Static and kinematic approaches for collapse analysis of non-symmetric masonry arches with Coulomb’s friction

The present paper examines the collapse analysis - under the assumption of Coulomb friction - of non-symmetric masonry arches. This subject, studied for the first time by Monasterio in 1805-06, results to be of great theoretical interest also within the modern plasticity theory. The collapse analysis of non-symmetric masonry arches is performed according to both static and kinematic approaches. The first one consists in comparing the two domains of statically admissible solutions with respect to rotational and sliding equilibrium, respectively, so that the thrust line remains inside the arch thickness. The second one is used as a heuristic method. The analysis is conducted by starting from the a priori choice of the mechanisms and local criteria to identify the collapse condition. Each of the mechanisms are separately investigated. The two approaches are re-formulated in terms of upper and lower bound theorems of the plastic theory, with a particular attention to the case of non-standard behavior; more in detail, the difficulties merging in the search of the collapse conditions in the case of finite friction are thoroughly examined. The theoretical formulation is applied to a non-symmetric masonry arch (case-study), whose collapse conditions are investigated by varying both thickness and friction coefficient. Through an appositely developed numerical procedure, for each value of the arch’s thickness, the limit friction coefficient is obtained, by considering the corresponding mechanism. The present research studies relevant aspects of theory of plasticity in relation to standard and non-standard behavior. In this respect, static and kinematic approaches can be properly used even in the presence of finite friction, by allowing to obtain a general and complete chart related to the activation of the various collapse modes, as a function of geometric and mechanical parameters.