A General Solution for the Bending of Beams on an Elastic Foundation of Arbitrary Continuity

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Abstract
In the analysis of beams which are supported elastically along their entire length, it is usually assumed that the elastic support is provided either by a series of independent springs, or by a completely continuous elastic medium. The present paper proposes a method of solution for the intermediate cases, that is, for foundations of partial continuity, by assuming that such foundations may be represented by beams imbedded into an otherwise discontinuous supporting material. In a foundation of this type, there are three independent elastic constants, the resilience of the discontinuous spring layers above and below the beam that is within the foundation, and the flexural rigidity of the foundation beam itself. By changing the values of these three constants, elastic foundations of a wide variety may be produced or, conversely, the constants may be adjusted in such a manner as to represent approximately the characteristics of any given elastic supporting medium. In the paper a general procedure is presented from which solutions can be derived for the bending of beams on such foundations under any loading or end conditions. The method is illustrated by examples showing the range of pressure distributions that may occur under beams supported on foundations of this type.

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