Issue 77

M. V. Boniardi et alii, Fracture and Structural Integrity, 77 (2026) 405-420; DOI: 10.3221/IGF-ESIS.77.23

The stress concentration factor K t depends on the cross-sectional geometry and, in the specific case shown in Fig. 3b, on: (i) the fillet radius, (ii) the maximum and (iii) minimum diameters of the shaft; K t is normally tabulated for the most common notch shapes used in mechanical design (Fig. 4).

Figure 3: Stress distribution generated by bending applied to (a) a smooth shaft and (b) a notched shaft.

Figure 4: Stress concentration factor K t for a shaft with a shoulder subjected to bending [14]. Although the value of K t can only be applied to the surface of the component, i.e. near the notch, there are equations which, for various specific cases, allow the stress gradient caused by the notch to be calculated. In the case of bending condition shown in Fig. 3b, Nakonieczny [15] proposed the following equation to evaluate the maximum stress (  r,max ) at every position along the section due to the stress gradient:   3 2 , 0, 2 [1 ] t K r max t sup r K d      (3) where K t is the stress concentration factor,  0,sup is the nominal surface stress, calculated using Eqn. (1bis), and r and d are the radial position and the diameter of the cylindrical section, respectively. Using (1), (1bis), (2) and (3), it is therefore possible to calculate the stress state at every point along a cylindrical section, whether smooth or notched, under the effect of bending. Fig. 5 shows an application of (3) for a cylindrical section ( d = 6 mm) subjected to bending, with a maximum nominal stress of 100 MPa and different values of K t .

408