Limit analysis of masonry domes with oculus and lantern: A comparison between different approaches

This paper aims to illustrate and compare different approaches for the limit analysis of masonry domes of revolution with an oculus at the top. It specifically focuses on the influence of the limited compressive and tensile strength of masonry on the bearing capacity of the dome. The first assessment is conducted through a semi-analytical formulation that revisits Durand-Claye's method within the framework of the lower bound theorem of limit analysis. The second investigation is performed using a kinematic approach, which allows for closed-form solutions by exploiting the upper bound theorem of limit analysis and the virtual work theorem. These approaches are applied to a case study that was experimentally tested, involving a hemispherical dome with an oculus. The dome is subjected to its self-weight and a vertical load at the crown. Parametric investigations are presented to compare the results obtained through the proposed methods with those derived from the classical limit analysis of masonry structures, based on Heyman's hypotheses.