Analytical Solutions for Timoshenko Beam-Columns on Elastic Foundations

In the present work, static and dynamic stability parameters of a Timoshenko beam-column resting on a two-parameter foundation are investigated. Analytical solutions using recursive differentiation method are obtained considering both the angular inertia and shear stress induced from the axial load. Obtained solutions are verified and then used to capture the significance of different beam foundation parameters on the stability parameters. Different approaches dealing with the shear stress induced from the axial load are investigated. Solutions based on Euler-Bernoulli beam and Timoshenko beam theories are compared. The comparison indicated that the solutions of the two theories converge as the slender ratio of the beam increases. In case of beams resting on soils, the soil influence on stability parameters may be neglected for beams with slenderness ratio <20. It is highlighted that the proposed solutions are simple, straight-forward and accurate compared with the available solutions in literature.