Direct Strength Prediction of Cold-Formed Z-Section Purlins with Support Torsion Braces Combined with Span Lateral Braces

The Direct Strength Method is a powerful tool to evaluate the buckling behavior of cold-formed steel structural members. Recent studies have shown that when the Direct Strength method is used in conjunction with analytical procedures that quantify the changes in stress distribution caused by biaxial bending and torsion, the strength of Z-section purlins with one flange attached to sheathing can be accurately predicted. The industry has long assumed a constrained bending stress distribution, but in reality, the distribution of stresses depends on the nature of the external bracing applied. This study investigates the local and distortional buckling strength as predicted by the Direct Strength method for simple span Z-sections with torsion restraints at the support location and combined lateral-torsional braces applied along the length of the purlin. With this bracing configuration, although the lateral displacement of the Z-section is effectively restrained, the Z-section experiences a concentration of stresses at the brace location. As a result of this concentration of stresses, the Z-section may fail at a load level below what is predicted using a constrained bending stress distribution. An analytical model has been developed that predicts the distribution of stresses in the purlin cross section for systems of purlins with supports torsional braces and paired lateral-torsional braces along the span. The analytical model considers the lateral restraint provided by the flexible diaphragm. Lateral restraints along the span are considered flexible while the span torsion restraints are considered rigid. The model is demonstrated by comparing the predicted strength of several bracing configurations.

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