## 5 Conclusions  
The work described in this paper was able to show that the geometrical and mathematical non-linear design of slender members, such as columns in the ultimate limit state, is still a matter of controversy because of the known inconsistencies in the design concepts. The analyses which were carried out show that the stability failure of the investigated compressed slender concrete columns calculated by non-linear numerical format occur before reaching the material capacity in the critical cross-section and hence failure occurs before the scattering Interactions Diagrams (_I-D_) according to EN 1992-1. In addition, the probabilistic non-linear finite element analyses (P-NLFEM), based on an advanced Latin Hyper Cube Sampling technique, indicate that the computed structural responses in terms of axial forces are higher than those derived from experiments, which can be evaluated as a failure to meet the required safety level. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Safety Level**} & \multicolumn{4}{c}{\(\beta\) = 3.8} & \multicolumn{4}{c}{\(\beta\) = 4.2} \\ \hline  & \(\gamma_{\text{RN}}\) & \(\begin{array}{c}\mathbf{N_{d}}\\ \mathbf{(k\mathbf{N})}\end{array}\) & \(\gamma_{\text{RTM}}\) & \(\begin{array}{c}\mathbf{M_{d}}\\ \mathbf{(k\mathbf{N})}\end{array}\) & \(\gamma_{\text{RN}}\) & \(\begin{array}{c}\mathbf{N_{d}}\\ \mathbf{(k\mathbf{N})}\end{array}\) & \(\gamma_{\text{RTM}}\) & \(\begin{array}{c}\mathbf{M_{d}}\\ \mathbf{(k\mathbf{N})}\end{array}\) \\ \hline Stiffness Method & 1.28 & 170.27 & 1.28 & 21.64 & 1.32 & 165.88 & 1.32 & 21.08 \\ \hline \multirow{4}{*}{\(\gamma_{Rd}=1.1\)} & BOKU & 1.37 & 246.33 & 1.32 & 17.87 & 1.41 & 238.36 & 1.36 & 17.35 \\ \cline{2-10}  & STUBA & 1.41 & 228.90 & 1.24 & 16.11 & 1.46 & 220.81 & 1.27 & 15.75 \\ \cline{2-10}  & U-MINHO & 1.41 & 232.15 & 1.32 & 20.96 & 1.46 & 223.93 & 1.36 & 20.35 \\ \cline{2-10}  & UNIZG-FCE & 1.32 & 226.80 & 1.24 & 22.70 & 1.36 & 220.23 & 1.27 & 22.18 \\ \hline \multirow{4}{*}{\(\gamma_{Rd}=1.06\)} & BOKU & 1.37 & 255.67 & 1.32 & 18.54 & 1.32 & 247.30 & 1.32 & 18.00 \\ \cline{2-10}  & STUBA & 1.41 & 237.49 & 1.24 & 16.71 & 1.41 & 229.10 & 1.36 & 16.33 \\ \cline{1-1} \cline{2-10}  & U-MINHO & 1.41 & 240.91 & 1.32 & 21.75 & 1.46 & 232.34 & 1.27 & 21.12 \\ \cline{1-1} \cline{2-10}  & UNIZG-FCE & 1.32 & 235.38 & 1.24 & 23.55 & 1.46 & 228.51 & 1.36 & 23.02 \\ \hline \multicolumn{2}{c}{Experiments} & 1.24 & 235.41 & 1.28 & 20.91 & 1.23 & 230.07 & 1.32 & 20.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Global resistance factor and design resistance according to ECOV format. The modeling uncertainties used for this study came from the previous modeling for NLFEM models and were 1.04 for the C45/55 columns and 1.06 for the C100/115 columns. In the following global resistance factor studies, model uncertainties of 1.06 and 1.10 were taken into account. The global resistance factors determined using the \"Estimation of the Coefficient of Variation\" (ECOV) and the resulting slender column axial capacity showed, as expected when using a model uncertainty factor of 1.10, an overestimation of the axial capacity for the majority of the columns. According to such findings, higher model uncertainty factors (i.e., \(\gamma_{Rd}>\) 1.10) are recommended for the design and safety assessment of slender columns using standard NLFEM. From the sensitivity studies at the cross-sectional level in the middle height of the column on one side and the sensitivity studies of the whole column on the other side, it can be seen that the sensitivities behave very differently in relation to the normal force and the horizontal force. The concrete modulus of elasticity is most significant in relation to the normal force at the cross-sectional level compared to the component level, but its importance diminishes with increasing load.