Closed form solutions in limit analysis for masonry cloister vaults and domes subjected to concentrated vertical loads applied at the top crown

Two cases technically relevant are investigated in the field of the prediction of the load carrying capacity of masonry double curvature structural elements, namely hemispherical domes and square cloister vaults subjected to concentrated vertical loads at the top crown. Such loading condition is encountered quite frequently in practice, for instance for domes with lanterns and for cloister vaults belonging to historical buildings loaded in the middle span. A failure mechanism is hypothesised and analytical expressions for the different contributions in the internal and external power dissipation are deduced. The collapse multiplier is then obtained through the application of the principle of virtual powers. The advantage stands in the applicability of the method for a large variety of domes and cloister vaults (with a generalisation to additional special conditions, such as for instance in case of elliptic and rectangular in-plane geometries, presence of oculi and so on). The approach proposed is benchmarked on two case-studies experimentally tested, for which several numerical results coming from different models are already available.