Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.