## 4 Calculation Model for Determining the Shear Strength of the Tested Samples
### Methodology of Calculating Shear Strength of the Control RC Beams
Current codes [1; 2; 3] regulate shear strength calculation according to the \"truss model\". The bearing capacity in the zone of action of the transverse force, where is no shear reinforcement, is considered the strength of the concrete in a section at an angle of 45\({}^{\circ}\). The shear strength of reinforced concrete beams, according to current standards [1; 3], is considered similar to condition (2):  
\[V_{Ed}\leq V_{Rd,c} \tag{5}\]  
\(V_{Ed}=Q\)--the calculated value of the transverse force from the external load. This is the value of the transverse force that a support area can absorb without transverse rebar and prestressed longitudinal reinforcement or axial force, according to the codes [2; 3], is determined by the dependence:  
\[V_{Rd,c1}=\frac{\left[C_{Rd,c}\cdot k\cdot\left(100\cdot\rho_{1}\cdot f_{ck} \right)^{\frac{1}{3}}\right]\cdot b_{w}\cdot d}{\beta} \tag{6}\]  
However, if the value is not less than:  
\[V_{Rd,c2}=\
u_{\min}\cdot b_{w}\cdot d \tag{7}\]  
\(C_{Rd,c}\)--concrete shear strength [39], codes [2; 3] recommend taking 0.18; \(k=1+\sqrt{200/d}\) --coefficient, which takes into account the influence of the beam cross-section depth; \(\rho_{1}=\frac{A_{d}}{b_{w}d}\)--reinforcement ratio for longitudinal reinforcement; \(A_{sl}\)--cross-sectional area of tensile reinforcement, mm\({}^{2}\); \(f_{ck}\)--characteristic value of concrete compressive strength at the age of 28 days, MPa; \(b_{w},d\)--respectively, the smallest width of the cross-section in the tensile area and the effective depth of the cross-section, mm; \(\
u_{\min}=0.035\cdot k^{3/2}\cdot f_{ck}^{1/2}\)--theminimum value of the shear strength that can lead to failure before yielding occurs in the longitudinal reinforcement, MPa. Longitudinal reinforcement was taken into account in the calculation only if it was installed at a distance \(l_{bd}\) beyond the projection of the calculated section at an angle of 45\({}^{\circ}\). In this case, \(l_{bd}\)--the minimum required anchoring length of longitudinal reinforcement (Figure 4). The coefficient \(\beta\) is equal to \(a_{v}/2d\) when loading the design elements from above within limits \(0.5\cdot d\leq a_{v}\leq 2\cdot d\) (Figure 5) as a reducing coefficient of the shear force. In this model, it is proposed to consider it in the calculation by dividing the determined bearing capacity by this coefficient. When using the coefficient \(\beta\), the following condition must be met:  
\[V_{Ed}\leq 0.5\cdot b_{w}\cdot d\cdot\
u\cdot f_{cd} \tag{8}\]  
\(f_{cd}\)--design value of concrete compressive strength, MPa; \(\
u\)--coefficient of reduction shear strength of cracked concrete. It is recommended to determine the coefficient \(\
u\) according to the dependence [3]:  
Figure 3:0  
Make calculations of the control samples according to the above dependencies. For convenience, we summarize the main calculation parameters in Figure 3:1  
The results of the calculation are given in the Figure 3:2  
According to the engineering method, the calculation showed convergence within 32-46% in the direction of exaggeration of experimental results. Such an indicator is a satisfactory result, considering the complex stress-strain state, lacking influence of longitudinal reinforcement in the methodology, and the suddenness and speed of exhaustion of the bearing capacity on the shear. Figure 3:3 A model of the influencing factors on the shear strength of a support area [2; 3]. Figure 3:4 Case of applying load for the coefficient \(\beta\)[2; 3]. The overestimation of experimental data compared to calculation ones determined according to the current code is much greater. Considering the progress of the calculation, it can be established that all values, except for one, change during the calculation process. Only the value of \(C_{Rd,c}\) (shear strength of concrete [39]) was constant in all calculations and was 0.18 MPa. This value is accepted as a minimum and does not depend on the change in concrete class.