## 4 Calculation
### Moment-Curvature Relation Calculation
Note that for the moment-curvature relation (based on the simplified expressions for the tensile strength values from the _fib Model Code for Concrete Structures 2010_[17]), the strains \(\varepsilon_{\text{SLS}}\) and \(\varepsilon_{\text{ULS}}\) were calculated considering the CMOD values for the crack width in Equation (3). In Figure 8, key strains at the notched cross-section's bottom edge (\(\varepsilon_{\text{bot}}\)) are additionally marked. The maximum load-bearing capacity is reached after the cross-section cracks and the load slightly increases. The strain at the bottom of the notched cross-section, corresponding to the maximum load, also marked in Figure 8, is greater than the strain corresponding to the tensile strength (\(\varepsilon_{\text{F}}\)). The comparison of the bending moment versus curvature relations of the notched and the gross cross-section shows how the chosen notch depth ensures that at the load corresponding to crack formation in the notched cross-section,  
Figure 8: Calculated bending moment versus curvature relation for the gross cross-section, for the notched cross-section with tensile strength values determined from expressions in the _fib Model Code for Concrete Structures 2010_[17], and for the notched cross-section with marked strains at the bottom edge (\(\varepsilon_{\text{bot}}\)) of the notched cross-section (corresponding to specific curvature values). the gross cross-section curvature is still in the elastic region. The comparison of the bending moment versus curvature relations of the notched cross-section based on the constitutive law in Figure 7 and based on the constitutive law with tensile strength values according to the simplified expressions of the _fib Model Code for Concrete Structures 2010_[17]) shows how the latter assumes an almost constant load-bearing capacity for large strains and how the latter results in a greater load-bearing capacity for strain values close to the strain \(\varepsilon_{\text{SLS}}\). The normal stress distributions on the notched cross-section for the load stages corresponding to the marked strains at the bottom of the notched cross-section in the moment-curvature diagram in Figure 8 are given in Figure 9.  
The stress distributions across the notched cross-section height in Figure 9 show how the cross-section is already partially plasticized (cracked, respectively) when the maximum load-bearing capacity is reached. When the strain at the bottom of the cross-section increases, the plasticized region increases almost to the top of the cross-section, as does the crack (see Figure 6). This fact is also used for the rigid plastic model from the _fib Model Code for Concrete Structures 2010_[17], where the compressive stress distribution is considered as a concentrated compression force at the top of the notched cross-section, and tensile stresses equal to the residual tensile stress \(\text{f}_{\text{Ftu}}\) are evenly distributed over the whole cross-section. Load-Displacement Calculation  
A force-displacement relation calculation was performed to evaluate the two bending moment-curvature relations for the notched cross-section in Figure 8. The total deflection was calculated as the sum of the deflection from flexural and shear deformation. The displacement was calculated for load steps (values) corresponding to each curvature (\(\kappa\)) value from the moment-curvature relation (Figure 8) of the notched cross-section. For the load steps corresponding to the curvatures (\(\kappa\)) of the notched cross-section less than the curvature corresponding to the maximum bending moment (\(\kappa(\text{M}_{\text{max}})\)), the flexural deflection was calculated by integrating the curvature over the prism length (\(\kappa(\text{x})\)) with the virtual bending moments resulting from a vertical virtual unit force at the midspan. For load steps corresponding to larger curvature values of the notched cross-section (\(\kappa>\kappa(\text{M}_{\text{max}})\)), the plastic hinge approach was applied.