Research Article
Oct 1979
Beam Equation with Variable Foundation Coefficient
Publication: Journal of the Engineering Mechanics Division
Volume 105, Issue 5
Abstract
The equation w4(x) + xpw(x)=0 in the region (0<x<infinity) is of value in describing the behavior of loaded beams resting on, or imbedded (piles) in soils. Its solution when p=0 is elementary, but for other values of p, solutions have formerly been obtained only by the finite difference method. Herein, an analytical solution is obtained and evaluated for the case of p=l, and a numerical technique is developed for obtaining two of the solutions for other values of p. The solutions are those which tend to zero as x tends to infinity; they are of use in the case of the semi-infinite beam. In practice most piles in soil fall into this category.
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Published In
Journal of the Engineering Mechanics Division
Volume 105 • Issue 5 • October 1979
Pages: 811 - 827
Copyright
© 1979 American Society of Civil Engineers.
History
Published in print: Oct 1979
Published online: Feb 3, 2021
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Joel N. Franklin
Prof. of Applied Mathematics, Div. of Engrg. and Applied Sci., California Inst. of Tech., Pasadena, Calif.
Ronald F. Scott, M.ASCE
Prof. of Civ. Engrg., Div. of Engrg. and Applied Sci., California Inst. of Tech., Pasadena, Calif.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.