Flexural Performance of Concrete Beams Reinforced with Continuous FRP Bars and Discrete Steel Fibers under Cyclic Loads

This research investigated the flexural behavior of high-strength concrete beams reinforced with continuous basalt fiber-reinforced polymer (BFRP) bars and discrete steel fibers. Five concrete beams with the dimensions of 150 × 300 × 2100 mm3 were constructed and tested to failure under four-point bending cyclic loading. The specimens consisted of four BFRP-reinforced concrete beams with various reinforcement ratios (ρf), namely, 0.56%, 0.77%, 1.15%, and 1.65%, and one conventional steel-reinforced concrete beam for comparison purposes. The cracking behavior, failure modes, load-deflection behavior, residual deformation, and stiffness degradation of the beams were studied. Additionally, a deformation-based approach was used to analyze the deformability of the beams. The results show that an increase in the ρf effectively restrained the crack widths, deflections, and residual deformation while also enhancing the flexural bearing capacity of the beams. In comparison to the first displacement cycle, the bearing capacity dropped by 10% on average in the third cycle. The stiffness exhibited a fast to slow degradation trend until failure. The residual stiffnesses were higher in beams with a higher ρf. The over-reinforced beams had superior deformability than the under-reinforced beams, according to the deformability factors.


Introduction
Reduced load-bearing capacity and durability caused by steel corrosion in conventional reinforced concrete (RC) structures have become major problems in engineering today. Engineering practice shows that when exposed to aggressive environments, corrosion of steel reinforcement accelerates and the durability and service life of RC structures is severely reduced [1][2][3][4][5]. Fiber-reinforced polymer (FRP) bars are increasingly being used to replace steel bars in conventional RC members, owing to their excellent corrosion resistance. In addition, FRP bars are electrically insulating and possess a high tensile strength and strength-to-weight ratio compared to steel bars [6,7]. They have been widely applied in engineering structures in recent decades, especially in aggressive environments [8][9][10][11].
There are several types of FRP materials used as reinforcement in concrete structures, such as aramid FRP (AFRP), carbon FRP (CFRP), glass FRP (GFRP), and basalt FRP (BFRP). The most commonly used types are CFRP, GFRP, and AFRP [12,13]. However, according to Sim's [14] research findings, the performance of GRRP and AFRP could be significantly affected by the alkaline environment within the concrete, whereas the CFRP bars are too expensive to realize large-scale application in civil engineering structures [15]. Advances in FRP technology resulted in increasing demand to introduce new types of fibers. Under these circumstances, a new type of FRP, basalt FRP (BFRP), with superior performance In practical engineering, many structures, such as highway and railway bridges, airport pavements, and offshore elements, are continuously subjected to cyclic loads during their service life, such as traffic loads, wind loads, and seismic loads [42,43]. To date, studies regarding BFRP-RC structures reinforced with or without fibers under monotonic loading have been widely conducted and published [12,13,19,20,24,36]. However, studies on these structures subjected to cyclic loading are still limited. Therefore, the influence of the dynamic load on the FRP-RC structures should be investigated to eliminate the negative impact of the dynamic load on the structural design and construction.
The objective of this research was to study the flexural behavior of steel fiber-reinforced concrete (SFRC) beams reinforced with different ratios of BFRP bars under cyclic loading. A four-point bending test was carried out to evaluate the flexural behavior of these beams on cracking pattern, failure modes, load-deflection behavior, and stiffness degradation under cyclic loading. In addition, a deformation-based approach, which is suitable for FRP-RC members, was employed to assess the deformability of BFRP-SFRC beams.

Materials and Mix Proportion
The composition and mix proportion (by weight) of the concrete are given in Table 1. Ordinary Portland cement of 42.5 grades (P. O 42.5), which was produced in Tianrui Cement Co., Ltd., Zhengzhou, China, was used as the cementitious material in the mix. Natural river sand with a maximum size of 5 mm was used as fine aggregate. Gravel within a size range of 5-20 mm was used as coarse aggregate. Polycarboxylic acid water reducer produced by Sobute New Materials Co., Ltd., Nanjing, China, was used for good workability of the concrete. 0.55 mm diameter SF with a total length of 35 mm were incorporated at a volume ratio of 1%. SF was manufactured by Bekaert, Shanghai, China. The dimension and detailed properties of the SF are shown in Figure 1 and Table 2, respectively. The 28 day average cubic compressive strength and splitting tensile strength of SFRC was 72.5 MPa and 6.30 MPa, respectively. BFPR bars with diameters of 12 mm and 14 mm (see Figure 2) and 14 mm diameter steel bars were used as longitudinal reinforcements. Steel bars with diameters of 10 mm and 6 mm were used as stirrup and erection bars, respectively. BFPR bars were manufactured by GMV New Material Technology Development Co., Ltd., Nanjing, China. Figure 2 shows the surface features of BFRP bars. Table 3 shows the mechanical properties of the reinforcing bars.     Figure 1. Dimensions of SF.

Test Specimens
A total of five beams were designed, four of which were reinforced with different amounts of BFRP bars and one with steel bars. The beams had the same dimensions of 150 × 300 × 2100 mm 3 with a concrete cover of 15 mm. The longitudinal reinforcements were 12 mm and 14 mm diameter BFRP bars and 14 mm diameter steel bars. Steel bars with a 10 mm diameter were used as stirrups at 75 mm spacing to prevent shear failure. The cross-sectional dimensions and reinforcement details are illustrated in Figure 3. Four different ρf values were selected in this test: 0.56% (2Ф12), 0.77% (2Ф14), 1.15% (3Ф14), and 1.65% (4Ф14). Accordingly, each beam was assigned a unique identification, i.e., B56, B77, B115, B165, and S77, in which the letters B and S denote the BFRP and steel reinforcement, respectively, and the number represents the ρf in ‱.

Test Specimens
A total of five beams were designed, four of which were reinforced with different amounts of BFRP bars and one with steel bars. The beams had the same dimensions of 150 × 300 × 2100 mm 3 with a concrete cover of 15 mm. The longitudinal reinforcements were 12 mm and 14 mm diameter BFRP bars and 14 mm diameter steel bars. Steel bars with a 10 mm diameter were used as stirrups at 75 mm spacing to prevent shear failure. The cross-sectional dimensions and reinforcement details are illustrated in Figure 3. Four different ρ f values were selected in this test: 0.56% (2Φ12), 0.77% (2Φ14), 1.15% (3Φ14), and 1.65% (4Φ14). Accordingly, each beam was assigned a unique identification, i.e., B56, B77, B115, B165, and S77, in which the letters B and S denote the BFRP and steel reinforcement, respectively, and the number represents the ρ f in ‱.

Test Setup, Instrumentation and Loading Procedure
The test setup and instrumentation are illustrated in Figure 4. The beams were all simply supported and tested to failure under four-point bending cyclic loading. Each beam had a clear span of 1800 mm and a 150 mm extension outside each support. The constant moment region had a length of 600 mm, which was the same as the shear region. A hydraulic actuator with a load capacity of 500 kN was utilized to exert the load, which was connected to a steel I-beam to transfer the load to the loading points. Five linear variable differential transformer (LVDT) sensors were employed to record the deformation of the beams. Crack width detectors (see Figure 5) were used to measure the crack widths.

Test Setup, Instrumentation and Loading Procedure
The test setup and instrumentation are illustrated in Figure 4. The beams were all simply supported and tested to failure under four-point bending cyclic loading. Each beam had a clear span of 1800 mm and a 150 mm extension outside each support. The constant moment region had a length of 600 mm, which was the same as the shear region. A hydraulic actuator with a load capacity of 500 kN was utilized to exert the load, which was connected to a steel I-beam to transfer the load to the loading points. Five linear variable differential transformer (LVDT) sensors were employed to record the deformation of the beams. Crack width detectors (see Figure 5) were used to measure the crack widths.

Test Setup, Instrumentation and Loading Procedure
The test setup and instrumentation are illustrated in Figure 4. The beams were all simply supported and tested to failure under four-point bending cyclic loading. Each beam had a clear span of 1800 mm and a 150 mm extension outside each support. The constant moment region had a length of 600 mm, which was the same as the shear region. A hydraulic actuator with a load capacity of 500 kN was utilized to exert the load, which was connected to a steel I-beam to transfer the load to the loading points. Five linear variable differential transformer (LVDT) sensors were employed to record the deformation of the beams. Crack width detectors (see Figure 5) were used to measure the crack widths.  The cyclic loading was executed under displacement control with a target loadingunloading rate of 2 mm/min. The displacement increment Δ was set at 6 mm. Three loading-unloading cycles were applied to the specimens at each displacement level (Δ, 2Δ, 3Δ…), after which the displacement increased to a higher level, as Figure 6 shows.  The cyclic loading was executed under displacement control with a target loadingunloading rate of 2 mm/min. The displacement increment ∆ was set at 6 mm. Three loading-unloading cycles were applied to the specimens at each displacement level (∆, 2∆, 3∆ . . . ), after which the displacement increased to a higher level, as Figure 6 shows. When the bearing load of beams dropped below 80% of the ultimate load, the test stopped. The cyclic loading was executed under displacement control with a target loadingunloading rate of 2 mm/min. The displacement increment Δ was set at 6 mm. Three loading-unloading cycles were applied to the specimens at each displacement level (Δ, 2Δ, 3Δ…), after which the displacement increased to a higher level, as Figure 6 shows. When the bearing load of beams dropped below 80% of the ultimate load, the test stopped.

Results and Discussion
In this section, the cracking behavior, failure modes, load-deflection behavior, stiffness degradation, and ductility and deformability of the beams are discussed. The flexural test results are summarized in Table 4.

Results and Discussion
In this section, the cracking behavior, failure modes, load-deflection behavior, stiffness degradation, and ductility and deformability of the beams are discussed. The flexural test results are summarized in Table 4.

Cracking Behavior and Failure Modes
The initial cracks all appeared in the pure bending zone of the beams. Compared with beam B56, the ρ f of beams B77, B115, and B165 increased 38%, 105%, and 195%, respectively, while the crack loads increased only 5%, 14%, and 24%, respectively, which indicates that the ρ f increasing had a minor influence on the crack load. Beam S77 had the largest crack load due to the high stiffness of steel reinforcement. The crack distribution diagram is presented in Figure 7. When the displacement reached 0.5∆, the maximum crack widths reached 0.20 mm, 0.16 mm, 0.14 mm, 0.10 mm, and 0.10 mm for beams B56, B77, B115, B165, and S77 at the corresponding loads of 57.0 kN, 60.3 kN, 63.8 kN, 69.8 kN, and 84.4 kN, respectively. When the displacement level was increased to 1∆, the crack widths and number of cracks both increased. New cracks initiated and propagated at the shear zone of beams. However, the crack widths hardly changed after the second and third cycles. When the displacement level was increased to 2∆, cracks in the pure bending zone had developed completely and propagated to a considerable height (over 70% of the beam depth). Cracks in the shear zone developed rapidly during this stage. With further loading, new cracks initiated and propagated only in the shear zone. The cracks widths kept increasing with the increasing displacement level until the beam failed. Figure 7 shows that the number of cracks in beams B115 and B165 is more than that in beams B56 and B77, thereby resulting in smaller crack spacing. third cycles. When the displacement level was increased to 2Δ, cracks in the pure bending zone had developed completely and propagated to a considerable height (over 70% of the beam depth). Cracks in the shear zone developed rapidly during this stage. With further loading, new cracks initiated and propagated only in the shear zone. The cracks widths kept increasing with the increasing displacement level until the beam failed. Figure 7 shows that the number of cracks in beams B115 and B165 is more than that in beams B56 and B77, thereby resulting in smaller crack spacing.  Figure 8 illustrates the load-maximum crack widths curves of the beams. In BFRP-RC beams, the crack widths reduced with the ρf increasing under the same load level. At the average service load (30% of the average ultimate load), the maximum crack widths decreased 34%, 52%, and 76% with the ρf increased from 0.56% to 0.77%, 1.15%, and 1.65%, respectively. In beam S77, the crack widths were small under the initial loading due to the high elastic modulus of steel bars. After yielding, the crack widths increased dramatically and were much wider than that of the BFRP-SFRC beams. ACI440.1R-15 [28] suggests 0.7  Figure 8 illustrates the load-maximum crack widths curves of the beams. In BFRP-RC beams, the crack widths reduced with the ρ f increasing under the same load level. At the average service load (30% of the average ultimate load), the maximum crack widths decreased 34%, 52%, and 76% with the ρ f increased from 0.56% to 0.77%, 1.15%, and 1.65%, respectively. In beam S77, the crack widths were small under the initial loading due to the high elastic modulus of steel bars. After yielding, the crack widths increased dramatically and were much wider than that of the BFRP-SFRC beams. ACI440.1R-15 [28] suggests 0.7 mm as the maximum crack width limit for FRP-RC flexural structures. The crack widths under the service load (30% of the ultimate load) in Table 4 and under the average service load in Figure 8 are all within the ACI crack width limit for all the beams. For beams that failed by concrete crushing, B165 had a larger crack width under the ultimate load but a smaller one under the service load compared to that of B115, which indicates that the increase in the ρ f improves the serviceability of beams.  Table 4 and under the average service load in Figure 8 are all within the ACI crack width limit for all the beams. For beams that failed by concrete crushing, B165 had a larger crack width under the ultimate load but a smaller one under the service load compared to that of B115, which indicates that the increase in the ρf improves the serviceability of beams. During the test, the beams exhibited two typical failure modes: tension failure and compression failure, as Figure 9 shows. Beams B56 and B77 exhibited tension failure and the BFRP bars ruptured '/ bars ruptured. When the load of beam B165 dropped below 80% During the test, the beams exhibited two typical failure modes: tension failure and compression failure, as Figure 9 shows. Beams B56 and B77 exhibited tension failure and the BFRP bars ruptured '/bars ruptured. When the load of beam B165 dropped below 80% of the maximum load, the BFRP bars were still working. The deformation of beam B165 could almost be restored after unloading.  Figure 10 presents the load-deflection curves of the beams. The enclosed area of the loading-unloading curves of the BFRP-SFRC beams decreased gradually with the ρf increasing. This indicates that the stiffness of the beams was enhanced by increasing the amount of BFRP bars. As a result, the beams with a higher ρf reached a higher displacement level and experienced more loading-unloading cycles. For each beam, the loading-unloading curves of the second and third cycle almost coincided when the deflection was at a lower level. As the deflection grew larger, the spacing between the loading-unloading curves of the second and third cycle grew gradually larger. This demonstrates that the stiffness of the beams degraded with the increase in displacement and load cycles. In beam S77, the deflection increased linearly with the load at the initial stage. After yielding, the deflection increased rapidly while the bearing load remained unchanged. The enclosed area by the loading-unloading curve was similar at each displacement level, which indicates that the stiffness of the beam reduced significantly after yielding.  Figure 10 presents the load-deflection curves of the beams. The enclosed area of the loading-unloading curves of the BFRP-SFRC beams decreased gradually with the ρ f increasing. This indicates that the stiffness of the beams was enhanced by increasing the amount of BFRP bars. As a result, the beams with a higher ρ f reached a higher displacement level and experienced more loading-unloading cycles. For each beam, the loading-unloading curves of the second and third cycle almost coincided when the deflection was at a lower level. As the deflection grew larger, the spacing between the loading-unloading curves of the second and third cycle grew gradually larger. This demonstrates that the stiffness of the beams degraded with the increase in displacement and load cycles. In beam S77, the deflection increased linearly with the load at the initial stage. After yielding, the deflection increased rapidly while the bearing load remained unchanged. The enclosed area by the loading-unloading curve was similar at each displacement level, which indicates that the stiffness of the beam reduced significantly after yielding. Under the same displacement level, the bearing capacity of the beams slightly decreased with the increase of load cycles due to damage accumulation inside the beam. While at the late loading stage, the decrement of flexural bearing capacity increased significantly, indicating that the beam was on the verge of destruction. Table 5 summarizes the flexural bearing capacity degradation factor at each displacement level Under the same displacement level, the bearing capacity of the beams slightly decreased with the increase of load cycles due to damage accumulation inside the beam. While at the late loading stage, the decrement of flexural bearing capacity increased significantly, indicating that the beam was on the verge of destruction. Table 5 summarizes the flexural bearing capacity degradation factor at each displacement level for all the beams. The flexural bearing capacity degradation factor was the ratio of bearing capacity at the third cycle to that at the first cycle at each displacement level [44]. It can be seen that the majority of the factors were all above 90% until the beams failed. The average degradation factor of beams failed by compression failure is only 1% larger than that of beams failed by tension failure, which indicates that the BFRP ρ f had a negligible effect on the bearing capacity degradation of the beams.  Figure 11 presents the skeleton curves of the beams. The beams with higher a ρ f obtained higher ultimate flexural capacities. The ultimate flexural bearing capacity of the beams B77, B115, and B165 increased by 48%, 76%, and 117%, respectively, compared with that of B56, which were much larger than the increments in crack load. The deflections of the BFRP-SFRC beams grew non-linearly with the load increasing but decreased significantly with the ρ f increasing. At the service load (30% of the ultimate load), the deflections of the over-reinforced beams B115 and B165 were 4.73 mm, and 4.80 mm, respectively, which were all within the limitation in ACI (l/180, l is the clear span of the beam). With the ρ f increased from 1.15% to 1.65%, the deflection increased 5% under the ultimate load but 1.4% under the service load. This demonstrates that the increase in the ρ f had a stronger influence on the deflections under the serviceability limit state than the ultimate limit state, which is consistent with the conclusion on the crack width. Before yielding, the deflection of beam S77 increased linearly with the load and was smaller than that of the BFRP-SFRC beams. Afterward, the deflection increased continuously with the load sustained at approximately 150 kN, which was far larger compared to that of the BFRP-SFRC beams. degradation factor of beams failed by compression failure is only 1% larger than that of beams failed by tension failure, which indicates that the BFRP ρf had a negligible effect on the bearing capacity degradation of the beams.  Figure 11 presents the skeleton curves of the beams. The beams with higher a ρf obtained higher ultimate flexural capacities. The ultimate flexural bearing capacity of the beams B77, B115, and B165 increased by 48%, 76%, and 117%, respectively, compared with that of B56, which were much larger than the increments in crack load. The deflections of the BFRP-SFRC beams grew non-linearly with the load increasing but decreased significantly with the ρf increasing. At the service load (30% of the ultimate load), the deflections of the over-reinforced beams B115 and B165 were 4.73 mm, and 4.80 mm, respectively, which were all within the limitation in ACI (l/180, l is the clear span of the beam). With the ρf increased from 1.15% to 1.65%, the deflection increased 5% under the ultimate load but 1.4% under the service load. This demonstrates that the increase in the ρf had a stronger influence on the deflections under the serviceability limit state than the ultimate limit state, which is consistent with the conclusion on the crack width. Before yielding, the deflection of beam S77 increased linearly with the load and was smaller than that of the BFRP-SFRC beams. Afterward, the deflection increased continuously with the load sustained at approximately 150 kN, which was far larger compared to that of the BFRP-SFRC beams. The load-residual deflection curves are presented in Figure 12. Similar to the skeleton curves, the residual deflection decreased significantly with the ρf. Considering the linear elastic characteristic of BFRP bars, the deformation of the BFRP-SFRC beams can be partly restored after unloading at each displacement level. Therefore, the residual deflection of The load-residual deflection curves are presented in Figure 12. Similar to the skeleton curves, the residual deflection decreased significantly with the ρ f . Considering the linear elastic characteristic of BFRP bars, the deformation of the BFRP-SFRC beams can be partly restored after unloading at each displacement level. Therefore, the residual deflection of beams B56, B77, B115, and B165 increased at a relatively lower rate in the initial loading stage. With the load cycles and displacement levels increasing, the internal damage of concrete gradually accumulated, resulting in a faster increase in residual deflection. Large plastic deformation appeared after steel bar yielding in beam S77, resulting in a rapid increase in residual deformation, which was larger than that of the BFRP-SFRC beams. At the failure stage of the test, the break of BFRP bars in beams B56, B77, and B115 resulted in a much larger ultimate residual deflection than beam B165. Since beam B165 was failed by concrete crushing, the ultimate deflection kept decreasing after unloading due to the linear elastic stress-strain relationship of the BFRP bars. Therefore, it can be concluded that the residual deformation of BFRP-SFRC beams with a higher ρ f can be effectively controlled under cyclic loading. concrete gradually accumulated, resulting in a faster increase in residual deflection. Large plastic deformation appeared after steel bar yielding in beam S77, resulting in a rapid increase in residual deformation, which was larger than that of the BFRP-SFRC beams. At the failure stage of the test, the break of BFRP bars in beams B56, B77, and B115 resulted in a much larger ultimate residual deflection than beam B165. Since beam B165 was failed by concrete crushing, the ultimate deflection kept decreasing after unloading due to the linear elastic stress-strain relationship of the BFRP bars. Therefore, it can be concluded that the residual deformation of BFRP-SFRC beams with a higher ρf can be effectively controlled under cyclic loading.

Stiffness Degradation
In this study, equivalent stiffness was utilized to study stiffness degradation. The equivalent stiffness (K) was defined as the secant of the skeleton curve, namely, the ratio of the peak load to the corresponding deflection at the first cycle of each displacement level. Figure 13 illustrates the stiffness degradation of the beams. The stiffness of the beams had a similar degradation trend. At the initial loading stage, all beams had high stiffnesses and stiffness degradation rates. This is mainly due to the continuous initiation and propagation of new cracks in the early stage of loading, which leads to damage accumulation in concrete. With further loading, the stiffness degradation rate decreased significantly. This can be attributed to the bridging effect of SF, which restrained the deformation of the beams during this stage. With a further increase in the displacement, the stiffness degraded at a lower rate until the beams failed. It is noticeable that the beams with a higher ρf had higher residual stiffnesses. In beam S77, the stiffness degraded more slowly in the early stage of loading and faster in the later stages compared with the BFRP-SFRC beams.

Stiffness Degradation
In this study, equivalent stiffness was utilized to study stiffness degradation. The equivalent stiffness (K) was defined as the secant of the skeleton curve, namely, the ratio of the peak load to the corresponding deflection at the first cycle of each displacement level. Figure 13 illustrates the stiffness degradation of the beams. The stiffness of the beams had a similar degradation trend. At the initial loading stage, all beams had high stiffnesses and stiffness degradation rates. This is mainly due to the continuous initiation and propagation of new cracks in the early stage of loading, which leads to damage accumulation in concrete. With further loading, the stiffness degradation rate decreased significantly. This can be attributed to the bridging effect of SF, which restrained the deformation of the beams during this stage. With a further increase in the displacement, the stiffness degraded at a lower rate until the beams failed. It is noticeable that the beams with a higher ρ f had higher residual stiffnesses. In beam S77, the stiffness degraded more slowly in the early stage of loading and faster in the later stages compared with the BFRP-SFRC beams.

Ductility and Deformability
Ductility is one of the most important structural design criteria, and is defined as th ability of a beam to maintain inelastic deformation without losing its load-bearin capacity before failure [31]. Structures with good ductility can exhibit early warnin before failure, whereas for brittle structures, little or no warning is presented befor failure. In traditional RC structures, the ductility index is defined as the ratio of ultimat deflection to yield deflection. However, this definition is no longer applicable to FRP-R members, since FRP bars present linear elasticity until failure [37,45]. Accordingly, severa methods were suggested to evaluate the ductility for FRP-RC structures. Naaman an Jeong [46] and Jaeger et al. [47] first introduced the energy-based method and th deformation-based method, respectively, to determine the ductility index for FRP-R beams. However, the deformation-based method was reported to be more applicable tha the energy-based method when considering the contribution of SF on the ductility of FRP RC beams [46,48]. Consequently, in this study, the deformation concept was adopted t assess the ductility of BFRP-SFRC beams. The deformability factor J is defined as follow The calculation results are shown in Table 6. It is suggested by Jaeger et al. [47] an CSA-S6-06 [27] that the deformability factor for FRP-RC beams should not be less than The deformability factor J varied from 6.54 to 10.68 in Table 6. This suggests that BFRP SFRC beams have excellent deformability. For under-reinforced beams (i.e., B56 and B77 the high compressive strength and ultimate strain of SFRC in the compression zone wer not fully developed due to the rupture of the BFRP bars. Therefore, the deformabilit factor was lower. For over-reinforced beams (i.e., B115 and B165), the high compressiv strength and ultimate strain of SFRC were fully exploited before the BFRP bars ruptured The values of factor J were larger than that of under-reinforced beams but slightly reduce with the ρf further increased, which indicates that a further increase in BFRP ρf did no

Ductility and Deformability
Ductility is one of the most important structural design criteria, and is defined as the ability of a beam to maintain inelastic deformation without losing its load-bearing capacity before failure [31]. Structures with good ductility can exhibit early warning before failure, whereas for brittle structures, little or no warning is presented before failure. In traditional RC structures, the ductility index is defined as the ratio of ultimate deflection to yield deflection. However, this definition is no longer applicable to FRP-RC members, since FRP bars present linear elasticity until failure [37,45]. Accordingly, several methods were suggested to evaluate the ductility for FRP-RC structures. Naaman and Jeong [46] and Jaeger et al. [47] first introduced the energy-based method and the deformation-based method, respectively, to determine the ductility index for FRP-RC beams. However, the deformation-based method was reported to be more applicable than the energy-based method when considering the contribution of SF on the ductility of FRP-RC beams [46,48]. Consequently, in this study, the deformation concept was adopted to assess the ductility of BFRP-SFRC beams. The deformability factor J is defined as follows: where C S = the moment coefficient; C C = the curvature coefficient; M u = ultimate Moment; φ u = ultimate curvature; M ε = 0.001 = moment at a concrete compressive strain of 0.001; and φ ε = 0.001 = curvature at a concrete compressive strain of 0.001. The calculation results are shown in Table 6. It is suggested by Jaeger et al. [47] and CSA-S6-06 [27] that the deformability factor for FRP-RC beams should not be less than 4. The deformability factor J varied from 6.54 to 10.68 in Table 6. This suggests that BFRP-SFRC beams have excellent deformability. For under-reinforced beams (i.e., B56 and B77), the high compressive strength and ultimate strain of SFRC in the compression zone were not fully developed due to the rupture of the BFRP bars. Therefore, the deformability factor was lower. For over-reinforced beams (i.e., B115 and B165), the high compressive strength and ultimate strain of SFRC were fully exploited before the BFRP bars ruptured. The values of factor J were larger than that of under-reinforced beams but slightly reduced with the ρ f further increased, which indicates that a further increase in BFRP ρ f did not improve the deformability of over-reinforced beams. Therefore, to obtain better deformability, the ρ f of over-reinforced beams should be conservative.

Conclusions
The objective of this work was to investigate the flexural behavior of BFRP-SFRC beams under four-point bending cyclic loads. The following conclusions were derived from the above discussions on the BFRP-SFRC beams: (1) The increase in reinforcement ratio led to a notable decrease in crack widths. The enclosed area by the loading-unloading curves gets smaller with the increase in the reinforcement ratio. This reveals that the stiffness of the beams was strengthened by the increase in the reinforcement ratio. The beams with a higher reinforcement ratio could bear larger displacement levels and more loading-unloading cycles. (2) The BFRP-SFRC beams exhibited good serviceability with the increase in the reinforcement ratio for over-reinforced beams. The crack widths and deflections of all the beams at service load were all within the ACI limit. (3) With the increase in the displacement level and load cycles, the stiffness of the beams gradually reduced. The midspan deflections and residual deflections were effectively restrained by increasing the amount of BFRP reinforcement. (4) The bearing capacity of the beams slightly degraded with the load cycles. The flexural bearing capacity degradation factors were mostly above 90% before failure and were negligibly influenced by the reinforcement ratio under different displacement levels.
The ultimate flexural capacities of the beams were significantly improved by increasing the BFRP reinforcement ratio. (5) The stiffness of the beams degraded rapidly in the early stage of loading and then slowly until failure. The beams with higher reinforcement ratios had larger residual stiffnesses. The stiffness of the beams reinforced with steel bars degraded more slowly in the initial loading, but faster after yielding compared with beams reinforced with BFRP bars. (6) The ductility of the BFRP-SFRC beams was evaluated by the deformability-based approach. The deformability factor ranged from 6.54 to 10.68, which indicates that the beams had good ductility. For over-reinforced beams, the value of the deformability factor reduced as the reinforcement ratio increased from 1.15% to 1.65%. Therefore, it is suggested that the reinforcement ratio for the over-reinforced beams should be conservative. Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.