Machine Design Databook Episode 1 part 5 pot

FIGURE 4-22 Reproduced with permission. Stress-concentration factor K
for notched flat bar in tension. (R. E. Peterson,

‘‘Design Factors for Stress Concentration,’’ Machine Design, Vol. 23, Nos. 2 to 7, 1951.)

(iii) Bar with shallow V-groove in tension for

r

h1

> 1

(iv) Elliptical groove at the edge of plate in

tension

(v) Bar with symmetrical U, semicircular

shallow grooves in bending (Fig. 4-23).

K
v ¼ 1 þ ðK
v 1Þ 1



180

1 þ 2:4 ffiffiffiffiffiffi

r=h1

( ) p

ð4-25Þ

K
¼ 1 þ

2h1

b ð4-26aÞ

K
¼ 1 þ 2

ffiffiffiffiffi

h1

r

r

ð4-26bÞ

K
¼ 1 þ

1

4:27 D

d 4

h1

r

2

4

3

5

0:85

ð4-27aÞ

or

K
¼ 1 þ

D

d 1

2

4:27 D

d 4

d

r

2

66

6

4

3

77

7

5

0:85

ð4-27bÞ

Stress concentration factor theoretical/empirical

or otherwise

Particular Extreme value Formula

4.14 CHAPTER FOUR

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STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS

FIGURE 4-23 Reproduced with permission. Stress-con￾centration factor K
for notched flat bar in bending. (R. E.

Peterson, ‘‘Design Factors for Stress Concentration,’’

Machine Design, Vol. 23, Nos. 2 to 7, 1951.)

For stress-concentration factors for small grooves

in a shaft subjected to torsion.

(o) Bar containing shoulders

(i) Bar with shoulders in tension (Fig. 4-24)

TABLE 4-4

Stress-concentration factors for relatively small

grooves in a shaft subject to torsion, K

h1

r

Included angle of V, deg 0.5 1 3 5 2

0 1.85 2.01 2.66 3.23 4.54

60 1.84 2.00 2.54 3.06 3.99

90 1.81 1.95 2.40 2.40 3.12

120 1.66 1.75 1.95 2.00 2.13

FIGURE 4-24 Reproduced with permission. Stress-con￾centration factor K
for filleted flat bar in tension. (R. E.

Peterson, ‘‘Design Factors for Stress Concentration,’’

Machine Design, Vol. 23, Nos. 2–7, 1951.)

Refer to Table 4-4.

K
¼ 1 þ

1

2:8 D

d 2

h1

r

2

4

3

5

0:85

ð4-28aÞ

or

K
¼ 1 þ

D

d 1

2

2:8 D

d 2

d

r

2

66

6

4

3

77

7

5

0:85

ð4-28bÞ

Stress concentration factor theoretical/empirical

or otherwise

Particular Extreme value Formula

STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS 4.15

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STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS

(ii) Bar with shoulders in bending (Fig. 4-25)

(p) Press-fitted or shrink-fitted members (Table 4-5):

(i) Plain member

(ii) Grooved member

(iii) Plain member

(iv) Grooved member

(q) Bolts and nuts (Tables 4-6 and 4-7)

Bolt and nut of standard proportions

Bolt and nut having lip

FIGURE 4-25 Reproduced with permission. Stress-concentration factor K
for stepped bar in bending. (R. E. Peterson,

‘‘Design Factors for Stress Concentration,’’ Machine Design, Vol. 23, Nos. 2 to 7, 1951.)

K
¼ 1 þ

1

5:37 D

d 4:8

h1

r

2

4

3

5

0:85

ð4-29aÞ

or

K
¼ 1 þ

D

d 1

2

5:37 D

d 4:8

d

r

2

66

6

4

3

77

7

5

0:85

ð4-29bÞ

K
¼ 1:95

K
¼ 1:34

Kf
¼ 2:00

Kf
¼ 1:70

K
¼ 3:85

K
¼ 3:00

TABLE 4-5

Stress-concentration factors in shrink-fitted members

Particular K Kf

Plain 1.95 2.00

Grooved 1.34 1.70

Stress concentration factor theoretical/empirical

or otherwise

Particular Extreme value Formula

4.16 CHAPTER FOUR

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STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS

TABLE 4-6

Stress-concentration factors for screw threads

Analysis

Types of thread Seely and Smith Black (8) Peterson (1) Suggested value

Square 2.0

Sharp V 3.0

Whitworth 2.0 3.35 5 to 6

US standard

Medium

Carbon steel 2.5

National coarse thread

Heat-treated 2.84

Nickel steel 3.85

TABLE 4-7

Stress-concentration factors Kf for screw threads

Annealed Hardened

Type of thread Rolled Cut Rolled Cut

Sellers, American

National, square thread

2.2 2.8 3.0 3.8

Whitworth rounded roots 1.4 1.8 2.6 3.3

TABLE 4-8

Stress-concentration factors for welds

Location K

End or parallel fillet weld 2.7

Reinforced butt 1.2

Tee of transverse fillet weld 1.5

T-butt weld with sharp corners 2.0

TABLE 4-9

Index of sensitivity for repeated stress

Average index of sensitivity q

Material Annealed or soft

Heat-treated and drawn

at 921 K (6488C)

Heat-treated and drawn

at 755 K (4828C)

Armco iron, 0.02% C 0.15–0.20

Carbon steel

0.10% C 0.05–0.10

0.20% C (also cast steel) 0.10

0.30% C 0.18 0.35 0.45

0.50% C 0.26 0.40 0.50

0.85% C 0.45 0.57

Spring steel, 0.56% C, 2.3 Si, rolled 0.38

SAE 3140, 0.73 C; 0.6 Cr; 1.3 Ni. 0.25 0.45

Cr–Ni steel 0.8 Cr; 3.5 Ni 0.25 0.70

Stainless steel, 0.3 C; 8.3 Cr, 19.7 Ni 0.16

Cast iron 0–0.05

Copper, electrolitic 0.07

Duraluminum 0.05–0.13

STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS 4.17

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STRESS CONCENTRATION AND STRESS INTENSITY IN MACHINE MEMBERS