Three dimensional ultimate strength analysis of beam-columns.

A rigorous formulation for the structural response of thin-walled members of arbitrary open cross-section acted upon by a general system of loads is developed based on energy principles and virtual work concepts. Full account is taken of three dimensional behaviour, including sectorial warping effects. The analysis incorporates the effect of initial geometrical deflections. Different patterns of residual stress, non-coincidence of the shear centre and centroid, a complete absence of symmetry in the section and the influence of higher order terms in the strain-displacement relationships including products of the derivatives of axial displacements are also incorporated. A computer program based on finite element analysis suitable for application in both the elastic and inelastic ranges is developed. This is used to solve the differential equations governing the ultimate strength of beam-columns in space. The program is written in the Fortran 77 Language. The main function of the program is to follow the loss of stiffness due to spread of yield and hence to trace the full load-deflection response up to collapse. It may be used in a wide variety of ways. Three types of analysis have been conducted in this study. These are: Linear, Partial Non-linear and Full Non-linear. The Linear involves only the small deflection theory. Partial Non-linear analysis uses non-linear strains while the Full Non-linear analysis incorporates both non-linear strains and nonlinear stiffness matrices. Several illustrative examples, previously investigated either theoretically or experimentally, have been chosen to check the validity of both the analytical approach and the computer program. These examples cover flexural, flexural-torsional, biaxial bending, and bending and torsional behaviour in the elastic and inelastic ranges. They contain a wide range of parameters e.g. different cross-section shapes, loading, boundary conditions and initial imperfections. Finally the program has been used to study the ultimate strength of steel members subjected to compression, bending and torsion in a more rigorous fashion than has previously been possible