Analysis of the Plastic Bending of Beams, Taking into Account Subsequent Elastic Unloading

Abstract

   At first glance, the plastic bending of a beam might seem easily subject to mathematical analysis. In reality, a precise solution remains unknown, and all existing theories, which rely on certain assumptions, refine results to varying degrees of accuracy. These approximate theories are highly useful if applied within specific assumptions and for experimentally verified individual cases.

     In transverse bending, it is generally assumed that shear stresses are minor compared to normal stresses. This holds true when the length of the beam significantly exceeds its cross-sectional dimensions. The same assumption is made during plastic bending. This paper presents an attempt to avoid such inaccuracies when solving similar problems.