Keywords: composites, constraint relaxation, masonry vaults, reinforcement.

In this paper, starting from the theoretical background previously developed by the authors concerning the statics of masonry vaults and aimed at the selection of families of load shapes equilibrated by sets of admissible solutions, a strategy is outlined for identifying the areas of the vault to be reinforced with fibre reinforced polymer (FRP) provisions. As shown in the numerical investigation, higher intensities of the stress state are then allowed by the introduction of the reinforcement and the local relaxation of some of the constraints of the problem.

The fundamental premise of this paper describes the need for setting up procedures for properly identifying the type, shape and distribution of reinforcement to be introduced in masonry structures. The results from the wide theoretical research developed for establishing more reliable models, analytical methods and calculus codes for analysing masonry structures and forecasting their behaviour, may be successfully exploited for the purpose. The paper focuses on the possibility of identifying the regions of a masonry vault to be equipped with FRP reinforcement starting from the premise that the solution of the problem of the "no tension" (NT) vault under assigned loads may be searched for. As shown by the authors in some previous papers [1,2], the search , after identifying the set of admissible solutions relevant to specific load families, basically starts from a set of inequalities which is referred to as the vault inequality system (VIS). The presence of the reinforcement allows some local relaxing of some of the NT admissibility constraints governing the problem, which, in the case of arched and vaulted structures, allowed the funicular line to come out from the extrados and, or intrados profiles of the vault, depending on the position of the reinforcement. Therefore in essence the approach proposed in this paper shows that some easy application of the theoretical set up proposed by the authors for the treatment of masonry vaults modeled under the NT assumption may be performed, also with the specific objective of identifying the regions of the vault to be reinforced. By this approach, as shown in the numerical investigation, one may evaluate the extension and the position of the areas where the reinforcement should be applied according to the expected collapse mechanism of the vault and to the desired reduction of the thrust at given locations, which can be very useful when designing the FRP provision to be adopted.

1

A. Baratta, O. Corbi, "Notes on Statics of Masonry Vaults", in A. Pirrotta, G. Navarra, (Editors), "MDP07, International Symposium on Recent Advances in Mechanics, Dynamical Systems and Probability Theory", Patròn Editore, Mondello, Palermo, 25-36, 3-6 June 2009.

2

A. Baratta, O. Corbi, "On the equilibrium and admissibility coupling in NT vaults of general shape", Int J Solids and Structures, 47(17), 2276-2284, 2010. doi:10.1016/j.ijsolstr.2010.04.024

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