An accurate and unified study on non-symmetric tensile and compressive responses of elastoplastic bars and beams until failure

Abstract

A new and unified approach is proposed toward accurately analyzing overall elastoplastic responses of axially loaded bars and finite bending beams until failure. Results are presented for various constituent materials such as metals, reinforced concretes and reinforced composites, etc. Novelties in three respects are incorporated: (a) new uniaxial stress–strain functions are first presented in explicit forms for the purpose of accurately characterizing non-symmetric tensile and compressive behaviors of axially loaded bars from hardening to softening; (b) explicit solutions to both the varying neutral axis and the flexural moment of finite bending beams are then obtained directly in terms of these two uniaxial functions; and, hence, (c) the complex bending problem of various beams until failure is in a unified manner reduced to a simple issue of fitting two uniaxial functions to tension and compression data from uniaxial testing, thus bypassing the analytical and numerical complexity of various existing approaches. Numerical examples of model predictions are provided for typical constituent materials, including aluminium, meso-scopic heterogeneous concrete and ultra-high performance fiber-reinforced concrete with reinforcing rebars. Good agreement is achieved simultaneously with all experimental data for bars and beams made of these materials.