20.10 : 由弹塑性材料制成的构件

Consider a member made up of an elastoplastic material with a rectangular cross-section. Within the elastic limit, the stress distribution across the section is linear.

As the bending moment increases, the maximum stress in the member increases. The maximum bending moment is observed when the deformation in the member remains fully elastic.

The maximum elastic moment of the section can be calculated by substituting the ratio of the moment of inertia and length of the section.

With a further increase in bending moment, the plastic deformation takes place uniformly but with an opposing magnitude of stresses in the upper and lower zones. The elastic cores are present within plastic zones, and the stress for elastic cores varies linearly with thickness. 

The bending moment corresponding to the stress within the elastic cores can be estimated analytically using the maximum elastic moment equation.

As the bending moment is increased further to the limiting value, the deformation becomes fully plastic, and the plastic moment of the member is expressed in terms of the maximum elastic moment.