AN APPROACH TO THE ELASTIC COLUMN BUCKLING WITH ALLOWANCE FOR SHEAR DEFORMATION AND ROTARY INERTIA

This paper is concerned with the effects of shear deformation and rotary inertia on the critical buckling load of columns. An exact relation between the Timoshenko buckling load and the buckling load with ignoring the effects of shear deformation and rotary inertia have been found in this paper. Engesser derived a simple formula for the hinged-hinged end boundary conditions, which includes the effect of shear deformation on the lowest critical buckling load of columns. Later some writers have tried to derive similar equations for other end boundary conditions such as clamped-hinged. In this paper an exact formula for the case of hinged-hinged end boundary conditions including the effects of shear deformation and rotary inertia have been derived. The results are in a good agreement with those of Engesser. It have been shown that although the effect of shear deformation and rotary inertia in frequency analysis of Timoshenko's beams are remarkable but in metal columns, shear deformation has a little effect on the critical buckling and rotary inertia has no effect.