Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Author: C. A. M. Gray
Journal: Quart. Appl. Math. 11 (1953), 263-271
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/57144
MathSciNet review: 57144
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Abstract: 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.


References [Enhancements On Off] (What's this?)

  • [1] L. N. G. Filon, Phil. Trans. (A) 201, 63 (1903).
  • [2] Th. v. Kármán, see TIMOSHENKO, Theory of elasticity, p. 99-104.
  • [3] N. Muschelisvili, Zeits. angew. Math. Mech. 13, 264 (1933).
  • [4] C. A. M. Gray, The analysis of infinitely long beams under normal loads, J. Proc. Roy. Soc. New South Wales 85 (1951), 20–25 (1952). MR 0055926

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DOI: https://doi.org/10.1090/qam/57144
Article copyright: © Copyright 1953 American Mathematical Society


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