# Experimental Research on Mechanical Performance of SSRC Columns under Eccentric Compression
## 4 Analysis of Normal Section Capacity
### Model Optimization  
The deviation between test value \(N_{\text{u}}\) and calculated value \(N_{\text{u}}^{t}\) is related to the additional bending moment generated by the SSRC columns during loading. In the existing empirical theory, for columns with a length-to-section-height ratio of \(l_{0}/h_{0}\leq 8\), the additional bending moment (second-order effect) caused by the lateral displacement \(f\) is not considered. This means that specimens SSRC1-SSRC8 are regarded as short columns, and it is not necessary to consider the second-order effect when calculating their ultimate load. However, as depicted in Figure 6, the experimental SSRC columns produced significant lateral displacements, which varied with the load. Therefore, the second-order effect should be considered when calculating the ultimate load of SSRC columns.  
The mechanical properties of SSRC members are different. When using the increasing eccentricity method in GB50010-2010 or the increasing bending moment method in ACI 318-14, the deviation is reduced; however, the results are still not accurate. As is evident from the data in Table 3, this deviation is also linked to relative eccentricity \(e_{0}/h_{0}\). Therefore, based on the test and simulation results, a calculation method for amplification factor \(\eta\) of eccentricity for SSRC columns is proposed. As depicted in Figure 10, the initial eccentricity can be calculated as  
\[e_{\text{i}}=e_{0}+f=\bigg{(}1+\frac{f}{e_{0}}\bigg{)}e_{0}=\eta e_{0} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**Column**} & \(f_{\text{c}}\) & \multirow{2}{*}{\(e_{0}\)} & \(A_{s}/A^{{}^{\prime}s}_{s}\) & \multirow{2}{*}{\(N_{\text{u}}\) (kN)} & \multicolumn{2}{c}{**Equation (1)**} & \multicolumn{2}{c}{**Optimization Model**} \\ \cline{5-10}  & & & & **(MPa)** & & & **(mm\({}^{2}\))** & & **\(N_{\text{u}}^{t}\)** & \(N_{\text{u}}^{t}/N_{\text{u}}\)** & \(N_{\text{u}}^{t}/N_{\text{u}}\) \\ \hline \multirow{5}{*}{**Test results**} & SSRC1 & 20.1 & 80 & 226 & 1075 & 813.9 & 0.757 & 821.3 & 0.764 \\ \cline{2-10}  & SSRC2 & 20.1 & 270 & 226 & 173 & 202.7 & 1.172 & 158.3 & 0.915 \\ \cline{1-1}  & SSRC3 & 20.1 & 80 & 402 & 1135 & 913.7 & 0.805 & 919.0 & 0.810 \\ \cline{1-1}  & SSRC4 & 20.1 & 150 & 402 & 640 & 677.9 & 1.059 & 639.0 & 0.998 \\ \cline{1-1}  & SSRC5 & 20.1 & 200 & 402 & 358 & 422.3 & 1.180 & 347.7 & 0.971 \\ \cline{1-1}  & SSRC6 & 20.1 & 270 & 402 & 220 & 281.6 & 1.280 & 222.5 & 1.011 \\ \cline{1-1}  & SSRC7 & 20.1 & 80 & 982 & 1280 & 1273.9 & 0.995 & 1275.0 & 0.996 \\ \cline{1-1}  & SSRC8 & 20.1 & 270 & 982 & 465 & 566.9 & 1.219 & 464.7 & 0.999 \\ \hline \multirow{5}{*}{**FEA results**} & & 20.1 & 150 & 226 & 525 & 558.2 & 1.063 & 519.6 & 0.990 \\  & & 20.1 & 200 & 226 & 267 & 319.0 & 1.195 & 257.2 & 0.963 \\ \cline{1-1}  &  
Assuming that the lateral displacement curves of the SSRC columns are sinusoidal, the lateral deflection is given as  
\[f=\phi\frac{l_{0}^{2}}{\pi^{2}} \tag{3}\]  
where \(\phi\) is the sectional curvature at failure, as seen in Figure 10b. The relationship among concrete strain \(\varepsilon_{\text{cu}}\), reinforcement strain \(\varepsilon_{\text{y}}\), and \(\phi\) can be denoted as follows:  
\[\phi=\frac{\varepsilon_{\text{cu}}+\varepsilon_{\text{y}}}{h_{0}} \tag{4}\]  
Based on the above equations and considering the impact of the relative eccentricity, \(\eta\) can be expressed as  
\[\eta=1+\frac{(\varepsilon_{\text{cu}}+\varepsilon_{\text{y}})l_{0}^{2}}{\pi^ {2}h_{0}e_{0}} \tag{5}\]  
where \(\zeta\) is the correction coefficient of the sectional curvature related to the relative eccentricity. Based on the test and FEA results, \(\zeta\) can be denoted as follows:  
\[\zeta=7.4\frac{e_{0}}{h_{0}}-0.3 \tag{6}\]