Improved engineering theory for uniform beams


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.

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Kathnelson, A.N. Improved engineering theory for uniform beams. Acta Mechanica 114, 225–229 (1996).

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  • Fluid Dynamics
  • Governing Equation
  • Small Parameter
  • Plane Problem
  • Axial Coordinate