Structural Stability Theory and Practice

3Inelastic and Metal Columns

3.1 Introduction

Structures can fail either due to material failure or to instability. But they can also fail due to a combination of both. The material failure is usually preceded by inelastic phenomena, which generally has a destabilizing influence on structures, and must therefore be taken into consideration. Even for structures that are elastic under service loads, achievement of a uniform safety margin requires the consideration of overloads, and overloads inevitably involve inelastic deformations. The strength of a perfectly straight prismatic column with concentric loading is the Euler buckling load, as long as the material is still elastic when the buckling occurs. Many practical columns are found in a range of slenderness where, at buckling, portions of the column are no longer elastic, and thus one of the key assumptions underlying the Euler column theory is violated. Essentially the stiffness of the column is reduced by yielding.

Before considering the theory of inelastic column behavior, let us briefly review the historical development of column buckling theories. The Euler formula was derived by Leonhard Euler in 1744. Later on, it was found that the formula gave higher values of critical load than found from experiments on short columns, in other words the formula was unconservative for these columns. Engesser and Considère in 1889 and 1891 respectively [1,2] found that Euler's formula was valid only for slender columns. They also ...