## 3 Wind Load Calculation
### Three-Component Force Coefficient and Three-Component Force Calculation Results and Analysis  
Five typical cross-sections are selected: side span 1/4 span (3.721 m), side span middle span (4.460 m), abutment (7.300 m, as shown in Figure 12), middle span 1/4 span (5.668 m) and middle span center (3.500 m as shown in Figure 13). Since there is no measured wind attack angle data, selecting a smaller range of the wind attack angle can increase a certain degree of security. A total of seven wind angles of attack \(-3^{\circ}\), \(-2^{\circ}\), \(-1^{\circ}\), \(0^{\circ}\), \(1^{\circ}\), \(2^{\circ}\) and \(3^{\circ}\) are simulated for each calculation section and the incoming wind speed is taken as the design basic wind speed of 30.69 m/s in the 100-year return period of the most unfavorable wind direction. As shown in Figures 14-16, when the angle of attack remains unchanged, the drag coefficient and lift moment coefficient increase with the increase in beam height, while the lift coefficient decreases with the increase in beam height. When the beam height is the same, the drag coefficient and pitching moment coefficient decrease with the increase in the angle of attack, and the lift coefficient increases with the increase in the angle of attack. A concept of relative three-component force coefficient is introduced here, which is calculated as follows [24]:  
\[ \begin{array}{l}C_{H0}=\frac{C_{H}}{C_{H(0^{\circ})}}\\ C_{V0}=\frac{C_{V}}{C_{V(0^{\circ})}}\\ C_{M0}=\frac{C_{M}}{C_{M(0^{\circ})}}\end{array}  \tag{10}\]  
where \(C_{H0}\), \(C_{V0}\) and \(C_{M0}\) indicate relative drag coefficient, relative lift coefficient, and relative lift moment coefficient; \(C_{H(0^{\circ})}\), \(C_{V(0^{\circ})}\) and \(C_{M(0^{\circ})}\) indicate the drag coefficient, lift coefficient, and lift moment coefficient of the bridge at \(0^{\circ}\) wind angle of attack. Figure 12: Mid-span section of main girder. Figure 13: Pier top section of main girder. The effect of introducing the relative three-component coefficient is that the wind load at the known 0\({}^{\circ}\) wind attack angle can be multiplied by the relative three-component coefficient to obtain the wind load at different attack angles. Because the drag coefficient, lift coefficient and lift moment coefficient are quite different, the change trend of the three-component force coefficient under different wind attack angles can be analyzed more intuitively by the relative three-component force coefficient. Figure 16: Lift moment coefficient of different beam heights under different wind attack angles. Figure 14: Drag coefficient of different beam height under different wind attack angle. Figure 15: Lift coefficient of different beam height under different wind attack angle. Because the variation law of wind attack angle-relative three-component coefficient of different beam heights is the same, only the wind attack angle-relative three-component coefficient diagram of the mid-span section of the bridge is given. As can be seen from the above Figure 17, the relative lift coefficient and relative lift moment coefficient gradually increase, and the relative drag coefficient gradually decreases as the wind angle of attack increases. The relative drag coefficient and the relative lift moment coefficient vary less, while the relative lift coefficient grows faster and takes the maximum value at 3\({}^{\circ}\) wind angle of attack, with a value of 1.81. It can be seen that the wind load is the most unfavorable wind attack angle when the wind attack angle is 3\({}^{\circ}\). It can be determined that the most unfavorable wind load direction is NNE and the most unfavorable wind angle of attack is 3\({}^{\circ}\).