PLASTICITY, COULOMB FRICTION AND SLIDING IN THE LIMIT ANALYSIS OF MASONRY ARCHES

In the framework of plasticity theory, limit analysis in the presence of large value of friction is a consolidated approach to analyse the collapse of the arch and identify the corresponding collapse mechanism. Inclusion of Coulomb friction and sliding in the limit analysis, however, points out an extremely delicate question, since in accordance with the plastic theory, as first outlined by Drucker, for non-standard materials Coulomb friction results in a non-associated flow rule which invalidates the general bounding theorems. Thus, the limit load can be evaluated by means of more restrictive theorems. By adopting, for example, a normality rule, the correct limit load can be reached, even if it may result in incorrect failure modes since the normality rule is not obeyed by mechanisms involving Coulomb friction. Purpose of this paper is that of revisiting the bounding theorems of plasticity for masonry arches in the presence of finite Coulomb friction and sliding by applying and extending Drucker's and Radenkovic's theorems. It will be demonstrated that for a masonry arch subject to its own weight, although finite friction makes it locally possible activation of sliding characterized by a non-associated flow rule, corresponding mechanisms for the whole arch are kinematically not-admissible with the exception of the "mechanism for the arch of minimum-thickness with finite friction" in the range 0.395 >= ? >= 0.310. This result gives a greater consistency to the statement that the collapse of the arch due to sliding in the presence of typical values of the friction coefficient is unlikely.