# 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 deflection of the bridge was analyzed based on the initial equilibrium state prior to the occurrence of cable loss. Subsequently, the maximum downward and upward deflections of the girder immediately after cable loss, as well as after the stabilization of the vibration due to the cable loss, were examined. The shape of the instantaneous maximum deflection is illustrated in Figure 8, and a graph comparing the deflection of each case with the deflection limit specified in the design criteria is shown in Figure 9. Table 5 provides the values of the downward and upward deflections for each case. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Instantaneous**} & \multicolumn{3}{c}{**After Stabilization**} \\ \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Downward**} & \multirow{2}{*}{**Upward**} & \multirow{2}{*}{**Downward**} & \multirow{2}{*}{**Upward**} & \multirow{2}{*}{**Upward**} \\  & & **(mm)** & & & & \\ \hline
0 & & 0 & 0 & 0 & 0 & - \\ \hline  & 1-1 & 314.3 & 47.4 & 223.8 & 35.8 & OK \\  & 1-2 & 579.3 & 101.8 & 522.9 & 78.8 & OK \\
1 & 1-3 & 995.0 & 137.1 & 904.0 & 119.7 & OK \\  & 1-4 & 1524.2 & 179.6 & 1371.5 & 162.9 & OK \\  & 1-5 & 2098.8 & 190.7 & 2029.8 & 219.8 & NG \\ \hline  & 2-1 & 611.8 & 32.2 & 458.3 & 7.3 & OK \\
2 & 2-2 & 1396 & 64.5 & 1216.4 & 36.5 & OK \\  & 2-3 & 2604.6 & 38.2 & 2362 & 60.0 & NG \\ \hline  & 3-1 & 218.7 & 127.7 & 142.3 & 83.6 & OK \\  & 3-2 & 374.1 & 219.1 & 223.8 & 197.3 & OK \\
3 & 3-3 & 635.9 & 379.8 & 559.4 & 348.5 & OK \\  & 3-4 & 952.0 & 567.5 & 840.8 & 517.5 & OK \\  & 3-5 & 1234.5 & 702.3 & 1196.6 & 680.0 & OK \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Deflections due to cable loss. Figure 7: El-Centro earthquake ground motion: (**a**) longitudinal acceleration; (**b**) longitudinal displacement; (**c**) lateral acceleration; and (**d**) lateral displacement. Figure 8: Instantaneous maximum deflection shape: (**a**) Case 1-1; (**b**) Case 1-2; (**c**) Case 1-3; (**d**) Case 1-4; (**e**) Case 1-5; (**f**) Case 2-1; (**g**) Case 2-2; (**h**) Case 2-3; (**i**) Case 3-1; (**j**) Case 3-2; (**k**) Case 3-3; (**l**) Case 3-4; and (**m**) Case 3-5. As a result of analyzing the effect of cable loss on deflection, it was found that, in all cases, the deflection of the girder increases geometrically rather than linearly as the number of lost cables increases. The maximum downward deflection occurs at the center span, and the maximum upward deflection occurs at the side span, regardless of the location of the lost cables. Furthermore, it was shown that if more than five cables are lost in the center span, the design limit is exceeded. The change in cable force due to cable loss and earthquakes was also shown in Figure 10 according to the position of the lost cable. In all cases, the cable force shows a  
Figure 9: Deflection after cable loss: (**a**) Case 1 instantaneous deflection; (**b**) Case 1 deflection after stabilization; (**c**) Case 2 instantaneous deflection; (**d**) Case 2 deflection after stabilization; (**e**) Case 3 instantaneous deflection; and (**f**) Case 3 deflection after stabilization. large change in the cable closest to the lost cable, but it was below the yield stress. However, in Case 1, the stress exceeded allowable stress when more than three cables were lost, and in Cases 2 and 3, the stress exceeded allowable stress when more than four cables were lost. In addition to the changes in shape (upward or downward deflection) and cable tension caused by cable loss on the bridge, the changes in the axial forces of the girders were also numerically evaluated. The variation in girder axial force was examined at the  
Figure 10: Cable forces after cable loss: (**a**) Case 1 instantaneous cable force; (**b**) Case 1 cable force after earthquake; (**c**) Case 2 instantaneous cable force; (**d**) Case 2 cable force after earthquake; (**e**) Case 3 instantaneous cable force; and (**f**) Case 3 cable force after earthquake. location where the girder crosses the pylon, where the axial force is maximum.