Extraction of the beam elastic shape from uncertain FBG strain measurement points

Aim of the present paper is the analysis of the strain along the beam that is equipped with Glass Fibers Reinforced Polymers (GFRP) with an embedded set of optical Fiber Bragg Grating sensors (FBG), in the context of a project to equip with these new structural elements an Italian train bridge. Different problems are attacked, and namely: (i)during the production process [1] it is difficult to locate precisely the FBG along the reinforcement bar, therefore the following question appears: How can we associate the strain measurements to the points along the bar? Is it possible to create a signal analysis procedure such that this correspondence is found?(ii)the beam can be inflected and besides the strain at some points, we would like to recover the elastic shape of the deformed beam that is equipped with the reinforcement bars. Which signal processing do we use to determine the shape of the deformed beam in its inflection plane?(iii)if the beam is spatially inflected, in two orthogonal planes, is it possible to recover the beam spatial elastic shape? Object of the paper is to answer to these questions.