# Global Buckling Resistance of Cold-Formed Steel Beams with Omega-Shaped Sections
## 4 Numerical Models
### GBTUL Model  
The modeling process in GBTUL is straightforward due to its simple and clear interface. It involves the following steps:  
Step 1: Definition of the geometry of the structure, including dimensions, shape, and material properties such as Young's modulus (210 GPa) and Poisson's ratio (0.3). All units are typically specified in the International System of Units (SI), with forces in kilonewtons (kN) and lengths in meters. Figure 15 shows the geometry input for the 170 \(\times\) 2.0 profile.  
Step 2: Validation of the buckling modes: before proceeding with the analysis, it is essential to validate the buckling modes of the structure. This involves confirming that all essential modes are present and that they make sense for the given case. For the three profiles under examination, all the buckling modes were considered in the analysis; however, the essential modes are the first five modes, which are the (1) axial mode; (2) major axis bending mode; (3) minor axis bending mode; (4) torsional mode; and (5) distortional mode. Step 3: Application of loads and boundary conditions: within this step the software makes use of computational methods to analyze the structure under various loads and boundary conditions. To do so it is necessary to define the following parameters:  
1. The number of partitions/elements (mesh). The evaluation of the appropriate mesh density is crucial to accurately capture the behavior of the structure. This involves dividing the structure into smaller elements for numerical analysis. The mesh considered for the 170 \(\times\) 2.0 profile with a length of 4.0 m was 20.  
Figure 14: Failure modes of the 170 \(\times\) 2.0 profile under uplift loading: (**a**) failure in the experimental test and (**b**) failure in the ABAQUS model.  
Figure 13: Failure modes of the 170 \(\times\) 2.0 profile under downward loading: (**a**) failure in the experimental test and (**b**) failure in the ABAQUS model.  
2. Support conditions: all the tested profiles were simply supported on both sides.
3. Define unit loads: the loads applied to the structure are point loads at the locations indicated in Layout 1 (see Figure 16) for the case of the \(70\times 1.5\) and \(170\times 2.0\) profiles and in Layout 2 for the case of the \(300\times 2.5\) profiles.
4. Lengths to evaluate: the length of interest to simulate the experimental tests is \(4.0\) m.
5. Number of eigenmodes to be calculated: the number of eigenmodes (buckling modes) depends on the complexity of the structure and the desired level of accuracy. For the \(170\times 2.0\) profiles, the number of eigenmodes calculated was \(180\).
6. Observation of results: after performing the numerical analysis, observe the results to gain insights into the behavior of the structure under the applied loads and boundary conditions. The results obtained for the \(170\times 2.0\) profiles are shown in Figure 17.  
Figure 16: Load type and locations for the case of the \(70\times 1.5\) and \(170\times 2.0\) profiles.  
Figure 17: Buckling curve and GBT modal participation diagram obtained for the \(170\times 2.0\) profile.  
The analysis of Figure 17 allows us to conclude that the buckling load is 1.18 kN, which corresponds to a critical elastic buckling moment of 3.77 kN.m, with a major contribution of the torsional mode (98%).