Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

184
TORSION
3.0
2.8
T
2r
T
2.6
D
d
Stress-concentration factor K
2.4
2.2
2.0
1.8
1.6
1.4
D
d
≥ 2.00
D
1.30
d = D
1.20
d
=
r
τ max
τ nom
K , τ
16T
= nom = πd 3
1.2
1.0
0 0.05 0.10 0.15 0.20 0.25
0.30
Ratio r d
FIGURE 6.17 Stress-concentration factors K for a circular shaft with a U-shaped groove.
The full shaft diameter D at the
discontinuity is termed the major
diameter. The reduced shaft
diameter d at the discontinuity is
termed the minor diameter.
Stress-concentration factors K for circular shafts with U-shaped grooves and for stepped
circular shafts are shown in Figures 6.17 and 6.18, respectively. 4 For both types of discontinuity,
the stress-concentration factors K depend upon (a) the ratio D/d of the major diameter D to
the minor diameter d and (b) the ratio r/d of the groove or fillet radius r to the minor diameter d.
An examination of Figures 6.17 and 6.18 suggests that a generous fillet radius r should be used
wherever a change in shaft diameter occurs. Equation (6.21) can be used to determine localized
maximum shear stresses as long as the value of τ max does not exceed the proportional limit
of the material.
Stress-concentration factor K
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
D
d
= 1.11
D
d
= 1.25
D
d
= 1.67
D
d
= 2.00
D
d
T
D
τ max
τ nom
d
r
T
K , τ
16T
= nom =
πd 3
= 2.50
1.1
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Ratio r d
FIGURE 6.18 Stress-concentration factors K for a stepped shaft with shoulder fillets.
4
Adapted from Walter D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed. (New York: John Wiley &
Sons, Inc., 1997).