## 4 Experimental Results and Discussions  
### Mechanical Properties  
The compressive strengths of all cylindrical specimens are shown in Figure 4. The compressive strengths, found to be approximately 50 MPa, were not influenced by the fiber volume fraction and the number of hook ends. This is consistent with the findings of [PERSON] and [PERSON] (1998) and [PERSON] and [PERSON] (2000), who reported that the addition of fibers yields a negligible change in the compressive strength of concrete. This is because the steel fibers incorporated lead to positive and negative effects on the compressive strength simultaneously, i.e., inhibition of crack formation and propagation and their inhomogeneous dispersion. [PERSON] and [PERSON] [PERSON] and [PERSON] (2000) reported that the fibers enhance the resistance to nucleation and growth of cracks in concrete, based on fundamental fracture tests. Thus, it is concluded that the inclusions of 3D, 4D, and 5D hooked-end steel fibers into the concrete mixture do not result in any significant change in the compressive strength up to a volume fraction of 1%. The flexural load versus CMOD curves of all tested beams are shown in Figure 5. Regardless of the number of hook ends, a higher flexural strength was obtained with increased fiber volume fraction. At the low volume fraction of 0.37%, the specimens with 3D and 4D hooked-end fibers exhibited a deflection-softening behavior, while that with 5D hooked-end fiber provided a vague deflection-hardening behavior. When the volume fraction was 0.6%, all specimens showed a higher post-cracking flexural strength (\(f_{\text{MOR}}\)) than the initial cracking strength (\(f_{\text{LOP}}\)), although there was a sharp decrease in load immediately after the formation of matrix cracking. The sharp decreases in loads after cracking, observed in the specimens with a fiber volume fraction of less than 0.6%, were attributed to the fact that the amounts of fibers existing at the crack surface were insufficient to immediately sustain the cracking tensile force. Once the crack is formed in the matrix, a steep decrease in load with increasing CMOD, called matrix softening, is obtained. However, for fiber-reinforced concrete, the post-cracking tensile stress can increase again owing to the fiber bridging effect, and their total post-cracking behavior is determined by adding the matrix softening and fiber bridging curves ([PERSON] and [PERSON], 2000). The sharp decrease in load immediately after cracking is therefore dependent on the slope of the matrix softening and fiber bridging stiffness. Based on a micromechanical analysis, [PERSON] et al. [PERSON]  
Figure 3: Test setup for SFRC pedestrian deck: (**a**) picture, (**b**) schematic description. the fiber bridging stiffness increases with increasing fiber volume fraction; thus, the sharp load drop was mitigated by increasing the fiber contents in all types of steel fibers in Figure 5. In general, slightly higher flexural strengths (\(\
ot{V}_{\text{MOR}}\)) were observed in the SFRC beams with 4D and 5D hooked-end fibers compared to 3D hooked-end fibers because of the improved mechanical anchorage at the fiber ends. Several important parameters regarding flexural strengths of SFRCs are summarized in Table 2, based on _fib_ Model Code 2010 [26; 27]. The flexural strength at the limit of proportionality (\(f_{L}\)) was  
Figure 4: Summary of compressive strengths. Figure 5: Summary of three-point flexural test results: (**a**) \(v_{f}\) of 0.37%, (**b**) \(v_{f}\) of 0.60%, and (**c**) \(v_{f}\) of 1.00%. calculated by using Equation (4) and the highest value of the load was recorded up to a CMOD of 0.05 mm [5]. In addition, residual flexural strengths (\(f_{R,j}\)) were calculated using Equation (4) with load values corresponding to CMODs of 0.5, 1.5, 2.5, and 3.5 mm, respectively.