## 3 Results and Discussion
### Effects of Fibers on Tensile and Flexural Strength  
The principal reason for developing fiber reinforced concrete (FRC), was to enhance the tensile and flexural strength and improve concrete post-cracking behavior. Figure 6 shows the split tensile strength and the flexural strength of various concrete mixes measured at 28 days of curing. In analyzing the fiber's performance, results were compared to the reference mix (CM) and the strength efficiency index. SI was calculated, and is tabulated in Table 4. It was observed that the addition of 0.3% volume fraction of CCS and PVA fibers increased the split tensile and flexural strength by about 7% in 100% cement concrete and up to 25% in the fly ash based concrete, which is a significant improvement. As highlighted in the literature, unlike compression strength, fibers make a complex network of concrete matrices and maintain the mix's integrity [36]. It is stated that longer fibers contribute to improving a concrete's flexure properties [37]. Both types of fibers, CCS and PVA, possessed similar aspect ratios of 100 and 90, respectively; therefore, they showed more or less similar tensile and flexural strength values. Because the flexural strength of concrete \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Mix ID**} & \multicolumn{4}{c}{**Compressive Strength, \(f_{cut}\) (MPa) and Strength Efficiency Index (SI)**} \\ \cline{2-9}  & \(f_{cut}\) & **SI** & \(f_{cut}\) & **SI** & \(f_{cut}\) & **SI** & \(f_{cut}\) & **SI** \\ \cline{2-9}  & \multicolumn{2}{c}{**3 Days**} & \multicolumn{2}{c}{**7 Days**} & \multicolumn{2}{c}{**28 Days**} & \multicolumn{2}{c}{**56 Days**} \\ \hline CM & 54.14 & 1.00 & 60.45 & 1.00 & 66.77 & 1.00 & 70.88 & 1.00 \\ P0.3 & 54.25 & 1.00 & 60.45 & 1.00 & 69.00 & 1.03 & 73.61 & 1.04 \\ S0.3 & 58.86 & 1.09 & 65.81 & 1.09 & 72.60 & 1.09 & 78.28 & 1.10 \\ CF & 42.94 & 0.79 & 50.10 & 0.83 & 65.97 & 0.99 & 72.00 & 1.02 \\ PF0.3 & 35.38 & 0.65 & 55.62 & 0.92 & 64.00 & 0.96 & 74.50 & 1.05 \\ SF0.3 & 46.22 & 0.85 & 55.37 & 0.92 & 69.32 & 1.04 & 83.57 & 1.18 \\ \hline \hline \end{tabular} NOTE: Strength Efficiency Index (SI) = Ratio of the \(f_{cut}\) of concrete mix with the \(f_{cut}\) of the mix CM.  
\end{table} 
Table 3: Compressive Strength (Cube) of all Concrete Mixes. depends on its tensile strength, Figure 7 shows a linear correlation between tensile strength, \(f_{t}\), and flexural strength, \(f_{fl}\), given in the following Equation (1). \[f_{fl}=1.3349f_{t}-1.2298 \tag{1}\]  
The literature has indicated that the flexural strength of fiber reinforced concrete is usually related to the ultimate compressive strength of the concrete; \(f_{cu}\) as \(f_{fl}=(0.62\) to \(0.83)\sqrt{f_{cu}}\)[29; 30]. Figure 8 shows the correlation between the flexural strength and the ultimate compressive strength, and the following correlation was obtained:  
\[f_{fl}=0.6641\sqrt{f_{cu}} \tag{2}\]  
Equation (2), obtained in this research study, is stated above and presented in the literature [30; 31; 32]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mix ID**} & \multicolumn{2}{c}{**Tensile Strength, \(f_{t}\)**} & \multicolumn{2}{c}{**Flexural Strength, \(f_{fl}\)**} \\ \cline{2-5}  & **MPa** &
\begin{tabular}{c} **Strength Index** \\ **(SI)** \\ \end{tabular} & **MPa** & **SI** \\ \hline CM & 4.72 & 1.00 & 5.21 & 1.00 \\ P0.3 & 5.08 & 1.08 & 5.5 & 1.06 \\ S0.3 & 5.05 & 1.07 & 5.5 & 1.06 \\ CF & 4.02 & 0.85 & 4.08 & 0.78 \\ PF0.3 & 5.19 & 1.10 & 5.52 & 1.06 \\ SF0.3 & 5.14 & 1.09 & 5.79 & 1.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Split tensile and flexure strength of concrete mixes determined at 28 days. Figure 5: Compressive strength development in different concrete mixes at different ages. Figure 8: Correlation between compressive strength, \(f_{\text{c}u}\), and flexural strength, \(f_{\text{f}}\). Figure 6: Split Tensile and Flexural strength of different concrete mixes measured at 28 days.