Effect of the Initial Out-of-Straightness on the Lateral Torsional Buckling Strength of Steel Beams
Creators: name: Li, Ming
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 2018
Subjects: Initial Out-of-Straightness
Lateral Torsional Buckling
Steel Beams
Southwell Plot

description: The effect of initial out-of-straightness of steel beams with wide flange cross-sections on their elastic lateral torsional buckling strength is investigated analytically and numerically. A variational principle is first developed and then used to obtain the governing equilibrium conditions and associated boundary conditions for a beam with general patterns of initial out-of-straightness and initial angles of twist. The principle is then used to develop a finite element formulation to characterize the lateral torsional response of beams with initial out-of-straightness under general transverse loading. The validity of the finite element formulation is verified through comparison against results from models based thin-walled beam finite element and shell element models available in ABAQUS. Since the load lateral displacement responses do not exhibit a distinct point of loss of stability, two design criteria are proposed for the characterization of the failure. The first criterion is based on a threshold value for additional lateral displacement and the second criterial is based on a threshold value for the normal stresses. Both criteria are applied in conjunction with the analytical solution and finite element formulation in order to determine a moment resistance based on lateral torsional buckling that incorporates the effect of initial out-of-straightness. The moment capacity based on the displacement-based criterion is shown to solely depend on the ratio between the initial out-of-straightness component associated with the first buckling mode and the additional displacement threshold value specified. To the contrary, moment capacity based on the stress criterion, was found to depend upon the initial out-of-straightness magnitude, the normal stress threshold value and the geometry of the cross-section. The effects of the above parameters on the predicted moment capacity were investigated for beams with common sections in a systematic parametric study. Possible means of modifying the present provisions of CAN-CSA S16 relating to elastic lateral torsional buckling to incorporate the effect of initial out-of-straightness effects are discussed and illustrated through examples. The load-deformation plots for beams with initial out-of-straightens as predicted by the formulations developed in the present study are then used to extend the Southwell plot technique, originally developed for buckling of column with initial out-of-straightness, to the lateral torsional buckling of beams with initial out-of-straightness. The study shows that the plot, either experimentally or analytically obtained, of the applied load versus lateral displacement, at any point or angle of twist at any section, for a beam with initial out-of-straightness case can predict (a) the elastic critical moment of an analogous initially straight beam, and (b) the first buckling mode contribution to the initial out-of-straightness.