UBC Theses and Dissertations
The lateral torsional buckling of open thin-walled beams DeVall, Ronald Homer
This thesis is concerned with the development of a stiffness matrix for the study of a large range of stability problems for beams of arbitrary, open, thin-walled cross sections. This is done by first developing, using a consistent set of common engineering assumptions, a non-linear relation between the forces and the displacements of the beam. These relations are then substituted into the beam equilibrium equations to give a set of three differential equations of equilibrium in terms of the displacements. These differential equations are solved using an iteration technique. A member stiffness matrix is generated when the iterated solution is used with the non-linear deflection relations. The resulting fourteen by fourteen matrix includes the regular six forces plus a bi-moment at each end. The matrix is tested against known solutions and agreement is seen to be excellent in all cases. All the terms necessary for the building of the matrix are given in the Appendices.
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