Masonry Domes: A study on proportion and similarity

A study of the old master builder's rules for structural design of arches, vaults and domes, reveals a persistent presence of 'proportional rules', rules that produce structures geometrically similar. The square-cube law, however, demonstrates that in structures subject to their own weight, stresses grow linearly with size, invalidating these rules from an elastic point of view. A more detailed examination taking into account the problem of stability, i.e. the position of lines or surfaces of thrust, shows that the condition of sufficient stability in masonry structures is what causes an overall geometry for the structure. This excess of dimensions makes that, in fact, the square-cube law begins to apply only to very large spans. The size at which elastic design begins depends on the form of the structure, but for traditional forms, it clearly includes the dimensions of all historical architecture. The rigorous theoretical proof of this argument was implicit in Rankine's theorem of parallel projection as applied to masonry structures. In the present discussion the methods and concepts of Dimensional Analysis have been applied