Optimum Shape, Failure Load and Buckling Load of Persian Historical Brick Masonry Domes

The building of domes in Persia dates back to the third millennium B.C. Since then, the architecture of Persia has produced many types of dome structures using traditional methods to make the best forms of domical shapes. The earliest Iranian dome that still stands was built in Firuzabad, South-west Iran, about 1,800 years ago. Round, ovoid and parabolic domes were built until the seventh century A.D. Low saucer-like domes were constructed later. Double-shell domes appeared in the eleventh century A.D. In the twelfth century A.D., round and smooth, or octagonal domes, rising to a sharp peak, crowned circular or octagonal structures. High domes were placed on tall drums in the fourteenth century A.D. Bulbous domes became current later. The onion-shaped domes were built on shrines in the eighteenth century A.D. The brick masonry dome is an important element of Persian historical architecture. The identification of its structural behavior and the study of the effect the dome shape on its behavior is an important issue. Domes in this study have the most common shapes in Persian architecture and no study has been done about their optimum shape.
In this research, shape optimisation of Persian historical brick masonry domes with different geometrical shapes under uniform pressure has been studied and then the failure load under concentric loading and buckling load under uniform pressure have been determined for optimal domes. The studied domes have semi-circular, pointed and four-centred cross-sections. Pointed and four-centred domes have three types of drop, ordinary and raised shapes. Seven types of domes with spans of 12 m, 15 m and 18 m have been analysed by the finite element method using the ANSYS code. Material behaviour has been assumed non-linear and the Willam-Warnke failure criterion and, in some cases, the maximum principal stress theory has been used. The parameter used for optimisation is the minimum ratio of apex thickness to base thickness (K) for which the failure load to weight ratio is a maximum. For uniform pressure, K=0.2 is the optimum ratio for semi-circular domes. For pointed domes the optimum ratio is K=0.3, except for the ordinary pointed dome with a span of 18 m for which the optimum ratio is K=0.08. The optimum value is K=0.3 for ordinary four-centred dome with a span of 12 m and raised four-centred dome with a span of 15 m, it is K=0.54 for raised four-centred dome with a span of 12 m , and it is K=0.144 for other types of four-centred domes. The failure load of domes with optimum shapes under concentrated loads is more than that of non-optimum shapes. Buckling load of optimal domes is much more than failure load under uniform pressure. Buckling load increases by decreasing the span. The maximum and minimum values of buckling load belong to pointed and semi-circular domes, respectively.