## 4 Numerical Investigation  
To model the test set-up including channel sections and top load-bearing plate, the multi-application finite element (FE) software programme ABAQUS 6.25 [28] was utilised in the numerical investigation. The cross-sectional sizes and details of the channel models were based on measurements conducted in the lab and the nonlinearity of the material was considered in the numerical investigations. In addition, consistent with recent research by [PERSON] et al. [33] and [PERSON] et al. [34], where explicit dynamic analysis was considered, in this study, a quasi-static procedure was adopted based on implicit integration analysis. This analysis type is found advantageous considering the complex nonlinearity material behaviour of cold-formed stainless steel beams. The finite element modelling details are presented below. More detailed modelling has been described by the authors [35; 36; 37] while further modelling techniques are described in recent studies [38; 39; 40]. From the ABAQUS 6.25 [28] library, S4R thin-shell elements representing channel models were used for modelling. This element is appropriate for applications with complex buckling behaviour such as thin-walled sections. Accordingly, a general purpose C3D8R element taking into account strain and plasticity applications and considering large deformation effects was used to model the top load-bearing plate. Using the following Equations (1) and (2) obtained from the ABAQUS 6.25 manual [28], the engineering stress-strain curve from tensile coupon tests from this study was converted to a true stress-strain curve and applied to the models. Figure 5 demonstrates the finite element (FE) models for the channel models having different bearing stages subjected to bearing failure under interior loading conditions. In addition, from this figure, the typical FE meshes for channel models and top load-bearing plates have been illustrated. The mesh sizes of 5 \(\times\) 5 mm and 8 \(\times\) 8 mm were used for channel models and top load-bearing plates, respectively, wherein the conjunction of the web and flanges, finer mesh size was utilised. Figure 4: Experimental web deformation curves for channels with various cross-section sizes [11]. From the ABAQUS 6.25 manual [28], the engineering stress-strain curve from tensile coupon tests from this study was converted to a true stress-strain curve and applied to the models. The equations for this conversion have been presented below:  
\[\sigma_{true}=\sigma(1+\epsilon) \tag{12}\]  
\[\epsilon_{true(pl)}=ln(1+\epsilon)-\frac{\sigma_{true}}{E} \tag{13}\]  
In which \(\sigma_{true}\) is the true stress, \(\epsilon_{true(pl)}\) is the logarithmic plastic strain, E is the modulus of Young, and \(\sigma\) is the engineering stress, while \(\epsilon\) is the engineering strain. To verify the suitability and accuracy of the FE models, the results from laboratory tests were compared against the results obtained from FE modelling. This ultimate bearing capacity comparison from lab tests and numerical modelling for single web channels (\(\mathrm{F_{EXP}}\) and \(\mathrm{F_{FEA}}\)) is summarised in Table 3. The results showed a very good match achieved between the results from the tests and FE models. Looking at the same table in more detail, the average ratio of the test results over FE results (\(\mathrm{F_{EXP}}/\mathrm{F_{FEA}}\)) is 0.99, with a coefficient of variation of 0.01. The channels labelled as C125\(\times\)50-t1.50-N100 and C250\(\times\)75-t3.0-N100 have shown only 3% differences between the results from the tests and FE models with other channels have shown less than 3% errors. Figure 5: Deformation under progressive loading of the C150\(\times\)60 under IL loading. (a) Initial; (b) Before peak; (c) Peak; (d) Post-peak [11]. In addition, the mode of failure comparison from a tested channel specimen against a simulated FE model is shown in Figure 3. This confirms a good web-bearing mode of failure prediction between the developed FE model and lab tests.