The Brazier effect for elastic pipe beams with foam cores

Pipe beams are considered under the action of bending. In case of elastic material, an analytical model of a one-dimensional beam is introduced, where the internal constraint between ovalization and bending curvature is deduced from mechanical considerations. Then, the softening moment-curvature relationship, able to describe the Brazier effect, is evaluated applying equilibrium equations in the nonlinear field. The same model is extended to the case where a structural foam is present as core of the pipe. The contribution of the core is analyzed in terms of its action in preventing instability phenomena. Finally, a model of lumped ovalization is discussed.