# 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
However, it can be seen from Figure 22c that the load-displacement curve of the C2K1 frame structure has a very small ascending section after the arch compression mechanism, indicating that the catenary effect of the structure has not been fully exerted at this time. However, the curves of C2K2 and C2K3 show an obvious ascending section after the arch compression mechanism, which indicates that the catenary effect has been effectively exerted. From the data point of view, the load amplification factor of C2K1 after the end of the arch compression mechanism is 1.35, and the ultimate load amplification factor is 1.39. The increase in the collapse resistance performance of the structure brought about by the catenary effect is only 3.0%, while the ultimate load amplification factor of C2K2 and C2K3 is 1.52 and 1.85, respectively. Compared with 1.37 and 1.58 at the end of the arch compression mechanism, it increases by 10.9% and 17.1%, and the increase in the collapse performance of the structure brought about by the catenary effect is much greater than that of the C2K1 frame structure. According to the research results in Section 3 of this paper, the catenary effect of the dropped ground slopeside column will appear in the story closest to the failure column within the failure span that satisfies both side constraints. Therefore, the internal axial forces of beam13, beam23, and beam33 of C1K2, C2K2, and C3K2 frame structures are extracted, respectively, in Figure 23. As can be seen from the figure, the axial force of the beam changes from axial pressure to axial tension when the vertical displacement of the failure point increases, which indicates that the structure does change from arch compression mechanism to catenary mechanism. However, the tension of the beam in the C2K1 frame appears too late, and the tension does not appear until the vertical displacement of the structure has reached 1951 mm, which is close to 2000 mm, and the structure is on the edge of collapse. Therefore, the catenary effect is very limited. In C2K2, axial tension appears in the beam when the vertical displacement of the failure point is 1771 mm, while the C2K3 frame with the best catenary effect has tension in the beam when the vertical displacement of the failure point is 1389 mm. The reduction in redundancy means the reduction in the force transmission path and the load bearing members, so the structure with less redundancy will take significantly longer time to transfer the load borne by the failure column to the adjacent components than the greater one. This easily explains why the final catenary of the C1K2 structure is significantly later than that of the C2K2 and C3K2 structures. In summary, it is not difficult to see that there are three factors affecting the catenary mechanism: one is the mechanical performance of the joints, and the others are the amount of reinforcement in the beam and the structural redundancy. The larger the internal reinforcement of the beam, the larger the bearing capacity of the beam in the catenary stage, and the stronger the catenary effect. The greater the redundancy, the earlier the structure can transfer the failure load of the failure column to the adjacent members, the earlier the catenary mechanism will appear, and the stronger the catenary effect will be. These factors influence the development of structural catenary effects in different ways. Based on the above analysis, in the failure working conditions of the dropped ground slopeside column, it can be concluded that the progressive collapse performance of the structure increases with the increase in the number of dropped spans, and the catenary effect of the structure will be stronger and appear earlier with the increase in the number of dropped spans. Due to very few members in the dropped stories being able to bear the load, the catenary effect of the structure is very weak, and the collapse resistance performance of the structure is also lower, so the step-terrace structure with one span should be avoided if possible.