## 4 Calculation
### Finite Element Simulation of the Three-Point Bending Test
From the normal stress distribution of the last load step prior to the occurrence of equivalent plastic strain, it can be seen how near point 1, the stress increases, but away from this region, the normal stress distribution is rather uniform and can be described as linear. The cross-section is already partially plasticized (cracked, respectively) for the load step with the maximum load. As for the stress distributions of the calculation based on the moment-curvature relation in Figure 9, with increasing displacement, the plasticized region increases almost to the top of the cross-section. Comparison of the Experimental, Moment-Curvature-Based Calculation, and Finite Element Analysis Results  
The averaged load-displacement results of the experiments, the calculations based on the back-calculated tensile strength values, the calculations based on tensile strength values from the expressions in the _fib Model Code for Concrete Structures 2010_[17], and the  
Figure 19: Stress path (**left**) and normal stress distributions (**right**) for different load steps (CRACK—last load step prior to occurrence of equivalent plastic strain, M\({}_{\text{max}}\)—load step with maximum bending moment (or load) at the notched cross-section, SLS—load step corresponding to CMOD = 0.5 mm, and ULS—load step corresponding to CMOD = 2.5 mm). finite element analysis are collected in Figure 20. The experimental results are additionally depicted with a shaded area representing the envelope of all six tested fiber-reinforced concrete prisms' load-displacement results. It is evident in Figure 20 that all considered computational procedures show similar results for displacements smaller than the displacement corresponding to the maximum load and are in agreement with the averaged experimental results. The force-displacement results of the calculation based on the back-calculated tensile strength values (M-\(\kappa\)) and the finite element analysis are for all displacements inside the gray area, which represents the region of the experimentally determined load-displacement relations of all test specimens. This is not the case for the force-displacement results of the calculation based on the tensile strength values from expressions in the _fib Model Code for Concrete Structures 2010_[17] (M-\(\kappa\) (fib)), which overestimates the loads in the region between the displacement corresponding to the maximum load and the displacement of 0.47 mm. The M-\(\kappa\) calculation results match the averaged experimental results at the displacements of 0.47 mm and 2.17 mm, for which the residual tensile strength values were determined and between which the residual tensile strength was assumed to be linearly varying. The M-\(\kappa\) (fib) calculation results match the averaged experimental results only at the displacement of 2.17 mm. The finite element analysis results are not necessarily less accurate for other displacements, even though a constant residual strength (equal to \(\mathrm{f_{Ffs}}\)) was considered in the material model. The chosen constant residual tensile strength value equal to \(\mathrm{f_{Ffs}}\) is also the reason that for the corresponding displacement of 0.47 mm. The finite element results are quite close to the average experimental results. The load and displacement result values at the maximum load, the crack mouth opening displacement of 0.5 mm, and the crack mouth opening displacement of 2.5 mm are collected in Table 11.  
Figure 20: Averaged experimental values (Exp. ), values calculated based on the back-calculated tensile strength (M-\(\kappa\)), and values calculated based on tensile strength values from expressions in the _fib Model Code for Concrete Structures 2010_[17] (M-\(\kappa\) (fib)) and finite element analysis (FEA) load-displacement relations (with the shaded area representing the envelope of all experimental results).