Simple double shooting approach with bisection for FRCM reinforced curved masonry prisms subjected to shear

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In this study, curved masonry pillars reinforced with FRCM subjected to standard shear tests are analyzed through a novel mono-dimensional model, where failure is governed by Mode II. Three approaches with different accuracy are proposed: i) the first, where the outer matrix is neglected; ii) the second, where the inner matrix is assumed rigid; and iii) the third which considers both matrix layers. Matrix and fiber are assumed subjected to a monoaxial state of stress and exchange tangential stresses at the interfaces. The load is applied by incrementing the displacement at the free fiber edge. Material properties of matrix, fiber and interfaces are assumed constant on small portions of the bonded length. Non-linearity is considered penalizing the elastic modulus using the results of the previous time step. The substrate is assumed rigid. The substrate curvature influence is manifested through interface normal stresses, incorporated into the bond-slip constitutive behavior via the Mohr-Coulomb law. The normal stresses can be determined by enforcing radial equilibrium. For the first two models, the field problem is constituted by a system of two 2nd order differential equations into two variables, namely the displacement of the inner (or outer) layer of mortar and of the fiber textile. A 1D shooting is employed, after having converted the boundary value problem (BVP) into an initial value one (IVP), being the latter fully explicit. For the third model, the field problem is constituted by a system of three 2nd order differential equations, and an additional displacement variable is introduced, necessitating a 2D shooting. The validation is carried out through comparisons with existing experimental data. Good predictions of the load-slip curves, for different strengthening configurations (extrados and intrados with two curvature radii), are observed. In addition, an insight into local stress distributions and material degradation for matrix layers and interfaces is obtained.