The masonry arch between 'limit' and 'elastic' analysis. A critical re-examination of Durand-Claye's method

The historical evolution of the theory of the masonry arch is marked by two alternative structural philosophies corresponding to what we modernly call «limit» and «elastic» analysis. According to the first approach, global stability is the main question and the safety of the arch is guaranteed if any equilibrium condition preventing rigid mechanisms exists. This is the equilibrium approach followed in the first 18th century studies on the masonry arch and successfully developed in the first half of the 19th century on the basis of Coulomb' s method of maxima and minima. According to the second approach, local stress becomes the object of nvestigation and the safety of the arch is assured if actual stresses at each cross section are below the admissible strength of materials. This approach, which necessarily involves the complete set of equilibrium, compatibility and stress-strain equations, was the unavoidable result of the developments of structural mechanics starting from thc twenties of the 19th century, when «elasticity» and «strength» became the new passwords of the theoretical research. Nevertheless, the alternative between limit and elastic structural philosophies - stability versus stress - is not so radical as it may seem at first sight. As a matter of fact, it can be rationally removed by following an intermediate approach proposed by the French scholar Alfred Durand-Claye in 1867. This approach aims at verifying, as the author wrote, «s'il existe des solutions d'équilibre compatibles avec un effort limite donné». This methodology preserves the non deterministic character of the limit analysis and, at the same time, embodies the main aspect of the elastic analysis by imposing a restriction in the stress level.