Real-time structural stability of domes through limit analysis: application to St. Peter's dome

Abstract

A digital tool is presented and made available for the rapid structural assessment of historic masonry domes. It is especially suited for masonry domes that present long meridian cracks; ergo partitioned slices governed by a pushing failure mode. The proposed procedure considers a Heyman's no-tension mechanical model that has been implemented within a user-friendly visual programming environment. The numerical approach includes parametric modelling of the failure mechanism that allows exploring the domain of solutions using the kinematic theorem of limit analysis. A heuristic search method is subsequently adopted to refine the geometry of the collapse mechanism and to compute the value of the horizontal trust. Validation of the results has been achieved considering St. Peter's dome. As reported in the literature, the behaviour of this dome shifted from a rigid shell-type - stiffened by hoop stresses - towards a pushing type of dome partitioned by long meridian cracks. Unlike time-consuming and advanced methods of analysis, the present procedure allows the users to perform a structural assessment of a historic masonry dome in a few seconds and offers the possibility of including: (i) the dome's drum in the analysis, if applicable; and (ii) rings as strengthening measure, whose number, position (dome or drum) and material (capacity) are user-defined. The goal is to make the tool easily and freely available at the disposal of students, researchers, and structural engineers.