# Progressive Collapse Performance of Prefabricated Step-Terrace Frame Structures in Mountain Cities
## 4 Analysis of Progressive Collapse Performance of Prefabricated Step-Terrace Frame Structures
### Model Establishment
#### 4.2.2 Results Analysis of Different Number of Dropped Spans  
The number of dropped stories and dropped spans are two important design factors for the structure of the step-terrace structure in mountain cities. The change in the number of dropped stories and dropped spans directly leads to the change in the overall stiffness, ratio of reinforcement, redundancy of the structure, etc. These factors have an important control effect on the performance of the structure to progressive collapse. Therefore, it is necessary to study the influence of the number of dropped spans on the performance of the structure to resist progressive collapse. However, the change in the number of dropped spans will affect the position of the upper and dropped ground columns. As shown in Figure 22a,b, column C in C2K1 is the upper ground slopeside column, while column C in C2K2 is the dropped ground slopeside column. If the failure of column C of the three frame structures is compared and analyzed, it is not only the number of dropped spans that affects the progressive collapse-bearing performance of the structure, it also includes the change of mechanical properties caused by the ground position of the column [24]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model Number**} & **Dropped** & **Dropped** & \multirow{2}{*}{**Working Condition 1**} & \multirow{2}{*}{**Working Condition 2**} & \multirow{2}{*}{**Working Condition 3**} \\  & **Stories** & **Spans** & & & \\ \hline C1K2 & 2 & 1 & Remove the dropped & Remove the upper & Remove the dropped \\  & & & ground edge column A & ground edge column F & ground column B \\ C2K2 & 2 & 2 & Remove the dropped & Remove the upper & Remove the dropped \\  & & & ground edge column A & ground edge column F & ground column C \\ C3K2 & 2 & 3 & Remove the dropped & Remove the upper & Remove the dropped \\  & & & ground edge column A & ground edge column F & ground column D \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Structure removal conditions information. Figure 21: Elevations of frame structures with different numbers of dropped spans..  
To sum up, three different removal working conditions will be compared in this section. Working conditions 1 and 2 are, respectively, the failure of the dropped ground edge column A and the failure of the upper ground edge column F. Working condition 3 is the failure of the dropped ground slopeside column. The positions of the dropped ground slopeside column are different in different working conditions; C2K1 is column B, C2K2 is column C, and C2K3 is column D.  
The load-displacement curves of prefabricated step-terrace frame structures with different number of dropped spans under static nonlinear analysis are shown in Figure 22. In working condition 1, the ultimate load amplification factor of the step-terrace structure is smaller than that of the flat frame structure, and the ultimate load amplification factor of the flat frame structure is 1.92. The ultimate load amplification coefficients of C2K1, C2K2, and C2K3 are 1.32, 1.39, and 1.45, which are 31.17%, 27.5%, and 24.4% lower than that of the flat frame structure. It shows that when the edge column A fails, the progressive collapse resistance performance of the step-terrace frame structure is weaker than that of the flat frame structure. With the increase in the number of dropped spans, the ultimate load amplification factor of the structure increases. From the point of redundancy, increasing the number of dropped spans of a step-terrace structure essentially means adding members for load distribution in the dropped stories of the original step-terrace frame structure. Therefore, with the increase in the number of dropped spans, the redundancy of the dropped stories increases, and the load-transfer path also increases, which is conducive to the structure's performance to resist progressive collapse.