## 4 Global Analysis  
### Numerical Modeling  
Given the planned test execution, the geometry of the girder's interior was slightly simplified, but the initial stiffness of the bulkheads was maintained. The geometry used in the computations and in the later experimental determination of the buckling load is shown in Figure 4. Only a fourth of the girder is shown due to the inherent double symmetry of the structure. However, the computations were performed using the entire model. Figure 4: Model of the geometry used in the computations. Only a quarter of the structure is displayed. Figure 3: Wind tunnel tests on the new cross-section design. The investigations presented were carried out with the commercial finite element program Ansys, Version 2021R1 [30]. Meshing was performed using SHELL281, an eight-node shell element suitable for analyzing thin to moderately thick shells [31]. Because small imperfections compared with the model's size must be considered with a sufficient resolution, the upper limit of the mesh size was approximated using Equation (1) [32; 33]. \[L_{Element}\approx 0.49\cdot\sqrt{R\cdot t} \tag{1}\]  
With a radius of \(R=749\) mm and a plate thickness of \(t=3\) mm, the required mesh size is approximately 23 mm. As the first eigenmode obtained by the linear buckling analysis (LBA) showed a pattern of several short waves (later shown in Figures 8 and 9), the mesh size was further reduced, which also proved beneficial to the mesh quality in the region of the free cuts of the bulkheads. In addition, the mesh size convergence study on the first buckling mode of the linear buckling analysis (LBA) confirmed that the mesh size is sufficient. Boundary conditions were set according to those commonly used in studies of bending-dominated problems, e.g., [21]. The nodes at the end of the girder were rigidly coupled to a master node, where the constraints were applied. On one side, as shown in Figure 5, all translational degrees of freedom were constrained. In addition, the lateral rotations about the longitudinal (z) and vertical (y) axes were fixed, and the structure was only allowed to rotate about the x-axis. On the other end, the translation of the master node was allowed to shift in the longitudinal direction. It should be emphasized that a crane's main girder might be under the influence of a complex loading scenario consisting of forces and moments acting around more than one axis. As it is not realistic to represent such a complex loading scenario in a set of experiments, the investigations are focused on the main action of the girder. This main action is the weight of a container, the spreader, and the trolley, which transfer the load on the girder over the trolley's wheels. For the numerical investigation, this scenario is simplified by introducing the loads directly into the main girder's web using force elements. The material behavior is considered elastic-plastic with a Young's modulus of \(E=210\) GPa and Poisson's Ratio of \(\
u=0.3\). To represent a steel grade of S355, the yield strength was set to \(f_{y}=420\) MPa, compensating for the assumed and often higher yield strength. Material hard  
Figure 5: Boundary conditions and loading (schematic). ening was neglected. For path tracing, the implemented version of Riks arclength algorithm was utilized. Because the solver might miss a bifurcation point, the smallest pivot element was monitored during the solving process. In addition, the eigenvalues of at least one hundred load steps on the pre-buckling path were checked after the solver run. The load application was organized into three loading steps. Firstly, the imperfections were introduced into the model. After that, the self-weight of the structure was activated before the loading was applied and ramped up as the third step until the defined failure criterion (bifurcation or snap-through) was reached. Additional failure criteria are defined in EN 1993-1-6 [3], which were also tested but not explicitly reported, as bifurcation or the snap-through was always the first to occur.