## 4 Conclusions  
For all experimental work, the following conclusion can be drawn:  
Inclusion of low volume fraction (0.3%) of short (18 to 20 mm long) copper coated steel, CCS, and PVA fibers in 100% cement/20% fly ash concrete enhanced the mechanical properties. The effects were clearly seen in an improvement in the split tensile and flexural strength; they were enhanced by more than 10% compared to the control mixes CM and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mix ID** & \begin{tabular}{c} **Ultimate Stress,** \\ **\(\sigma_{u}\) (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Ultimate Strain,** \\ **\(\epsilon_{u}\) (\%)** \\ \end{tabular} & \begin{tabular}{c} \(\sigma_{d0}\) = 0.4\(\sigma_{u}\)** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Strain at \(\sigma_{d0}\), \(\epsilon_{d0}\)** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Scant Modulus** \\ **(\(E_{d0}\) = \(\frac{\sigma_{u}}{\epsilon_{d0}}\))** GPa** \\ \end{tabular} & **Ductility Index (\(\frac{\sigma_{u}}{\epsilon_{d0}}\))** \\ \hline CM & 63.49 & 1900 & 25.4 & 747 & 34 & 2.54 \\ P0.3 & 61.3 & 1600 & 24.52 & 515 & 47.61 & 3.11 \\ S0.3 & 66 & 3350 & 26.4 & 705 & 37.45 & 4.75 \\ CF & 64 & 1940 & 25.6 & 790 & 32.41 & 2.46 \\ PF0.3 & 60.1 & 2300 & 24.04 & 686 & 35.04 & 3.35 \\ SP0.3 & 62 & 3400 & 24.8 & 720 & 34.44 & 4.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Modulus of elasticity (E), and the ductility index of concrete determined according to BS EN 192-2-2 [34]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Mix Type** & \begin{tabular}{c} **Toughness at First** \\ **Crack, \(\mathbf{FT_{fc}}\) (kN-mm)** \\ \end{tabular} & \begin{tabular}{c} **Toughness Index** \\ **I5** \\ \end{tabular} & \begin{tabular}{c} **Flexural Toughness, FT** \\ **(kN-mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Residual Strength** \\ **Factor** \\ \end{tabular} &
\begin{tabular}{c} **Deflection,** \\ **\(\mathbf{\xi}\) **(mm)** \\ \end{tabular} \\ \hline CM & 5.57 & 1.3 & 1.3 & 1.3 & 7.23 & 0 & 0.’00’ & 1.34 \\ P0.3 & 6.24 & 1.82 & 2.02 & 2.05 & 12.82 & 4.03 & 0.34 & 7.2 \\ S0.3 & 7.91 & 2.45 & 3.04 & 3.33 & 26.38 & 11.93 & 2.86 & 15.5 \\ CF & 5.33 & 1.26 & 1.26 & 1.26 & 6.72 & 0 & 0 & 1.46 \\ PF0.3 & 7.53 & 1.59 & 1.84 & 1.91 & 14.38 & 4.84 & 0.73 & 12.6 \\ SF0.3 & 8.37 & 1.84 & 2.18 & 2.21 & 18.47 & 6.77 & 0.24 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Post cracking characteristics of concrete, determined according to ASTM1018 [30]. CF. A valid correlation (within the specified range, as discussed in ASTM C1018) between the compressive strength and the flexural strength was obtained. The fundamental reason for reinforcing concrete with short, randomly oriented fibers is to improve the load-carrying capacity and energy absorption capability after the onset of the first crack. PVA and CCS fibers increased the first crack toughness by more than 40% compared to the control mixes and increased the flexural toughness to 1.8 and 3.6 times that of the control mixes' FT. The fibers also enhanced the toughness indices I\({}_{5}\), I\({}_{10}\), and I\({}_{20}\) and the residual strength factors. These indices indicate the performance of concrete in the plastic region. Modulus of elasticity is an essential characteristic of concrete for controlling the deformation behavior of the structural members. The secant modulus of PVA and CCS reinforced concrete was obtained between 35 Gpa and 47 Gpa, which could reduce the structural members' size. The fibers also improved the ductility of the concrete by 22-91%, which could help avoid a structural collapse in abnormal loading conditions. [PERSON] conducted the experimental analysis, data collection, and analysis. [PERSON] reviewed the data and wrote the draft manuscript. [PERSON] supervised the research activities and vetted and corrected the analysis and the manuscript. All authors have read and agreed to the published version of the manuscript.