Refined calculation of lateral bracing systems due to global geometrical imperfections

•Work shows refined model of calculation of forces due to global, geometrical imperfections of roof rafters.•Proposed model incorporate the parabolic distribution of compressive forces in the member and its parabolic bow imperfection.•The lack of verticality described by angle ϕ0 and entire distortion of the main plane of the truss rafter are studied.•Results have been discussed and illustrated by an example.

In Eurocode 3 the analysis of equivalent stabilizing forces due to global geometrical imperfections and in consequence the calculation of the lateral bracing systems of the roof girders is given. The forces are assumed to be uniform N(x) = const within the span of restrained member that has an initial bow imperfection e0. This simplifying assumption is not adequate for the actual non-uniform distribution of forces N(x) ≠ const and is considered in [6] as slightly conservative. Apart of it the model from Eurocode 3 ignores the geometrical imperfections of the main plane of the restrained truss roof girder, which affect the stress state of purlins and lateral bracing as well. The object of the work is presentation of refined models of calculation of forces due to global, geometrical imperfections of restrained roof rafters, purlins and lateral bracings. Those models incorporate the parabolic distribution of compressive forces in the restrained member N(x) ≠ const, and its parabolic bow imperfection e0 in the roof plane. Additionally, both the effect of the lack of verticality described by angle ϕ0 and the entire distortion of the main plane of the truss rafter (lack of flatness as an effect of the bow e0 of the compressed upper chord of the truss) are studied. The formulas for equivalent stabilizing forces assuming the parabolic distribution due to above mentioned global, geometrical imperfections, have been proposed. Obtained results have been discussed and illustrated by an example.