ON THE PRINCIPLE OF SAINT-VENANT,

The principle asserts that the stress tensor in points of a beam or cylinder sufficiently far removed from its bases does not depend practically on the distribution of the applied forces in the bases, but depends only on their resultant force and resultant moments. Since 1855, when B. de Saint-Venant expressed the principle, its formulation has been modified by Boussinesq 1885, von Mises 1945 and others in order to make easier a mathematical proof of it. Although in its original and most practical form the principle has remained unproved, its formulation has been extended to a large class of bodies. In the first section, the principle in its original form for bounded bodies was considered. It is shown by means of a counterexample that in order to ensure its validity some restriction must be imposed on the shape of the body. Section 2 considered a cylinder and through construction of a virtual stress tensor and application of the theorem of minimum strain energy, an upper estimate of the total potential elastic energy, which is independent of the length of the cylinder was obtained. In section 3 consideration was given to the infinite cylinder and prove that there cannot be any other stress-bounded solution than those of Saint-Venants type. This, seems to be, therefore, a proof of the principle of SaintVenant in its original form. Author