## 4 Discussion
### Removal of the Convex-Corner Column  
Figure 10 shows the structure displacement nephogram of Models 1 and 2 at 5 s after the first-layer F4 column is removed. Figure 11 shows the vertical displacement time-history curve of the nodes above the failure column after the first-layer F4 column is removed. As can be seen from the figure, the vertical displacement in the original irregular structure increased significantly before 0.75 s, and gradually stabilized to 96.6 mm after 2.6 s. If the value is much smaller than the failure criterion of progressive collapse of the structure, the structure model does not collapse. In Model 1, after the steel truss is added to the roof, the vertical displacement increases rapidly before 0.8 s, then slows down, and gradually becomes stable at 53.4 mm after 2.1 s. Compared with the original structure, the vertical displacement is reduced by 44.7%. In Model 2, the vertical displacement increased rapidly before 0.92 s after the addition of the X-type tensile-strengthening structure, and gradually stabilized to 76.3 mm after 1.3 s. Compared with the original structure, the vertical displacement is reduced by 21.1%. Figure 9: Top resistance–displacement curve of failure column. The vertical displacement development trend of each model is consistent with the original model. By comparing the vertical displacement above the failure column with the convex-corner column in the balance, we can see that adding a steel truss to the roof can reduce the vertical displacement caused by the failure of the corner column more effectively; additionally, adding X-tie strengthening to the structure can also reduce the vertical displacement caused by the failure of the corner column, but the effect is not as significant as the former. Figures 12 and 13 show internal force diagrams of the F-axis 5 s after the first-layer F4 column is removed. In the modified Model 1, the square column above the failure column is subjected to axial tension, and the maximum bending moment of the F-axis is 375.6 KN\(\cdot\)m. The maximum axial force of the adjacent column a is 5365 KN. This shows that the horizontal steel truss on the roof forms an alternative load transfer path with the columns above the failure column, and the part of the load above the failure column is transferred to the top steel truss through the columns above, and then is transferred to the adjacent columns. There is also a part of the load that is transferred through the layers of beams to the adjacent columns. In the modified Model 2, the maximum bending moment  
Figure 11: Time-history diagram of removal displacement of columns at convex corners of each model. Figure 10: Displacement nephogram of structure at convex-corner column-removal condition: (a) Model 1 with roof-added steel trusses; (b) X-tension reinforcement is added to Model 2 structure. of the F-axis is 453.4 KN\(\cdot\)m. The maximum axial force of the adjacent column a is 5136 KN. The change in the internal force indicates the change in the load transfer path at the lower end of the failure column due to the action of the X-tension reinforcement. In addition, the beam end above the adjacent column a is still a negative bending moment, which increases significantly with the failure of the corner column and is greater than the bending moment of the corresponding beam in Model 1. Figure 12: The bending moment diagram of F-axis 5 s after column F4 is removed: (**a**) is the bending moment diagram of Model 1; (**b**) is the bending moment diagram of Model 2. Figure 13: Axial force diagram of F-axis 5 s after column F4 is removed: (**a**) is the axial force diagram of Model 1; (**b**) is the axial diagram of Model 2. By comparing the bending moment diagram and axial force diagram of the two models, it can be seen that the maximum bending moment above the failure column of Model 1 is smaller than that of Model 2. The maximum axial force value of the adjacent columns in Model 1 is greater than that in Model 2.