Distortional lateral-torsional buckling theories assume that the flanges remain undistorted, while the web is free to distort as a thin plate. Most theories adopt a cubic polynomial distribution along the web height to relate the lateral displacement of the web to the displacements and angles of twist both flanges. The present study develops a family of finite element solutions for the distortional buckling of wide flange beams in which the flanges are assumed to remain undistorted. In contrast to past theories, the lateral displacement distribution along the web height is characterized by superposing (a) two linear modes intended to capture the classical non-distortional lateral-torsional behavior and (b) any number of user-specified Fourier terms intended to capture additional web distortion. In the longitudinal direction, all displacement fields characterizing the lateral displacements are taken to follow a cubic distribution. The first contribution of the thesis develops a finite element formulation that is able to replicate the classical non-distortional lateral torsional buckling solutions when the distortional modes are suppressed while enabling more accurate predictions for distortional lateral torsional buckling compared to those solutions based on the conventional cubic interpolation of the lateral displacement. The formulation is used to conduct an extensive parametric study to quantify the reduction in critical moments due to web distortion relative to the classical non-distortional predictions in the case of simply-supported beams, cantilevers, and beams with an overhang. The solution is then used to generate interaction curves for beams with an overhang subjected to various proportions of uniformly distributed and point loads. The second contribution of the thesis adds two additional features to the formulation (a) to capture the destabilizing effect due to the load height relative to the shear center and (b) a module that incorporates any number of user-defined multi-point kinematic constraints. The additional features are employed to investigate the effect of load height, bracing height, and combined effects thereof in practical design problems. A distortional indicator is then introduced to characterize the distribution of web distortion along the beam span as the beam undergoes distortional lateral buckling. A systematic design optimization technique is then devised to identify the location(s) along the span at which the addition of transverse stiffeners would maximize the critical moment capacity.

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