# Numerical Analysis on Spanwise Correlation of Vortex-Induced Force of Split Double-Box Beam
## 4 Results and Analysis
### Three-Dimensional Bypass of the Bridge in Static State  
#### 4.2.1 Spanwise Correlation of Aerodynamic Coefficients When the Bridge Is in Static State  
Based on the results of two-dimensional numerical simulation, four kinds of reduced wind velocities of 5.65, 6.21, 6.68, and 7.44 were selected in this section to simulate the aerodynamic spanwise correlation of the split double-box beam in a static state, and obtained the aerodynamic coefficients of the six measuring sections shown in Figure 4b. The aerodynamic force of the main beam section is mainly determined by the forced load caused by the wind velocity in the static state, therefore, Formula (1) is used to fit the numerical simulation results of the spanwise correlation coefficients of aerodynamic coefficients of the main beam section. The attenuation coefficient (\(c_{i}\)) can be obtained from Formula (2). The results are shown in Table 4 and Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Aerodynamic Coefficient**} & \multicolumn{5}{c}{**Reduced Wind Velocity**} \\ \cline{3-6}  & & **5.65** & **6.21** & **6.68** & **7.44** \\ \hline \multirow{3}{*}{(attenuation coefficient)} & lift coefficient & 0.105 & 0.091 & 0.086 & 0.083 \\  & resistance coefficient & 0.296 & 0.365 & 0.313 & 0.265 \\ \cline{1-1}  & torque coefficient & 0.117 & 0.125 & 0.110 & 0.100 \\ \cline{1-1} \cline{2-6} \(L\) & lift coefficient & 9.51 & 10.98 & 11.56 & 12.03 \\ \cline{1-1} \cline{2-6} (spanwise correlation length) & resistance coefficient & 3.38 & 2.74 & 3.19 & 3.77 \\ \cline{1-1} \cline{2-6}  & torque coefficient & 8.55 & 8.00 & 9.07 & 9.97 \\ \hline \end{tabular}
\end{table}
Table 4: Fitting value of aerodynamic spanwise correlation coefficient parameters and spanwise correlation length of the main beam in a static state.  
Figure 6: FFT transformation of main beam section displacement curves. (**a**) Reduced wind velocity \(\mathrm{Vr}=5.18\); (**b**) Reduced wind velocity \(\mathrm{Vr}=6.12\); (**c**) Reduced wind velocity \(\mathrm{Vr}=6.59\); (**d**) Reduced wind velocity \(\mathrm{Vr}=8.47\).  
It can be seen in Table 4 and Figure 7:  
* Comparing the attenuation coefficient of the aerodynamic coefficients under different wind velocities, it can be seen that the attenuation coefficient corresponding to the spanwise correlation coefficient of the lift and torque coefficient, and changes slightly, and decreases gradually with the increase of reduced wind velocity. The attenuation coefficient corresponding to the spanwise correlation coefficient of the resistance coefficient changes greatly with the wind velocity, which is significantly greater than that of the lift and torque coefficient. Therefore, the resistance decays the fastest in the process of the aerodynamic force decaying along the spanwise direction.
* The spanwise correlation length of lift and torque increases with the increase of wind velocity, while that of resistance varies greatly.
* The spanwise correlation of all three kinds of aerodynamic coefficients decreases with the increase of the spanwise length in the static state. The lift has the slowest decay rate, followed by torque, and drag has the fastest decay rate.