# Effect of Load Transfer Section to Toughness for Steel Fiber-Reinforced Concrete
## 4 Analysis and Discussion
### Load Displacement Curve Analysis by Material  
For a detailed analysis of the flexural behavior characteristics, the curve was divided into zones based on the load transfer type. First, as with the other toughness assessment methods, the point at which brittle fracture occurred on the load deflection curve was considered the first peak load point, and the section was set to the first section (sections 1a and 1b). Section 1a was the zone where the concrete matrix exhibited elastic behavior, and Section 1b was the zone where fine cracks occurred with curved behavior up to the first peak point. These two sections were separated from each other based on the fact that the elastic behavior of the material showed a straight line. When a linear regression curve of a linear equation (\(y=ax\)) was applied to the load displacement graph, the maximum displacement in which the coefficient of determinant to the actual load displacement graph was 0.99 or higher was set as the end of section 1a, and the curved-behavior zone from the end of section 1a to the first peak load point was set as section 1b. The second section was the load reduction zone caused by the different material properties in the load transfer process to the steel fiber after the first peak load. The third section was the load reascending zone due to the interaction between the steel fiber and the surface to which the concrete was attached, which was from the end of the second section to the second peak load point. The fourth section was the zone where load reduction occurred as the remaining load was gradually dissipated, which was from the end of the second section if the third section did not exist, or from the end of the third section to 2.0, the end point of the overall toughness. Shown in Table 5 is a summary of the range of each section, and Figure 7 shows the diagram of the slope and area (toughness) by section.  
Figure 6: Load transfer characteristics by steel fiber type and fiber content.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Category**} & & & \\ \hline \multirow{2}{*}{**Section**} & **Toughness** & **Slope by** & **Range (d: displacement, mm)** & **Energy Absorption** & **Energy-Absorptive Material** \\  & **by Section** & **Section** & & & \\ \hline \multirow{4}{*}{1} & \(S_{1a}\) & \(g_{1a}\) & 0 \textless{} d \(\leq\) initial crack point & Linear elastic behavior & Concrete \\  & \multirow{2}{*}{\(S_{1b}\)} & \(g_{1b}\) & Initial crack point \textless{} d \(\leq\) first & Progress of fine cracks & Concrete \\  & & & peak load & inside the matrix & Concrete \\ \hline \multirow{2}{*}{2} & \(S_{2}\) & \(g_{2}\) & First peak load \textless{} d \(\leq\) lowest & Concrete-fiber load & Concrete, fiber \\  & & & load point & transfer section & Concrete, fiber \\ \hline \multirow{2}{*}{3} & \(S_{3}\) & \(g_{3}\) & Lowest load point \textless{} d \(\leq\) second peak load & Fiber bridging and & Fiber \\  & & & second peak load & pullout action & Fiber \\ \hline \multirow{2}{*}{4} & \(S_{4}\) & \(g_{4}\) & Second peak load \textless{} d \(\leq\) 2.0 & Fiber bridging and & Fiber \\  & & & pullout action & Fiber \\ \hline \hline \end{tabular}
\end{table}
Table 5: Range by section.  
The regression analysis targeted a total of six types of steel fiber-reinforced concrete, and due to the characteristics of the regression curve in which the nonlinear and linear zones coexisted, the standard equation was a quadratic equation (Equation (1)).  
\[y=ax^{2}+bx+c \tag{1}\]