Plastic Deformations

For pure bending, when maximum stress exceeds the yield strength of the member's material, it undergoes plastic deformation.

The strain at any point in the member is expressed in terms of maximum strain. For plastic deformations, the neutral axis of the member may not pass through the centroid of the member.

Here, the neutral axis of the member is located using an iterative method until the stress distribution curve is formed.

For members with a vertical and horizontal plane of symmetry and the same stress-strain relationship for both axes, the neutral axis coincides with the horizontal axis of symmetry. The stress distribution curve can be plotted using a specified maximum stress value.

Here, the bending moment of such a member is given in terms of the member's width and the stress at the distance y from the neutral axis. The ultimate value of the bending moment that causes a member to fail can be found experimentally.

This ultimate bending moment gives the corresponding maximum stress, known as the modulus of rupture.