Non-linear biaxial bending of steel Z-beams

Abstract

Confusion as to the way in which the bending of Z-section beams has been described has led to misleading descriptions of the limiting moments of beams which undergo non-linear biaxial bending and twisting as being elastic buckling moments. Further difficulties arise from the use of the same symbols to describe both the principal and the rectangular axes of Z-sections.A constrained beam with restraints which prevent lateral displacement of the compression region does not buckle laterally, and only needs to be designed against in-plane failure. A beam with restraints which prevent lateral displacement of the tension region should be designed against lateral-distortional buckling, which may be approximated by lateral buckling with an enforced centre of rotation.An unconstrained beam bent about its minor principal axis does not buckle laterally, and should be designed against in-plane failure. An unconstrained beam bent about its major principal axis may buckle laterally.An unconstrained beam under biaxial bending deflects and twists as soon as loading commences and reaches very large deformations as a limiting moment is approached. The large deformations cause premature yielding before the limiting moment is reached. Pre-buckling effects reduce these large deformations somewhat, but not sufficiently that the limiting moment can be safely used in first yield design. Instead, interaction equations may be used. The linear interaction equation is unnecessarily conservative, and may be replaced by a parabolic interaction equation.