Statics of buttressed masonry arches in light of traditional design rules

The mechanical behavior of masonry arches is governed by equilibrium not by strength. Consequently, the traditional design rules obey to geometrical parameters and relative ratios. In this framework, state of art rules developed up to 18th century by Leonardo, Alberti, Palladio, De La Hire, De Belidor, Mascheroni et al., as well as the design indications of treatises and handbooks of 19th and 20th centuries, consist of simple geometrical values to be assigned to the arch and supporting buttress in order to build safe arches under the acting force of gravity. The validity of these design rules is confirmed by the presence of many ancient arched structures that withstood the test of time. In the light of previous considerations, the paper aims at providing an overview of the design rules used in the past centuries for buttressed arches with circular outline and characterized by different angles of embrace. To this end, the state-of-art on the design of the least thickness required for the stability of circular arches is firstly discussed. The inherent design rules have been classified in three generations depending on time when they were formulated. Afterwards, the state-of-art rules for the design of buttresses supporting arches are illustrated and compared. The design indications are provided in terms of minimum thickness required for the stability of buttress carrying the actions (vertical loads and horizontal thrust) induced by the supported arch. The design rules for buttress are also classified into three classes depending on the used approach. The overall aim of this study is an historical rereading of the design rules conceived over the centuries for circular buttressed arches, which are here compared and summarized in diagrams allowing for an immediate understanding of the influence of geometrical parameters characterizing itself on its mechanical behavior.