IV. On an approximate solution for the bending of a beam of rectangular cross-section under any system of Lond, with special reference to points of concentrated or discontinuous loading

Abstract

The consideration of the stresses and strains which occur in a rectangular parallelopiped of elastic material subjected to given surface forces over its six faces leads to one of the most general, as it is one of the oldest, problems in the Theory of Elasticity. Lame, in his ‘Lemons sur l’Elastieite des Corps solides,’ published in 1852, describes it as “le plus difficile peut-etre de la theorie mathematique de ’elasticity.” In spite of repeated attempts, however, the problem remains still unsolved. In its complete form it may he stated as follows:—