To understand the true behavior of thin-walled open-sectioned members subjected to torsion, it requires solution of differential equation involving hyperbolic functions. In many practices, Flexural Analogy being an approximation is used to avoid tangling with tedious hyperbolic functions, nevertheless it is a simplified method based on a 2D flexure model mimicking the 3D torsional response by passing over certain higher-ordered torsional effects.
In terms of longitudinal stress, Flexural analogy works fine for symmetrical sectioned steel members because by calculation, flexural bending stress is proven greater than warping normal stress; it might work from flexural shear to certain extent. However, it becomes questionable when it comes to (1) application to certain unsymmetrical sectioned members, (2) the correctness of angular rotation θ about the shear center and (3) application to crane runway girders in general.
For crane runway girders, when the accuracy of θ value is inaccurate to begin with then there is no way to quantify the deflection at the rail top for meeting serviceability requirement. Several higher-ordered torsional effects ensued from θ function’s derivatives whereby θ’ controls St. Venant shear stress while θ’’’ controls warping shear stress; to crane girders, both are critical in justifying a crane girder’s strength against metal fatigue.