Finite Element Formulations for Lateral Torsional Buckling of Shear Deformable Planar Frames
Creators: name: Wu, Liping
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 2010
Subjects: subject: Engineering, Civil.

description: Laterally unsupported steel frames commonly occur in industrial structures and pipe racks. In these applications, frames are typically unsupported in the lateral direction at the beam to column junctions, a key difference from typical details in commercial applications. Present design procedures in structural steel standards are not intended for the design of these types of structures. It is thus of interest to develop analysis and design tools for such structures that are reliable, systematic, and simple enough to be implemented in structural analysis software and used in design offices. Towards this goal, this doctoral thesis contributes to two aspects of importance to the lateral torsional buckling analysis of laterally unsupported plane frames: (a) the incorporation of shear deformation effects in the buckling analysis of thin walled members, and (b) the quantification and modelling of partial warping restraints provided by moment connections in typical moment resisting plane frames to adjoining beams and columns. The theory and finite element developed under item (a) deviate from conventional theories in three respects: 1) It is based on general non-orthogonal coordinates, which makes it particularly suited for the effective modeling of members with eccentric supports (i.e., supports that do not coincide with the location of the shear centre; 2) It captures shear deformation effects due to bending and warping; 3) It incorporates the effect of load position relative to the shear centre. A new variational principle for the problem is developed from first principle. The variational principle is used to formulate the governing differential equations for thin-walled members based on the principle of stationary total potential energy. The closed form solutions of the resulting field equations and boundary conditions are developed for the cases of column flexural buckling, column torsional buckling, and lateral torsional buckling of beams under uniform moments, and comparisons to classical solutions were conducted. A finite element is then developed for more general cases of loading schemes and boundary conditions and compared to predictions based on classical solutions and general finite element analysis results undertaken. In all cases examined, the present solution provides buckling resistance predictions lower than those based on the classical solution that do not include the effect of shear deformation. Shear deformation effects are found negligible when predicting buckling resistances for columns of typical geometries, but it can be significant when predicting the buckling resistance of beams under high moment gradients. Towards item (b), a formulation of the partial warping restraint provided by common moment connections to adjoining members is developed based on a shell formulation. The finite element developed is designed to interface with other collinear elements such as that developed under task (a), to accurately and efficiently predict the lateral buckling resistance of moment resisting plane frames. Comparisons between the predictions based on the present formulation and those based on established shell finite element analysis illustrate the ability of the model to efficiently and reliably predict the lateral buckling resistance of laterally unsupported frames.