Abstract: Removing constraints of internal supports of continuous cracked beam and instead of them with unknown reaction forces, the continuous cracked beam was simplified as a single span with unknown reaction forces. Based on the linear torsional spring model of transverse crack in beam, the general analytical solution of continuous Euler-Bernoulli beam with arbitrary number of open cracks on Winkler foundation was presented by Laplace transform and its inverse transformation. On the basis of verifying the correctness of the analytical solution using Abaqus finite element software, the influences of the foundation reaction coefficient, crack depth and location as well as beam length-height ratio on the bending deformation of continuous cracked beam were analyzed numerically. It is revealed that the deflection of the continuous cracked beam on Winkler foundation decreases with the foundation reaction coefficient increase. And the deflection cusp and rotation angle jump of beam at the crack location become more remarkable with increase of the crack depth; The influences of location, depth and numbers of the crack on the bending of cracked beam on Winkler foundation are remarkable. Furthermore, when the foundation reaction coefficient is larger, the influence of the crack on bending deformation of continuous beam on Winkler foundation diminishes gradually. These conclusions can provide certain guiding significance for structure design and structural health detection and monitoring.

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