# Studying the Cable Loss Effect on the Seismic Behavior of Cable-Stayed Bridge
## 3 The Effect of Incremental Cable Loss on the Seismic Behavior
### Analysis Results
The position of the corresponding beam element of the FE model is shown in Figure 11.  
Figure 12 and Table 6 show the variation in the girder axial force due to gradual cable loss, while Figure 13 represents the axial force change due to seismic loads acting after cable loss. The results of CASE 0 are also included so that the results before and after cable damage can be compared. In the case of CASE 0, the left and right girders are subjected to \(-282.75\) tonf of axial force, showing that the compressive effect on the girder caused by the cable tension is properly reflected. Figure 12: Time–girder axial force diagram under cable loss: (**a**) Case 0; (**b**) Case 1-1; (**c**) Case 1-2; (**d**) Case 1-3; (**e**) Case 1-4; (**f**) Case 1-5; (**g**) Case 2-1; (**h**) Case 2-2; (**i**) Case 2-3; (**j**) Case 3-1; (**k**) Case 3-2; (**l**) Case 3-3; (**m**) Case 3-4; and (**n**) Case 3-5. The analysis of the variation in the girder axial force due to cable loss revealed that as the number of lost cables increases, the amount of variation in the girder axial force increases, and the difference in the axial force acting on the left and right girders increases. For example, comparing CASE 1-1 and CASE 1-5, when one cable is lost, the girder axial force undergoes significant changes but still remains within the compression range. However, when five cables are lost, the girder undergoes alternating tension and compression  
Figure 13: Time-girder axial force diagram under earthquake after cable loss: (**a**) Case 0; (**b**) Case 1-1; (**c**) Case 1-2; (**d**) Case 1-3; (**e**) Case 1-4; (**f**) Case 1-5; (**g**) Case 2-1; (**h**) Case 2-2; (**i**) Case 2-3; (**j**) Case 3-1; (**k**) Case 3-2; (**l**) Case 3-3; (**m**) Case 3-4; and (**n**) Case 3-5. (Figure 12b,f). It is believed that such phenomena can induce fatigue on the girder due to the alternating stresses (CASE 1-3, 1-4, 1-5, 2-2, and 2-3). In addition, after the vibration due to cable loss stabilizes, the compressive force acting on the girder on the left side of the bridge (3154), where the cable was lost, decreases significantly according to the amount of cable loss. This consequently creates a difference in axial force between the left (3154) and right (1154) girders because the decrease in the compressive force acting on the left girder is greater than that on the right girder (Table 6, (C) \(-\) (C\({}^{\prime}\))). The results of the analysis of the axial force on the girders caused by seismic loads acting after cable loss are presented in Figure 13 and Table 7. If an earthquake occurs after the cable loss and vibration have stabilized, the maximum compressive force (right girder) and maximum tensile force (left girder) generated in the girders increase compared to Case 0, where only earthquake loads act without cable damage. The amount of increase in axial force was proportional to the number of lost cables. Comparing the changes in axial forces in the girders due to cable loss and those due to seismic loads, it can be observed that the difference in axial forces due to cable loss (Table 6, (C) \(-\) (D)) shows a similar trend to the changes in axial forces due to seismic loads after cable loss (Table 7, (A) \(-\) (B)). Based on the initial equilibrium state where the compression force on the girders was 282.75 tonf, the range of axial forces (\(-\)1140.25-1022.55 tonf) induced on the girders by the earthquake load appears to be at a level that can impair the stability of the bridge. However, since this is a result of linear elastic analysis, further analysis considering material nonlinearity is necessary to more precisely analyze the seismic response. In addition, in the case of cable breakage, it was found that the axial force in the girder caused by seismic loads can increase up to an additional 42%, and from the perspective of the axial force in the girder, cable loss can significantly reduce the resistance to earthquakes.