## 3 Sectional Model Wind Tunnel Test
### Vortex-Induced Vibrations  
Vortex forms in large volumes on non-streamlined bodies and decks, due to knuckle lines, wind screen, or other ancillary facilities. An elastically suspended model with correctly scaled mass and damping characteristics was used to measure the VIV. Table 3 lists the test conditions that were used to study the VIV in construction and service states. The vertical and torsional VIV limitations for construction and service states ruled by Chinese Specification are shown in Equation (3). The Chinese Specification specifies the VIV allowable magnitude of bridges with a span that is less than 200 m, but the VIV allowable magnitude of longer span bridges should be specially discussed. The vertical VIV allowable magnitude adopted by the Chinese Specification and Wind Resistant Design Manual for high-way Bridges in Japan [30] (\"Japan Specification\" for short) is presented in Equation (3). Because bridge VIV is generally symbolized by single-mode harmonic vibration, the displacement response of VIV can be approximately represented by a sine or cosine function. Then the corresponding allowable acceleration value A\({}_{\rm v}\) can be taken as Equation (4). The first vertical mode frequency obtained by modal analysis is 0.2688 Hz. It is easy to calculate that the acceleration is 0.42 m/s\({}^{2}\) by substituting into Equation (4). Compared with the specifications of various countries and the technical report of RWDI, when 0.25 Hz \(<\)\(f_{\rm v}\) \(<\) 1.0 Hz, the VIV allowable magnitude of RWDI UK is the most stringent [31], that is, when the wind speed is less than 20 m/s, the vertical acceleration amplitude of the deck does not exceed 0.4 m/s\({}^{2}\), which is slightly different from the allowable acceleration value derived from the Chinese Specifications. ISO-2631-3-1985 lists the root mean square limit of human vibration acceleration that may lead to motion sickness, which is called severe discomfort boundary (SDB). The SDB is related to the time and frequency of vibration. It is divided into three classes according to the time of vibration, which are 30 min, 2 h, and 8 h, respectively. Considering that the time of vehicles passing through the bridges is often less than 30 min and the time of pedestrians passing through the bridges is basically less than 2 h, the \"2 h motion sickness limit\" can be conservatively adopted as the VIV limit of the bridge. When 0.1 Hz \(<\)\(f_{\rm v}\) \(<\) 0.315 Hz, the root mean square value of acceleration corresponding to \"2 h motion sickness limit\" is equal to 0.5 m/s\({}^{2}\). Meantime, the results calculated by Chinese Specifications meet the requirements of ISO-2631-3-1985. Furthermore, the visual impact of the oscillations could distract motorists and possibly impede road safety, for the high-order modal VIV with three or more half waves, the VIV amplitude shall be limited to less than 0.35 m at least [31], and the vertical VIV allowable magnitude calculated by Chinese Specification is h\({}_{\rm v}\) = 0.04/0.2688 = 0.1488 m \(<\) 0.35 m. Therefore, when the span exceeds 200 m, the VIV allowable magnitude specified in the Chinese Specification is overly strict and can still be used. The results are included in Table 3.  
\[h_{\rm v}<\gamma_{\rm v}\frac{0.04}{f_{\rm v}},\ \theta_{\rm t}<\gamma_{\rm v} \frac{4.56}{Bf_{\rm t}} \tag{3}\]  
\[A_{\rm v}=\gamma_{\rm v}\frac{0.04}{f_{\rm v}}\omega_{\rm b}^{2}=\frac{0.04}{ f_{\rm v}}\left(4\pi^{2}f_{\rm v}^{2}\right)=1.58f_{\rm v} \tag{4}\]  
\(h_{\rm v}\) is the vertical VIV amplitude (m);\(f_{\rm v}\) is the first vertical mode frequency (Hz); \(\gamma_{\rm v}\) is the VIV coefficient, which is set to 1.0 when taking wind tunnel test to obtain, \(\theta_{\rm t}\) is the torsional VIV amplitude (\({}^{\circ}\));\(f_{\rm t}\) is the first torsional mode frequency (Hz).