Plastic Deformations

During plastic bending, the neutral axis shifts away from the centroid, unlike elastic bending where it coincides with the centroid. An iterative method locates the neutral axis by adjusting its assumed position until the stress distribution curve stabilizes. For members with vertical and horizontal symmetry and identical stress-strain relationships, the neutral axis aligns with the horizontal plane of symmetry.

In plastic deformation, the strain at any point in the member is expressed in terms of maximum strain. This relationship allows engineers to predict how different locations within the member will deform relative to the point experiencing the highest strain value during bending.

The modulus of rupture is the maximum stress corresponding to the ultimate bending moment—the maximum moment a member can endure before failure. This critical value represents the material's ultimate strength under bending stresses and is determined experimentally by testing the member until it fails.

When bending stress exceeds the material's yield strength, permanent plastic deformation occurs, altering the stress distribution throughout the member. This changed stress distribution requires the neutral axis to shift from the centroid to a new location where internal forces remain balanced, necessitating iterative calculation methods to determine its exact position.

The bending moment for a plastically deforming member is expressed in terms of the member's width and the stress at distance y from the neutral axis. By plotting the stress distribution curve using specified maximum stress values, engineers can determine the moment capacity and predict when the member will fail.

For members with both vertical and horizontal planes of symmetry and identical stress-strain relationships along both axes, the neutral axis coincides with the horizontal axis of symmetry during plastic bending. This simplifies stress distribution analysis and neutral axis location determination for symmetric structural designs.

Elastic bending produces temporary deformation that reverses when load is removed, with the neutral axis at the centroid. Plastic deformation permanently alters the member's shape when stress exceeds yield strength, and the neutral axis shifts away from the centroid, requiring iterative methods to locate its new position.