Geometrically and materially nonlinear buckling analysis of eccentrically loaded angles by the finite element method

Single steel angles are used in structures such as steel joists, roof trusses and latticed transmission towers because of ease in fabrication, transportation and connection. They are usually connected eccentrically at their ends. At the same time, restraining moments at the ends of the member are also present due to the flexural rigidity of the connected elements. The determination of the compression capacity under eccentric loading along with end restraints is complex due to the asymmetry or monosymmetry of the angle cross section.An efficient nonlinear finite element model is provided to understand the behavior of eccentrically loaded single angles. Theoretical buckling and the experimental failure loads of pin ended, concentrically and eccentrically loaded angles were predicted by eigenvalue and load-deformation analyses of various models developed in ABAQUS 6.5. The angles were modeled by shell elements considering geometrically and materially nonlinear behavior. Initial imperfections, residual stresses, end support conditions, geometry and material property variation of the angles were included differently in each model. The load-carrying capacity of the single angles are investigated by performing an extensive parametric study obtaining the most realistic estimations. It is seen that compression capacities of eccentrically loaded angles are overestimated according to TS 648.A more precise geometric stiffness matrix was derived for geometrically nonlinear analysis of asymmetric thin-walled open section members such as angles. To this end, all the higher order terms were incorporated in the total potential energy equation of the thin-walled beam-column element with 2 nodes and 14 degrees of freedom. Bifurcation loads of angles with different end conditions were predicted exactly. An updated Lagrangian formulation, coupled with modified Newton-Raphson technique, were employed to trace the pre-buckling and post-buckling load-displacement paths. Numerical examples of large deflection analysis of eccentrically loaded angles were solved by a program coded.