A generalisation of the Hillerborg's model for the analytical evaluation of ductility of RC beams in bending

In this study, a generalised analytical model for the evaluation of the plastic rotations of reinforced concrete beams in bending is proposed. To this aim, the pioneering Hillerborg's model is here extended by taking into account also the contribution of reinforcement in compression. Moreover, a detailed comparison with the experimental results by Bosco and Debernardi on three-point bending reinforced concrete beams by varying the reinforcement percentage and the size-scale of the structural elements is carried out. This permits study of the influence of the parameter beta, related to the length of strain localisation of concrete in compression, on the ductility response and how to tune this parameter according to experiments. The proposed generalisation of the Hillerborg model is then suitably applied to over-reinforced concrete beams in bending, where concrete crushing is the prevailing non-linearity; it is shown that the model is able to capture the phenomenon of size-scale effects.