Three-Dimensional Elasticity Solution for the Buckling of Moderately Thick Orthotropic Columns

Abstract

The buckling of an axially compressed orthotropic column is investigated by using a three-dimensional elasticity formulation. In this manner, an assessment of the thickness and othotropy effects can be accurately performed. The column is in the form of a hollow circular cylinder. The critical loads from this elasticity solution are compared with the ones from the Euler or Timoshenko transverse shear correction formulas based on the axial modulus. Furthermore, a comparison is made with a recenly suggested new formula for column buckling that adds a second term to the Euler load expression and is supposed to account for thickness effects. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. It is found that the elasticity approach predicts in all cases a lower than the Euler value critical load. Moreover, the degree of non-conservatism of the Euler formula is strongly dependent on the reinforcing direction; the axially reinforced columns show the highest deviation from the elasticity value. The first Timoshenko shear correction formula is in all cases examined conservative. The second Timoshenko shear correction formula is in most cases (but not always) conservative. However, the second estimate is always closer to the elasticity solution than the first one. For the istotropic case both Timoshenko formulas are conservative estimates. The recent new formula for column buckling that adds a second term to the Euler load expression is a non-conservative estimate but performs very well with very thick sections, being closest to the elasticity solution; for moderate thickness it is in general no better than the Timoshenko formulas.