A non-linear 3D beam finite element for the study of steel frames with tapered members

This paper presents the essentials of an original geometrically and materially nonlinear 3-D tapered beam finite element. The theoretical bases of the element are described, with particular attention paid to the choice of an appropriate displacement field and to the corresponding non-linear axial strains. Specific numerical problems met in the development of the finite element are examined, concerning mainly shear and membrane locking and the handling of rigid body motions. Worked examples on isolated members are presented for various types of analyses: elastic linear, elastic critical and geometrically and materially
non-linear analyses. Good accuracy with reference to numerical results is shown, as well as good convergence properties. It is also demonstrated – analytically and numerically – that the use of prismatic beam finite elements for the analysis of tapered beams (segmentation technique) may lead to significant discrepancies when the behaviour is influenced by torsional aspects. Then, the behaviour of two different portal frames with tapered members is proposed, and the results obtained using shell elements, tapered beam elements and prismatic beam elements are compared. This comparison shows that the use of tapered elements leads to results in close agreement with those obtained by shell elements, unlike the prismatic ones. The convenience of the tapered beam element is also highlighted since the total number of degrees of freedom required is significantly reduced compared to a shell modelling, leading to easier meshing, shorter computation time and easier interpretation of results.