An iterative solution to the effects of concentrated loads applied to long rectangular beams

The analysis of the bending of thin deep rectangular beams by concentrated loads has already been treated by L.N.G. Filon and Th. v. Kármán. These authors consider an infinitely long beam and express the load as a Fourier integral, obtaining integral solutions for the stresses and displacements. In their integral form, these results are rather difficult to interpret, although F. Seewald, using Kármán’s analysis, has calculated numerical values for the case of a single concentrated load.