In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even after the load is removed.

The unloading phase begins as the bending moment decreases to zero. Unlike purely elastic materials, the stress in an elastoplastic member during unloading does not retrace the original loading path but instead follows a new, linear path. This change indicates the presence of residual stresses, which persist due to the irreversible plastic strains induced during loading.

These residual stresses are calculated using the superposition principle, combining stresses from the elastoplastic loading phase with those from the elastic unloading phase.

During unloading, the stress-strain relationship becomes linear again, allowing for the use of elastic flexure formulas. This phase is critical for engineering applications, as residual stresses can influence structural behavior under repeated loads, potentially leading to unexpected failures. Understanding these dynamics enables the design of safer, more reliable structures by accurately predicting and managing the stresses that arise from complex loading scenarios.