Optimal strengthening of masonry arch bridges with externally bonded reinforcing layers

Strengthening is a natural step following a failed bridge assessment. Referring to masonry bridges, a numerical tool is presented to find the optimal distribution of reinforcement to be externally bonded to two-dimensional elastic no-tension structural elements, with the aim of maximizing their overall stiffness. Notwithstanding the non-linearity of the adopted material model, no incremental procedure is needed to prescribe equilibrium of the strengthened element. Indeed, the same minimization procedure handles both the energy-based solution of the no-tension elastic body and the topology optimization problem that distributes the optimal reinforcement. A few numerical simulations are presented to assess the capabilities of the proposed procedure in defining the optimal reinforcement layouts for masonry arches and arch bridges, subjected to gravity loads and resting on fixed or elastic foundations. Designers can exploit the tool to sketch a preliminary layout of the FRP strengthening, which should be subsequently detailed according to technical codes.