Nonlinear Finite Element Analysis of Angle and Tee Beam‐Columns

Abstract

Asymmetric thin‐walled open sections such as angles are used widely in trusses and transmission towers. Such members have relatively low torsional and bending stiffnesses and are connected eccentrically. The geometrical nonlinear second order analysis of frames comprising this type of member is not generally available. This paper derives the element geometric stiffness matrix for angle and tee beam‐columns. The total potential energy of a general thin‐walled beam‐column element is formulated, incorporating member geometrical nonlinearity. The validity and accuracy of the formulation are demonstrated on different problems, for which the buckling loads and the load‐deformation relationships are derived. The latter is obtained by formulating the incremental and the total force‐deformation equilibrium equations and using the numerical arc‐length method to trace the load‐deformation path. The influence of the prebuckling deformations is incorporated in the analysis by modifying the structural tangent stiffness continuously for geometry updates.