Shear correction factors and an energy-consistent beam theory

Presented here is a new derivation of shear correction factors for isotropi c beams by matching the exact shear stress resultants and shear strain ener gy with those of the equivalent first-order shear deformation theory. Moreo ver, a new method of deriving in-plane and shear warping functions from ava ilable elasticity solutions is shown. The derived exact warping functions d an be used to check the accuracy of a two-dimensional sectional finite-elem ent analysis of central solutions. The physical meaning of a shear correcti on factor is shown to be the ratio of the geometric average to the energy a verage of the transverse shear strain on a cross section. Examples are show n for circular and rectangular cross sections, and the obtained shear corre ction factors are compared with those of Cowper (1966). The energy-averaged shear representative is also used to derive Timoshenko's beam theory. (C) 1998 Elsevier Science Ltd. All rights reserved.