Dimensional analysis approach to the plastic rotation capacity of over-reinforced concrete beams

The development of ductility in reinforced concrete beams in bending is a complex nonlinear phenomenon characterised by several variables. For this reason, an exhaustive and synthetic description of the rotational capacity is impossible to be achieved on the basis of the individual values of the variables involved in the phenomenon. In the present paper, such a drawback is overcome by means of the application of dimensional analysis to the numerical results obtained from a model based on nonlinear fracture mechanics concepts. Although the proposed model relies on several mechanical and geometrical parameters, in fact, it is demonstrated that only two nondimensional numbers, NP and NC, are responsible for the available ductility. Experimental confirmations to the numerical approach are also proposed.