 & Negative & \(-\)142.50 & 28.36 & \multirow{2}{*}{48.77} & 0.29 \\  & B5 & Positive & 401.25 & 43.55 & \multirow{2}{*}{48.77} & 0.82 \\  & B5 & Negative & \(-\)271.25 & 53.98 & \multirow{2}{*}{48.77} & 0.55 \\ \hline \multirow{4}{*}{4 (W1)} & B5 & Positive & 347.50 & 46.41 & \multirow{2}{*}{47.10} & 0.71 \\  & B5 & Negative & \(-\)380.00 & 47.80 & \multirow{2}{*}{47.10} & 0.78 \\  & B8 & Positive & 401.25 & 53.59 & \multirow{2}{*}{52.90} & 0.82 \\  & B8 & Negative & \(-\)415.00 & 52.20 & \multirow{2}{*}{52.90} & 0.85 \\ \hline \multirow{4}{*}{5 (W2)} & B5 & Positive & 497.50 & 55.43 & \multirow{2}{*}{56.59} & 1.02 \\  & B5 & Negative & \(-\)440.00 & 57.74 & \multirow{2}{*}{56.59} & 0.90 \\ \cline{1-1}  & B8 & Positive & 400.00 & 44.57 & \multirow{2}{*}{43.41} & 0.82 \\ \cline{1-1}  & B8 & Negative & \(-\)322.50 & 42.26 & \multirow{2}{*}{43.41} & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: \(Cont.\)Figure 18. It can be seen the maximum inter-story displacement angle \(\theta_{\text{max}}\) is located at the 6 th floor when subjected to HOLLYWOOD and ELCENTRO waves, and the value is within the code limitation. When subjected to NRIDGE and artificial waves, the value reached 0.0016 and 0.0022, which exceed the specified limitation. Figure 19 shows shear distribution between the ground frame and core tube. At the initial stage, the shear ratios of frame to core tube under HOLLYWOOD, ELCENTRO, NRIGDE and artificial seismic waves are 1:3.29, 1:3.17, 1:3.01, and 1:2.96 respectively. The core tube is responsible for the majority of the lateral load. With the stiffness degradation of the core tube, the shear ratios of frame to core tube change to 1: 2.35, 1:2.28, 1:2.18, and 1:2.14 respectively. It means that the core tube plays  
Figure 17: Displacement-time curve of top under different seismic wave in case 1: **(a)** HOLLYWOOD, **(b)** ELCENTRO, **(c)** NRIGDE and **(d)** Artificial wave. Figure 18: Inter-story displacement angle in case 1.  
a role as the first line of defense against lateral load, and the frame plays a role as the second line of defense against lateral load. Table 11 shows force condition of beams adjacent to C1 after the sudden failure of C1 under earthquake action. The maximum DCR value of the beams is smaller than 2.0 in the cases of HOLLYWOOD and ELCENTRRO seismic waves. In the cases of NRIGDE and Artificial seismic wave, the maximum DCR value of B8 and B10 are 2.92 and 3.04, greater than 2.0. That is to say, the progressive collapse will not occur under the failure of the C1 scenario when subjected to the frequent earthquake or fortification earthquake, but it will occur when subjected to the rare earthquake. Compared to Table 9 in nonlinear static analysis, the loads transferred to B4 and B10 are increased while the load transferred to B8 is reduced. The reason for these changes is the frame has played a greater role of defense against the earthquake load.