Generalized model of imperfection forces for design of transverse roof bracings and purlins

The EN 1993-1-1 calculation model of initial, equivalent bow imperfection forces qd acting on the bracing system assumes that the stabilized member is uniformly compressed within his length. But this assumption is incorrect. The distribution of the axial compression force in the restrained roof rafter varies along its length and usually has a parabolic shape. This paper proposes refined generalized models for identifying the imperfection forces in members to be restrained, having an initial bow imperfection with maximum amplitude e0. The models were derived on the basis of the real parabolic shape of the axial forces distribution in restrained roof girders. The effect of lateral imperfection amplitude e0 of the restrained girder is accompanied by twist imperfection ϕ0 measured as the angle of rotation of the webbed girder plane or the plane passing through the truss top and the bottom chords. The latter imperfection profile component generates additional horizontal imperfection forces H1,i not included in the current design codes. Analytical relations for calculating imperfection force qdi and force H1,i are provided in order to evaluate the state of stress in both the purlins and the bracings. The considered problem is illustrated with a calculation example.