Limit analysis of masonry arches with finite compressive strength and externally bonded reinforcement

The collapse load of masonry arches with limited compressive strength and externally bonded reinforcement, such as FRP, is evaluated by solving the minimization problem obtained by applying the upper bound theorem of limit analysis. The arch is composed of a finite number of blocks. The nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated in the interface between two adjacent blocks. The crushing in the collapse mechanism is schematised by the interpenetration of the blocks with the formation of hinges at internal or boundary points of the interface. The minimization problem is solved with linear optimization, taking advantages of the robust algorithms offered by linear programming (LP). The optimal solution of the linear programming problem approximates the exact solution to any degree of accuracy. The dual of the minimization problem is also formulated and is solved in order to present the statics (thrust curve, locus of feasible internal reactions, etc.) of the reinforced arch as a consequence of the kinematical assumptions used in the primal minimization problem. Numerical examples are presented in order to show the effectiveness of the proposed method. Finally, it is shown that the results provided by the proposed LP are in good agreement with an experiment on a FRP-strengthened arch characterized by crushing failure of the masonry.