Plastic Deformations

A cantilever beam, when subjected to a load at its free end, develops the maximum bending moment at its fixed end.

Until the bending moment surpasses the beam's elastic limit, the normal stress remains under the yield strength. Beyond this point, yielding is initiated from the fixed end.

The boundary between the elastic and plastic zones can be obtained by measuring the half-thickness of the elastic core.

When the load reaches a certain threshold, the section near the fixed end becomes fully plastic, forming a plastic hinge. This hinge represents the maximum load the beam can support.

In a partially plastic section, the normal stresses on the faces are uniformly distributed and equal to the yield strength.

The shearing force on the lower face is zero, resulting in a zero average value of the shearing stress. The vertical shear is distributed entirely over the elastic portion of the cross-section.

As the area of the elastic portion decreases, the maximum shearing stress increases and eventually reaches the yield strength, contributing to the ultimate failure of the beam.