  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.
