Members Made of Elastoplastic Material

Initially, stress distribution is linear and elastic, following Hooke's Law across the rectangular cross-section. As bending moment increases beyond the elastic limit, outer fibers yield while inner fibers remain elastic. Plastic zones form at the top and bottom with an elastic core exhibiting linear stress variation within reduced thickness. This transition marks the shift from purely elastic to elastoplastic behavior.

The maximum elastic moment occurs when deformation remains fully elastic across the entire cross-section. It is calculated by substituting the ratio of moment of inertia and section length into the elastic stress equation. This moment represents the threshold beyond which plastic deformation begins in the outer fibers of the member.

During partial plastic deformation, elastic cores persist within plastic zones at the top and bottom of the section. Stress within elastic cores varies linearly with thickness, maintaining elastic behavior. The bending moment during this phase can be estimated analytically using the maximum elastic moment equation, accounting for the reduced elastic region.

The plastic moment represents the maximum bending moment the section can sustain when deformation becomes fully plastic across the entire cross-section. It is significantly higher than the maximum elastic moment and is calculated assuming uniform stress distribution at yield stress. The plastic moment marks the final stage of elastoplastic bending behavior.

The neutral axis serves as the reference line where stress transitions from compression to tension during bending. In elastoplastic bending, stress increases linearly from the neutral axis to maximum at outer fibers during the elastic phase. As plastic deformation progresses, the neutral axis location may shift as the elastic core reduces in size.

Opposing stresses develop because the upper and lower zones experience opposite bending effects: compression in one zone and tension in the other. During partial plastic deformation, both zones yield simultaneously but with opposite stress magnitudes. This symmetric stress distribution about the neutral axis is characteristic of bending in rectangular cross-sections.

The bending moment during elastoplastic transition can be estimated using the maximum elastic moment equation adapted for the reduced elastic core area. This analytical approach accounts for the presence of plastic zones while recognizing that the elastic core still exhibits linear stress variation. The calculation bridges elastic and fully plastic bending regimes.