Analytical Solution of Masonry Domes

The object of this investigation was to develop analytical formulas for pyramoidal and conoidal masonry domes, analogous to the equations which have been established for spherical and conical shapes. The usual method of considering the forces on an elementary voussoir was adopted; that is, all the factors which may vary independently were kept separate, and appear in the final equations. These equations give the meridional and ring stresses at any point in any dome the plan of which is radially symmetrical. There is also an expression for the strength required in the tension ring at the top of a cylindrical support for a dome. The formulas have this advantage, that the designer, once having assented to them, can comfortably forget how they were derived.

Having developed these ' general equations, it was necessary to justify them by showing that the established formulas for special cases can be derived from them. This proves to be true in every instance.

Finally, the general equations give occasion to discuss certain facts which have been overlooked or confused in some of the previous writings on the subject. The paper aims to show that the conclusions derived from the formulas are those which might be expected and involve no reductio ad absurdum.