Elastic Lateral and Restrained Distortional Buckling of Doubly Symmetric I-beams

Based on the energy principle, a theoretical study of the elastic lateral distortional buckling (LDB) and restrained distortional buckling (RDB) of I-beams is presented. First, because the existing potential energy expressions for LDB are not suitable for members under a transverse distributed load, a new general potential energy expression of I-beams for lateral buckling is derived by using the nonlinear elastic theory. The proposed expression is equivalent to the classical potential equation when web distortion is suppressed and caters for I-beams under transverse distributed load, transverse concentrated load, and end moments, and when the web is flexible. Then, an LDB equation for simply supported, doubly symmetric, I-beams under uniform distributed load is developed by invoking the Ritz method. In addition, an RDB equation for continuous composite beams is also deduced by using some simplifications. The corresponding simplifications and equations are verified by the finite element method. Suggestions for further study are also presented. The outcomes of the present paper have important theoretical and practical significance and provide a rational basis for practical design methods.