Advances in Lateral Torsional Buckling Analysis of Beam-Columns and Plane Frames
Creators: name: Sahraei, Arash
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 2017

description: The present study provides a series of contributions to the advancement of methods of lateral torsional buckling analysis of beam-columns and plane frames. The first contribution develops a family of three finite elements for the lateral torsional buckling analysis of members with doubly symmetric cross-sections. The elements capture warping, shear deformation, and load position effects as well as the destabilizing effects due to strong axis bending, associated shear forces, and axial forces. The formulation starts with a recently developed variational principle based on an advanced kinematic model that incorporates shear deformation effects due to flexure and warping. Unlike previous shear deformable solutions that exhibit slow convergence due to shear locking, the present study develops an innovative interpolation scheme that circumvents shear locking. One of the elements is devised to attain fast convergence. The second element is devised to guarantee convergence to the buckling loads from below while the third element is guaranteed to converge from above, thus providing lower and upper bounds for the buckling loads. The formulation is equipped with a versatile multi-point constraint feature enabling the analyst to model, among other applications, the effect of lateral braces that are offset from the shear center. The second contribution extends the formulation to members with mono-symmetric sections. A closed-form shear deformable solution is derived for the case of a mono-symmetric simply supported beam subjected to uniform bending moments. A beam finite element is developed and adopted to provide solutions for simply supported beams, cantilevers, and developing moment gradient factors for beams under linear moments. The formulation is shown to successfully capture interaction effects between axial forces and bending moments and the destabilizing effect of loads offset from the shear center. The third contribution devises a technique to extend present lateral torsional buckling solutions originally intended for beam analysis to the modelling of plane frames. The technique involves developing a generalized four-node joint finite element that accurately quantifies the partial warping restraint provided by common moment connections to adjoining members framing at right angles. The joint element is intended to seamlessly interface either with the classical beam buckling elements or the shear deformable finite elements developed in the present study. A systematic static condensation scheme is devised to adapt the joint element for cases where a joint interfaces with only two or three elements. Careful consideration is taken to incorporate for the finite rotation effect for the joints. The formulation adopts multi-point constraints to characterize the in-plane pre-buckling behavior and out-of-plane buckling behavior of the joints. The methodology is shown to involve considerably fewer degrees of freedom than shell based solutions while leading to accurate predictions of the buckling loads. The technique is then adopted to characterize the elastic lateral torsional buckling of sample plane frame configurations and thus provides a basis to assess the validity of the Salvadori hypothesis commonly adopted in present design standards whereby buckling loads for members are quantified by separating the members from the entire structure. The study suggests that for plane frames with lateral restraints at the joints, the application of the Salvadori hypothesis typically leads to conservative buckling load estimates. In contrast, for cases where some of the joints are laterally free, the Salvadori hypothesis may overestimate the buckling strength.