# Static Wind Reliability Analysis of Long-Span Highway Cable-Stayed Bridge in Service
## 4 Case Analysis of Static Wind Instability and Parameter Influence of Xiangshan Harbor Bridge
### Calculation of Critical Wind Speed for Static Wind Instability of the Bridge  
Combined with the finite element model of the Xiangshan Harbor cable-stayed bridge established in Section 4.1 and the internal and external -two-iterative method for static wind instability analysis of the bridge in Section 2.1.2, the calculation program including three modules which are the information input module (AVINPUT), wind load processing module (WIND_SOLVE) and post-processing module (JUDGE) is written to automatically analyze the static response of the bridge and judge the convergence, the analysis interface is also developed on basis of APDL in ANSYS software. The flow chart of this program is shown in Figure 7.  
In the information input module enter the initial wind attack angle and initial wind speed, and initialize the torsion angle of each node of the main beam. In the wind load processing module calculate the wind load on the bridge corresponding to the static wind speed and wind attack angle from the previous module, then solve the displacement of the bridge. And in the post-processing module obtain the torsional displacement of the main beam nodes, take it into the effective wind attack angle and recalculate the corresponding three-component force coefficient, then further calculate the Euclidean norm of each three-component force coefficient and judge whether it is no more than the presupposed allowable value. If it is no more than the allowable value, gradually increase the wind speed and jump to the information input module again, otherwise, the calculated results of the torsion \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Calculated** & **Measured** & \multirow{2}{*}{**Error/\%**} & **Mode Shape** \\  & **Frequency/Hz** & **Frequency/Hz** & & \\ \hline
1 & 0.129 & — — & — & Longitudinal drift of main beam \\
2 & 0.206 & 0.213 & 2.82 & First-order symmetrical lateral bending of main beam \\
3 & 0.249 & 0.250 & 0.40 & First-order symmetrical vertical bending of main beam \\
4 & 0.316 & 0.300 & 5.33 & First-order antisymmetric vertical bending of main beam \\
5 & 0.453 & 0.438 & 3.20 & First-order antisymmetric lateral bending of bridge tower \\
6 & 0.457 & — — & — & First-order symmetrical lateral bending of bridge tower \\
7 & 0.482 & — & — & Second-order symmetrical vertical bending of main beam \\
8 & 0.570 & 0.525 & 9.52 & First-order antisymmetric lateral bending of main beam \\
9 & 0.578 & 0.600 & 3.17 & Second-order antisymmetric vertical bending of main beam \\
10 & 0.628 & — & — & Third-order symmetrical vertical bending of main beam \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Modal analysis results of Xiangshan Harbor Bridge. Figure 7: Flowchart of the static wind instability solution program. angle of the main girder are added to the effective wind angle of attack, then the calculation is jumped to the wind load processing module. When calculating the aerostatic instability wind speed, it is necessary to frequently call the information input module, wind load processing module, and post-processing module. But it is time-consuming, inefficient, and very cumbersome to call these modules simply by command flow. Therefore, the above three modules are created as toolbar buttons. When these buttons are clicked, the corresponding module program can be run, thereby realizing the parameterized customization of the toolbar and greatly improving the operating efficiency of the program. After defining the toolbar, the defined toolbar is displayed under the ANSYS Toolbar menu, as shown in Figure 8a. Click the button to realize its corresponding operation, as shown in Figure 8b. Taking the initial wind angle of attack \(\alpha=0^{\circ}\) as an example, the calculation process of the aerostatic instability wind speed is described.