65
r = radius of gyration = I/A J = polar moment of inertia Z p = polar section modulus Circle A–1 Properties of areas.* *Symbols used are: A = area I = moment of inertia S = Section modulus Circumference = πD = 2πR A = s 2 A = A = bh r = D 2 + d 2 4 r x = s 12 I x = s 4 12 S x = s 3 6 r x = h 12 r y = b 12 I x = bh 3 12 I y = hb 3 12 S y = hb 2 6 S x = bh 2 6 J = π(D 4 d 4 ) 32 A = π(D 2 d 2 ) 4 I = π(D 4 d 4 ) 64 S = π(D 4 d 4 ) 32D Z p = π(D 4 d 4 ) 16D r = = R 2 D 4 J = πD 4 32 πD 2 = πR 2 4 I = πD 4 64 S = πD 3 32 Z p = πD 3 16 Hollow circle (tube) Square Rectangle Y X X s h X C X s/2 h/2 b/2 b Y s R D D d Appendix 690 Untitled-1.indd 1 05/02/15 6:37 PM

Mott Appendix

Embed Size (px)

DESCRIPTION

DATA ASTM

Citation preview

r = radius of gyration = I/A J = polar moment of inertiaZp = polar section modulus

Circle

A–1 Properties of areas.**Symbols used are:

A = areaI = moment of inertiaS = Section modulus

Circumference = πD = 2πR

A = s2

A =

A = bh

r = D2 + d2

4

rx =s12

Ix =s4

12

Sx =s3

6

rx =h12

ry =b12

Ix =bh3

12

Iy =hb3

12Sy =

hb2

6

Sx =bh2

6

J = π(D4 – d4)32

A = π(D2 – d2)4

I = π(D4 – d4)64

S = π(D4 – d4)32D Zp = π(D4 – d4)

16D

r = = R2

D4

J = πD4

32

πD2= πR2

4

I = πD4

64

S = πD3

32 Zp = πD3

16

Hollow circle (tube)

Square

RectangleY

X X s

hXCX

s/2

h/2

b/2b

Y

s

R

D

Dd

Appendix

690

Untitled-1.indd 1 05/02/15 6:37 PM

Appendix 691

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 691 TEAM-B 103:PEQY138:Appendix:

0.015 6250.031 250.062 50.093 750.125 0

5.00055 5.250

5.5005.7506.000

0.0100.0120.0160.0200.025

0.0320.0400.050.060.08

0.100.120.160.20

0.240.300.40

0.500.600.801.00

1.201.401.601.80

6.507.007.508.00

19.0019.5020.00

5.405.605.806.00

17.0017.5018.00

15.5016.0016.50

13.5014.0014.5015.00

11.0011.5012.0012.5013.00

8.50 1

1.2

1.6

2

2.5

3

4

5

6

8

1.1

1.4

1.8

2.2

2.8

3.5

4.5

5.5

7

9

11

14

18

22

28

35

45

55

70

90

10

12

16

20

25

30

40

50

60

80

110

140

180

220

280

350

450

550

700

900

100

120

160

200

250

300

400

500

600

800

1000

9.009.50

10.0010.50

18.50

4.805.005.20

4.004.204.404.60

3.003.203.403.603.80

2.002.202.402.602.80

6.5007.0007.5008.0008.500

9.0009.500

10.00010.500

11.00011.50012.000

12.50013.00013.50014.000

14.50015.00015.50016.000

16.50017.00017.50018.000

18.50019.00019.50020.000

0.156 250.187 50.250 00.312 50.375 0

0.437 50.500 00.562 50.625 0

0.687 50.750 00.875 0

1.0001.2501.5001.750

2.0002.2502.5002.750

3.0003.2503.5003.750

4.0004.2504.5004.750

Fractional (in)

A–2 Preferred basic sizes.

Decimal (in) First Second First Second First

Metric (mm)

Second

14

1641

321

163

3218

5323

16145

1638

716129

1658

11163478

5 12

67

8

9

10

12

7 12

8 12

9 12

10 12

1111 1

212

12 12

1313 1

2

11

14

1 12

1 34

22

14

2 12

2 34

33

14

3 12

3 34

44

14

4 12

4 34

14

14 12

1516

12

1617

12

1718

12

18 12

1919

20

12

15

56

34

692 Appendix

Untitled-1.indd 2 05/02/15 6:37 PM

A–3 Screw threads.

Size

Basic majordiameter, D

(in)

Tensilestress area

(in2)

Tensilestress area

(in2)�reads

per inch, n�reads

per inch, n

Basic majordiameter, D

(in)�reads

per inch, n�reads

per inch, nSize

Tensilestress area

(in2)

Tensilestress area

(in2)

0123

456

81012

0.060 00.073 00.086 00.099 0

—645648

0.112 00.125 00.138 0

0.164 00.190 00.216 0

404032

322424

—0.002 630.003 700.004 87

0.006 040.007 96 0.009 09

0.014 00.017 5 0.024 2

80726456

484440

363228

0.001 80

0.036 40.058 00.087 80.118 70.159 9

0.2030.2560.3730.509

0.6630.8561.0731.315

1.581——

2824242020

18181614

12121212

12——

2018161413

1211109

8776

65

0.002 780.003 940.005 23

0.006 610.008 300.010 15

0.014 740.020 00.025 8

(a) American Standard thread dimensions, numbered sizes

(b) American Standard thread dimensions, fractional sizes

Coarse threads: UNC

Coarse threads: UNC Fine threads: UNF

Fine threads: UNF

4 12

1 12

1 38

11

18

78

34

58

916

12

716

38

145

16

1 14

12

34

0.225 00.312 50.375 00.437 50.500 0

0.562 50.625 00.750 00.875 0

1.0001.1251.2501.375

1.5001.7502.000

0.031 80.052 40.077 50.106 30.141 9

0.1820.2260.3340.462

0.6060.7630.9691.155

1.4051.902.50

Appendix  693

Untitled-1.indd 3 05/02/15 6:37 PM

694 Appendix

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 694 TEAM-B 103:PEQY138:Appendix:

Y Y

Sect

ion

mod

ulus

, Sx

in3

mm

3

Mom

ent o

f ine

rtia

, Ix

in4

mm

4

Are

a of

sect

ion

in2

mm

2

Act

ual s

ize

Nom

inal

size

A–4

Pro

pert

ies o

f sta

ndar

d w

ood

beam

s.

inm

m

X

50.1

× 1

03

124

× 10

3

215

× 10

3

351

× 10

3

518

× 10

3

117

× 10

3

289

× 10

3

503

× 10

3

818

× 10

3

1211

× 1

03

454

× 10

3

846

× 10

3

1355

× 1

03

1983

× 1

03

1152

× 1

03

1852

× 1

03

2704

× 1

03

2343

× 1

03

3425

× 1

03

2.23

× 1

06

8.66

× 1

06

19.8

× 1

06

41.2

× 1

06

74.1

× 1

06

5.21

× 1

06

20.2

× 1

06

46.2

× 1

06

96.1

× 1

06

172

× 10

6

31.8

× 1

06

80.3

× 1

06

164

× 10

6

290

× 10

6

110

× 10

6

223

× 10

6

396

× 10

6

283

× 10

6

501

× 10

6

4146

× 1

03

3.39

× 1

03

5.32

× 1

03

7.01

× 1

03

8.95

× 1

03

10.8

8 ×

103

7.90

× 1

03

12.4

2 ×

103

16.3

9 ×

103

20.9

0 ×

103

25.4

2 ×

103

19.5

5 ×

103

26.6

5 ×

103

33.7

4 ×

103

40.8

4 ×

103

36.3

2 ×

103

46.0

0 ×

103

55.6

8 ×

103

58.2

6 ×

103

70.5

2 ×

103

85.3

5 ×

103

2 ×

42

× 6

2 ×

82

× 10

2 ×

124

× 4

4 ×

64

× 8

4 ×

104

× 12

6 ×

66

× 8

6 ×

106

× 12

8 ×

88

× 10

8 ×

1210

× 1

010

× 1

212

× 1

2

1.5

× 3.

51.

5 ×

5.5

1.5

× 7.

251.

5 ×

9.25

1.5

× 11

.25

3.5

× 3.

53.

5 ×

5.5

3.5

× 7.

253.

5 ×

9.25

3.5

× 11

.25

5.5

× 5.

55.

5 ×

7.5

5.5

× 9.

55.

5 ×

11.5

7.5

× 7.

57.

5 ×

9.5

7.5

× 11

.59.

5 ×

9.5

9.5

× 11

.511

.5 ×

11.

5

38 ×

89

38 ×

140

38 ×

184

38 ×

235

38 ×

286

89 ×

89

89 ×

140

89 ×

184

89 ×

235

89 ×

286

140

× 14

014

0 ×

191

140

× 24

114

0 ×

292

191

× 19

119

1 ×

241

191

× 29

224

1 ×

241

241

× 29

229

2 ×

292

5.25

8.25

10.8

713

.87

16.8

712

.25

19.2

525

.432

.439

.430

.341

.352

.363

.356

.371

.386

.390

.310

9.3

132.

360

7 ×

106

3.06

7.56

13.1

421

.431

.6 7.15

17.6

530

.749

.973

.927

.751

.682

.712

1 70.3

113

165

143

209

253

X

5.36

20.8

47.6

98.9

178 12

.51

48.5

111.

123

141

5 76.3

193

393

697

264

536

951

679

1204

1458

695

Untitled-1.indd 4 05/02/15 6:37 PM

A–5

Pro

pert

ies

of s

teel

ang

les

(L-s

hape

s) U

.S.C

usto

mar

y un

its.

Sec

tion

pro

pert

ies

Wei

ght

Axi

s X

-XA

xis

Y-Y

Axi

s Z

-ZS

hape

per

foot

Are

a, A

I xS x

yI y

S yx

r�

Ref

.(i

n)(i

n)(i

n)(l

b/ft

)(i

n2 )(i

n4 )(i

n3 )(i

n)(i

n4 )(i

n3 )(i

n)(i

n)(d

eg.)

aL

8 �

8 �

151

.315

.189

.115

.82.

3689

.115

.82.

361.

5645

.0

bL

8 �

8 �

26.7

7.84

48.8

8.36

2.17

48.8

8.36

2.17

1.59

45.0

cL

8 �

4 �

137

.611

.10

69.7

14.0

03.

0311

.63.

941.

040.

844

13.9

dL

8 �

4 �

19.7

5.80

38.6

7.48

2.84

6.75

2.15

0.85

40.

863

14.9

eL

6 �

6 �

28.8

8.46

28.1

6.64

1.77

28.1

6.64

1.77

1.17

45.0

fL

6 �

6 �

14.9

4.38

15.4

3.51

1.62

15.4

3.51

1.62

1.19

45.0

gL

6 �

4 �

23.5

6.90

24.4

6.23

2.08

8.63

2.95

1.08

0.85

723

.2

hL

6 �

4 �

12.2

3.58

13.4

3.30

1.94

4.84

1.58

0.94

00.

871

24.1

iL

4 �

4 �

12.7

3.75

5.52

1.96

1.18

5.52

1.96

1.18

0.77

645

.0

jL

4 �

4 �

6.58

1.93

3.00

1.03

1.08

3.00

1.03

1.08

0.78

345

.0

kL

4 �

3 �

11.1

3.25

5.02

1.87

1.32

2.40

1.10

0.82

20.

633

28.5

lL

4 �

3 �

5.75

1.69

2.75

0.98

81.

221.

330.

585

0.72

50.

639

29.2

mL

3 �

3 �

9.35

2.75

2.20

1.06

0.92

92.

201.

060.

929

0.58

045

.0

nL

3 �

3 �

4.89

1.44

1.23

0.56

90.

836

1.23

0.56

90.

836

0.58

545

.0

oL

3 �

2 �

7.70

2.26

1.92

1.00

1.08

0.66

70.

470

0.58

00.

425

22.4

pL

3 �

2 �

4.09

1.20

1.09

0.54

10.

980

0.39

00.

258

0.48

70.

431

23.6

qL

2 �

2 �

4.65

1.37

0.47

60.

348

0.63

20.

476

0.34

80.

632

0.38

645

.0

rL

2 �

2 �

3.21

0.94

40.

346

0.24

40.

586

0.34

60.

244

0.58

60.

387

45.0

sL

2 �

2 �

1.67

0.49

10.

189

0.12

90.

534

0.18

90.

129

0.53

40.

391

45.0

1 81 43 81 41 21 41 21 41 21 41 23 83 43 83 41 21 2

696

X

Y

X

Z

Yx

Z

y

Cen

troi

d

α

XX

Z

Z

Y

Yx

y

Cen

troi

d

α

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 696 TEAM-B 103:PEQY138:Appendix:

A–5(S

I)P

rope

rtie

s of

ste

el a

ngle

s (L

-sha

pes)

SI

units

.

Sec

tion

pro

pert

ies

Mas

sW

eigh

tA

xis

X-X

Axi

s Y-

YA

xis

Z-Z

Sha

pepe

r m

per

mA

rea,

AI x

S xy

I yS y

xr

Ref

.(m

m)

(mm

)(m

m)

(kg/

m)

(N/m

)(m

m2 )

(mm

4 )(m

m3 )

(mm

)(m

m4 )

(mm

3 )(m

m)

(mm

)(d

eg.)

aL

203

�20

3 �

25.4

76.3

749

9740

3.71

E�

072.

59E

�05

59.9

3.71

E�

072.

59E

�05

59.9

39.6

45.0

bL

203

�20

3 �

12.7

39.7

390

5060

2.03

E�

071.

37E

�05

55.1

2.03

E�

071.

37E

�05

55.1

40.4

45.0

cL

203

�10

2 �

25.4

55.9

549

7160

2.90

E�

072.

29E

�05

77.0

4.83

E�

066.

46E

�04

26.4

21.4

13.9

dL

203

�10

2 �

12.7

29.3

288

3740

1.61

E�

071.

23E

�05

72.1

2.81

E�

063.

52E

�04

21.7

21.9

14.9

eL

152

�15

2 �

1942

.942

054

601.

17E

�07

1.09

E�

0545

.01.

17E

�07

1.09

E�

0545

.029

.745

.0

fL

152

�15

2 �

9.5

22.2

217

2830

6.41

E�

065.

75E

�04

41.1

6.41

E�

065.

75E

�04

41.1

30.2

45.0

gL

152

�10

2 �

1935

.034

344

501.

02E

�07

1.02

E�

0552

.83.

59E

�06

4.84

E�

0427

.421

.823

.2

hL

152

�10

2 �

9.5

18.2

178

2310

5.58

E�

065.

41E

�04

49.3

2.01

E�

062.

59E

�04

23.9

22.1

24.1

iL

102

�10

2 �

12.7

18.9

185

2420

2.30

E�

063.

21E

�04

30.0

2.30

E�

063.

21E

�04

30.0

19.7

45.0

jL

102

�10

2 �

6.4

9.79

96.0

1250

1.25

E�

061.

69E

�04

27.4

1.25

E�

061.

69E

�04

27.4

19.9

45.0

kL

102

�76

�12

.716

.516

221

002.

09E

�06

3.06

E�

0433

.59.

99E

�05

1.80

E�

0420

.916

.128

.5

lL

102

�76

�6.

48.

5683

.910

901.

14E

�06

1.62

E�

0431

.05.

54E

�05

9.59

E�

0318

.416

.229

.2

mL

76

�76

�12

.713

.913

617

709.

16E

�05

1.74

E�

0423

.69.

16E

�05

1.74

E�

0423

.614

.745

.0

nL

76

�76

�6.

47.

2871

.492

95.

12E

�05

9.33

E�

0321

.25.

12E

�05

9.33

E�

0321

.214

.945

.0

oL

76

�51

�12

.711

.511

214

607.

99E

�05

1.64

E�

0427

.42.

78E

�05

7.70

E�

0314

.710

.822

.4

pL

76

�51

�6.

46.

0959

.777

44.

54E

�05

8.87

E�

0324

.91.

62E

�05

4.23

E�

0312

.410

.923

.6

qL

51

�51

�9.

56.

9267

.988

41.

98E

�05

5.70

E�

0316

.11.

98E

�05

5.70

E�

0316

.19.

8045

.0

rL

51

�51

�6.

44.

7846

.960

91.

44E

�05

4.00

E�

0314

.91.

44E

�05

4.00

E�

0314

.99.

8345

.0

sL

51

�51

�3.

22.

4824

.431

77.

87E

�04

2.11

E�

0313

.67.

87E

�04

2.11

E�

0313

.69.

9345

.0

X

Y

X

Z

Yx

Z

y

Cen

troi

d

α

697

XX

Z

Z

Y

Yx

y

Cen

troi

d

α

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 697 TEAM-B 103:PEQY138:Appendix:

A–6

Pro

pert

ies

of A

mer

ican

Sta

ndar

d st

eel c

hann

els

(C-s

hape

s) U

.S.C

usto

mar

y un

its.

Sec

tion

pro

pert

ies

Web

Fla

nge

Axi

s X

-XA

xis

Y-Y

Sha

peA

rea,

AD

epth

, dT

hick

ness

, tw

Wid

th, b

fT

hick

ness

, tf

I xS x

I yS y

xR

ef.

(in)

(lb/

ft)

(in2 )

(in)

(in)

(in)

Ave

rage

(in

)(i

n4 )(i

n3 )(i

n4 )(i

n3 )(i

n)

aC

15

�50

14.7

15.0

0.71

63.

720.

650

404

53.8

11.0

3.77

0.79

9

bC

15

�40

11.8

15.0

0.52

03.

520.

650

348

46.5

9.17

3.34

0.77

8

cC

12

�30

8.82

12.0

0.51

03.

170.

501

162

27.0

5.12

2.05

0.67

4

dC

12

�25

7.35

12.0

0.38

73.

050.

501

144

24.0

4.45

1.87

0.67

4

eC

10

�30

8.82

10.0

0.67

33.

030.

436

103

20.7

3.93

1.65

0.64

9

fC

10

�20

5.88

10.0

0.37

92.

740.

436

78.9

15.8

2.80

1.31

0.60

6

gC

9 �

205.

889.

00.

448

2.65

0.41

360

.913

.52.

411.

170.

583

hC

9

�15

4.41

9.0

0.28

52.

490.

413

51.0

11.3

1.91

1.01

0.58

6

iC

8

�18

.75

5.51

8.0

0.48

72.

530.

390

43.9

11.0

1.97

1.01

0.56

5

jC

8

�11

.53.

388.

00.

220

2.26

0.39

032

.58.

141.

310.

775

0.57

2

kC

7

�14

.75

4.33

7.0

0.41

92.

300.

366

27.2

7.78

1.37

0.77

20.

532

lC

7

�9.

82.

877.

00.

210

2.09

0.36

621

.26.

070.

957

0.61

70.

541

mC

6

�13

3.83

6.0

0.43

72.

160.

343

17.3

5.78

1.05

0.63

80.

514

nC

6

�8.

22.

406.

00.

200

1.92

0.34

313

.14.

350.

687

0.48

80.

512

oC

5

�9

2.64

5.0

0.32

51.

890.

320

8.89

3.56

0.62

40.

444

0.47

8

pC

5

�6.

71.

975.

00.

190

1.75

0.32

07.

482.

990.

470

0.37

20.

484

qC

4

�7.

252.

134.

00.

321

1.72

0.29

64.

582.

290.

425

0.33

70.

459

rC

4

�5.

41.

594.

00.

184

1.58

0.29

63.

851.

920.

312

0.27

70.

457

sC

3

�6

1.76

3.0

0.35

61.

600.

273

2.07

1.38

0.30

00.

263

0.45

5

tC

3

�4.

11.

213.

00.

170

1.41

0.27

31.

651.

100.

191

0.19

60.

437

698

X

Y Y

X

xC

entr

oid

Web

Flan

ge

Dep

th

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 698 TEAM-B 103:PEQY138:Appendix:

A–6

(SI)

Pro

pert

ies

of A

mer

ican

Sta

ndar

d st

eel c

hann

els

(C-s

hape

s) S

I un

its.

Sec

tion

pro

pert

ies

Web

F

lang

eA

xis

X-X

Axi

s Y-

Y

Sha

peW

t/m

Are

a, A

Dep

th, d

Thi

ckne

ss, t

wW

idth

, bf

Thi

ckne

ss, t

fI x

S xI y

S yx

Ref

.(m

m)

(kg/

m)

(KN

/m)

(mm

2 )(m

m)

(mm

)(m

m)

(mm

)(m

m4 )

(mm

3 )(m

m4 )

(mm

3 )(m

m)

aC

380

�74

0.73

094

8038

118

.294

.416

.51.

68E

�08

8.82

E�

054.

58E

�06

6.18

E�

0420

.3

bC

380

�60

0.58

476

1038

113

.289

.416

.51.

45E

�08

7.62

E�

053.

82E

�06

5.47

E�

0419

.8

cC

300

�45

0.43

856

9030

513

.080

.512

.76.

74E

�07

4.43

E�

052.

13E

�06

3.36

E�

0417

.1

dC

300

�37

0.36

547

4030

59.

8377

.412

.75.

99E

�07

3.93

E�

051.

85E

�06

3.06

E�

0417

.1

eC

250

�45

0.43

856

9025

417

.177

.011

.14.

29E

�07

3.39

E�

051.

64E

�06

2.70

E�

0416

.5

fC

250

�30

0.29

237

9025

49.

6369

.611

.13.

28E

�07

2.59

E�

051.

17E

�06

2.15

E�

0415

.4

gC

230

�30

0.29

237

9022

911

.467

.310

.52.

53E

�07

2.21

E�

051.

00E

�06

1.92

E�

0414

.8

hC

230

�22

0.21

928

5022

97.

2463

.110

.52.

12E

�07

1.85

E�

057.

95E

�05

1.66

E�

0414

.9

iC

200

�27

.90.

274

3560

203

12.4

64.2

9.91

1.83

E�

071.

80E

�05

8.20

E�

051.

66E

�04

14.4

jC

200

�17

.10.

168

2180

203

5.59

57.4

9.91

1.35

E�

071.

33E

�05

5.45

E�

051.

27E

�04

14.5

kC

180

�22

0.21

527

9017

810

.658

.49.

301.

13E

�07

1.28

E�

055.

70E

�05

1.27

E�

0413

.5

lC

180

�14

.60.

143

1850

178

5.33

53.1

9.30

8.82

E�

069.

95E

�04

3.98

E�

051.

01E

�04

13.7

mC

150

�19

.30.

190

2470

152

11.1

54.8

8.71

7.20

E�

069.

47E

�04

4.37

E�

051.

05E

�04

13.1

nC

150

�12

.20.

120

1550

152

5.08

48.8

8.71

5.45

E�

067.

13E

�04

2.86

E�

058.

00E

�03

13.0

oC

130

�13

0.12

817

0012

78.

2647

.98.

133.

70E

�06

5.83

E�

042.

60E

�05

7.28

E�

0312

.1

pC

130

�10

.40.

102

1270

127

4.83

44.5

8.13

3.11

E�

064.

90E

�04

1.96

E�

056.

10E

�03

12.3

qC

100

�10

.80.

106

1370

102

8.15

43.7

7.52

1.91

E�

063.

75E

�04

1.77

E�

055.

52E

�03

11.7

rC

100

�8

0.07

8810

2010

24.

6740

.27.

521.

60E

�06

3.15

E�

041.

30E

�05

4.54

E�

0311

.6

sC

80

�8.

90.

0876

1140

76.2

9.04

40.5

6.93

8.62

E�

052.

26E

�04

1.25

E�

054.

31E

�03

11.6

tC

80

�6.

10.

0598

777

76.2

4.32

35.8

6.93

6.87

E�

051.

80E

�04

7.95

E�

043.

21E

�03

11.1

X

Y Y

X

xC

entr

oid

Web

Flan

ge

Dep

th

699

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 699 TEAM-B 103:PEQY138:Appendix:

A–7

Pro

pert

ies

of s

teel

wid

e-fla

nge

shap

es (

W-s

hape

s) U

.S.C

usto

mar

y un

its.

Sec

tion

pro

pert

ies

Web

Fla

nge

Axi

s X

-XA

xis

Y-Y

Sha

peA

rea,

AD

epth

, dT

hick

ness

, tw

Wid

th, b

fT

hick

ness

,tf

I xS x

I yS y

Ref

.(i

n)(l

b/ft

)(i

n2 )(i

n)(i

n)(i

n)(i

n)(i

n4 )(i

n3 )(i

n4 )(i

n3 )

aW

30

� 1

7351

.030

.40.

655

15.0

1.07

082

3054

159

879

.8

bW

30

�10

831

.729

.80.

545

10.5

0.76

044

7029

914

627

.9

cW

27

�14

643

.127

.40.

605

14.0

0.97

556

6041

444

363

.5

dW

27

�10

230

.027

.10.

515

10.0

0.83

036

2026

713

927

.8

eW

24

�76

22.4

23.9

0.44

08.

990.

680

2100

176

82.5

18.4

fW

24

�68

20.1

23.7

0.41

58.

970.

585

1830

154

70.4

15.7

gW

21

�73

21.5

21.2

0.45

58.

300.

740

1600

151

70.6

17.0

hW

21

�57

16.7

21.1

0.40

56.

560.

650

1170

111

30.6

9.35

i W

18

�55

16.2

18.1

0.39

07.

530.

630

890

98.3

44.9

11.9

jW

18

�40

11.8

17.9

0.31

56.

020.

525

612

68.4

19.1

6.35

kW

14

�43

12.6

13.7

0.30

58.

000.

530

428

62.7

45.2

11.3

lW

14

�26

7.69

13.9

0.25

55.

030.

420

245

35.3

8.91

3.54

mW

12

�65

19.1

12.1

0.39

012

.00.

605

533

87.9

174

29.1

nW

12

�30

8.79

12.3

0.26

06.

520.

440

238

38.6

20.3

6.24

oW

12

�16

4.71

12.0

0.22

03.

990.

265

103

17.1

2.82

1.41

pW

10

�60

17.6

010

.20.

420

10.1

0.68

034

166

.711

623

.0

qW

10

�30

8.84

10.5

0.30

05.

810.

510

170

32.4

16.7

5.75

rW

10

�12

3.54

9.87

0.19

03.

960.

210

53.8

10.9

2.18

1.10

sW

8

�40

11.7

08.

250.

360

8.07

0.56

014

635

.549

.112

.2

tW

8

�21

6.16

8.28

0.25

05.

270.

400

75.3

18.2

9.77

3.71

uW

8

�10

2.96

7.89

0.17

03.

940.

205

30.8

7.81

2.09

1.06

vW

6

�15

4.43

5.99

0.23

05.

990.

260

29.1

9.72

9.32

3.11

wW

6

�12

3.55

6.03

0.23

04.

000.

280

22.1

7.31

2.99

1.50

xW

5

�19

5.54

5.15

0.27

05.

030.

430

26.2

10.2

9.13

3.63

yW

5

�16

4.68

5.01

0.24

05.

000.

360

21.3

8.51

7.51

3.00

zW

4

�13

3.83

4.16

0.28

04.

060.

345

11.3

5.46

3.86

1.90

700

Flan

ge

Dep

thW

eb

XX

YY

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 700 TEAM-B 103:PEQY138:Appendix:

A–7(S

I)P

rope

rtie

s of

ste

el w

ide-

flang

e sh

apes

(W

-sha

pes)

SI

units

.

Sec

tion

pro

pert

ies

Web

Fla

nge

Axi

s X

-XA

xis

Y-Y

Sha

peW

t/m

Are

a, A

Dep

th, d

Thi

ckne

ss, t

wW

idth

, bf

Thi

ckne

ss, t

fI x

S xI y

S yR

ef.

(mm

)(k

g/m

)(K

N/M

)(m

m2 )

(mm

)(m

m)

(mm

)(m

m)

(mm

4 )(m

m3 )

(mm

4 )(m

m3 )

aW

760

�25

72.

525

3290

077

216

.638

127

.23.

43E

�09

8.87

E�

062.

49E

�08

1.31

E�

06

bW

760

�16

11.

576

2050

075

713

.826

719

.31.

86E

�09

4.90

E�

066.

08E

�07

4.57

E�

05

cW

690

�21

72.

131

2780

069

615

.435

624

.82.

36E

�09

6.79

E�

061.

84E

�08

1.04

E�

06

dW

690

�15

21.

489

1940

068

813

.125

421

.11.

51E

�09

4.38

E�

065.

79E

�07

4.56

E�

05

eW

610

�11

31.

109

1450

060

711

.222

817

.38.

74E

�08

2.88

E�

063.

43E

�07

3.02

E�

05

fW

610

�10

10.

993

1300

060

210

.522

814

.97.

62E

�08

2.52

E�

062.

93E

�07

2.57

E�

05

gW

530

�10

91.

066

1390

053

811

.621

118

.86.

66E

�08

2.47

E�

062.

94E

�07

2.79

E�

05

hW

530

�85

0.83

210

800

536

10.3

167

16.5

4.87

E�

081.

82E

�06

1.27

E�

071.

53E

�05

iW

460

�82

0.80

310

500

460

9.91

191

16.0

3.70

E�

081.

61E

�06

1.87

E�

071.

95E

�05

jW

460

�60

0.58

476

1045

58.

0015

313

.32.

55E

�08

1.12

E�

067.

95E

�06

1.04

E�

05

kW

360

�64

0.62

881

3034

87.

7520

313

.51.

78E

�08

1.03

E�

061.

88E

�07

1.85

E�

05

lW

360

�39

0.38

049

6035

36.

4812

810

.71.

02E

�08

5.79

E�

053.

71E

�06

5.80

E�

04

mW

310

�97

0.94

912

300

307

9.91

305

15.4

2.22

E�

081.

44E

�06

7.24

E�

074.

77E

�05

nW

310

�44

.50.

437

5670

312

6.60

166

11.2

9.91

E�

076.

33E

�05

8.45

E�

061.

02E

�05

oW

310

�23

.80.

233

3040

305

5.59

101

6.73

4.29

E�

072.

80E

�05

1.17

E�

062.

31E

�04

pW

250

�89

0.87

611

400

259

10.7

257

17.3

1.42

E�

081.

09E

�06

4.83

E�

073.

77E

�05

qW

250

�44

.80.

439

5700

267

7.62

148

137.

08E

�07

5.31

E�

056.

95E

�06

9.42

E�

04

rW

250

�17

.90.

176

2280

251

4.83

101

5.33

2.24

E�

071.

79E

�05

9.07

E�

051.

80E

�04

sW

200

�59

0.57

975

5021

09.

1420

514

.26.

08E

�07

5.82

E�

052.

04E

�07

2.00

E�

05

tW

200

�31

.30.

307

3970

210

6.35

134

10.2

3.13

E�

072.

98E

�05

4.07

E�

066.

08E

�04

uW

200

�15

0.14

619

1020

04.

3210

05.

211.

28E

�07

1.28

E�

058.

70E

�05

1.74

E�

04

vW

150

�22

.50.

221

2860

152

5.84

152

6.60

1.21

E�

071.

59E

�05

3.88

E�

065.

10E

�04

wW

150

�18

0.17

522

9015

35.

8410

27.

119.

20E

�06

1.20

E�

051.

24E

�06

2.46

E�

04

xW

130

�28

.10.

276

3570

131

6.86

128

10.9

1.09

E�

071.

67E

�05

3.80

E�

065.

95E

�04

yW

130

�23

.80.

233

3020

127

6.10

127

9.14

8.87

E�

061.

39E

�05

3.13

E�

064.

92E

�04

zW

100

�19

.30.

189

2470

106

7.11

103

8.76

4.70

E�

068.

95E

�04

1.61

E�

063.

11E

�04

Flan

ge

Dep

thW

eb

XX

YY

701

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 701 TEAM-B 103:PEQY138:Appendix:

A–8

Pro

pert

ies

of A

mer

ican

Sta

ndar

d st

eel b

eam

s (S

-sha

pes)

U.S

.Cus

tom

ary

units

.

Sec

tion

pro

pert

ies

Web

Fla

nge

Axi

s X

-XA

xis

Y-Y

Sha

peA

rea,

AD

epth

, dT

hick

ness

, tw

Wid

th, b

fT

hick

ness

, tf

I xS x

I yS y

Ref

.(i

n)(l

b/ft

)(i

n2 )(i

n)(i

n)(i

n)(i

n)(i

n4 )(i

n3 )(i

n4 )(i

n3 )

aS

24

�12

135

.524

.50.

800

8.05

1.09

031

6025

883

.020

.6

bS

24

�90

26.5

24.0

0.62

57.

130.

870

2250

187

44.7

12.5

cS

20

�96

28.2

20.3

0.80

07.

200.

920

1670

165

49.9

13.9

dS

20

�75

22.0

20.0

0.63

56.

390.

795

1280

128

29.5

9.25

eS

20

�66

19.4

20.0

0.50

56.

260.

795

1190

119

27.5

8.78

fS

18

�70

20.5

18.0

0.71

16.

250.

691

923

103

24.0

7.69

gS

18

�54

.716

.018

.00.

461

6.00

0.69

180

189

.020

.76.

91

hS

15

�50

14.7

15.0

0.55

05.

640.

622

485

64.7

15.6

5.53

iS

15

�42

.912

.615

.00.

411

5.50

0.62

244

659

.414

.35.

19

jS

12

�50

14.6

12.0

0.68

75.

480.

659

303

50.6

15.6

5.69

kS

12

�35

10.2

12.0

0.42

65.

080.

544

228

38.1

9.84

3.88

lS

10

�35

10.3

10.0

0.59

44.

940.

491

147

29.4

8.30

3.36

mS

10

�25

.47.

4510

.00.

311

4.66

0.49

112

324

.66.

732.

89

nS

8 �

236.

768.

000.

441

4.17

0.42

564

.716

.24.

272.

05

oS

8

�18

.45.

408.

000.

271

4.00

0.42

557

.514

.43.

691.

84

pS

6

�17

.25

5.06

6.00

0.46

53.

570.

359

26.2

8.74

2.29

1.28

qS

6

�12

.53.

666.

000.

232

3.33

0.35

922

.07.

341.

801.

08

rS

5

�10

2.93

5.00

0.21

43.

000.

326

12.3

4.90

1.19

0.79

5

sS

4

�9.

52.

794.

000.

326

2.80

0.29

36.

83.

380.

887

0.63

5

tS

4

�7.

72.

264.

000.

193

2.66

0.29

36.

053.

030.

748

0.56

2

uS

3

�7.

52.

203.

000.

349

2.51

0.26

02.

911.

940.

578

0.46

1

vS

3

�5.

71.

663.

000.

170

2.33

0.26

02.

501.

670.

447

0.38

3

702

Flan

ge

Dep

thW

eb

XX

YY

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 702 TEAM-B 103:PEQY138:Appendix:

A–8(S

I)P

rope

rtie

s of

Am

eric

an S

tand

ard

stee

l bea

ms

(S-s

hape

s) S

I un

its.

Sec

tion

pro

pert

ies

Web

Fla

nge

Axi

s X

-XA

xis

Y-Y

Sha

peW

t/m

Are

a, A

Dep

th, d

Thi

ckne

ss, t

wW

idth

,bf

Thi

ckne

ss, t

fI x

S xI y

S yR

ef.

(mm

)(k

g/m

)(K

N/m

)(m

m2 )

(mm

)(m

m)

(mm

)(m

m)

(mm

4 )(m

m3 )

(mm

4 )(m

m3 )

aS

610

�18

01.

766

2290

062

220

.320

427

.71.

32E

�09

4.23

E�

063.

45E

�07

3.38

E�

05

bS

610

�13

41.

314

1710

061

015

.918

122

.19.

36E

�08

3.06

E�

061.

86E

�07

2.05

E�

05

cS

510

�14

31.

401

1820

051

620

.318

323

.46.

95E

�08

2.70

E�

062.

08E

�07

2.28

E�

05

dS

510

�11

21.

095

1420

050

816

.116

220

.25.

33E

�08

2.10

E�

061.

23E

�07

1.52

E�

05

eS

510

�98

.20.

963

1250

050

812

.815

920

.24.

95E

�08

1.95

E�

061.

14E

�07

1.44

E�

05

fS

460

�10

41.

022

1320

045

718

.115

917

.63.

84E

�08

1.69

E�

069.

99E

�06

1.26

E�

05

gS

460

�81

.40.

799

1030

045

711

.715

217

.63.

33E

�08

1.46

E�

068.

62E

�06

1.13

E�

05

hS

380

�74

0.73

094

8038

114

.014

315

.82.

02E

�08

1.06

E�

066.

49E

�06

9.06

E�

04

iS

380

�64

0.62

681

3038

110

.414

015

.81.

86E

�08

9.74

E�

055.

95E

�06

8.51

E�

04

jS

300

�74

0.73

094

2030

517

.413

916

.71.

26E

�08

8.29

E�

056.

49E

�06

9.33

E�

04

kS

300

�52

0.51

165

8030

510

.812

913

.89.

49E

�07

6.24

E�

054.

10E

�06

6.36

E�

04

lS

250

�52

0.51

166

5025

415

.112

512

.56.

12E

�07

4.82

E�

053.

45E

�06

5.51

E�

04

mS

250

�37

.80.

371

4810

254

7.9

118

12.5

5.12

E�

074.

03E

�05

2.80

E�

064.

74E

�04

nS

200

�34

0.33

643

6020

311

.210

610

.82.

69E

�07

2.66

E�

051.

78E

�06

3.36

E�

04

oS

200

�27

.40.

269

3480

203

6.9

102

10.8

2.39

E�

072.

36E

�05

1.54

E�

063.

02E

�04

pS

150

�25

.70.

252

3260

152

11.8

90.7

9.1

1.09

E�

071.

43E

�05

9.53

E�

052.

10E

�04

qS

150

�18

.60.

182

2360

152

5.9

84.6

9.1

9.16

E�

061.

20E

�05

7.49

E�

051.

77E

�04

rS

130

�15

0.14

618

9012

75.

476

.28.

35.

12E

�06

8.03

E�

044.

95E

�05

1.30

E�

04

sS

100

�14

.10.

138

1800

102

8.3

71.1

7.4

2.81

E�

065.

54E

�04

3.69

E�

051.

04E

�04

tS

100

�11

.50.

113

1460

102

4.9

67.6

7.4

2.52

E�

064.

97E

�04

3.11

E�

059.

21E

�03

uS

80

�11

.20.

110

1420

76.2

8.9

63.8

6.6

1.21

E�

063.

18E

�04

2.41

E�

057.

56E

�03

vS

80

�8.

50.

083

1070

76.2

4.3

59.2

6.6

1.04

E�

062.

74E

�04

1.86

E�

056.

28E

�03

Flan

ge

Dep

thW

eb

XX

YY

703

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 703 TEAM-B 103:PEQY138:Appendix:

A–9

Pro

pert

ies

of s

teel

str

uctu

ral t

ubin

g (H

SS

-sha

pes)

U.S

.Cus

tom

ary

units

.

Des

ign

Sec

tion

pro

pert

ies

wal

lth

ickn

ess

Wei

ght

Axi

s X

-XA

xis

Y-Y

Tors

iona

l con

stan

ts

Sha

pet w

per

foot

Are

a, A

I xS x

r xI y

S yr y

JC

Ref

. (i

n) (

in)

(in)

(in)

(lb/

ft)

(in2 )

(in4 )

(in3 )

(in)

(in4 )

(in3 )

(in)

(in4 )

(in3 )

aH

SS

8 �

8 �

1/2

0.46

548

.713

.512

531

.23.

0412

531

.23.

0420

452

.4

bH

SS

8 �

8 �

1/4

0.23

325

.87.

1070

.717

.73.

1570

.717

.73.

1511

128

.1

cH

SS

8 �

4 �

1/2

0.46

535

.19.

7471

.817

.92.

7123

.611

.81.

5661

.124

.4

dH

SS

8 �

4 �

1/4

0.23

319

.05.

2442

.510

.62.

8514

.47.

211.

6635

.313

.6

eH

SS

8 �

2 �

1/4

0.23

315

.64.

3028

.57.

122.

572.

942.

940.

827

9.36

6.35

fH

SS

6 �

6 �

1/2

0.46

535

.19.

7448

.316

.12.

2348

.316

.12.

2381

.128

.1

gH

SS

6 �

6 �

1/4

0.23

319

.05.

2428

.69.

542.

3428

.69.

542.

3445

.615

.4

hH

SS

6 �

4 �

1/4

0.23

315

.64.

3020

.96.

962.

2011

.15.

561.

6123

.610

.1

iH

SS

6 �

2 �

1/4

0.23

312

.23.

3713

.14.

371.

972.

212.

210.

810

6.55

4.70

jH

SS

4 �

4 �

1/2

0.46

521

.56.

0211

.95.

971.

4111

.95.

971.

4121

.011

.2

kH

SS

4 �

4 �

1/4

0.23

312

.23.

377.

803.

901.

527.

803.

901.

5212

.86.

56

lH

SS

4 �

2 �

1/4

0.23

38.

782.

444.

492.

251.

361.

481.

480.

779

3.82

3.05

mH

SS

3 �

3 �

1/4

0.23

38.

782.

443.

022.

011.

113.

022.

011.

115.

083.

52

nH

SS

3 �

2 �

1/4

0.23

37.

081.

972.

131.

421.

041.

111.

110.

751

2.52

2.23

oH

SS

2 �

2 �

1/4

0.23

35.

381.

510.

747

0.74

70.

704

0.74

70.

747

0.70

41.

311.

41

704

XX

XX

Y

Y YY

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 704 TEAM-B 103:PEQY138:Appendix:

A–9(S

I)P

rope

rtie

s of

ste

el s

truc

tura

l tub

ing

(HS

S-s

hape

s) S

I un

its.

Des

ign

Sec

tion

pro

pert

ies

wal

l th

ickn

ess

Mas

sW

eigh

tA

rea

Axi

s X

-XA

xis

Y-Y

Tors

iona

l co

nsta

nts

Sha

pet w

per

mpe

r m

AI x

S xr x

I yS y

r yJ

CR

ef.

(mm

) (m

m)

(mm

)(m

m)

(kg/

m)

(N/m

)(m

m2 )

(mm

4 )(m

m3 )

(mm

)(m

m4 )

(mm

3 )(m

m)

(mm

4 )(m

m3 )

aH

SS

203

�20

3 �

12.7

11.8

72.5

711

8710

5.20

E�

075.

11E

�05

77.2

5.20

E�

075.

11E

�05

77.2

8.49

E�

078.

59E

�05

bH

SS

203

�20

3 �

6.4

5.92

38.4

377

4580

2.94

E�

072.

90E

�05

80.0

2.94

E�

072.

90E

�05

80.0

4.62

E�

074.

61E

�05

cH

SS

203

�10

2 �

12.7

11.8

52.2

512

6280

2.99

E�

072.

93E

�05

68.8

9.82

E�

061.

93E

�05

39.6

2.54

E�

074.

00E

�05

dH

SS

203

�10

2 �

6.4

5.92

28.3

277

3380

1.77

E�

071.

74E

�05

72.4

5.99

E�

061.

18E

�05

42.2

1.47

E�

072.

23E

�05

eH

SS

203

�51

�6.

45.

9223

.222

827

701.

19E

�07

1.17

E�

0565

.31.

22E

�06

4.82

E�

0421

.03.

90E

�06

1.04

E�

05

fH

SS

152

�15

2 �

12.7

11.8

52.2

512

6280

2.01

E�

072.

64E

�05

56.6

2.01

E�

072.

64E

�05

56.6

3.38

E�

074.

61E

�05

gH

SS

152

�15

2 �

6.4

5.92

28.3

277

3380

1.19

E�

071.

56E

�05

59.4

1.19

E�

071.

56E

�05

59.4

1.90

E�

072.

52E

�05

hH

SS

152

�10

2 �

6.4

5.92

23.2

228

2770

8.70

E�

061.

14E

�05

55.9

4.62

E�

069.

11E

�04

40.9

9.82

E�

061.

66E

�05

iH

SS

152

�51

�6.

45.

9218

.217

821

705.

45E

�06

7.16

E�

0450

.09.

20E

�05

3.62

E�

0420

.62.

73E

�06

7.70

E�

04

jH

SS

102

�10

2 �

12.7

11.8

32.0

314

3880

4.95

E�

069.

78E

�04

35.8

4.95

E�

069.

78E

�04

35.8

8.74

E�

061.

84E

�05

kH

SS

102

�10

2 �

6.4

5.92

18.2

178

2170

3.25

E�

066.

39E

�04

38.6

3.25

E�

066.

39E

�04

38.6

5.33

E�

061.

08E

�05

lH

SS

102

�51

�6.

45.

9213

.112

815

701.

87E

�06

3.69

E�

0434

.56.

16E

�05

2.43

E�

0419

.81.

59E

�06

5.00

E�

04

mH

SS

76

�76

�6.

45.

9213

.112

815

701.

26E

�06

3.29

E�

0428

.21.

26E

�06

3.29

E�

0428

.22.

11E

�06

5.77

E�

04

nH

SS

76

�51

�6.

45.

9210

.510

312

718.

87E

�05

2.33

E�

0426

.44.

62E

�05

1.82

E�

0419

.11.

05E

�06

3.65

E�

04

oH

SS

51

�51

�6.

45.

928.

0178

.597

43.

11E

�05

1.22

E�

0417

.93.

11E

�05

1.22

E�

0417

.95.

45E

�05

2.31

E�

04

XX

XX

Y

Y YY

705

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 705 TEAM-B 103:PEQY138:Appendix:

A–10

Pro

pert

ies

of A

lum

inum

Ass

ocia

tion

stan

dard

cha

nnel

s U

.S.C

usto

mar

y un

its.

Sec

tion

pro

pert

ies

Fla

nge

Web

Axi

s X

-XA

xis

Y-Y

Sha

peD

epth

,AW

idth

, BA

rea

Thi

ckne

ss, t

1T

hick

ness

, tI x

S xr x

I yS y

r yx

Ref

. (i

n)(l

b/ft

)(i

n)(i

n)(i

n2 )(i

n)(i

n)(i

n4 )(i

n3 )(i

n)(i

n4 )(i

n3 )(i

n)(i

n)

aC

2

�0.

577

2.00

1.00

0.49

10.

130.

130.

288

0.28

80.

766

0.04

50.

064

0.30

30.

298

bC

2

�1.

071

2.00

1.25

0.91

10.

260.

170.

546

0.54

60.

774

0.13

90.

178

0.39

10.

471

cC

3

�1.

135

3.00

1.50

0.96

50.

200.

131.

410.

941.

210.

220.

220.

470.

49

dC

3

�1.

597

3.00

1.75

1.35

80.

260.

171.

971.

311.

200.

420.

370.

550.

62

eC

4

�1.

738

4.00

2.00

1.47

80.

230.

153.

911.

951.

630.

600.

450.

640.

65

fC

4

�2.

331

4.00

2.25

1.98

20.

290.

195.

212.

601.

621.

020.

690.

720.

78

gC

5

�2.

212

5.00

2.25

1.88

10.

260.

157.

883.

152.

050.

980.

640.

720.

73

hC

5

�3.

089

5.00

2.75

2.62

70.

320.

1911

.14

4.45

2.06

2.05

1.14

0.88

0.95

i C

6

�2.

834

6.00

2.50

2.41

00.

290.

1714

.35

4.78

2.44

1.53

0.90

0.80

0.79

jC

6

�4.

030

6.00

3.25

3.42

70.

350.

2121

.04

7.01

2.48

3.76

1.76

1.05

1.12

kC

7

�3.

205

7.00

2.75

2.72

50.

290.

1722

.09

6.31

2.85

2.10

1.10

0.88

0.84

lC

7

�4.

715

7.00

3.50

4.00

90.

380.

2133

.79

9.65

2.90

5.13

2.23

1.13

1.20

mC

8

�4.

147

8.00

3.00

3.52

60.

350.

1937

.40

9.35

3.26

3.25

1.57

0.96

0.93

nC

8

�5.

789

8.00

3.75

4.92

30.

410.

2552

.69

13.1

73.

277.

132.

821.

201.

22

oC

9

�4.

983

9.00

3.25

4.23

70.

350.

2354

.41

12.0

93.

584.

401.

891.

020.

93

pC

9

�6.

970

9.00

4.00

5.92

70.

440.

2978

.31

17.4

03.

639.

613.

491.

271.

25

qC

10

�6.

136

10.0

03.

505.

218

0.41

0.25

83.2

216

.64

3.99

6.33

2.56

1.10

1.02

rC

10

�8.

360

10.0

04.

257.

109

0.50

0.31

116.

1523

.23

4.04

13.0

24.

471.

351.

34

sC

12

�8.

274

12.0

04.

007.

036

0.47

0.29

159.

7626

.63

4.77

11.0

33.

861.

251.

14

tC

12

�11

.822

12.0

05.

0010

.053

0.62

0.35

239.

6939

.95

4.88

25.7

47.

601.

601.

61

706

XC

entr

oid

YY

XA

R

B

t 1t x

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 706 TEAM-B 103:PEQY138:Appendix:

A–10(S

I)P

rope

rtie

s of

Alu

min

um A

ssoc

iatio

n st

anda

rd c

hann

els

SI

units

.

Sec

tion

pro

pert

ies

Fla

nge

Web

A

xis

X-X

Axi

s Y-

Y

Sha

peW

t/m

Dep

th, A

Wid

th, B

Are

aT

hick

ness

, t1

Thi

ckne

ss, t

I xS x

r xI y

S yr y

xR

ef.

(mm

)(k

g/m

)(N

/m)

(mm

)(m

m)

(mm

2 )(m

m)

(mm

)(m

m4 )

(mm

3 )(m

m)

(mm

4 )(m

m3 )

(mm

)(m

m)

aC

51

�0.

859

8.42

5125

317

3.3

3.3

1.20

E�

054.

72E

�03

19.4

61.

87E

�04

1.05

E�

037.

707.

57

bC

51

1.59

415

.63

5132

588

6.6

4.3

2.27

E�

058.

95E

�03

19.6

65.

79E

�04

2.92

E�

039.

9312

.0

cC

76

1.68

916

.57

7638

623

5.1

3.3

5.87

E�

051.

54E

�04

30.7

39.

16E

�04

3.61

E�

0311

.94

12.4

dC

76

�2.

376

23.3

176

4487

66.

64.

38.

20E

�05

2.15

E�

0430

.48

1.75

E�

056.

06E

�03

13.9

715

.7

eC

102

2.58

625

.37

102

5195

45.

83.

81.

63E

�06

3.20

E�

0441

.40

2.50

E�

057.

38E

�03

16.2

616

.5

fC

102

3.46

834

.03

102

5712

797.

44.

82.

17E

�06

4.26

E�

0441

.15

4.25

E�

051.

13E

�04

18.2

919

.8

gC

127

3.29

132

.29

127

5712

146.

63.

83.

28E

�06

5.16

E�

0452

.07

4.08

E�

051.

05E

�04

18.2

918

.5

hC

127

4.59

645

.09

127

7016

958.

14.

84.

64E

�06

7.29

E�

0452

.32

8.53

E�

051.

87E

�04

22.3

524

.1

iC

152

4.21

741

.37

152

6415

557.

44.

35.

97E

�06

7.83

E�

0461

.98

6.37

E�

051.

48E

�04

20.3

220

.1

jC

152

6.00

58.8

152

8322

118.

95.

38.

76E

�06

1.15

E�

0562

.99

1.56

E�

062.

88E

�04

26.6

728

.4

kC

178

4.77

46.8

178

7017

587.

44.

39.

19E

�06

1.03

E�

0572

.39

8.74

E�

051.

80E

�04

22.3

521

.3

lC

178

7.02

68.8

178

8925

879.

75.

31.

41E

�07

1.58

E�

0573

.72.

14E

�06

3.65

E�

0428

.70

30.5

mC

203

6.17

60.5

203

7622

758.

94.

81.

56E

�07

1.53

E�

0582

.81.

35E

�06

2.57

E�

0424

.38

23.6

nC

203

8.61

84.5

203

9531

7610

.46.

42.

19E

�07

2.16

E�

0583

.12.

97E

�06

4.62

E�

0430

.48

31.0

oC

229

7.41

72.7

229

8327

348.

95.

82.

26E

�07

1.98

E�

0590

.91.

83E

�06

3.10

E�

0425

.91

23.6

pC

229

� 1

0.37

101.

722

910

238

2411

.27.

43.

26E

�07

2.85

E�

0592

.24.

00E

�06

5.72

E�

0432

.26

31.8

qC

254

9.13

89.6

254

8933

6710

.46.

43.

46E

�07

2.73

E�

0510

1.3

2.63

E�

064.

20E

�04

27.9

425

.9

rC

254

� 1

2.44

122.

025

410

845

8712

.77.

94.

83E

�07

3.81

E�

0510

2.6

5.42

E�

067.

33E

�04

34.2

934

.0

sC

305

� 1

2.31

120.

830

510

245

4011

.97.

46.

65E

�07

4.36

E�

0512

1.2

4.59

E�

066.

33E

�04

31.7

529

.0

tC

305

� 1

7.59

172.

630

512

764

8615

.78.

99.

98E

�07

6.55

E�

0512

4.0

1.07

E�

071.

25E

�05

40.6

440

.9

XC

entr

oid

YY

XA

R

B

t 1t x

707

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 707 TEAM-B 103:PEQY138:Appendix:

A–11

Pro

pert

ies

of A

lum

inum

Ass

ocia

tion

stan

dard

I-b

eam

sha

pes

U.S

.Cus

tom

ary

units

.

Sec

tion

pro

pert

ies

Fla

nge

Web

Axi

s X

-XA

xis

Y-Y

Sha

peD

epth

,AW

idth

, BA

rea

Thi

ckne

ss, t

1T

hick

ness

, tI x

S xr x

I yS y

r yR

ef.

(in)

(lb

/ft)

(in)

(in)

(in2 )

(in)

(in)

(in4 )

(in3 )

(in)

(in4 )

(in3 )

(in)

aI

3 �

1.63

73.

002.

501.

392

0.20

0.13

2.24

1.49

1.27

0.52

0.42

0.61

bI

3 �

2.03

03.

002.

501.

726

0.26

0.15

2.71

1.81

1.25

0.68

0.54

0.63

cI

4 �

2.31

14.

003.

001.

965

0.23

0.15

5.62

2.81

1.69

1.04

0.69

0.73

dI

4 �

2.79

34.

003.

002.

375

0.29

0.17

6.71

3.36

1.68

1.31

0.87

0.74

eI

5 �

3.70

05.

003.

503.

146

0.32

0.19

13.9

45.

582.

112.

291.

310.

85

fI

6 �

4.03

06.

004.

003.

427

0.29

0.19

21.9

97.

332.

533.

101.

550.

95

gI

6 �

4.69

26.

004.

003.

990

0.35

0.21

25.5

8.50

2.53

3.74

1.87

0.97

hI

7 �

5.80

07.

004.

504.

932

0.38

0.23

42.8

912

.25

2.95

5.78

2.57

1.08

iI

8 �

6.18

18.

005.

005.

256

0.35

0.23

59.6

914

.92

3.37

7.30

2.92

1.18

jI

8 �

7.02

38.

005.

005.

972

0.41

0.25

67.7

816

.94

3.37

8.55

3.42

1.20

kI

9 �

8.36

19.

005.

507.

110

0.44

0.27

102.

0222

.67

3.79

12.2

24.

441.

31

lI

10 �

8.64

610

.00

6.00

7.35

20.

410.

2513

2.09

26.4

24.

2414

.78

4.93

1.42

mI

10 �

10.2

8610

.00

6.00

8.74

70.

500.

2915

5.79

31.1

64.

2218

.03

6.01

1.44

nI

12 �

11.6

7212

.00

7.00

9.92

50.

470.

2925

5.57

42.6

05.

0726

.90

7.69

1.65

oI

12 �

14.2

9212

.00

7.00

12.1

530.

620.

3131

7.33

52.8

95.

1135

.48

10.1

41.

71

708

XA

X

R t

t 1

YYB

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:17 AM Page 708 TEAM-B 103:PEQY138:Appendix:

A–11(S

I)P

rope

rtie

s of

Alu

min

um A

ssoc

iatio

n st

anda

rd I

-bea

m s

hape

s S

I un

its.

Sec

tion

pro

pert

ies

Fla

nge

Web

Axi

s X

-XA

xis

Y-Y

Sha

peW

t/m

Dep

th, A

Wid

th, B

Are

aT

hick

ness

, t1

Thi

ckne

ss, t

I xS x

r x

I yS y

r yR

ef.

(mm

) (k

g/m

)(N

/m)

(mm

)(m

m)

(mm

2 )(m

m)

(mm

)(m

m4 )

(mm

3 )(m

m)

(mm

4 )(m

m3 )

(mm

)

aI

76 �

2.43

623

.90

7664

898

5.1

3.3

9.32

E�

052.

44E

�04

32.2

62.

16E

�05

6.88

E�

0315

.49

bI

76 �

3.02

129

.63

7664

1114

6.6

3.8

1.13

E�

062.

97E

�04

31.7

52.

83E

�05

8.85

E�

0316

.00

cI

102

�3.

439

33.7

310

276

1268

5.8

3.8

2.34

E�

064.

61E

�04

42.9

34.

33E

�05

1.13

E�

0418

.54

dI

102

�4.

156

40.7

710

276

1532

7.4

4.3

2.79

E�

065.

51E

�04

42.6

75.

45E

�05

1.43

E�

0418

.80

eI

127

�5.

506

54.0

112

789

2030

8.1

4.8

5.80

E�

069.

15E

�04

53.5

99.

53E

�05

2.15

E�

0421

.59

fI

152

�5.

997

58.8

315

210

222

117.

44.

89.

15E

�06

1.20

E�

0564

.26

1.29

E�

062.

54E

�04

24.1

3

gI

152

�6.

982

68.4

915

210

225

748.

95.

31.

06E

�07

1.39

E�

0564

.26

1.56

E�

063.

06E

�04

24.6

4

hI

178

�8.

630

84.6

617

811

431

829.

75.

81.

79E

�07

2.01

E�

0574

.93

2.41

E�

064.

21E

�04

27.4

3

iI

203

�9.

197

90.2

220

312

733

918.

95.

82.

48E

�07

2.45

E�

0585

.60

3.04

E�

064.

79E

�04

29.9

7

jI

203

�10

.45

102.

520

312

738

5310

.46.

42.

82E

�07

2.78

E�

0585

.60

3.56

E�

065.

61E

�04

30.4

8

kI

229

�12

.44

122.

022

914

045

8711

.26.

94.

25E

�07

3.72

E�

0596

.27

5.09

E�

067.

28E

�04

33.2

7

lI

254

�12

.87

126.

225

415

247

4410

.46.

45.

50E

�07

4.33

E�

0510

7.7

6.15

E�

068.

08E

�04

36.0

7

mI

254

�15

.31

150.

125

415

256

4412

.77.

46.

48E

�07

5.11

E�

0510

7.2

7.50

E�

069.

85E

�04

36.5

8

nI

305

�44

.50

436.

530

517

864

0411

.97.

41.

06E

�08

6.98

E�

0512

8.8

1.12

E�

071.

26E

�05

41.9

1

oI

305

�23

.80

233.

530

517

878

4115

.77.

91.

32E

�08

8.67

E�

0512

9.8

1.48

E�

071.

66E

�05

43.4

3

XA

X

R t

t 1

YYB

709

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 709 TEAM-B 103:PEQY138:Appendix:

A–12

Pro

pert

ies

of s

teel

pip

e U

.S.C

usto

mar

y un

its.

Wal

l

Sec

tion

pro

pert

ies

Out

side

Insi

deth

ickn

ess,

Tors

iona

l co

nsta

nts

Nom

inal

siz

eD

iam

eter

Dia

met

ert w

Are

a, A

IS

rJ

Zp

Ref

.(i

n)

(in)

(in)

(in)

(in2 )

(in4 )

(in3 )

(in)

(in4 )

(in3 )

Sch

edul

e 40

pip

e

a1/

8 in

0.40

50.

269

0.06

80.

072

1.06

E-0

35.

25E

-03

0.12

22.

13E

-03

1.05

E-0

2

b1/

4 in

0.54

00.

364

0.08

80.

125

3.31

E-0

31.

23E

-02

0.16

36.

62E

-03

2.45

E-0

2

c3/

8 in

0.67

50.

493

0.09

10.

167

7.29

E-0

32.

16E

-02

0.20

91.

46E

-02

4.32

E-0

2

dP

IPE

1/2

ST

D0.

840

0.62

20.

109

0.25

01.

71E

-02

4.07

E-0

20.

261

3.42

E-0

28.

14E

-02

eP

IPE

3/4

ST

D1.

050

0.82

40.

113

0.33

33.

70E

-02

7.05

E-0

20.

334

7.41

E-0

20.

1411

fP

IPE

1 S

TD

1.31

51.

049

0.13

30.

494

8.73

E-0

20.

1328

0.42

10.

1747

0.26

57

gP

IPE

1-1

/4 S

TD

1.66

01.

380

0.14

00.

669

0.19

470.

2346

0.54

00.

3894

0.46

92

hP

IPE

1-1

/2 S

TD

1.90

01.

610

0.14

50.

799

0.30

990.

3262

0.62

30.

6198

0.65

24

iP

IPE

2 S

TD

2.37

52.

067

0.15

41.

075

0.66

570.

5606

0.78

71.

331

1.12

1

jP

IPE

2-1

/2 S

TD

2.87

52.

469

0.20

31.

704

1.53

01.

064

0.94

73.

059

2.12

8

kP

IPE

3 S

TD

3.50

03.

068

0.21

62.

228

3.01

71.

724

1.16

46.

034

3.44

8

lP

IPE

3-1

/2 S

TD

4.00

03.

548

0.22

62.

680

4.78

82.

394

1.33

79.

575

4.78

8

mP

IPE

4 S

TD

4.50

04.

026

0.23

73.

174

7.23

33.

214

1.51

014

.47

6.42

9

nP

IPE

5 S

TD

5.56

35.

047

0.25

84.

300

15.1

65.

451

1.87

830

.32

10.9

0

oP

IPE

6 S

TD

6.62

56.

065

0.28

05.

581

28.1

48.

496

2.24

556

.28

16.9

9

pP

IPE

8 S

TD

8.62

57.

981

0.32

28.

399

72.4

916

.81

2.93

814

5.0

33.6

2

qP

IPE

10

ST

D10

.750

10.0

200.

365

11.9

0816

0.7

29.9

03.

674

321.

559

.81

r12

in

12.7

5011

.938

0.40

615

.745

300.

247

.09

4.36

760

0.4

94.1

8

s16

in

16.0

0015

.000

0.50

024

.347

731.

991

.49

5.48

314

6418

3.0

t18

in

18.0

0016

.876

0.56

230

.788

1171

130.

26.

168

2343

260.

3

NO

TE

:All

val

ues

show

n ar

e fo

r st

anda

rd s

ched

ule

40 s

teel

pip

e.

Row

s d–

q co

nfor

m to

AIS

C s

tand

ards

for

dim

ensi

ons

of s

tand

ard

wei

ght p

ipe.

Row

s a–

c an

d r–

t do

not.

Man

y ot

her

size

s of

rou

nd h

ollo

w s

truc

tura

l sec

tion

s (H

SS

) ar

e av

aila

ble.

See

AIS

C M

anua

l.

710

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 710 TEAM-B 103:PEQY138:Appendix:

A–12(S

I)P

rope

rtie

s of

ste

el p

ipe

SI

units

.

Wal

l

Sec

tion

pro

pert

ies

Out

side

Insi

deT

hick

ness

,To

rsio

nal

cons

tant

s

Nom

inal

siz

eD

iam

eter

Dia

met

ert w

Are

a, A

IS

rJ

Zp

Ref

.(m

m)

(mm

)(m

m)

(mm

)(m

m2 )

(mm

4 )(m

m3 )

(mm

)(m

m4 )

(mm

3 )

Sch

edul

e 40

pip

e

a3.

2 m

m10

.29

6.83

1.73

46.4

544

2.7

86.0

73.

087

885.

417

2.1

b6.

4 m

m13

.72

9.25

2.24

80.6

213

7920

1.0

4.13

527

5740

2.1

c9.

5 m

m17

.15

12.5

22.

3110

7.7

3035

354.

05.

308

6069

708.

0

dP

IPE

13

ST

D21

.34

15.8

02.

7716

1.5

7114

666.

96.

637

1422

813

34

eP

IPE

19

ST

D26

.67

20.9

32.

8721

4.6

1541

611

568.

475

3083

123

12

fP

IPE

25

ST

D33

.40

26.6

43.

3831

8.6

3635

521

7710

.68

7271

043

54

gP

IPE

32

ST

D42

.16

35.0

53.

5643

1.3

8104

438

4413

.71

1.62

E�

0576

88

hP

IPE

38

ST

D48

.26

40.8

93.

6851

5.8

1.29

E�

0553

4615

.81

2.58

E�

0510

691

i P

IPE

51

ST

D60

.33

52.5

03.

9169

3.2

2.77

E�

0591

8719

.99

5.54

E�

0518

374

jP

IPE

64

ST

D73

.03

62.7

15.

1610

996.

37E

�05

1743

624

.06

1.27

E�

0634

873

kP

IPE

75

ST

D88

.90

77.9

35.

4914

381.

26E

�06

2825

329

.55

2.51

E�

0656

506

lP

IPE

89

ST

D10

1.6

90.1

25.

7417

291.

99E

�06

3922

833

.95

3.99

E�

0678

457

mP

IPE

102

ST

D11

4.3

102.

36.

0220

483.

01E

�06

5267

638

.34

6.02

E�

061.

05E

�05

nP

IPE

127

ST

D14

1.3

128.

26.

5527

746.

31E

�06

8932

747

.70

1.26

E�

071.

79E

�05

oP

IPE

152

ST

D16

8.3

154.

17.

1136

011.

17E

�07

1.39

E�

0557

.04

2.34

E�

072.

78E

�05

pP

IPE

203

ST

D21

9.1

202.

78.

1854

193.

02E

�07

2.75

E�

0574

.62

6.03

E�

075.

51E

�05

qP

IPE

254

ST

D27

3.1

254.

59.

2776

836.

69E

�07

4.90

E�

0593

.32

1.34

E�

089.

80E

�05

r30

5 m

m32

3.9

303.

210

.31

1015

81.

25E

�08

7.72

E�

0511

0.9

2.50

E�

081.

54E

�06

s 40

6 m

m40

6.4

381.

012

.70

1570

83.

05E

�08

1.50

E�

0613

9.3

6.09

E�

083.

00E

�06

t45

7 m

m45

7.2

428.

714

.27

1986

34.

88E

�08

2.13

E�

0615

6.7

9.75

E�

084.

27E

�06

NO

TE

:All

val

ues

show

n ar

e fo

r st

anda

rd s

ched

ule

40 s

teel

pip

e, c

onve

rted

to S

I un

its.

Row

s d–

q co

nfor

m to

AIS

C s

tand

ards

for

dim

ensi

ons

of s

tand

ard

wei

ght p

ipe.

Row

s a–

c an

d r–

t do

not.

Man

y ot

her

size

s of

rou

nd h

ollo

w s

truc

tura

l sec

tion

s (H

SS

) ar

e av

aila

ble.

See

AIS

C M

anua

l.

711

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 711 TEAM-B 103:PEQY138:Appendix:

A–13

Pro

pert

ies

of s

teel

mec

hani

cal t

ubin

g U

.S.C

usto

mar

y un

its.

Wal

l

Sec

tion

pro

pert

ies

Out

side

Insi

deth

ickn

ess,

Tors

iona

l co

nsta

nts

Nom

inal

siz

eD

iam

eter

Dia

met

ert w

Are

a, A

IS

rJ

Zp

Ref

.O

D (

in)

Wal

l ga

ge(i

n)(i

n)(i

n)(i

n2 )(i

n4 )(i

n3 )(i

n)(i

n4 )(i

n3 )

a17

0.50

00.

384

0.05

80.

081

0.00

200

0.00

800

0.15

80.

0040

00.

0160

b14

0.50

00.

334

0.08

30.

109

0.00

246

0.00

983

0.15

00.

0049

10.

0197

c1

161.

000

0.87

00.

065

0.19

10.

0210

0.04

190.

331

0.04

190.

0839

d1

101.

000

0.73

20.

134

0.36

50.

0350

0.07

000.

310

0.07

000.

140

e1

161.

500

1.37

00.

065

0.29

30.

0756

0.10

10.

508

0.15

10.

202

f1

101.

500

1.23

20.

134

0.57

50.

135

0.18

10.

485

0.27

10.

361

g2

162.

000

1.87

00.

065

0.39

50.

185

0.18

50.

685

0.37

00.

370

h2

102.

000

1.73

20.

134

0.78

60.

344

0.34

40.

661

0.68

70.

687

i2

102.

500

2.23

20.

134

0.99

60.

699

0.55

90.

838

1.39

81.

119

j2

52.

500

2.06

00.

220

1.57

61.

034

0.82

70.

810

2.06

71.

654

k3

103.

000

2.73

20.

134

1.20

71.

241

0.82

81.

014

2.48

31.

655

l3

53.

000

2.56

00.

220

1.92

11.

868

1.24

50.

986

3.73

62.

490

m3

103.

500

3.23

20.

134

1.41

72.

010

1.14

91.

191

4.02

02.

297

n3

53.

500

3.06

00.

220

2.26

73.

062

1.75

01.

162

6.12

53.

500

o4

54.

000

3.56

00.

220

2.61

34.

682

2.34

11.

339

9.36

44.

682

p4

14.

000

3.40

00.

300

3.48

76.

007

3.00

31.

312

12.0

136.

007

q4

54.

500

4.06

00.

220

2.95

86.

791

3.01

81.

515

13.5

836.

037

r4

14.

500

3.90

00.

300

3.95

88.

773

3.89

91.

489

17.5

467.

798

s5

55.

000

4.56

00.

220

3.30

49.

456

3.78

21.

692

18.9

117.

564

t5

15.

000

4.40

00.

300

4.43

012

.281

4.91

21.

665

24.5

629.

825

1 21 21 21 21 21 21 21 21 21 2

712

Z01_MOTT8490_05_SE_APP.QXD 6/8/10 7:01 PM Page 712

A–13(S

I)P

rope

rtie

s of

ste

el m

echa

nica

l tub

ing

SI

units

.

Wal

l

Sec

tion

pro

pert

ies

Out

side

Insi

deth

ickn

ess,

Tors

iona

l co

nsta

nts

Nom

inal

siz

eD

iam

eter

Dia

met

ert w

Are

a, A

IS

rJ

Zp

Ref

.O

D (

mm

) W

all

gage

(mm

)(m

m)

(mm

)(m

m2 )

(mm

4 )(m

m3 )

(mm

)(m

m4 )

(mm

3 )

a12

.717

12.7

09.

754

1.47

351

.96

833

131.

14.

0016

6526

2.3

b12

.714

12.7

08.

484

2.10

870

.15

1023

161.

13.

8220

4532

2.1

c25

.416

25.4

022

.098

1.65

112

3.2

8726

687.

18.

421.

75E

�04

1374

d25

.410

25.4

018

.593

3.40

423

5.2

1.46

E�

0411

477.

872.

91E

�04

2294

e38

.116

38.1

034

.798

1.65

118

9.1

3.15

E�

0416

5112

.96.

29E

�04

3303

f38

.110

38.1

031

.293

3.40

437

1.0

5.64

E�

0429

5912

.31.

13E

�05

5918

g50

.816

50.8

047

.498

1.65

125

4.9

7.71

E�

0430

3417

.41.

54E

�05

6068

h50

.810

50.8

043

.993

3.40

450

6.8

1.43

E�

0556

3216

.82.

86E

�05

1.13

E�

04

i63

.510

63.5

056

.693

3.40

464

2.6

2.91

E�

0591

6621

.35.

82E

�05

1.83

E�

04

j63

.55

63.5

052

.324

5.58

810

174.

30E

�05

1.35

E�

0420

.68.

60E

�05

2.71

E�

04

k76

.210

76.2

069

.393

3.40

477

8.4

5.17

E�

051.

36E

�04

25.8

1.03

E�

062.

71E

�04

l76

.25

76.2

065

.024

5.58

812

407.

77E

�05

2.04

E�

0425

.01.

55E

�06

4.08

E�

04

m88

.910

88.9

082

.093

3.40

491

4.2

8.37

E�

051.

88E

�04

30.3

1.67

E�

063.

76E

�04

n 88

.95

88.9

077

.724

5.58

814

631.

27E

�06

2.87

E�

0429

.52.

55E

�06

5.74

E�

04

o10

1.6

510

1.60

90.4

245.

588

1686

1.95

E�

063.

84E

�04

34.0

3.90

E�

067.

67E

�04

p10

1.6

110

1.60

86.3

607.

620

2250

2.50

E�

064.

92E

�04

33.3

5.00

E�

069.

84E

�04

q11

4.3

511

4.30

103.

124

5.58

819

082.

83E

�06

4.95

E�

0438

.55.

65E

�06

9.89

E�

04

r 11

4.3

111

4.30

99.0

607.

620

2554

3.65

E�

066.

39E

�04

37.8

7.30

E�

061.

28E

�05

s12

7.0

512

7.00

115.

824

5.58

821

313.

94E

�06

6.20

E�

0443

.07.

87E

�06

1.24

E�

05

t12

7.0

112

7.00

111.

760

7.62

028

585.

11E

�06

8.05

E�

0442

.31.

02E

�07

1.61

E�

05

713

Z01_MOTT8490_05_SE_APP.QXD 6/8/10 7:01 PM Page 713

36

PercentelongationMPaksiksi

MaterialAISI no. MPa

Ultimatestrength, su

A–14 Typical properties of carbon and alloy steels.*

Yieldstrength, sy

Condition†

36203025161922243225121317232614

152028261215182317

121723

9

9

1020102010201040104010401040104010401040108010801080108010801141114111411141114111414140414041404140414051605160516051605160

576575759097

127118107

8789

189179145117

87112193146116

9495

231187147118105263196149115

393448517517621669876814738600614

130312341000

807600772

13311007

800648655

159312891014

814724

181313511027

793

4348645160829390806354

141129103

705195

172129

976860

212173131101

40238179132103

296331441352414565641621552434372972889710483352655

1186889669469414

14621193

903696276

16411234

910710

AnnealedHot-rolled

Cold-drawnAnnealedHot-rolled

Cold-drawnWQT 700WQT 900

WQT 1100WQT 1300AnnealedOQT 700OQT 900

OQT 1100OQT 1300

OQT 700OQT 900

OQT 1100OQT 1300

OQT 700OQT 900

OQT 1100OQT 1300

AnnealedCold-drawn

Annealed

OQT 700OQT 900

OQT 1100OQT 1300

Annealed

*Other properties approximately the same for all carbon and alloy steels: Modulus of elasticity in tension = 30 000 000 psi (207 GPa) Modulus of elasticity in shear = 11 500 000 psi (80 GPa) Density = 0.283 lbm/in3 (7680 kg/m3)†OQT means oil-quenched and tempered. WQT means water-quenched and tempered.

714  Appendix

Untitled-1.indd 5 05/02/15 6:37 PM

A–15

Typi

cal p

rope

rtie

s of

sta

inle

ss s

teel

s an

d no

nfer

rous

met

als.

Ult

imat

eY

ield

M

odul

us o

f st

reng

th, s

ust

reng

th, s

yD

ensi

tyel

asti

city

, EM

ater

ial

and

Perc

ent

cond

itio

nks

iM

Paks

iM

Pael

onga

tion

lb/i

n3†kg

/m3

psi

GPa

Stai

nles

s st

eels

AIS

I 30

1 an

neal

ed11

075

840

276

600.

290

8030

28 �

106

193

AIS

I 30

1 fu

ll h

ard

185

1280

140

965

80.

290

8030

28 �

106

193

AIS

I 43

0 an

neal

ed75

517

4027

630

0.28

077

5029

�10

620

0

AIS

I 43

0 fu

ll h

ard

9062

180

552

150.

280

7750

29 �

106

200

AIS

I 50

1 an

neal

ed70

48

330

207

280.

280

7750

29 �

106

200

AIS

I 50

1OQ

T 1

000

175

1210

135

931

150.

280

7750

29 �

106

200

17-4

PH

H90

021

014

5018

512

8014

0.28

177

8028

.5 �

106

197

PH

13-

8 M

o H

1000

215

1480

205

1410

130.

279

7720

29.4

�10

620

3

Cop

per

and

its

allo

ys

C14

500

copp

er,

soft

3222

110

6950

0.32

389

4017

�10

611

7

hard

4833

144

303

20

C17

200

Ber

ylli

um c

oppe

r,so

ft72

496

2013

820

0.29

882

5019

�10

613

1

hard

195

1344

145

1000

4

C36

000

bras

s,

soft

4430

518

124

200.

308

8530

16 �

106

110

hard

7048

035

240

4

C54

400

bron

ze,

hard

6846

957

393

200.

318

8800

17 �

106

117

Mag

nesi

um—

cast

AS

TM

AZ

63A

-T6

4027

619

131

50.

066

1830

6.5

�10

645

Zin

c—ca

st-Z

A 1

258

400

4732

45

0.21

860

3012

�10

683

715

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 715 TEAM-B 103:PEQY138:Appendix:

Tita

nium

and

its

all

oys

Pur

e al

pha

Ti-

65A

Wro

ught

6544

855

379

180.

163

4515

15 �

106

103

Alp

ha a

lloy

Ti-

0.2P

d

Wro

ught

5034

540

276

200.

163

4515

14.9

�10

610

3

Bet

a al

loy

Ti-

3Al-

13V

-11C

r

Age

d18

512

8017

512

106

0.17

648

7516

.0 �

106

110

Alp

ha-b

eta

allo

y T

i-6A

1-4V

Age

d17

011

7015

510

708

0.16

044

3216

.5 �

106

114

Nic

kel-

base

d al

loys

N06

600—

anne

aled

70°F

(21

°C)

9364

037

255

450.

304

8420

30 �

106

207

800°

F (

427°

C)

8961

430

207

49

1200

°F (

649°

C)

6544

827

186

39

N06

110—

40%

col

d w

orke

d

70°F

(21

°C)

175

1205

150

1034

180.

302

8330

30 �

106

207

500°

F (

260°

C)

130

896

18

800°

F (

427°

C)

120

827

18

N04

400—

anne

aled

[A

t 70

°F (

21°C

]

Ann

eale

d80

550

3020

750

0.31

888

0026

�10

618

1

Col

d dr

awn

100

690

7551

730

† Thi

s ca

n be

use

d as

spe

cifi

c w

eigh

t or

mas

s de

nsit

y in

lbm

in3 .

A–15

(con

tinue

d)

716

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 716 TEAM-B 103:PEQY138:Appendix:

Appendix 717

A–16 Properties of structural steels.

Ultimate Yield strength, su* strength, sy*

PercentMaterial elongation

ASTM no. and products ksi MPa ksi MPa in 2 in

A36—Carbon steel: shapes,

plates, and bars 58 400 36 248 21

A 53—grade B-pipe 60 414 35 240 —

A242—HSLA corrosion resistants:

shapes, plates, and bars

in thick 70 483 50 345 21

to in thick 67 462 46 317 21

to 4 in thick 63 434 42 290 21

A500—Cold-formed structural tubing

Round, grade B 58 400 42 290 23

Round grade C 62 427 46 317 21

Shaped, grade B 58 400 46 317 23

Shaped, grade C 62 427 50 345 21

A501—Hot-formed structural tubing,

round or shaped 58 400 36 248 23

A514—Quenched and tempered

alloy steel; plate

in thick 110 758 100 690 18

to 6 in thick 100 690 90 620 16

A572—HSLA columbium-vanadium

steel: shapes, plates and bars

Grade 42 60 414 42 290 24

Grade 50 65 448 50 345 21

Grade 60 75 517 60 414 18

Grade 65 80 552 65 448 17

A913—HSLA, grade 65: shapes 80 552 65 448 17

A992—HSLA: W-Shapes only 65 448 50 345 21

*Minimum values; may range higher.

HSLA-High strength low-alloy

The American Institute of Steel Construction specifies E � 29 � 106 psi (200 GPa) for structural steel.

212

…212

112

112

34

…34

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 717 TEAM-B 103:PEQY138:Appendix:

Material typeand grade

Ultimate strength

A—17 Typical properties of cast iron.*

A—18 Typical properties of aluminum alloys.*

Yieldstrength

PercentelongationGPaMPa psiksiMPaksiMPaksiMPaksi

Modulus ofelasticity, E‡syt‡suc‡su† sus

Gray iron ASTM A48Grade 20Grade 40Grade 60

204055

80140170

84134148

<1<0.8<0.5

552965

1170

325772

221393496

———

———

180

———

1240

———

12.2 × 106

19.4 × 106

21.5 × 106

24 × 106

24 × 106

24 × 106

23 × 106

138276379

Ductile iron ASTM A53660-40-18

80-55-6100-70-3120-90-2

6080

100120

414552690827

393503

——

40557090

276379483621

165165165159

18632

5773——

————

————

24 × 106

24 × 106

24 × 106

24 × 106

Austempered ductile iron (ADI)Grade 1Grade 2Grade 3Grade 4

125150175200

862103412071379

————

80100125155

552690862

1069

165165165159

10741

————

240240240

165016501650

26 × 106

27 × 106

27 × 106

Malleable iron ASTM A220450086000480002

*�e density of cast iron ranges from 0.25 to 0.27 lbm/in3 (6920 to 7480 kg/m3).†Minimum values; may range higher.‡Approximate values; may range higher or lower by about 15%.

658095

448552655

338448517

456080

310414552

170186186

842

496575

Alloyand

temper

Ultimatestrength, su

Yieldstrength, sy

Shearstrength, sus

MPaksiPercent

elongationMPaksiMPaksi

*Modulus of elasticity E for most aluminum alloys, including 1100, 3003, 6061, and 6063, is 10 × 106 psi(69.0 Gpa). For 2014, E = 10.6 × 106 psi (73.1 GPa). For 5154, E = 10.2 × 106 psi (70.3 GPa). For 7075,E = 10.4 × 106 psi (71.7 GPa). Density of most aluminum alloys is approximately 0.10 lbm/in3 (2770 kg/m3).

(permanent mold castings)Casting alloys

1100-H121100-H182014-02014-T42014-T63003-03003-H123003-H185154-05154-H325154-H386061-06061-T46061-T67075-07075-T6

16242762701619293539481835453383

110165186427483110131200241269331124241310228572

1522144260

61827173039

821401573

103152

97290414

41124186117207269

55145276103503

25151820134020102715103025171611

10131838421112162222281224302248

6990

124262290

7683

110152152193

83165207152331

204.0–T4206.0–T6356.0–T6

486541

331445283

295930

200405207

86

10

———

———

718 Appendix

Untitled-1.indd 6 05/02/15 6:37 PM

Allo

wab

le st

ress

A—

19 T

ypic

al p

rope

rtie

s of w

ood.

Bend

ing

psi

No.

1N

o. 2

No.

3

1750

1450 80

0

12.1

10.0 5.5

7.2

5.9

3.3

95 95 95

0.66

0.66

0.66

385

385

385

2.65

2.65

2.65

1250

1000 60

0

8.62

6.90

4.14

1800

1700

1500

12.4

11.7

10.3

1050 85

047

5

Type

and

grad

e

Dou

glas

fir—

2 to

4 in

thi

ck, 6

in an

d w

ider

No.

1N

o. 2

No.

3

1400

1150 62

5

9.6

7.9

4.3

5.7

4.7

2.6

75 75 75

0.52

0.52

0.52

245

245

245

1.69

1.69

1.69

1000 80

050

0

6.90

5.52

3.45

1500

1400

1200

10.3 9.7

8.3

825

675

375

Hem

lock

—2

to 4

in th

ick,

6 in

and

wid

er

No.

1N

o. 2

No.

3

1400

1000 65

0

9.6

6.9

4.5

5.7

4.0

2.6

80 70 70

0.55

0.48

0.48

270

230

230

1.86

1.59

1.59

850

550

400

5.86

3.79

2.76

1600

1300

1300

11.0 9.0

9.0

825

575

375

Sout

hern

pin

e —2½

to 4

in

thic

k, 6

in an

d w

ider

MPa

psi

MPa

psi

MPa

psi

MPa

psi

MPa

ksi

GPa

Tens

ion

para

llel

to g

rain

Hor

izon

tal

shea

rM

odul

us o

fel

astic

ityPa

ralle

lto

gra

in

Com

pres

sion

Perp

endi

cula

rto

gra

in

719

Untitled-1.indd 7 05/02/15 6:37 PM

A–20

Typi

cal p

rope

rtie

s of

sel

ecte

d pl

astic

s. Tens

ile

Tens

ile

Fle

xura

l F

lexu

ral

Impa

ct

stre

ngth

mod

ulus

stre

ngth

mod

ulus

stre

ngth

IZ

OD

(f

t�1b

/in

Mat

eria

lTy

pe(k

si)

(MPa

)(k

si)

(MPa

)(k

si)

(MPa

)(k

si)

(MPa

)of

not

ch)

Nyl

on 6

6 D

ry21

.014

612

0087

0032

.022

111

0079

00

30%

Gla

ss50

% R

.H.

15.0

102

800

5500

AB

SM

ediu

m-i

mpa

ct6.

041

360

2480

11.5

7931

021

404.

0

Hig

h-im

pact

5.0

3425

017

208.

055

260

1790

7.0

Poly

carb

onat

eG

ener

al-p

urpo

se9.

062

340

2340

11.0

7630

020

7012

.0

Acr

ylic

Sta

ndar

d10

.572

430

2960

16.0

110

460

3170

0.4

Hig

h-im

pact

5.4

3722

015

207.

048

230

1590

1.2

PV

CR

igid

6.0

4135

024

1030

020

700.

4–20

.0

(var

ies

wid

ely)

Poly

imid

e25

% g

raph

ite

5.7

3912

.888

900

6210

0.25

pow

der

fill

er

Gla

ss-f

iber

fil

ler

27.0

186

50.0

345

3250

22 4

0017

.0

Lam

inat

e50

.034

570

.048

340

0027

580

13.0

Ace

tal

Cop

olym

er8.

055

410

2830

13.0

9037

525

901.

3

Poly

uret

hane

Ela

stom

er

5.0

3410

069

00.

64

No

brea

k

Phe

noli

c G

ener

al6.

545

1100

7580

9.0

6211

0075

800.

3

Poly

este

r w

ith

glas

s-fi

ber

mat

rei

nfor

cem

ent

(app

rox.

30%

gla

ss b

y w

eigh

t)

Lay

-up,

con

tact

mol

d9.

062

16.0

110

800

5520

Col

d pr

ess

mol

ded

12.0

8322

.015

213

0089

60

Com

pres

sion

mol

ded

25.0

172

10.0

6913

0089

60

720

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 720 TEAM-B 103:PEQY138:Appendix:

Appendix 721

A–21 Design stress guidelines.

Direct Normal Stresses—General machine and structural design

Manner of Ductile Materials Brittle Materials loading (% Elongation �5%) (% Elongation �5%)

Static loads sd � sy �2 sd � su�6Repeated loads sd � su�8 sd � su�10Impact or shock sd � su�12 sd � su�15

Direct Normal Stresses—Static loads on steel members of building-like structures

AISC Code: sd � sy �1.67 � 0.60 sy or sd � su�2.00 � 0.50 su

Whichever is lower.

Direct Normal Stresses—Static loads on aluminum members of building-like structures

Aluminum Association: sd � sy�1.65 � 0.61 sy or sd � su�1.95 � 0.51 su

Whichever is lower.

Design Shear Stresses—For direct shear and for torsional shear stresses

Based on maximum shear stress theory of failure:

td � sys�N � 0.5 sy�N � sy �2N

Manner of Design Design loading factor shear stress

Static loads Use N � 2 td � sy�4Repeated loads Use N � 4 td � sy �8Shock or impact Use N � 6 td � sy �12

Estimates for the Ultimate Strength in Shear

Formula Material

sus � 0.65 su Aluminum alloyssus � 0.82 su Steel—Plain carbon and alloysus � 0.90 su Malleable iron and copper alloyssus � 1.30 su Gray cast iron

Allowable Bearing StressSteel—Flat surfaces or the projected area of pins in reamed, drilled, or bored holes:

sbd � 0.90 sy

Allowable Bearing Load, Ra,—Steel roller on flat steel plateU.S. Customary Units SI Metric Units

Ra � (sy 13) (0.03 dL) Ra � (sy 90) (3.0 � 105dL)

Where: Ra � Allowable bearing load in kips or kNsy � Yield strength of steel in ksi or MPad � Roller diameter in inches or mmL � Length of roller in inches or mm

(continued)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 721 TEAM-B 103:PEQY138:Appendix:

722 Appendix

.35

1.0 2.0 3.0 4.0

.40

.50

.60

.70

F F

SteelSteel

Concrete Concrete

A2/A1 = 1.0 A2/A1 > 1.0

K = 0.34

A2/A1

A2/A1

A1 = Bearing areaA2 = Support area

A–21 (continued)0

Allowable bearing stresses on masonry and soils for use in this book.

Allowable bearing stress, �bd

Material psi MPa

Sandstone and limestone 400 2.76Brick in cement mortar 250 1.72Solid hard rock 350 2.41Shale or medium rock 140 0.96Soft rock 70 0.48Hard clay or compact gravel 55 0.38Soft clay or loose sand 15 0.10

Concrete: (But maximum )

Where: � Rated strength of concreteA1 � Bearing areaA2 � Full area of the support

f ¿c

sbd = 0.68 f ¿csbd = Kf ¿c = 10.342A2>A12f ¿c

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 722 TEAM-B 103:PEQY138:Appendix:

Appendix 723

Allowable Bearing Stresses on Masonry and Soils

Allowable bearing stress, sbd

Material psi MPa

Sandstone and limestone 400 2.76Brick in cement mortar 250 1.72Solid hard rock 350 2.41Shale or medium rock 140 0.96Soft rock 70 0.42Hard clay or compact gravel 55 0.38Soft clay or loose sand 15 0.10

Where: f ′c 5 Ratedstrength of concrete

A1 5 Bearing areaA2 5 Full area of the support

Design Bending Stresses—General machine and structural design

Manner of Ductile Materials Brittle Materials loading (% Elongation .5%) (% Elongation ,5%)

Static loads sd 5 sy /2 sd 5 su /6Repeated loads sd 5 su /8 sd 5 su /10Impact or shock sd 5 su /12 sd 5 su /15

Design Bending Stresses—AISC specifications for structural steel carrying static loads on building-like structures

sd 5 sy /1.5 5 0.66 sy

Design Bending Stresses—Aluminum Association specifications for aluminum carrying staticloads on building-like structures

sd 5 sy /1.65 5 0.61 sy or sd 5 su /1.95 5 0.51 su

Whichever is lower.

Design Shear Stresses for Beams in BendingRolled structural steel beam shapes—allowable web shear stress (AISC)

td 5 0.40 sy

General ductile materials carrying static loads: Based on yield strength of the material in shearwith design factor, N 5 2:

td 5 sys /N 5 0.5 sy /N 5 sy /2N 5 sy /2(2) 5 sy /4 5 0.25 sy

Concrete: sbd = Kf ¿c = (0.342A2>A1)f ¿c (But maximum sbd = 0.68f ¿c)

A–21 (continued)

Z01_MOTT8490_05_SE_APP.QXD 8/24/09 3:40 PM Page 723

724 Appendix

r = Groove radius

0 0.05 0.10 0.15 0.20 0.25

σmax = Kt σnom

σnom = F/(πd2g/4)

D/dg = 2.0

D/dg = 1.2

r/dg

2.5

2.4

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Kt

D/dg = 1.1

D/dg = 1.05

DF Fdg

A–22 Stress Concentration Factors

A–22–1 Axially loaded grooved round bar in tension.

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:19 AM Page 724 TEAM-B 103:PEQY138:Appendix:

Appendix 725

A–22–2 Axially loaded stepped round bar in tension.

0 0.05 0.10 0.15 0.20 0.25

r = Fillet radius

2.5

2.4

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Kt

r/d

F d FD

σmax = Kt σnom

σnom = F/(πd2g/4)

D/d = 3.0

D/d = 2.0

D/d = 1.1D/d = 1.2

D/d = 1.05

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:19 AM Page 725 TEAM-B 103:PEQY138:Appendix:

726 Appendix

A–22–3 Axially loaded stepped flat plate in tension.

σmax = Kt σnom

F

Kt

FH h

Thickness = t

r

σnom = = F Amin

Ft h

H/h = 2.0

1.2

3.4

1.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32

1.4

1.8

2.2

2.6

3.0

1.1

1.01

r/h

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:19 AM Page 726 TEAM-B 103:PEQY138:Appendix:

Appendix 727

A–22–4 Flat plate with central hole in tension and bending

d

F

F F = total load Note: Kt = 1.0 for d/w < 0.5

M M

w

σmax = Kt σnom

Thickness = t

Basic geometry

σnom based on

net sectionA B

C

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

5.0

4.0

3.0

2.0

1.0

Kt

Curve A

Direct tensionon plate

Tension loadapplied througha pin in the hole

Curve B

Bending inthe plane ofthe plate

Curve C

σnom = = F Anet

F(w – d)t

F(w – d)t

σnom = = F Anet

σnom = =Mc Inet

6Mw(w3 – d3)t

d/w

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:19 AM Page 727 TEAM-B 103:PEQY138:Appendix:

728 Appendix

A–22–5 Round bar with transverse hole in tension, bending, and torsion.

0

11.0

10.0

9.0

8.0

7.0

6.0Ktg

5.0

4.0

3.0

2.0

1.00.1

Note: Ktg is based on the nominal stress in a round

bar without a hole (gross section).

0.2 0.3

d/D

B A C

0.4

C

B

A

0.70.60.5

Basic geometry

D

d

Curve ATension

Curve BBending

Curve CTorsion

tmax=Ktg tgrossσmax=Ktg σgross

F F

M M T T

σgross = =F A

F πD2/4

σgross = =M S

M πD3/32

tgross = =T Zp

T πD3/16

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:20 AM Page 728 TEAM-B 103:PEQY138:Appendix:

Appendix 729

A–22–6 Grooved round bar in torsion.

01.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

0.05 0.10 0.15 0.20 0.25

r/dg

Kt

D/dg = 1.2

D/dg = 2.0

D/dg = 1.05

r = Groove radius

tmax=Kt tnom

tnom=T/ (πdg3/16)

T

D dgT

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 729 TEAM-B 103:PEQY138:Appendix:

730 Appendix

A–22–7 Stepped round bar in torsion.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0 0.05 0.10 0.15 0.20 0.25

r/dg

Kt

= 1.25Dd

= 1.67Dd

= 1.11Dd

= 2.5Dd

r = Fillet radius

TD d

T

tmax=Kt tnom

tnom=T/ (πdg3/16)

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:20 AM Page 730 TEAM-B 103:PEQY138:Appendix:

Appendix 731

A–22–8 Grooved round bar in bending.

r = Groove radius

MM

Ddg

smax = Kt snomsnom = M/(π d3

g /32)

D/dg = 2.0

D/dg = 1.2

D/dg = 1.05

0 0.05 0.10 0.15 0.20 0.25

r/dg

2.5

2.4

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Kt

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 731 TEAM-B 103:PEQY138:Appendix:

732 Appendix

A–22–9 Stepped round bar in bending.

0 0.05 0.10 0.15 0.20 0.25

d

r = Fillet radius

2.5

2.4

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Kt

r/d

D

D/d = 3.0

D/d = 1.50

D/d = 1.10

M M

D/d = 2.0

D/d = 1.2

smax = Kt snomsnom = M/(p d3

/32)

D/d = 1.05

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:21 AM Page 732 TEAM-B 103:PEQY138:Appendix:

Appendix 733

A–22–10 Stepped flat plate in bending.

smax = Kt snom

Kt

H h

Thickness = t

r

3.4

1.00 0.04 0.08 0.12 0.16

r/h

H/h = 2.0

1.2

1.05

0.20 0.24 0.28 0.32

1.4

1.8

2.2

2.6

3.0

MM

snom = =Smin t h2/6M M

1.01

A–22–11 Shafts with keyseats—bending and torsion.

Type of keyseat Kt*

Sled-runner 1.6Profile 2.0

*Kt is to be applied to the stress computed for

the full nominal diameter of the shaft where the

keyseat is located.

Z01_MOTT8490_05_SE_APP.QXD 8/24/09 3:42 PM Page 733

734 Appendix

L

a a

x

A B CE

D

P P

L

ax1

bc

x v

A B C D

Pa > b

L

L/2

x

y

A B C

P

Between A and B:

Between A and B (the longer segment):

Between B and C (the shorther segment):

At end of overhang at D:

Between A and B:

Between B and C:

y =

-Pa

6EI (3Lx - 3x

2- a2)

y =

-Px

6EI (3aL - 3a2

- x2)

yB = yC =

-Pa2

6EI (3L - 4a) at loads

yE = ymax =

-Pa

24EI (3L2

- 4a2) at center

yD =

Pabc

6EIL (L + a)

y =

-Pav

6EIL (L2

- v 2

- a2)

y =

- Pbx

6EIL (L2

- b2- x2)

yB =

- Pa2b2

3EIL at load

at x1 = 2a(L + b)�3

ymax =

Pab(L + b)23a(L + b)

27EIL

y =

- Px

48EI (3L2

- 4x2)

yB = ymax =

- PL3

48EI at center

(a)

(b)

(c)

Z01_MOTT8490_05_SE_APP.QXD 6/9/10 4:05 PM Page 734

L a

0.577L

B

RA

RB

P

A D Cx

L

a b

B

MB

A C

xy

Appendix 735

w = uniformilydistributed load

a

Lx

A B

C

L/2 a

Total load = W = wL

w = uniformily distributed load

Lx

A B C

D

A–23 (continued)

Between A and B:

At D at end:

Between A and B:

Between B and C:

Between A and B:

Between B and C:

At C at end of overhang:

At D, maximum upward deflection:

yD = 0.06415 PaL2

EI

yC =

- Pa2

3EI (L + a)

y =

MB

6EI c3a2

+ 3x 2

-

x 3

L- a2L +

3a2

L bx d

y =

-MB

6EI c a6a -

3a2

L- 2Lbx -

x3

Ld

MB = concentrated moment at B

y =

-wa2(L - x)

24EIL (4Lx - 2x

2- a

2)

y =

- wx

24EIL [a2(2L - a)2

- 2ax 2(2L - a) + Lx 3]

yD =

wL3a

24EI

y =

- wx

24EI (L3

- 2Lx 2

+ x 3)

yB = ymax =

-5wL4

384EI=

-5WL3

384EI at center

(d )

(e)

( f )

(g)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 735 TEAM-B 103:PEQY138:Appendix:

aa

LL /2

B

P P

D

C EA

L a

0.577L

BA DC

w = uniformly distributed load

L

a aB

AD E

C

Total load = W = wL

w = uniformly distributed load

736 Appendix

A–23 (continued)

At C at center:

At A and E at ends:

At C at center:

At A and E at ends at loads:

At B:

At D at end:

y =

- wa3

24EI (4L + 3a)

y = 0.03208 wa2L2

EI

y =

- Pa2

3EI aa +

3

2Lb

y =

PL2a

8EI

y =

-W(L - 2a)3a

24EIL c - 1 + 6a

a

L - 2ab

2

+ 3aa

L - 2ab

3d

y =

-W(L - 2a)3

384EI c

5

L (L - 2a) -

24

L a

a2

L - 2ab d

(h)

(i)

( j)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 736 TEAM-B 103:PEQY138:Appendix:

Appendix 737

L

a

A

x

CB

P

b

L

A

x

Bw � uniformly distributed load

L

A

x

B

MB

LA

y

x

B

P

At B at end:

Between A and B:

At B at load:

At C at end:

Between A and B:

Between B and C:

W � total load � wL

At B at end:

Between A and B:

MB � concentrated moment at end

At B at end:

Between A and B:

y =

-MB x 2

2EI

yB = ymax =

- MB L2

2EI

y =

-Wx2

24EIL [2L2

+ (2L - x)2]

yB = ymax =

-WL3

8EI

y =

- Pa2

6EI (3x - a)

y =

- Px 2

6EI (3a - x)

yC = ymax =

-Pa2

6EI (3L - a)

yB =

- Pa3

3EI

y =

- Px2

6EI (3L - x)

yB = ymax =

-PL3

3EI

(a)

(b)

(c)

(d )

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 737 TEAM-B 103:PEQY138:Appendix:

738 Appendix

A

vx

0

0

Shearingforce,V

Bendingmoment,

M

C

RA

RA

MA

MB �RC

RC

�MA

L

a

CB

Pb

L

L/2A B D

y

vx

0

0

Shearingforce,V

Bendingmoment,

M

C

P

P

PL/2

0.447L

RC � 516

516

P1116

5PL32

PRA � MA 11

16

� MB

–3PL16 � –MA

DeflectionsAt B at load:

Between A and B:

Between B and C:

Reactions

Moments

DeflectionsAt B at load:

Between A and B:

Between B and C:

y =

-Pa2v

12EIL3 [3L2b - v

2(3L - a)]

C1 = aL(L + b); C2 = (L + a)(L + b) + aL

y =

- Px2b

12EIL3 (3C1 - C2x)

yB =

- Pa3b2

12EIL3 (3L + b)

MB =

Pa2b

2L3 (b + 2L)

MA =

- Pab

2L2 (b + L)

RC =

Pa2

2L3 (b + 2L)

RA =

Pb

2L3 (3L2

- b2 )

y =

-Pv

96EI (3L2

- 5v2)

y =

-Px2

96EI (9L - 11x)

yD = ymax =

- PL3

107EI

ymax is at v = 0.447L at D:

yB =

- 7

768

PL3

EI

(a)

(b)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 738 TEAM-B 103:PEQY138:Appendix:

Appendix 739

A–25 (continued)

RB

B

P

MA

– RA

RA

L a

– MB

0

0

MA

A C

P

Shearingforce, V

Bendingmoment,

M

y

x

MA

RA

ME = Mmax

– MA

RA RB

A

D B

B

C

E

A

W = total load = wL

w = uniformly distributed load

L/2

L

0.579L

L38

0

0

Shearingforce, V

Bendingmoment,

M

– RB

L/4

Ractions

Moments

DeflectionsAt C at x � 0.579L:

At D at center:

Between A and B:

Reactions

Moments

DeflectionAt C at end:

yC =

-PL3

EI a

a2

4L2 +

a3

3L3b

MB = - Pa

MA =

Pa

2

RB = Pa1 +

3a

2Lb

RA =

- 3Pa

2L

y =

-Wx 2(L - x)

48EIL (3L - 2x)

yD =

- WL3

192EI

yC = ymax =

-WL3

185EI

ME = 0.0703WL

MA = - 0.125WL

RB =

3

8 W

RA =

5

8 W

(c)

(d )

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:18 AM Page 739 TEAM-B 103:PEQY138:Appendix:

740 Appendix

MA MC

x v

a(a > b)

b

LP

BD CA

RA

x1RC

RA

MB

0

0– MA

– RC

– MC

Shearingforce, V

Bendingmoment,

M

y

0

0

MA MC

x

L/2

L

P

B CA

RA = P/2

MB = PL/8

RC = P/2

L/4

RA

– MA

– RC

– MC

Shearingforce, V

Bendingmoment,

M

A–25 (continued)

Moments

DeflectionsAt B at center:

Between A and B:

Reactions

Moments

DeflectionsAt B at load:

Between A and B (longer segment):

Between B and C (shorter segment):

y =

- Pv 2a2

6EIL3 [2b(L - v) + L(b - v)]

y =

- Px 2b2

6EIL3 [2a(L - x) + L(a - x)]

yD = ymax =

- 2Pa3b2

3EI(3a + b)2

At D at x1 =

2aL

3a + b

yB =

- Pa3b3

3EIL3

MC =

- Pa2b

L2

MB =

2Pa2b2

L3

MA =

- Pab2

L2

RC =

Pa2

L3 (3b + a)

RA =

Pb2

L3 (3a + b)

y =

- Px2

48EI (3L - 4x)

yB = ymax =

- PL3

192EI

MA = MB = MC =

PL

8

(e)

( f )

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 740 TEAM-B 103:PEQY138:Appendix:

y

Shearingforce, V

Bendingmoment,

M

MA MC

A

B C

W = total load = wL

w = uniformly distributed load

L/2x

RA = W/2 RC = W/2

L

0

0

RA

MB

– MA

– RC

– MC

Shearingforce, V

Bendingmoment,

M

RC

B CA

w = uniformly distributed load

L L

RA

x1 x1

RB

0

0

VA

VB

MD ME

A D

B

E C

– VC– VB

3L8

3L8

– MB

A–25 (continued)

Appendix 741

Moments

DeflectionsAt B at center:

Between A and C:

Reactions

Shearing forces

Moments

Deflections

At x1 � 0.4215L from A or C:

Between A and B:

y =

-w

48EI (L3x - 3Lx

3+ 2x4)

ymax =

- wL4

185EI

MB = - 0.125wL2

MD = ME = 0.0703wL2

VB =

5wL

8

VA = VC = RA = RC =

3wL

8

RB = 1.25wL

RA = RC =

3wL

8

y =

- wx 2

24EI (L - x)2

yB = ymax =

-WL3

384EI

MB =

WL

24

MA = MC =

-WL

12

(g)

(h)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 741 TEAM-B 103:PEQY138:Appendix:

742 Appendix

+VA

+VB

+VC

+VD

RC RD RE

B C D EA

w = uniformly distributed load

L L L LRA RB

0.54L

0.39L

0.54L0

0

Shearingforce, V

Bendingmoment,

M

0.39L

– VB

MB

MC

MD

– VC – VD

– VE

MI

MHMG

MF

0.4L

0.4wL 0.5wL 0.6wL

–0.6wL –0.5wL –0.4wL

ME

MG

MF

– MB – MC

RC RD

B C DA

w = uniformly distributed load

L L LRA RB

y

0.4L0.5LShearingforce, V

Bendingmoment,

M

0

0E G F

A–25 (continued)

Reactions

Moments

Reactions

Shearing forces

Moments

MG = MH = 0.0364wL2

MC = - 0.0714wL2

MF = MI = 0.0772wL2

MB = MD = -0.1071wL2= Mmax

-VE = - 0.393wL

+VD = + 0.607wL

- VD = - 0.536wL

+VC = + 0.464wL

-VC = + 0.464wL

+VB = + 0.536wL

- VB = - 0.607wL

VA = + 0.393wL

RC = 0.928wL

RB = RD = 1.143wL

RA = RE = 0.393wL

MG = 0.025wL2

MB = MC = -0.10wL2 = Mmax

ME = MF = 0.08wL2

RB = RC = 1.10wL

RA = RD = 0.4wL

(i)

( j)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 742 TEAM-B 103:PEQY138:Appendix:

Appendix 743

A–26 Conversion factors.

Mass Standard SI unit: Kilogram (kg). Equivalent unit: N�s2/m.

Force Standard SI unit: Newton (N). Equivalent unit: kg�m/s2.

Length

Area

Volume

Section Modulus

Moment of Inertia or Second Moment of an Area

Density (Mass/Unit Volume)

Specific Weight (Weight/Unit Volume)

Bending Moment or Torque

Pressure, Stress, or Loading Standard SI unit: Pascal (Pa). Equivalent units: N m2 or kg m�s2.

Energy Standard SI unit: Joule (J). Equivalent units: N�m or kg�m2 s2.

Power Standard SI unit: Watt (W). Equivalent unit: J/s or N�m/s.

General approach to application of conversion factors: Arrange the conversion factor from the table in such a manner that, when multiplied by

the given quantity, the original units cancel out, leaving the desired units. See examples on next page.

1.341 hp

kW

3.412 Btu�hr

W

1.356 W

lb�ft�s550 lb�ft�s

hp

1.0 W

N�m�s745.7 W

hp

778 ft�lb

Btu

3.600 kJ

W�hr

1.055 kJ

Btu

8.85 lb�in

J

1.0 J

N�m

1.356 J

lb�ft

6.895 MPa

ksi

1 Pa

N�m2

6895 Pa

lb�in2

47.88 Pa

lb�ft2144 lb�ft2

lb�in2

��

1.356 N�m

lb�ft

8.851 lb�in

N�m

1728 lb�ft3lb�in3

157.1 N�m3

lbf�ft3

16.018 kg�m3

lbm�ft332.17 lbm�ft3

slug�ft31000 kg�m3

gram�cm3

515.4 kg�m3

slug�ft3

1012 mm4

m4

4.162 * 105 mm4

in4

109 mm3

m3

1.639 * 104 mm3

in3

35.3 ft3

m3

3.785 L

gal

264 gal

m3

7.48 gal

ft3231 in3

gal

1728 in3

ft3

104 m2

hectare

43,560 ft2

acre

106 mm2

m2

645.2 mm2

in2

10.76 ft2

m2

144 in2

ft2

5280 ft

mi

1.609 km

mi

25.4 mm

in

12 in

ft

39.37 in

m

3.281 ft

m

1000 lb

K

224.8 lbf

kN

4.448 * 105 dynes

lbf

105 dynes

N

4.448 N

lbf

1000 kg

metric tonm

2000 lbm

tonm

453.6 grams

lbm

2.205 lbm

kg

32.174 lbm

slug

14.59 kg

slug

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 743 TEAM-B 103:PEQY138:Appendix:

744 Appendix

Example 1. Convert a stress of 36 ksi to MPa.

Example 2. Convert a stress of 1272 MPa to ksi.

A–27 Review of the fundamentals of statics.

Introduction

The study of strength of materials depends on accurate knowledge of the forces acting onthe load-carrying member being analyzed or designed.

It is expected that readers of this book have completed the study of a course in staticsin which the principles of physics mechanics are used to determine the forces and momentsacting on members of a structure or a machine.

Presented here is a brief review of the principles of statics to help readers recallfundamental principles and problem-solving techniques.

Forces

A force is a push or pull effort applied to a structure or a member of the structure. If theforce tends to pull a member apart, it is called a tensile force. If the force tends to crush themember, it is called a compressive force. See Figure A–27–1 for examples of these kinds offorces applied in line with the axis of the members. These are called axial forces.

Forces on members in static equilibrium are always balanced in such a way that themember will not move. Thus in the two cases in Figure A–27–1, the two axial forces, F,are equal in magnitude but they act in opposite directions so they are balanced. You shouldalso note that every part of these members experiences an internal force equal to the exter-nally applied force, F. Figure A–27–2 shows this principle by illustrating a part of the ten-sile member cut anywhere between its ends. The force on the left is the externally appliedforce, F. The force on the right is the total internal force acting on the material of the mem-ber across its cross section.

Moments

A moment is the tendency for a force to cause rotation of a member about some point oraxis. Figure A–27–3 shows two examples. Each of the forces shown would tend to rotatethe member on which they act about the point identified as A.

The magnitude of the moment of a force is the product of the force times the per-pendicular distance from the line of action of the force to the point about which themoment is being computed. That is,

The direction is simply observed from the figure to be clockwise or counterclockwise.

M = Force times distance = F * d

s = 1272 MPa *

1.0 ksi

6.895 MPa= 184 ksi

s = 36 ksi *

6.895 MPa

ksi= 248 MPa

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 744 TEAM-B 103:PEQY138:Appendix:

Appendix 745

F

F

(a) Tensile force

(b) Compressive force

FF

Cut at any section

FInternal force

FExternal force

12 in

8 in

a

b

F2 = 60 lb

F1 = 100 lb

Line ofaction of F1

Point A

(a)

Line ofaction of F2

0.8 mc

0.5 ma

0.6 mb

F3 = 5.0 kN

F2 = 4.0 kNF1 = 3.0 kN

Point A

(b)

Line ofaction of F3

Line ofaction of F2

Line ofaction of F1

FIGURE A–27–1Types of axial forces.

FIGURE A–27–2Internal force.

FIGURE A–27–3Illustrations ofmoments.

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 745 TEAM-B 103:PEQY138:Appendix:

746 Appendix

Example from Figure A–27–3(a)

Example from Figure A–27–3(b)

Free-Body Diagrams

The ability to draw a complete free-body diagram of a structure and its members is anessential element of static analysis. You must show all externally applied forces and momentsand determine all reaction forces and moments that will result in the structure being inequilibrium.

Example from Figure A–27–4

Show the free-body diagram for the complete structure and for each of the two members.The applied force is F1 acting perpendicular to member BC.

See Figure A–27–5 for the result. The following discussion summarizes the importantpoints.

a. The structure is comprised of members AB and BC that are connected by a pin jointat B. AB is connected to the pin support at A. BC is connected to the pin support at C.Pin joints can provide a reaction force in any direction but they cannot resist rotation.We normally work with the horizontal and vertical components of the reaction forceson a pin joint. Therefore, we show in Figure A–27–5(a) the two components, Ax andAy, at A. Similarly, we show Cx and Cy at C.

b. Figure A–27–5(b) is the free-body diagram of member AB. You should recognize thatthe member would be in tension under the applied forces. The pin at B pulls downand to the right. Therefore, the pin at A must pull up and to the left to keep AB inequilibrium.

c. You should further recall that member AB is an example of a two-force memberbecause it is loaded only through pin joints. The resultant forces on a two-forcemember always act along the line between the two pins. We label that force as AB.Its components in the x and y directions are also shown. Note that the force system atA is equal and opposite to that at B.

Moment about A due to F3: MA = F3 * c = (5.0 kN)(0.8 m) = 4.0 kN�m CounterclockwiseMoment about A due to F2: MA = F2 * b = (4.0 kN)(0.6 m) = 2.4 kN�m ClockwiseMoment about A due to F1: MA = F1 * a = (3.0 kN)(0.5 m) = 1.5 kN�m Counterclockwise

Moment about A due to F2: MA = F2 * b = (60 lb)(8 in) = 480 lb�in CounterclockwiseMoment about A due to F1: MA = F1 * a = (100 lb)(12 in) = 1200 lb�in Clockwise

0.3 ma

0.5 mb

A

BC 20° = θ

F1

FIGURE A–27–4Support structure.

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:21 AM Page 746 TEAM-B 103:PEQY138:Appendix:

Appendix 747

d. Figure A–27–5(c) is the free-body diagram of member BC. This member is called abeam because it carries a load, F1, acting perpendicular to its long axis. There must bean upward reaction force at both B and C to resist the downward force F1. We callthose forces By and Cy. Member AB exerts the supporting force on member BC at B.That force acts upward and to the left. We call the horizontal component of that forceBx. The total force at B is equal to the force AB described in (c). Finally, to balance thehorizontal forces, there must be a force Cx acting toward the right at C.

Static Equilibrium

When a structure or a member is in static equilibrium, all forces and moments are balancedin such a way that there is no movement. The equations that describe static equilibrium are:

aM = 0 About any point

aFx = 0 aFy = 0 aFz = 0

0.3 ma

0.5 mb

A

BC 20° = θ

F1

Cx

Ax

Ay

Cy

(a) Free-body diagram of entire structure

AABx

20°

20° = θ

ABy

ABy

ABxB

AB

AB

(b) Free-body diagram of member AB

l

F1

Cx BBx

θBy

B

(c) Free-body diagram of member BC

ba

Cy

C

FIGURE A–27–5Free-body diagrams ofstructure and itscomponents.

Z01_MOTT8498_05_SE_APP.QXD 4/4/08 3:22 AM Page 747 TEAM-B 103:PEQY138:Appendix:

748 Appendix

The first three equations state that the sum of all forces in any direction must add to zero.We typically do the analysis in three perpendicular directions, x, y, and z. The fourth equa-tion states that the sum of the moments about any point must be zero.

We use the equations of equilibrium to determine the values of unknown forces andmoments when certain forces and moments are known and when suitable free-bodydiagrams are available.

Example from Figures A–27–4 and A–27–5

Determine the forces on all members and at all joints for the structure shown in FigureA–27–4. The given data are: F1 � 18.0 kN, a � 0.3m, b � 0.5m, � � 20°.

Solution. We use the free-body diagrams shown in Figure A–27–5.

Step 1. Use part (c) first. We sum moments about point C to find the force By.

Then,

We then sum moments about point B to find the force Cy.

Then,

We can check to see if all vertical forces are balanced by summing forces in the verticaldirection.

Step 2. Consider the forces acting at B. We know that By � 6.75 kN. We also knowthat the total resultant force, B, acts at an angle of 20° above the horizontal toward the left.This is because it is applied through the pin by the force AB. The free-body diagram in(b) indicates that AB acts along the direction of the member AB because it is a two-forcemember. We can then say,

Then,

Step 3. The forces acting at pin B on both member AB and member BC must beequal and opposite because of the principle of action-reaction. Therefore, the axial forceon member AB is: AB � 19.74 kN. The force AB acts at both A and B along the line betweenthe two pins in a manner that places the member AB in tension. The components of AB atpin A are equal to the components at pin B, but they act in opposite directions.

Bx = B cos 20° = (19.74 kN)(cos 20°) = 18.55 kN

B = By �(sin 20°) = (6.75 kN) �(sin 20°) = 19.74 kN

Bx = B cos 20°

By = B sin 20°

aFy = Cy + By - F1 = 11.25 kN + 6.75 kN - 18.0 kN = 0 (Check)

Cy = (18.0 kN)(0.5 m)�(0.8 m) = 11.25 kN

aMB = 0 = F1b - Cy l = (18.0 kN)(0.5 m) - Cy (0.8 m)

By = (18.0 kN)(0.3 m) �(0.8 m) = 6.75 kN

aMC = 0 = F1 a - By l = (18.0 kN)(0.3 m) - By (0.8 m)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 748 TEAM-B 103:PEQY138:Appendix:

Appendix 749

Step 4. The only unknown now is Cx, the horizontal force acting at C on memberBC. We can use the free-body diagram of member BC again from part (c) of the figure.

Then,

Equilibrium of Concurrent Force Systems

When the line of action of all forces acting on a member pass through the same point, thesystem is called a concurrent force system. For static equilibrium to exist in such a sys-tem, the vector sum of all forces must add to zero. Two methods can be used to analyze aconcurrent force system to determine unknown forces.

The Component Method

This method calls for each force to be resolved into perpendicular components, usuallyhorizontal and vertical. Then the classic equations of equilibrium are applied.

Example Using Figure A–27–6

Determine the force in each cable when the mass of the load is 1500 kg and the angle� � 25°

Cx = Bx = 18.55 kN

aFx = 0 = Cx - Bx

A

B

Load

(a) Cable system

D

C

θ = 25°

AByAB

(b) Free-body diagram of B with components of AB

ABx

BC

BD

AB

(c) Free-body diagram of B with vectors drawn to scale

BC

BD

Bθ = 25°

O

BD

AB

BC

65°

90° 25°

Intersection oflines of actionof AB and BC

(d) Vector triangle showing vector sum BD + BC + AB

FIGURE A–27–6Load carried by threecables showing forceanalysis.

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 749 TEAM-B 103:PEQY138:Appendix:

750 Appendix

Solution. There are three cables that we will call AB, BC, and BD. All three aretwo-force members and pass through point B as shown in part (b). Therefore, they areconcurrent.

Step 1. Determine the weight of the load. (See Section 1–5.)

This is also the force in the cable BD.

Step 2. Draw the free-body diagram of point B and resolve each force into its x andy components. This is done in part (b) of the figure.

Step 3. Use ∑Fy � 0 to solve for the unknown force AB.

Then,

But ABy is the vertical component of the cable force AB. Then,

Step 4. Use ∑Fx � 0 to find the unknown force BC.

Then,

Summary: The three cable forces are:

The Vector Polygon Method

This method calls for the vector addition of all forces acting at a point. When the forcesare in equilibrium, the polygon created by the vectors will close, indicating that the vectorsum is equal to zero.

Example Using Figure A–27–6(c)

Determine the force in each cable when the mass of the load is 1500 kg and the angle� � 25°

Solution. We must add the vectors, AB � BC � BD, as shown in part (d) of the fig-ure. The graphical solution would call for drawing each vector in its proper direction andwith a length scaled to its magnitude. The vectors are connected “tip to tail.” We will sketcha graphical vector diagram but solve for the required forces analytically.

AB = 34.8 kN BC = 31.6 kN BD = 14.7 kN

BC = ABx = AB cos 25° = (34.8 kN)(cos 25°) = 31.6 kN

aFx = 0 = BC - ABx

AB = ABy �(sin 25°) = (14.7 kN)�(sin 25°) = 34.8 kN

ABy = AB sin u = AB sin 25°

ABy = BD = 14.7 kN

aFy = 0 = ABy - BD

w = mg = (1500 kg)(9.81 m�s2) = 14 715 N = 14.7 kN

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 750 TEAM-B 103:PEQY138:Appendix:

Appendix 751

Step 1. The sum can be done in any order and we could start at any point, say pointO. We will actually sum the forces in the order BD � BC � AB. Let’s first draw the knownvector BD vertically downward to scale. The value is BD � 14.7 kN as found in the com-ponent method.

Step 2. Add vector BC from the tip of BD and acting horizontally to the right. Itslength is unknown at this time, but its line of action is known. Draw the line of indefiniteextent for now.

Step 3. Then, adding vector AB to the end of vector BC should cause the vectorpolygon to close by having the tip of AB fall right on point O. We can pass a line throughpoint O in the direction of AB. Where this line crosses the line of action of vector BC estab-lishes where the tip of BC is. Similarly, the tail of AB is also at that point.

Step 4. In the vector triangle thus formed, we know all three angles and the lengthof one side, BD. We can use the law of sines to find the lengths of the other two sides.

Then,

Also,

Then,

Summary. The results for the cable forces are identical to those found from the com-ponent method.

Law of Cosines Applied to Force Analysis

In some vector triangle solutions, you will know the magnitudes of two forces and theangle between them. You can solve for the third force using the law of cosines.

Say for example, in Figure A–27–6(d), you know the magnitudes of AB � 34.8 kN,BC � 31.6 kN, and that the angle between them is 25°. You could solve for the magnitudeof the force BD from:

Then,

You must carefully model the sides and angle to match the form of this equation.

BD = 1216 = 14.7 kN

= (34.8)2+ (31.6)2

- 2(34.8)(31.6) cos 25° = 216

(BD)2= (AB)2

+ (BC)2- 2(AB)(BC) cos 25°

AB = 34.8 kN BC = 31.6 kN BD = 14.7 kN

BC = (BD)(sin 65°) �(sin 25°) = (14.7 kN)(sin 65°)�(sin 25°) = 31.6 kN

BD

sin 25°=

BC

sin 65°

AB = (BD)(sin 90°)�(sin 25°) = (14.7 kN)(sin 90°)�(sin 25°) = 34.8 kN

BD

sin 25°=

AB

sin 90°

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 751 TEAM-B 103:PEQY138:Appendix:

752 Appendix

Trusses

A truss is a structure comprised of only straight members connected by pin joints withloads applied only at joints. The result is that all members are two-force members carry-ing either tensile or compressive loads. Figure A–27–7 shows an example. Next wedescribe the method of joints for analyzing the forces in all members of a truss.

Example Using Figure A–27–7

Find the forces in all members of the truss shown in Figure A–27–7. Determine both themagnitude and direction (tension or compression) for each force.

F1 = 1200 lbAy Fy

F2 = 1500 lb

Fx = 0

(b) Free-body diagram of complete truss

B C

D E FA α = 45° 45°θ = 33.7°

θ = Tan−1 = 33.7°

4 ft 4 ft6 ft

4 ft 4 ft

46

F1 = 1200 lb F2 = 1500 lb

(a) Complete truss with its supports

B C

D E FA α αθ4 ft 4 ft6 ft

4 ft 4 ft

Ay

ABy

(c) FBD of Joint A

AB

AD

ABx

A45°

CE

EFDE E

F2 = 1500 lb

(f) FBD of Joint E

CDy

CD

CDxAD DED

BD

F1 = 1200 lb

(e) FBD of Joint D

33.7°

CFy

Fy

(g) FBD of Joint F

CFx

CF

EFF

45°

ABy

ABBD

(d) FBD of Joint B

BCBABx

45°

( )

FIGURE A–27–7Forces on a truss andits joints.

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:19 AM Page 752 TEAM-B 103:PEQY138:Appendix:

Appendix 753

Analysis by Method of Joints

There are nine members in the truss. The general method for finding the forces in eachmember is described next.

a. Solve for the reactions at the supports for the entire truss.

b. Isolate one joint as a free body and show all forces acting on it. The selected jointmust have at least one known force acting on it. It is recommended that there be nomore than two unknown forces.

c. When a member is in tension, the force pulls out on the joint at either end. Conversely,a compression member pushes into a joint. Try to draw unknown forces in the properdirection that will ensure that the joint is in equilibrium.

d. Use the equations of static equilibrium for forces in the horizontal and vertical direc-tions to determine the unknown forces at the selected joint.

e. Forces found at the first joint become known forces for analyzing other joints. Moveto nearby joints and repeat steps b, c, and d repeatedly until the forces in all jointshave been found.

Completion of the Analysis of the Truss in Figure A–27–7

Step 1. Using the entire truss as a free body, solve for the support reactions at jointsA and F. See part (b) of the figure.Sum moments about support A to find support force Fy at point F.

Sum moments about support F to find support force Ay at point A.

Step 2. Isolate joint A as a free body. See part (c) of the figure. Work with compo-nents of the force AB. ABx � AB cos 45°. ABy � AB sin 45°.

Then,

Step 3. Isolate joint B as a free body. See part (d) of the figure.

BC = 1286 lb CompressionaFx = 0 = ABx - BC = 1286 lb - BC

BD = 1286 lb Tension

AD = ABx = AB cos 45° = (1818 lb)(cos 45°) = 1286 lb Tension

aFx = 0 = AD - ABx

AB = ABy �(sin 45°) = (1286 lb) �(sin 45°) = 1818 lb Compression

ABy = Ay = 1286 lb

aFy = 0 = Ay - ABy

Ay = [(12 000 + 6000) lb ft]�14 ft = 1286 lb Upward

aMF = F1(10 ft) + F2(4 ft) - Ay(14 ft) = (1200 lb)(10 ft) + (1500 lb)(4 ft) - Ay(14 ft)

Fy = [(4800 + 15 000) lb ft] �14 ft = 1414 lb Upward

aMA = F1(4 ft) + F2(10 ft) - Fy(14 ft) = (1200 lb)(4 ft) + (1500 lb)(10 ft) - Fy(14 ft)

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:20 AM Page 753 TEAM-B 103:PEQY138:Appendix:

Step 4. Isolate joint D as a free body. See part (e) of the figure.

Then,

Step 5. Isolate joint E as a free body. See part (f) of the figure.

Step 6. Isolate joint F as a free body. See part (g) of the figure.

Summary of Forces in Members of the Truss

DE = 1416 lb (T) EF = 1416 lb (T) CF = 2000 lb (C)

BC = 1286 lb (C) CE = 1500 lb (T) CD = 155 lb (C)

AB = 1818 lb (C) AD = 1286 lb (T) BD = 1286 lb (T)

CF = 1414 lb �(sin 45°) = 2000 lb CompressionaFy = 0 = Fy - CFy = 1414 lb - CFy = 1414 lb - CF sin 45°

EF = 1416 lb TensionaFx = 0 = EF - DF = EF - 1416 lb

CE = 1500 lb TensionaFy = 0 = 1500 lb - CE

DE = 1286 lb + 130 lb = 1416 lb TensionaFx = 0 = DE - AD - CDx = DE - 1286 lb - (155 lb)(cos 33.7°)

CD = CDy �(sin 33.7°) = (86 lb)>(sin 33.7°) = 155 lb Compression

CDy = 86 lb

aFy = 0 = 1200 lb - BD + CDy = 1200 lb - 1286 lb + CDy = CDy - 86 lb

754 Appendix

Z01_MOTT8498_05_SE_APP.QXD 4/3/08 1:20 AM Page 754 TEAM-B 103:PEQY138:Appendix: