Beam-column finite element with embedded discontinuities for modelling damage in reinforced concrete prismatic elements

Beam-column elements with embedded discontinuities to model the occurrence of damage as the development of hinges are formulated. In these kinds of elements, the development of hinges occurs as the result of axial, transverse or rotation discontinuities. These elements are developed from variational formulations; whose finite element approximations yield symmetric stiffness matrices. The effects of the axial force, the shear force and the moment were considered as uncouple in the constitutive models of the reinforced concrete prismatic sections. The formulated beam-column elements with embedded discontinuities were validated with the energy necessary to develop a hinge. The beam-column elements and constitutive models were implemented in the software FEAP. The capability of the formulated elements for modelling damage is validated with numerical examples of beams and frames. In these numerical examples, the load-displacement curves were in agreement with those reported in the literature and with the results computed in the commercial software SAP2000. One advantage of these formulated elements is that extra degrees of freedom generated at the hinges are statically condensed, keeping only the degrees of freedom at the ends.