Plastic Hinge Integration Methods for Force-Based Beam–Column Elements

A new plastic hinge integration method overcomes the problems with nonobjective response caused by strain-softening behavior in force-based beam–column finite elements. The integration method uses the common concept of a plastic hinge length in a numerically consistent manner. The method, derived from the Gauss–Radau quadrature rule, integrates deformations over specified plastic hinge lengths at the ends of the beam–column element, and it has the desirable property that it reduces to the exact solution for linear problems. Numerical examples show the effect of plastic hinge integration on the response of forcebased beam–column elements for both strain-hardening and strain-softening section behavior in the plastic hinge regions. The incorporation of a plastic hinge length in the element integration method ensures objective element and section response, which is important for strain-softening behavior in reinforced concrete structures. Plastic rotations are defined in a consistent manner and clearly related to deformations in the plastic hinges.