## 4 Numerical Analysis
### Comparative Analysis of the Results  
Since there are currently no specific models incorporated in the design codes to simulate the behavior of SCC in terms of material modeling, this section presents a comparative analysis of the results obtained by experimental and numerical research using Abaqus/Standard. The aim of this comparative analysis was to confirm the adequate choice of finite elements, as well as material models  
Figure 10: Concrete damage parameters depending on the inelastic strain: (a) compression \(\mathrm{d_{c}}\); (b) tension \(\mathrm{d_{t}}\)  
of concrete and steel for modeling the behavior of continuous beams. In this way, a valid and verified numerical model is proposed that can be applied for further parametric analysis of the examined problem without expensive experimental tests.  
Figure 12 show a comparison between the experimental results and the results obtained by the numerical model, from the aspect of the relationship between loads and deformations of the tested beams. In general, the load-deflection curves obtained by the numerical model show the same trend as the experimentally determined curves. It can be concluded that the results obtained by numerical analysis in terms of ultimate load agree well with the experimentally obtained results.  
Figure 11: (**a**) Limit conditions and load; (**b**) bond of concrete and reinforcement.  
Figure 12: Load vs. deflection curves for the section in the middle of left span—Section I, for: (**a**) Beam B–1; (**b**) Beam B–2; (**c**) Beam B–3.  
Figures 13 and 14 show diagrams of the dependence between loads and strains in tensioned steel reinforcement and strains in compressed concrete in Section I (section in the middle of the span) and Section III (section above the middle support). It can be noticed that there is a discrepancy between the values obtained experimentally and those obtained numerically. One reason for this is the different stiffness of the experimental and numerical model after the emergence of cracks, which indicates the need for further research.  
During the testing of reinforced SCC, the load-displacement curve is linear and the beam is in the elastic region up to the load that causes the emergence of the first crack. The load at which the first crack occurs can be read from the curve as the load at which there is a significant change in the slope of the curve. The initial crack occurs when the stress occurring in the beam exceeds the rupture modulus of the beam. This occurs at the point of maximum moment, which in the case of the tested beams is the cross section above the central support. The linear response of the beam to the appearance of the first crack is followed by a nonlinear response. It can be said that concrete now \"flows\", i.e., exhibits inelastic properties. Cracks propagate along the height of the beam. Eventually the beam fails. In the numerical model, the failure load manifests itself as the convergence failure of the model, while in the experimental model the failure of the beam occurs.  
Using proposed model, it is not possible to plot cracks in the Abaqus/Standard software, but it is possible to display the damage distribution in both tensioned and compressed zones using the DAMAGET and DAMAGEC functions. The obtained distribution of damage indicates the appearance of cracks in the beams. Figure 15 shows the distribution of damage of the beams at the time of failure.  
Figure 13: Load vs. microstrain curves in tensioned reinforcement in Section I for: (**a**) Beam B–1; (**b**) Beam B–2; (**c**) Beam B–3.