# 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
At the same time, calculation results from PKPM software show that with the increase in the number of dropped spans, the horizontal shear assigned to the dropped stories also increases, and the reinforcement of the dropped stories also increases slightly. Therefore, with the increase in the number of  
Figure 22: Comparison of load–displacement curves with different dropped spans. dropped spans, the performance to resist progressive collapse of the structure gradually increases. In working condition 2, at the initial stage of failure of the upper ground column F, the load amplification coefficient of each frame structure increases rapidly with the increase in the displacement of the failure point, and the load amplification coefficient of the flat frame structure rises faster and is greater than that of the step-terrace frame structure. However, when the ultimate load amplification coefficient finally reaches collapse, the step-terrace frame structure is greater than that of the flat frame structure. The reason for this phenomenon is that although the redundancy of the flat frame structure is greater than that of the step-terrace frame structure, the reinforcement of the step-terrace frame structure in the upper ground is also larger than that of the flat frame structure. Therefore, the progressive collapse resistance performance of the step-terrace frame structure is slightly better than that of the flat frame structure when column F fails. With the increase in the number of dropped spans, the ultimate load amplification coefficients of each step-terrace frame structure during the failure of column F also increase successively, and the ultimate load amplification coefficients of C2K1, C2K2, and C2K3 are 1.97, 2.06, and 2.10, respectively. Compared with the C2K1 frame structure, the C2K2 and C2K3 frame structures are 4.6% and 6.6% higher, respectively. For the failure of the upper ground column F, the increase in redundancy caused by the increase in dropped spans does not bring structural members that can bear the load to the upper grounding stories, so the load transfer path will not be increased. Therefore, the increase in the redundancy of the structure is not an effective redundancy for the upper grounding stories, but the calculation shows that the increase in dropped spans of the structure will lead to the increase in the reinforcement of the upper grounding stories. Therefore, when the upper ground column F fails, the reason why the structural collapse performance increases with the dropped spans is caused by the increase in structural reinforcement rather than the increase in redundancy. Working condition 3 is the load-displacement curve comparison diagram of the failure of the dropped ground slopeside column in each step-terrace frame structures. Although the position of the column is different in different structures, it is all located in the dropped stories and close to the slope. For buildings in mountain cities, the examples of column damage or failure near the slope caused by slope instability are quite common, so the failure rule is studied under working condition 3. According to the calculation results, with the increase in the number of dropped spans, the ultimate load magnification of the structure also increases; C2K1 is 1.39, and C2K2 and C2K3 are 1.52 and 1.85, respectively, which are 9.4% and 33.1% higher than that of C2K1. The dropped ground slopeside column has only one side constraint on the dropped grounding platform, but for frame structures with different numbers of dropped spans, the number of missing horizontal constraints on the dropped ground slopeside column is the same, the horizontal constraints of the first and second stories of dropped ground are missing, and the horizontal constraints on both sides are restored on the upper grounding first story (the third story of the overall structure). Therefore, there are conditions for the occurrence of catenary mechanism when the dropped ground slopeside column fails.