# Dynamic Response Analysis of RC Frame against Progressive Collapse Based on Orthogonal Test
## 3 Application of Orthogonal Test Method
### Orthogonal Test Method
#### 3.2.2 Range Analysis  
To obtain the degree of influence of each factor on the dynamic response of the remaining structure, the data will be analyzed using polar difference analysis. The data in the table will be obtained according to Equations (1)-(3). The maximum vertical displacement of the top of the failed column indicates the dynamic response of the structure. Figure 7 shows that when the initial displacement is positive, the more significant the velocity ki, the greater the average effect of increasing velocity on the dynamic response of the structure. When the displacement is negative, the initial displacement's average effect on the structure's dynamic response decreases slightly from 0 to \(-\)10 mm. The average effect on the bottom corner and bottom side columns increases slightly from \(-\)10 mm to \(-\)20 mm, with a more pronounced increase in the bottom inner column. Figure 5: Vertical displacement of column top after bottom side column failure. Figure 6: Vertical displacement of column top after the failure of bottom inner column. From Figure 8, when the velocity is up, the average influence degree of the increase in the initial velocity on the dynamic response of the structure tends to be a slight increase. When the direction of the initial rate is downward, the average degree of influence on the dynamic response of the structure increases at the initial speed of 0 to \(-\)30 m/s. In contrast, the average degree of influence decreases slightly from \(-\)30 to \(-\)60 mm/s. The average degrees of influence of the initial velocity on the dynamic response of the structure after the failure of the bottom corner column, bottom side column, and bottom inner column follow the same trend. From Figure 9, when the failure time gradually increases, the average influence of the failure time on the dynamic response of the structure tends to be flat and weakened. The  
Figure 8: Initial velocity. Figure 7: Initial displacement. change in failure time has little effect on the dynamic response of the structure after the failure of the column in the three positions. The maximum average degree of influence of each factor to derive the most unfavorable combination affecting the dynamic response of the structure. The maximum average influence degree of initial displacement is 20 mm, the maximum average influence degree of initial velocity is 60 mm/s, and the maximum average influence degree of failure time is 0.05 T. The combination that produces the most significant structural dynamic response is the failure time of 0.05 T; the initial speed is 60 mm/s, and the initial displacement is 20 mm. In the case of failure of all three types of columns at the bottom corner, side, and inner columns, this combination produces the greatest dynamic response to the structure. This is the most detrimental to the structure's resistance to continuous collapse. Figures 10-12 are the most unfavorable combination displacement deformation diagrams under the failure of the three columns. Figure 10: The most unfavorable combination displacement diagram of the bottom side column. Figure 9: Element failure time. The extreme difference values R in Tables 1-3 were obtained by Equation (3): the failure time R1 of the bottom side column is 3.14; the initial velocity R2 is 4.84; the initial displacement R3 is 48.2; the bottom corner column R1 is 3.62; R2 is 5.72; R3 is 38.54. The bottom inner column R1 is 6.3, R2 is 5.75, and R3 is 60.85. The failure time and initial velocity have little influence on the dynamic response of the structure under the three failure conditions of the bottom corner, side, and inner column. Furthermore, the time interval selected for the failure time was small, resulting in less influence on the factor of failure time. However, the initial displacement has a more significant influence on the dynamic response of the structure under the three failure conditions of the bottom corner column, side column, and inner column.