# Static Wind Reliability Analysis of Long-Span Highway Cable-Stayed Bridge in Service
## 6 Conclusions  
In this paper, taking the existing Xiangshan Harbor cable-stayed bridge as the background, the finite element model established by ANSYS 15.0 software is used to solve the aerostatic instability of wind speed. At the same time, the parameter impact analysis is discussed, and the static wind reliability calculation is conducted to obtain the static wind reliability index of the cable-stayed bridge. There are some conclusions as follows:  
1. According to the results for the static wind stability of Xiangshan Harbor Bridge at the initial wind angle of attack \(\alpha=0^{\circ}\), it is found that the static wind instability mode for Xiangshan Harbor Bridge is bending-torsional coupling instability, and the critical wind speed of static wind instability is the highest when the initial wind attack angle is \(0^{\circ}\), the aerostatic instability wind speed of the bridge commonly reduces with the increase of the initial wind angle of attack. So other wind attack angles shall also be analyzed in the bridge design besides the \(0^{\circ}\) wind attack angle. 2. The aerostatic instability wind speed does not vary obviously with the change of the steel wire breakage rate of the stay cables, but it is necessary to closely monitor the situation that the steel wire breakage rate of the stay cable exceeds 10%. The aerodynamic drag coefficient and moment coefficient of the main girder play a more important role than the lift coefficient in causing static wind instability. And the stay cable broken position has a great impact on the static wind stability of the bridge structure, especially when the broken cables locating at the mid-span of the main beam, the wind environment should be closely monitored when replacing the stay cables. \begin{table}
\begin{tabular}{c c c c c} \hline
**Stay Cable Broken Position** & **Random Location** & **Near to Bridge Tower** & **1/4 of the Main Span** & **1/2 of the Main Span** \\ \hline Reliability index & 6.1908 & 6.3063 & 6.2559 & 5.9371 \\ Failure probability & \(2.993\times 10^{-10}\) & \(1.429\times 10^{-10}\) & \(1.976\times 10^{-10}\) & \(1.450\times 10^{-9}\) \\ \hline \end{tabular}
\end{table} 
Table 10: Static wind instability probability corresponding to different broken cable positions. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Steel Wire Breakage Rate** & **0\%** & **5\%** & **10\%** & **15\%** & **20\%** \\ \hline Reliability index & 6.3645 & 6.3344 & 6.2836 & 6.1050 & 5.9757 \\ Failure probability & \(9.795\times 10^{-11}\) & \(1.199\times 10^{-10}\) & \(1.654\times 10^{-10}\) & \(5.133\times 10^{-10}\) & \(1.145\times 10^{-9}\) \\ \hline \end{tabular}
\end{table} 
Table 9: Static wind instability probability corresponding to different steel wire breakage rates. 3. The uncertainty analysis of static wind instability for the bridge is conducted by combining the LHS method and the checking point method. The uncertain influence of three key parameters including moment coefficient, steel wire breakage rate, and the stay cable broken position is considered for Xiangshan Harbor Bridge in service. Then the static wind reliability indexes are obtained when these three key parameters are taken as random variables, respectively, which are 6.3375, 5.9757, and 6.1908. The static wind reliability of Xiangshan Harbor Bridge is very high. 4. The static wind reliability indexes of Xiangshan Harbor Bridge in service under different steel wire breakage rates and different cable broken positions are compared. It is found that the most unfavorable situation is that the steel wire breakage rate is 20% and the broken position of the stay cable is at the midspan of the main beam, the reliability index is 5.9757 and 5.9371, respectively. But corresponding to these two unfavorable conditions the order of magnitude of failure probability is \(10^{-9}\), which also proves that the static wind stability of Xiangshan Harbor Bridge is very good. Conceptualization, T.Z. ; Software, X.C. and X.Q. ; Validation, X.C. and X.Q. ; Formal analysis, W.G. ; Resources, W.G.