# Cracking Behavior of Fiber-Reinforced Concrete Beams Made of Waste Sand
## 3 Materials and Methods  
The compositions of the fine aggregate fiber concrete mixtures were established based on the guidelines outlined in [69]. These guidelines are based on experimentally determined relationships between the actual volume of water and pores in the concrete mixture and the properties of sand concrete. Subsequently, the established composition of the sand concrete mixture was modified by adding a superplasticizer and steel fibers. The water  
Figure 4: Concrete beam reinforced with flexible bars in four-point bending test: **(a)** the initial load phase, where the first cracks appear; **(b)** the load-deflection diagram illustrating the response of the beam; **(c)** the formation of additional cracks as a result of increased loading; **(d)** failure of the beam characterized by crushing in the compression zone [68].  
Figure 3: Schemes of work of fibers in the matrix: **(a)** the Cook-Gordon effect, **(b)** behavior of the matrix, **(c)** deformation fiber [68].  
content was adjusted to obtain a mixture with a plastic consistency, in accordance with the recommendations [70]. The composition of plain (commercial) concrete was designed for a target cube strength of 45 MPa.  
The final compositions of the mixtures used in the tests are presented in Table 1.  
The test specimens were produced in 10 series. These varied in the type of concrete mixture (fiber-reinforced fine aggregate concrete and plain concrete), the steel fibers used (50/0.8 mm and 30/0.55 mm), the longitudinal reinforcement ratio (\(\rho_{\text{L}}\)) in beams (0.6%, 0.9%, 1.3%, and 1.8%), and the application (or absence) of compressive reinforcement, as well as stirrups oriented vertically to the element axis spaced every 130 mm (see Table 2). Each series of test specimens contained 2 beams, 6 cylinders, and 12 cubic samples intended for the determination of strength properties. They were demolded 24 h after the concrete was poured. The thermal and humidity conditions during the preparation and curing of the test specimens were uniform. The tests were conducted 28 days after molding.  
The test for the limit state of cracking caused by a temporary load was conducted on beams with dimensions of 15 \(\times\) 20 \(\times\) 330 cm. The beams were subjected to two concentrated forces applied at one-third of the span through a steel traverse. The load scheme of the tested beams is illustrated in Figure 5.  
The longitudinal reinforcement of the beams was made of ribbed steel (34 GS grade) with diameters of 8, 10, 12, and 14 mm, while the transverse reinforcement was made of smooth steel (St3 SX-b grade) with a diameter of 4.5 mm. Small-sized elements, such as cubes and cylinders, were used to determine the basic strength properties of the concrete.  
Figure 5: Geometry and static scheme of the tested beams.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Plain Commercial Concrete** & \multicolumn{3}{c}{**Fiber-Reinforced Fine Aggregate Concrete**} \\ \hline  & & **M1** & **M2** \\ \hline Components & (kg/m\({}^{3}\)) & Components & (kg/m\({}^{3}\)) \\ \hline Cement CEM I & & & \\
32.5 R & 410 & Cement CEM II/B-V 32.5 R & 374 & 378 \\ \hline Water & 188 & Water & 150 & 140 \\ \hline Superplasticizer & 1.89 & Superplasticizer & 4.08 & 4.13 \\ \hline Aggregate (0–2) & 646 & Waste sand (0–4) & 1835 & 1855 \\ \hline Aggregate (2–8) & 576 & Steel fibers loose 50/0.8 mm & 33 & - \\ \hline Aggregate (8–16) & 523 & Steel fibers glued 30/0.55 mm & - & 34 \\ \hline  & & & Fiber-reinforcement ratio by volume (\%) & 0.42 & 0.43 \\ \cline{2-4} w/c & 0.46 & w/c & 0.40 & 0.37 \\ \hline \hline \end{tabular} Consistency of mixtures: plastic, V3—according to Ve-Be method [71]. M1—Series: A, B, C, D, G; M2—Series: H, I, J, K.  
\end{table}
Table 1: Composition of the concrete mixtures used in tests [50; 51].