On a kinematically exact rod model for thin-walled open section members

Resumo

In the context of frame structures, kinematically exact rod models are pivotal to correctly describe
critical loads and post-critical behaviour. For thin-walled open-section members, such formulations need to take
cross-sectional warping into account, since it becomes a relevant load-carrying mechanism due to the very small

torsion stiffness of such members. Most thin-walled rod models available in the literature consider only the so-
called primary warping, which is the warping in the direction of the cross-section ́s walls lengths. The walls ́

thickness warping, or secondary warping, is typically neglected. Although primary warping generally suffices to
properly capture the rod ́s deformation, there are particular cases wherein secondary warping becomes relevant,

and to which existing models often fail to perform. This work develops a kinematically exact rod model for thin-
walled open section members taking into account both primary and secondary cross-sectional warpings. Advanced

elastic constitutive equations are then incorporated in order to enable full bending, compression and torsional strain
couplings in the finite strain regime. The model is implemented in an in-house finite element program and its
outcomes are validated against reference solutions obtained using hierarchically higher order formulations, having
as reference large deformation ANSYS’s shell 181 elements.