Direct Strength Approach to Predict the Flexural Strength of Cold-Formed Z-Section Purlins on Sloped Roofs

In this study, the strength of cold-formed Z-section purlins is predicted considering the effects of roof slope in real roof systems. The study applies to simple span purlins with torsion restraints at support locations and at paired locations along the length of the member. A previously developed method has shown through comparisons to base tests that when the biaxial bending and torsion stresses are incorporated into the analysis, the Direct Strength Method can accurately predict the strength of a purlin. These stress distributions can deviate substantially from the constrained bending approximation typically assumed in analysis and therefore impacts the local and distortional buckling behavior. The method was modified to represent the system conditions in real roofs and to include roof slope. The base test is a test intended to represent real roof conditions, however second order stresses can be introduced as a result of the limitations of the test. Real roof systems are not subject to some of these second order effects. Similarly, as slope effects are included in the analysis, biaxial bending and torsion stresses can change significantly relative to the flat roof condition, particularly for flexible standing seam diaphragms. This change in stresses in turn changes the local and distortional buckling behavior of the purlin. Initially, for low slope roofs, the predicted strength increases relative to the flat roof condition. As the roof slope increases and the mid-span of the purlin displaces downslope, the flexural strength of the purlin can be less than the flat roof condition. Using the analytical model developed in this study, the strength of purlins is evaluated at different roof slopes and compared to the "real" flat roof condition.

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