## 3 Analysis of Test Results
### Skeleton Curve
The ultimate bearing capacity of the BFRPC composite column specimen is 592 kN, which is much larger than that of the PRC and PHC tube column specimens, indicating that the installation of FRP tube is equivalent to an increase in the reinforcement ratio of the concrete column. Furthermore, the PHC tube column specimen has a short descending section of the skeleton curve before failure, presenting certain brittle failure behaviors. Whereas, the PRC tube column specimen has a long descending section of the skeleton curve before failure, presenting significant ductile failure behaviors. For the BFRPC composite column specimen, the FRP tube made of the CBF material breaks during failure, causing its bearing capacity to drop suddenly, and thus the skeleton curve does not have a descending section due to yielding. However, the BFRPC composite column specimen has large deformation before failure, resulting in significant failure signs. The failure of the BFRPC composite column specimen belongs to ductile failure without yield point, and thus its ductility is significantly less than that of the PRC tube column specimen. In summary, compared with PRC and PHC tube column specimens, the BFRPC composite column specimen has the better bearing capacity, deformation behavior, and ductility performance. Consequently, to facilitate the wide application of the BFRPC composite column in engineering designs, the functional expression of the skeleton curve obtained from BFRPC composite column test is fitted by the rational function fitting method in this work. The fitting result is exhibited in Figure 12. The functional expression of the skeleton curve is  
\[P=\frac{a+b\Delta}{1+c\Delta+d\Delta^{2}} \tag{1}\]  
where \(P\) and \(\Delta\) stand for the load value and the displacement value, respectively. The coefficients \(a\) = 2.66, \(b\) = 5.63, \(c\) = \(-\)2.89 \(\times\) 10\({}^{-4}\), and \(d\) = 1.97 \(\times\) 10\({}^{-5}\) with standard errors of 4.49, 0.08, 8.99 \(\times\) 10\({}^{-5}\), and 8.99 \(\times\) 10\({}^{-6}\), respectively. The coefficient of determination for the fitting function (R\({}^{2}\)) reaches 0.99995, indicating that the fitting value has high accuracy. The functional form of the skeleton curve can be represented by the inverse hyperbolic sine function. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Column Type**} & \multirow{2}{*}{
\begin{tabular}{c} **Load (kN) and** \\ **Displacement (mm)** \\ \end{tabular} } & \multicolumn{3}{c}{**Forward Loading**} & \multicolumn{3}{c}{**Reverse Loading**} \\ \cline{3-7}  & & **Cracking Point** & **Peak Point** & **Extreme Point** & **Peak Point** & **Extreme Point** \\ \hline \multirow{2}{*}{PRC} & Load & 60 & 174.96 & 169.59 & \(-\)169.14 & \(-\)156.93 \\  & Displacement & 3.77 & 50.96 & 81.76 & \(-\)47.94 & \(-\)78.74 \\ \hline \multirow{2}{*}{PHC} & Load & 75 & 119.94 & 118.77 & \(-\)122.08 & \(-\)107.44 \\  & Displacement & 4.06 & 18.48 & 23.21 & \(-\)12.05 & \(-\)22.21 \\ \hline \multirow{2}{*}{BFRPC} & Load & / & 592.07 & 592.07 & \(-\)553.72 & \(-\)553.72 \\  & Displacement & / & 140 & 140 & \(-\)140 & \(-\)140 \\ \hline \end{tabular}
\end{table} 
Table 3: The feature points of the skeleton curves.