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

the factor K depends only upon the geometry of the member, curves can be developed that
show the stress-concentration factor K as a function of the ratios of the parameters involved.
Such curves for notches and fillets in rectangular cross sections subjected to pure
bending are shown in Figures 8.17 and 8.18. 1 Similar curves for grooves and fillets in circular
shafts subjected to pure bending are shown in Figures 8.19 and 8.20. 2
303
STRESS CONCENTRATIONS
uNdER FLExuRAL LOAdINgS
Stress-concentration factor K
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
D
d
= 1.20
D
d
= 2.00
D
d
= 1.50
D
d
= 1.10
M
D
2r
d
M
r t = thickness
σ
K max
= , σ
σ nom = 6M
nom td 2
1.2
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Ratio r d
FIGURE 8.17 Stress-concentration factors K for bending of a flat bar with opposite
U-shaped notches.
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
= 3.00
D
d
D
d
= 2.00
D
d
= 1.10
= 1.50
M
t = thickness
D
r
σ
K
max
= , σ
σ nom = 6M
nom td 2
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
d
M
Ratio r d
FIGURE 8.18 Stress-concentration factors K for bending of a flat bar with shoulder fillets.
1 Adapted from Walter D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed. (New York: John Wiley &
Sons, Inc., 1997).
2 Ibid.