## 3 Numerical Study
### Results and Discussion of Finite Element Modelling
#### 3.4.2 Crack Propagations and Failure Mechanisms  
The crack progression was investigated in order to validate the capacity of the model with experimental results. The ABAQUS software package [30] was able to satisfactorily indicate the inclined crack propagations. The major cracks appeared to be vertical. This agrees with the results obtained by [PERSON] et al. [42]. Figures 15-18 show the formation of cracks due to the flexural and compression damage in the model at maximum load. The vertical cracks are due to tension and the horizontal cracks are due to compression. The capability of the developed model for mixed-mode cracking was further confirmed by the fact that the onset of the vertical cracks inclined at the shear span. This can be separately studied by applying two-point loading. Therefore, the mixed-mode cracking was a combination of flexural, compression, and shear-flexural cracking. This represents a typical real-life case for the nature of the damage induced in the beam structures.  
The tensile damage contours shown in Figures 15-18 were obtained from the FE models and the experimental results at different levels for the CB and the BCSP beams. All beams failed under flexural loading. The tensile damage was initiated at the extreme tension fibres of the beam in the zones subjected to pure bending. The cracks were propagated towards the compression zone as the load levels increased. The failure mechanisms observed in the experiments are reported in Table 3. The bending failure mechanisms match the mode failures of the FE analysis. The CB beam failed suddenly at the compression zone. Figure 15, shows the compression failure of the CB beam. The BSCP-6 beam failed under shear compression. After the peak load, the loading decreased gradually, and the beam failed in a ductile manner. There was a wider spread of tensile damage between the loading points and the supports of the shear span. The tensile damage was more concentrated under the loading point. As the steel plate began to yield, the intensity of the tensile damage significantly increased. This was exhibited by more cracks appearing in the beam than the ones observed in the BCSP-10 and BCSP-15 beams at that stage, as shown in Figure 16. Thirdly, the type of failure observed in the BCSP-10 beam was characterized by the crushing of the concrete in the flexural compression zone. The resulting flexural compression failure occurred between the two loading plates, as shown in Figure 17. Finally, the BCSP-15 beam displayed more ductile behavior than the rest of the specimens. The BCSP-15 beam sustained the ultimate load for a longer time, with an increase in its deflection. The mid-span of the beam was its critical section. The maximum damage tension of the beam was concentrated in its mid-span. This is demonstrated by the micro-cracks displayed in the FE model, as shown in Figure 18.  
Hence, the FE model has the ability to capture the locations and patterns of cracks, from the application of loading until the failure of a beam. The predictions made by the FE models were in line with the experimental observations.  
Figure 14: Comparison of the energy absorption between the experiment and FEM.  
Figure 16: Comparison between (**a**) the experimental tests with the FE modelling of the (**b**) compressive and (**c**) tensile damage cracks in the BCSP-6 beam at the point of failure.  
Figure 17: Comparison between (**a**) the experimental tests with the FE modelling of the (**b**) compressive and (**c**) tensile damage cracks in the BCSP-10 beam at the point of failure.