## 5 Relationship between Shear Behavior of Anchors and Tensile Performance of SFRC  
The load and deflection curves of both the SFRC beams and anchors exhibited linear and elastic behavior before concrete cracking. This means that the tensile stress generated from the external loads is smaller than the cracking strength of the concrete and, thus, all of the materials including the concrete effectively endure the external loads. The inclusion of steel fibers has little effect on the cracking strength of the SFRC beams and anchors. As shown in Figures 3 and 9, the cracking strength of the beams, \(f_{cr}\), and the cracking shear load of the anchors, \(V_{cr}\), are almost constant regardless of the fiber volume fractions. On the other hand, the ultimate strength of the beams, \(f_{u}\), and the maximum concrete breakout shear load of the anchors, \(V_{u}\), increased almost linearly with increasing fiber volume fractions. According to the linear trend analysis, \(f_{u}\) and \(V_{u}\) increase by approximately 4.04 MPa and 19.90 kN per percent of fiber volume fraction, respectively. The design shear resistance of anchors embedded in the non-reinforced plain concrete is dependent on the edge distance, embedded depth, and diameter of the anchor, as well as the compressive strength  
Figure 12: Energy absorption capacities \(E_{u}\) and \(E_{r}\) of the anchors in the plain concrete and SFRC with increasing fiber volume percentages from zero to 1.00%. of the concrete [8; 9]. As mentioned, the steel fibers had little effect on the compressive and cracking strengths but greatly improved the ultimate flexural strength of the concrete. Thus, the concrete breakout shear resistance of the anchors needs to be determined using the ultimate flexural strength of the concrete, \(f_{u}\), which can account for the improvement of the tensile capacity of concrete by the steel fibers rather than the compressive strength of the concrete specified in the ACI 318 design standards [7; 8]. Figure 13 shows the relationships between the ratios of \(f_{u}\) and \(\sqrt{f_{u}}\) of the SFRC beams and \(V_{u}\) of the SFRC anchors with the increasing fiber volume fractions to those of the non-reinforced plain concrete. \(f_{u,\phi}\) is the ultimate flexural strength of the plain concrete beam, which corresponds to \(f_{cr}\). \(V_{u,\phi}\) is the concrete breakout shear resistance of the plain concrete anchor. \(f_{u}\) tends to increase exponentially, while \(\sqrt{f_{u}}\) and \(V_{u}\) show linear increases as the fiber volume fraction increases. Furthermore, the rate of increase of \(\sqrt{f_{u}}\) is very similar to that of \(V_{u}\), which corresponds to the design equation expressed as a function of \(\sqrt{f_{c}^{\prime}}\), in which \(f_{c}^{\prime}\) is the compressive strength of concrete. Thus, based on the design equation specified in the ACI 318 [7; 8], the concrete breakout shear resistance of an anchor in the SFRC can be expressed as  
\[V_{u} = k\Big{(}\frac{h_{0}}{d_{0}}\Big{)}^{2}\sqrt{d_{0}}\sqrt{f_{u}}(c_{0} )^{1.5} \tag{2}\]  
where the influence factors of the anchor diameter, embedded depth, and edge distance are taken as those specified in the ACI 318 [7; 8], and the term for the compressive strength of concrete, \(\sqrt{f_{c}^{\prime}}\), is replaced with a term for the ultimate flexural strength of concrete, \(\sqrt{f_{u}}\), which includes the effect of the steel fibers on the tensile capacity of concrete. For the plain concrete anchor, \(\sqrt{f_{u}}\) corresponds to the flexural tensile strength of concrete. The factor \(k\) in Equation (2) can be determined by comparing the measured maximum shear load of anchors with the shear capacity calculated by Equation (2) without the \(k\) term. Figure 14 shows the variation in the factor \(k\) with the change in the fiber volume percentages from zero to 1.00%. The average and standard deviation of \(k\) are 3.83 and 0.19, respectively. Thus, \(k\) is simplified as a constant equal to 4.0.