Lateral torsional buckling of unsymmetric beams by FEM with linear elements

Abstract

As the exact solution of lateral torsional buckling of elastic prismatic beams is practically limited to the simple case of simply supported beams under equal end moments, other loading conditions and boundary conditions require more practical solutions to the problem. As the general solution of lateral torsional buckling of unsymmetric beams is a function of the sign of the bending moment along the axis of the beam, i.e. location of the shear center concerning the compression zone of the cross section, application of the current traditional empirical expressions such as coefficient of the moment, Cb, becomes highly inconsistent and unwarranted to capture the correct critical moment as acknowledged by the American Institute of Steel Construction, AISC. The finite element method, FEM, offers a feasible alternative to overcome these shortcomings. FEM is formulated in its simplest form of linear elements for the general case of lateral torsional buckling of unsymmetric cross sections. Finite element development shows that the characteristic equation is of the nonlinear quadratic eigenvalue problem type. Using the classical polynomial shape functions for beams, FEM proves to be extremely accurate and can overcome the high inconsistencies and discrepancies embedded in the application of the classical methods.