# Experimental Study on Slender CFRP-Confined Circular RC Columns under Axial Compression
## 4 Comparisons for FRP-Confined RC Columns
### Stability Coefficient  
The stability coefficient of FRP-confined RC column is defined as  
\[\varphi=\frac{N_{ul}}{N_{ub}} \tag{1}\]  
where \(N_{ul}\) = experimental ultimate load of slender columns, and \(N_{ub}\) = experimental ultimate load of columns with a base slenderness of 12. In Table 4, because there is no bearing capacity data of columns with a slenderness of 12 in group 2, group 4 and group 5, interpolation method is used to calculate the bearing capacity in group 4 and group 5. The bearing capacity of a column with a slenderness of 12 in group 2 can be calculated by the equation  
\[N_{ub}=f_{cc}^{\prime}A_{g}+f_{y}A_{st} \tag{2}\]  
\[f_{cc}^{\prime}=f_{cc}^{\prime}+3.3f_{l,a}\] \[f_{l,a}=\frac{2F_{ul}r_{l}r_{f,c}}{D} \tag{3}\]  
where \(f_{cc}^{\prime}\) = compressive strength of the FRP-confined concrete. Equation (3) is proposed by [PERSON] and [PERSON] [18]. All parameters are illustrated in Table 5.  
Figure 5: Load vs. strain curve. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Specinness** & **H (mm)** & **D (mm)** & **L/D** & \(\lambda\) & \(f_{\mathbf{m}}\) & \(f_{\mathbf{m}}\) & \(E_{t}\) & \(\epsilon_{\mathbf{m}}\) & \(t_{t}\) (mm) & \(f_{\mathbf{m}}\) & \(\mathbf{A}_{s}\)\({}^{\prime}\) & \(N_{\mathbf{u}}\) (\(\mathbf{b}\)N) & \(\boldsymbol{\varphi}\) & **Type** & **Reference** \\ \hline  & C-1-12-2 & 600 & & 3 & 12 & & & & & & & & 1214 & 1.0 & & \\  & C-1-24 & 1000 & & 5 & 20 & & & & & & & & 1218 & 1.0 & & \\
1 & C-1-32-6 & 1600 & 200 & 8 & 32 & & & & & & & & 1145 & 0.94 & CFRP & Present study \\  & C-1-40-8 & 2000 & & 10 & 40 & 21.4 & 4330 & 237 & 0.017 & 0.167 & 240 & (648) & 1100 & 0.91 & cloth & Present study \\  & C-1-48-10 & 2400 & & 12 & 48 & & & & & & & & 1010 & 0.83 & & \\  & C-1-56-12 & 2800 & & 14 & 56 & & & & & & & & 890 & 0.73 & & \\ \hline  & G1-1C & 610 & & 4 & 16 & & & & & & & & & 772 & 0.98 & CFRP & Ghali [16] \\
2 & G2-1C & 915 & 150 & 6 & 24 & 20 & 3500 & 233.333 & 0.015 & 0.16 & 365 & 392.31 & 720 & 0.92 & cloth & & \\  & G3-1C & 1220 & & 8 & 32 & & & & & & & & 658 & 0.84 & & \\ \hline  & 8-S-I & 610 & & 4 & 8 & & & & & & & & 1652 & - & \\
3 & 12-S-I & 912 & & 6 & 12 & & & & & & & & 471 & 1454 & 1.00 & CFRP & Abdallah [7] \\  & 16-S-I & 126 & 152 & 8 & 16 & 30 & 345 & 20.690 & 0.012 & 2.65 & 460 & (6410) & 1202 & 0.83 & tube & & \\  & 20-S-I & 1500 & & 10 & 20 & & & & & & & & 1127 & 0.78 & \\ \hline  & SG-S3 & 300 & & 2 & 8 & & & & & & & & 1370 & - & \\
4 & SHC-3 & 600 & & 4 & 16 & & & & & & & & 1300 & 0.97 & GFRP & Sarkvanan [17] \\  & S2 HC-3 & 900 & & 6 & 24 & 42.6 & 446.9 & 13.965 & 0.0302 & 3 & 450 & (648) & 1275 & 0.96 & cloth & \\  & 532G-3 & 1200 & & 8 & 32 & & & & & & & & 1190 & 0.89 & & \\ \hline  & R-C & 1305 & & 2.1 & 4 & & & & & & & & 1659.1 & - & \\  & RC-2 & 813 & & 5.5 & 11 & & & & & & & & 1362.2 & - & \\  & RC-3 & 1372 & & 9.3 & 18 & & & & & & & & 102.5 & 0.78 & & \\
5 & RC-4 & 1651 & 147.3 & 11.2 & 22 & 22.4 & 218.6 & 69.640 & 0.031 & 3.68 & - & - & - & 387.7 & 0.64 & \\  & RC-5 & 2286 & & 15.5 & 31 & & & & & & & & 648.6 & 0.49 & tube & \\  & RC-6 & 2951 & & 17.6 & 35.2 & & & & & & & & & 952 & 0.45 & \\  & RC-7 & 2743 & & 18.6 & 37.2 & & & & & & & & 475.2 & 0.36 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of test results of FRP-confined circular RC columns. Table 4 shows the stability coefficient obtained by Equation (1). The relationship between stability coefficient and slenderness ratio according to the experimental results is presented in Figure 6. By quadratic regression, the equation of stability coefficient is presented as  
\[\varphi=1.03679-0.00221\lambda-0.000052\lambda^{2} \tag{4}\]  
\[\varphi =1.46406-0.04474\ \lambda+0.000425\lambda^{2} \tag{5}\]  
Equation (4) is proposed according to the fitting results of three groups of experimental data, with the slenderness ratio from 12 to 56. Equation (5) is proposed according to the fitting results of two groups of experimental data, with the slenderness ratio from 12 to 37.