Lower Bound Limit Analysis of Masonry Arches with CFRP Reinforcements: A Numerical Method

Abstract

This paper presents a numerical method to predict the ultimate load of masonry arches strengthened with carbon-fiber-reinforced polymer (CFRP) strips bonded to the intrados. The voussoirs of the arch and the CFRP strip, ideally divided into the same number of parts as the voussoirs, are modeled as rigid blocks. A finite set of stress resultants represents the stress state acting on interfaces of the rigid blocks. The local failure modes at the block interfaces are defined according to experimental evidence. The model is developed within an associated framework in such a way that the normality rule is satisfied: the upper- and lower-bound theorems of classical limit analysis apply. The ultimate load is predicted by a lower bound approach. The feasible domain is defined by the equilibrium equations and by the linear constraints imposed on the stress resultants. All the relations defining the model are linear, so that a linear programming problem is imposed. The predictions of the numerical model compare well with experimental results.