Non linear analysis of FRP reinforced masonry arches

In this paper two structural models of arches strengthened with fibre-reinforced composite materials and the relevant numerical procedures for the analysis are proposed. Both models describe the structure by an assemblage of rigid blocks connected together and with the ground by joints capable both to simulate the presence and the lack of the mortar. What differentiates them regards the description of the reinforcement: the first model considers the reinforcement composed of elements both with a structural function and with constraint one, placed in series and bonded to the substrate, the second one, instead, considers it only as an additional inner constraint. Such structures can be put into a class of problems known as unilateral constraints. The numerical algorithm, through the opportune use of Moore-Penrose generalized inverse, is based on the introduction of suitable distortion terms capable to generate internal coactions such as to give back the compatibility in the sign conditions where tensile stresses are not admissible. At first the linear elastic and bilateral solution is evaluated, then the distortion terms are introduced to correct it, in a procedure step by step. Such a method has already been practiced by Castigliano in 1879. According to the Colonnetti’s theorem, the maximum number of imposed linear independent terms of distortion - that is the maximum number of the iterations in the procedure - is, at most, equal to the degree of statically indeterminacy of the structure. Through the results of the numerical procedure it is possible both to define the cracking failure pattern, highlighting the actual reacting structure within the apparent one, and to evaluate the width of the cracks located in the mortar joints.