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 foran, 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. In this paper, a totally different approach to the problem is made. The loaded area is conformally transformed to a circle, and, using Muschelisvili's transformation of the boundary conditions, the problem is solved in the plane of the circle. The solution is then obtained in the form of a complex power series. In this manner, a direct solution, to any required degree of accuracy, is readily obtained.

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displacements stresses fourier integral muschelisvilis transformation of the boundary rectangular beams complex power krmns f seewald concentrated loads circle and

C. A. M. GRAY,.AN ITERATIVE SOLUTION TO THE EFFECTS OF CONCENTRATED LOADS APPLIED TO LONG RECTANGULAR BEAMS. 11 (3),.

C. A. M. GRAY,"AN ITERATIVE SOLUTION TO THE EFFECTS OF CONCENTRATED LOADS APPLIED TO LONG RECTANGULAR BEAMS" 11

C. A. M. GRAY,"AN ITERATIVE SOLUTION TO THE EFFECTS OF CONCENTRATED LOADS APPLIED TO LONG RECTANGULAR BEAMS"