## 2 Materials and Methods
### CFD Simulation  
The CFD simulations of the airflow around the studied lattice structure of the studied tower crane were performed with the use of the ANSYS R22 Fluent with Meshing module. The computations were carried out for various configurations of the crane geometry concerning the wind direction as well as for three different wind profiles (for urban terrain, village terrain, and open terrain). In Figure 3, it is depicted how the geometry of the crane is defined concerning the wind direction. The assumed wind direction is parallel to the \(X\)-axis of the global Cartesian coordinate system. The geometry configuration is defined by the angle \(\theta\) between the \(X\)-axis of the coordinate system and the horizontal jib. The computations were performed for the following angles, namely: \(\theta=0^{\circ},15^{\circ},30^{\circ},45^{\circ},60^{\circ},\)\(75^{\circ},\) and \(90^{\circ}\) for each assumed wind profile.  
Figure 2: Details of the CAD model of the fast-erecting crane: (**a**) crane basis; (**b**) tower lattice; (**c**) join of the tower and jib; (**d**) jib lattice.  
The investigated structure is immersed in the cuboid volume filled with an air of geometrical dimensions: width \(\times\) length equal to 125 m \(\times\) 130 m, and height equal to 65 m. One wall is assumed to be an inlet (blue wall in Figure 4), and the opposite one is the outlet, as shown in Figure 4. The ground (the wall on which the crane is installed) is stationary, while the rest of the walls are assumed to be movable. The wind speed on these walls varies according to the predefined wind profile for the inlet. The external dimensions of the cuboid seem to be enough. The lattice structures, like tower cranes, cause a limited disturbance of the airflow due to the relatively small area of the whole structure. Standard air properties at sea level (temperature T = 15 \({}^{\circ}\)C, ambient pressure p\({}_{0}\) = 101,325.25 Pa) were assumed, namely: kinematic viscosity v = 1.7894 \(\times\) 105 kg/(m-s), density \(\rho\) = 1.225 kg/m\({}^{3}\).  
Figure 4: The investigated crane inside the cuboid volume filled with air.  
Figure 3: The assumed configuration of the crane geometry.  
For simulation of the turbulent flow of air, the standard k-\(\epsilon\) model with a standard wall function is exploited. According to the authors' experience so far [22; 23; 36], this model allows obtaining sufficiently precise results in a situation where the magnitude of the resultant aerodynamic forces (static pressure) is mainly determined by the drag force, while the lift force is several orders of magnitude smaller. Furthermore, the k-\(\epsilon\) model of turbulent flow is still successfully exploited by other authors, for example [8; 11; 38]. Here, it is worth noting that the other available models of turbulent flow are rather difficult to use in this case. For example, the use of the Reynolds stress model [24] causes the convergence of the numerical solution to be unacceptably slow. Another possibility is to involve the k-\(\omega\) turbulent flow [14; 39; 40]. In the ANSYS R22 Fluent software, this model is available in several different variants. Depending on the variant of this model used, the results in the form of aerodynamic force values may vary significantly. Moreover, when using the k-\(\omega\) model, it is necessary to generate an appropriate FEM mesh in the boundary layer. This results in a significant increase in the number of elements, which seems unacceptable in the case of the currently considered structure.