# Buckling Resistance of Tapered Steel Columns
## 5 Conclusions  
The presented research highlights the complexity of calculating the buckling resistance for tapered members. The findings can guide structural engineers in selecting the appropriate calculation methodologies for specific scenarios and help bridge the existing gap in design standards. Future research should be focused on conducting experiments to validate these findings further and refine these methodologies. In conclusion, our study on the buckling resistance of members with varying cross-sections revealed several significant findings and implications. * Regulatory gap: Modern standards, such as EN 1993 and AISC 360, lack clear guidelines for calculating the buckling resistance of members with variable cross-sections. This regulatory gap often causes engineers to make conservative assumptions, resulting in suboptimal designs. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & \multicolumn{4}{c}{\(\gamma\) = 1.00–6.00} \\ \hline  & & [PERSON] & & & & & & & \\  & & et al. [26] & [PERSON] et al. [8] & Baptista & & & & & \\  & & et al. [21] & & et al. [32] & [PERSON] [44] & & & & \\ \hline \multirow{4}{*}{**Cond.**} & Mean value & 10.00 & 9.84 & 7.68 & 8.23 & 8.34 & 9.31 & 9.84 \\ \cline{2-10}  & Coefficient of & & & & & & & & \\ variation & & & & & & & & \\ \cline{2-10}  & Number of & & & & & & & \\ variables & & & & & & & & \\ \hline \multicolumn{10}{c}{**Total (Weighted)**} & 7.50 & 8.60 & 7.39 & 6.94 & 7.58 & 6.28 & 8.60 \\ \hline \multicolumn{10}{c}{**Rank**} & 3. & 1. & 4. & 5. & 2. & 6. & 1. \\ \hline \multicolumn{10}{c}{\(\gamma\) = 1.00–8.00} \\ \hline  & & Marques & & & & & & & \\  & & et al. [26] & [PERSON] et al. [8] & [PERSON] & & & & \\  & & et al. [21] & & et al. [32] & [PERSON] [44] & & & \\  & & & & & & & & \\ \hline \multirow{4}{*}{**Cond.**} & Mean value & 10.00 & 3.25 & & 4.95 & 5.51 & 9.40 & 7.79 \\ \cline{2-10}  & Coefficient of & & & & & & & \\ variation & & & & & & & & \\ \cline{2-10}  & Number of & & & & & & & \\ variables & & & & & & & & \\ \hline \multicolumn{10}{c}{**Total (Weighted)**} & 7.50 & 4.13 & 4.66 & 5.53 & 6.15 & 7.15 \\ \hline \multicolumn{10}{c}{**Rank**} & 1. & 6. & 5. & 4. & 3. & 2. \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Assessment and ranking of the applicability of the observed calculation methodologies for non-uniform members, depending on the examined area of the tapering ratio \(\gamma\). * Relevance of the issue: Recent research in well-cited journals highlight the continued relevance and importance of addressing the challenges associated with variable cross-section members. * Calculation proposals: Several calculation methodologies have been proposed for non-uniform elements, each with unique strengths and limitations. These methodologies include the works by [PERSON] et al. [8], [PERSON] et al. [21], [PERSON] et al. [32], [PERSON] [44], [PERSON] et al. [33], and [PERSON] et al. [26]. * Discrepancies across the methodologies: Through an extensive parametric analysis, we observed discrepancies in the calculated buckling resistance of non-uniform members, especially with varying tapering ratios and slenderness values. These variations were particularly pronounced for medium-slenderness members and decreased as the tapering ratio increased. * Optimal tapering ratios: The optimal tapering ratio for the resistance-to-mass gain differed depending on the slenderness category. For low-slenderness members, ratios below \(\gamma\) = 3.0 were economically optimal, while for medium-slenderness members, \(\gamma\) = 1.25 provided the best balance between the resistance and mass gain. High-slenderness members saw a more significant increase in the resistance with the tapering ratio. * Comparison with the benchmark method: Compared to the benchmark method ([PERSON] et al. [26]), various calculation methods projected lower resistances for low to medium-slenderness members. However, beyond a tapering ratio of \(\gamma\) = 3.0, they predicted higher resistances than the benchmark.