Chapter 4 - Buckling of Columns

Abstract

This chapter discusses an approach by means of an analogy for deriving the exact relationship between the elastic buckling loads of columns based on the Euler-Bemoulli beam theory, the Timoshenko beam theory, and the Reddy-Bickford beam theory. The exact relationship applies to axially loaded columns with boundary conditions that result in zero lateral force in the members. The resulting Reddy-Bickford buckling solutions are found to be higher than the Timoshenko buckling solutions. For the cases of pinned-pinned and fixed-free columns the buckling loads are practically the same for the two types of columns. However, in the case of fixed-fixed columns, the buckling loads are somewhat different, especially when the columns have relatively large values of the shear parameter Ω=Dxx/(KsAxzL2). The chapter emphasizes that the advantage of the Bickford-Reddy theory over the Timoshenko theory is that the former does not require a shear correction factor.