# 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
The catenary effect provides collapse performance to the structure through the tensile strength of the reinforcement in the failed beam. The weak catenary effect of the flat frame structure indicates that the reinforcement of the failed beam is insufficient when column E fails, and the axial tension that the failed beam can provide is limited. The ultimate load amplification factor of the flat frame structure is 1.99, and the load amplification factor at the end of the arch compression mechanism is 1.86. The collapse performance of the structure is only increased by 6.5% in the catenary stage. The step-terrace frame structure is different; the C1K2 frame increases by 9.6%, C2K2 by 11.6%, and C3K2 by 15.9% in the catenary stage, which are not only greater than the flat frame structure, but also show an upward trend with the increase in the number of dropped stories. This shows that the additional reinforcement of span DE and span EF can effectively improve the collapse resistance performance of the structure through the catenary effect. In addition, with the increase in the number of dropped stories, the increases in the reinforcement in the span DE and span EF are also larger, so the catenary effect of the structure is also stronger with the increase in the number of dropped stories. However, the increase in beam and column reinforcement does not mean that the performance to progressive collapse of the structure will increase significantly. When the upper ground edge column F is removed in working condition 6, the failure of the edge column will not produce a catenary effect, and the increased reinforcement can only bear the axial pressure together with the concrete as a whole in the arch compression stage. The collapse resistance bearing performance cannot be provided by the reinforcement tension in the beam similar to the failure of columns in the structure. Therefore, although the reinforcement is increased, the collapse resistance bearing performance provided is relatively small, and the ultimate load amplification coefficients of C1K2, C2K2, and C3K2 are all around 2.0. This also validates the conclusion in Section 5 of this paper; it is not recommended to increase the internal reinforcement of the failed beam to improve the collapse performance of the structure when the edge column fails. The vertical displacement-time history curve of prefabricated step-terrace frame structures with different dropped stories numbers obtained under the dynamic nonlinear analysis method at the failure point is shown in Figure 20, and the failure point is defined as the upper end of the failure column. From the perspective of the oscillation form of the curve, it can be divided into two types: one is the irregular attenuation oscillation formed by working conditions 1 and 6, and the other is the regular attenuation oscillation formed by working conditions 2 to 5. The reason for this phenomenon is still the insufficient horizontal constraint of the edge column, which cannot effectively resist the sudden change of the structure geometry and stiffness after the failure of the edge column. Therefore, compared with the failure of the inner column, the failure of the edge column is not only an irregular oscillation form, but also takes a longer time for the oscillation to stabilize. The vertical displacement of each failure point in working conditions 2 to 5 has become stable at about 6 s. However, working conditions 1 and 6 still have a small amplitude of oscillation when the analysis time is 7 s. For the same bottom ground edge column, the analysis results of column C are different from those of column A and column F. This is because column C also lacks the beam on the right side to provide an effective pulling effect in the dropped story part, but the horizontal constraints on both sides can be restored in the upper ground part. Therefore, column C, as the bottom ground edge column, can also form the same oscillation rule as the inner column.