Advanced Equilibrium Analysis of Spherical Masonry Domes: An Integral Formulation

Abstract

The equilibrium of spherical domes is a fundamental topic in structural engineering, particularly for masonry structures, where the material’s inability to resist tension influences the force distribution. This study proposes an integral formulation for the equilibrium of a spherical dome, incorporating normal stresses and shear stresses, explicitly considering their spatial variations. The formulation extends classical membrane and bending theories by integrating the effects of stress gradients and torsional moments, providing a more detailed understanding of force equilibrium. The proposed approach aligns with and extends the concept of thrust surfaces, as discussed by Sajtos et al. (2020), introducing a framework that accommodates general force distributions and possible cracking patterns. The results suggest that the inclusion of moment equilibrium considerations leads to a more precise determination of the structural safety of cracked domes. This study contributes to the ongoing research on the stability and failure mechanisms of domes by offering a more comprehensive analytical framework.

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