Lower Bound Limit Analysis of Masonry Arches with the CFRP Reinfocements: a numerical method

This paper presents a numerical method to predict the ultimate load of the masonry arches with the CFRP strip reinforcement bonded at the intrados. In this work, the voussoirs of the arch and the CFRP strip, divided ideally in the same number of parts of the voussoirs, are modeled with rigid blocks; the stress state, acting on interfaces of the rigid blocks , is represented by a finite set of the stress resultants. Furthermore, as it is observed experimentally, the possible failure modes of these reinforced masonry arches are four: hinge mode, masonry crushing, debonding and peeling between the CFRP strips and the voussoirs. These failure modes at the block interface, in this model, are expressed in the linear constraints imposed on the stress resultants. It is assumed that the shear force associated with debonding, between the CFRP strips and the voussoirs, is independent of the normal force associated with peeling. This assumption means that the normality rule is satisfied; therefore, the upper-bound and lower-bound theorems of classical limit analysis apply. The ultimate load is predicted by a lower bound approach: the maximum of the load factors is searched in the domain defined by the equilibrium equations and by the linear constraints imposed on the stress resultants. The maximum of the load factor is obtained resolving a Linear Programming (LP) problem.