Equilibrium analysis of masonry domes. on the analytical interpretation of the Eddy-Lévy graphical method

The nineteenth-century graphic method of Eddy-Lévy is analysed and proposed in an analytical form as an assessment tool for masonry domes. The method determines the neutral hoop that separates the upper part of the dome that behaves as a compressed membrane from and the bottom that behaves as independent arches, due to the presence of vertical cracks. This method allows determining a no-tension equilibrated solution, accounting for the natural behaviour of masonry domes of fracturing along meridian planes. Six case studies were investigated, considering spherical and pointed dome, complete, with hole and with hole and lantern. A modified version has been studied to model the biaxial stress of upper part properly through the membrane theory, and compared to the solution obtained by a numeric discrete block model. Limit thickness-to-radius ratio was identified, and a parametric analysis was carried out to investigate the extension of meridian fracture varying dome shape and thickness.