Buckling of parallel purlins inter-braced by sag-rods

This paper studied buckling of parallel Z- and C-purlin systems inter-braced by sag-rods at mid-span under pure hogging moment. The purlins are connected to metal sheeting by self-drilled screws and the lateral movement of the top flange is prevented. The paper studied first in detail the buckling of a single purlin, and then buckling of parallel purlin systems. The alternate offset of the sag-rods in adjacent bays and the local deformation of the purlin web have been taken into consideration in parallel purlin systems. For one-purlin system, the buckling moments are given, valid for different combinations of sag-rod and distributed rotational stiffness. The threshold stiffness of the sag-rod, at which the buckling mode changes from symmetrical buckling to anti-symmetrical buckling, is also given. For parallel purlin systems, the buckling moments are calculated by the formulas of one-purlin system, but with a reduced equivalent sag-rod stiffness used in the calculation. Numerical examples for the reduced sag-rod stiffness reveal that an astonishingly large reduction of the sag-rod effective stiffness occurs when the purlin number and the sag-rod offset increase, and the sag-rod stiffness is maximum if the sag-rod is set as close to the bottom flange as possible. And finally some strengthening practices and details are recommended.