## 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  
The bearing capacity of the RC beams on the shear, which is strengthened with composite system in the form of fabric strips, is calculated according to the method of the truss analogy [2; 3]. It is calculated based on the condition that the shear force is perceived only by the shear reinforcement. In this case, the stressed-strained state of the support area is considered by the truss analogy (Figure 7). The concrete compressed zone is taken as a top, compressed chord (Figure 7A), and the working tensile reinforcement, respectively, as a bottom, tensile truss chord (Figure 7C). In this case, compressed struts of the webs are reduced to compressed strips of concrete in the support area of the beams (Figure 7B)  
In Ukraine, codes do not allow the design of reinforced concrete elements strengthened with composite materials. Therefore, to calculate the bearing capacity on the shear, we accept the following prerequisites for the operation:  
* there is a valid hypothesis of flat sections for the supporting areas;
* reinforcement with composite material works as additional external reinforcement;
* the reinforcement system works together with the concrete in the support area. In this way, the external composite reinforcement is included in the design model, as with tensile elements of the truss web. Provided that the accepted prerequisites are correct, it is proposed to calculate the shear strength of the strengthening element, such as internal shear reinforcement. Therefore, to calculate the shear strength of the strengthening system, we use an equation from codes [2; 3], substituting the parameters of the composite fabric:  
\[V_{Rd}^{add}=\frac{A_{sw}^{add}}{s}\cdot z\cdot f_{ywd}^{add}\cdot\cot\theta \tag{14}\]  
\(A_{fw}=(0.00455\times 7)\times 2=0.0637\) mm\({}^{2}\)--cross-sectional area of the composite fabric; \(s_{f}=100\) mm--step of strengthening elements. The angle \(\theta\) was determined along the diagonal crack in which the destruction of the element took place. However, it should be noted that the angle of inclined struts extends from the point of the center of force applied to the face of the element's support (Figure 8). With the determined bearing capacity of the additional reinforcement, the angle of inclined struts was \(21.8^{\circ}\), which was defined from experimental data (Figure 9). The obtained value of the angle of inclination corresponds to the maximum value from the code cot\(\theta=2.5\)[2; 3]. The calculated shear strength of the composite reinforcement was determined by relationship (15), taking into account the calculation recommendations given in the report [42]:  
\[f_{ywd}^{add}=k\cdot\varepsilon_{fd,e}\cdot E_{fud}=k\cdot\frac{\varepsilon_{ fk,e}}{\gamma_{f}}\cdot 0.4\cdot E_{fuk} \tag{15}\]  
Figure 8: Location of the inclined struts [41]. Figure 9: The angle of inclined struts in the sample BS 1.1.1–0. \(\varepsilon_{fd,e}\)--design value of limit strains for composite reinforcement; \(\varepsilon_{fk,e}=\frac{\varepsilon_{f,e}}{\gamma_{f}}\)--characteristic value of limit strains for composite reinforcement; \(\gamma_{f}=1.3\)--partial factor by material, according to recommendations [42], which is accepted when there is a possibility of slipping through the fabric or \(\gamma_{f}=1.35\) if there is a possibility of tissue rupture (or the coefficient is taken equal to 1 in the case of the impossibility of the above-described conditions); \(k=0.8\) --reducing coefficient showing the dependence of the shear strength to the tensile strength of the reinforcement, described in the code [2] and Fib recommendations [42]; \(E_{fud}\)--the design value of the modulus of elasticity of the composite material, which is taken at the level of 40% of the characteristic value. According to Fib recommendations [38], the joint operation of concrete and reinforcement elements occurs only with such an underestimation of the characteristic value of the composite material modulus of elasticity.