An analytical model to determine the ultimate load on masonry arch bridges

This paper proposes an analytical elasto–plastic model to describe the behavior of arches. The modeling is carried out using the equations of (i) horizontal equilibrium, (ii) vertical equilibrium and (iii) equilibrium of moments. The latter equations of equilibrium are ordinary differential equations which can easily be solved by adding boundary conditions, imposing restrictions on the horizontal and vertical movement and on the rotation in the abutments of the arch. For masonry arches, including material properties allowing the occurrence of cracks and the subsequent formation of hinges is required. The latter theory has been implemented in a computer program (Matlab), offering numerical simulations. The software was used to illustrate two case-studies, i.e., the assessment of an arch loaded with a vertical point load and one with a horizontal point load.