# 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
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & **Beam Number** & **Seismic Wave** & **Average Bending Moment/N-m** & **Fortion (\%)** & **DCR** \\ \hline \multirow{6}{*}{1 (C1)} & & HOLLYWOOD & 457.50 & 27.98 & 0.94 \\  & & ELCENTRRO & 588.75 & 23.99 & 1.15 \\  & & NRIGDE & 885.00 & 23.30 & 1.82 \\  & & Artificial wave & 763.75 & 22.36 & 1.57 \\ \hline \multirow{6}{*}{1 (C1)} & & HOLLYWOOD & 555.00 & 33.95 & 1.14 \\  & & ELCENTRRO & 900.00 & 38.65 & 1.79 \\  & & NRIGDE & 1440.00 & 37.91 & 2.92 \\  & & Artificial wave & 1347.50 & 39.46 & 2.77 \\ \hline \multirow{6}{*}{1 (C1)} & & HOLLYWOOD & 622.50 & 38.07 & 1.28 \\  & & ELCENTRRO & 870.00 & 37.36 & 1.87 \\ \cline{1-1}  & & NRIGDE & 1473.75 & 38.79 & 3.04 \\ \cline{1-1}  & & Artificial wave & 1303.75 & 38.18 & 2.68 \\ \hline \end{tabular}
\end{table} 
Table 11: Force condition of beams in case 1. Figure 19: Shear distribution of bottom under different seismic wave in case 1: (**a**) HOLLYWOOD, (**b**) ELCENTRRO, (**c**) NRIGDE and (**d**) Artificial wave. 4.5.2. The Results from Cases 2 to Case 5  
Table 12 shows the \(\theta_{\text{max}}\) of structure. It can be seen, when the structure is subjected to the same seismic wave, the \(\theta_{\text{max}}\) in case 3 is smaller than other cases. Compared to case 4, the horizontal displacement of structure becomes obviously smaller in case 5. Table 13 shows the shear distribution between the frame and core tube. It is obvious that the core tube is responsible for more shear than the frame. It obviously increases the shear the frame bears in the cases of shear wall removal. That means the shear is redistributed, the core tube plays 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. Compared to the shear distribution between the ground frame and core tube in case 1, it can be found that the portion of shear assumed by the frame in case 5 is more than double of it in case 1. Table 14 shows force condition of beams. Compared to Table 10 in nonlinear static analysis, DCRs of the corresponding component in nonlinear dynamic analysis become obviously larger. With increasing earthquake intensity, the DCR under the failure of W2 is larger than 2.0, even in the frequent earthquake. DCR under the failure of W1 and W2 is larger than DCR under the failure of columns. Compared to the failure of C1, the DCR of adjacent beams becomes obviously larger under the failure of C2. That is to say, the failure of the corner column is more likely to cause progressive collapse of the structure than failure of side column. Moreover, the DCRs of adjacent beams under the failure of C1 are obviously larger than that under the failure of C3. That is to say, the failure of side columns is more likely to cause progressive collapse of structure. Compared to the failure of W1, DCRs of adjacent beams become obviously larger under the failure of W2. The failure of shear wall without opening is more likely to cause progressive collapse. Compared to Table 10 in nonlinear static analysis, in terms of cases 2, 4 and 5, due to the structural symmetry, the change of load transfer is not obvious. However, it is obvious for case 3, similar to case 1, the loads transferred to B1 and B2 are increased while the load transferred to B5 is reduced. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **Seismic Wave** & \(\theta_{\text{max}}\) \\ \hline \multirow{4}{*}{2 (C2)} & HOLLYWOOD & 0.00078 \\  & ELCENTRO & 0.00108 \\  & NRIGDE & 0.00206 \\  & Artificial wave & 0.00149 \\ \hline \multirow{4}{*}{3 (C3)} & HOLLYWOOD & 0.00076 \\  & ELCENTRO & 0.00105 \\  & NRIGDE & 0.00199 \\  & Artificial wave & 0.00142 \\ \hline \multirow{4}{*}{4 (W1)} & HOLLYWOOD & 0.00077 \\  & ELCENTRO & 0.00101 \\  & NRIGDE & 0.00209 \\  & Artificial wave & 0.00151 \\ \hline \multirow{4}{*}{5 (W2)} & HOLLYWOOD & 0.00074 \\  & ELCENTRO & 0.00093 \\ \cline{1-1}  & NRIGDE & 0.00192 \\ \cline{1-1}  & Artificial wave & 0.00136 \\ \hline \hline \end{tabular}
\end{table}