## 4 Comparison of Critical Buckling Force with Design Codes  
Experimentally obtained buckling forces for the CFT columns N\({}_{\text{TEST}}\) are compared with three design codes: Eurocode 4-EC4 [18], American standard--ACI [30] and the Australian standard--AS [31,32]. The buckling forces were calculated as proposed in design codes but with an experimentally obtained effective column buckling length of 0.8 L. The input parameters for the material characteristics of steel are E = 210 GPa, f\({}_{\text{y}}\) = 355 MPa and the concrete cylinder compressive strength f\({}_{\text{c}}\)\({}^{\prime}\) = 26.70 MPa. Following the EC4, two different stiffnesses are used: results with the effective stiffness of the composite cross-section according to the first-order analysis are denoted as EC4\({}_{\text{I}}\), and results with the effective stiffness of the composite cross-section according to the second-order analysis are denoted as EC4\({}_{\text{II}}\).  
Table 7 compares tests and the results calculated by the design codes: N\({}_{\text{EC4,I}}\), N\({}_{\text{EC4,II}}\) and N\({}_{\text{ACI/AS}}\).  
These differences among the values of the critical buckling forces calculated according to design codes occur due to differences in the stiffness of the composite section. Design  
\begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **Pile Diameters [mm]** & **Leff, num/L** & **P\({}_{\text{c,num}}\) [kh]** \\ \hline \multirow{3}{*}{CS1} & \(\mathcal{O}\)350 & 0.845 & 233.6 \\  & \(\mathcal{O}\)450 & 0.789 & 251.6 \\  & \(\mathcal{O}\)600 & 0.724 & 273.7 \\ \hline \multirow{3}{*}{CS2} & \(\mathcal{O}\)350 & 0.850 & 309.4 \\  & \(\mathcal{O}\)450 & 0.795 & 327.3 \\  & \(\mathcal{O}\)600 & 0.727 & 356.2 \\ \hline \multirow{3}{*}{CS3} & \(\mathcal{O}\)350 & 0.853 & 347.4 \\  & \(\mathcal{O}\)450 & 0.802 & 373.6 \\  & \(\mathcal{O}\)600 & 0.731 & 406.9 \\ \hline \multirow{3}{*}{CS4} & \(\mathcal{O}\)350 & 0.857 & 451.2 \\  & \(\mathcal{O}\)450 & 0.811 & 483.7 \\ \cline{1-1}  & \(\mathcal{O}\)600 & 0.734 & 528.3 \\ \hline \end{tabular}
\end{table}
Table 6: Numerical results for the effective buckling length and buckling force for different pile diameters for the specimen CS1–CS4.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **N\({}_{\text{TEST}}\)/N\({}_{\text{EC4,I}}\)** & **N\({}_{\text{TEST}}\)/N\({}_{\text{EC4,II}}\)** & **N\({}_{\text{TEST}}\)/N\({}_{\text{ACUAS}}\)** \\ \hline CS1 & 0.934 & 1.087 & 1.141 \\ CS2 & 0.938 & 1.076 & 1.074 \\ CS3 & 0.946 & 1.106 & 1.182 \\ CS4 & 0.928 & 1.069 & 1.081 \\ Median & 0.936 & 1.081 & 1.111 \\ \hline \end{tabular}
\end{table}
Table 7: Comparison between the buckling force obtained by experiments and calculated by design codes.  
codes do not consider the stiffness of the concrete portion of the section in the same way. According to EC4, the stiffness of the uncracked concrete portion of a section is multiplied by a coefficient of 0.6 (in the theory of the first order) or 0.45 (in the theory of the second-order--EC4,II). In ACI/ AS calculations, this coefficient is 0.2 (the long-term effects were not considered). Additionally, in EC4,II calculations, the stiffness of the steel tube is decreased by 10% (i.e., multiplied by 0.9).  
These results show that buckling forces predicted by the EC4 are more accurate than the results predicted by the ACI and AS. However, the first-order EC4 analysis predictions of critical buckling force are not on the safe side. Therefore, it is advised to perform the second-order EC4 analysis in practice. The ACI and AS codes obtained are the same, on the safe side but slightly more conservative.