Numerical modeling of the cracking behavior of RC and SFRC shear-critical beams

Numerical simulation of early-age shrinkage effects on RC member deflections and cracking development

“…As already mentioned, this model, which is based on a smeared-fixed crack approach, was developed for a concrete membrane element containing n reinforcing layers with different orientations, subjected to plane stress conditions. The main features of 2D-PARC, as well as its governing equations can be found in [10][11][12], to which reference is made. In the following Sections the attention will be only focused on the main changes made to the original structure of the model in order to include concrete shrinkage.…”

“…where [D c ] and [D s ] respectively represent concrete and steel stiffness matrix, whose construction has been discussed elsewhere ( [10] and [12], in a more recently revised form).…”

“…Crack formation takes place when the current state of stress violates the concrete failure envelope in the cracking region (see [12]). In presence of shrinkage, the transition from uncracked to cracked stage occurs in correspondence of a lower load level, since the restraint provided by the embedded reinforcement causes the appearance of tensile stresses in concrete even before the application of any external load.…”

“…In more detail, the equilibrium condition in RC between cracks is formally identical to Eq. 2, even if concrete and steel stiffness matrices, [D c ] and [D s ], are slightly modified with respect to the uncracked stage, so as to consider the degradation I that occurs after cracking, as explained in [10,12]. Moreover, since in the cracked stage the hypothesis of perfect bond is no longer valid (and consequently the two strain vectors {εc} and {εs} cannot be set equal to each other), the steel strain {ε s } is assumed coincident with the total average strain {ε}, with a negligible approximation in excess.…”

“…To this aim, concrete shrinkage can be explicitly considered by treating it as a prescribed deformation or as a fictitious force in the analyses [5][6][7][8][9]. In this work, an existing smeared-crack model for RC elements subjected to in-plane stresses, named 2D-PARC [10][11][12], is extended so as to correctly take into account early-age shrinkage effects. In more detail, concrete shrinkage is rigorously modelled by inserting it explicitly into 2D-PARC general algorithm as a prescribed deformation.…”