Convenient stress concentration formula useful for any shape of fillet (Torsion of stepped round bar with fillet)

To ensure the strength and safety of shafts, which are basic components of machines, it is important to accurately evaluate the stress concentration factor (SCF) of stepped round bar fillets. Noda et al. analyzed the SCF of stepped round bar with fillet under tension and bending by using the body force method and proposed SCF formulas valid for all dimensional ranges. These formulas are very useful in design practice. Since shafts generally transmit power, the SCF of torsion is also important, but there is no solution for the torsional SCF that is valid for all dimensional ranges. In this study, therefore, the stepped round bar subjected to torsion is investigated for all dimensional ranges. The finite element method for an axisymmetric body subjected to a non-axisymmetric load is applied to torsional problems by confirming the coincidence with the SCF solution by the body force method for a round bar with a semicircular notch under torsion. The SCF formula proposed for all dimensional range under torsion shows that SCF charts in literature commonly used in design practice have large errors about 10% because they are based on old research results. Peterson's SCF equation is simple and useful, but the application range of the equation for torsion is extremely narrow and inconvenient to be used in machine design.