## 6 Conclusions  
This study examined the effects of hooked-end steel fiber geometry and volume content on the flexural behavior of concrete pedestrian decks. For this, three different geometries, i.e., 3D, 4D, and 5D hooked ends, and three different volume fractions of 0.37%, 0.6%, and 1.0% were considered. In order to simulate their flexural behaviors, sectional analyses considering the material models recommended by RILEM [15] were conducted. Based on the experimental and numerical results, the following conclusions can be drawn:  
1. For the high-strength concrete with a compressive strength of approximately 50 MPa, all the uniaxial beams with a low fiber volume fraction of 0.37% showed a deflection-softening behavior, whereas others with a higher volume fraction of 0.6% or 1.0% exhibited a deflection-hardening behavior. Regardless of the steel fiber type, the flexural performance of SFRC was improved by increasing the amounts of fibers.
2. Increasing the number of hook ends in hooked-end steel fibers can effectively increase the flexural strength and induce ductile flexural behavior of SFRC beams. Therefore, the specimens with 5D  
Figure 14: Calculated neutral axis depth and deflection relationships: (**a**) 3D fiber, (**b**) 4D fiber, (**c**) 5D fiber.  
hooked-end steel fibers resulted in the greatest flexural strengths and flexural strength margins (=\(f_{\text{MOR}}/f_{\text{LOP}}-1\)) at all volume fractions, followed by the 4D and 3D hooked-end fibers.
3. To guarantee a ductile flexural behavior and replace the minimum longitudinal steel rebars of concrete pedestrian decks based on ACI 318 code, 0.6% of 4D and 5D hooked-end fibers and 1.0% of 3D hooked-end fibers were required to be incorporated. Furthermore, in order to satisfy the DI value of 0.39 for the minimum reinforcement ratio given by [PERSON] et al. [1], the required amount of all the hooked-end fibers (i.e., 3D, 4D, and 5D) was approximately 0.98%-1.10%.
4. Regardless of the number of hook ends, a multiple cracking behavior was observed only when the fiber volume fraction is 1.0%.
5. The flexural strength ratios of experiments and simulations, based on RILEM recommendation [15] and sectional analyses, were found to be 0.75, 0.81, and 0.93 on average for the 3D, 4D, and 5D hooked-end fiber specimens, respectively. The numerical results indicated that to guarantee a deflection-hardening response of pedestrian decks, the fiber volume fraction needs to be 1.0%, regardless of the steel fiber type.
6. Consequently, a volume fraction of 1.0% of hooked-end steel fibers is recommended to replace the minimum longitudinal steel rebars and guarantee a ductile flexural behavior with multiple cracks for concrete pedestrian decks.  
Conceptualization, D.-Y.M.; methodology, D.-Y.M. and S.-J.L.; software, D.-Y.Y.; validation, D.-Y.M. and D.-Y.Y.; formal analysis, D.-Y.Y.; investigation, D.-Y.Y.; resources, D.-Y.M.; data curation, D.-Y.M.; writing--original draft preparation, D.-Y.Y.; writing--review and editing, S.-J.L.; visualization, D.-Y.Y.; supervision, D.-Y.Y.; project administration, D.-Y.M.; funding acquisition, D.-Y.M.  
This research was supported by a grant (18 CTAP-C117247-03) from Technology Advancement Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.  
The authors declare no conflict of interest.