# Validation of AISI Design of Cold-Formed Steel Beams Using Non-Linear Finite Element Analysis
## 4 Conclusions  
In this paper, a comparative study is conducted on eight selected CFS channel members. To control torsion, loads are applied at the shear center of each respective section, and to control torsional buckling, bracing is provided at a regular interval of L/3. The four-point bending method is adopted. Manual calculations are performed on the basis of the AISI DSM method to capture the non-linear buckling behavior. CUFSM is used to perform linear analysis, then these results are used to perform a non-linear analysis via DSM to identify the failure strengths. In ABAQUS, models are developed to perform a non-linear FEM analysis. It is observed that the governing failure modes for all the eight specimens were local, distortional, and a combination of these modes. The results acquired by all three methods mentioned are compared with the AISI charts, and the following conclusions can be drawn:  
1. The AISI charts can be used by designers with confidence for practical designs because of their conservative nature, in most cases. However, to achieve economy and for speedy design, the CUFSM software may be employed. For detailed design  
Figure 12: Comparison of nominal flexural capacities predicted by AISI charts, DSM, ABAQUS, and CUFSM. ing, when sufficient time is available, ABAQUS can provide economical, safe, and reliable solutions. 2. DSM is a scientifically sound method that aligns closely with the AISI chart, providing reliable predictions, with only minor discrepancies. 3. The ABAQUS finite element analysis results show a small to moderate deviation from the AISI charts, with percentage differences ranging from \(-2.47\%\) to \(+14.03\%\). 4. CUFSM consistently predicts higher moment capacities compared to those in the AISI charts, with positive percentage differences ranging from \(+5.35\%\) to \(+10.49\%\). 5. The difference between the DSM and ABAQUS flexural strength results with respect to the AISI charts varies on both the plus and minus sides. 6. In the selected sections, as the thickness decreases, the results from all the four approaches come closer to each other. This means that the thin wall behavior is captured well by all of these methods. 7. It is to be noted that for the selected sections and their specific unbraced lengths, AISI charts predict higher strengths for three out of eight sections when compared with the ABAQUS results, with a maximum difference of \(2.47\%\). 8. The DSM values vary from those in the AISI charts on both the plus and minus sides, with a maximum difference of \(13.68\%\) and the charts being on the unsafe side. Conceptualization, M.A.K. and Z.A.S. ; methodology, M.A.K., R.F.M. and Z.A.S. ; software, M.A.K. and R.F.M. ; validation, R.F.M. ; formal analysis, M.A.K. and R.F.M. ; investigation, R.F.M. ; resources, M.A.K., R.F.M. and Z.A.S. ; data curation, R.F.M. ; writing--original draft preparation, R.F.M. ; writing--review and editing, R.M. ; visualization, M.A.K., R.F.M. and Z.A.S. ; supervision, Z.A.S. ; project administration, M.A.K. and Z.A.S. ; funding acquisition, M.A.K. and Z.A.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the Higher Education Commission of Pakistan, grant number NRPU-15859, in collaboration with Banu Mukhtar Steel (Pvt.) Ltd. Pakistan. Not applicable. The data used to support the findings of this study are available from the authors upon request. The authors would like to thank the University of Engineering and Technology Lahore for their support in allowing us to use the licensed student version of ABAQUS.