A linear theory for bending stress–strain analysis of a beam with an edge crack

In this paper, a new linear theory for bending stress–strain analysis of a cracked beam has been developed. A displacement field has been suggested for the beam strain and stress calculations. The bending differential equation for the beam has been written using equilibrium equations. The required constant for this model is also obtained from fracture mechanics. The bending equation has been solved for a simply supported beam with rectangular cross-section and the results are compared with finite element and empirical results. There is an excellent agreement between theoretical results and those obtained by numerical and empirical methods. The model developed in this research is a simple and precise approximation of the behavior of the cracked beams in bending.