# Experimental Study on Slender CFRP-Confined Circular RC Columns under Axial Compression
## 4 Comparisons for FRP-Confined RC Columns
### Stability Coefficient
Two different curves are shown in Figure 6 probably bec \begin{table}
\begin{tabular}{c c c} \hline \hline
**Codes** & **Bearing Capacity Formulas** & **Comments** \\ \hline GB 50367-2013 & \(\begin{array}{c}N\leq\\ 0.9\Big{[}(f_{c0}+4\sigma_{l})A_{cor}+f^{\prime}_{y0}A^{\prime}_{s0}\Big{]} \end{array}\) & \(\begin{array}{c}\sigma_{l}=0.5\xi_{lc}k_{c}\rho_{f}F_{\ell}\varepsilon_{fc} \\ \rho_{f}=4 nt_{f}/D\end{array}\) \\ \hline CSA 806-12 & \(\begin{array}{c}f^{\prime}_{cc}=0.85f^{\prime}_{c}+k_{l}\xi_{c1}f_{f}\\ P_{0}=\alpha_{1}f^{\prime}_{cc}\big{(}A_{g}-A_{st}\big{)}+f_{y}A_{st}\\ \end{array}\) & \(\begin{array}{c}f^{\prime}_{cc}=0.85f^{\prime}_{c}+k_{l}\xi_{c1}f_{f}\\ \kappa_{1}=0.85-0.0015f^{\prime}_{c}\geq 0.67\\ f_{l}=6.7(k_{c1}f_{l})-0.127\\ f_{l}=2 nt_{f}F_{f}/D;f_{f}=\varepsilon_{fc}E_{f}\end{array}\) \\ \hline ACI 440.2R-17 & \(\begin{array}{c}p_{n,\max}=\\ 0.8\big{[}0.85f^{\prime}_{cc}\big{(}A_{g}-A_{st}\big{)}+f_{y}A_{st}\big{]} \end{array}\) & \(\begin{array}{c}f^{\prime}_{cc}=f^{\prime}_{c}+\psi_{f}3.3\kappa_{d}f_{l}\\ f_{l}=\frac{E_{l}nt_{f}\varepsilon_{fc}}{f_{d}};\varepsilon_{fc}=\kappa\epsilon \varepsilon_{fu}\\ \end{array}\) \\ \hline CNR DT200-2013 & \(\begin{array}{c}N_{Rcc,d}=\frac{1}{\tau_{hd}}A_{c}f_{ccd}+f_{yd}A_{s}\end{array}\) & \(\begin{array}{c}\frac{f_{tot}}{f_{sd}}=1+2.6\Big{(}\frac{f_{tot}}{f_{sd}} \Big{)}^{2/3}\\ f_{d\ell,d\ell}=\frac{1}{2}\rho_{f}E_{f}\varepsilon_{fd,d\ell};\\ \varepsilon_{fd,d\ell}=\kappa\epsilon_{fc}E_{f}\end{array}\) \\ \hline \hline \end{tabular} Note: \(N_{f}P_{0},P_{n,\max},N_{Rcc,d}=\) factored axial capacity; \(f^{\prime}_{fc},f_{sd}=\) confined concrete compressive strength; \(f^{\prime}_{c},f_{0},f_{sd}=\) unconfined cylinder compressive strength of concrete; \(f^{\prime}_{y},f^{\prime}_{y0},f_{yd}=\) specified yield strength of steel reinforcement; \(A_{st},A^{\prime}_{s0},A_{s}=\) total area of longitudinal reinforcement \(A_{g},A_{c},A_{sat}\) = gross area of concrete section; \(\sigma_{l},f_{l},f_{l,eff}=\) effective confinement pressure; \(\rho_{f}=\) geometric strengthening ratio; \(\beta_{c}=\) influence coefficient of concrete strength taken as 1.0; \(k_{c},k_{c1},\kappa_{a}=\) confinement efficiency factor for circular columns, taken as 0.95,1,0.1,0 respectively; \(E_{f},E_{f}=\) modulus of elasticity of FRP; \(\varepsilon_{fc},\varepsilon_{fc,d\ell}=\) effective strain in FRP reinforcement; \(f_{l},f_{l}=\) thickness of one only of FRP; \(n=\) number of piles of FRP; \(D=\) diameter of circular columns; \(f_{f}=\) stress in FRP composite; \(f_{fx}=\) ultimate tensile strength of FRP composite; \(\alpha_{1}=\) ratio of average stress in rectangular compression block to the specified concrete strength; \(\psi_{f}=\) FRP strength reduction factor taken as 0.95; \(\gamma_{Rd}=\) partial factor taken as 1.10; \(\varepsilon_{fc}=\) effective strain in FRP; \(\kappa_{a}=\) efficiency factor for FRP strain; \(\varepsilon_{f_{av}},\varepsilon_{fx}=\) ultimate strain of FRP reinforcement.  
\end{table} 
Table 5: Comparisons of bearing capacity formulas in concrete structure design codes. Figure 6: Effect of slenderness on the stability coefficient. reinforcement ratio of longitudinal reinforcement considerably affect the stability for FRP-confined RC columns. Equation (4) is applicable to circular RC columns constrained by FRP cloth in the hoop direction, whereas Equation (5) is applicable to circular RC columns constrained by FRP tubes. The stability coefficient between the test results and the code (GB 50010) is compared in Figure 7[19]. The stable performance of specimens confined through lateral confinement with CFRP is slightly different from that of unwrapped RC columns. With the increasing of slenderness ratio, the stability coefficient of CFRP-confined specimens is below that of unwrapped specimens, as proposed by GB50010.