A FBG strain sensor arrangement includes a sensor carrier of steel sheet to which a FBG strain sensor is fastened. A protective cover has a first part configured thin and narrow and bonded to the sensor carrier along an optical fiber so that the optical fiber lying underneath is fixed with a fiber Bragg grating on the sensor carrier. The protective cover is enlarged at each end portion of the optical fiber to thereby form a cavity underneath, with edges of the enlarged second part of the protective cover being bonded to the sensor carrier. Arranged in the cavity is an elastic filler which embeds the coupling points in a vibration damping manner. The protective cover with elastic filler accommodates thermal expansions and functions for dynamic measurements by the vibration damping.