## 2 Analytical Methods for Calculating the Failure Load
Following the parametric analysis, modified equations and coefficients were introduced to account for prestressing when the prestressed tendons induced force P\({}_{2}\), as illustrated in Figure 2.  
According to EC2, two primary scenarios for diagonal section calculations can be identified. The first scenario occurs when there is no shear reinforcement in the element, and thus, the concrete alone withstands the shear forces. The second scenario arises when the shear reinforcement bears the tensile forces and the concrete struts are thereby subjected to compression. In the first case, the diagonal section's load-bearing capacity is determined by the larger value according to the formulas provided below[7]:  
\[V_{Rd,c}=\left[C_{Rd,c}\cdot k\cdot(100\cdot\rho_{1}\cdot f_{cm})^{\frac{1}{3} }+k_{1}\cdot\sigma_{cp}\right]\cdot b_{w}\cdot d, \tag{1}\]  
Figure 4: The parameters examined in the parametric analysis. \[V_{Rd,c}=\left[v_{min}+k_{1}\cdot\sigma_{cp}\right]\cdot b_{w}\cdot d, \tag{2}\]  
where \(C_{Rd,c}\) is a coefficient with a recommended value of \(\frac{0.18}{\gamma_{c}};k\) is a coefficient evaluating the effective depth, which is calculated using the following formula:  
\[k=1+\sqrt{\frac{200}{d}}\leq 2.0, \tag{3}\]  
where \(d\) is the effective cross-sectional depth. \(\rho_{1}\) is a coefficient representing the amount of tensile reinforcement within the distance of \(l_{bd}+d\), and it is calculated as follows:  
\[\rho_{1}=\frac{A_{s1}}{b_{w}\cdot d}\leq 0.02, \tag{4}\]  
where \(A_{s1}\) is the cross-sectional area of the tensile reinforcement; \(b_{w}\) is the minimum width of the examined element within the analyzed zone. \(f_{cm}\) is the average compressive strength of concrete; \(k_{1}\) is the coefficient evaluating the influence of cross-sectional stresses from axial forces on the diagonal section, which is recommended to be equated to 0.15; \(\sigma_{cp}\) is the average of stresses across the entire cross-section resulting from axial forces. These are limited by the following condition:  
Figure 3:0  
where: \(N_{Ed}\) is the axial force in the cross-section resulting from the load or prestressing; \(A_{c}\) is the area of the element's cross-section; \(f_{cm}\) is the average compressive strength of the concrete. \(v_{min}\) is calculated according to the following equation:  
Figure 3:1  
When the element is reinforced with shear reinforcement, the shear capacity is determined with the subsequent equation:  
Figure 3:2  
where \(V_{Rd,s}\) is the shear strength of shear reinforcement; \(V_{Rd,max}\) is the maximum shear strength of compressive concrete struts. The shear strength of vertical shear reinforcement is calculated as follows:  
Figure 3:3  
where \(A_{sw}\) is the cross-sectional area of shear reinforcement; \(s\) is the spacing between stirrups; \(z\) is the inner lever arm, which can be equated to approximately 0.9\(d\); \(f_{yum}\) is the average yield strength of shear reinforcement; \(\theta\) is the angle of the diagonal strut, which is limited to a range of 22 degrees to 45 degrees. When the angle is 45 degrees, the shear strength \(V_{Rd,s}\) has the lowest value. The shear strength of the compressive concrete strut is calculated as follows:  
Figure 3:4  
where \(b_{w}\) is the minimum width of the element in the analyzed zone; \(z\) is the inner lever arm, which can be equated to approximately 0.9\(d\); \(\
u_{1}\) is a coefficient assessing the strength of the cracked concrete in the diagonal section, calculated using the formula specifiedearlier in this section for the \(v_{\rm min}\); \(\theta\) is the angle of the compressive struts, which is limited to being between 22 degrees and 45 degrees. At a strut angle of 22 degrees, \(V_{Rd,max}\) is at its minimum. The coefficient \(\alpha_{cw}\) accounts for the influence of the stress state in the cross-section on the shear capacity. For structures without prestressing, it equates to 1.0.