Seismic vulnerability of different in geometry historic masonry towers

In the present paper, a simple predictive approach for the seismic vulnerability of existing masonry towers is proposed evaluating it on a series of “idealized” benchmark cases using different simplified approaches, namely the procedure proposed by the Italian code and pushover conducted with two commercial codes (UDEC and 3Muri). In UDEC the geometry is intentionally idealized into quadrilateral elements with different thickness, in order to properly reproduce the hollow square cross-section. The utilization of a 2D approach drastically reduces the computational effort required in carrying out medium scale systematic computations. In 3Muri macro-elements are used, providing very fast predictions as well. Within such simplified frameworks, 16 different cases that can be encountered in practice are critically analyzed, changing two key parameters that proved to be important for the vulnerability determination, namely slenderness and transversal shear cross area. The simplifications introduced in the modelling phase allow for fast sensitivity analyses in the inelastic range and an estimation of the acceleration factor in that range of slenderness that is useful for practical purposes. Simplified formulas fairly representing the obtained seismic vulnerability are also reported and put at disposal to any practitioner interested in a preliminary estimation of the behavior of the towers before doing any calculation.