A study of the apse of the cathedral of Milan

The Apse is the most ancient part of Milan's cathedral, which originated in 1386 and presents a complex geometry. According to measurements made since 1960, consulted in the archives of the Veneranda Fabbrica del Duomo, the outer buttresses display an out of plumb of east buttresses. Therefore a first analysis of the structural response and state of conservation of the structure in relation to its construction configuration has been carried out. The static approach of limit analysis is used, providing synthetic results. A geometric model was set up based on the available survey drawings. The loads of each structural element were calculated as the first step for analysis of the internal forces. For the semi-dome above the choir, the membrane theory is used, adapting it to the existing geometry. The double exterior and interior vaulting system is analyzed, highlighting its role in the global structural response. The relevant role of the Lombard buttressing system [20] is analyzed, with radial and circumferential walls, bearing on piers and buttresses. Foundation structures were considered too, and the stability of the structure was verified. The comparison between the results obtained by limit analysis and the experimental observations of the damage, shows a correct geometric and structural conception, historically challenged by external factors, mainly soil subsidence, causing structural deformation and damage. The study shows the effectiveness of the analytical method in three-dimensional statics, under simplifying hypotheses.