## 3 Determination of the Wind Load
### Wind Tunnel Tests

Table 1: Details of the wind tunnel test cases. Figure 3: Photos of wind tunnel tests: (**a**) wind tunnel test arrangement; and (**b**) group-arranged rigid models. crane is demonstrated in Figure 5. The crane models are numbered 1\(\mu\), 2\(\mu\), and 3\(\mu\) along the wind direction. When suffering storms, the crane may slide along the rail according to the berthage of the ship, so that the forces along or perpendicular to the rail are always the key design parameter. Thus, the force and moment are decomposed along the body-fitted axis instead of the wind direction axis. The test model was connected to an ATI Delta high-frequency force balance (HFFB) installed on the center of the turn table. Azimuths of 0\({}^{\circ}\)-180\({}^{\circ}\) with a step of 15\({}^{\circ}\) were tested. A TFI Cobra Probe was installed in the upstream direction at the reference height to measure the reference velocity \(U_{\rm H}\). As reported in previous studies ([PERSON] & [PERSON] [16], [PERSON] [17]), the effect of the Reynolds number is negligible in such structures. The test wind speed was approximately 10 m/s at the reference height. The sampling rate (\(f_{s}\)) of the wind force/moment was 1000 Hz, and the duration of sampling (\(T_{\rm s}\)) was 60 s. The test cases are listed in Table 1.  
\(F_{i}\) and \(M_{i}\) indicate the forces and moments measured along the body axes, where \(i\) is X or Y axis. These wind force/moments were transformed into nondimensional coefficients using the following equations at each sampling time:  
\[C_{F_{i}}=\frac{F_{i}}{0.5\rho U_{0}^{2}A} \tag{1}\]  
Figure 4: Simulated wind parameters in the wind tunnel tests: (**a**) mean speed and turbulence intensity; and (**b**) longitudinal turbulence spectrum at the reference height. Figure 5: The top view of the group-arranged cranes. \[C_{M_{i}}=\frac{M_{i}}{0.5\rho U_{0}^{2}AH} \tag{2}\]  
where \(A\) refers to the windward projected area and \(H\) is the reference area and reference height, respectively. The mean and root mean square (RMS) values of wind force/moment coefficients \(\overline{C}_{\lambda}\) and \(\widetilde{C}_{\lambda}\) are calculated by the following equations:  
\[\overline{C}_{\lambda}=\frac{1}{N}\sum_{i=0}^{N-1}C_{\lambda}(t_{i}) \tag{3}\]  
\[\widetilde{C}_{\lambda}=\sqrt{\frac{1}{N-1}\sum_{i=0}^{N-1}\left[C_{\lambda}( t_{i})-\overline{C}_{\lambda}\right]^{2}} \tag{4}\]  
where \(\lambda=F_{x},F_{y},M_{x}\) or \(M_{y}\). It is the arbitrary wind force/ moment component. \(N\) is the length of the sampling time points. \(t_{i}\) is the \(i\)-th time point of the series. It is proved that the probability distributions of the resultant force coefficient for both isolated and group-arranged cranes obey the Gaussian distribution. And the peak force/moment coefficients \(\tilde{C}_{\lambda}\) are calculated by:  
Figure 3:0  
where \(g\) is the peak factor. According to the Davenport Method [34] for calculating the peak factor of a Gaussian process, the value of which is taken as 3. It was found that the RMS wind force/moment coefficients are usually 12-15% of the mean wind coefficients. The most unfavorable cases and the corresponding coefficient values are summarized in Figure 3:1 It shows that the most unfavorable cases of \(C_{\text{Fy}}\) and \(C_{\text{Mx}}\) always occur at 90 \(\pm\) 15\({}^{\circ}\), and the most unfavorable also occur at the azimuths, which deviate 15\({}^{\circ}\) perpendicular to the rail direction.