expansion loops color

7/23/2019 Expansion Loops Color

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What we need to know before designing an Expansion LoopWhat we need to know before designing an Expansion Loop

(Code)(Code)

SpecificationSpecification ASTM AASTM A5353 Grade B, etc.Grade B, etc.

(Pipe schedule)(Pipe schedule)


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Piping layoutPiping layout terminal pointsterminal points (anchor points)(anchor points)

end reactionsend reactions

terminal pointsterminal points

A.S.M.E. Boiler and Pressure Vessel CodesA.S.M.E. Boiler and Pressure Vessel Codes

A.S.M.E. BA.S.M.E. B3131..11 20012001 -- Power PipingPower Piping

A.S.M.E. BA.S.M.E. B3131..22 19681968 -- Fuel Gas PipingFuel Gas Piping

A.S.M.E. BA.S.M.E. B3131..33 20022002 -- Process PipingProcess Piping

A.S.M.E. BA.S.M.E. B3131..44 20022002 -- Pipeline Transportation SystemsPipeline Transportation Systems

for Liquid Hydrocarbons and Other Liquidsfor Liquid Hydrocarbons and Other Liquids

. . . .. . . . .. --

Transfer ComponentsTransfer Components

A.S.M.E. BA.S.M.E. B3131..88 20032003 -- Gas Transmission andGas Transmission and

Distribution Piping SystemsDistribution Piping Systems


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Piping CodePiping Code CodeCode A.S.M.E.A.S.M.E. editionedition A.S.M.E. BA.S.M.E. B3131..11 ((ANSI BANSI B3131..11)) ::

anchor pointsanchor points

22

::

2

0.03nD Y

L U

= nominal pipe size= nominal pipe size Y =Y = U = anchor distanceU = anchor distance

anchor pointanchor point L = developed lengthL = developed length

nD

UAnchor pointAnchor point


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Four Components of StressesFour Components of Stresses

componentcomponent piping flexibilitypiping flexibility ::

1.1. Longitudinal stress,Longitudinal stress, SSLL(())

2.2. CircumferentialCircumferential hoop stress,hoop stress, SSCC ((

3.3. Radial stress,Radial stress, SSRR(())

4.4. Torsional shear stress, STorsional shear stress, STT

(())

SSRR

SSCC

Four Components of StressesFour Components of Stresses

SSRR

SSCC

SSLL

SSLL

SSTT

SSTT

PP

Longitudinal stress,Longitudinal stress, SSLL(())

CircumferentialCircumferential hoop stress,hoop stress, SSCC(())

Radial stress,Radial stress, SSRR(())

Torsional shear stress, STorsional shear stress, STT

(())


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Longitudinal stress,Longitudinal stress, SSLL

33componentscomponents stressstress ::

1.1. Bending stressBending stress looploop

Bendin stressBendin stress

B

m

MS

S

B

m

MS i

S

22. Bending stress. Bending stress (())

W

m

MS

S

LL


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33..

IPA

SteamSteam

P

MA

AAII

AAMM

L B W PS S S S

PS

PS

Circumferential or Hoop Stress,Circumferential or Hoop Stress, SSCC

= == =

2

C

D tS P

t

P

CS CS


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Radial Stress,Radial Stress, SSRR

componentcomponent

PP

Torsional Shear Stress,Torsional Shear Stress, SSTT

TT

2T

m

T

S Sh

b

L

Fx

B

B

C

C

Fx

A

A


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Combined StressCombined Stress (())

Piping flexibilityPiping flexibility . . . .. . . . .. ower p ngower p ng

(Max. shear theory)(Max. shear theory)

2 2( ) 4( )

E B TS S S

Expansion Stress,Expansion Stress, SSEE

A.S.M.E.A.S.M.E. BB3131..11,, SSEE

Expansion stressExpansion stress,, SS

AA(Allowable stress)(Allowable stress)

SSEE max.max.

SSBB

((max.max. SSTT))

max.max. SSTT

((max.max. SSBB))

SSTTSS

BBmax.max.

expansion stressexpansion stress SS

BB


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SSTT

Piping FlexibilityPiping Flexibility A.S.M.E. BA.S.M.E. B3131..11

SSSS

((SSTT

== 00 )) Piping FlexibilityPiping Flexibility

SSBB

SSAA

A.S.M.E. BA.S.M.E. B3131..11 SSBB

SSTT

Allowable Stress,Allowable Stress, SSAA

A.S.M.E. BA.S.M.E. B3131..11

SSCC

= Allowable stress= Allowable stress

(1.25 0.25 )A c hS f S S

SShh= Allowable stress= Allowable stress

ff = Fatigue factor= Fatigue factor (()) Cyclic conditionCyclic condition ((--))


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Fatigue FactorFatigue Factor

Fatigue factor,Fatigue factor, ff

77,,000000 11..00

1414,,000000 00..99

2222,,000000 00..88

4545 000000 00..77

100100,,000000 00..66

250250,,000000 00..55

Seamless carbon steel pipe to ASTM A106 Grade A ( ASTM A53 Grade A)

0F -20 650 700 750 775

7 Allowable Expansion Stress

, ps , , , ,

Seamless carbon steel pipe to ASTM A106 Grade B ( ASTM A53 Grade B)

0F -20 650 700 750 775

, psi 15,000 ( ) 14,300 12,900 11,850

Seamless carbon steel pipe to ASTM A106 Grade C

c

cS

0F -20 650 700 750 775

, psi 17,500 ( ) 16,600 14,700 13,350c

S


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TablesTables Expansion LoopsExpansion Loops

Table 1 Properties of Pipes

Dn= Nominal pipe size D = Outside diameter

t = Wall thickness d = inside diameter = D 2t

Inside area,2

4I

dA

Metal area, ( )mA t D t

Moment of inertia, 4 4 2 20.0491( ) 0.0625 ( )P mI D d A D d

Section modulus,2

Pm

IS

Nominal Sch. Nominal d t AI AM IP Sm

and

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

1(1.315)

40

80160

Std.

XS

XXS

1.049

0.9570.815

0.599

0.133

0.1790.250

0.358

0.864

0.7190.522

0.282

0.494

0.6390.836

1.076

0.0874

0.10560.1252

0.1405

0.133

0.1610.190

0.214

40 Std. 1.380 0.140 1.496 0.699 0.1948 0.235

11/4 (1.660) 80

160

XS

XXS

1.278

1.160

0.896

0.191

0.250

0.382

1.283

1.057

0.631

0.881

1.107

1.534

0.2418

0.2839

0.3411

0.291

0.342

0.411

11/2

(1.900)

40

80

160

Std.

XS

XXS

1.610

1.500

1.338

1.100

0.145

0.200

0.281

0.400

2.036

1.767

1.406

0.950

0.799

1.068

1.429

1.885

0.3099

0.3912

0.4826

0.5678

0.326

0.412

0.508

0.598

2

(2.375)

40

80

160

Std.

XS

XXS

2.067

1.939

1.689

1.503

0.154

0.218

0.343

0.436

3.356

2.953

2.240

1.774

1.075

1.477

2.190

2.656

0.6657

0.8679

1.1626

1.3120

0.561

0.731

0.979

1.104


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Properties of Pipes (2)

Nominal Sch. Nominal d t AI AM IP Smand

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

8

(8.625)

20

30

40 Std.

8.125

8.071

7.981

0.250

0.277

0.322

51.8

51.2

50.0

6.58

7.26

8.40

57.7

63.4

72.5

13.39

14.69

16.81

80

100

120

140

160

XS

XXS

.

7.625

7.439

7.189

7.001

6.875

6.813

.

0.500

0.593

0.718

0.812

0.875

0.906

.

45.7

43.5

40.6

38.5

37.1

36.5

.

12.76

14.96

17.84

19.93

21.30

21.97

.

105.7

121.4

140.6

153.8

162.0

165.9

.

24.52

28.14

32.61

35.65

37.56

38.48

10

(10.75)

20

30

40

60

80

100120

Std.

XS

10.250

10.136

10.020

9.750

9.564

9.3149.064

0.250

0.307

0.365

0.500

0.593

0.7180.843

82.5

80.7

78.9

74.7

71.8

68.164.5

8.26

10.07

11.91

16.10

18.92

22.6326.24

113.7

137.5

160.8

212.0

244.9

286.2324.3

21.16

25.57

29.90

39.43

45.56

53.2560.34

160

.

8.500

.

1.125

.

56.7

.

34.01

.

399.4

.

74.31

12

(12.75)

20

30

40

60

80

100

120

140

160

Std.

XS

12.250

12.090

12.000

11.938

11.750

11.626

11.376

11.064

10.750

10.500

10.126

0.250

0.330

0.375

0.406

0.500

0.562

0.687

0.843

1.000

1.125

1.312

117.9

114.8

113.1

111.9

108.4

106.2

101.6

96.1

90.8

86.6

80.5

9.84

12.88

14.58

15.74

19.24

21.52

26.04

31.53

36.91

41.08

47.14

191.9

248.5

279.3

300.3

361.5

400.5

475.2

561.8

641.7

700.7

781.3

30.1

39.0

43.8

47.1

56.7

62.8

74.5

88.1

100.7

109.9

122.6



and

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

16

(16.00)

10

20

30

40

Std.

XS

15.500

15.376

15.250

15.000

0.250

0.312

0.375

0.500

188.7

185.7

182.6

176.7

12.37

15.38

18.41

24.35

384.0

473.0

562.1

731.9

48.0

59.2

70.3

91.5

80

100

120

140

160

.

14.314

13.938

13.564

13.126

12.814

.

0.843

1.031

1.218

1.437

1.593

.

160.9

152.6

144.5

135.3

129.0

.

40.14

48.48

56.56

65.75

72.10

.

1156.6

1365.0

1555.8

1760.3

1894.0

.

144.6

170.6

194.5

220.0

236.7

18

(18.00)

10

20

30

40

60

80

100

Std.

XS

17.500

17.376

17.250

17.126

17.00016.876

16.500

16.126

15.688

0.250

0.312

0.375

0.437

0.5000.562

0.750

0.937

1.156

240.5

237.1

233.7

230.4

227.0223.7

213.8

204.2

193.3

13.94

17.34

20.76

24.11

27.4930.79

40.64

50.23

61.18

549.0

678.0

806.6

930.5

1053.01172.0

1515.0

1833.9

2180.2

61.0

75.5

89.6

103.4

117.0130.2

168.3

203.8

242.2

120

140

160

15.250

14.876

14.438

1.375

1.562

1.781

182.6

173.8

163.7

71.81

80.66

90.74

2498.8

2749.8

3020.6

277.6

305.5

335.6

20

(20.00)

10

20

30

40

60

80

100

120

140

160

Std.

XS

19.500

19.250

19.000

18.814

18.376

17.938

17.438

17.000

16.500

16.064

0.250

0.375

0.500

0.593

0.812

1.031

1.281

1.500

1.750

1.968

298.6

291.0

283.5

178.0

265.2

252.7

238.8

227.0

213.8

202.7

15.51

23.12

30.6

36.2

48.9

61.4

75.3

87.2

100.3

111.5

757

1114

1457

1704

2257

2772

3316

3755

4217

4586

75.7

111.4

145.7

170.4

225.7

277.2

331.6

375.5

421.7

458.6


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Table 2 Moduli of Elasticity and Torsional Rigidity for FerrousMaterials

psixGpsixE 66 10,10

Material Modulus Temp.0F

70 200 300 400 500 600 700 800 900 1000 1100 1200

Carbon steel,

C 0.30 %

E

G

27.9

10.8

27.7

10.7

27.4

10.6

27.0

10.4

26.4

10.2

25.7

9.9

24.8

9.6

23.4

9.0

18.5

7.1

15.4

5.9

13.0

5.0

-

ar on stee,

C 0.30 % G

.

11.6

.

11.4

.

44.2

.

10.9

.

10.7

.

10.3

.

9.8

.

9.2

.

8.3

.

7.2

.

5.7

.

Carbon-moly

steel low

chrome-moly

E

G

29.9

11.6

29.5

11.4

29.0

11.2

28.6

11.0

28.0

10.8

27.4

10.6

26.6

10.2

25.7

9.9

24.5

9.4

23.0

8.8

20.4

7.8

15.6

5.9

steel through

3 % Cr

Intermediate

chrome-moly

steel

E

G

27.4

10.6

27.1

10.4

26.8

10.3

26.4

10.1

26.0

9.9

25.4

9.7

24.9

9.5

24.2

9.2

23.5

8.9

22.8

8.6

21.9

8.3

20.8

7.8

(5%-9% Cr),

austenitic

stainless steel

Straight

Chromium

stainless steel

E 29.2 28.7 28.3 27.7 27.0 26.0 24.8 23.1 21.1 18.6 15.6 12.2

(12 Cr, 17 Cr,

27 Cr)

G 11.4 11.2 11.0 10.8 10.5 10.1 9.6 9.0 8.2 7.2 6.0 4.7

Material Coef.0F

70 200 400 600 800 1000 1200

Carbon steel; carbon-moly steel; 6.38 6.82 7.23 7.65 7.97 8.19

Table 3 Thermal Expansion Data

Mean coefficient of thermal expansion 610 x inch/inch/0F (

700F )

Linear thermal expansion inch/100 ft, .(1 0 0 ) .(1 2 ) ( 7 0 )ft in c h t

ow c rome stee s (t roug r) . . . . . .

Intermediate alloy steels; (5 Cr-Mo 6.04 6.34 6.66 6.96 7.22 7.41through 9 Cr-Mo) 0 0.94 2.50 4.24 6.10 8.06 10.00

Austenitic stainless steels 9.34 9.59 9.82 10.05 10.29 10.48 0 1.46 3.80 6.24 8.80 11.48 14.20

Straight chromium stainless steels: 5.50 5.81 6.13 6.39 6.63 6.7812 Cr, 17 Cr and 27 Cr 0 0.86 2.30 3.90 5.60 7.40 9.20

r- . . . . . .

0 1.21 3.20 5.33 7.60 9.95 12.31

Wrought iron 7.32 7.61 7.88 8.13 8.39 - 0 1.14 3.01 5.01 7.12 9.36 -

Brass 9.76 10.23 10.69 11.16 11.63 12.09 0 1.52 4.05 6.80 9.78 12.98 16.39


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Table 4 Expansion Factors, c

Temp0F

Carbon

steel,

C

.30%

Carbon

steel,

C

0.30%

Carbon-

moly

steel low

Cr-moly

Cr 3%

Carbon-

moly

steel

5%-9%

Cr

Austenitic

stainless

steels

Chromium

stainless

steels (12

Cr, 17 Cr,

27 Cr)

25 Cr-

20 Ni

Wrought

iron

70 0 0 0 0 0 0 0 0

100 37 40 40 35 54 34 47 44

150 98 106 106 92 143 90 125 120

200 160 171 171 149 232 145 204 195

250 228 244 244 212 323 204 287 273

300 294 315 315 271 414 264 368 352

350 365 391 391 335 509 326 455 434

400 436 467 467 396 603 289 541 514

450 510 547 547 465 699 455 629 598

500 584 626 626 531 794 520 716 681

550 664 711 711 603 893 590 809 768

600 743 796 796 672 989 659 901 855

650 827 886 886 714 1089 730 995 946700 909 974 974 815 1189 799 1088 1035

775 1038 1113 1113 929 1344 909 1235 1171

800 - - 1159 967 1395 946 1284 1216

825 - - 1208 1005 1448 983 1335 -

850 - - 1256 1043 1500 1022 1384 -

875 - - 1303 1081 1552 1061 1435 -

900 - - 1351 1121 1605 1097 1484 -

Note: Expansion factor0 070 70

100 .

1728 100 1728 100

F FExpansion in inches per ft x E x E

cx x

TableTable 55

Table of Common ShapesTable of Common Shapes

For calculation of Thermal Stresses andFor calculation of Thermal Stresses and


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Table 5.1 : 900Turn

Reacting forces lbL

IckF Pxx 2..

lbL

IckF Pyy 2..

Max. bending stress

. .B b

DS k c psi

L

L, feet, D, inches, IP, inches4

h

Fy

Fx

Fy

L

Fx

L

h x

k yk bk

1.0 12.0 12.0 36

1.2 17.2 12.5 46

1.4 23.0 13.4 58

1.6 32.0 14.1 71

1.8 42.0 15.4 85

2.0 54.0 16.6 102

2.2 68.3 17.8 120

2.4 84.4 19.2 140

2.6 103 20.6 161

2.8 125 22.0 184

3.0 150 23.5 209

3.2 175 25.0 234

3.4 207 26.5 259

3.6 237 28.0 287

3.8 274 29.5 318

4.0 315 31.5 349

4.2 356 33.0 381

4.4 406 34.6 414

4.6 456 36.2 450

4.8 510 37.8 487

5.0 570 39.5 528

Table 5.2 : Hooked Z Shape

Reacting forces

lbL

IckF Pxx 2..

lbL

IckF P

yy 2..

Max. bending stress

. .B b

DS k c psi

L

Fxh

Fy

L

Fy

L/2

Fx

h/2

L

h x

k yk bk

0.6 1.18 1.31 5.9

0.8 2.7 2.2 9.4

1.0 4.3 3.3 13.1

1.2 7.8 4.7 17.31.4 11.2 6.2 22.0

1.6 15.2 7.7 26.7

1.8 19.7 9.2 31.4

2.0 24.3 10.9 36.4

L, feet, D, inches, IP,

. . . .

2.4 37.0 15.1 46.6

2.6 45.0 17.2 51.7

2.8 54.0 19.3 58.0

3.0 64.8 21.6 64.8

3.2 76.0 24.0 72.0

3.4 88.0 26.5 79.5

3.6 100.0 29.0 87.0

3.8 113.5 31.6 95.0

4.0 128.7 34.5 103

4.2 144 37.4 112

4.4 160 40.4 121

4.6 178 43.4 130

4.8 198 46.4 139

5.0 219 49.4 148


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Table 5.3 : Z Shape

Reacting forces

lbL

IckF P

xx 2..

lbL

IckF P

yy 2..

Max. bending stressD

Fx

h

Fy

Fx

a

b

a/b 1 1.5 2 3 4

L/hx

k yk bk xk yk bk xk yk bk xk yk bk xk yk bk

0.6 9.25 43.0 83.8 8.5 38 91 7.3 32 85 6.5 25 73 6.0 22 66

0.8 12.8 39.0 69.0 11.8 35 76 10.5 29 71 9.2 23 62 8.5 20 56

1.0 17.2 37.9 61.9 15.9 34 69 14.4 29 66 12.6 22 52 11.8 19 50

1.2 22.5 37.8 57.8 21.0 35 69 18 29 66 16.0 23 53 14 20 511.4 28.3 37.7 60.6 27 36 69 22 30 67 20 24 55 19 21 52

. .B b

L


Fy

L

. . . .

1.8 43.0 43.2 72.0 41 39 75 38 33 71 34 26 60 30 22 58

2.0 52.8 45.7 79.3 50 41 81 46 35 76 42 27 67 40 24 63

2.2 63.0 48.0 86.5 60 43 88 57 38 83 51 29 73 48 25 68

2.4 76.0 51.0 93.8 71 46 96 68 40 90 61 31 80 58 27 74

2.6 89.0 54.5 101.2 83 49 102 79 43 97 71 33 86 69 29 80

2.8 102 58.2 109.0 96 53 110 91 46 105 82 35 92 80 30 87

3.0 116 62.2 116.1 110 56 118 104 49 115 92 37 99 90 32 93

3.2 132 66.0 124.5 124 59 126 118 51 121 106 39 107 104 34 99

3.4 149 70.0 133.0 140 63 134 133 54 128 121 41 114 118 36 105

3.6 168 74.0 141.0 168 66 143 149 57 135 136 44 120 132 38 111

3.8 188 78.0 149.0 177 70 151 165 60 142 151 46 127 147 40 117

4.0 210 82.0 157.8 197 73 159 181 63 150 166 49 133 163 42 124

Table 5.4 : U Shape (1)

Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B b

DS k c psi

L


FxFx

h

L

a

L/a 2 4 5 6

L/hx

k b

k x

k b

k x

k b

k x

k b

k

2.0 12.00 18.00 13.24 24.8 13.87 27.1 14.4 28.8

2.2 14.85 20.25 16.6 28.5 16.9 31.0 17.5 33.4

2.4 18.00 22.50 20.4 32.2 20.8 35.3 21.3 38.0

2.6 21.52 24.83 24.4 35.9 25.5 39.7 26.2 42.7

2.8 25.32 27.10 28.9 39.7 30.6 44.0 31.7 47.5

4.0 54.9 41.1 64.0 64.0 69.1 72.5 73.6 79.7

4.4 67.3 45.9 78.9 72.4 87.2 82.5 91.0 90.8

4.6 73.9 45.2 87.0 76.6 96.3 87.5 101.7 96.3

4.8 81.0 50.6 95.8 80.8 105.4 92.5 112.4 101.9

5.0 88.2 52.9 104.6 85.2 114.7 97.8 122.5 107.5

. . . . . . . . .

5.6 112.1 60.1 134.0 98.3 147.6 113.5 159.0 126.2

5.8 120.7 62.4 144.6 102.7 159.0 118.8 172.0 132.5

6.0 129.6 64.8 155.8 107.0 171.3 124.1 185.2 138.8

6.4 148.4 69.6 179.1 116.0 198.0 134.9 213.0 151.4

6.6 158.2 71.9 191.0 120.5 212.2 140.3 228.0 157.7

6.8 168.4 74.3 204.0 125.0 226.4 145.7 244.2 164.0

7.0 178.9 76.7 217.0 129.4 240.7 151.1 261.8 170.3

7.2 189.8 79.1 230.5 133.9 256.0 156.6 279.8 176.7

7.4 200.9 81.5 244.2 138.4 271.5 162.1 297.8 183.1

7.6 312.4 83.8 259.2 142.9 287.5 167.6 316 189.5

7.8 224.2 86.2 274.5 147.4 304.3 173.1 334 195.9

8.0 236.2 88.6 289.8 152.0 322 178.6 352 202.4


17/29

9/11/2011

17

Table 5.5 : U Shape 12

2L

L

Reacting forces

lbL

IckF P

xx 2..

lbL

IckF P

yy 2..

Max. bending stress

. .B bD

S k c psiL

Fx

h

L

a

Fx

Fy Fy

L1 L2

L/a 2 4 6 8

L/hx

k y

k b

k x

k y

k b

k x

k y

k b

k x

k y

k b

k

1.0 2.5 0.5 8.7 2.7 1.1 9.9 2.8 1.4 10.7 2.9 1.5 10.9

1.2 4. 4 0.7 11.7 5.3 1.6 12.5 5.0 1.8 14.6 5.5 2.0 15.5

1.4 6. 4 1.0 14.6 8.0 2.1 15.1 7.6 2.2 18.8 8.2 2.5 20.1

1.6 8.4 1.2 17.5 10.8 2.6 17.1 10.2 2.7 23.0 10.9 2.9 24.8

1.8 10.4 1.5 20.7 13.6 3.1 20.4 12.9 3.1 27.2 13.6 3.4 29.5

2.0 12.4 1.7 23.3 16.5 3.6 23.3 15.6 3.6 31.5 16.5 3.8 34.2

2.2 16.0 2.0 26.6 20.3 3.9 28.3 20.6 4.0 36.6 20.0 4.2 39.02.4 19.7 2.3 29.9 24.1 4.3 33.4 25.6 4.5 41.7 24.0 4.7 44.0

2.6 23.4 2.7 33.2 28.0 4.6 38.5 30.6 4.9 46.8 28.0 5.1 49.1


2.8 27.1 3.0 36.5 32.0 4.9 43.6 35.6 5.4 51.9 33.0 5.6 54.6

3.0 30.9 3.3 40.1 36.1 5.3 48.7 40.7 5.9 57.0 40.8 6.0 59.6

3.2 36.3 3.7 43.7 41.0 5.7 53.2 48.0 6.3 62.8 47.0 6.5 68.0

3.4 41.7 4.0 47.3 47.0 6.2 57.7 56.0 6.8 69.0 55.0 7.0 75.0

3.6 46.1 4.4 50.9 53.0 6.6 62.0 64.0 7.3 74.0 65.0 7.4 83.0

3.8 51.5 4.8 54.5 60.0 7.1 67.0 72.0 7.8 80.0 76.0 7.9 91.0

4.0 58.0 5. 2 58.0 69.0 7.5 71.0 80.0 8.2 86. 0 87.0 8.4 100

4.2 65.0 5. 5 62.0 77.0 8.0 76.0 90.0 8.7 92. 0 98.0 8.9 107

4.4 72.0 5.9 65.0 86.0 8.4 80.0 100 9.1 99.0 109 9.4 115

4.6 79.0 6.3 69.0 95.0 8.8 85.0 111 9.5 105 120 9.8 122

4.8 86.0 6.7 72.0 104 9.0 89.0 122 9.9 111 133 10.3 130

5.0 94.0 7. 0 76.0 113 9. 6 94.0 132 10.4 116 147 10.8 138

5.2 103 7.5 80.0 124 10.0 99.0 145 10.9 122 158 11.3 146

5.4 112 7.9 84.0 135 10.5 104 158 11.3 128 173 11.7 154

5.6 121 8.3 88.0 146 10.9 108 172 11.8 134 189 12.2 162

5.8 131 8.7 92.0 157 11.4 113 185 12.3 140 206 12.6 171

6.0 140 9.2 96.0 168 11.8 118 199 12.7 146 224 13.1 179

Table 5.8 : U Shape

Reacting forces

lbL

IckF Pxx 2..

lbL

IckF Pyy 2..

Max. bending stress

. .B bD

S k c psiL

Fx

h

L

a

Fx

Fy

Fy

L/a 2 3 4

L/hx

k y

k b

k x

k y

k b

k x

k y

k b

k

1.0 2.8 1.41 11.3 3.3 2.3 12.5 3.6 2.7 13.0

1.2 4.8 2.28 15 6 3.5 18.3 6.0 3.9 18.4

1.4 7 3.15 20 9 4.8 24.1 9.0 5.1 23.8

1.6 9 4.0 25 12 6.0 30 12.0 6.3 29.2

1.8 12 4.9 30 16 7.2 36 16.5 7.5 34.62.0 16 5. 8 28 20 8.4 42 21.3 8.8 40

2.2 20 7.1 44 25 10.0 49 28 10.5 48

2.4 24 8.4 50 30 11.5 56 34 12.1 55

2.6 30 9.8 58 36 13.0 63 40 13.8 62

. . . .

3.0 45 12.4 75 53 16 77 59 17.2 77

3.2 52 14.1 82 62 18 87 69 19.0 85

3.4 60 15.8 90 71 20 96 80 21.0 93

3.6 70 17.5 99 81 22 105 91 23.0 101

3.8 80 19 109 94 24 114 103 24.6 110

4.0 91 21 120 108 26 124 117 26.5 118

4.2 102 23 130 121 28 134 131 29 127

4.4 114 25 140 135 30 144 147 31 136

4.6 128 27 151 150 33 154 164 33 145

4.8 142 29 162 167 35 164 181 35 154

5.0 156 31 173 185 37 174 198 37 163

5.2 171 33 185 203 39 183 218 39 173

5.4 188 36 197 221 41 193 238 41 182


18/29

9/11/2011

18

Table 5.9 : U Shape

Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B b

DS k c psi

L

Fx

h

L

Fx

L/hx

k bk

1.0 3.00 12.00

1.2 4.88 16.74

1.4 7.37 22.26

1.6 10.55 28.56

1.8 14.48 35.52

2.0 19.2 43.20

2.2 24.6 52.32

2.4 31.4 60.72

2.6 39.2 70.56

2.8 48.0 81.243.0 57.8 92.64

3.2 69.1 104.5

3.4 82.2 118.2

3.6 95.6 130.8

3.8 111.0 138.4

4.0 128.1 160.0

4.2 147.0 176.1

4.4 166.6 192.0

4.6 189.0 208.8

4.8 213.0 227.4

5.0 239.0 246.0

5.2 266.0 264.0


Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B bD

S k c psiL

Torsional stressD

h

b

L

Fx

AA

B

B

C

C

1. tk torsional shear stress 2. maximum bending stress maximum torsional shear stress3. combined stress

L/b 1 2 3 4

L/h xk bk tk xk bk tk xk bk tk xk bk tk

. .T tc psiL

Fx

. .

(A)

.

(A)

. .

(A)

. . .

(A)

.

(A)

. .

(A)

.

(A)

2 1.24 3.31

(A)

1.73

(A)

4.40 11.2

(A)

3.0 7.65 18.9

(A)

3.4

(A)

11.0 24.8

(A)

3.4

(A)

4 1.72 5.65

(B)

- 7.70 10.5

(A)

6.5 16.6 22.2

(A)

9.7

(A)

27.7 36.7

(A)

12.0

(A)

5 1.86 6.34

(B)

- 8.74 15.6

(B)

- 20.0 22.0

(A)

12.2

(A)

34.5 37.2

(A)

16.0

(A)

6 1.99 6.95

(B)

- 9.55 17.6

(B)

- 22.4 28.4

(B)

- 40.0 44.6

(B)

-

7 2.08 7.40

(B)

- 10.2 19.3

(B)

- 24.5 32.0

(B)

- 44.7 44.9

(B)

-

8 2.16 7.80

(B)

- 10.9 21.0

(B)

- 26.5 35.4

(B)

- 49.0 51.4

(B)

-


19/29

9/11/2011

19


Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B bD

S k c psiL

Torsional stress

h

b

a

F

L

A

A

BB

C

C

D

D

1.

tk torsional shear stress 2. maximum bending stress maximum torsional shear stress

L/a = 6

a/b0.50 1 2 3


1 1.5 4.7

(A)

- 1.90 6.1

(C)

- 2.2 7.5

(C)

- 2.32 8.1

(C)

-

. .T t

DS k c psi

L

F

2 5.86 9.7

(D)

4.10

(D)

8.65 14.3

(C)

- 10.7 19.

(C)5

- 11.8 22.0

(C)

-

4 15.95 25.0

(D)

5.45

(D)

32.6 27.0

(D)

13.7

(D)

47.4 45.0

(C)

- 54.2 53.7

(C)

-

6 23.0 35.0

(D)

5.18

(D)

60.9 49.3

(D)

17.0

(D)

104 68.0

(C)

- 125 84.0

(C)

-

8 27.3 40.8

(D)

4.59

(D)

86.0 68.6

(D)

18.3

(D)

173 72.0

(D)

42.50

(D)

220 114

(C)

-

9 28.6 42.5

(D)

4.29

(D)

96.6 76.5

(D)

18.2

(D)5

209 86.5

(D)

45.75

(D)

274 128

(C)

-

10 29.8 44.2

(D)

4.02

(D)

106 84.0

(D)

18.15

(D)

244 100.5

(D)

48.25

(D)

330 137.5

(C)

8.9

(C)

1188 ASTM AASTM A106106 Grade BGrade B750750 00FF cyclic loadingcyclic loading 77,,000000 allowable stressallowable stress

77 :: SSCC== 1515,,000000 psi,psi, SS

hh== 1212,,900900 psipsi

SSAA

= f(= f(11..2525SSCC++00..2525SS

hh))

= (= (11)()(11..2525xx1515,,000000++00..2525xx1290012900))

== ,,


20/29

9/11/2011

20

Seamless carbon steel pipe to ASTM A106 Grade A ( ASTM A53 Grade A)

0F -20 650 700 750 775

7 Allowable Expansion Stress

, ps , , , ,

Seamless carbon steel pipe to ASTM A106 Grade B ( ASTM A53 Grade B)

0F -20 650 700 750 775

, psi 15,000 ( ) 14,300 12,900 11,850

Seamless carbon steel pipe to ASTM A106 Grade C

c

cS

0F -20 650 700 750 775

, psi 17,500 ( ) 16,600 14,700 13,350c

S

2288 Sch.Sch. 4040 ASTM AASTM A106106 Grade BGrade B looploop 909000 TurnTurn

00 ,,A.S.M.E. BA.S.M.E. B3131..11

FFyy

FFxx

L=L=2828..55 mm

h =h = 1111..55 mm

FFyy

FFxx

FF

AnchorAnchor


21/29

9/11/2011

21



and

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

8

(8.625)

20

30

40 Std.

8.125

8.071

7.981

0.250

0.277

0.322

51.8

51.2

50.0

6.58

7.26

8.40

57.7

63.4

72.5

13.39

14.69

16.81

60

80

100

120

140

160

XS

XXS

7.813

7.625

7.439

7.189

7.001

6.875

6.813

0.406

0.500

0.593

0.718

0.812

0.875

0.906

47.9

45.7

43.5

40.6

38.5

37.1

36.5

10.48

12.76

14.96

17.84

19.93

21.30

21.97

88.8

105.7

121.4

140.6

153.8

162.0

165.9

20.58

24.52

28.14

32.61

35.65

37.56

38.48

10

(10.75)

20

30

40

60

80

100120

140

Std.

XS

10.250

10.136

10.020

9.750

9.564

9.3149.064

8.750

0.250

0.307

0.365

0.500

0.593

0.7180.843

1.000

82.5

80.7

78.9

74.7

71.8

68.164.5

60.1

8.26

10.07

11.91

16.10

18.92

22.6326.24

30.63

113.7

137.5

160.8

212.0

244.9

286.2324.3

367.8

21.16

25.57

29.90

39.43

45.56

53.2560.34

68.43

160 8.500 1.125 56.7 34.01 399.4 74.31

12

(12.75)

20

30

40

60

80

100

120

140

160

Std.

XS

12.250

12.090

12.000

11.938

11.750

11.626

11.376

11.064

10.750

10.500

10.126

0.250

0.330

0.375

0.406

0.500

0.562

0.687

0.843

1.000

1.125

1.312

117.9

114.8

113.1

111.9

108.4

106.2

101.6

96.1

90.8

86.6

80.5

9.84

12.88

14.58

15.74

19.24

21.52

26.04

31.53

36.91

41.08

47.14

191.9

248.5

279.3

300.3

361.5

400.5

475.2

561.8

641.7

700.7

781.3

30.1

39.0

43.8

47.1

56.7

62.8

74.5

88.1

100.7

109.9

122.6

1 D = 8.625

PI = 72.5 inch

4

4 c = 996

28.52.48

11.5

L

h

84.4 103

. .2

x

19.2 20.619.9

2y

k

140 161150.5

2bk

8.625. . 150.5 996 13, 622.828.5 3.33

B b

DS k c x x psiL x

, . . . . .

2 2

72.5. . 93.7 996 751.2

(28.5 3.33)P

x x

IF k c x x lb

L x

2 2

72.5. . 19.9 996 159.5

(28.5 3.33)

Py y

IF k c x x lb

L x

2 2x y

F F F = 2 2(751.2) (159.5) = 767.9 lb


22/29

9/11/2011

22

Table 5.1 : 900Turn

Reacting forces lbL

IckF Pxx 2..

lbL

IckF Pyy 2..

Max. bending stress

. .B bD

S k c psiL


h

Fy

Fx

Fy

L

Fx

L

h x

k y

k b

k

1.0 12.0 12.0 36

1.2 17.2 12.5 46

1.4 23.0 13.4 58

1.6 32.0 14.1 71

1.8 42.0 15.4 85

2.0 54.0 16.6 102

2.2 68.3 17.8 120

2.4 84.4 19.2 1402.6 103 20.6 161

. .

3.0 150 23.5 209

3.2 175 25.0 234

3.4 207 26.5 259

3.6 237 28.0 287

3.8 274 29.5 318

4.0 315 31.5 349

4.2 356 33.0 381

4.4 406 34.6 414

4.6 456 36.2 450

4.8 510 37.8 487

5.0 570 39.5 528

331010 Sch.Sch. 4040 ASTM AASTM A106106Grade AGrade A loop Uloop U--ShapeShape

00 1818,,000000 psipsi hh

h

Fx

L=18 m

Fx

Anchor


23/29

9/11/2011

23



and

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

8

(8.625)

20

30

40 Std.

8.125

8.071

7.981

0.250

0.277

0.322

51.8

51.2

50.0

6.58

7.26

8.40

57.7

63.4

72.5

13.39

14.69

16.81

80

100

120

140

160

XS

XXS

.

7.625

7.439

7.189

7.001

6.875

6.813

.

0.500

0.593

0.718

0.812

0.875

0.906

.

45.7

43.5

40.6

38.5

37.1

36.5

.

12.76

14.96

17.84

19.93

21.30

21.97

.

105.7

121.4

140.6

153.8

162.0

165.9

.

24.52

28.14

32.61

35.65

37.56

38.48

10

(10.75)

20

30

40

60

80

100

120

140

Std.

XS

10.250

10.136

10.020

9.750

9.564

9.314

9.064

8.750

0.250

0.307

0.365

0.500

0.593

0.718

0.843

1.000

82.5

80.7

78.9

74.7

71.8

68.1

64.5

60.1

8.26

10.07

11.91

16.10

18.92

22.63

26.24

30.63

113.7

137.5

160.8

212.0

244.9

286.2

324.3

367.8

21.16

25.57

29.90

39.43

45.56

53.25

60.34

68.43

160 8.500 1.125 56.7 34.01 399.4 74.31

12

(12.75)

20

30

40

60

80

100

120

140

160

Std.

XS

12.250

12.090

12.000

11.938

11.750

11.626

11.376

11.064

10.750

10.500

10.126

0.250

0.330

0.375

0.406

0.500

0.562

0.687

0.843

1.000

1.125

1.312

117.9

114.8

113.1

111.9

108.4

106.2

101.6

96.1

90.8

86.6

80.5

9.84

12.88

14.58

15.74

19.24

21.52

26.04

31.53

36.91

41.08

47.14

191.9

248.5

279.3

300.3

361.5

400.5

475.2

561.8

641.7

700.7

781.3

30.1

39.0

43.8

47.1

56.7

62.8

74.5

88.1

100.7

109.9

122.6

1 D = 10.75

PI = 160.8 inch

4

4 c = 743

18, 000 18 3.33

. . , 135BB b b

S LD x xS k c k

.

5.9 3.6, 130.8, 95.6b x

Lk k

h

3.8, 138.4, 111b x

Lk k

h

135 130.8

135, 3.6 3.8 3.6 3.71138.4 130.8b

Lk h

18

4.85 16.2h m t 3.71

3.71 3.6

95.6 111 95.6 1043.8 3.6

xk

2 2

743 160.8104 3, 458

(18 3.33)

Px x

cI xF k x lb

L x


24/29

9/11/2011

24

Table 5.9 : U Shape

Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B bD

S k c psiL

Fx

h

L

Fx

L/hx

k b

k

1.0 3.00 12.00

1.2 4.88 16.74

1.4 7.37 22.26

1.6 10.55 28.56

1.8 14.48 35.52

2.0 19.2 43.20

2.2 24.6 52.32

2.4 31.4 60.72

2.6 39.2 70.56

2.8 48.0 81.243.0 57.8 92.64

. . .

3.4 82.2 118.2

3.6 95.6 130.8

3.8 111.0 138.4

4.0 128.1 160.0

4.2 147.0 176.1

4.4 166.6 192.0

4.6 189.0 208.8

4.8 213.0 227.4

5.0 239.0 246.0

5.2 266.0 264.0

44Loop U ShapeLoop U Shape Sch.Sch. 4040 ASTM AASTM A106106 Grade BGrade B 121270070000 FF cycliccyclic

loadingloading 2020,,000000 L=L= 100100 aa== 2020 LoopLoop hh A.S.M.E. BA.S.M.E. B3131..11

a

Fx

h

L

Fx


25/29

9/11/2011

25



and

outside

diameters,

Dn, (D),

inch.

No. wall Inside

diameter

inches

Wall

thickness.

inches

Inside

area

inches2

Metal

area

inches2

Moment

of

inertia

inches4

Section

modulus

inches3

8

(8.625)

20

30

40

60

Std.

8.125

8.071

7.981

7.813

0.250

0.277

0.322

0.406

51.8

51.2

50.0

47.9

6.58

7.26

8.40

10.48

57.7

63.4

72.5

88.8

13.39

14.69

16.81

20.58

80

100

120

140

160

XS

XXS

7.625

7.439

7.189

7.001

6.875

6.813

0.500

0.593

0.718

0.812

0.875

0.906

45.7

43.5

40.6

38.5

37.1

36.5

12.76

14.96

17.84

19.93

21.30

21.97

105.7

121.4

140.6

153.8

162.0

165.9

24.52

28.14

32.61

35.65

37.56

38.48

10

(10.75)

20

30

40

60

80

100

120140

Std.

XS

10.250

10.136

10.020

9.750

9.564

9.314

9.0648.750

0.250

0.307

0.365

0.500

0.593

0.718

0.8431.000

82.5

80.7

78.9

74.7

71.8

68.1

64.560.1

8.26

10.07

11.91

16.10

18.92

22.63

26.2430.63

113.7

137.5

160.8

212.0

244.9

286.2

324.3367.8

21.16

25.57

29.90

39.43

45.56

53.25

60.3468.43

. . . . . .

12

(12.75)

20

30

40

60

80

100

120

140

160

Std.

XS

12.250

12.090

12.000

11.938

11.750

11.626

11.376

11.064

10.750

10.500

10.126

0.250

0.330

0.375

0.406

0.500

0.562

0.687

0.843

1.000

1.125

1.312

117.9

114.8

113.1

111.9

108.4

106.2

101.6

96.1

90.8

86.6

80.5

9.84

12.88

14.58

15.74

19.24

21.52

26.04

31.53

36.91

41.08

47.14

191.9

248.5

279.3

300.3

361.5

400.5

475.2

561.8

641.7

700.7

781.3

30.1

39.0

43.8

47.1

56.7

62.8

74.5

88.1

100.7

109.9

122.6

1 D = 12.75

PI = 300.3 inch4

4 c = 909

1005

20

L

a

6 f = 0.8

7 15, 000 , 14, 300c hS psi S psi

(1.25 0.25 ) (0.8)(1.25 15000 0.25 14300) 17,860A c hS f S S x x psi

. . , AA B b b

s LDS S k c k

L cD

17800 100153.6

909 12.75b

xk

x

5.4 : 7.0, 151.1, 240.7b x

L

k kh

7.2, 156.6, 256b x

Lk k

h

153.6 151.1

153.6, 7.0 7.2 7.0 7.09156.6 151.1

b

Lk

h

100

14.17.09

h ft

7.09 7.0

240.7 256 240.7 247.67.2 7.0

xk

2 2

300.3. . 247.6 909 6, 759

100

Px x

IF k c x x lb

L


26/29

9/11/2011

26

Table 5.4 : U Shape

Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B b

DS k c psi

L


FxFx

h

L

a

L/a 2 4 5 6

L/hx

k bk xk bk xk bk xk bk

2.0 12.00 18.00 13.24 24.8 13.87 27.1 14.4 28.8

2.2 14.85 20.25 16.6 28.5 16.9 31.0 17.5 33.4

2.4 18.00 22.50 20.4 32.2 20.8 35.3 21.3 38.0

2.6 21.52 24.83 24.4 35.9 25.5 39.7 26.2 42.7

2.8 25.32 27.10 28.9 39.7 30.6 44.0 31.7 47.5

4.0 54.9 41.1 64.0 64.0 69.1 72.5 73.6 79.7

4.4 67.3 45.9 78.9 72.4 87.2 82.5 91.0 90.8

4.6 73.9 45.2 87.0 76.6 96.3 87.5 101.7 96.3

4.8 81.0 50.6 95.8 80.8 105.4 92.5 112.4 101.95.0 88.2 52.9 104.6 85.2 114.7 97.8 122.5 107.5

. . . . . . . . .

5.6 112.1 60.1 134.0 98.3 147.6 113.5 159.0 126.2

5.8 120.7 62.4 144.6 102.7 159.0 118.8 172.0 132.5

6.0 129.6 64.8 155.8 107.0 171.3 124.1 185.2 138.8

6.4 148.4 69.6 179.1 116.0 198.0 134.9 213.0 151.4

6.6 158.2 71.9 191.0 120.5 212.2 140.3 228.0 157.7

6.8 168.4 74.3 204.0 125.0 226.4 145.7 244.2 164.0

7.0 178.9 76.7 217.0 129.4 240.7 151.1 261.8 170.3

7.2 189.8 79.1 230.5 133.9 256.0 156.6 279.8 176.7

7.4 200.9 81.5 244.2 138.4 271.5 162.1 297.8 183.1

7.6 312.4 83.8 259.2 142.9 287.5 167.6 316 189.5

7.8 224.2 86.2 274.5 147.4 304.3 173.1 334 195.9

8.0 236.2 88.6 289.8 152.0 322 178.6 352 202.4

55LoopLoop U ShapeU Shape 22 44Sch.Sch. 3300 ASTM AASTM A106106 Grade BGrade B 202068068000 FF cyclic loadingcyclic loading ,, .. ..LoopLoop A.S.M.E. BA.S.M.E. B3131..11

b

a

Fx

A

C

C

D

D

h

Fx

LA

BB


27/29

9/11/2011

27

1 D = 20

PI = 1,457 inch4

ASTM A106 Grade B 7: psiSpsiS 300,14,000,15 700650

psiSSh 580,14650700

680700)300,14000,15(300,14680

psixxSA 395,22)580,1425.0000,1525.1)(1(

4 6500F, c = 827, 700

0F, c = 909

6800F 2.876

650700

685680)827909(827

c

5.05

5.2,10

5.1

15,6

5.2

15

b

a

h

L

a

L

5.11 02.4,2.44,8.29 tbx kkk

22

1457. . 29.8 876.2 15, 248

15 3.33

Px x

IF k c x x lb

L x

20D

680 650827 (909 827) 876.2

700 650c

. . 44.2 876.2 15,50615 3.33

B bS k c x x psiL x

20. . 4.02 876.2 1, 410

15 3.33T t

DS k c x x psi

L x

max. bending moment max. torsional shear stress

2 22 2( ) 4( ) 15,506 4 1, 410 15,570

E B TS S S psi

ES AS A.S.M.E. B31.1


Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B bD

S k c psiL

h

b

a

F

L

A

BB

C

C

D

D

1. tk torsional shear stress 2.

maximum bending stress maximum torsional shear stressL/a = 6

a/b0.50 1 2 3


1 1.5 4.7 - 1.90 6.1 - 2.2 7.5 - 2.32 8.1 -

. .T tD

S k c psiL

F

(A) (C) (C) (C)

2 5.86 9.7

(D)

4.10

(D)

8.65 14.3

(C)

- 10.7 19.

(C)5

- 11.8 22.0

(C)

-

4 15.95 25.0

(D)

5.45

(D)

32.6 27.0

(D)

13.7

(D)

47.4 45.0

(C)

- 54.2 53.7

(C)

-

6 23.0 35.0

(D)

5.18

(D)

60.9 49.3

(D)

17.0

(D)

104 68.0

(C)

- 125 84.0

(C)

-

8 27.3 40.8

(D)

4.59

(D)

86.0 68.6

(D)

18.3

(D)

173 72.0

(D)

42.50

(D)

220 114

(C)

-

9 28.6 42.5

(D)

4.29

(D)

96.6 76.5

(D)

18.2

(D)5

209 86.5

(D)

45.75

(D)

274 128

(C)

-

10 29.8 44.2

(D)

4.02

(D)

106 84.0

(D)

18.15

(D)

244 100.5

(D)

48.25

(D)

330 137.5

(C)

8.9

(C)


28/29

9/11/2011

28

66Sch.Sch. 4040 ASTM AASTM A106106 Grade BGrade B 44 1212 pipe guidepipe guide h =h = 2020 stressstress

Fx

h = 20

a = 20

Fx

Anchor

L = 40Restrained pipe guide

L1= 100

1 D = 12.75

PI = 300.3 inch4

4 c = 909

40 402, 2

20 20

L L

a h

5.4 : 12, 18x bk k

1

22

300.3 100. . 12 909 5,118

4040

Px x

I LF k c x x x lb

L L

1 12.75 100. . 18 909 13, 03840 40

B b

LDS k c x x x lb

L L

17,860AS psi


29/29

9/11/2011

29

Table 5.4 : U Shape (1)

Reacting forces

lbL

IckF Pxx 2..

Max. bending stress

. .B b

DS k c psi

L


FxFx

h

L

a

L/a 2 4 5 6

L/hx

k bk xk bk xk bk xk bk

2.0 12.00 18.00 13.24 24.8 13.87 27.1 14.4 28.8

2.2 14.85 20.25 16.6 28.5 16.9 31.0 17.5 33.4

2.4 18.00 22.50 20.4 32.2 20.8 35.3 21.3 38.0

2.6 21.52 24.83 24.4 35.9 25.5 39.7 26.2 42.7

2.8 25.32 27.10 28.9 39.7 30.6 44.0 31.7 47.5

4.0 54.9 41.1 64.0 64.0 69.1 72.5 73.6 79.7

4.4 67.3 45.9 78.9 72.4 87.2 82.5 91.0 90.8

4.6 73.9 45.2 87.0 76.6 96.3 87.5 101.7 96.3

4.8 81.0 50 .6 95.8 80.8 105.4 92.5 112.4 101.95.0 88.2 52.9 104.6 85.2 114.7 97.8 122.5 107.5

. . . . . . . . .

5.6 112.1 60.1 134.0 98.3 147.6 113.5 159.0 126.2

5.8 120.7 62.4 144.6 102.7 159.0 118.8 172.0 132.5

6.0 129.6 64.8 155.8 107.0 171.3 124.1 185.2 138.8

6.4 148.4 69.6 179.1 116.0 198.0 134.9 213.0 151.4

6.6 158.2 71.9 191.0 120.5 212.2 140.3 228.0 157.7

6.8 168.4 74.3 204.0 125.0 226.4 145.7 244.2 164.0

7.0 178.9 76.7 217.0 129.4 240.7 151.1 261.8 170.3

7.2 189.8 79.1 230.5 133.9 256.0 156.6 279.8 176.7

7.4 200.9 81.5 244.2 138.4 271.5 162.1 297.8 183.1

7.6 312.4 83.8 259.2 142.9 287.5 167.6 316 189.5

7.8 224.2 86.2 274.5 147.4 304.3 173.1 334 195.9

8.0 236.2 88.6 289.8 152.0 322 178.6 352 202.4

End of esign of Steam Pipingnd of esign of Steam Pipingg f p gg f p g

systems Lecture Krubystems Lecture Krub

expansion loops color

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