## 2 Research Objective and Design Process of Novel Pedestrian Decks  
The major objective of this study is to examine the effects of the number of end hooks and volume fraction of steel fibers on the structural behavior of pedestrian concrete decks since most of previous studies were focused on only the material properties. Also, the feasibility of using various types of hooked steel fibers on pedestrian decks made of high-strength concrete instead of the conventional steel rebars is evaluated. A pedestrian deck requiring a minimum flexural reinforcement was targeted. To achieve this, three hooked-end steel fibers with different hook geometries, i.e., 3D, 4D, and 5D, were adopted along with three different volume fractions of 0.37%, 0.60%, and 1.00%. The medium volume fraction of hooked-end fibers (i.e., 0.60%) was determined as the threshold value, exhibiting a similar cracking load (\(P_{\sigma}\)) and post-cracking ultimate load (\(P_{u}\)) based on three-point bending tests. The lower volume fraction of 0.37% provides a deflection-softening behavior, whereas the higher volume fraction of 1.00% exhibits a deflection-hardening behavior. [PERSON] et al. [1] studied the development of lightweight concrete slabs for maintaining the Soleri Viaduct using polymeric fibers without conventional steel rebars and suggested the suitable amount (15.5 kg/m\({}^{3}\)) of polymer fibers, which can replace the minimum flexural reinforcement given by Eurocode 2 [4], based on a ductility index (DI) of \(DI=\frac{P_{u}-P_{\sigma}}{P_{\sigma}}\), where \(p_{u}\) is the ultimate flexural load and \(P_{\sigma}\) is the cracking load. Some international codes such as ACI 318-14 [3] and Eurocode 2 [4], have suggested an equation for determining the minimum flexural reinforcement area (\(A_{s,\min}\)) to prevent sudden failure immediately after crack generation and to guarantee a ductile failure mode, as follows (in SI units):  
\[A_{s,\min}=\frac{0.25\sqrt{f_{ck}}}{f_{y}}b_{w}d\geq\frac{1.4}{f_{y}}b_{w}d \ [\text{ACI 318}] \tag{1}\]  
\[A_{s,\min}=\frac{0.26f_{ctm}}{f_{y}}b_{w}d\geq 0.0013b_{w}d\ [\text{ Eurocode 2}] \tag{2}\]  
where \(f_{ck}\) is the compressive strength of concrete, \(f_{y}\) is the yield strength of steel rebar, \(b_{w}\) is the beam width, \(d\) is the effective depth of beam, and \(f_{ctm}\) is the tensile strength of concrete.  
Equations (1) and (2) were suggested to satisfy the assumption that the nominal moment capacity is greater than or at least equal to the cracking moment (\(M_{n}\geq M_{\sigma}\)). The nominal moment capacity, \(M_{n}\), is calculated by multiplying the resistance factor (\(\phi\)) of 0.9 and the ultimate moment given by the yield strength of steel rebar and moment arm; the cracking moment, \(M_{\sigma}\), is evaluated using the modulus of rupture and sectional geometry. Accordingly, to replace the minimum amount of steel rebars with discontinuous fibers, it should be confirmed that the SFRC provides the deflection-hardening response, leading to a higher load-carrying capacity after the formation of cracks.  
In particular, based on some assumptions, i.e., (1) the plane section remains plane, (2) concrete exhibits linear elastic behavior, and (3) neutral axis depth is located at the center, the ratio of nominal moment and cracking moment (\(M_{n}/M_{\sigma}\)) can be calculated. If the beam height is considered as 1.2 times the effective depth of beam (\(h=1.2d\)) [16], the nominal and cracking moment ratio from ACI 318 code can be obtained (approximately 1.19), which means that the nominal moment capacity is 19% higher than the cracking moment. Thus, the ultimate flexural strength of deflection-hardening SFRCs needs to be at least 20% higher than the first cracking strength conservatively to guarantee the ductile flexural behavior.