Accounting axial-moment-shear interaction for force-based fiber modeling of RC frames

Abstract

This paper presents a novel fiber force-based finite element to predict the nonlinear static response of reinforced concrete frame/wall structures incorporating the axial force – bending moment – shear force interaction. The proposed formulation is especially suited for short elements with low span to depth ratio, where shear dominant behavior can be expected. An iterative algorithm is developed to find the transverse strain that results in negligible transverse clamping stresses, to obtain a complete strain state at the fiber level. The axial force – bending moment – shear force interaction is considered at the fiber level by computing the corresponding stress state for a given strain state through Modified Compression Field Theory. A new algorithm is developed for section state determination that iteratively updates the section deformation vector until section level equilibrium is satisfied, eliminating the generation of residual section deformations that violates compatibility. Hence, an iterative procedure is not required at the element state determination. The proposed method of explicitly satisfying equilibrium at the section level improves upon the existing force based finite element formulations, in which section level equilibrium is only implicitly satisfied by limiting the residual element deformations at the element level. The proposed element has been tested with experimental data of short structural walls in order to demonstrate the capability of predicting the axial force – bending moment – shear force interaction. The proposed formulation is stable and provides excellent agreement with experimental data.