## 9 Examination of Shear Strength Equation Provided in ACI 318-19 Code  
According to ACI 318-19 [45], the shear strength of non-prestressed members is a function of concrete strength, axial load acting on section, size effect, section area, effective depth, member width, and longitudinal reinforcement ratio. In ACI 318-19, Equations (18a) and (18b) are the equations for calculating the shear strength of RC members containing the shear reinforcement greater than the minimum shear reinforcement. For other cases, Equation (19) shall be used. The parameter \(\lambda_{\mathrm{s}}\) is the size modification factor that shall be determined by Equation (20), in which the effective depth of beam to determine \(\lambda_{\mathrm{s}}\) shall be expressed in inch unit.  
\[\mathrm{V_{c,SF}}=\left(0.17\sqrt{f^{\prime}{}_{c}}+\frac{\mathrm{N_{u}}}{6 \mathrm{A_{g}}}\right)\mathrm{F_{eff}b_{w}d} \tag{18a}\]  
\[\mathrm{V_{c,SF}}=\left(0.66(\rho_{\mathrm{w}})^{\frac{1}{3}}\sqrt{f^{\prime} {}_{c}}+\frac{\mathrm{N_{u}}}{6\mathrm{A_{g}}}\right)\mathrm{F_{eff}b_{w}d} \tag{18b}\]  
\[\mathrm{V_{c,SF}}=\left(0.66\lambda_{\mathrm{s}}(\rho_{\mathrm{w}})^{\frac{1} {3}}\sqrt{f^{\prime}{}_{c}}+\frac{\mathrm{N_{u}}}{6\mathrm{A_{g}}}\right) \mathrm{F_{eff}b_{w}d} \tag{19}\]  
\[\lambda_{\mathrm{s}}=\sqrt{\frac{2}{1+\frac{\mathrm{d}}{10}}} \tag{20}\]  
Due to the absence of shear reinforcing bars in this study, the SFRC beam with a fiber volume fraction of 0.75% or greater is classified as a RC beam with minimum shear reinforcement; otherwise, SFRC beams are classified as RC beams with the shear reinforcement less than the minimum shear reinforcement. Multiplying Equation (18) or (19) with the fiber effectiveness factor is performed to examine the applicability of the shear strength equation provided in ACI 318-19 as the basic equation for predicting the shear strength of SFRC beam.  
The relationship between measured strengths and predicted shear strengths using the multiplication between ACI 318-19 and the fiber effectiveness factor is shown in Figure 11. The shear strength database is used to evaluate the accuracy of the equations. The predicted shear strength shown in Figure 11a is determined by either Equation (18a) or (19), while Figure 11b shows the predicted shear strength determined by either Equation (18b) or (19). Figure 11a,b show similar results. Both the mean and COV shown in those figures are greater than the mean and COV shown in Figure 10. In addition, the number of data appearing above the upper dashed line in Figure 11a,b is 174 and 171, respectively, and the number of data appearing below the upper dashed line is 14 and 13 for Figure 11a,b, respectively.  
Figure 11: Comparison between experimental and prediction results based on ACI 318-19 Equations.  
In Table 7, the mean and COV values exhibited by Equation (18) can be seen. Since the fiber volume fraction in the experimental program was 1.50%, Equation (18) governed the prediction of shear strengths for all SFRC beam specimens. It can be seen that the prediction results obtained by using either Equations (18a) or (18b) are not as accurate as the results obtained by using Equation (17); however, it can be proved that Equation (18) is more conservative than Equation (17).