Buckling of Finite Beams in Elastic Continuum

The problem of buckling of piles driven into soil and of fibers embedded in a matrix can be studied by idealizing the same as a beam in elastic continuum. In case of pile foundations, the beams are of finite length. A method has been developed to estimate the buckling loads of a beam embedded in an elastic continuum using Mindlin's equations for calculating displacements of the continuum. Results are compared with subgrade reaction theories to show that the latter underestimates the buckling loads. Buckling loads calculated for two end conditions, pinned and fixed, are shown to depend on the relative stiffness factor, length to width ratio, and the ratio of the elastic moduli of the beam and the continuum.