Horizontal force capacity of a hemi-spherical dome

The assessment of the ultimate load capacity of masonry domes and vaults is a complex open issue of both professional and research concern. 3D curved geometry of such structures entails biaxial stress states and highly nonlinear mechanical behaviors which require advanced computational strategies to be rigorously dealt with. This study focuses on the assessment of the capacity of masonry hemispherical domes subjected to horizontal forces (such as those produced by wind and earthquake). In the framework of Limit Analysis (LA), a parametric Membrane Equilibrium Analysis (MEA) is proposed based on No-Tension (NT) material assumptions in the sense of Heyman: the unilateral membrane must lay inside the boundary surfaces of the dome and the membrane stress must have a non-positive concave potential. The membrane equilibrium problem for the dome is then formulated in Pucher form and controlled by a few parameters to be optimized. Two elementary examples are also provided to illustrate the method.