Shear correction factors and an energy-consistent beam theory

Abstract Presented here is a new derivation of shear correction factors for isotropic beams by matching the exact shear stress resultants and shear strain energy with those of the equivalent first-order shear deformation theory. Moreover, a new method of deriving in-plane and shear warping functions from available elasticity solutions is shown. The derived exact warping functions can be used to check the accuracy of a two-dimensional sectional finite-element analysis of central solutions. The physical meaning of a shear correction factor is shown to be the ratio of the geometric average to the energy average of the transverse shear strain on a cross section. Examples are shown for circular and rectangular cross sections, and the obtained shear correction factors are compared with those of Cowper (1966) . The energy-averaged shear representative is also used to derive Timoshenkos beam theory.

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