Effects of 2012 Earthquake on the behavior of Ghirlandina tower in Modena

Collapse events, that occurred in the past (such as the Venice Bell Tower in 1902 and the Civic Tower in Pavia in 1989) claimed for the need to assess the long-term behavior of such monuments. A significant effort has been therefore devoted to clarify the reasons for these collapses after many centuries from the construction date. In addition, recent earthquakes in Italy have once again put into evidence the seismic vulnerability of the cultural heritage. To assess this aspect, in many cases the soil-structure interaction cannot be neglected. In this context, a simple but consistent framework for soil-structure interaction analysis is here presented with reference to a case history. It is discussed how the difference in the fundamental frequency observed during seismic events can be associated to non-linearity in soil response, leading to a rotational stiffness of the soil-foundation system consistent with the shear strain level derived from the seismic ground response analysis. Thereafter, the validated soil-structure interaction model has been used to define an equivalent SDOF model of the structure that explains the differential settlements suffered by the Ghirlandina tower in Modena during the 2012 seismic events as well as its behavior since those events

Repeated derivatives of hyperbolic trigonometric functions and associated polynomials

Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functionscan usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by other authors and develop a complementary point of view for the repeated derivatives of sec(.), tan(.) and for their hyperbolic counterparts