Improved engineering theory for uniform beams

Research paper by A. N. Kathnelson

Indexed on: 01 Mar '96Published on: 01 Mar '96Published in: Acta mechanica


A small static symmetric bending deformation of isotropic linear elastic beams under arbitrary transverse loading varying slowly with the axial coordinate is considered. An asymptotic analysis of the three-dimensional variational equation — in which the small parameter is the ratio of maximum cross-sectional dimension to beam length — gives Timoshenko type governing equations, corresponding boundary conditions, improved formulae for the displacements, and, unlike known beam theories, for all stresses a plane problem in the cross-sectional domain to be solved. Predictions of the theory for beams of narrow rectangular and circular cross-sections are compared with explicit elasticity solutions.