Rotational ductility of R.C. beams: a parametric analysis

The evaluation of plastic rotation capacity in reinforced concrete beams is essential to prevent brittle failures. In order to facilitate practical applications, the methods usually adopted in International Codes (see EC2, MC90 or DIN), provide approximate functions ϑpl vs (x/d)u,conv in which the following principal parameters appear: (i) ultimate concrete strength; (ii) ductility characteristics of the reinforcement steel; (iii) shear slenderness. Indeed, more accurate formulations have highlighted, especially for slender beams, a fundamental importance of additional variables. Hence, it is here proposed a mechanical model through the use of dimensionless expressions able to examine in a more accurate way the effects of the bending rupture for rectangular sections. The analytical approach allows to perform simple parametric analyses and evaluate the significancy of mechanical characteristics that are usually neglected in other formulations. The following simplifications are made: (i) after the first cracking, the contribution of the concrete in the tension region is neglected; (ii) tension-stiffening effects are disregarded. The parameters included in the model are: a) material constitutive laws; b) mechanical tensile reinforcement ratio; c) compressive-tensile reinforcement ratio; d) characteristics of the plastic part in the idealised moment-curvature relationship.