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

TLDR

Plastic rotations are consistently defined and directly linked to deformations within plastic hinges. The study introduces a new plastic hinge integration method to eliminate nonobjective responses caused by strain‑softening in force‑based beam‑column finite elements. It employs a plastic‑hinge‑length concept derived from the Gauss–Radau quadrature rule, integrating deformations over specified lengths at element ends and reducing to the exact solution for linear problems. Numerical examples demonstrate that incorporating a plastic hinge length yields objective responses for both strain‑hardening and strain‑softening behaviors, improving the accuracy of force‑based beam‑column elements.

Abstract

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 force-based 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.