E. De Chiara1, C. Cennamo2, A. Iannuzzo3, M. Angelillo1, A. Fortunato1, A. Gesualdo3
1)  Department of Civil Engineering, University of Salerno
via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
e-mail: elenadechiara@gmail.com, {mangelillo, a.fortunato}@unisa.it
2)  Department of Architecture and Industrial Design, University of Campania L. Vanvitelli
via San Lorenzo 1, 81031 Aversa (CE), Italy
3)  Department of Structures for Engineering and Architecture, University of Naples Federico II
via Claudio 21, 80125 Naples, Italy
{antonino.iannuzzo, gesualdo}@unina.it

Keywords: Masonry, Vaults, No-Tension materials, Airy’s stress function, Pucher equilibrium.

Abstract. The objective of the present work is to develop an automated numerical method for the analysis of thin masonry shells. The material model for masonry that we adopt is the socalled “Normal Rigid No-Tension” material. For such a material, the kinematical and the safe theorems of Limit Analysis are valid, and the present study focusses on the application of the second theorem to masonry vaults and domes. In particular, the method we propose is devoted to the determination of a class of purely compressive stress regimes, which are balanced with the load. The mere existence of such a class is a proof that the structure is safe, and members of this class may be used to assess the geometric degree of safety of the structure and to estimate bounds on the thrust forces exerted by the structure on its boundary. By taking up the simplified model of Heyman, the equilibrium problem for the membrane S can be formulated in terms of projected stresses defined on the planform of . The search of the stress reduces to the solution of a second order pde, in terms of the stress potential . In order that the membrane stress on be compressive, the potential must be concave. As for the thrust line in an arch, the surface is not fixed and may be changed, given that it remains inside the masonry. Under these simplifying assumptions, the whole class of equilibrated stress regimes for a masonry shell, is obtained by moving and deforming inside the masonry, and also, for any fixed shape, by changing the boundary data for , that is the distribution of thrust forces along the boundary.