Ductility study in reinforced concrete beams: analytical approach based on ABNT NBR 6118:2014 and numerical by finite element method considering nonlinear material behavior

Abstract

Reinforced concrete structures are widely used in several kinds of constructions nowadays, since simple buildings to extensive bridges. Among many project criteria that are necessary to ensure reinforced concrete civil structures safety, functionality and durability, the ductility is, in present times, a mandatory requirement by the modern design codes, both for cross sections with negative and positive bending moments. By having the warranty of a ductile behaviour, it is possible to ensure considerable deformations before an occasional cracking (creation of plastic hinges in Ultimate Limit State), as well as the occurrence of moment redistribution in statically indeterminate structures. In general, the approach used by the worldwide design codes, including Brazilian code ABNT NBR 6118 (2014), consists in fixing a maximum value for the neutral axis relative depth, according to the compression resistance of concrete. Attending this criteria, the codes claim that ductility is ensured for reinforced concrete elements in bending. However, that approach does not allow designers to quantify ductility in structures and, consequently, is not possible to know how ductile or not the behaviour of one or more structural elements are. So, this paper has the main purpose to quantify, in a systemic way, ductility in reinforced concrete beams, considering in the beginning constitutive laws for compressed concrete (parable-rectangle diagram) and, after, non-linear models for concrete (damage mechanics) and steel (plasticity theory), by using a computer program based on Unidimensional Finite Elements Method. With the results of several designed beams using the current criteria, an alternative method of design, based on explicit ductility, will be proposed. The initial parameter that will be adopted is the ductility factor and, since that, other parameters will be obtained for the design of reinforced concrete beams. The results obtained with the alternative method of design will be compared with the current design model used by the Brazilian code, and also numerically analysed using Finite Elements Method.