Crack non-destructive test in Timoshenko beams based on crack-induced chord-wise deflection

A method for crack position identification and crack-damage evaluation in cracked Timoshenko beams using beam's static deflection was proposed. At first, representing a switching crack with gap as a unidirectional rotational spring, the equivalent flexural rigidity of the beam with arbitrary number of switching cracks was presented by the generalized Delta function and the Heaviside function. The general explicit closed-form solution for the bending of the cracked Timoshenko beams was derived, and an iteration method for determining unknown constants of the closed-form solution was given. Subsequently, the crack-induced chord-wise deflection function was proposed, and it was proven that there existed an abrupt change in the slope of the crack-induced chord-wise deflection curve at the crack location, which provided the theoretical basis for crack position identification. On this basis, an approximate formula of the equivalent rotational spring rigidity of the crack was given. Finally, the proposed methodology was applied to crack position identification and crack-damage evaluation of simply-supported and clamped cracked Timoshenko beams with known crack locations and crack-damage levels, respectively, by means of numerical experiment It has been demonstrated that the proposed methodology for crack-damage identification not only has the general validity, but also a high level of precision and reliability. © 2016, Engineering Mechanics Press. All right reserved.