On Timoshenko Beams of Rectangular Cross-Section

Abstract

It was recently shown that the shear coefficient for a rectangular Timoshenko beam is highly dependent on the aspect ratio of the beam. This research investigates the reasons for that behavior by comparison of the Timoshenko beam solution with a new three-dimensional solution for a simply supported beam. The new solution is a series solution that converges to any desired accuracy. Comparisons are also made to both elementary and Mindlin plates. The Mindlin plate solution is in excellent agreement with the three-dimensional solution for the simply supported case, and is used as a basis of comparison for a free-free beam. It is found that a shear coefficient which would cause matching of the three-dimensional and Mindlin solutions would have to be a function of the wave length as well as the aspect ratio. Physical explanations are given for the high dependence on aspect ratio and for the dependence on wave length.