## 5 Generation of 3D Models of the Studied Columns and Finite Element (FE) Analysis
### FE Analysis Using ABAQUS
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & \(\lambda_{\text{l}}\) & \begin{tabular}{c} \(\text{P}_{\text{u-EXP}}\) \\ (**kN**) \\ \end{tabular} & \begin{tabular}{c} \(\mu(\text{P}_{\text{u-rand}})\) \\ (**kN**) \\ \end{tabular} & \begin{tabular}{c} \(\mu(\text{P}_{\text{u-rand}})\) \\ (**\text{P}_{\text{u-EXP}}\)** \\ \end{tabular} & \begin{tabular}{c} \(\text{COV}(\text{P}_{\text{u-rand}})\) \\ \end{tabular} & \begin{tabular}{c} \(\text{|\epsilon_{\text{max}}|}\) \\ \end{tabular} \\ \hline R1L1200 & 1.07 & 167.0 & 153.5 & 1.02 & 0.129 & 0.115 \\ R1L2000 & 0.97 & 141.3 & 137.9 & 0.999 & 0.088 & 0.055 \\ R3L2000 & 0.79 & 394.0 & 355.7 & 1.071 & 0.071 & 0.047 \\ \hline \hline \
\begin{tabular}{c} \(\text{SHS}100\times 100\times 2\)-LC-2 m \\ \end{tabular} & 1.04 & 176.0 & 183.0 & 1.066 & 0.162 & 0.096 \\ RHS100 \(\times 50\times 2\)-LC-2 m & 0.92 & 157.0 & 145.3 & 1.041 & 0.085 & 0.117 \\ \hline
\begin{tabular}{c} \(\text{RHS}100\times 50\times 2\)-LC-1 m \\ \end{tabular} & 0.96 & 163.0 & 151.4 & 1.090 & 0.133 & 0.102 \\ RHS120 \(\times 80\times 3\)-LC-1 m & 0.79 & 448.0 & 415.5 & 1.053 & 0.079 & 0.086 \\ \hline \hline \(160\times 80\times 3\) & 1.24 & 537.3 & 505.0 & 0.939 & 0.158 & 0.139 \\ \(200\times 110\times 4\) & 1.07 & 957.0 & 928.0 & 0.958 & 0.081 & 0.070 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._On the other hand, both COV (P\({}_{\text{u-rand}}\)) and \(|\epsilon_{\text{max}}|\) increase as \(\lambda_{\text{l}}\) increases. One explanation is that, the larger the cross-sectional slenderness, the more sensitive the column is to initial localized imperfection. Consequently, the change in the value of modelled localized imperfection can result in a larger discrepancy in the ultimate compressive strength. For the columns with relatively lower cross-sectional slenderness (\(\lambda_{\text{l}}<1.0\)), the values of COV (P\({}_{\text{u-rand}}\)) and \(|\epsilon_{\text{max}}|\) are less than 0.13 and 0.12, respectively. The result indicates that uncertainty in \(\omega\) has no considerable influence on the ultimate compressive strength of these columns. This may be because the columns with relatively lower cross-sectional slenderness are still not sensitive to initial localized imperfection. Besides, the result indicates that \(\omega\) can statistically be modelled as deterministic for these columns, such as using measured \(\omega\) in the experimental study. For the columns with \(\lambda_{\text{l}}\geq 1.2\), COV (P\({}_{\text{u-rand}}\)) are around 0.139-0.238 and the maximum value of \(|\epsilon_{\text{max}}|\) is 17.5%. It demonstrates that random \(\omega\) results in largely scattered ultimate compressive strength for the columns with larger cross-sectional slenderness, and it is important to consider the effect of uncertainty in \(\omega\) on these columns. The distribution of P\({}_{\text{u-rand}}\) for a typical column (R1L1200) is shown in Figure 11. In the figure, P\({}_{\text{u-rand}}\) is normalized by P\({}_{\text{u-EXP}}\). It is found that the distribution of P\({}_{\text{u-rand}}\)/P\({}_{\text{u-EXP}}\) can be fitted by a normal distribution.