Limit analysis of conical and parabolic domes based on semi-analytical solution

The evaluation of limit loads of masonry domes has received increasing interest especially due to the importance of historical buildings where domes mainly are one of the most relevant structures. The limit design is used to obtain the safety assessment and the design guidance for restoration and transformation toward preservation and reuse of historical heritage. In the following paper, we present a formulation of the limit analysis based on the semi-analytical approach that starts on Melan's theorem. The self-equilibrated Melan's residual is obtained through the discretization of the analytical form of the equilibrium equation of the spherical dome. The procedure provides a finite-dimensional map of the eigenstress of the structure. Furthermore, the superimposition of the elastic solution to actual loads, obtained by finite element calculation, completes the admissible stress evaluation. Such amissible stress is introduced into the maximization algorithm, based on the lower bound theorem, which results in the collapse load. The same approach is used to get the safety assessment under prescribed load that allows checking the safety of prescribed load pattern and geometry.