## 5 Conclusions  
Based on the CFD analysis results, the aerodynamic force coefficients \(C_{x}\) and \(C_{y}\) are calculated. These coefficients allow for estimating the magnitude of the aerodynamic forces acting on the examined structure of the top-slewing tower crane as a function of the average wind speed. An example of such a structure is the Liebherr 71 EC-B crane, which features a flat top. This structure allows a maximum payload of 1000 kg at the end of a 50 m jib length. The obtained results are compared with the applicable standard [7]. This standard concerns the estimation of the wind load of the cranes, openwork construction, and lattice structures. The determination of the wind force is based on the so-called reference area \(A_{ref}\) and the static pressure distribution induced by the blowing wind. The estimation is performed concerning the most unfavorable crane configuration to the tippling line and the wind direction. In our case, it relates to the crane configuration for \(\theta=90^{\circ}\). Next, the total (resultant) stabilizing and overturning moments are determined concerning the selected tipping line for the exemplary top-slewing tower crane 71 EC-B. The four cases are possible. In the first case, the jib is parallel to the wind direction without payload, and the upper counterweight is against the wind. The second case is similar, but the jib carries a payload. Both these cases relate to when the crane is out of service and the slewing platform is unlocked. The third case is when the jib is parallel to the wind direction without payload; however, the upper counterweight is on the opposite side than in the previous cases. Consequently, in the fourth case, the jib is in an identical geometrical configuration as the previous one but now carries a payload. The third and fourth cases relate to when the crane is in service and the slewing platform is locked. The second and third cases are chosen for further analysis. Having prepared the values of the aerodynamic forces induced by the wind obtained from the CFD analysis and computed according to EuroCODE, the characteristics of the overturning moment for both investigated variants are shown. These characteristics are the function of the jib rotation angle \(\theta\) for the wind speed with increment value 5 m/s. The range of the dangerous jib rotation angle for which the studied crane loses its stability (for both cases) is determined. The specified range of angle \(\theta\) shows dangerous angles due to loss of crane stability for both variants of the jib setting and \(\theta=\pm 75^{\circ}\) (the least favorable). For these values of the angle \(\theta\), when the crane loses its stability and is close to tipping over, the wind speed value equals 35 m/s. For better-studied problem visualization, the trace of the center of gravity with wind forces taken into account is created using an analytical approach. The results are shown on the appropriate graphs, where the tipping lines are marked. This study shows that the approach based solely on the \(Mo<Ms\) condition according to EuroCODE does not take into account the change in the angle of the jib rotation to the wind direction and, consequently, the change in its reference area \(A_{n\!rg}(\theta)\), an example of which is the angle of \(\pm 75^{\circ}\), for which the value of the wind force is the greatest. This approach defines one location of the jib for the angle \(\theta=0^{\circ}\) for variant 1 or \(90^{\circ}\) for variant 2 where \(\theta=90^{\circ}\), and in both cases, we have \(A_{n\!rg}\) corresponding to the area for the angle \(\theta=90^{\circ}\). In summary, the described analytical approach, taking into account the jib rotation angle \(\theta\), specifies the values of moments acting on the crane structure with the simultaneous action of the wind force on this system. Having the values of \(F_{x}\) i \(F_{y}\) as a function of jib rotation angle \(\theta\), it is possible to specify the approach based on the EuroCODE.