Published elastic stress concentration factors are shown to underestimate stresses in the root of a shoulder filleted shaft in bending by as much as 21 percent, and in tension by as much as forty percent. For this geometry, published charts represent only approximated stress concentration factor values, based on known solutions for similar geometries. In this study, detailed finite element analyses were performed over a wide range of filleted shaft geometries to define three useful relations for bending and tension loading: (1) revised elastic stress concentration factors, (2) revised elastic von Mises equivalent stress concentration factors and (3) the maximum stress location in the fillet. Updated results are presented in the familiar graphical form and empirical relations are fit through the curves which are suitable for use in numerical design algorithms. It is demonstrated that the first two relations reveal the full multiaxial elastic state of stress and strain at the maximum stress location. Understanding the influence of geometry on the maximum stress location can be helpful for experimental strain determination or monitoring fatigue crack nucleation. The finite element results are validated against values published in the literature for several geometries and with limited experimental data.

1.
Gooyer
L. E.
, and
Overbeeke
J. L.
,
1991
, “
The Stress Distributions in Shoulder Shafts under Axisymmetric Loading
,”
Journal of Strain Analysis
, Vol.
26
, No.
3
, pp.
181
184
.
2.
Hardy
S. J.
, and
Malik
N. H.
,
1992
, “
A Survey of Post-Peterson Stress Concentration Factor Data
,”
Int. J. Fatigue
, Vol.
14
, No.
3
, pp.
147
153
.
3.
Hartman
J. B.
, and
Leven
M. M.
,
1951
, “
Factors of Stress Concentration for the Bending Case of Fillets in Flat Bars and Shafts with Central Enlarged Section
,”
Proceedings SESA
, Vol.
9
, No.
1
, p.
53
53
.
4.
Neuber, H., 1946, Kerbspannungslehre, Springer, Berlin, 1937. Translation, Theory of Notch Stresses, J. W. Edwards Co., Ann Arbor, Michigan.
5.
Peterson, R. E., 1953, Stress Concentration Design Factors, John Wiley and Sons, Inc., New York.
6.
Peterson, R. E., 1974, Stress Concentration Factors, John Wiley and Sons, Inc., New York.
7.
Wilson
I. H.
, and
White
D. J.
,
1973
, “
Stress Concentration Factors for Shoulder Fillets and Grooves in Plates
,”
Journal of Strain Analysis
, Vol.
18
, pp.
43
51
.
8.
Young, Y. C, 1989, Roark’s Formulas for Stress and Strain, Sixth Edition, McGraw Hill Book Company, New York.
This content is only available via PDF.
You do not currently have access to this content.