Distortion and warping at beam supports

When a doubly symmetric I-beam buckles elastically in a lateral-distortiona l mode, its web distorts, so that the two flanges have increased relative l ateral displacements and may have different twist rotations. The centroid, shear center, and principal axes of the distorted cross section are all dif ferent from those of the undistorted cross section. The end connections to adjacent members may induce flange restraining moments that oppose warping deformations and modify the elastic buckling resistance. This paper investi gates the effects on the lateral-distortional buckling of beams of web dist ortion and of the warping restraints induced by end-support conditions. It is found that a doubly symmetric I-section becomes unsymmetric during later al-distortional buckling and that web distortion reduces the effective tors ional and warping rigidities. The proposed approximations for the elastic l ateral-distortional buckling resistances of beams without and with end warp ing restraints provide good predictions. Equations for the warping restrain t stiffness induced by some commonly used end conditions are established. C omparisons with ABAQUS shell element results show that they provide good ap proximations.