# Cracking Behavior of Fiber-Reinforced Concrete Beams Made of Waste Sand
## 5 Test Results and Their Analysis
In a properly designed and manufactured fiber-reinforced concrete element, the beneficial effects of steel fibers become apparent after the first crack appears. The use of appropriately effective reinforcement with steel fibers leads to the dispersion of cracks, whereby wide and sparse cracks are replaced with so-called micro-cracks [78]. This also results in a reduction in the distance between cracks [41]. Figure 9 illustrates the average crack spacing (\(\rm{s_{m}}^{\rm{exp}}\)) in the section of the constant bending moment (M\({}_{\rm{ed}}\)) (the area between the forces is shown in Figure 1) across the different load phases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Diameter** & **Cross** & **The Yield** & **Tensile** & **Modulus of** \\
**(mm)** & **Section** & **Point** & **Strength** & **Elasticity** \\
**(mm\({}^{2}\))** & **(mm\({}^{2}\))** & **(MPa)** & **(MPa)** & **(GPa)** \\ \hline
8.2 & 53.0 & 424 & 695 & 223 \\ \hline
10.2 & 81.1 & 454 & 714 & 220 \\ \hline
12.2 & 116.7 & 430 & 678 & 205 \\ \hline
14.3 & 160.6 & 451 & 688 & 214 \\ \hline \hline \end{Figure 9 shows that the average crack spacing (\(\rm{s_{m}}^{\rm{EXP}}\)) in the section of constant bending moment (\(\rm{M_{ed}}\)) decreases with increasing load. The crack stabilization moment was not the same for all beams. Its calculated values, consistent with [79] (80% of the ultimate moment), were underestimated because, practically until the moment of beam destruction, single cracks were formed. However, these did not significantly affect the average spacing, even with a large number of perpendicular cracks. Examples of crack spacing for beams from selected series are shown in Figures 10-14. In the tested beams containing steel fibers, the observed crack patterns on the section of the constant bending moment do not differ substantially from one another, except for the beams with the highest reinforcement ratio (\(\rm{\rho_{L}}\)) of 1.8%. Aside from this case, the longitudinal reinforcement ratio (\(\rm{\rho_{L}}\)), which ranges from 0.6% to 1.3%, slightly affected the average crack spacing and their range during the individual loading phases. This is most likely because the tensile strength of the fiber-reinforced fine aggregate concrete matrix determines the crack morphology [33]. No significant influence of the reinforcement in the  
Figure 10: Morphology of cracks in individual loading phases (series A beams)—# means the diameter of the reinforcement. Figure 9: The average crack spacing during individual load phases of the tested beams. compression zone or the stirrups used on the number, spacing, and extent of cracks during the individual loading phases was observed (as analyzed in beams from series A and D). Comparing beams made of ordinary concrete (series F) with identically dimensioned elements (in terms of dimensions and reinforcement) made of fiber-reinforced fine aggregate concrete (series B--fibers 50/0.8 mm and series J--fibers 30/0.55 mm), it can be seen that at the same load level, the number of cracks is almost the same; however, their spacing and course are more regular in beams with the addition of fibers. This is likely due to the fact that fiber-reinforced concrete is a more homogeneous material than ordinary concrete [78]. The spacing of perpendicular cracks measured during the tests in the individual loading stages for selected beams with different fibers is presented in Tables 6 and 7. According to [80], the limit state of crack spacing corresponds to the load at which the number of cracks stabilizes. This condition is equivalent to establishing a specific distance between cracks. Further increases in load only result in an increase in the width of the cracks.