A unified analysis for distortional and lateral buckling of C-purlins in flexure

• A unified model for distortional and lateral torsional buckling of C-purlins.
• The inter-influence between lateral displacement and rotation is considered.
• The results derived from the present method match excellently with the FEM results.

This paper developed a unified model for the distortional and lateral buckling of cold-formed C-purlins subjected to bending in the plane of symmetry. It can study not only the distortional buckling, but also the global lateral buckling. Different from Hancock's model, the new model includes two interactive springs between lateral and rotational restraints provided by the web to the flange-lip section. A closed-form solution is acquired by the Ritz method. And the elastic buckling coefficients of 20 purlin sections predicted by the solution are compared with those from Finite Element Method (FEM), showing excellent agreement between them. Comparison is also provided with Hancock's method. The closed form solutions are also substituted into the Direct Strength Method to obtain nominal flexure strength of the purlins, and it is found that the proposed model predicted almost the same strength as the software Schafer's CUFSM with differences less than 1%. A good correlation is observed between test results and the proposed method.