## 2 Materials and Methods
### Numerical Model  
The numerical model was created using the Abaqus Simulia 2022 software [19], which employs the finite element method for calculations. The entire geometry of the system was modeled using shell-type surface elements [19], with an effort to replicate the real conditions of laboratory tests as closely as possible. The dimensions and mutual positioning of the model elements were identical to the real-life conditions. The model utilized the symmetry of the system to reduce the size of the task and the time consumption of calculations. The mutual positioning of the model elements is shown in Figure 1, which represents half of the analyzed system (utilizing task symmetry). The variable parameter of the model's geometry was the length of the beams. For modeling the geometry of the system, finite elements S4R (a 4-node doubly curved thin or thick shell, reduced integration, hourglass control, finite membrane strains) from the Abaqus 2022 software library [19] were used. Figure 1 shows the discretization of the system with a 3 m-long beam. An automatic meshing technique using a progressive front algorithm was applied to generate the finite element mesh throughout the model. This technique generated the mesh from the boundaries of the geometry and extended it deep into the model area. This allowed control of the mesh density and ensured good-quality elements with complex shapes. The generated mesh consisted of quadrilateral elements. The number of elements depended on the span; for a system with a span of 3 m there were  
Figure 1: Geometry and discretization of the model. 36,815 elements, and for a span of 6 m there were 65,171 finite elements. The following boundary conditions were applied in the model:  
* Connectors were fixed at the location of mounting holes on a surface with a diameter of 40 mm. * Connectors were connected to the beams using a \"Tie\"-type contact [19], which corresponds to a rigid connection of the connector to the beam. * Symmetric boundary conditions were applied to the axis of symmetry of the system on the steel grating and beams. In the model, a \"General contact\" type [19] was used between the bridge deck and the beams. The following contact parameters were adopted:  
* Normal Behavior--\"Hard\" Contact. * Tangential Behavior--Penalty, Friction coefficient = 0.3. The steel grating was modeled with real dimensions. The only simplification applied was the substitution of the round cross-section transverse rods with square cross-sections with the same surface area. The load in the form of a concentrated force applied at the RP point, generated by the strength testing machine, was modeled as a Pressure load, evenly distributed over a surface 160 mm wide, which corresponded to the real conditions during the test. The method of loading the system is shown in Figure 2. During the validation of the model, an ideally elastic-plastic material was assumed with the following parameters. For the beams:  
* [PERSON]'s modulus E = 205.5 GPa, determined based on laboratory tests. * Poisson's ratio \(\
u\) = 0.3. * Yield strength \(\mathrm{R_{H}}\) = 490 MPa, determined based on laboratory tests. For the connectors and the steel grating:  
* [PERSON]'s modulus E = 200 GPa, determined based on laboratory tests. * Poisson's ratio \(\
u\) = 0.3. * Yield strength \(\mathrm{R_{H}}\) = 362 MPa, determined based on laboratory tests. In real structural conditions, thin-walled beams often exhibit imperfections resulting from manufacturing processes, assembly, and natural characteristics of the material. Such imperfections significantly influence the behavior of the structure, especially in terms of sensitivity to buckling and other nonlinear effects. Incorporating these imperfections into the analysis allows for a more realistic and reliable simulation, which is crucial for the safety and durability of the structure. Additionally, this is in line with the recommendations of engineering standards and allows for a more accurate prediction and understanding of the critical operating conditions of the beams.