HSC was produced using cement, pure water, fine aggregate, coarse aggregate, silica fume, superplasticizer, and hybrid polypropylene-steel fibers. The cement used was ordinary Portland cement. The coarse aggregate was formed of crushed dolomite with a particle size of 10 mm and an apparent specific gravity of 2.6, while the fine aggregate was a siliceous natural with a fineness modulus of 3.35. Silica fume was added to the concrete mixture to fill the voids and thus improve the strength, while a superplasticizer was added to improve the workability of the concrete. The forms of the fibers are shown in Figure 1 and Table 1 displays the steel and polyethylene fiber characteristics as reported by the suppliers. The binder component was dry-mixed for about 3 min in a mechanical mixer before adding the full quantity of water and superplasticizer to the concrete mixture. Polypropylene and steel fibers were added to the mixture after the wet mixing process and mixed for around 5 min. The transverse reinforcement showed a tensile yield strength of 240 MPa and ultimate strength of 385 MPa, compared to the longitudinal reinforcement’s tensile yield strength of 520 MPa and ultimate strength of 690 MPa. The mix quantities, which are based on Tawfik et al. (2022) are shown in Table 2. For the best mechanical characteristics in terms of compressive, tensile, flexural strength, and cracking control, the concrete mixture contains .45% of polypropylene fiber and 7% of steel fiber as a replacement ratio for the cement weight.

Five hybrid-polypropylene-steel-fiber-reinforced-high-strength-concrete (HFRHSC) beams and one control high-strength reinforced concrete beam are included in the experimental program. The beams are labeled according to the shown in Figure 2. The control beam (CB0-2.8) was 120 mm and 250 mm in width and depth, respectively, while being 2,100 mm long, with no stirrups or fibers, and the flexure longitudinal reinforcement used was 4Ø25. All HFRHSC beams contain 7.45% hybrid fibers as a substitute for the weight of cement, which was divided into 7% steel fibers and .45% polypropylene fibers. The first hybrid FRC beam (HFCB0-2.8), was similar to the control beam in dimensions and proportion of longitudinal steel reinforcement, but the difference was the presence of a hybrid of polypropylene-steel fibers. The second hybrid FRC beam (HFCB0.24-2.8), was similar to the concrete beam (HFCB0-2.8) in dimensions, concrete type, and proportion of longitudinal steel reinforcement, except for the presence of 5Ø6/m transverse reinforcement. The transverse reinforcement ratio of the hybrid FRC beam (HFCB0.42-2.8) was higher than that of the concrete beam (HFCB0.24-2.8), while the dimensions, concrete type, and longitudinal reinforcement ratio were the same in both concrete beams. The hybrid FRC beams (HFCB0.42-2.3) and (HFCB0.42-1.75) differed from the concrete beam (HFCB0.42-2.8) in depth, which was 300 mm and 400 mm, respectively, however, they were similar in terms of width, length, concrete type, and proportion of longitudinal and transverse steel reinforcement. Figure 3 and Table 3 show the details for all concrete beams. To evaluate the mechanical characteristics, including compressive strength, tensile strength, and modulus of elasticity, six concrete cubes (150 × 150 × 150 mm) and 12 concrete cylinders (150 × 300 mm for diameter and height, respectively) were taken from that concrete mixture of each beam. The samples were prepared and examined as per the Egyptian code of concrete specifications.

The transverse reinforcement ratio (ρ) can be calculated using Eq. 1 as the area of transverse reinforcement (Av) multiplied by the spacing between stirrups (s) and the width of the beam (b). ρ = A v b × s % (1) The wooden forms of all concrete beams were prepared and thoroughly sprayed with water before the pouring process to maintain the water in the mixture and not being absorbed by the wood. Electrical strain gauges with a length of 10 mm and a resistance of 120.3 ± .5 Ω were attached to the longitudinal and transverse reinforcement bars in the location as seen in Figure 3, which is responsible for monitoring the strain in the reinforcements along the loading history. The reinforcement was then positioned in the forms as illustrated in Figure 4. The casting process then began, with a vibrator used during the casting to prevent separation between the concrete mortar and the coarse aggregate and to ensure regular fibers distribution. Following 24 h of casting, the forms were withdrawn, and the concrete beams were continually moistened with water for 28 days before being examined.

Figure 5 illustrates the testing procedure used to examine the shear behavior of HFRHSC beams. The beams were supported by two supports (hinged and roller), with a distance of 2,000 mm between them. The load was applied using a hydraulic jack positioned in the middle of the beam. The hydraulic jack’s load was transmitted through an I-steel beam so that it concentrated symmetrically in two points, provided that the distance between the concentrated load and the support was 700 mm on either side. Three LVDTs were installed in the critical sections as shown in Figure 5 to monitor the displacement values during loading. The deflection of concrete beams and reinforcement strain were measured every 10 kN of loading, as well as cracks, were marked. The load steadily increased until the concrete beam collapsed.

Table 4 displays the mechanical properties of the concrete mix implemented for the casting of the specimens, which are represented in tensile and compressive strength as well as modulus of elasticity. The results were calculated as the average of three samples tested under the same conditions. For each mix, six cube specimens with a cross-section of 15 cm × 15 cm, and a height of 15 cm were implemented to measure the compressive strength. Three cube specimens were tested at 7-day, and three as well at 28-day. Furthermore, the elastic modulus was determined for each cementitious material by examining concrete cylinder specimens at 7-day as well as another three at 28-day. The cylinder specimens have a diameter of 15 cm and a height of 30 cm. Whereas the flexural strength of each cementitious material is evaluated by examining three concrete beam specimens at 7-day as well as three more at 28-day. The concrete beams have all been 70 cm long, 15 cm × 15 cm in cross-section.

This section displays the results of (shear load, mid-span deflection, and ductility) at the failure and cracking stages for every concrete beam specimen. Furthermore, relationships between load and various parameters such as mid-span deflection, stirrup strain, and longitudinal bar strain were studied. The strain in the stirrup was calculated by taking the average of the two strain gauges installed in the stirrup’s vertical legs in the critical shear zone. While the longitudinal reinforcement strain was measured at the maximum flexure stress, which is at mid-span. Table 5 represents the experimental results for all concrete beams.

Figure 9 shows the failure mode for all concrete beam specimens. Vertical cracks appeared in the flexure region for control beam CB0-2.8 which does not contain fibers, and then a single diagonal tension crack due to shear appeared in the shear region at the bottom and spread upwards with the increase in loading until it reached the location of the load’s impact, and then a brittle collapse occurred as a result of a widening diagonal shear crack, recognizing that the beam collapsed shortly after the initiation of diagonal shear cracks, indicating low ductility. Also, just before failure, spalling was observed on the external surface of the concrete beam at the compression zone and extended along with the diagonal crack, indicating that the applied stresses exceeded the compressive strength of the concrete. The hybrid FRC beam HFCB0-2.8 failed due to the widening of a diagonal shear crack. The first diagonal shear crack for hybrid FRC beam HFCB0-2.8 appeared at a load of 20 kN while it appeared at a load of 12 kN for the control beam, demonstrating the significance of fibers in preventing crack initiation and propagation. More shear and flexure cracks appeared for the hybrid FRC beam HFCB0-2.8 than in the control beam due to the presence of fibers which prevents cracks from widening and spreading, causing high tensile stresses to be transmitted from the location of the existing cracks to the region between them. This leads to the development of new cracks, increasing the total number of cracks (Tahenni et al., 2016; Alrefaei et al., 2018; Shaaban et al., 2021). Hybrid FRC beam HFCB0-2.8 did not experience significant concrete spalling because the fibers improved the stiffness and strength. When transverse reinforcement was added to the prior hybrid FRC beam, the failure mechanism remained the same as the diagonal shear crack caused the collapse of the hybrid FRC beams HFCB0.24-2.8 and HFCB0.42-2.8. However, increasing the transverse reinforcement ratio resulted in higher shear strength, a slower rate of shear cracking, and more cracks, demonstrating the effectiveness of adding transverse reinforcement in delaying the cracking process and enhancing concrete’s ductility, stiffness, and shear strength. The failure for both hybrid FRC beams HFCB0.42-2.3 and HFCB0.42-1.75 occurred due to diagonal shear cracks and was followed by crushing of concrete in the compression zone. However the shear crack width decreased, and the shear strength was noticeably improved for concrete beam HFCB0.42-1.75 more than the concrete beam HFCB0.42-2.3. This is due to a substantial proportion of the shear being immediately transferred to the support via an inclined strut. The direct load transfer’s magnitude develops with a lowering span to depth ratio and has been known as the arch action mechanism (Ali et al., 2021; Ebid and Deifalla, 2021; Deifalla, 2021b; Li et al., 2021; Deifalla and Mukhtar, 2022a; Deifalla and Mukhtar, 2022b; Zhou and Wan, 2022). This mechanism inhibits cracks from growing larger and delays stirrup yielding. Additionally, it was observed that flexural cracks began growing larger and deeper as the span-to-depth ratio decreased. This refers to an increase in the tensile stresses caused by flexure in addition to the strain of the longitudinal reinforcement, however, the failure mode remained diagonal shear failure and did not transform for being combined shear-flexure or flexure failure since the longitudinal steel bars had not yet reached yielding.

The use of hybrid polypropylene-steel fibers improved ultimate and cracking shear strength, as well as ductility, in concrete beams. As shown in Figure 10, the values of ultimate shear load, cracking shear load, maximum deformation, and ductility for hybrid FRC beam HFCB0-2.8 increased by 18%, 66%, 13%, and 60%, respectively, over the control beam CB0-2.8. Ductility is the ability of concrete to plastically deform without fracturing when subjected to tensile stress greater than its strength. It can be computed by dividing the ultimate deformation that occurs at the ultimate shear force by the cracking deformation that occurs at the cracking shear force (Pakravan et al., 2016; Yan et al., 2021). The fact that when the hybrid fibers were added, the cracking and ultimate shear strengths increased supports their ability to withstand macro and micro cracks at different stress levels, delaying the cracking process and improving stiffness and strength (Tahenni et al., 2016; Sivakumar et al., 2020; Ismail and Hassan, 2021; Shaaban et al., 2021; Yang et al., 2021; Tawfik et al., 2022). The increase in ultimate deformation and ductility values is a further indication of the efficacy of hybrid fibers in reducing concrete’s brittleness and improving its capability for plastic deformation without fracture. Table 6 illustrates the analysis of shear failure load, shear cracking load, maximum deformation, and ductility results for all concrete beams.

Transverse reinforcement improved ultimate shear strength, cracking behavior, and ductility in concrete beams as shown in Figure 11. In comparison to the hybrid FRC beam HFCB0-2.8, the values of ultimate shear load, cracking shear load, maximum deformation, and ductility for hybrid FRC beam HFCB0.42-2.8 improved by 35%, 55%, 22%, and 11%, respectively. Additionally, the values of the ultimate shear load, cracking shear load, maximum deformation, and ductility increased by 12%, 19%, 6%, and 17%, respectively, as the transverse reinforcement ratio increased from .24% to .42%. Transverse steel reinforcement, which is similar to hybrid fibers, could postpone shear cracking while simultaneously enhancing shear strength and ductility (Alrefaei et al., 2018; Torres and Lantsoght, 2019; Yang et al., 2021).

As shown in Figure 12, the ultimate shear load and cracking shear load for hybrid FRC beam HFCB0.42-1.75, which has a span to depth ratio of 1.75 improved by 23% and 15%, respectively, more than for hybrid FRC beam HFCB0.42-2.3, which has a span to depth ratio of 2.3, and by 71% and 62%, respectively, more than for hybrid FRC beam HFCB0.42-2.8, which has a span to depth ratio of 2.8. These findings support the fact that lowering the span-to-depth ratio greatly improves shear strength because a considerable percentage of the shear force is transferred directly to the support by an inclined strut (arch action mechanism). This mechanism slows down the cracking process while enhancing stiffness and shear strength, which results in minor deformation occurring under the same load. In contrast, the hybrid FRC beam HFCB0.42-1.75, which has a span to depth ratio of 1.75, displayed the lowest deformation values at the same load and ductility, where they decreased by 16% and 13%, respectively, more than for the hybrid FRC beam HFCB0.42-2.3, which has a span to depth ratio of 2.3, and by 2% and 38%, respectively, more than for the hybrid FRC beam HFCB0.42-2.8, which has a span to depth ratio of 2.8. This indicates that although lowering the span to depth ratio increases the concrete’s shear strength, it has a detrimental effect on the ductility because the concrete beam was unable to withstand inelastic deformation and collapsed suddenly once the first diagonal shear crack appeared.

The defined parameters of the concrete are shown in Table 7 and include the elastic modulus, Poisson’s ratio, uniaxial crushing, uniaxial cracking, open shear, and close shear coefficient. The non-linear behavior of hybrid FRC beams was modeled using the stress-strain relationship shown in Figure 13, which was derived from the result of the uniaxial confined compressive strength test. Shear transfer coefficients are typically measured in the range of .0–1.0, with .0 denoting a smooth crack (total loss of shear transfer) and 1.0 denoting a rough crack (no loss of shear transfer). According to (Tahenni et al., 2021), the shear transfer coefficient for open and closed fractures was estimated, and the results were reasonably close to the experimental results. The longitudinal and transverse reinforcements were modeled using the Link 180 element. Table 8 represents the inserted properties of the transverse and longitudinal reinforcements including modulus of elasticity, Poisson’s ratio, and yield stress. The non-linear behaviors of transverse and longitudinal reinforcements were modeled based on the tensile test results. At a distance of 700 mm from the support on either side, double lines of nodes on the upper steel plates are where the force is acting. Two lines of nodes on the bottom end of the beam represent the hinged and roller supports. The roller support was restricted from moving in Y-direction, while the hinged support was restricted from moving in both X, Y, and Z-directions. The steel plates were represented by Link185 element.

The software performs a linear solution for the numerical simulations, gradually increasing the load value, and analyzing convergence. When the requirements are not met, various solution is developed by modifying the stiffness matrix. Collapse can be recognized by cracking patterns, concrete compressive strain approaching maximum, steel reinforcing strain reaching yield, or non-convergence resulting from a total loss of load-bearing capacity. The convergence criteria throughout the current investigation were dependent on force and displacement.

The finite element and experimental outputs were compared to validate the experimental findings. This was accomplished to guarantee that the concrete beam’s convergence conditions are suitable. Figure 14 illustrates the crack patterns and failure modes of hybrid FRC beams based on finite element models. All finite element models cracked similarly to all concrete beams in the experimental program. Where flexural cracks first appeared at the flexure region, followed by shear-flexure cracks, and finally diagonal shear cracks initiated and propagated upward at a 45-degree angle towards the applied load until the beams failed. The failure mode of the finite element model HFCB0-2.8 was similar to that of its experimental equivalent, where diagonal shear cracks occurred, followed by stirrup yielding, which caused the collapse. The finite element model differs in that the diagonal shear crack did not extend to the point where the load was impacting. This is likely because the stirrup reached yield stress before the diagonal shear crack was fully completed. This shows that the finite element model did not exhibit the same level of ductility as in the experimental beam sample to allow for the formation of a full diagonal crack before the collapse, but the failure mode is still the same for both as a diagonal shear crack followed by stirrup yielding. Regarding the finite element model HFCB0.24-2.8, the shown failure mode demonstrated that the addition of stirrups improved its ductility in such a way that it resulted in the formation of a full diagonal shear crack from the support up to the upper edge, followed by the stirrup yielding, which was very similar failure behavior to that experimental equivalent. The failure mode for finite element model HFCB0.42-2.8 did not differ significantly from finite element model HFCB0.24-2.8, as the collapse occurred as a result of a full diagonal shear crack occurring and the stirrups reached yield except with clearer shear-flexure cracks, because the beam could bear higher loads and thus the flexure stresses increased, and consequently, the flexure cracks increased, however, this was ineffective in changing the failure mode. The failure mode and crack pattern for finite element model HFCB0.42-2.8 were very similar to the corresponding experimental sample. The failure mode of finite element model HFCB0.24-2.3 was very similar to that of finite element model HFCB0.24-2.8, but with more and clearer flexural cracks since the strength of the beam increased as the span to depth ratio decreased, and thus the flexure stresses and flexure cracks increased. This failure and crack pattern were quite similar to the equivalent experimental beam. The failure mode of finite element model HFCB0.42-1.75 was comparable to that of the corresponding experimental beam model, except that the diagonal shear crack did not reach the top edge. This confirms that decreasing the span to depth ratio reduced the ductility of the beam, and thus the stirrup reached yield before a complete diagonal shear crack occurred. Additionally, the experimental one had more concrete crushing at the compression zone although this had no effect on the collapse because it was governed by the diagonal shear crack followed by stirrup yielding. Figure 15 shows a comparison between the finite element and experimental load versus deflection curves for all concrete beams. The finite element failure load was higher than the experimental failure load by 29%, 19%, 18%, 13%, and 6% for hybrid reinforced concrete beams HFCB0-2.8, HFCB0.24-2.8, HFCB0.42-2.8, HFCB0.42-2.3, and HFCB0.42-1.75, respectively. The coefficient of variance between the finite element and the experimental results of failure load was 6.5%. The deflection values of all finite element and experimental samples appeared to be nearly equal as shown in the figure, and the relationship between load and deflection seemed to be linear until the crack occurs. Following the occurrence of the crack, the relationship became non-linear with an increase in the experimental sample’s deflection values compared to the finite element model at the same load. The finite element maximum deflection was 2%, 10%, 16%, 22%, and 23% less than the experimental maximum deflection for hybrid reinforced concrete beams HFCB0-2.8, HFCB0.24-2.8, HFCB0.42-2.8, HFCB0.42-2.3, and HFCB0.42-1.75, respectively. The maximum deflection experimental results and the finite element results have a 9% coefficient of variation. Figure 16 compares the finite element and experimental load-transverse strain curves for all concrete beams. The strain values in stirrups for all finite element and experimental samples were insignificant until the cracking load. Following that, the strain in the stirrups increased dramatically until it reached yield stress. The figure shows that the strain values for the experimental samples after the cracking load were greater than the strain values for the finite element models under the same load. For all experimental and finite element models, the strain in the stirrups reached yield. The finite element transverse reinforcement strain values at failure were 15%, 6%, 12%, 1%, and 2% lower for the hybrid reinforced concrete beams HFCB0-2.8, HFCB0.24-2.8, HFCB0.42-2.8, HFCB0.42-2.3, and HFCB0.42-1.75, respectively compared to the experimental transverse reinforcement strain values at failure. Transverse reinforcement strain experimental results and the results from the finite element had a 7.3% coefficient of variation. The comparison revealed that the experimental and finite element results were perfectly correlated.