Finite element formulation for lateral torsional buckling analysis of shear deformable mono-symmetric thin-walled members

• A FEA is formulated for lateral torsional buckling analysis of mono-symmetric members.
• Solution is validated through comparison with other established solutions.
• Formulation accounts for shear deformation and load position effects.
• Closed-form expression is developed for elastic lateral torsional buckling resistance of beams.
• For long span beams, closed-form solution reverts to classical solution.
• Solution is applied to simple beams, cantilevers, and beam-columns.
• Moment gradient factors are developed for mono-symmetric beams under linear moments.

A shear deformable theory and a computationally efficient finite element are developed to determine the lateral torsional buckling capacity of beams with mono-symmetric I-sections under general loading. A closed-form solution is also derived for the case of a mono-symmetric simply supported beam under uniform bending moments. The finite element is then used to provide solutions for simply supported beams, cantilevers, and developing moment gradient factors for the case of linear moments. The formulation is shown to successfully capture interaction effects between axial loads and bending moments as well as the load height position effect. The validity of the element is verified through comparisons with other established numerical solutions.