Admissible shell internal forces and safety assessment of masonry domes. (1st March 2023) - Barsi, F.; Barsotti, R.; Bennati, S.
Highlights: Safety assessment of masonry domes. The solution method is based on the static theorem of limit analysis. Domes are modelled as thin shells. Membrane forces and bending moments are suitably combined to find statically admissible internal forces. The internal force distribution that maximizes the safety factor is searched by means of a constrained optimization method. The solution is pursued numerically by means of an expressly developed procedure that uses the collocation method. The paper illustrates application of the method to the dome of Pisa cathedral. Abstract: The present paper illustrates a methodology for the safety assessment of masonry domes. The dome is modelled as a thin shell made of a material satisfying Heyman's hypotheses. Based on the static theorem of limit analysis, the method searches for statically admissible distributions of internal forces within the shell, suitably combining membrane forces and bending moments, by solving a convex optimisation problem. The solution is pursued numerically by means of an expressly developed collocation method that enables obtaining the analytical expressions for each internal force component. In its present formulation the method can be applied to domes of any shape, as well as to arbitrary load distributions. After validation against the benchmark case of the spherical dome under its self-weight, the paper illustrates application of the method to the dome of Pisa Cathedral under vertical loads as a first real case study.