Renaissance ogival domes of unreinforced stone masonry can be analyzed as structures of rigid material with no tensile strength. Solutions can be obtained for the static equilibrium of the structure; the results represent an extension or variant to membrane shell theory. A limiting shell thickness is found at which a kinematic collapse mechanism develops. The limit state analysis also identifies the role of hoop stress in permitting the construction of such a shell without centering. The analysis has its counterpart in a study published in 1742, that being the first modern structural analysis. The analysis procedure shows the clear relation between geometry (shell shape) and internal forces.
[1]
K. S. Kölbig,et al.
Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints
,
1972
.
[2]
Jacques Heyman.
Equilibrium of shell structures
,
1977
.