## 6 Shear Strength of the Beams Tested in Lab
### Shear Strength of the Beams after Retrofitting by CFRP Reinforcement  
For the beams retrofitted by means of EB-CFRP reinforcement, the transverse steel and the CFRP contributions to the shear resistance should be calculated using the angle of the concrete compressive strut (\(\theta\)) equal to 45\({}^{\circ}\). In fact, the plastic force redistribution in the shear steel reinforcement is limited by the CFRP reinforcement that is characterized by a brittle failure, and the angle \(\theta\) does not reduce much with respect to 45\({}^{\circ}\). The predicted shear strength values were calculated by Equation (15) or (16) for the retrofitted beams indicated in SS6 with steel and FRP shear reinforcement, and for the beams DB1-R and DB2-R assuming the partial factors are equal to one; the angle \(\theta\) is equal to 45\({}^{\circ}\); the material mechanical characteristics, the beam concrete geometries and the reinforcement configurations given in Tables 11 and 12. The effective depth for flexure is about 750 mm for the beams DB1-R and DB2-R.  
Figure 10: Beam before retrofitting: experimental and predicted shear strength values considering (**a**) the fixed or (**b**) the variable inclination angle of the concrete compressive strut. \begin{table}
\begin{tabular}{l l c c c c c c c} \hline \hline  & & **Mean** & \begin{tabular}{c} **St.** \\ **Deviation** \\ \end{tabular} & **CoV** & **max** & **min** & \begin{tabular}{c} **5\%** \\ **Percentile** \\ \end{tabular} & \
\begin{tabular}{c} **95\%** \\ **Percentile** \\ \end{tabular} \\ \hline \multirow{2}{*}{\(\mathrm{V_{Rd,exp}}/\mathrm{V_{Rd}}\)} & Fixed & 2.12 & 0.48 & 0.23 & 3.04 & 1.43 & 1.48 & 2.91 \\  &
\begin{tabular}{c} Variable \\ angle \(\theta\) \\ \end{tabular} & 0.88 & 0.18 & 0.21 & 1.22 & 0.57 & 0.67 & 1.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical values of the predictions: mean, Standard deviation, Coefficient of Variation, max, min, 5% and 95% percentile of the ratio \(\mathrm{V_{Rd,exp}}/\mathrm{V_{Rd}}\). The experimental shear strength (\(\mathrm{V_{Rd,r\,exp}}\)) of the selected beams is given by the authors (SS6) that tested these beams. In Figure 11, each point gives information about the predicted and the experimental shear strength values for each tested beam. The line \"m\" indicates the perfect correspondence between the predicted and the measured shear strength values. Figure 11a shows a model with large scatter. The shear strength values predicted by Equation (15), in which the contribution of the concrete is added to the ones of the CFRP and the transverse steel reinforcements, overestimate the experimental shear strength values for many tested beams. This happens despite the assumption of the angle \(\theta\) equal to \(45^{\circ}\) that underrates the transverse steel contribution (SS6.1). Partial factors should be considered to properly reduce the prediction of the Equation (15) to consider the scatter, but this is not investigated in this study. Alternatively, Figure 11b shows a large scatter but the predicted values by Equation (16), that do not consider the concrete contribution, are safer because many points are below the line \"m\". The partial factors may improve the safety of the prediction for the a few points above the line \"m\" in Figure 11b. The statistical values of the ratio \(\mathrm{V_{Rd,r\,exp}}/\mathrm{V_{Rd,r}}\) calculated by Equation (15) or Equation (16) for each beam, are given in Table 6.  
The predicted value of the retrofitted beam shear strength is, on average, 82% of the experimental one if the contribution of concrete is not considered. For that reason, the concrete contribution, which is uncertain, should be not considered in the prediction equation. The application of the two models (Equation (15) or (16)) on the \"real\" beams DB1-R and DB2-R gives result similar to the ones obtained for the beam tested in the literature.