Minimum thrust and minimum thickness of spherical masonry domes: A semi-analytical approach

A semi-analytical approach is proposed for addressing the minimum thrust and minimum thickness analysis of spherical masonry domes under their self-weight. The classical differential equilibrium equations of axially symmetric shells are resorted to, calling for the exact computation of self-weight and center of mass of an infinitesimal dome voussoir. The minimum thrust analysis is accomplished by determining a statically admissible stress state in the dome, that is associated to a kinematically admissible settlement mechanism of minimum thrust. Such a stress state entails vanishing hoop stresses in the lower part of the dome, where the opening of meridional cracks occurs. An original numerical scheme is proposed for automatically computing a distribution of hoop stresses in the dome cap, producing a statically admissible stress state. A suitable modification of the semi-analytical procedure for the minimum thrust analysis is then adopted to perform the minimum thickness analysis. Numerical results are presented for spherical domes with parameterized oculus and embrace angles, complemented by the comparison with alternative equilibrium models, and with approximate treatments of the dome self-weight adopted in the literature. The merit of the proposed procedure is finally proved in application to a real case. As an iconic result, a refined estimate of the minimum thickness of a hemispherical dome is derived, resulting in 0.04284 times the radius of the mid-surface.