# Validation of AISI Design of Cold-Formed Steel Beams Using Non-Linear Finite Element Analysis
## 3 Results
### Comparison  
The AISI chart, the AISI DSM method, CUFSM, and ABAQUS nominal strengths for non-linear buckling are compared; the evaluation is shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**S/No**} & \multirow{2}{*}{**Section**} & \multirow{2}{*}{**\(M_{n}\)**} \\  & & & **N-mm (Kip-in)** \\ \hline \multirow{2}{*}{1} & 203 CS64 \(\times\) 2.7 & 19,413,400 \\  & (8 CS2.5 \(\times\) 105) & (171.8) \\ \hline \multirow{2}{*}{2} & 203 CS64 \(\times\) 2.2 & 14,546,490 \\  & (8 CS2.5 \(\times\) 085) & (128.7) \\ \hline \multirow{2}{*}{3} & 203 CS64 \(\times\) 1.8 & 11,243,500 \\  & (8 CS2.5 \(\times\) 070) & (99.5) \\ \hline \multirow{2}{*}{4} & 203 CS64 \(\times\) 1.7 & 11,537,300 \\  & (8 CS2.5 \(\times\) 065) & (102.1) \\ \hline \multirow{2}{*}{5} & 152 CS64 \(\times\) 2.7 & 14,452,700 \\  & (6 CS2.5 \(\times\) 105) & (127.9) \\ \hline \multirow{2}{*}{6} & 152 CS64 \(\times\) 2.2 & 11,492,100 \\  & (6 CS2.5 \(\times\) 085) & (101.7) \\ \hline \multirow{2}{*}{7} & 152 CS64 \(\times\) 1.8 & 8,904,400 \\  & (6 CS2.5 \(\times\) 070) & (78.8) \\ \hline \multirow{2}{*}{8} & 152 CS64 \(\times\) 1.6 & 7,797,000 \\  & (6 CS2.5 \(\times\) 065) & (69.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ABAQUS flexural capacities of selected sections. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**S/No**} & \multirow{2}{*}{**Section**} & \multirow{2}{*}{**AISI**} & \multirow{2}{*}{**DSM**} & \multirow{2}{*}{**ABAQUS**} & \multirow{2}{*}{**CUFSM**} \\  & & & & **Percentage** & & & **Percentage** \\  & & \(M_{n}\) & \(M_{n}\) & **Difference** & \(M_{n}\) & **Difference** \\  & & **kN-m** & **kN-m** & **with AISI** & **kN-m** & **with AISI** & **kN-m** & **with AISI** \\  & & **(kip-in)** & **(kip-in)** & **CHART** & **(kip-in)** & **CHART** & **(kip-in)** & **CHART** \\  & & & **(\%)** & & **(\%)** & & **(\%)** \\ \hline \multirow{2}{*}{1} & 203 CS64 \(\times\) 2.7 & 19.89 & 18.32 & \(-8.57\) & 19.41 & \(-2.47\) & 21.76 & +9.44 \\  & (8 CS2.5 \(\times\) 105) & (176.00) & (162.10) & & (171.80) & & (192.61) & \\ \hline \multirow{2}{*}{2} & 203 CS64 \(\times\) 2.2 & 14.80 & 14.90 & +0.68 & 14.55 & \(-1.72\) & 16.11 & +8.80 \\  & (8 CS2.5 \(\times\) 085) & (131.00) & (131.90) & & (128.73) & & (142.53) & \\ \hline \multirow{2}{*}{3} & 203 CS64 \(\times\) 1.8 & 11.27 & 11.83 & +4.97 & 11.24 & \(-0.27\) & 12.34 & +9.54 \\  & (8 CS2.5 \(\times\) 070) & (99.70) & (104.70) & & (99.50) & & (109.21) & \\ \hline \multirow{2}{*}{4} & 203 CS64 \(\times\) 1.7 & 10.12 & 10.63 & +5.04 & 11.54 & +14.03 & 11.04 & +9.04 \\  & (8 CS2.5 \(\times\) 065) & (89.60) & (94.10) & & (102.10) & & (97.7) & \\ \hline \multirow{2}{*}{5} & 152 CS64 \(\times\) 2.7 & 14.13 & 12.43 & \(-13.68\) & 14.45 & +2.26 & 14.88 & +5.35 \\  & (6 CS2.5 \(\times\) 105) & (125.00) & (110.00) & & (127.90) & & (131.69) & \\ \hline \multirow{2}{*}{6} & 152 CS64 \(\times\) 2.2 & 10.66 & 10.14 & \(-5.13\) & 11.49 & +7.79 & 11.61 & +8.94 \\  & (6 CS2.5 \(\times\) 085) & (94.30) & (89.70) & & (101.70) & & (102.73) & \\ \hline \multirow{2}{*}{7} & 152 CS64 \(\times\) 1.8 & 8.16 & 8.40 & +2.89 & 8.90 & +9.07 & 8.91 & +9.22 \\  & (6 CS2.5 \(\times\) 070) & (72.20) & (74.30) & & (78.80) & & (78.86) & \\ \hline \multirow{2}{*}{8} & 152 CS64 \(\times\) 1.6 & 7.36 & 7.76 & +5.43 & 7.80 & +5.98 & 8.13 & +10.49 \\  & (6 CS2.5 \(\times\) 065) & (65.10) & (68.70) & & (69.00) & & (71.93) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between the AISI chart, AISI DSM, CUFSM, and ABAQUS. The results of Table 5 are graphically shown in Figure 12. The comments regarding the results shown in Table 5 are given below:  
1. The DSM results are in relatively good agreement with the AISI chart, with percentage differences ranging from \(-8.57\%\) to \(+5.43\%\). The observed differences are likely due to the basic approximations in the DSM for predicting the strength of cold-formed steel sections. 2. ABAQUS provides a more detailed and potentially more accurate prediction of moment capacities.