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

304
bENdINg
Stress-concentration factor K
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
D
d
= 1.20
D
d
D
d
= 1.10
= 2.00
D
d
= 1.50
D
d
= 1.30
M
D
2r
r
σ
K = max
, σ
σ nom = 32M
nom πd 3
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
d
M
Ratio r d
FIGURE 8.19 Stress-concentration factors K for bending of a circular shaft with a
U-shaped groove.
Stress-concentration factor K
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
D
d
= 1.10
D
d
= 3.00
D
d
= 2.00
D
d
= 1.50
D
d
M
= 1.20
D
d
r
σ
K = max
, σ
σ nom = 32M
nom πd 3
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
M
Ratio r d
FIGURE 8.20 Stress-concentration factors K for bending of a stepped shaft with shoulder fillets.
ExAmpLE 8.12
80 mm 40 mm
Radius r
M
A cantilever spring made of SAE 4340 heat-treated steel is 50 mm
thick. As shown in the figure, the depth of the rectangular cross
section is reduced from 80 mm to 40 mm, with fillets at the transition.
A factor of safety (FS) of 2.5 with respect to fracture is specified
for the spring. Determine the maximum safe moment M for
the spring if
(a) the fillet radius r is 4 mm.
(b) the fillet radius r is 12 mm.