Flexural to shear and crushing failure transitions in RC beams by the bridged crack model

The bridged crack model has been developed for modelling the flexural behaviour ofreinforced concrete beams and related size effects explaining brittle-ductile-brittle failure mode transitions. In the present paper the model is extended to analyze shear cracks and concrete crushing, introducing a given shape for the hypothetical crack trajectory and determining the initial crack position and the load versus crack length curve for three point bending problems. The proposed formulation reproduces the pure Mode I flexural behaviour as a particular case, so that the flexural and the diagonal tension (shear) failures modes can be immediately compared to detect which one dominates and determine the relevant failure load. A concrete crushing criterion completes the model. All the mutual transitions between the different collapse mechanisms can be predicted. In the paper these transitions are shown by varying the governing nondimensional parameters.