Cellular buckling from mode interaction in I-beams under uniform bending

TL;DR

This paper develops a nonlinear analytical model to study complex buckling phenomena in thin-walled I-beams under uniform bending, revealing the interaction of global and local buckling modes and predicting cellular buckling behavior.

Contribution

It introduces a variational-based nonlinear formulation and numerical continuation approach to analyze mode interaction and cellular buckling in I-beams, a novel theoretical insight.

Findings

Model predictions match experimental results

Cellular buckling occurs after initial localization

Global-local mode interaction causes complex buckling patterns

Abstract

Beams made from thin-walled elements, whilst very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on variational principles for the ubiquitous I-beam with thin flanges under uniform bending is presented. The resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post-buckling range can be portrayed. The interaction between global lateral-torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling (snaking) being predicted theoretically for the first time. Solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling.