The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment surpasses this initial elastic phase, the outer fibers begin to yield while the inner fibers remain elastic. This transition is marked by plastic zones forming at the top and bottom of the section, with an elastic core that continues to exhibit linear stress variation within a reduced thickness. During this phase, the bending moment can still be analyzed by adapting the initial calculations for elastic stress distribution to account for the reduced effective area.
The final stage in the bending response occurs when the deformation across the entire cross-section becomes fully plastic, known as the plastic moment. This moment is the maximum the section can sustain and is significantly higher than the elastic limit. The plastic moment is calculated assuming a uniform stress distribution at the yield stress across the entire section.
