Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames

An Euler–Bernoulli stress resultant beam finite element for static collapse analysis of planar reinforced concrete beams and frames is presented in detail. The pre-failure inelastic effects are described by the (axial force dependent) bending elastoplasticity with bi-linear isotropic hardening. To capture the response of the beam after the localized failure of the critical cross-section, the softening plastic hinge is incorporated at the location of the failure. The dissipative effects of the softening hinge are introduced into the finite element formulation by enhanced kinematics, with singular curvature in the softening hinge, within the framework of finite elements with embedded strong discontinuities. The implementation details of the finite element formulation are provided. Several numerical examples are presented to illustrate the performance of the element.