# A Field Investigation on Vortex-Induced Vibrations of Stay Cables in a Cable-Stayed Bridge
## 4 Correlation between Cable Response and Wind Characteristics  
### Vibration Amplitude Versus Wind Characteristics  
The wind data of two anemometers installed on the upstream and downstream sides of the mid-span section of the deck were collected to investigate the wind characteristics and their correlation with the cable response. The wind data of two anemometers are denoted as \"incoming flow\" and \"wake flow\", respectively. It should be noted that \"incoming flow\" and \"wake flow\" do not absolutely indicate the inflow and wake flow and that they are only used to distinguish the wind data measured by the two anemometers. Figure 7 shows 10 min mean wind speeds and directions of incoming and wake flows in April, July, and August, measured by the two anemometers, respectively. It is found that the data measured by two anemometers are close to each other for most of the samples, and the 10 min mean wind speeds are almost less than 15 m/s, with only several points larger than 15 m/s. The wind direction between the flow and the longitudinal bridge axis shows that the wind is nearly perpendicular to the bridge axis when the wind blows from the south. Figure 8 shows the time histories of 10 min mean wind speeds, directions, and turbulence intensities of incoming and wake flows measured by two anemometers in April (16 April 2010 to 29 April 2010). The 10 min mean wind speeds are primarily located in the range of 3 to 12 m/s, as shown in Figure 8a. It was found that, while 10 min mean wind speed histories are close to each other, there is a smaller phase difference of the wind direction between the incoming flow and wake flow, as shown in Figure 8b. The largest difference between two anemometers happens in the turbulence intensity (Iu) of the stream-wise direction, as shown in Figure 8c, because one anemometer is located in the incoming flow and the other is inevitably in the wake flow when the flow is nearly perpendicular to the bridge axis. The turbulence intensity in the incoming flow is certainly less than that in the wake flow. The larger numerical values of the turbulence intensities measured by two anemometers alternately change with time. Whatever the incoming flow or wake flow, the turbulence intensities are mainly less than 0.2. The large value of the turbulence intensity is mainly induced by a small mean wind speed, as shown in Figure 8a. Figure 7: Ten-minute mean wind speed and direction in April, July, and August. Figure 9 shows the relationship between the acceleration RMSs of 10 min for the cable CAC20 and the corresponding 10 min mean wind speed in three months of April, July, and August. It is found that the vibration amplitude initially increases with the mean wind speed, reaches the largest amplitude  
Figure 8: Ten-minute mean wind characteristics at the mid-span section of the investigated bridge in April (16 April 2010 to 29 April 2010). at the mean wind speed of approximately 4 to 6 m/s, and then decreases with the mean wind speed. The large amplitude is mainly located in the range of 3 to 12 m/s. According to the characteristics of the distribution of the vibration amplitude with the mean wind speed, the relationship between the maximum vibration amplitude and the mean wind speed can be fitted and denoted by the following form of expression:  
\[f(U)=kU+\frac{1}{\sqrt{2\pi}\sigma}\exp\left(\frac{\left(U-\mu\right)^{2}}{2 \gamma\sigma^{2}}\right) \tag{1}\]  
where \(U\) is the mean wind speed, \(k\) is fitted to be 0.1, \(\mu\) is 5.75 m/s, \(\sigma\) is 0.07 m/s, and the factor \(\gamma\) is 1200. The first term of the right side of Equation (1) is a linear function, which means the forced vibration component increases with the mean wind speed. The second term of the right side is a modified function of normal distribution, which has a factor of \(\gamma\) to meet the statistical samples.