## 4 Results and Discussion
### Flexural Test Results
#### 4.4.2 Cracking and Yielding Moments  
The bending moment capacity of all RC beams corresponding to experimental loads at first cracking (i.e., cracking moment) and yielding of steel bars (i.e., yielding moment) were determined and then compared with theoretical values of cracking and yielding bending moments computed as per the guidelines of ACI-318 [46] by employing Equations (14) and (15). In these equations, \(M_{cr}\) = cracking moment, \(f_{r}\) = modulus of rupture calculated as \(0.62\sqrt{f_{c}^{2}}\), \(I_{g}\) = gross moment of inertia, \(y_{t}\) = distance from the centroid to the extreme fiber in tension fiber, \(M_{yield}\) = yield moment capacity, \(A_{s}\) = area of bottom longitudinal reinforcement, \(f_{y}\) = yielding stress of steel, \(d\) = distance from the extreme compression fiber to the center of bottom steel bar, and \(a\) = depth of rectangular stress block from the top. \[M_{cr}=\frac{f_{r}I_{g}}{y_{t}} \tag{14}\]  
\[M_{yield}=A_{s}f_{y}\Big{(}d-\frac{a}{2}\Big{)} \tag{15}\]  
The comparison of theoretical and experimental values of cracking and yielding moment capacity of RC beams prepared with concrete mixes presented in Table 1 is graphically presented in Figures 15 and 16, respectively. For all beams, the experimental value of the cracking moment was higher than the theoretical value. RC beams prepared using mixes containing 100% fine RAs (RBAs or RCAs) and 100% coarse NAs exhibited a cracking moment similar to that of the control RC beam. Since the theoretical prediction of Mcr mainly depends upon the modulus of rupture of the concrete matrix (calculated  
Figure 13: Comparison of experimental and predicted bond strength: (**a**) Coarse RBA replacement percentage, (**b**) Coarse RCA replacement percentage. as \(0.62\sqrt{f_{c}}\)), the variation in Mcr due to aggregate type and its content followed a trend similar to compressive strength. Figure 14: Load vs. deflection responses of RC beams: (**a**) Fine aggregates (RBA), (**b**) Fine aggregates (RCA), (**c**) Fine aggregates (RBA) and coarse aggregates (RBA and NA), (**d**) Fine aggregates (RCA) and coarse aggregates (RCA and NA). Figure 15: Cracking moment. Variation in the strain in tension steel of RC beams measured using strain gages pasted at their midspan is shown in Figure 17. The trend of strain development or evolution in tension steel bars was found to depend on the type of fine and coarse aggregates used in the concrete mixes. Since in the case of reinforced concrete, the composite action between steel bars and concrete directly influences the transfer of stress to the steel bars and ultimately strain level, the pattern of changes in the tension steel strain was similar to the one observed for bond stress development with respect to the type and content of aggregates in concrete. Figure 16: Yielding moment. Figure 17: Strain in steel bars. Moreover, the deflections at cracking (\(\delta\)cr) and yielding (\(\delta\)yield) were also measured, and the corresponding stiffness of the beams, kcr and kyield, respectively, were also calculated using Equation (16), where \(k\) is the stiffness of the beam at cracking or yielding, F is the load for cracking or yielding, and \(\delta\) is the corresponding deflection at cracking and yielding points. The cracking and yielding stiffness were defined, as illustrated in Figure 18.  
\[k=\frac{F}{\delta} \tag{16}\]  
Figure 19 illustrates the stiffness of the concrete with different replacement levels of coarse RAs (RBAs or RCAs) by NAs. The increase in the cracking stiffness of concrete prepared with the replacement of coarse NAs by 25% of RBAs was observed. However, with the increase in the content of coarse RBAs, a further decrease in cracking stiffness was observed. While, with the replacement of 100% coarse NAs with coarse RCAs, similar cracking stiffness was obtained for the specimens prepared with 100% NAs (control).