## 3 Wind Load Description
### Wind Load Expression  
To better characterize the aerodynamic stiffness and damping properties of the bridge structure, this study adopted a novel aerodynamic model distinct from the conventional Scanlan flutter-derivative framework, as proposed in Reference [25]. Assuming the mean wind attack angle at equilibrium state is \(\alpha_{0}(x)\), with an additional wind attack angle \(\Delta\alpha(x,t)\) induced by turbulence, and \(\alpha(x,t)\) denoting the torsional angle of the girder, the three-component forces per unit length acting on the main girder cross-section in the instantaneous wind-axis coordinate system can be expressed as follows:  
\[D^{\prime}(x,t)=\frac{1}{2}\rho BU^{2}(x,t)C_{D}[\alpha_{0}+\Delta\alpha(x,t)+ \alpha(x,t)] \tag{6}\]  
\[L^{\prime}(x,t)=\frac{1}{2}\rho BU^{2}(x,t)C_{L}[\alpha_{0}+\Delta\alpha(x,t)+ \alpha(x,t)] \tag{7}\]  
\[M^{\prime}(x,t)=\frac{1}{2}\rho B^{2}U^{2}(x,t)C_{M}[\alpha_{0}+\Delta\alpha(x,t)+\alpha(x,t)] \tag{8}\]  
where \(D^{\prime}(x,t)\), \(L^{\prime}(x,t)\), \(M^{\prime}(x,t)\) denote the aerodynamic drag, lift, and moment per unit length acting on the main girder cross-section in the instantaneous wind-axis coordinate system, respectively; \(x\) is the longitudinal bridge coordinate; \(\rho\) represents the air density (\(\rho=1.25\) kg/m); \(C_{D}\), \(C_{L}\), and \(C_{M}\), functions of effective wind angle of attack, are the aerodynamic drag, lift, and torque coefficients, respectively. The aerodynamic coefficients [26], obtained from wind tunnel tests by a rigid section model of the bridge deck, are plotted against the wind angle of attack in Figure 10.  
\(\alpha_{0}\) is the initial wind attack angle; \(\alpha(x,t)\) is the torsional angle of the girder; and \(\Delta\alpha(x,t)\) denotes the additional attack angle induced by turbulent wind at time \(t\) calculated as follows:  
\[\Delta\alpha(x,t)=\tan^{-1}\biggl{\{}\frac{\omega(x,t)}{[U_{0}+u(x,t)]} \biggr{\}}, \tag{9}\]  
Figure 10: Aerostatic force coefficients of deck section.  
\(U(x,t)\) represents the instantaneous wind speed at time \(t\), which is calculated by combining the mean wind speed \(U_{0}\), the horizontal turbulent wind component \(u(x,t)\), and the vertical turbulent wind component \(\omega(x,t)\), as follows:  
\[U(x,t)=\sqrt{\left[U_{0}+u(x,t)\right]^{2}+w(x,t)^{2}} \tag{10}\]  
This model incorporates the higher-order terms in the turbulent wind and accounts for aerodynamic stiffness effects in the torsional direction, while neglecting aerodynamic damping effects. Consistent with the wind load calculation procedure, the aerodynamic forces acting on the main girder in the wind-axis coordinate system must be transformed into the ANSYS global coordinate system for loading via Equation (11):  
\[\begin{bmatrix}F(x,t)\\ L(x,t)\\ M(x,t)\end{bmatrix}=\begin{bmatrix}\cos[\alpha_{0}+\Delta\alpha(x,t)]&-\sin[ \alpha_{0}+\Delta\alpha(x,t)]&0\\ -\sin[\alpha_{0}+\Delta\alpha(x,t)]&\cos[\alpha_{0}+\Delta\alpha(x,t)]&0\\ 0&0&1\end{bmatrix}\begin{bmatrix}D^{\prime}(x,t)\\ L^{\prime}(x,t)\\ M^{\prime}(x,t)\end{bmatrix} \tag{11}\]  
For the wind loads acting on the pylons, auxiliary piers, and stay cables, this study considered only the aerodynamic drag forces. The aerodynamic drag per unit length can be calculated using the following equation:  
\[F_{d}=\frac{1}{2}[U_{0}+u(x,t)]^{2}C_{d}A_{n} \tag{12}\]  
where \(A_{n}\) is the along-wind projected area of the pylons/auxiliary piers or diameter of stay cables; \(C_{d}\) is the drag coefficient of the component.  
Due to the regular rectangular or circular aerodynamic shape of the pylon, auxiliary pier, and stay cable, the resistance coefficients of each component were obtained using interpolation according to wind resistance design specifications. In this article, the stay cable is taken as 0.8; the auxiliary pier is taken as 1.39; and the range of resistance coefficients for the pylon is 1.984-2.086.