Elastic lateral-torsional buckling of beams with warping restraints at supports

Abstract

Analytical formulations for the evaluation of the critical bending moment for lateral-torsional buckling of a beam taking into account warping restraints at supports are proposed in this paper. A theoretically exact solution is firstly derived from differential equilibrium equations using infinite power series for the twist rotation. Next, the deflected shape is approximated using a single or several base functions for the displacement and rotation fields. The energy method is then used to derive approximate expressions of the critical bending moment of beams subjected to various loading conditions: constant/linear bending moment distributions, mid-span pointwise transverse force or uniformly distributed load. The warping coefficient kw does not depend on the bending moment diagram. The equivalent uniform moment factor C1 can be conveniently expressed as a product of two coefficients, one related to the bending moment distribution and the other to the warping restraints stiffness. Finite Element analyses of beams with warping restraints at supports have been performed considering a shell elements model created in ANSYS and a beam elements model developed in LTBeamN.