Error in Stress Concentration Factors Currently Used for Tension and Bending of Stepped Round Bar with Fillet

Abstract

The stress concentration factor (SCF) of a stepped round bar with fillets is fundamental in machine design and SCF diagrams are included in many textbooks and handbooks on mechanics of materials and machine design. Among them, Peterson's handbook, for example, is continuously used around the world. Noda et al. analyzed such stepped round bar under tension and bending accurately by using the body force method and proposed a calculation formula for the entire range of geometries. However, the above textbooks and handbooks still indicate different stress concentration diagrams throughout. Therefore, in this study, for the entire range of fillet shape dimensions including the range of very small fillet radius, Peterson's results are compared with Noda and Takase's results to clarify the error. As a result, Peterson's stress concentration factor is found to have an error of up to 25% in tension and up to 15% in bending. The errors of stress concentration factors in other books are also discussed.