## 2 Materials and Methods
### CFD Simulation  
Scaled Sectional Models  
The CFD analysis was performed to estimate the magnitude of the aerodynamic forces acting on the studied sectional models of the gantry crane and the whole gantry (in the real scale) crane. The numerical simulations were carried out with the commercially available software ANSYS FLUENT 2022R2. All performed simulations were performed under the assumption of the steady state of the airflow. Moreover, the standard air properties (density, temperature, ambient pressure, and viscosity) were also assumed, namely \(\rho\) = 1.225 kg/m\({}^{3}\), \(p_{0}\) = 101,325.25 Pa, and \(\mu\) = 1.7894 \(\times\) 10\({}^{-5}\) Pa s, and \(T\) = 15 \({}^{\circ}\)C.  
The CFD computations in the case of the scaled sectional models were performed under the assumption that the simulations recreate the conditions in the aerodynamic tunnel. The transversal dimensions of the measurement are 2200 \(\times\) 1400 mm. The length of the considered part of the aerodynamic tunnel is equal to \(L_{t}\)= 2500 mm. The sectional models were placed at a distance \(L_{1}\) = 1000 m from the inlet (Figure 11a,b, where the inlet is shown as a blue wall).  
We decided to use the standard k-\(\varepsilon\) model because the dominant effect is the aerodynamic drag in the current work. This model of turbulent flow ensures relatively accurate precision when predicting aerodynamic forces under the assumption of ideal rigidity of the investigated models of structures. Moreover, this model has been successfully used in different works [29; 38; 39; 42; 43].  
However, it is worth noting that besides the k- \(\varepsilon\) model, the following models are exploited, namely the Reynolds stress model and k-omega model. The Reynolds model [44] can cause significant problems with computation convergence, and the computation process is prolonged. On the other hand, the k-\(\omega\) model [45; 46; 47] demands creating a special mesh of finite cells at the stationary boundaries, which consists of very small elements. Consequently, it causes the number of cells, nodes, and degrees of freedom to be significantly large. Moreover, this model has several variants that can, unfortunately, generate completely different results depending on the problem.  
Figure 12a,b shows the meshes generated for the box and truss girders, respectively. For the box girder model, the approximate size of the tetrahedral elements varies from \(l_{c}\) = 2.5 mm to \(l_{c}\) = 60 mm. The total number of cells is equal to 2,763,302, and the total  
Figure 11: Studied sectional models immersed in the volume filled with the air: (**a**) box girder; (**b**) truss girder.  
number of nodes is 689,675. For the model of the truss girder, the size of tetrahedral elements varies from \(l_{c}\) = 2 mm to \(l_{c}\) = 60 mm (3,646,476 cells and 889,314 nodes).  
Several CFD simulations were performed with different sizes of the elements to estimate the impact of the element size on the aerodynamic forces. The convergent test was made for the sectional model of the box girder mainly due to the possibility of the change of size of the elements being strongly limited in the case of truss structures. The computations were performed for wind speed \(V\) = 17.1 m/s and a turbulence intensity of 12%. The hydraulic diameter is equal to \(D_{H}\) = 1.712 m. The wind direction (Figure 9) is assumed to be equal to \(\theta\) = 0\({}^{\circ}\). The results are reported in Table 2.  
As observed, the finite cell size equal to \(l_{c}\) = 2.5 mm seems to be optimal concerning the time of calculation and the obtained precision. To obtain a convergent solution, 111 iterations are required. However, the solution could not be converged concerning the assumed default criteria for larger elements. The problem is mainly caused by the continuity criterion. For the smaller elements, the obtained results differ not significantly, but the time of calculation (154 iterations) is radically and unacceptably longer.