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Lateral-torsional buckling of an I-section purlin
A simply supported I-section purlin is slightly inclined, which renders hand calculations relatively difficult. The purlin is loaded in biaxial bending, biaxial shear forces, torsion, and warping. When we add the possibility of lateral-torsional buckling because the roof sheeting is not very stiff, we have a real pickle.
See how this purlin can be easily designed in IDEA StatiCa Member.