# 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
Although the catenary effect appears in all frame structures to resist the progressive collapse of the structure when column C fails, the strength of the catenary effect varies with the number of dropped stories. The catenary effect of the step-terrace frame structures is 14.9% weaker than that of the common flat frame structures, and the catenary effect continues to weaken with the increase in the number of dropped stories. This shows that the reduction in redundancy does affect the development of catenary effects in the beam when column C fails. However, from the review of working conditions 4 to 6 of the removal of the upper ground column, the collapse resistance performance of the step-terrace frame structure is not weaker than that of the common flat frame structure in all stages of collapse. In working condition 4, the maximum load-displacement curve of the flat frame structure is still the largest (the maximum load-displacement curve refers to the maximum load amplification factor when the vertical displacement of the failure point is the same), the load-displacement curve of the step-terrace frame structure is smaller than that of the flat frame structure, and the ultimate load amplification factor \(\alpha\) decreases with the increase in the number of dropped stories. However, in working conditions 5 and 6, the load-displacement curve of the step-terrace frame structure still decreases with the increase in the number of dropped stories. Although the load amplification factor of the prefabricated flat frame structure in the beam mechanism stage is greater than that of the prefabricated step-terrace frame structure, the ultimate load amplification factor of the prefabricated step-terrace frame structure when it collapses is greater than that of the prefabricated flat frame structure. This is caused by the significant increase in beam and column reinforcement in the upper ground part compared with the common flat structure, and the increase amplitude of reinforcement in different spans of the upper ground part is also different. The reinforcement of span CD, span DE, and span EF increases successively, and is greater than that of the corresponding flat structure. Although the upper grounding part has an increase in reinforcement, the members that can bear the load are also reduced compared with the flat ground structure. The increase in reinforcement is a favorable factor for the collapse performance of the structure, while the decrease in the load members is a negative factor. When the upper ground column D in the working condition 4 fails, the load-displacement curve of the flat frame structure is still larger than that of the step-terrace frame structure. This is because although the step-terrace frame structure has more reinforcement of the span CD than that of the flat frame structure, the increase is not large. Currently, the redundancy of the ground structure plays a controlling role in the progressive collapse of the structure, and the redundancy of the flat frame structure is greater than that of the step-terrace frame structure. Therefore, the load-displacement curve of the flat frame structure is larger than that of the step-terrace frame structure in working condition 4. However, in working conditions 5 and 6, the beam reinforcement of the failure span DE and span EF is increased more than that of the flat frame structure. In this case, the influence of the reinforcement on the structure is greater than that of the redundancy on the structure. Therefore, the results of working conditions 5 and 6 show that the ultimate load amplification factor of the step-terrace frame structure is greater than that of the flat frame structure. The analysis results of removing upper ground column E in working condition 5 show that although the load-displacement curve of the flat frame structure has an ascending section, the ascending amplitude is not large, which indicates that the structure has a catenary effect, but it is not obvious.