Detecting Multiple Open Cracks in Elastic Beams by Static Tests

This paper concerns with the identification of multiple open cracks in a beam by measurements of the damage-induced variations in the static deflection of the beam under a prescribed load condition. Each crack is simulated by an equivalent linear spring connecting the two adjacent segments of beam. Sufficient conditions on the static measurements which allow for the unique identification of the damage are presented and discussed for nonuniform beams under some ideal boundary conditions. The inverse analysis is based on an explicit expression of the crack-induced variation in the deflection of the beam under a given load distribution and it provides exact closed-form expressions of position and severity of the cracks in terms of the measured data. The theoretical results are confirmed by a comparison with static tests carried out on a steel beam with localized damages.