Table A–28

3 0 Table A–28

Decimal Equivalents of Wire and Sheet-Metal Gauges* (All Sizes Are Given in Inches) (Continued)

e D M u B si

Steel Wire

n ,E n a a yn s−

Name American

of is or Brown or Stubs States facturers Washburn Music Steel Twist th b

Gauge: & Sharpe

Iron Wire

Strip, Flat

Sheet and

Principal Sheet, Wire,

Wire, and

Drills and

Use: and Rod

Spring Steel

480 lbf/ft 3

Sheet M Music Wire Wire Rod Drill Steel

27 b 0.014 20 0.016 0.017 187 5 0.016 4 0.017 3 0.067 0.143 0.144 0 le

*Specify sheet, wire, and plate by stating the gauge number, the gauge name, and the decimal equivalent in parentheses. † Reflects present average and weights of sheet steel.

1028 Budynas−Nisbett: Shigley’s

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Mechanical Engineering

Companies, 2008

Design, Eighth Edition

Useful Tables

Table A–29

Dimensions of Square and Hexagonal Bolts

WR

Head Type

Nominal Square

Structural Hexagonal Size, in

Regular Hexagonal

Heavy Hexagonal

Nominal Size, mm

M16 24 10.75 0.6 27 10.75 0.6 27 10.75 0.6 M20

30 13.40 0.8 34 13.40 0.8 34 13.40 0.8 M24

36 15.90 0.8 41 15.90 0.8 41 15.90 1.0 M30

46 19.75 1.0 50 19.75 1.0 50 19.75 1.2 M36

Budynas−Nisbett: Shigley’s

1029 Mechanical Engineering

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Companies, 2008

Design, Eighth Edition

Mechanical Engineering Design

Table A–30

Minimum

Type of Screw

Dimensions of

Hexagonal Cap Screws

Size, in

Radius

and Heavy Hexagonal 1

Screws (W = Width

across Flats; H = Height

8 16 of Head; See Figure 64

8 in Table A–29) 32

Nominal Size, mm

M5

M6

M8

M10

M12

M14

M16

M20

M24

M30

M36

1030 Budynas−Nisbett: Shigley’s

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Mechanical Engineering

Companies, 2008

Design, Eighth Edition

Useful Tables

Table A–31

Height H

Dimensions of

Thick or

Hexagonal Nuts

Size, in

Nominal Size, mm

M5

M6

M8

M10

M12

M14

M16

M20

M24

M30

M36

Budynas−Nisbett: Shigley’s

1031 Mechanical Engineering

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Companies, 2008

Design, Eighth Edition

Table A–32

Basic Dimensions of

American Standard

Plain Washers (All

Dimensions in Inches)

N = narrow; W = wide; use W when not specified.

1032 Budynas−Nisbett: Shigley’s

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Mechanical Engineering

Companies, 2008

Design, Eighth Edition

Useful Tables

Table A–33

Dimensions of Metric Plain Washers (All Dimensions in Millimeters)

Washer Minimum

Maximum Maximum Size*

ID OD Thickness

N = narrow; R = regular; W = wide. *Same as screw or bolt size.

Budynas−Nisbett: Shigley’s

1033 Mechanical Engineering

Back Matter

Appendix A: Useful Tables

© The McGraw−Hill

Companies, 2008

Design, Eighth Edition

Mechanical Engineering Design

Table A–34

Values of Ŵ( n)

e −x x = n −1 dx ; Ŵ(n + 1) = nŴ(n)

Gamma Function* 0 Source: Reprinted with

permission from William H. Beyer (ed.), Handbook of

1.75 .919 06 Tables for Probability and

1.76 .921 37 Statistics, 2nd ed., 1966.

Copyright CRC Press, Boca

1.77 .923 76 Raton, Florida.

*For large positive values of x, Ŵ(x) approximates the asymptotic series

x 1 + 12x + 288x 2 −

51 840x 3 − 2 488 320x 4 +···

1034 Budynas−Nisbett: Shigley’s

Back Matter

Appendix B: Answers to

© The McGraw−Hill

Mechanical Engineering

Selected Problems

Companies, 2008

Design, Eighth Edition

Answers to Selected Problems

Appendix

B–1 Chapter 1

3–18 σ 1 = 30 MPa, σ 2 = 10 MPa, σ 3 = −20 MPa,

τ max = 25 MPa

1–5 (a) 1368 cars/h, (b) loss of throughput ⫽ 12%, (c) increase in speed ⫽ 5.5%

3–22 (a) M max = 21 600 kip · in, (b) x max = 523 in

from left or right supports 1–8 (a) e 1 = 0.006 067 977, e 2 = 0.009 489 743,

e 3–23 (a) σ A B = 0.015 557 720, (b) e C

= 42 kpsi, σ = 18.5 kpsi, σ = 2.7 kpsi,

3–27 = 13.1 MPa, (b) σ = 70 MPa, M max = 219 lbf · in, σ = 17.8 kpsi,

(c) y = 15.5 mm, (d) θ = 5.18 ◦ τ max = 3.4 kpsi, both models 3–33 The same

3–37 Two 1 16 -in-thick strips: T max = 31.25 lbf · in,

8 B–2 Chapter 2 -in-thick

= 0.200 rad, k 1 = 156 lbf · in/rad. One

strip: T max = 62.5 lbf · in, θ = 0.100 rad, 2–9 E = 30 Mpsi, S y = 45.5 kpsi, S ut = 85.5 kpsi,

k t = 625 lbf · in/rad

area reduction = 45.8 percent

3–43 d C = 45 mm

2–15 ¯S ut = 125.2 kpsi, ˆσ S ut = 1.9 kpsi 3–48 σ max = 11.79 kpsi, τ max = 7.05 kpsi 2–17 (a) u .

. R = 34.5 in · lbf/in 3 , (b) u T =

3–54 p

i = 639 psi

66.7(10 ) in · lbf/in 3

3–58 (σ r ) max = 3656 psi

2–22 Steel, Titanium, Aluminum, and Composites 3–66 δ max = 0.038 mm, δ min = 0.0175 mm,

p max = 147.5 MPa, p min = 67.9 MPa

B–3 Chapter 3

3–70 For δ max , p = 33.75 kpsi, (σ t ) o = 56.25 kpsi, 3–4 (a) V (x)

0 0 (σ t + ) i = −33.75 kpsi, δ o = 0.001 10 in,

71.43 0 0 lbf

δ i = −0.000 398 in

M(x)

3–73 σ i = 26.3 kpsi, σ o = −15.8 kpsi

3–78 σ i = 71.3 kpsi, σ o = −34.2 kpsi 3–6 (a) M max = 253 lbf · in, (b) (a/l) ∗ = 0.207,

71.43 1 1 lbf · in

3–81 p max = 399F 1/3 MPa, σ max = 399F 1/3 MPa, M ∗ = 214 lbf · in

τ max = 120F 1/3 MPa

3–8 (a) σ 1 = 14, σ 2 = 4, σ 3 = 0, φ p = 26.6 ◦ cw ;

τ 1 = 5, σ ave = 9, φ s = 18.4 ◦ ccw

B–4 Chapter 4

(b) σ 1 = 18.6, σ 2 = 6.4, σ 3 = 0, φ p = 27.5 ◦ ccw ;

τ 1 = 6.10, σ ave = 12.5, φ s = 17.5 ◦ cw 4–1 (a) k = (1/k 1 + 1/k 2 + 1/k 3 ), (b) k =k 1 +

k 2 +k 3 , (c) k = [1/k 1 + 1/(k 2 +k 3 ) ] −1 τ 1 = 9.22, σ ave = 17, φ s = 24.7 ◦ ccw

(c) σ 1 = 26.2, σ 2 = 7.78, σ 3 = 0, φ p = 69.7 ◦ ccw ;

70 [w/(24EI )]

1 = 9.43, σ ave = 14, φ s = 16.0 ◦ cw

4–12 σ max = −20.4 kpsi, y B

3–13 σ left = −1.565 mm, y right = −1.565 mm,

4–15 y

= 10.2 kpsi, δ = 0.0245 in, ǫ 1 = 0.000 340,

midspan = 0.5868 mm

= 0.292, ǫ 2 −0.000 049 7 in

4–18 y max = −0.0130 in

Budynas−Nisbett: Shigley’s

1035 Mechanical Engineering

Back Matter

Appendix B: Answers to

© The McGraw−Hill

Selected Problems

Companies, 2008

Design, Eighth Edition

Mechanical Engineering Design

4–20 z A = 0.0368 in, z B = −0.00430 in

B–6 Chapter 6

4–26 Use d =1 3 8 in

6–1 S e = 85.7 kpsi

4–30 y B = −0.0459 in 6–3 S e ′ = 33.1 kpsi, σ F ′ = 112.4 kpsi, b = −0.08426, 4–37 y A = −0.101 in, y x =20 in = −0.104 in

f = 0.8949, a = 106.0 kpsi, S f = 47.9 kpsi, 4–46 y A = −0.138 in

N = 368 250 cycles

4–49 y x =10 in = −0.0167 in 6–5 ( S f ) ax = 162N −0.0851 kpsi, 10 3 ≤

4–52 (a) σ b = 76.5 kpsi, σ c = −15.2 kpsi,

N ≤ 10 cycles

(b) σ b = 78.4 kpsi, σ c = −13.3 kpsi

6–6 S e = 241 MPa

6–10 S e ′ = 220 MPa, k a = 0.899, k b = 1, k c = 0.85, same direction

4–58 R O = 3.89 kip, R C = 1.11 kip, both in

S e = 168.1 MPa, K t = 2.5, K f = 2.28,

4–61 σ BE = 140 MPa, σ DF = 71.2 MPa,

F a = 19.7 kN, F y = 98.7 kN

6–12 Yield: n y = 1.18. Fatigue: (a) n f = 1.06, y D = −0.339 mm

y B = −0.670 mm, y C = −2.27 mm,

(b) n f = 1.31, (c) n f = 1.32

6–17 n y = 5.06, (a) n f = 2.17, (b) n f = 2.28 4–69 δ = 0.476 mm

4–66 δ A = (π + 4)P R 3 /( 4E I ), δ B =πPR 3 /( 4E I )

6–23 At the fillet n f = 1.61

4–75 (a) t = 0.5 in, (b) No 6–24 (a) T = 3.22 N · m, (b) T = 3.96 N · m,

4–83 y max = 2k 1 a/(k 1 +k 2 )

(c) n y = 1.91 6–27 (a) P all = 16.0 kN, n y = 5.73, (b) P all = 51.0 kN,

n y = 3.90

B–5 Chapter 5

6–29 (a) 24 900 cycles, (b) 27 900 cycles 5–2 (a) MSS: n = 4.17, DE: n = 4.17, (b) MSS:

6–34 Rotation presumed. S ′ e = 55.7 LN(1, 0.138) kpsi, n = 4.17, DE: n = 4.81, (c) MSS: n = 2.08, DE:

k a = 0.768 LN(1, 0.058), k b = 0.879, S e = n = 2.41, (c) MSS: n = 4.17, DE: n = 4.81