LATERAL-TORSIONAL BUCKLING OF STRUCTURES WITH MONOSYMMETRIC CROSS-SECTIONS

Lateral-torsional buckling is a method of failure that occurs when the in-plane bending capacity of a member exceeds its resistance to out-of-plane lateral buckling and twisting. The lateral-torsional buckling of beam-columns with doubly-symmetric cross-sections is a topic that has been long discussed and well covered. The buckling of members with monosymmetric cross-sections is an underdeveloped topic, with its derivations complicated by the fact that the centroid and the shear center of the cross-section do not coincide. In this paper, the total potential energy equation of a beam-column element with a monosymmetric cross-section will be derived to predict the lateral-torsional buckling load. The total potential energy equation is the sum of the strain energy and the potential energy of the external loads. The theorem of minimum total potential energy exerts that setting the second variation of this equation equal to zero will represent a transition from a stable to an unstable state. The buckling loads can then be identified when this transition takes place. This thesis will derive energy equations in both dimensional and non-dimensional forms assuming that the beam-column is without prebuckling deformations. This dimensional buckling equation will then be expanded to include prebuckling deformations. The ability of these equations to predict the lateral-torsional buckling loads of a structure is demonstrated for different loading and boundary conditions. The accuracy of these predictions is dependent on the ability to select a suitable shape function to mimic the buckled shape of the beam-column. The results provided by the buckling equations derived in this thesis, using a suitable shape function, are compared to examples in existing literature considering the same boundary and loading conditions.The finite element method is then used, along with the energy equations, to derive element elastic and geometric stiffness matrices. These element stiffness matrices can be transformed into global stiffness matrices. Boundary conditions can then be enforced and a generalized eigenvalue problem can then be used to determine the buckling loads. The element elastic and geometric stiffness matrices are presented in this thesis so that future research can apply them to a computer software program to predict lateral-torsional buckling loads of complex systems containing members with monosymmetric cross-sections