Limit analysis of FRP strengthened masonry arches via nonlinear and linear programming

The collapse load of masonry arches strengthened with FRP materials is determined. The arch is made of quadrangular blocks and the nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated at the interface between the blocks. Two methods are used to solve the problem. In the first method, a nonlinear programming problem (NLP) is formulated and is solved by using the successive quadratic programming algorithm (SQP) and combinatorial analysis. This method finds the optimal solution in the analysed cases. In the second method, a linear programming problem (LP) is formulated and is solved with classical techniques. LP approximates the optimal solution to any desired degree of accuracy. Although the number of variables of LP is much larger than that of NLP, LP process time can result much lower than NLP process time. Numerical examples are provided in order to show the advantages of the two methods and the effectiveness of FRP strengthening for different arch geometries.