# Progressive Collapse Analysis of SRC Frame-RC Core Tube Hybrid Structure
## 3 Finite Element Model
### Validation of the FE Model  
The model size, section dimensions, loading and boundary conditions are exactly replicated in the experiment [6]. The test results are provided in this section. To validate the proposed FE model, simulation and test results are compared focusing on hysteretic curve, skeleton curve, bearing capacity, deformation and dynamic characteristics.  
In Figure 10a, the calculating and the test curves are both full and in spindle shaped, the yielding, limiting and failure stages are obvious. In Figure 10b, the calculating and the test curves are consistent in elastic-plastic segment and degenerate segment. Table 4 shows the characteristic values at yielding, limiting, and failure stages. It can be seen that the calculation results are consistent with the test.  
Figure 10: Comparison of hysteretic and skeleton curves: (**a**) Hysteretic curve and (**b**) Skeleton curve.  
Figure 9: The finite element (FE) model.  
Figure 11 shows a comparison of lateral displacement at the 1 st, 2 nd, 3 rd, 4 th, 5 th, 6 th and 9 th floors resulting from test and simulation. The dotted line is the test value and the solid line is the simulation value. It can be seen that structural deformation resulting from the two approaches are in a good agreement when the top displacements are 8 mm, 24 mm, 56 mm, 88 mm and 136 mm respectively.  
Table 5 shows the frequencies of the first five vibration modes at the initial and failure state. It can be seen that the natural frequency of structure decreases along with damage accumulation, and that the absolute errors between calculating results and test results is within 5%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Load**} & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Test Value/kN**} & **Calculating** & \multirow{2}{*}{**Absolute Error/\%**} \\  & & & & **Value/kN** & \\ \hline \multirow{2}{*}{\(P_{\text{y}}\)} & Positive & 238.49 & 256.72 & 7.64 \\  & Negative & \(-\)243.52 & \(-\)251.89 & 3.43 \\ \hline \multirow{2}{*}{\(P_{\text{max}}\)} & Positive & 351.72 & 373.69 & 6.24 \\  & Negative & \(-\)356.12 & \(-\)333.91 & 6.23 \\ \hline \multirow{2}{*}{\(P_{\text{u}}\)} & Positive & 308.47 & 338.44 & 9.72 \\  & Negative & \(-\)304.96 & \(-\)300.55 & 1.44 \\ \hline \hline \end{tabular} where, \(P_{\text{y}}\), \(P_{\text{max}}\) and \(P_{\text{u}}\) are yield strength, ultimate strength and failure strength respectively.  
\end{table}
Table 4: Comparison of characteristic value.  
Figure 11: Comparison of lateral displacement.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vibration**} & \multicolumn{4}{c}{**Initial State**} & \multicolumn{4}{c}{**Failure State**} \\ \cline{2-7}  & **Test** & **Calculating** & **Absolute** & **Test** & **Calculating** & **Absolute** \\  & **Value/Hz** & **Value/Hz** & **Error/\%** & **Value/Hz** & **Value/Hz** & **Error/\%** \\ \hline
1 & 5.94 & 5.86 & 1.31 & 3.26 & 3.35 & 2.73 \\
2 & 18.98 & 18.13 & 4.50 & 6.22 & 6.01 & 3.23 \\
3 & 25.13 & 23.97 & 4.60 & 15.96 & 15.25 & 4.47 \\
4 & 37.93 & 36.47 & 3.87 & 31.82 & 32.47 & 2.06 \\
5 & 50.03 & 48.43 & 3.20 & 42.01 & 40.85 & 2.76 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of frequencies.