The generalised beam theory with finite difference applications

The conventional design of steel beams considers that any deformation of a member due to applied load must be a combination of the four rigid body modes (axial deformation, major axis bending, minor axis bending and twisting) i. e. the member retains its cross sectional shape without distortion. In a hot rolled member the warping stresses which arise due to violation of the assumption that plane sections remain plane can often be neglected. In thin walled sections, however, these warping stresses are typically of the same order of magnitude as the primary bending stresses induced in the member by the applied loading and therefore cannot be neglected. In addition, if plane sections do not remain plane, the cross section distorts when a load is applied.The first part of this Thesis presents a method of analysis for any open unbranched thin walled section which considers both rigid body movement and cross section distortion (including localbuckling). The method is such that the four rigid body modes are automatically identified and separated from the remaining cross section distortion modes. The second part of this Thesis develops a finite difference method of analysis, in conjunction with the theory of part I, toconsider the behaviour of a member subject to any arbitrary loading condition and end restraint. Both first order linear problems and second order elastic critical buckling problems are solved, including the interaction of local buckling, overall buckling and cross section distortion