Unbraced Length Requirements for Steel I-Beams

Solutions are obtained for inelastic buckling of I-shaped beams of structural steel and the relationship between unsupported length and the extent of flexural deformation sustained at the onset of buckling is examined. The load consists of a uniform moment. End conditions assumed include full fixity, free rotation about the minor principal axis with restrained warping and free rotation about the minor axis with unrestrained warping. The extensional stiffness is obtained from a theory that considers partially yielded steel to consist of an inhomogeneous mass consisting of unyielded steel and steel which has passed into strain hardening. Of the parameters examined, the minor axis radius of gyration divided by the yield stress appeared to best correlate unsupported length with the amount of flexural deformation sustained at the onset of buckling. Restraining warping at the ends of simply supported beams significantly suppresses their tendancy to buckle.