The internal force relationship of rectangular and I-section for bi-linear hardening material with limit strain

Abstract

Based on bilinear stress-strain constitutive law σ = f (e), the elastic to fully plastic analysis of bending of rectangular-section and bi-symmetrical I-section beams with the influence of axial load is presented for hardening material with limit strain. The variation of the applied bending moment with the axial force for the fully elastic, elastic-plastic, and fully plastic conditions is given in analytical form. The Internal force relationship of the elastic limit is the same for both hardening and non-hardening material and independent of the geometry of the beam section. However, for the elastic-plastic and plastic limits, the relationships are dependent of the hardening parameter β q, limit strain e lim and the geometry of the beam section for neutral axis (N.A) inside the cross section. When N.A outside the cross section, the relationships are dependent of hardening parameter β q and limit strain e lim but independent of the geometry of the beam section. The results given by the analytical expressions reduce to the ones for non-hardening material are in good agreement with the existing results.