*3.3. Residual Deflection*

The residual deflection was defined as the irrecoverable deflection of a beam after the load was unloaded to 0 [36]. Figure 9 presents the load-residual deflection curves of beams. From Figure 9, it can be found that the residual deflection of all beams increased with the increase of the applied load and the number of unloading–reloading cycles under the same deflection. Moreover, the influence of the number of unloading–reloading cycles on the residual deflection became more significant under higher load. For beam B1.15C60V1.0S3, the residual deflection after the third unloading–reloading cycle was only 5.15% higher than that of the first loading when the deflection was 6 mm, while the residual deflection after the third unloading–reloading cycle was nearly 10% higher than that of the first loading when the deflection increased to 42 mm. The residual deflection of other beams demonstrated a similar trend. The reason was that the stiffness of a beam was larger at the initial stage of loading, the unloading–reloading cycle had a little cumulative effect on the internal damage of the beam, but the stiffness of the beam degraded rapidly at the later stage of loading, the damage accumulation of concrete and BFRP bars increased with the increase of a number of unloading–reloading cycles, resulting in larger residual deflection.

Figure 10 illustrates the load-residual deflection curves of the beams under the first unloading–reloading cycle. The influences of the four variables on the load-residual deflection curves of the beams are elaborated in Figure 10. The BFRP reinforcement ratio had the greatest influence on the load-residual deflection curves. The stress growth rate of beams with a high BFRP reinforcement ratio was lower than that of beams with a low BFRP reinforcement ratio after cracking. Therefore, beams with a low reinforcement ratio had a larger residual deflection. The residual deflection of B0.77C60V1.0S3, B1.15C60V1.0S3, and B1.65C60V1.0S3 under the 110 kN load was 40.31%, 62.61%, and 76.13%, respectively, lower than that of B0.56C60V1.0S3.

**Figure 9.** *Cont*.

**Figure 9.** Load-residual deflection curves for beams: (**a**) B0.56C60V1.0S3; (**b**) B0.77C60V1.0S3; (**c**) B1.15C60V1.0S3; (**d**) B1.65C60V1.0S3; (**e**) B1.15C60; (**f**) B1.15C60V0.5S3; (**g**) B1.15C60V1.5S3; (**h**) B1.15C60V1.0S4; (**i**) B1.15C60V1.0S5; (**j**) B1.15C30V1.0S3.

**Figure 10.** Load-residual deflection (first cycle) for beams with different: (**a**) BFRP reinforcement ratio; (**b**) steel fiber content; (**c**) steel fiber shape; (**d**) concrete strength.

Secondly, concrete strength and steel-fiber volume fraction also had significant effects on the load-residual deflection curves. From Figure 10a,b, the residual strength of the beam decreased with the increase of concrete strength and steel-fiber volume fraction. Compared with beam B1.15C30V1.0S3 with low-strength concrete grade 30, the residual deflection of beam B1.15C60V1.0S3 with high-strength concrete grade 60 at 110 kN reduced by increased by 5.56%. The increase of steel-fiber volume fraction increased the bridging action between concrete and steel fibers, which hindered the development of concrete cracking in the tensile zone, and then enhanced the stiffness of the beams, therefore reducing their residual deflection [36]. Compared with beam B1.15C60 without steel fibers, the residual deflection of beam B1.15C60V1.5S3 with a steel-fiber volume fraction of 1.5% at 110 kN applied load was reduced by 30.36%.

Finally, the steel fiber shape had the least influence on the load-residual deflection curves, as shown in Figure 10d. 3D, 4D, and 5D steel fibers all had the same fiber aspect ratio but different lengths, numbers of hook-ends, and tensile strength. The results indicated that all three types of steel fibers had a bond-slip failure, and no steel fibers were broken during testing. Longer fibers and more hook-ends are both beneficial for improving the bond between concrete and steel fibers, but the strength of steel fibers had little influence on the bond between concrete and fibers. Therefore, the residual deflection of the beams with 5D steel fibers was lower than that of beams with 3D steel fibers. However, the influence of steel fiber shape on the residual deflection was less obvious than the other three variables.
