# Static Wind Reliability Analysis of Long-Span Highway Cable-Stayed Bridge in Service
## 2 Reliability Theory of Static Wind Instability Analysis for Bridges  
### Aerostatic Instability Analysis Theory for Bridges  
#### 2.1.1 Static Wind Load Calculation on Bridges  
(1) Static wind load on main girders  
At present, the established nonlinear theory of static wind load refers to that the main girder section will be twisted under static wind load which causes the effective wind attack angle to change, and the change of the effective wind attack angle will also cause the variation of the static three-component force coefficient. Therefore, the final static wind forces acting on the main beam should be the actual static wind forces after modifying the deformation of the main beam. The static wind force can be described in the body axis coordinate system, namely, the coordinate system is represented along the main beam with the cross-section centroid as the origin and the directions of the coordinate axes are parallel or perpendicular to the bridge deck in Figure 1 below, then the static wind forces on the main girder are calculated by Equation (1). \[ \begin{array}{l}F_{H}(\alpha)=\frac{1}{2}\rho V^{2}C_{H}(\alpha)D\\ F_{V}(\alpha)=\frac{1}{2}\rho V^{2}C_{V}(\alpha)B\\ M(\alpha)=\frac{1}{2}\rho V^{2}C_{M}(\alpha)B^{2}\end{array}  \tag{1}\]where \(C_{H}(\alpha)\), \(C_{V}(\alpha)\) and \(C_{M}(\alpha)\) are the drag, lift, and torsion moment coefficient of the beam section in the body axis coordinate system when the wind attack angle is \(\alpha\), respectively; \(F_{H}(\alpha)\), \(F_{V}(\alpha)\), and \(F_{M}(\alpha)\) are the drag force, lift force, and torsion moment per unit length at the centroid of the main beam section in the same coordinate system when the wind attack angle is \(\alpha\), respectively; \(D\) and \(B\) are the lateral projection height and width of the main beam section, respectively; \(\alpha\) is the effective wind attack angle, when the incoming wind direction is diagonally upward, the wind attack angle is positive, otherwise the wind attack angle is negative; \(\rho\) is the air density (kg/m\({}^{3}\)), equals to 1.25 kg/m\({}^{3}\) in this research, and \(V\) is the equivalent static gust wind speed at the bridge site. The static three-component force coefficient including the drag coefficient, lift coefficient, and torsion moment coefficient of the main beam section in Equation (1) is obtained from the segmental model wind tunnel test. For the cross-section of the main beam in the Xiangshan Harbor highway cable-stayed bridge, the variation curve of the aerodynamic force coefficient with the wind attack angle [21] is shown in Figure 2.  
Static wind load on stay cables  
According to the different wind directions, the wind load acting on the stay cables is divided into the transverse wind load perpendicular to the driving direction of the bridge and the longitudinal wind load along the bridge direction. In actual projects, the wind load in the lateral direction is often an important factor for the aerostatic stability of the bridge, so only the wind load in the lateral bridge direction is considered for the stay cables. Figure 1: Three-component force on the girder section in the body axis coordinate system. Figure 2: Aerodynamic force coefficient of the main girder of Xiangshan Harbor Bridge in body axis coordinate system. According to the \"Wind-resistant Design Specification for Highway Bridges\" (JTG/T 3360-01-2018) [22] in China, the wind force on the stay cables is calculated by the following formula under the action of the lateral wind:  
\[F_{H}=\frac{1}{2}\rho V^{2}C_{H}A_{n} \tag{2}\]  
where \(F_{H}\) is the static wind force on the stay cable under the action of the lateral wind; \(C_{H}\) is the drag coefficient of the stay cable which can be taken as 0.8 when calculating the static wind stability of the bridge; \(A_{n}\) is the projected area of the stay cable in downwind direction which can be calculated by multiplying the diameter by the downwind projection height of the stay cable.