On Elementary Theory of Tangent Stresses at Simple Bending of Beams

摘要

The article contains three additions to the elementary theory of flexural shear stresses developed by the author, which is a generalization of Zhuravsky's theory. First, we derive a formula for the cross-sectional shape coefficient, which takes into account the deplanation of the cross section in Mor's integrals for energy and displacements. The new form factor, in contrast to the classical one, depends on the Poisson ratio and the ratio of the cross-sectional dimensions. Secondly, a very simple formula is given expressing the potential potential energy of deformation of the rod, connected with the vertical tangential stress. Thirdly, this formula is used for the energy analysis of the author's theory, that establish the new properties of Zhuravsky's. It is stated that, for certain values of the Poisson's ratio (of its own for each type of cross section), Zhuravskii's theory yields exact results that coincide with the results of the theory of elasticity.