## 1 Introduction  
In general, pedestrian bridge decks only require minimal longitudinal steel reinforcing bars (rebars), compared to conventional bridge decks that are subjected to wheel loads because of the smaller magnitude of loads applied. Thus, only the minimum amount of steel rebars is installed in some pedestrian decks, such as the Soleri Viaduct [1] and other civil structures, e.g., tunnel linings [2]. Inclusion of conventional steel rebars in concrete structures has several benefits such as achieving a ductile behavior under flexure or tension; however, it also has some drawbacks, e.g., an increased thickness of concrete element needed to obtain a sufficient cover depth in terms of enough bond strength, reduced durability due to corrosion of steel rebars, and a work volume increase at construction sites. According to ACI 318 [3] and Eurocode 2 [4], minimum reinforcement ratios are recommended to prevent sudden brittle failure after cracking; hence, they derived equations for the minimum reinforcement ratio based on an assumption that the moment capacity is greater than or at least equal to the cracking moment (\(M_{n}\geq M_{cr}\)), where \(M_{n}\) is the nominal moment capacity and \(M_{cr}\) is the cracking moment. Therefore, if the concrete material itself can achieve a deflection-hardening characteristic,which increases the load carrying capacity even beyond the matrix cracking point, we can theoretically eliminate the conventional steel rebars from some concrete structures that only require the minimum reinforcement ratio and overcome the limitations of incorporating steel rebars. To achieve an excellent post-cracking flexural (or tensile) performance of concrete, many researchers [5; 6; 7; 8; 9] have incorporated discontinuous fibers into the concrete mixture. The incorporated fibers could improve the flexural performance of concrete by effectively bridging the cracks. [PERSON] and [PERSON] [7] experimentally verified that concrete reinforced with deformed steel fibers exhibit a higher flexural strength and toughness than that reinforced with polymeric fibers under static flexure. In addition, according to a previous study by [PERSON] and [PERSON] [8], using hooked-end steel fibers is more effective in enhancing the flexural performance of normal and mid-strength concretes with compressive strengths of approximately 40 MPa and 52 MPa, in terms of the flexural strength and toughness, compared to other types of deformed steel fibers such as crimped and twin-coned. [PERSON] and [PERSON] [9] noted that using the steel fibers is most effective in enhancing the modulus of rupture of concrete than using polypropylene (PP) fibers or hybrid use of steel and PP fibers. Thus, it can be expected that hooked-end steel fibers can be effectively used to reinforce plain concrete under flexure and replace the minimum amount of conventional steel rebars in concrete with a design strength of 50 MPa. In recent years, some researchers [10; 11; 12; 13; 14] developed a novel multiple hook-end steel fiber and verified its effectiveness based on pullout and tensile tests. [PERSON] and [PERSON] [10] reported that the maximum pullout load and energy of conventional hooked-end steel fibers with three-dimensional (3D) geometry are significantly improved by using four-dimensional (4D) and five-dimensional (5D) geometries. The typical picture of 3D, 4D, and 5D hooked fibers used in this study is shown in Figure 1. The 5D hooked-end steel fiber provided 11% and 73% higher maximum pullout load and 53% and 92% higher pullout energy than the 4D and 3D hooked-end steel fibers, respectively [10]. Such a superior bond performance is achieved because of the improved mechanical anchorage, owing to the increased number of hook ends. The peak and post-peak tensile strengths of steel fiber-reinforced concrete (SFRC) with conventional 3D hooked-end fibers were significantly enhanced by using the 4D and 5D hooked-end fibers, according to a previous study performed by [PERSON] et al. [11].