Abstract: Based on the constructional characteristics of the crack-induced chord deflection function, the static damage identification method for cracks in Euler-Bernoulli beams with arbitrary boundary conditions is presented. First, with the crack taken as a linear torsional spring, the general analytical solution of the static bending deflection of the cracked Euler-Bernoulli beam with arbitrary boundary conditions was obtained. Second, its crack-induced chord deflection function was proven to be a piecewise cubic polynomial function, and a deflection-based numerical method was developed to identify the crack location and its equivalent torsional spring flexibility by fitting a crack-induced chord deflection function. Finally, the applicability and reliability of the crack damage identification method presented were verified numerically, and the influences of deflection measurement error, crack location, and depth on the damage identification results were examined. The accuracy of identifying the crack location was found to be higher than that of crack equivalent torsional spring flexibility, and the number of cracks and the selection of the crack identification interval have limited influence on the crack damage identification results. The identification method has strong robustness.

Key words: cracked beam, equivalent torsion spring model of crack, generalized function; crack-induced chord deflection, damage identification