Upper Bound limit analysis model for FRP-reinforced masonry curved structures. Part I: unreinforced masonry failure surfaces

A two-steps approach for the FE limit analysis of FRP reinforced curved masonry structures is presented in this paper. In step I, discussed extensively in the present Part I, a simplified kinematic procedure is proposed at a cell level to obtain macroscopic masonry behavior in the case of unreinforced masonry curved structures. In step II, discussed in the companying paper (Part II) strips are applied at a structural level on the already homogeneous material. Unreinforced masonry strength domain is obtained by means of a compatible approach in which each brick is supposed to interact with its six neighbors by means of rigid-plastic interfaces with frictional behavior representing mortar joints. A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in- and out-of-plane loads. Suitable internal macroscopic actions are applied on the boundary of the representative element of volume, in analogy to the flat case. The limit analysis problem at a cell level is finally solved adopting an upper bound approach and discretizing the seven bricks by means of six-noded rigid infinitely resistant wedge elements. In this way, internal power dissipation is possible only at the interfaces between wedge adjoining elements (brick–brick interfaces and mortar joints with zero thickness). Several examples consisting of single and double curvature elementary cells are analyzed. For each representative element of volume, in- and out-of-plane failure surfaces are provided. Macroscopic strength domains so recovered will be utilized in Part II for the limit analysis of entire vaults FRP reinforced.