## 4 Results and Discussion
### Parametric Study  
The cross-sectional area of the rebars in the RC beam is designed to resist the expected service loads on the structure. The selection of the number and diameter of the rebars is based on the required area, as well as the spacing requirements stipulated in building codes. These requirements typically include both minimum and maximum spacing between rebars. For example, the ACI Code [30] specifies a minimum spacing to adequately place the concrete, which must be at least equal to the diameter of the bar, the maximum size of aggregate, or one inch. Conversely, a maximum spacing is required to limit large cracks resulting from excessive distances between longitudinal bars. In the ACI Code, this maximum spacing is determined using the formula:  
\[\mathrm{s}\leq 4.42\left(\frac{40,000}{\mathrm{f_{s}}}\right)\,(\mathrm{cm}) \tag{14}\]  
where \(\mathrm{f_{s}}\) is the calculated stress in the reinforcement at the tension face (MPa). Therefore, this section presents a comprehensive parametric study to investigate how rebars' location and diameter affect the RC beam's characteristic load and crack behavior. The study utilized the well-validated simulation model and built upon experimental results from the Section 3. In a previous section, beam S1-2 was installed with five 14 mm diameter rebars in the tensile area with a cross-sectional area of 770 mm\({}^{2}\). Using the same cross-section, seven, four, and five reinforcing bars with diameters of 12 mm, 16 mm, and 18 mm were used to simulate crack propagation behavior in RC beams. The mechanical properties of the reinforcements were assumed to remain unchanged. The five 14 mm diameter rebars were then replaced with those rebars to examine the structural behavior of the beam. Table 8 shows the reinforcement design for each beam and the resulting cross-sectional area, with the largest error of 4.49% occurring in the B16 beam. Table 9 compares the cracking and ultimate load of the parametric beams. Decreasing the rebar diameter while increasing the number of rebars decreases the ultimate load and corresponding deflection at the ultimate load. Similarly, increasing the rebar diameter while decreasing the number of rebars also decreases the ultimate load and corresponding  
Figure 13: Comparison of crack patterns in simulated and experimental results of the beam S1-4. deflection. Therefore, an optimal combination of rebar diameter, number, and spacing can maximize the load-carrying capacity of an RC beam. During the first stage, reducing the diameter of reinforcements while simultaneously decreasing their spacing and increasing quantity results in approximately a 3.4% increase in crack load and a 5.9% increase in displacement. This increase can be explained by the fact that increasing the number of reinforcements while reducing their diameter and spacing results in a larger contact area between the concrete and rebars, leading to an increase in bonding between the two materials. This results in better performance of the RC beam compared to the reference beam. Conversely, increasing the diameter and spacing while reducing the number of reinforcements decreases the crack load and corresponding deflection. Figure 14 displays the crack patterns in each parametric beam. The results show that changes in the diameter, spacing, and number of rebars in the RC beam lead to variations in the width, length, and position of cracks. Figure 14 shows that changes in the diameter, spacing, and number of reinforcements in parametric beams have an impact on crack behavior. Increasing the diameter and spacing while decreasing the number of reinforcements resulted in wider cracks and vice versa. Increasing the diameter of the reinforcement from d12 to d18 resulted in a slight increase in the mean crack width of the RC beam at service load, from 80.85 \(\upmu\)m to 90.45 \(\upmu\)m, as shown in Table 10. The largest crack width of 176 \(\upmu\)m was observed in the B16 and B12 beams.