## 4 Calculation Model for Determining the Shear Strength of the Tested Samples
### Methodology of Calculating Shear Strength of the Strengthened RC Beams by FRCM System
To take into account the load level of the beam at which the strengthening took place, it is proposed to use a coefficient \(\gamma_{yw}^{add}\) that depends on the carrying capacity of the beam for shear strength and the load level. For the load factor of the element, it is suggested to use the dependence:  
\[\gamma_{yw}^{add}=\left(1-\frac{V_{Ed}}{V_{Rd}}\right)^{n} \tag{16}\]  
\(V_{Ed}\)--external transverse force; \(V_{Rd}\)--design value of the shear strength of the RC beams; n--the index, which considered influencing from internal steel reinforcement (3/2--for a support area without transverse reinforcement; 1/2--for a support area with transverse reinforcement). The bearing capacity is proposed to be calculated as the sum of the concrete and reinforcement composite system shear strength. This principle is proposed in Formula (1) [38], in Section 4.1 described above. Based on the described Equations (6), (14), and (16), the following dependence of determining the shear strength of the RC bent elements without transverse (shear) reinforcement strengthened with composite fabric under action of the load was obtained:  
\[V_{Rd}=V_{Rd,c}+V_{Rd}^{add}\cdot\gamma_{yw}^{add} \tag{17}\]  
Analogous expressions are proposed for providing the shear strength strengthened with composite materials by many researchers and are given in Fib recommendations [42]. The above expressions were tested to calculate the bearing capacity of tested samples without internal transverse reinforcement. The value of the shear strength of the control samples is determined according to the current code, and consider the refined value \(C_{Rd,c}\) determined according to Equation (13). Result of the theoretical calculation data is shown in the Table 6.  
Additionally, the obtained results are shown as curves in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Beam**} & \multicolumn{4}{c}{**Theoretical Data**} & \multicolumn{4}{c}{**Experimental Results**} & \multirow{2}{*}{\(V_{Rd,e}\)} \\ \cline{2-2} \cline{4-7}  & \multirow{2}{*}{\(V_{Rd,e}\), kH} & \multirow{2}{*}{\(\gamma_{yw}^{add}\)} & \multirow{2}{*}{\(V_{Rd}^{add}\)} & \multirow{2}{*}{\(V_{Rd}^{add}\)} & \multirow{2}{*}{\(V_{Rd}^{add}\)} & \multirow{2}{*}{\(V_{Ed}^{add}\)} & \multirow{2}{*}{\(V_{Ed}^{add}\)} & \multirow{2}{*}{\(V_{Rd}^{add}\)} \\ \cline{3-3} \cline{5-7}  & & & & & & & \\ \hline BO 1.1 & \multirow{3}{*}{81.6} & – & – & 81.6 & 95 & – & 1.16 & – \\ \cline{1-1} \cline{5-7}  & & 1.0 & 34.6 & 116.2 & 137.5 & 42.5 & 1.18 & 1.23 \\ \cline{1-1} \cline{5-7}  & & 0.7 & 20.3 & 101.9 & 120 & 25.0 & 1.17 & 1.23 \\ \cline{1-1} \cline{5-7}  & & 0.5 & 12.2 & 93.8 & 110 & 15.0 & 1.17 & 1.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison theoretical and experimental data of the shear strength of the tested RC beams without transverse reinforcement strengthened with a composite system. Satisfactory convergence of results was obtained for all experimental samples, within 16-18% in the direction of overstatement of experimental data. The calculation shear strength of the composite material as a transverse reinforcement, taking into account the proposed coefficient, shows a satisfactory convergence, namely an overestimation of the experimental data by 23% for all investigated levels of the active load.