A buckling question

TL;DR

This paper challenges the common belief that shorter, axially compressible beams always have higher buckling loads, showing that material softening can reduce the critical load despite reduced length.

Contribution

It provides a detailed elasticity-based analysis demonstrating conditions where reduced length does not increase buckling strength due to material softening effects.

Findings

Shorter beams can have lower buckling loads due to elastic softening.

Material properties significantly influence buckling behavior beyond length considerations.

The analysis clarifies misconceptions about axial compressibility and buckling loads.

Abstract

Although it is often asserted that, in view of their reduced length, axially compressible beams have a higher buckling load than their inextensible counterpart, a detailed analysis demnstrates that this is not necessarily the case. The argument to arrive at this conclusion is made in terms of relatively straightforward concepts of elasticity and structural mechanics. It is shown that for certain classes of materials the reduced pre-buckling length is more than compensated by a softening of the elastic response, leading to a reduction of the Euler critical load.