Lateral-Torsional Deformations of C-Section and Z-Section Beams with Continuous Bracing

Simply-supported, single-span, C-section and Z-section cold-formed steel beams subjected to a uniformly distributed load on the top flange are analyzed. Both gravity loading and wind uplift are considered. Continuous elastic restraints resist bending and twisting as the load is increased. The lateral restraint acts on the top flange. It is assumed that the thin-walled beams are linearly elastic and 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), for both gravity and uplift loading.

View content