Giuseppe Cocchetti1, and Egidio Rizzi2
1) Department of Civil and Environmental Engineering, Politecnico di Milano
piazza L. da Vinci 32, Milano, Italy.
2) Department of Engineering and Applied Sciences, University of Bergamo, School of Engineering
viale G. Marconi 5, Dalmine (BG), Italy.
Keywords: Circular masonry arches, Limit Analysis (LA), Minimum thickness, Collapse mechanisms, Reducing friction.
Abstract. The modern Limit Analysis (LA) of masonry arches classically takes off from Heyman’s hypotheses . A main one of them assumes an unbounded friction coefficient, ruling the interaction among adjacent blocks, namely as high as needed to prevent sliding. These hypotheses allow for the computation of the critical thickness of circular masonry arches under self-weight (Couplet-Heyman problem) and of the associated purely rotational collapse mode, by both static and kinematic LA approaches, through different analytical and numerical procedures [2-4]. The aim of this work is to further investigate the collapse of circular masonry arches at a reducing friction coefficient . Here, the normality flow rule may no longer apply and the whole analysis within the LA framework may need to be revisited. A new computational methodology is set forward, in order to investigate all the possible collapse states of the circular masonry arch, by looking at the same time at potential equilibrium solutions and associated kinematic compatibility, in the spirit of the mixed method of LA. Critical values of the friction coefficient are highlighted, marking the transitions of the collapse mode from a purely rotational one to a collapse mode involving sliding. Uniqueness of the solution in terms of collapse mechanism and critical thickness of the arch is revealed by the devised approach, within the present settlement, despite for the role of friction in shifting the appearance of the collapse mode.