Safety assessment by limit analysis methods of non-axisymmetric masonry domes subjected to vertical and horizontal loads

The research work described in the present thesis is addressed to an investigation of the analysis methods working within the framework of limit analysis for the stability assessment of masonry domes. The theoretical and numerical studies mainly focus on the development of an analysis method able to provide useful indications in the case a masonry dome is loaded upon by a system of vertical and horizontal loads, the latter somewhat representative of seismic loads. The dome shapes considered in the thesis are not axisymmetric. This is motivated by the fact that, although throughout the centuries masonry domes have been usually built in the shape of solids of revolution, in the Romanesque period and later, during the Renaissance, builders began constructing new domed structures characterised by oval shapes. These structures, which have already received special attention from the historical point of view, undoubtedly deserve as much attention from the perspective of their mechanical response, which study is made even more complicated by their complex geometry. The problem of determining the safety level of masonry domes with regard to structural collapse is an ancient one. Scholars involved in this issue effectively used graphical methods to assess the stability since the 18th century, long before limit analysis was formalised in the modern terms we are used nowadays. For this reason, together with a brief synthesis of the modern literature, a historical perspective of the methods used in the past centuries for modelling and designing masonry domes is presented. After a short survey of the historical methods, the thesis focuses on the investigation of different methods for the safety assessment of masonry domes by exploiting the static theorem of limit analysis. A suitable implementation of two methods widespread used and available in the literature, the “thrust network analysis (TNA)” and the “thrust surface analysis (TSA)” method, is illustrated. An expressly developed method for searching for statically admissible distributions of the internal forces is presented in which the dome is considered as a thin shell.