Timoshenko Beam Element Resting on Two‐Parameter Elastic Foundation

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Abstract
The objective of this paper is to present the complete force‐displacement relationship for a Timoshenko beam element resting on a two‐parameter elastic foundation. Both the stiffness matrix and nodal‐action column‐vector coefficients are derived from the transport matrix based on the exact solution of two differential equations governing the problem concerned herein. Explicit expressions for the element stiffness matrix and the nodal‐action column vectors are presented. Finally, a parametric study is carried out in the form of numerical examples and influence lines.

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