Improved Displacement-Based Timoshenko Beam Element with Enhanced Strains

Abstract

This paper presents an enhanced strain formulation for conventional displacement-based (DB) Timoshenko beam elements accounting for shear deformations. The proposed beam element is an extension of the original enhanced strain formulation developed for DB Euler-Bernoulli beams, and the inaccuracy due to weak satisfaction of equilibrium is remedied. A strain enhancement is introduced to the axial elongation of the section in such a way that the axial equilibrium is strictly fulfilled. The element formulation is established based on a locking-free finite-element approximation, and a modified fiber model is adopted for the section behavior. The numerical implementation of the element needs only minor changes to the state determination of the original DB element. Two typical reinforced concrete columns are analyzed to demonstrate the capacity of the novel Timoshenko beam element with enhanced strain.