A formulation to reduce mesh dependency in FE analyses of RC structures under imposed deformations

Abstract

It is well known that in analyses of plain concrete members using smeared crack models, the constitutive behaviour of cracked concrete has to be defined as a function of the crack bandwidth so that the results are not significantly affected by the adopted mesh discretization. Crack localization can also occur in reinforced concrete (RC) elements subjected to imposed (or restrained) deformations. In that case, a different approach has to be followed to reduce the influence of the adopted mesh discretization because the mechanical response in the vicinity of each crack is governed by tension stiffening effects. This paper presents an original formulation to define a tension stiffening diagram that reduces the dependency of the results with respect to the adopted mesh refinement in structures in which crack propagation is governed by mode I (crack opening). This formulation can be applied in FE analyses based on a large-scale, smeared crack approach. Simple closed-form equations are obtained to define this type of diagram. It is demonstrated that objective results are obtained in terms of both the stiffness decrease due to cracking and the crack opening values. Concrete creep and shrinkage effects are taken into account.