Limit analysis of masonry domes: the case of Hagia Sophia and Anime Sante

The conservation of cultural heritage is a challenge for the contemporary society. In recent decades, significant resources have been allocated for the conservation and restoration of the architectural heritage. Historical buildings were restored, protected and reinforced with the intent to limit the risks of degradation, due to phenomena of structural damage and to external factors such as differential settlements, earthquakes, etc. The wide diffusion of historic masonry constructions in the Mediterranean basin requires reliable tools for the evaluation of their structural safety. Masonry domes represent an important part of the architectural heritage. However domes haven\u2019t been studied as much as other masonry structures. The collapses happened in recent years, as a consequence of seismic actions or lack of maintenance, show the need of detailed studies. Here a limit analysis (Milankovitch, 1907; Heymann, 1969; Livesley, 1992; Milani and Cecchi, 2013) to the evaluation of the behavior of masonry domes is presented. An algorithm based on the kinematic approach has been developed to evaluate the minimum collapse multiplier and to determine the position of the hinges. The proposed method is compared with some real cases: the collapse of Anime Sante Church in L\u2019Aquila and the analysis developed on Hagia Sofia in Istanbul. This comparison is useful to tune and validate the proposed method