Force-based finite element formulation for nonlinear behaviour of reinforced concrete frames

This paper presents a nonlinear force-based finite element formulation which can predict the behaviour of reinforced concrete frames, explicitly satisfying section-level equilibrium. In the existing nonlinear force-based fibre beam–column element formulation, two nested iterative procedures are utilized at the structure and element levels. In the element-level iterative procedure, the strain states of the fibre level are iteratively altered by following the corrective forces suggested by the element level. When this algorithm is implemented with uniaxial material models, the element residual deformations can be minimized effectively by altering the axial strains, which is the only variable at the fibre level, implicitly achieving the section-level equilibrium to a reasonable accuracy. However, when a cracked reinforced concrete constitutive model, which accounts for axial–flexure–shear interaction, is implemented, element-level convergence becomes problematic because element residual deformations have to be minimized by altering all three strain components with additional constraints at the fibre level. To address this issue, this paper proposes a novel force-based finite element formulation by implementing an iterative procedure at the section level in order to minimize section unbalanced forces at section level itself, rather than transferring errors of the section level to element level. The current study focuses to test this algorithm for only axial force–bending moment interaction response. The proposed formulation was experimentally validated and was proved to be stable and accurate to predict the nonlinear responses of RC frames.