Minimum thrust and minimum thickness of hemispherical masonry domes

A masonry dome cracks when the tension stresses in the hoop rings near the springing reach the masonry’s weak tensile strength. These meridional cracks arrive and spread along the dome. In this condition, the pressure surface with zero hoop stresses represents the extension to the three-dimensional case of the problem of the catenary. This analytical approach is adopted in the paper first to develop an accurate description of the minimum thrust state for the hemispherical masonry dome and the corresponding configuration of the pressure surface. Furthermore, the minimum thickness state is studied. Contributions of the paper are either an analytical formulation of the minimum thrust, depending on the geometrical thickness–radius ratio, or a modification of the minimum thickness–radius ratio with respect to the commonly accepted value. In this last geometrical configuration, the pressure surface has to touch the intrados of the dome at the crown, instead of passing through the extrados at the springing.