## 4 Calculation
### Moment-Curvature Relation Calculation
The shear displacement contribution was calculated by integrating the shear forces (for each load step) with the virtual shear forces and considering the shear correction factor (\(\kappa_{\rm S}\)) equal to 0.83 (as, for example, per [26]). The shear displacement \(\Delta_{\rm s}\) was calculated with:  
Table 6.4  
where A(x) is the cross-section area at location x (on the interval \(0\leq x\leq(L-L_{\rm p})/2\) equal to the gross cross-section area and on the interval \((L-L_{\rm p})/2\leq x\leq L/2\) equal to the notched cross-section area), V(x) is the shear force distribution, \(\overline{\rm V(x)}\) is the virtual shear force distribution, and \(\
u\) is Poisson's ratio for concrete (0.2). The total deflection (vertical displacement at the midspan) was calculated as the sum of the flexural (\(\Delta_{\rm fl}\)) and shear displacement (\(\Delta_{\rm s}\)). The results in the form of a load-displacement curve are given in Table 6.5 The load-displacement results are also depicted based on the moment-curvature relation calculated by considering the tensile strength values determined directly by applying the expressions from the _fib Model Code for Concrete Structures 2010_[17]. Table 6.6 Specific points of the bending moment versus curvature relation considered for the displacement calculation. The results of the load-displacement calculation based on the back-calculated tensile strength values (by inverse analysis) in Figure 12 show post-crack hardening behavior, whereas the load-displacement results based on the tensile strength values from the expressions in the _fib Model Code for Concrete Structures 2010_[17] show an almost constant load-bearing capacity for larger displacements. Besides the load evaluation at different load stages, the calculated displacement values can be compared with the displacement relations from the EN14651 standard [19]. As the calculation model relates the curvature values (\(\kappa\)) of the notched cross-section directly to the crack tip opening displacement (CTOD) values and crack mouth opening displacement (CMOD) values, the calculated values (\(\delta_{\text{calculated}}\)) and the displacement values defined as per the EN14651 standard [19] (\(\delta_{\text{standard}}\)), which correspond to specific CMOD values and CTOD values, are, together with the corresponding loads (F), given in Table 7 (based on the back-calculated tensile strength values) and Table 8 (based on the tensile strength values from expressions in the _fib Model Code for Concrete Structures 2010_[17]) for comparison. Noting that the EN14651 standard [19] relations are based on rigid body rotations due to the rotation at the notch, the comparison of the \(\delta_{\text{calculated}}\) and \(\delta_{\text{standard}}\) values in Table 7 suggests that the presented calculation model (with the back-calculated tensile strength values) matches with the EN14651 standard [19] relations between, on one side, the CMOD and CTOD values and, on the other side, the vertical displacement values. The comparison of the \(\delta_{\text{calculated}}\) and \(\delta_{\text{standard}}\) values in Table 8, with the results based on the tensile strength values from the expressions in the _fib Model Code for Concrete Structures 2010_[17]), shows much larger discrepancies, with the difference between the \(\delta_{\text{calculated}}\) and \(\delta_{\text{standard}}\) displacement values being larger than 0.6 mm for larger displacements. This is a consequence of the _fib Model Code for Concrete Structures 2010_'s [17] consideration of the