## 4 Discussion
### The Wind Force Estimation According to the Standard  
The obtained values of the overturning moments induced by the wind and estimated from the CFD simulations are compared with those that are computed according to the standard [7]. The estimations are based on the reference area \(A_{\mathit{ref}}=48.27\) m\({}^{2}\) of the crane lattice structure. Utilizing the aerodynamic coefficients obtained from CFD results, the component values \(F_{X}\) and \(F_{Y}\) of the aerodynamic forces are determined as a function of the wind speed \(V(z)\), according to Formula (1). \[F_{X}=0.5\cdot V(z)^{2}\cdot A_{\mathit{ref}}\cdot\rho\cdot C_{X},\ F_{Y}=0.5 \cdot V(z)^{2}\cdot A_{\mathit{ref}}\cdot\rho\cdot C_{Y},\ F=\sqrt{\left(F_{X} \right)^{2}+\left(F_{Y}\right)^{2}} \tag{6}\]  
Next, the overturning moment \(M_{O\ CFD}\ \tau_{\mathit{1 EC-B}}\) is obtained as a function of the jib rotation angle \(\theta\), namely:  
\[M_{\mathit{0\ CFD}\ \tau_{\mathit{1 EC-B}}(\theta)}=M_{\mathit{0\ FG}}(\theta)+M_{ \mathit{0}}(\theta), \tag{7}\]  
where \(M_{\mathit{0\ FG}}=F(\theta)\cdot h_{1}\). It makes possible the estimation of the critical wind speed causing overturning of the whole structure depending on Case 1 or 4. **EuroCODE**. To determine the wind force W according to the standard [7], the reference area \(A_{\mathit{ref}}\) of the studied structure and the wind pressure distribution are needed. It is assumed that the wind speed is measured at the jib level, e.g., \(H=40\) m for the urban terrain. Because the wind speed changes (increases) together with height, the reference area of the whole structure, \(A_{\mathit{ref}}=48.27\) m\({}^{2}\), is divided into three parts, namely crane jib \(A_{\mathit{ref}-1}=25.69\) m\({}^{2}\), crane tower \(A_{\mathit{ref}-2}=16.58\) m\({}^{2}\), and upper counterweight \(A_{\mathit{ref}-3}=6\) m\({}^{2}\) \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Counter-Jib, Counterweight,** & \multirow{2}{*}{**Tower**} & \multirow{2}{*}{**Central Ballast**} & \multirow{2}{*}{**Cruciform Base**} \\
**Slewing Platform** & & & & & & & & & \\ \hline Mass & & & & & & & & \\ \hline
**Q10** & **Q11** & \(Q12\) & \(QT1\) & \(QT2\) & \(QT3\) & \(QB1\) & \(QB2\) & \(QK1\) & \(QK2\) & \\
**9750** & **2190** & 3310 & 2450 & 2450 & 3320 & 30,000 & 30,000 & 1950 & 1730 & (kg) \\
**95,648** & **21,484** & 32,471 & 24,035 & 24,035 & 32,569 & 294,300 & 294,300 & 19,130 & 16,971 & (N) \\ \hline \multicolumn{10}{c}{Distance from the tipping line} \\ \hline \(l10\) & \(l11\) & \(l12\) & \(l11\) & \(l12\) & \(l13\) & \(l1b1\) & \(l2\) & \(lk1\) & \(lK2\) & \\
12.91 & 9.30 & 2.57 & 2.45 & 2.45 & 2.45 & 3.85 & 1.05 & 2.45 & 2.45 & (m) \\ \hline Moments & & & & & & & & & \\ \hline \(M\)**I10** & **\(M\)I11** & \(M\)I12 & \(M\)I1 & \(M2\) & \(M3\) & \(Mb1\) & \(Mb2\) & \(Mk1\) & \(Mk2\) & \\
**1,234,338** & **199,850** & 83,372 & 58,885 & 58,885 & 79,795 & 1,133,055 & 309,015 & 46,867 & 41,580 & (Nm) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The values of the masses of Variant 2—stabilizing moments and overturning moments (bold values) from counter-jib, counterweight only (Description as in the case of Table 6). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **Stabilizing Moments \(\Sigma\ M_{\mathrm{S}}\)** & **Overturning Moments \(\Sigma\ M_{\mathrm{O}}\)** & \(\Sigma\ M_{\mathrm{S}}-\Sigma\ M_{\mathrm{O}}\) \\ \hline
1 & **3,245,465** & **1,203,620** & **2,041,845** \\
2 & 3,245,465 & 732,740 & 2,512,725 \\
3 & 3,270,948 & 861,055 & 2,409,893 \\
4 & **2,756,482** & **861,055** & **1,895,427** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Sums of the stabilizing and overturning moments for variants 1 and 2. Moreover, different standards assume that the load induced by the wind acting on the external surfaces of the structure is treated as a static normal pressure, with value \(p=245\) N/m\({}^{2}\) for wind speed equal to \(V=20\) m/s.