## 4 Experimental Results and Discussions
### Flexural Performance of Concrete Pedestrian Decks
#### 4.2.2 Ductility Evaluation  
To comparatively evaluate the effectiveness of adding hooked-end steel fibers and their amounts on the first-cracking and ultimate loads, the ratios of ultimate load and first-cracking load (\(P_{u}/P_{cr}\)) are shown in Figure 9. In general, increasing the volume fraction of hooked-end steel fibers led to an increased \(P_{u}/P_{cr}\) ratio. This means that an increase in fiber amount is more efficient in enhancing the ultimate load than the cracking load, because the fiber bridging is mainly activated after the formation of matrix cracks. Similarly, [PERSON] et al. [6] reported that the first-cracking flexural strength of SFRC beams with \(v_{f}\) of 0.5% was similar to that of plain concrete beams without fibers as it is more dependent on the matrix cracking strength than the fiber bridging effect; however, the SFRC beams with \(v_{f}\) of more than 1.0% provided a noticeably higher flexural strength than the plain concrete beams. Because a higher \(P_{u}/P_{cr}\) ratio guarantees a more ductile behavior, adding a higher amount of hooked-end steel fibers of up to 1% is beneficial in fabricating ductile pedestrian concrete decks without conventional steel rebars. It is interesting to note that, at the moderate volume fraction of 0.6%, steel fibers with a higher number of hook ends led to a higher \(P_{u}/P_{cr}\) ratio; however, that ratio decreased with an increase in the number of hook ends at the high volume fraction of 1.0%. To quantitatively investigate the ductility of pedestrian decks, two different DIs, based on flexural load and deflection, are adopted. First, DI is calculated by dividing the difference between the post-cracking ultimate load and cracking load by the cracking load [1]. Second, a deflection DI, calculated by dividing the deflection at the first-cracking point by the deflection at the maximum load, is adopted. The DIs are given as follows:  
\[DI=\frac{P_{pu}-P_{cr}}{P_{cr}} \tag{6}\]  
Figure 8: Summary of (**a**) cracking load and (**b**) peak load. \[\mu=\frac{\Delta_{cr}}{\Delta_{p}} \tag{7}\]  
where \(P_{pu}\) is the post-cracking ultimate load, \(P_{cr}\) is the cracking load, \(\mu\) is the deflection ductility index (DI), \(\Delta_{cr}\) is the deflection at the cracking point, and \(\Delta_{p}\) is the deflection at maximum load. The relationship between the load DI and fiber volume fraction is shown in Figure 10a. It is obvious that the DI increases with increasing volume fraction for all types of hooked-end steel fibers, which is consistent with the findings of [PERSON] et al. [1]. According to the minimum reinforcement ratio concept given by the ACI 318 code, the 4D and 5D hooked-end fibers can replace the minimum longitudinal rebars if their volume fraction is equal to 0.6%, whereas the 3D hooked-end fiber requires a higher volume fraction of 1.0%. The highest value of DI was found to be 0.43 in the specimen with 1.0 vol% of 3D hooked-end steel fibers, which is much higher than that (below 0.3) given by [PERSON] et al. [1] for sidewalk slabs made of lightweight SFRC and having a similar size. In particular, the DI value obtained in the lightweight slab reinforced with the minimum amount of conventional steel rebars was 0.39 [1], which is lower than the highest value of SFRC slabs without steel rebars tested in this study. The 3D hooked-end fiber specimens provided the steepest increase in the DI values according to the fiber volume fraction, followed by the 4D and 5D hooked-end fiber specimens. This is because the effectiveness of hooked-end steel fibers for enhancing the DI at the high volume fraction of 1.0% was greater in the specimens with a lower number of hook ends. Based on a previous study [1], if we assume the minimum value of DI as 0.39, the required amount of hooked-end steel fibers to satisfy it can be calculated based on a simple linear empirical equation: \(DI=\mathrm{a}\times v_{f}+b\), where \(v_{f}\) is the fiber volume fraction.