## 3 Results of CFD Simulation
### The Wind Force Estimation Based on the Experiment  
In Figure 10, there are three points that correspond to the overturning moments M\({}_{\text{O}\,\text{exp}\,\text{0}^{\circ}}\): 90\({}^{\circ}\). These moments are the sum of the values of the moments estimated based on the wind force for the position of the crane jib, corresponding to \(\theta\) = 0\({}^{\circ}\) and \(\theta\) = \(\pm\)90\({}^{\circ}\). The appropriate values are determined with the use of force coefficients C\({}_{\text{X}}\) obtained from experimental analysis [36] of the sectional models and the moments M\({}_{\text{O}}\) (Table 4). In the experimental investigations, two sectional models were analyzed, namely part of the crane tower and part of the crane jib. At the very beginning of the current analysis, the reference area of the tower A\({}_{\text{ref1}}\) and the reference area of the jib A\({}_{\text{ref1}}\) should be determined with the model scale considered. It should be noted here that the determination of the total wind force acting on the crane jib is relatively easy because all parts of the jib are located at the same height, namely h\({}_{\text{9}}\) in Figure 11. However, the crane tower consists of eight parts--sectional models. Thus, it is necessary to determine the value of the wind force that acts on each section (it is assumed that the force is applied in the middle of each section) and compute the appropriate moment. It results in eight forces acting on the eight heights. The resultant overturning moment induced by the wind is equal to the sum of the product of these eight pairs of force W\({}_{1}\)-W\({}_{8}\) and corresponding height h\({}_{1}\)-h\({}_{8}\), which is shown in Figure 11.  
Figure 10: The distribution of loads acting on the 63 K crane, which was considered in the calculations according to Eurocode [41] (\(\theta\) = 90\({}^{\circ}\)) in the case of the maximal load.  
The values of the wind speed at the assumed height can be determined according to Formula (1) for urban terrain. Next, the total wind force acting on the crane jib is determined using the following equation:  
\[W_{J}=\ 0.5\cdot(v_{9}(h_{9}))^{2}\cdot A_{refT}\cdot\rho\cdot C_{XJ}, \tag{4}\]  
In the case of the tower the particular wind forces are estimated for i = 1, 2, \(\ldots\), 8 as:  
\[W_{Ti}=\ 0.5\cdot(v_{i}(h_{i}))^{2}\cdot A_{refT}\cdot\rho\cdot C_{XT}, \tag{5}\]  
and, finally, moments for jib M\({}_{\rm WJ}\) and tower M\({}_{\rm WT}\):  
\[M_{WJ}=W_{J}\cdot h_{9},\ M_{WT}=\sum_{i=1}^{8}W_{Ti}\cdot h_{i} \tag{6}\]  
The numerical data and values of the calculated forces and moments for both angles are shown in Table 5. Similar computations were also carried out in the case of the laminar flow of the air. The results are presented in Table 6.  
Figure 11: The distribution of loads acting on the 63 K crane, which was considered in the calculations according to experimental results.  
act relative to the tipping edge of the investigated crane (63 K). These forces are defined as a function of wind speed.  
\[W_{X}=F_{X}\cos(\theta),\ \ \ W_{Y}=F_{Y}\sin(\theta),\ W=\sqrt{\left(W_{X}\right)^{2 }+\left(W_{Y}\right)^{2}} \tag{8}\]  
In the next step, the reduced forces W and overturning moment M\({}_{\text{oCFD63K}}\) are described as a function of the rotation angle theta of the jib position.  
\[M_{\text{O CFD 63K}}=M_{\text{O}}+W\cdot h_{1}. \tag{9}\]  
As is shown in Figure 10, the three isolated points from the experiment (turbulent and laminar flow). which correspond to the jib position for jib rotation angle theta equal to 0\({}^{\circ}\) and 90\({}^{\circ}\), almost overlap each other with the characteristic of the overturning moment. The overturning moment is based on the values of the wind forces obtained from CFD simulations.  
The determination of the wind forces in all cases was performed according to the standards [41; 46].