## 3 Results and Discussion
### Load-Displacement Relationship
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Specimen ID**} & \multicolumn{3}{c}{**35 OPC**} & \multicolumn{3}{c}{**45 OPC**} & \multicolumn{3}{c}{**55 OPC**} \\ \hline H.R & 0 & 50 & 100 & 0 & 50 & 100 & 0 & 50 & 100 \\ \hline \multirow{3}{*}{Initial crack} & \(P_{\text{cr}}\) (kN) & 34.15 & 25.36 & 23.85 & 22.22 & 29.88 & 18.36 & 22.31 & 23.57 & 22.03 \\ \cline{2-11}  & \(\Delta_{\text{cr}}\) (mm) & 0.62 & 0.59 & 0.49 & 0.31 & 0.69 & 0.18 & 0.32 & 0.66 & 0.48 \\ \hline \multirow{3}{*}{Yield Point} & \(P_{\text{y}}\) (kN) & 91.87 & 90.02 & 89.94 & 85.95 & 86.11 & 93.77 & 89.23 & 82.36 & 87.76 \\ \cline{2-11}  & \(\Delta_{\text{y}}\) (mm) & 4.00 & 4.30 & 4.58 & 3.83 & 4.28 & 3.96 & 3.91 & 4.13 & 4.43 \\ \hline \multirow{3}{*}{Peak point} & \(P_{\text{u}}\) (kN) & 108.24 & 107.40 & 99.93 & 101.97 & 100.85 & 97.81 & 99.82 & 93.57 & 93.16 \\ \cline{2-11}  & \(\Delta_{\text{u}}\) (mm) & 17.19 & 17.19 & 12.57 & 11.74 & 10.98 & 5.92 & 15.13 & 8.46 & 8.33 \\ \hline \multicolumn{2}{c}{Ductility Index} & 4.3 & 4.0 & 2.74 & 3.07 & 2.57 & 1.49 & 3.87 & 2.05 & 1.88 \\ \hline \multicolumn{2}{c}{**Specimen ID**} & \multicolumn{3}{c}{**45 FA20**} & \multicolumn{3}{c}{**45 BF550**} \\ \hline H.R & 0 & 50 & 100 & 0 & 50 & 100 & & & & \\ \hline \multirow{3}{*}{Initial crack} & \(P_{\text{cr}}\) (kN) & 27.72 & 31.26 & 25.07 & 33.58 & 31.15 & 28.73 & & & \\ \cline{2-11}  & \(\Delta_{\text{cr}}\) (mm) & 0.33 & 0.55 & 0.72 & 0.50 & 0.47 & 0.38 & & & \\ \hline \multirow{3}{*}{Yield Point} & \(P_{\text{y}}\) (kN) & 91.49 & 89.79 & 91.16 & 87.13 & 91.95 & 91.12 & & \\ \cline{2-11}  & \(\Delta_{\text{y}}\) (mm) & 4.31 & 3.95 & 3.72 & 3.8 & 3.88 & 3.73 & & \\ \hline \multirow{3}{*}{Peak point} & \(P_{\text{u}}\) (kN) & 114.51 & 103.99 & 99.21 & 111.38 & 112.38 & 104.25 & & & \\ \cline{2-11}  & \(\Delta_{\text{u}}\) (mm) & 17.11 & 15.10 & 9.95 & 17.2 & 17.2 & 10.9 & & & \\ \hline \multicolumn{2}{c}{Ductility Index} & 4.46 & 3.82 & 2.67 & 4.53 & 4.43 & 2.92 & & & \\ \hline \end{tabular}
\end{table} 
Table 7: Experimental results of ductility index of RC member. Figure 5: Load-displacement curves for RC beam. According to ACI 363 [23], ductility is explained as a ratio of the deflection (or cross-section curvature) at the ultimate load to the deflection (or curvature) at the load producing yield of the reinforcement (Equation (1)). \[\mu=\Delta\upmu/\Delta\yy \tag{1}\]  
where, \(\upmu\) is the ductility index; \(\Delta\upmu\) is the beam deflection at the ultimate load; \(\Delta\yy\) is the beam deflection at the yield load of the RC member. The ductility index is shown in Table 7. From the results, the ductility index of the RC members is affected significantly by the heavyweight waste glass substitution ratio. This implies that the increment of the substitution ratio of heavyweight waste glass in the RC member caused the reduced flexural ductility. As mentioned earlier, these phenomena were affected by the load capacity decrement at the large deformed stage. However, the ductility index of the RC members using heavyweight waste glass can be improved by a low water-binder ratio or mineral admixture.