Forced-based Shear-flexure-interaction Frame Element for Nonlinear Analysis of Non-ductile Reinforced Concrete Columns

An efficient frame model with inclusion of shear-flexure interaction is proposed here for nonlinear analyses of columns commonly present in reinforced concrete (RC) frame buildings constructed prior to the introduction of modern seismic codes in the Seventies. These columns are usually characterized as flexure-shear critical RC columns with light and non-seismically detailed transverse reinforcement. The proposed frame model is developed within the framework of force-based finite element formulation and follows the Timoshenko beam kinematics hypothesis. In this type of finite element formulation, the internal force fields are related to the element force degrees of freedom through equilibrated force shape functions and there is no need for displacement shape functions, thus eliminating the problem of displacement-field inconsistency and resulting in the locking-free Timoshenko frame element. The fiber-section model is employed to describe axial and flexural responses of the RC section. The modified Mergos-Kappos interaction procedure and the UCSD shear-strength model form the core of the shear-flexure interaction procedure adopted in the present work. Capability, accuracy, and efficiency of the proposed frame element are validated and assessed through correlation studies between experimental and numerical responses of two flexure-shear critical columns under cyclic loadings. Distinct response characteristics inherent to the flexure-shear critical column can be captured well by the proposed frame model. The computational efficiency of the force-based formulation is demonstrated by comparing local and global responses simulated by the proposed force-based frame model with those simulated by the displacement-based frame model.