On discontinuous influence functions for a concentrated moment to locate cracks in beams

The study discusses a novel property based on the use of a concentrated moment roving along a beam to be exploited for crack detection and location purposes. Specifically, functions expressing the influence on response parameters of a beam at a monitored cross section for different positions of a concentrated moment show abrupt discontinuities when rotation jumps occur along the beam axis. Since the Localised Flexibility Model (LFM), widely used in mechanics of fracture, macroscopically models the presence of damage with a rotational spring connecting two members of the structures, abrupt discontinuities are expected in the response influence functions when a concentrated moment crosses a cracked cross section. Both theoretical and numerical evidence of the latter concept is provided in the paper. The highlighted property can be easily construed as a strategy to detect and localise multiple cracks without any test on the undamaged configuration as well as the a priori knowledge of the number of cracks. With the aim of exploiting the denoted property, a distributional approach is employed for the formulation and integration of the governing equations of a multi-cracked Timoshenko beam. The main considerations are first proposed in a static context by discussing the so-called influence lines, then extension to the case of a roving harmonic moment by means of the Green's function theory is discussed. The presented applications show the reliability of the proposed property towards crack detection and location. Possible limitations of the proposed approach are also discussed and relevant solutions are indeed addressed.