# 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
#### 4.1.3 Results Analysis of Different Number of Dropped Stories
According to the results of dynamic nonlinear analysis, the vertical displacement of the failure point of the step-terrace frame structure is greater than that of the flat frame structure, indicating that the progressive collapse performance of the step-terrace frame structure is weaker than that of the flat frame structure. This conclusion is generally consistent with the results obtained by the static nonlinear analysis, but there are some differences in working conditions 5 and 6. The reasons are as follows: Firstly, the static nonlinear analysis method considers the dynamic effect of column removal through the dynamic amplification coefficient, which may be different from the actual situation; secondly, the static load applied in dynamic nonlinear analysis is when the load amplification factor \(\alpha=1\), and the static load applied in static nonlinear analysis is when \(\alpha\) gradually increases from 0 to the collapse of the structure. Therefore, the result of dynamic nonlinear analysis is equivalent to a point in the load-displacement curve obtained by static nonlinear analysis when \(\alpha=1\). It can also be seen from Figure 20e,f that the magnification factor of the ultimate collapse load of the step-terrace frame structure is larger than that of the flat frame structure, but the load-displacement curve of the flat frame structure in the beam mechanism stage is larger than that of the step-terrace frame structure, which is consistent with the results of the dynamic nonlinear analysis of the vertical displacement at the failure point of the flat frame structure in working conditions 4 and 5. Therefore, the step-terrace frame structure has more reinforcement in the upper ground than the flat frame structure, the dropped part has less reinforcement than the flat frame structure, and the reductions in structural redundancy and effective load-bearing members are unfavorable for the performance to the progressive collapse of the structure. By com  
Figure 20: Displacement–time history curves of failure point of prefabricated step-terrace frame structures with different dropped stories. bining various factors, it can be concluded that the performance to progressive collapse of a step-terrace frame structure is weaker than that of a flat frame structure. There are also differences in the performance to progressive collapse among the structures with different number of dropped stories. As shown in the figure, in various working conditions, the vertical displacement of the failure point will increase with the increase in the number of dropped stories, indicating that the greater the number of dropped stories, the worse the performance to progressive collapse. However, C1K2, C2K2, and C3K2 have different decreasing ranges of progressive collapse performance according to different removal conditions. The maximum vertical displacement of the failure point increases with the increase in the number of dropped stories, and the increase is becoming larger from the condition of failure of dropped stories (working conditions 1 to 3). In the condition of failure of the upper ground (working conditions 4 to 6), the maximum vertical displacement of the failure point also increases with the increase in the number of dropped stories, but the increase amplitude is smaller than that of the dropped ground. Taking working condition 2 as an example, the maximum vertical displacement of the structures with one, two, and three dropped stories is 79.16 mm, 82.97 mm, and 87.32 mm, respectively, which increases by 4.82%, 9.86%, and 15.62% compared with 75.52 mm of the flat frame structure. In working condition 5, the maximum vertical displacement of the structures with one, two, and three dropped stories are 78.20 mm, 78.95 mm, and 79.23 mm, respectively, which increases by 3.55%, 4.54%, and 4.91% compared with the 75.52 mm of the flat frame structure. The decrease in progressive collapse performance in working condition 5 with the increase in the number of dropped stories is much smaller than that in working condition 2.