## 4 Calculation Model for Determining the Shear Strength of the Tested Samples  
### Methodology of Calculating Shear Strength of the Control RC Beams  
For a long time in Eastern Europe, codes [38] allowed the calculation of the bearing capacity on the shear according to the engineering method. Figure 3 shows the distribution of forces in the calculation scheme from the distributed load \(q\) (or equivalent action \(F\)) and the occurrence of forces in concrete \(Q_{b}\) and transverse reinforcement \(R_{sw}A_{sw}\), which is located with step \(s\). The bearing capacity of such an element is considered at the section on the length of the projection of a diagonal crack on the longitudinal axis (c--length for reinforcement, c\({}_{0}\)--for concrete). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Beam** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Number of Tested** \\ **Support Area** \\ \end{tabular} & \begin{tabular}{c} **The Actual** \\ **Cross-Section** \\ **\(\mathbf{h\times b}\)****mm** \\ \end{tabular} & \begin{tabular}{c} **Span** \\ **\(\mathbf{l_{0}}\)****mm** \\ \end{tabular} & \begin{tabular}{c} **Shear** \\ **Span, \(\mathbf{al}\)** \\ **\end{tabular} & \begin{tabular}{c} **Shear** \\ **Capacity,** \\ **\(\mathbf{V_{Ed}^{\text{exp}}}\), kN** \\ \end{tabular} & \begin{tabular}{c} **Shear Bearing** \\ **Value,** \\ **\(\mathbf{V_{Ed}^{\text{exp}}}\), kN** \\ \end{tabular} & \
\begin{tabular}{c} **Average** \\ **Value,** \\ **\(\mathbf{V_{Ed}^{\text{exp}}}\), kN** \\ \end{tabular} \\ \hline \multirow{2}{*}{\(\text{BO}\ 1.1\)} &
\begin{tabular}{c} BO 1.1.1 \\ \end{tabular} & \multirow{2}{*}{\(201\times 101\)} & \multirow{2}{*}{\(1900\)} & \multirow{2}{*}{\(97\)} & \multirow{2}{*}{\(95\)} & \multirow{2}{*}{\(1.00\)} \\ \cline{2-2} \cline{5-6}  & BO 1.1.2 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.1.1-0 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.1.2-0 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.2.1-0.3 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.2.2-0.3 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.3.1-0.5 & & & & & & \\ \cline{2-2} \cline{5-6}  & BS 1.3.2-0.5 & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bearing capacity of strengthened research samples on the shear without internal transverse reinforcement. Figure 3: Scheme of the shear forces when calculating according to the engineering method [38]. The engineering method is based on the equilibrium of limit forces. The basis is the determination of the actual internal forces in the support section and their comparison with the external acting loads. The calculation of RC elements for the action of the transverse force was carried out under the condition:  
\[Q\leq Q_{b}+Q_{saw} \tag{1}\]  
This relationship determines the total shear force as the sum of the strength of shear reinforcement and the concrete shear strength that can be borne by the support section. Since there is no transverse reinforcement in the samples, condition (1) takes the form:  
\[Q\leq Q_{b} \tag{2}\]  
The shear force perceived by concrete was calculated based on the following:  
\[Q_{b,1}=\frac{\varphi_{b2}\cdot\left(1+\varphi_{f}+\varphi_{n}\right)\cdot R_ {bt}\cdot b\cdot h_{0}^{2}}{c} \tag{3}\]  
However, if the value is not less than:  
\[Q_{b,2}=\varphi_{b3}\cdot\left(1+\varphi_{f}+\varphi_{n}\right)\cdot R_{bt} \cdot b\cdot h_{0}. \tag{4}\]  
\(\varphi_{b2}=2;\varphi_{b3}=0.6\)--coefficient that takes into account the influence of the type of concrete (light or heavy); \(\varphi_{f}=0\)--a coefficient that takes into account the influence of compressed flanges in T-shaped and I-shaped elements (accepted no more than 0.5); \(\varphi_{n}=0\)--a coefficient that takes into account the influence of longitudinal compressive forces; \(c\)--the length of the projection of the most dangerous inclined section on the longitudinal axis of the element, cm; \(b,h_{0}\)--respectively, the width and effective depth of the section, cm; \(R_{bt}\)--design value of concrete axial tensile strength, MPa.