Abstract
A general analytical solution for the shape functions of a linear beam segment supported on a two-parameter elastic foundation is derived. The solution is not restricted to a particular range of magnitudes of the foundation parameters. The closed form shape functions are utilized to derive analytic expressions for work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. Each work equivalent nodal force and each coefficient of the element matrices is compared with its conventional counterpart for an ordinary beam segment supported by no foundation.
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