Constrained torsion of prismatic bars

  • Authors:

  • Steven W. Reagan;Walter D. Pilkey

  • Affiliations:

  • Department of Mechanical and Aerospace Engineering, Automobile Safety Laboratory, University of Virginia, 122 Engineer's Way, P.O. Box 400746, Charlottesville, VA;Department of Mechanical and Aerospace Engineering, Automobile Safety Laboratory, University of Virginia, 122 Engineer's Way, P.O. Box 400746, Charlottesville, VA

  • Venue:
  • Finite Elements in Analysis and Design - Robert J. Melosh medal competition
  • Year:
  • 2002

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Abstract

A theory is developed that allows the determination of three-dimensional displacements and stresses within finite length prismatic bars of arbitrary cross-section experiencing restrained torsion. This restraint arises from the twisting of a bar where one of its cross-sections is subject to displacement and slope constraints. The deformations within this bar are represented by an exponentially decaying residual solution superimposed on the classical Saint-Venant solution. Galerkin's method is used to solve the boundary value problem resulting from a simultaneous system of three quadratic eigenproblems subject to the stress free boundary condition due to the traction-free lateral surface of the bar. A three-dimensional finite element model is used for validation.