# Static Wind Reliability Analysis of Long-Span Highway Cable-Stayed Bridge in Service
## 5 Analysis of Static Wind Reliability for Xiangshan Harbor Bridge  
### Calculation of Static Wind Reliability  
For the cable-stayed bridges in service, the factors that affect the static wind stability are essentially stiffness and static wind load, where the main forms of expression are the change of the static three-component force coefficient, the rupture of the stay cables, the change of the stiffness of the main beam, the change of the constraint, etc. Combined with the parameter influence analysis of the static wind stability for Xiangshan Harbor Bridge in Section 4.1, it can be found that the influence of moment coefficient, stay cable broken position and steel wire breakage rate in stay cables cannot be ignored, and among these parameters, the moment coefficient, steel wire breakage rate in stay cables and stay cable broken position have random characteristics and important effects on the static wind stability of the bridge, so these three parameters are taken as random variables in the static wind reliability analysis of Xiangshan Harbor Bridge. The steel wire breakage rate is taken as 20% for static wind reliability analysis, so the design value of the sectional area of the stay cable is 0.20085 m\({}^{2}\), and its variation coefficient is taken as 0.05 according to relevant papers on bridge reliability calculation and suggestions in Uniform Standard for Reliability Design of Engineering Structures (GB 50153-2008) [31]. For the moment coefficient of the main girder, the design value is shown in Figure 2, and the variation coefficient of the aerodynamic force coefficient of the main girder from the boundary layer wind tunnel test is usually around 0.15 according to previous research [32], so the variation coefficient of the moment coefficient is taken as 0.15. But there is no corresponding standard for the value  
Figure 16: Maximum displacement curve of main beam with wind speed under different broken positions of the stay cable; (**a**) Lateral displacement; (**b**) Vertical displacement; (**c**) Torsion angle. of the stay cable broken location, the design value is taken as 5 considering the project practice, and the variation coefficient is taken as 0.5. These three random parameters and their distribution are listed in Table 4.  
Based on the theory in Section 2.2, the LHS method is used to sample these parameters 30 times in MATLAB 2020b, listed in Table 5. When analyzing static wind stability, the specific value of each parameter is equal to the design value multiplied by the sampling value in Table 5, then these specific values are input into analysis modules for the deterministic analysis of static wind instability of the bridge in Section 4.2 to obtain the critical aerostatic instability wind speed. During the calculation process, if one parameter takes the sampling value, other parameters take the design value. The 30 groups of instability wind speeds for every random parameter are given in Table 6, and the statistic characteristic values of the critical aerostatic instability wind speed are summarized in Table 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Random Parameters** & **Distribution Type** & **Average Value** & **Variation Coefficient** \\ \hline Moment coefficient & Normal distribution & 1.00 & 0.15 \\ Cross-sectional area of stay cable & Normal distribution & 1.00 & 0.05 \\ Stay cable broken position & Normal distribution & 1.00 & 0.50 \\ \hline \hline \end{tabular} Note: Average value represents the ratio of actual value to design value; In practice, the steel wire breakage rate in stay cables is simulated by changing the sectional area of the stay cable; About the stay cable broken position, the length between the mid-span of the bridge and the main tower is divided into equal parts, the stay cable broken position is obtained by the design value 5 multiplying by the sample value, if the calculated result is negative or more than 10, the stay cable broken position shall be the nearest to the main tower.  
\end{table}