Buckling of moderately thick orthotropic columns: comparison of an elasticity solution with the Euler and Engesser/Haringx/Timoshenko formulae

The objective of this paper is to answer the question of how accurately the simple Euler or transverse shear correction E.ngesser/Haringx/Timoshenko column buckling formulae are, when orthotropic composite material and moderate thickness are involved. The column is in the form of a hollow circular cylinder and the Euler or Timoshenko loads are based on the axial modulus. For this purpose, a three-dimensional elasticity solution is presented. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy or graphite/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. First, 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 degree of non-conservatism of the Euler load for the circumferentially reinforced columns is much smaller and is comparable to that of isotropic columns. Second, the Engesser or first Timoshenko shear correction formula is in all cases examined conservative, i.e., it predicts a lower critical load than the elasticity solution. The Haringx or second Timoshenko shear correction formula is in most cases (but not always) conservative. However, in all cases considered, the second estimate is always closer to the elasticity solution than the first one. For the isotropic case both Timoshenko formulas are conservative estimates. Examination of a new formula for column buckling that adds a second term to the Euler load expression and is supposed to account for thickness effects, shows that this estimate is a non-conservative estimate but performs very well with very thick sections, being closest to the elasticity solution, but in general no better than the Timoshenko formulas for moderate thickness. Copyright © 1966 Elsevier Science Ltd