# Studying the Cable Loss Effect on the Seismic Behavior of Cable-Stayed Bridge
## 4 Conclusions  
To evaluate the degradation in usability resulting from cable loss in a long-span cable-stayed bridge, two-stage dynamic time-history analyses were conducted. In the first stage, the dynamic behavior was analyzed by progressively removing the cable, and in the second stage, the usability was evaluated by applying far-field ground motion to the bridge with lost cables. The major results obtained from this are as follows: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Girder Maximum Axial Force**} \\  & & \multicolumn{6}{c}{**under Earthquake**} \\
**Case** & & \multicolumn{6}{c}{**(tonf)**} & **(A) \(-\) (A\({}^{\prime}\))** \\  & & \multicolumn{2}{c}{**Left (3154)**} & **Right (1154)** & \\ \cline{3-6}  & & **Max (A)** & **(A) \(-\) (B)** & **Min (A\({}^{\prime}\))** & **(A\({}^{\prime}\)) \(-\) (B\({}^{\prime}\))** & \\ \hline
0 & & 1022.55 **(B)** & - & \(-\)1140.25 **(B\({}^{\prime}\))** & - & 2162.80 \\ \hline \multirow{4}{*}{1} & 1-1 & 1068.54 & 45.99 & \(-\)1141.02 & \(-\)0.77 & 2209.56 \\  & 1-2 & 1129.92 & 107.37 & \(-\)1141.78 & \(-\)1.53 & 2271.70 \\  & 1-3 & 1204.24 & 181.69 & \(-\)1143.80 & \(-\)3.55 & 2348.04 \\  & 1-4 & 1312.74 & 290.19 & \(-\)1151.77 & \(-\)11.52 & 2464.51 \\  & 1-5 & 1455.08 & 432.53 & \(-\)1171.37 & \(-\)31.12 & 2626.45 \\ \hline \multirow{4}{*}{2} & 2-1 & 1017.19 & \(-\)5.36 & \(-\)1143.29 & \(-\)3.04 & 2160.48 \\  & 2-2 & 1049.48 & 26.93 & \(-\)1159.24 & \(-\)18.99 & 2208.72 \\  & 2-3 & 1163.16 & 140.61 & \(-\)1205.47 & \(-\)65.22 & 2368.63 \\ \hline \multirow{4}{*}{3} & 3-1 & 1011.50 & \(-\)11.05 & \(-\)1151.12 & \(-\)10.87 & 2162.62 \\  & 3-2 & 995.36 & \(-\)27.19 & \(-\)1168.33 & \(-\)28.08 & 2163.69 \\ \cline{1-1}  & 3-3 & 975.57 & \(-\)46.98 & \(-\)1191.10 & \(-\)50.85 & 2166.67 \\ \cline{1-1}  & 3-4 & 952.68 & \(-\)69.87 & \(-\)1220.65 & \(-\)80.40 & 2173.33 \\ \cline{1-1}  & 3-5 & 931.67 & \(-\)90.88 & \(-\)1251.19 & \(-\)110.94 & 2182.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Seismic analysis result by case. In all cases, the stress in the cables was found to be lower than the yield stress. However, as cables were gradually lost, significant changes in tension occurred in adjacent cables, and in some cases, the stress exceeded the allowable stress. Considering that the cable design tension for the target bridge was 41% to 71% of the allowable stress, indicating a considerable margin of safety, it is evident that cable loss has a non-negligible impact on the surrounding cables. However, even in cases where several cables were lost, the stress in the adjacent cables did not exceed the yield stress, and therefore, the possibility of cable failure occurring in a cascading manner is deemed to be low;
2. 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%. From the perspective of axial force in the girder, cable failure was found to significantly reduce the bridge's resistance to earthquakes. Through this study, it was confirmed that the safety and serviceability of the bridge are not seriously compromised even if a few cables are lost. However, if more than five cables are lost at once, it is expected that excessive deflection and an increase in axial force in the girder will occur, and safety and/or serviceability problems may be caused. Additionally, due to the impact of cable loss on adjacent cables, additional reinforcement is needed for the nearest cables when a stay cable is lost, the use of the bridge should be restricted, and the deflection of the central span should be continuously monitored until the repair work is completed. The target bridge in this study was the two-sided semi-harp type, which is one of the most common cable arrangements for cable-stayed bridges; therefore, further research is needed to investigate the structural behavior according to the cable arrangement and the shape of the pylon. Conceptualization, J.P. and C.P. ; methodology, C.P. ; software, J.Y. and C.P. ; supervision, J.P. and J.L.