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A low-cost sensing system specifically devised for structural monitoring, such as the evaluation of displacements of concrete beams or the evolutions of cracks, is presented. The developed system exploits the measurement of the phase variation in a light signal propagating along a plastic optical fiber integral with the structure whose elongations have to be measured. The choice of plastic optical fibers accounts for the possibility of achieving sub-millimetric resolution while keeping the overall costs low. Preliminary measurement campaigns have been performed to assess the performances of the system.