Nonlinear Stability Analysis of Steel Beams Restrained Laterally

The correct representation of real beam conditions, either at the extremities or along the beam, leads to a more precise calculation of the critical moment of lateral–torsional buckling (LTB). Therefore, the design resistance of the steel member can be computed more accurately. This paper presents an original theoretical approach that can be used to study the effects of elastic restraints on warping and lateral rotation at various points along the beam. To this end, an analytical model has been proposed to provide critical loads for a range of stiffness variations at the restrained nodes of the simply supported beam. The torsion angle and lateral displacement of the beam have been defined by means of trigonometric functions, which take into account the restraints by using the index of fixity to warping and lateral rotation. The proposed model is based on the principle of total potential energy realized in the context of linear elastic behavior. The Ritz method is employed to derive the nonlinear equilibrium equations, and the critical loads are then calculated using the corresponding tangent stiffness matrix. Computer programs have been developed for the numerical determination of critical loads which are compared with the values obtained from the LTBeamN software (FEM). Through these numerical examples, a very good concordance of the results was observed. A parametric study and detailed calculations have been carried out to show the influence of the fixity index on the critical torsional elastic buckling loads.