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Beam Equation with Variable Foundation Coefficient

Franklin, Joel N. and Scott, Ronald F. (1979) Beam Equation with Variable Foundation Coefficient. Journal of the Engineering Mechanics Division, 105 (5). pp. 811-827. ISSN 0044-7951. http://resolver.caltech.edu/CaltechAUTHORS:20140611-110441044

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Abstract

The equation w^4(x) + x^Pw(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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http://cedb.asce.org/cgi/WWWdisplay.cgi?9075PublisherArticle
Additional Information:Copyright © 1979, ASCE. Discussion open until March 1, 1980. To extend the closing date one month, a written request must be filed with the Editor of Technical Publications, ASCE. This paper is part of the copyrighted Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, Vol. 105 , No. EMS, October, 1979. Manuscript was submitted for review for possible publication on July 28, 1978. We would like to thank A. Chang of the Booth Computing Center of the California Institute of Technology for his assistance in evaluating the integrals involved in the analytical approach, and in computing the functions by the numerical method. A portion of this work was supported by a grant from the American Petroleum Institute.
Funders:
Funding AgencyGrant Number
American Petroleum InstituteUNSPECIFIED
Subject Keywords:Beams (supports); Elastic foundations; Foundations; Piles; Soil mechanics; Soil properties; Structural design
Record Number:CaltechAUTHORS:20140611-110441044
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140611-110441044
Official Citation:Franklin, Joel N., and Scott, Ronald F., " Beam Equation with Variable Foundation Coefficient," Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM5, Proc. Paper 14926, October, 1979, pp. 81 1-827
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46205
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:11 Jun 2014 19:10
Last Modified:11 Jun 2014 19:10

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