CONSTRAINED EULER BUCKLING

We consider elastic buckling of an inextensible beam confined to the p lane and subject to fixed end displacements, in the presence of rigid, frictionless side-walls which constrain overall lateral displacements . We formulate the geometrically nonlinear (Euler) problem, derive som e analytical results for special cases, and develop a numerical shooti ng scheme for solution. We compare these theoretical and numerical res ults with experiments on slender steel beams. In contrast to the simpl e behavior of the unconstrained problem, we find a rich bifurcation st ructure, with multiple branches and concomitant hysteresis in the over all load-displacement curves.