Flexural-torsional buckling of thin-walled beam members based on shell buckling theory

摘要

This paper summarized currently available techniques of setting up flexural-torsional buckling theory of thin-walled members. It is found that all the existing methods introduced a nonlinear load potential in their total potentials, while based on the classical variational principle for stability of a solid structure, no such load potential should be included. This situation has led to an inconsistency between some widely referenced monographs in buckling theories of beams with mono-symmetrical cross-sections. This paper provides a new theory for flexural-torsional buckling of thin-walled members based on the classical variational principle and the theory for thin-walled shells. No nonlinear load potential is included, but a new term: nonlinear strain energy from transverse stresses, which has been neglected in previous theories of thin-walled members, is introduced in. It is found that the nonlinear load potential is not equivalent to the contribution of transverse stresses for beams with mono-symmetrical cross-sections, which causes the inconsistency mentioned above. The comparison shows that the proposed theory and the traditional theory are the same for most cases encountered in practice.