Galileo, Coulomb, the origins of Yield Design Analyses

Abstract

The Memoir presented to the French Academy of Sciences by Coulomb in 1773 is often considered as the starting point for “yield design” stability analyses in geotechnics and, more generally, in various fields of civil and construction engineering. In this Essai (1773), Coulomb implemented a reasoning based on the necessary condition that the equilibrium of the structure under study and the resistance of its constituent materials should be mathematically compatible with each other. A previous out sketch of this rationale can be identified in Galileo’s solution to the problem of the bearing capacity of a cantilever beam in the Discorsi (1638). In the present contribution, after outlining the philosophy of Galileo’s argument, we will highlight Coulomb’s clarifying insight and essential input before the fundamental concepts of the mechanics of continuous media, such as the notion of stress and the principle of virtual velocities, were established. Various aspects of yield design or “limit equilibrium” stability analyses in geotechnics will be evoked. The theory of Yield design, in line with Coulomb’s reasoning, will be briefly presented, making it possible, in particular, to overcome the difficulties encountered when implementing “classical” methods and clarifying a possible confusion with the mathematical theory of plasticity.