Some refinements of the classical Bernoulli-Euler theory of the bending of beams are shown to be completely analogous to the effects produced by sources of self-stress in the Bernoulli-Euler beam. This is true for deflections, bending moments and shearing forces. They determine rotations, stresses and strains according to the specific refined theory consideration. Thus, by analogy, differences between the results of various refined theories, having been the object of discussions in recent literature, become accessible to a systematic classification.