## 3 Wind Tunnel Tests
### VIV Characteristics with Different Railing Ventilation Rates
#### 3.3.2 Test Results  
Figure 13 illustrates the wind tunnel test results of the truss girder with various railing ventilation rates, where the values correspond to the actual situation.  
Figure 13 demonstrates that as the pedestrian railing ventilation rates decrease, the maximum amplitude of both vertical and torsional VIV decreases. Specifically, the vertical VIV is only slightly affected by the change in railing ventilation rate, with a slightly reduced maximum amplitude and no change in the length of the locking range or starting wind speed. The airtight railing has the most significant effect on suppressing vertical VIV, with reductions of 22.7% and 24.8% at +3\({}^{\circ}\) and +5\({}^{\circ}\), respectively. Decreasing the railing ventilation rate significantly reduces the maximum amplitude of both major and minor locking ranges of torsional VIV, slightly shortens the length of the major locking range, and increases the starting wind speed. Table 3 displays the different ventilation rates' effects on torsional VIV. Similarly, the airtight railing has the most pronounced suppression effect, with the major and minor torsional VIV suppression effects at +5\({}^{\circ}\), reaching 71.6% and 78.7%, respectively, and the minor torsional VIV being almost entirely eliminated.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ventilation Rate** & **Minor Peak at +3\({}^{\circ}\)** & **Major Peak at +3\({}^{\circ}\)** & **Minor Peak at +5\({}^{\circ}\)** & **Major Peak at +5\({}^{\circ}\)** \\ \hline
66.7\% & 0.079\({}^{\circ}\) & / & 0.181\({}^{\circ}\) & / & 0.089\({}^{\circ}\) & / & 0.211\({}^{\circ}\) & / \\
50.0\% &  
To analyze the VIV occurrence mechanism, we calculated the Strouhal number of the truss girder when VIV occurred, defined as  
\[S_{t}=fD/U, \tag{4}\]  
and the results are presented in Table 4[49]. The values show that changing the railing ventilation rate does not alter the Strouhal number of the girder section corresponding to the primary peak of vertical VIV, suggesting that the railing ventilation rate minimally impacts the primary vortex driving the bridge to vertical VIV. However, the primary vortex driving torsional VIV was influenced.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Railing Ventilation Rate** & \multicolumn{2}{c}{**66.7\%**} & \multicolumn{2}{c}{**50.0\%**} & \multicolumn{2}{c}{**33.3\%**} & \multicolumn{2}{c}{**0.0\%**} \\ \cline{2-9}
**Wind Angle of Attack** & **+3\({}^{\circ}\)** & **+5\({}^{\circ}\)** & **+3\({}^{\circ}\)** & **+5\({}^{\circ}\)** & **+3\({}^{\circ}\)** & **+5\({}^{\circ}\)** & **+3\({}^{\circ}\)** & **+5\({}^{\circ}\)** \\ \hline \(S_{t}\) for vertical VIV & Major peak & 0.47 & 0.47 & 0.47 & 0.47 & 0.47 & 0.47 & 0.47 & 0.47 \\ \hline \(S_{t}\) for torsional VIV & Minor peak & 0.64 & 0.60 & 0.63 & 0.59 & 0.63 & 0.59 & 0.62 & 0.58 \\ Major peak & 0.36 & 0.33 & 0.35 & 0.33 & 0.35 & 0.32 & 0.34 & 0.31 \\ \hline \hline \end{tabular}
\end{table}
Table 4: \(S_{t}\) for the girder at different working conditions.  
Figure 13: VIV responses of the truss girder with different pedestrian railing ventilation rates (converted to actual bridge values). (**a**) vertical responses at +3\({}^{\circ}\). (**b**) vertical responses at +5\({}^{\circ}\). (**c**) torsional responses at +3\({}^{\circ}\). (**d**) torsional responses at +5\({}^{\circ}\).