## 3 Investigated Columns
### Layout and Test Results  
The studies and analyses are based on the following experimental research for validating non-linear calculations for slender column elements. Several series of tests on slender columns were carried out and the failure loads were compared to the results of non-linear analyses and simplified formats. The concrete material used to construct the first series of slender columns is C45/55 while the steel used is BST 500B. In the first series, 6 columns (see also [4]) were tested. Figure 5 shows the cross-sectional dimensions and layout of the tested columns while Table 1 lists the parameters used in the calculation according to different codes. Figure 6 presents the results of the experiments while Table 2 lists the descriptive parameters used for the slender columns. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Description** & **Symbol** & **Unit** & **Value** \\ \hline Width of column cross-section & \(b\) & mm & 240 \\ Height of column cross-section & \(h\) & mm & 150 \\ Distance from topmost compression face to the centroid of compression reinforcement & \(d^{\prime}\) & mm & 33 \\ Distance from topmost compression face to the centroid of tensile reinforcement & \(d\) & mm & 117 \\ Cross-sectional area of RC column & \(A_{\rm c}\) & mm\({}^{2}\) & 36,000 \\ Cross-sectional area of tensile reinforcement & \(A_{\rm s}\) & mm\({}^{2}\) & 307.88 \\ Cross-sectional area of compression reinforcement & \(A_{\rm s}\) & mm\({}^{2}\) & 307.88 \\ Characteristic compressive strength of concrete (for assoc. parameters see table in Section 4.5 & \(f_{\rm w}\) & N/mm\({}^{2}\) & 55 \\ Yield strength of reinforcing reinforcement & \(f_{\rm w}\) & N/mm\({}^{2}\) & 500 \\ Young modulus of reinforcing reinforcement & \(E_{\rm s}\) & N/mm\({}^{2}\) & 200,000 \\ Ultimate strain of concrete in compression & \(\epsilon_{\rm cu}\) & - & Varied \\ Ratio of the depth of equivalent compression block to that of actual compression & \(\beta\) & - & Varied \\ Eccentricity & \(e\) & mm & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of parameters used in the calculation. Figure 4: ECOV simulation procedure not including correlation between basic variables. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **Nmax (kN)** & **e2 (mm)** & **Mmax (kNm)** \\ \hline S1-1 & 324.4 & 57.6 & 31.7 \\ S1-2 & 323.4 & 42.7 & 26.8 \\ S1-3 & 332.6 & 38.3 & 26.0 \\ S1-4 & 271.2 & 58.4 & 26.7 \\ S1-5 & 296.0 & 59.4 & 29.4 \\ S1-6 & 311.4 & 55.0 & 29.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistical parameters of the experimental results of the considered test series. C45/55 without considering sample size aspects. Figure 5: Reinforcement and formwork drawings of the investigated slender columns. The points shown in Figure 6 represent the tested maximum axial force capacity \(N_{max}\) of each single column. All of the maximum \(N\)-\(M\) gradient points show the system stability failure before the mean \(I\)-\(D\) (left from the \(I\)-\(D_{m}\)) as defined in EN 1992-1-1 [8]. The right-hand graphic of Figure 6 shows the load-vs.-strain graphs in the fracture-prone cross-section at half the height of the columns. The concrete compressive strains in the compressed fiber of the cross-section were recorded for the column stability loss at between 1.4 and 1.8% and were far away from the permissible concrete compressive strains of 3.5%. The associated concrete/reinforcement tension strains in the pulled fiber of the cross-section were recorded at between 1.4 and 3.1%, see Figure 6. The model uncertainties of the experimental test results were derived following [30] and EN1990 Annex D (Edition: 2013-03-15) with \(\theta_{Y}=Y_{mm}/Y_{k}\). This results for \(N_{max}\) to \(\theta_{Nmax}\) = 1.06, for \(\varepsilon_{2}\) at \(N_{max}\) to \(\theta_{c2,N_{max}}\) = 1.02, and for \(M\) at \(N_{max}\) to \(\theta_{M,N_{max}}\) = 1.01.