Shear correction factors and an energy-consistent beam theory

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 _rst!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 _nite!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 "0855#[ The energy!averaged shear representative is also used to derive Timoshenko|s beam theory