Abstract: Based on the linear torsional spring model of a transverse crack in a beam, the general analytical solution of the Euler-Bernoulli beam considering an arbitrary num-ber of cracks on the Winkler foundation was presented through Laplace transform and its inverse transformation. The bending deformation for simply-supported and cantilever cracked beams under uniform loads were investigated to evaluate the analytical solution. The influences of the numbers and locations of cracks, foundation reaction coefficient and beam length-height ratio on the bending deformation of the cracked beam were analyzed. At the crack location, a cusp in deflection and a gap rotational angle of the beam were identified. The influences of the foundation reaction coefficient and crack depth on the bending of cracked beam were significant, in contrast to the effects caused by the number and locations of the crack and the length-height ratio of beam. These conclusions can be used for structural health detection and monitoring. 

Key words: Winkler foundation, Euler-Bernoulli cracked beam, generalized function, analytical solution, parameter study