Warping Restraint in Three-Dimensional Frames

The general solution of the restrained warping of beams in three-dimensional frames has been developed. The general beam strain-displacement relations are used in developing a finite element solution to this problem. The solution can account for arbitrary cross-sectional shapes and arbitrary loadings. It also accounts for the coupling between the different internal forces of the beam. The concepts of continuous and restrained warping are introduced as an aid in analyzing general three-dimensional framed structures. The known analytical solutions of simple problems are predicted by the finite element solution. The method is used in a case study of a massive three-dimensional turbine generator pedestal. The warping restraints are found to have a considerable effect on the computed displacements and stresses.