Equivalent nonlinear beam model for the 3-D analysis of shear-type buildings: Application to aeroelastic instability

• A new equivalent nonlinear, 1-D shear–shear–torsional beam model is introduced.
• The proposed model is able to reproduce the dynamic behavior of tower buildings.
• The model can be applied to different dynamic actions (e.g., earthquake, wind).
• The model highlights the influence of mechanics on aerodynamic instability.
• Classic 1 dof galloping predictions on square buildings are not always conservative.

Tower buildings can be very sensitive to dynamic actions and their dynamic analysis is usually carried out numerically through sophisticated finite element models. In this paper, an equivalent nonlinear one-dimensional shear–shear–torsional beam model immersed in a three-dimensional space is introduced to reproduce, in an approximate way, the dynamic behavior of tower buildings. It represents an extension of a linear beam model recently introduced by the authors, accounting for nonlinearities generated by the stretching of the columns. The constitutive law of the beam is identified from a discrete model of a 3D-frame, via a homogenization process, which accounts for the rotation of the floors around the tower axis. The macroscopic shear strain in the equivalent beam is produced by the bending of columns, accompanied by negligible rotation of the floors. A coupled nonlinear shear–torsional mechanical model is thus obtained. The coupling between shear and torsion is related to a non-symmetric layout of the columns, while mechanical nonlinearities are proportional to the slenderness of the columns. The model can be used for the analysis of the response of tower buildings to any kind of dynamic and static excitation. A first application is here presented to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions and on the postcritical behavior of tower buildings, based on a quasi-steady model of aerodynamic forces.