Lateral-torsional deformations of single-span and two-span thin-walled beams with continuous bracing

Abstract

C-section and Z-section cold-formed steel beams subjected to a uniformly distributed load on the top flange are analyzed. Single-span beams with each end pinned or fixed, and two-span beams with equal spans, are considered. Both gravity loading and wind uplift are treated. Continuous elastic restraints resist bending and twisting. The lateral restraint acts on the top flange. It is assumed that the beams are linearly elastic and that the cross section maintains its shape during deformation. Lateral-torsional deformation for the C-section beam involves twist and bending in the weak direction. For the Z-section beam, the deformation involves coupling between bending in both the weak and strong directions, along with the twist. The governing equilibrium equations are solved numerically. The problem is motivated largely by roof purlins in metal buildings. Numerical results demonstrate the effects of load magnitude, bending and twisting restraint stiffnesses, and roof slope (with top flange facing either upslope or downslope).