## 2 Literature Review
### Evaluation of Shear Strength Prediction Equations  
Eight equations are compared with test results. Two-hundred thirty-six test results from reinforced concrete and SFRC beams without shear reinforcement and with concrete compressive stress ranging from 20.6 to 194 MPa, shear span-to-effective depth ratio ranging from 1.0 to 6.0, and fiber volume fraction ranging from 0 to 2%, are collected [11; 13; 17; 21; 24; 25; 26; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39]. The relationship between measured and predicted shear strengths using previous shear strength prediction equations is shown in Figure 3. The statistic evaluation results, namely mean and coefficient of variation (COV) values for comparison between measured and predicted strengths are summarized in Table 1 and shown in Figure 3 as well. If a data point appears above the solid line, the measured strength is greater than the predicted stress; otherwise, the predicted strength is greater than the measured strength. Two dashed lines are shown as boundaries with 20% offset from the predicted shear strength. Figure 3: Cont. Figure 3: _Cont._  
Figure 3: Comparison between measured and predicted shear strengths. The shear strength model proposed by [PERSON] (Equation (2)) tends to overestimate the shear strength of SFRC beam. One-hundred specimens appear below the lower dashed line, which means that the measured shear strength values of 100 specimens are less than 80% of the corresponding predicted shear strength values. On the other hand, the measured shear strength values of 57 specimens are greater than 120% of the corresponding predicted shear strength values. Calculated shear strength values using the model proposed [PERSON] and [PERSON] (Equation (3)) and [PERSON] et al. (Equations (5) and (6)) show conservative results compared to results from [PERSON]'s equation (Equation (2)). This may have occurred due to the former three equations considering explicitly the parameters affecting the shear strength of SFRC beams. By contrast, [PERSON]'s model misses the effects of longitudinal reinforcement ratio and steel fiber parameters. By using Equations (3) and (5), most of the data appears above the lower dashed line; by contrast, using the second equation of [PERSON] et al. (Equation (6)) exhibits more data appearing below the bottom dashed line (Figure 3d) compared to results from Equations (3) and (5). [PERSON] [15] constructed a database by considering the shear span-to-effective depth ratio, cylinder concrete compressive strength, fiber volume fraction, steel fiber tensile strength, and fiber aspect ratio. [PERSON] [15] set \(0.3\sqrt{f^{r}_{c}}\) (Equation (7)) as a lower bound for evaluating the application of steel fibers in SFRC beams and for supporting the use of deformed steel fibers as the minimum shear reinforcement regardless of the shear span-to-effective depth ratio, concrete compressive strength, or the longitudinal tensile reinforcement ratio. [PERSON] [15] reported that the shear stress values of SFRC beams with fiber volume fraction of 0.75% or greater (based on [PERSON]'s database) were greater than \(0.3\sqrt{f^{r}_{c}}\) (MPa). Figure 3e shows that there are 60 specimens located below the lower dashed line. In general, the shear strength model from [PERSON] (Equation (7)) is more conservative than that derived by [PERSON] (Equation (2)). The equation proposed by [PERSON] et al. (Equation (8)) appears to be superior to the equations proposed by [PERSON] (Equation (2)), [PERSON] and [PERSON] (Equation (3)), and [PERSON] et al. (Equation (5)). Only 18 points appear below the lower dashed line. This number is slightly greater than the number exhibited by using Equation (6). The shear model proposed by [PERSON] et al. involves the important parameters affecting shear strength. [PERSON]'s shear strength model is not as conservative as the shear strength model proposed by [PERSON] et al., since the former has 131 specimens appearing above the upper dashed line, while the latter shows 137 specimens appearing above the upper dashed line.