Bounds to the probability of collapse of Monumental Buildings

In recent years, the seismic reliability of monumental buildings has been the object of several studies. In particular, it has been shown in previous papers that the probabilities of collapse and damage and their distributions can be obtained by looking at a monumental building as an assemblage of macroelements of known static and collapse behaviour, and considering the relevant mechanisms: in this way, the kinematic approach to limit analysis is followed, and in rigour only lower bounds to the probability of collapse are obtained. Conversely, in this paper the static theorem of probabilistic limit analysis is introduced in order to obtain upper (i.e. “safe”) bounds to the probability of collapse. These procedures are exemplified on a specific church in Friuli (North-east Italy), well studied after it was damaged in the 1976 earthquake: upper and lower bounds to the probability of collapse of each macroelement and of the whole church are obtained as a function of the applied horizontal load, i.e. of the earthquake intensity.