Distortional theory for the analysis of wide flange steel beams

• A distortional theory has been developed for the analysis of beams with mono-symmetric wide flange sections.
• The field equations and boundary conditions were derived based on variational principles.
• Closed form solutions were developed for the resulting coupled systems of equations under general loading.
• Comparisons with shell finite element solutions were conducted.
• Practical examples provide insight on the effect of twisting moments on distortion.

A distortional theory is developed for the analysis of doubly symmetric and mono-symmetric wide flange beams under general loading. The governing differential equations of equilibrium and associated boundary conditions are derived based on the principle of potential energy. The theory captures shear deformation effects in the web and local and global warping effects. In contrast to classical beam theories, the present study captures web distortion by accounting for its flexibility within the plane of the cross-section while considering the flanges as Euler–Bernoulli beams. The formulation yields two systems of coupled differential equations of equilibrium in seven displacements fields. The first system governs the longitudinal transverse response and involves three displacement fields, and the second system governs the lateral torsional response and involves four displacement fields. Closed form solutions are then developed for both coupled systems under general loading. Numerical solutions for practical problems are then provided to illustrate the applicability of the formulation. Comparisons to results based on 3D shell finite element solutions show the validity of the results. The theory preserves the relative simplicity of one dimensional beam theories while effectively capturing the three-dimensional distortional phenomena normally captured within computationally expensive 3D FEA.