# Effect of SIRRCCs with Varying Steel Fiber Volume Fractions on Flexural Behavior
## 2 Experimental Details
### Experimental Method  
To evaluate the flexural performance of SIFRCCs with respect to the steel fiber volume fraction, prismatic specimens of \(100\times 100\times 350\) mm were fabricated in this study based on ASTM C 1609 [21], and bending tests were conducted. As shown in Figure 1, third-point loading was applied using a 200-ton universal testing machine. In addition, the deflection displacement at the center was taken using a Japanese yoke [1; 9; 11; 12], to which two linear variable differential transducers (LVDTs) were attached to the center of the specimen. The load was applied at the rate of 1 mm/min in the displacement control method. To evaluate the flexural performance, the flexural strength was calculated using Equation (1) in ASTM C 1609 [21]. Figure 2 shows a drawing of the specimen and the Japanese yoke for LVDTs.  
\[f=\frac{PL}{bd^{2}} \tag{1}\]  
where,  
P = the maximum load;  
L = the span distance (300 mm);  
b = the specimen width (100 mm);  
d = the specimen height (100 mm)  
To evaluate the energy absorption capacity with respect to the fiber volume fraction, the flexural toughness was calculated based on ASTM C 1609. However, it is inappropriate to define this as the area to 1/150 of the span distance L in the load-deflection curve, as suggested in ASTM  
Figure 1: Bending test with third-point loading.  
Figure 2: Drawing of the specimen and Japanese yoke for linear variable differential transducers (LVDTs).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mechanical Properties**} & \multicolumn{3}{c}{**Fiber Volume Fraction**} \\ \cline{2-4}  & **4\%** & **5\%** & **6\%** \\ \hline Compressive strength (MPa) [3] & 65.5 & 74.5 & 82.9 \\ \hline Tensile strength (MPa) [2] & 10.9 & 14.1 & 15.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Compressive and tensile strength of SIFRCCs [2; 3].  
C 1609 [21], because of the flexural behavior characteristics of SIRCCs considered in this study. Therefore, to compare the energy absorption capacity with respect to the fiber volume fraction, the flexural toughness characteristics were instead analyzed using an area to 20 mm of deflection in the load-deflection curve [1; 9; 11; 12].  
In addition, if the load at the first peak is assumed to have linear elastic behavior, then deflection at the first load peak point could be obtained through Equation (2), and this could be considered an initial crack [22]. At ASTM C 1609 [21], the deflection at the first peak point of loading for a test specimen measuring \(100\times 100\times 350\) mm is approximately 0.04 mm [12].  
\[\delta_{1}=\frac{23P_{1}L^{3}}{1296\text{EI}}\bigg{[}1+\frac{216d^{2}(1+\mu)}{ 115L^{2}}\bigg{]} \tag{2}\]  
where,  
\(\delta_{1}=\) the first-peak deflection (mm);  
\(P_{1}=\) the first-peak load (N);  
\(L=\) the span length (mm)  
\(E=\) the estimated modulus of elasticity of the specimen (MPa);  
\(I=\) the cross-sectional moment of inertia (mm\({}^{4}\));  
\(d=\) the average depth of specimen at the fracture, as oriented for testing (mm);  
\(\mu=\) the Poisson's ratio