## 4 Discussion
### Variant 1: Determination of the Overturning and Stabilizing Moments  
Based on the information contained in the catalog card of the tower crane and the technical and operational documentation regarding the dimensions and weights of the individual elements of the supporting structure, a diagram is made showing the system of forces acting on the crane structure concerning the most unfavorable tipping line (Figure 9). \(W_{1}\) to \(W_{3}\) is the wind force at the corresponding height \(h_{1}\) to \(h_{3}\). The load resulting from the wind force will be presented later in the article. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Angle \(\theta\) (\({}^{\circ}\))** & \(C_{x}\) & \(C_{y}\) & \(C_{z}\) & \(C_{tip}\) \\ \hline
0 & 0.895 & 0.004 & 0.022 & 0.545 \\
15 & 1.077 & \(-\)0.057 & 0.037 & 0.724 \\
30 & 1.267 & \(-\)0.214 & 0.024 & 0.913 \\
45 & 1.545 & \(-\)0.349 & 0.024 & 1.183 \\
60 & 1.838 & \(-\)0.378 & 0.006 & 1.488 \\
75 & 2.052 & \(-\)0.273 & \(-\)0.004 & 1.697 \\
90 & 2.125 & \(-\)0.014 & \(-\)0.030 & 1.762 \\ \hline \hline \end{tabular} \(A_{ref}=48.27\) m\({}^{2}\), \(B_{ref}=37.9\) m, and \(\rho=1.225\) kg/m\({}^{3}\).  
\end{table} 
Table 3: Aerodynamic drag force coefficients for village terrain, \(V_{ref}=11.716\) m/s. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Angle \(\theta\) (\({}^{\circ}\))** & \(C_{x}\) & \(C_{y}\) & \(C_{z}\) & \(C_{tip}\) \\ \hline
0 & 0.898 & 0.005 & 0.013 & 0.613 \\
15 & 1.109 & \(-\)0.069 & 0.031 & 0.810 \\
30 & 1.325 & \(-\)0.253 & 0.016 & 1.028 \\
45 & 1.654 & \(-\)0.406 & 0.013 & 1.361 \\
60 & 1.996 & \(-\)0.443 & \(-\)0.004 & 1.697 \\
75 & 2.247 & \(-\)0.319 & \(-\)0.018 & 1.951 \\
90 & 2.332 & \(-\)0.015 & \(-\)0.052 & 2.030 \\ \hline \hline \end{tabular} \(A_{ref}=48.27\) m\({}^{2}\), \(B_{ref}=37.9\) m, and \(\rho=1.225\) kg/m\({}^{3}\).  
\end{table} 
Table 4: Aerodynamic drag force coefficients for urban terrain, \(V_{ref}=10.713\) m/s. According to the adopted system of forces, the overturning moments of the crane are calculated as the algebraic sum of the moments of the jib and load mass concerning the most unfavorable tipping line. The values of forces and moments for variant 1 acting on the structure of the Liebherr 71 EC-B5 crane are presented in Table 5.  
Based on the above data, the sum of overturning moments with a total value of \(\Sigma\,M_{Q}\) = 1,203,620 N  
Figure 9: Mass distribution diagram of the Liebherr 71 EC-B5, which is considered in the calculations according to Eurocode (\(A_{ref}\) computed for \(\theta\) = 90\({}^{\circ}\)). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Jib** & & & & & & & & & & & \\ \hline Mass & & & & & & & & & & & \\ \hline Q1 & Q2 & Q2-2 & Q3 & Q4 & Q5 & Q6 & Q7 & Q8 & Q9 & \\
1820 & 530 & 530 & 740 & 160 & 380 & 200 & 170 & 60 & 1000 & (kg) \\
17,854 & 5199 & 5199 & 7259 & 1570 & 3728 & 1962 & 1668 & 589 & 9810 & (N) \\ \hline \multicolumn{10}{c}{Distance from the tipping line.} \\ \hline \(l1\) & \(l2\) & \(l2\)-2 & \(l3\) & \(l4\) & \(l5\) & \(l6\) & \(l7\) & \(l8\) & \(l9\) & \\
3.41 & 10.72 & 15.86 & 23.51 & 29.91 & 34.90 & 41.07 & 46.04 & 48.68 & 48.00 & (m) \\ \hline \multicolumn{10}{c}{Moments} \\ \hline \(M1\) & \(M2\) & \(M2\)-2 & \(M3\) & \(M4\) & \(M5\) & \(M6\) & \(M7\) & \(M8\) & \(M9\) & \\ \hline
60,795 & 55,724 & 82,474 & 170,686 & 46,947 & 130,119 & 80,571 & 76,775 & 28,650 & 470,880 & (Nm) \\ \hline \end{tabular} where Q1—mass of the 1 th part (1), Q2—mass of the 2 nd part (2), Q2—mass of the 3 rd part (2), Q3—mass of the 4 th part (3), Q4—mass of the 5 th part (4), Q5—mass of the 6 th part (5), Q6—mass of the 7 th part (6), Q7—mass of the 8 th part (7), Q8—mass of the 9 th part (8), and Q9—mass of the payload at the end of the jib.  
\end{table} 
Table 5: The values of masses—overturning moments, variant 1. The stabilizing moments of the real object are the sum of the moments resulting from the mass of the tower with turntable, counter-jib with counterweight, crosspiece, and central ballast (Table 6).