# Effect of Load Transfer Section to Toughness for Steel Fiber-Reinforced Concrete
## 4 Analysis and Discussion
### Regression Curve Analysis  
Table 6 shows a summary of the coefficients of the derived regression curve by section, and Figure 8 shows the regression curves by specimen. The regression curve was derived by first dividing the load displacement curve of the specimen into sections, and by conducting a nonlinear regression analysis (the secondary curve) to produce a regression equation suitable for each section. The analysis of the regression curve by section showed that most of the correlation coefficients of the derived regression curve exceeded 99%, and considering that all three types of load transfer properties were shown, the section used for deriving the regression curve is believed to have had some reliability.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & **Displacement** & **Section 1a** & **Section 1b** & \begin{tabular}{c} **Second** \\ **Section** \\ \end{tabular} & **Third Section** & **Fourth Section** \\ \hline \multirow{4}{*}{H-SF 0.5} & Displacement & \(0\leq\chi\leq 0.03\) & \(0.03\leq\chi\leq 0.05\) & \(0.05\leq\chi\leq 0.16\) & - & \(0.16\leq\chi\leq 2.00\) \\ \cline{2-7}  & \begin{tabular}{c} a \\ Co-efficient \\ \end{tabular} & \begin{tabular}{c} 0 \\ b \\ c \end{tabular} & \begin{tabular}{c} \(-6827\) \\ \(455.5\) \\ \end{tabular} & \begin{tabular}{c} \(-2075.\) \\ \(94.4\) \\ \end{tabular} & \
\begin{tabular}{c} - \\ \(15.8\) \\ \end{tabular} & - &
\begin{tabular}{c} \(0.5\) \\ \  
_Appl. Sci._**2017**, \(7\), 549  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & **Displacement** & **Section 1a** & **Section 1b** & **Second** & **Third Section** & **Fourth Section** \\ \hline \multirow{4}{*}{C-SF 1.0} & Displacement & \(0\leq\chi\leq 0.01\) & \(0.01\leq\chi\leq 0.05\) & - & \(0.05\leq\chi\leq 0.18\) & \(0.18\leq\chi\leq 2.00\) \\ \cline{2-6}  & \begin{tabular}{c} a \\ Co-efficient \\ \end{tabular} & \begin{tabular}{c} 0 \\ b \\ \end{tabular} & \(-3924.5\) & \(0\) & \(-232\) & \(-3\) \\  & \begin{tabular}{c} b \\ c \\ \end{tabular} & \(492.3\) & \(516.7\) & \(0\) & \(91.8\) & \(4.2\) \\  & \begin{tabular}{c} c \\ Correlation coefficient \\ \end{tabular} & \(99.2\) & \(99.0\) & \(98.9\) & \(97.7\) & \(97.9\) \\ \hline \multirow{4}{*}{C-SLF 0.5} & Displacement & \(0\leq\chi\leq 0.01\) & \(0.01\leq\chi\leq 0.12\) & \(0.12\leq\chi\leq 0.15\) & \(0.15\leq\chi\leq 0.90\) & \(0.90\leq\chi\leq 2.00\) \\ \cline{2-6}  & \begin{tabular}{c} a \\ Co-efficient \\ \end{tabular} & \begin{tabular}{c} 0 \\ b \\ c \\ \end{tabular} & \(-361.6\) & \(-561.1\) & \(-7.7\) & \(-2.5\) \\  & \begin{tabular}{c} b \\ c \\ \end{tabular} & \(486.6\) & \(126.6\) & \(139.7\) & \(11.8\) & \(3\) \\  & \begin{tabular}{c} c \\ \end{tabular} & \(0\) & \(4.9\) & \(5.7\) & \(12.4\) & \(16.2\) \\ \cline{2-6}  & \begin{tabular}{c} Correlation coefficient \\ \end{tabular} & \(99.1\) & \(99.3\) & \(96.1\) & \(93.0\) & \(98.6\) \\ \hline \multirow{4}{*}{C-SLF 1.0} & Displacement & \(0\leq\chi\leq 0.04\) & \(0.04\leq\chi\leq 0.06\) & - & \(0.06\leq\chi\leq 0.58\) & \(0.58\leq\chi\leq 2.00\) \\ \cline{2-6}  & \begin{tabular}{c} a \\ Co-efficient \\ \end{tabular} & \begin{tabular}{c} 0 \\ b \\ c \\ \end{tabular} & \(-4628.5\) & \(0\) & \(-29.1\) & \(-1.7\) \\  & \begin{tabular}{c} b \\ c \\ \end{tabular} & \(422.3\) & \(549.1\) & \(0\) & \(31.3\) & \(0\) \\  & \
\begin{tabular}{c} c \\ c \\ \end{tabular} & \(0\) & \(0.6\) & \(0\) & \(15\) & \(23.6\) \\ \cline{2-6}  &
\begin{tabular}{c} Correlation coefficient \\ \end{tabular} & \(99.0\) & \(98.8\) & \(99.6\) & \(99.1\) & \(97.1\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._  
Figure 8: Regression curve of the flexural load displacement curve by specimen.