## 2 Literature Review  
### The General Behavior of SFRC Beams  
As summarized by [PERSON] in 2009 [PERSON] (2009), the steel fibers perform a role similar to that of shear reinforcement in the transversally-reinforced concrete beam. The presence of steel fibers supports the redistribution of tensile stress, prevents the propagation and opening of diagonal cracks, and is effective for controlling cracks and fostering the formation of multiple diagonal cracks. Furthermore, like shear reinforcement, the steel fibers can delay early concrete splitting along the tensile reinforcing bar. It is known that the orientation and distribution of steel fibers in concrete may not be well controlled due to possible segregation and fiber balling issues; therefore, the shear strength analysis for an SFRC beam faces several challenges. The proper distribution of the steel fibers for the improvement of mechanical properties is also the most important issue related to the steel fiber reinforcement in an SFRC member. Unlike normal concrete, the opening of wide diagonal cracks in an SFRC beam is the result of fiber pullout rather than shear reinforcement yielding. Moreover, the pullout behavior of steel fibers and the bond strength between the steel fibers and the concrete remain a complex problem [PERSON] (2009). The shear behavior of a simply-supported SFRC beam subject to two-point concentrated and monotonic loads is affected by beam cross section (shape and size), ratio of shear span-to-effective depth, tensile reinforcement ratio, concrete compressive strength, size of coarse aggregate, fiber volume fraction, and the bond stress between steel fibers and the surrounding matrix. The commonly considered parameters for calculating SFRC ultimate shear stress are the shear span-to-effective depth, the longitudinal tensile reinforcement ratio, the concrete compressive strength, the fiber volume fraction, and the bond stress between steel fibers and the surrounding matrix. The shear span-to-effective depth ratio has a significant effect on the SFRC ultimate shear strength, as shown in previous research studies. The arch action occurring in a beam with smaller shear span transfers load from the loading point to the support directly through a compressive strut. [PERSON] (2009) reported that [PERSON] et al. in 1972 proposed a critical value of a shear span-to-effective depth ratio of 3 for the SFRC beams. The relationship between normalized shear strength and the shear span-to-effective depth ratio reported by different researchers is shown in Figure 1([PERSON], 2009). The symbols \(\mathrm{V_{u}}\), \(\mathrm{b_{w}}\), \(\mathrm{d}\), \(f^{\prime}_{\ c}\), \(\mathrm{a}\), \(\mathrm{\rho}\), \(f_{yl}\), \(f_{u,SF}\), and \(\mathrm{V_{f}}\) shown in Figure 1 stand for beam ultimate shear strength, beam section width, section effective depth, concrete compressive strength, shear-span length, longitudinal reinforcement ratio, yield strength of longitudinal reinforcing bar, ultimate tensile strength of steel fiber, and fiber volume fraction, respectively. It can be seen that the beam shear strength becomes smaller, as the shear span-to-effective depth ratio increases. The longitudinal tensile reinforcement ratio in an SFRC beam was investigated as well. The SFRC beam with greater longitudinal tensile reinforcement ratio can resist more ultimate shear strength due to an increase of dowel action and height of compression zone [13; 22]. In general, the steel fibers must contribute to improving the dowel strength, since steel fibers provide bridging action across the microcracks in the matrix and improve resistance to crack opening. [PERSON] and [PERSON] [23] conducted an experimental study, in which they provided several beam specimens. They reported that the concrete strain prior to dowel cracking varied between \(600\times 10^{-6}\) to \(850\times 10^{-6}\), where these values were relatively high compared to the maximum tensile strain of normal and even fiber reinforced concrete.