Page 360 - Shigley's Mechanical Engineering Design

bud29281_ch06_265-357.qxd 12/7/09 9:42PM Page 335 ntt G4 Mac OS 9.2:Desktop Folder:MHDQ196/Budynas:

Fatigue Failure Resulting from Variable Loading 335
Table 6–15 √ √ √
a( in) , a( mm) , Coefficient of
Heywood’s Parameter Notch Type S ut in kpsi S ut in MPa Variation C Kf
√
a and coefficients of Transverse hole 5/S ut 174/S ut 0.10
variation C Kf for steels Shoulder 4/S ut 139/S ut 0.11
Groove 3/S ut 104/S ut 0.15

relate the statistical parameters of the fatigue stress-concentration factor K f to those of
notch sensitivity q. It follows that
¯ ¯
K f − 1 CK f
q = LN ,
K t − 1 K t − 1
where C = C Kf and
¯
K f − 1
¯ q =
K t − 1
¯
CK f
ˆ σ q = (6–77)
K t − 1
¯
CK f
C q =
¯
K f − 1
The fatigue stress-concentration factor K f has been investigated more in England than in
33
¯
the United States. For K f , consider a modified Neuber equation (after Heywood ),
where the fatigue stress-concentration factor is given by
K t
¯
K f = √
2(K t − 1) a (6–78)
1 + √
K t r
√
where Table 6–15 gives values of a and C Kf for steels with transverse holes,
shoulders, or grooves. Once K f is described, q can also be quantified using the set
Eqs. (6–77).
The modified Neuber equation gives the fatigue stress-concentration factor as

¯ (6–79)
K f = K f LN 1, C K f

EXAMPLE 6–18 Estimate K f and q for the steel shaft given in Ex. 6–6, p. 296.
Solution From Ex. 6–6, a steel shaft with S ut = 690 MPa and a shoulder with a fillet of 3 mm
.
was found to have a theoretical stress-concentration factor of K t = 1.65. From
Table 6–15,
√ 139 139 √
a = = = 0.2014 mm
S ut 690

33 R. B. Heywood, Designing Against Fatigue, Chapman & Hall, London, 1962.