On optimal spherical masonry domes of uniform strength

In this paper, the problem of spherical masonry domes of uniform strength is examined. For masonry domes of variable thickness it is proved that the change in the sign of the circumferential stresses can occur for considerably larger angles, depending on the shape of the shell profile. The uniform strength thickness is explicitly given solving an eigenvalue problem associated to the equilibrium integral equation. The thickness law for the closed dome subject to self-weight and, possibly, to a superimposed uniform distributed load, and for the open dome subject to the weight of a lantern is obtained. Finally, the problem for a dome exhibiting a bidimensional behavior in the upper calotte and a one-dimensional (1D) behavior below is solved. Masonry is assumed to be a material not able to resist against tensile stresses. Moreover, it is assumed to be either indefinitely resistant in compression or with a cutoff in compressive stresses.