## 5 Strengthened Column Bearing Capacity Calculation  
The Design Code for Strengthening Concrete Structures (GB50367-2013) [37] proposed a formula for the axial compression of RC columns strengthened by the concrete enlarged section method, as shown in Equation (1):  
\[N=0.9\varphi\Big{[}f_{\rm 0}A_{\rm c0}+f^{\prime}_{y0}A^{\prime}_{s0}+\alpha_{ cs}\Big{(}f_{c}A_{c}+f^{\prime}_{y}A^{\prime}_{s}\Big{)}\Big{]} \tag{1}\]  
where \(N\) is the design value of the axial pressure of the member after it was strengthened (kN); \(\varphi\) is the stability coefficient of the member and is obtained according to the Code for Design of Concrete Structures (GB50010-2010) [36] (see Table 7). \(A_{\rm c0}\) and \(A_{c}\) are the concrete cross-sectional area before strengthening and the new concrete cross-sectional area after strengthening of the member (mm\({}^{2}\)), respectively; \(f^{\prime}_{y0}\) and \(f^{\prime}_{y}\) are the compressive strengths of concrete before strengthening and concrete for strengthening of the members, respectively (MPa). The cross-sectional area of the existing longitudinal bar in the original column is \(A_{\rm c0}\) and the cross-sectional area of the strengthened longitudinal bar in the new part (mm\({}^{2}\)) is \(A^{\prime}_{s0}\); \(\alpha_{cs}\) is a comprehensive consideration of the new concrete and reinforcement strength using the degree of the correction factor. The specification recommends that ordinary concrete take \(\alpha_{cs}=0.8\).  
With continuous research, materials for strengthening have become abundant. This led to the fact that Equation (1) became inapplicable because of the inapplicability of \(\alpha_{cs}\). [PERSON] [39] derived the value of \(\alpha_{cs}\) for bamboo-reinforced recycled concrete by experimenting with 0.5. [PERSON] [40] used improved post-installed rebar to treat the interface and concluded that the utilization factor \(\alpha_{cs}\) was higher for the added portion of reinforcement and concrete with higher load capacity. This suggested that the existing studies also might not be applicable to this paper. Therefore, the \(\alpha_{cs}\) again needed to be determined when using all-light ceramics concrete for reinforcement. This was the basis for establishing a formula  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(l_{0}/b\) & \(\leq 8\) & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 & 26 & 28 \\ \hline \(l_{0}/d\) & \(\leq 7\) & 8.5 & 10.5 & 12 & 14 & 15.5 & 17 & 19 & 21 & 22.5 & 24 \\ \hline \(l_{0}/i\) & \(\leq 28\) & 35 for the axial compression of RC columns strengthened by the all-light ceramsite-concrete enlarged section method.  
To achieve this, the test values of C3-C6 were substituted into Equation (1). After calculation, the \(\alpha_{cs}\) for these four specimens were 0.807, 0.849, 0.810, and 0.916, respectively. This showed that \(\alpha_{cs}\) was significantly influenced by the interface treatment. Thus, considering the safety factor, \(\alpha_{cs}\) is recommended to take the value of 0.8 when using ceramsite concrete for reinforcement in the relevant practical works. In addition, if the interface treatment of implanting reinforcement and adding interface agent was planned to be used at the same time, \(\alpha_{cs}\) could be set as 0.9 for calculation.  
Additionally, the ratio of the ultimate bearing capacity after strengthening and the ultimate bearing capacity before strengthening (PUCn/PUC1) was used to measure the strengthening effect. The relationship between the reinforcement effect and \(\alpha_{cs}\) was established as shown in Table 8 and Figure 11. The linear relationship between the two is excellent and R\({}^{2}\) is 0.99. This pointed out that the utilization of reinforced concrete and reinforcing steel greatly affected the reinforcement effect.