## 4 Prediction of Shear Strength of Reinforced High-Strength Concrete Beams  
To verify the accuracy of the proposed analytical model for reinforced high-strength concrete beams, 64 experimental results [24; 25; 26; 27; 28; 29; 30; 31; 32; 33] with 90\({}^{\circ}\) stirrups were collected. All collected specimens were failed by shear before 90% of their predicted flexural yield strength. The specimens have a simple beam that receives a concentrated load and a beam that receives an anti-symmetric load. The shape of the cross-section is rectangular- and T-types. The collected specimens have a concrete compressive strength of 42.9-108.7 MPa, a beam width of 125-300 mm, an effective depth of 198-420 mm, a tension reinforcement ratio of 0.00228-0.00454, a shear reinforcement ratio of 0.001-0.0171, yield strengths of tension and shear reinforcement of 406.2-953.2 and 255.0-1431.4 MPa, respectively, and a shear span ratio of 1.7-5. All specimens with a shear span ratio of less than 2.5 appear to be subjected to anti-symmetrical moments. It is noted that a direct compression arch action is not formed, and the truss model is applicable. Table 1 presents the details of collected specimens and the comparison of the experimental results with the analytical ones. In Table 1, the analytical results by ACI 318-19 [34] were calculated according to the ACI shear provisions that the values of \(\sqrt{f_{c}^{{}^{\prime}}}\) greater than 8.3 MPa shall be permitted in the RC beams satisfying minimum shear reinforcement. The shear strength of concrete was calculated using the detailed formula recommended by ACI 318-19. In addition, the yield strength of steel bars was not limited to evaluate the applicability of ACI 318-19. As shown in Table 1 and Figure 6, the analytical results by ACI 318-19 conservatively predicted the experimental results with a mean of 1.28 and a coefficient of variation (COV) of 16.4%. In contrast, the proposed analytical model predicted the shear strength of 64 specimens well with a mean of 0.98 and a COV of 12.1%. Figure 7 shows the prediction results of the proposed model on test variables. As shown  
Figure 5: Calculation procedure. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  
[33] & H75/2 & 68.9 & 3.1 & 0.0228 & 500.0 & 0.00141 & 530.0 & 0.066 & 2.55 & 1.16 & 0.97 \\
[33] & H75/4 & 68.9 & 3.1 & 0.0228 & 500.0 & 0.00141 & 530.0 & 0.066 & 2.89 & 1.26 & 1.09 \\
[33] & H75/4 & 68.9 & 3.1 & 0.0299 & 500.0 & 0.00239 & 53 Table 2 shows the prediction results of the analytical models. TM-NM and TM-FA are the same as the proposed analytical model, but the former does not consider the moment effect, and the latter assumes that the transformation angle, \(\beta\), is zero. As shown in Table 2, TM-NM, which did not consider the moment effect of the beam, overestimated the experimental results with an average of 0.76. Figure 8a shows that TM-NM tends to overestimate the experimental results as the shear span-to-depth ratio increases. On the other hand, the proposed model was hardly affected by the concrete compressive strength and support conditions, and shear span-to-depth ratio, as shown in Table 2 and Figure 8b. As shown in Table 2, the TM-FA with the angle \(\beta\) fixed to zero greatly overestimated the experimental results with an average of 0.86 for the shear strength of 64 specimens. As shown in Figure 9a, this phenomenon becomes clearer when \(\eta\) is less than 0.2. That is, as \(\eta\) decreases, the difference between the crack direction and the principal stress direction increases. However, it can be seen from Figures 7d and 9b that the proposed model applying the transformation angle \(\beta\) is not significantly affected by \(\eta\). Therefore, the proposed shear analytical model can be reasonably used to predict the shear strength of reinforced high-strength concrete beams.