Mixed formulation for geometric and material nonlinearity of shear-critical reinforced concrete columns

Abstract

This study presents a new beam element formulation following a Hellinger-Reissner variational principle for shear critical reinforced concrete members, and considering large displacement and rotation effects. The corotational formulation is used to describe the large displacement at the element nodal level and degenerated Green-Lagrange strain measures are used at the basic element level. A new displacement shape function has been developed considering section kinematics and compatibility conditions to satisfy stability criteria. New explicit equations for the internal geometric stiffness matrix to consider large deformation effect has been developed. A robust state determination algorithm for the large deformation mixed-based formulation is proposed. The Timoshenko beam theory has been adopted to consider shear deformations in deriving the section kinematics equations. The multi-axial stress state in reinforced concrete fibre has been simulated through the fixed crack smeared softened membrane model. The developed shear fibre beam element is capable of accurately reproducing the experimentally-observed large displacement effect on the post-peak shear strength degradation in the softening region. The accuracy and efficiency of the mixed-based formulation was evaluated by examining the responses at local and global levels for both monotonic and reverse cyclic loading conditions along with the process of reproducing experimentally-observed failure modes.