Expansion loop calculation

Index

1 Expansion loop Routine for the expansion loop calculation

2 Deduction Deduction of the expansion loop equation

3 Table A-1. Allowable stress for the material as functiuon of tempera

4 Lambda. Coefficient of linear expansion of some of the most com

5 Elasticity module Elasticity modules of materials at different temperatures

6 Spiraxsarco. Spiraxsarco Chart for expansion loops sizing

7 Vitaulic. Vitaulic equation for expansion loops sizing

References
 Rev. cjc. 30.01.2014

loop calculation

n loop equation

aterial as functiuon of temperature

sion of some of the most common materials.

rials at different temperatures

ansion loops sizing

sion loops sizing

Expansion loop
Steel pipe expansion loop with nominal diameter "dn" shedule "SCH" and length "Linst"
The given length "Linst" refers to an installation at a temperature "tinst".
The pipe will expand with respect to its length "Linst", due to the temperature rise Dt = tmax - tinst
The maximum temperature could be reached due to the pipe temperature and solar radiation,
or due to fluid flowing through it.
Similarly, the pipe will shrink due to low temperatures and clear sky nights.

Data
Material: A 53 - Gr. B
dn = 10 in Elasticity module
SCH = 40 Elasticity module of selected material
Linst = 100 m at operation temperature
tinst = 10 ºC Polar inertia moment
toperation = 174.2 °C Material type, to obtain "E" I= p/4 *(re^4-ri^4)
Carbon steel C <= 0.3% de = #VALUE!
Allowable stress E= 1.93E+11 Pa re = #VALUE!
Allowable stress of selected material Auxiliary data di = #VALUE!
at operation temperature Pipe dimensions (Note 1) ri = #VALUE!
sallow = 137.9 MPa dn = 10 in I= #VALUE!
Linear expansion coefficient SCH = 40 - Temperature differential
Expansion coefficient of selected mater di = Pipe_Imp_CS_Dint_dn_sch Dt = toperation - tinst
at operation temperature di = #VALUE! mm toperation = 174.2
Carbon Steel de = Pipe_Imp_CS_Dext_dn tinst = 10
l= 1.29E-05 m/(m*K) de = #VALUE! mm Dt = 164.2
Note 1. The pipe dimensions are automatically calculated only for carbon steel materials. For other materials,
the interior and exterio diameter dimensions must be entered manually into the corresponding cells

Carbon steel expansion loop Length "L" of expansion loop

Length "L" of expansion loop

L=
E=
0.378 * ( (3 * E * d * DL) / (sallow) )^0.5
1.93E+11 Pa
L=0. 378⋅
√ 3⋅E⋅d⋅f tot
σ adm
L=

d= #VALUE! m
DL = 0.211 m
sallow = 1.38E+08 Pa
L= #VALUE! m
W= #VALUE! m

Expansion loop of PVC schedule 80 Length "L" of expansion loop

Length "L" of expansion loop
L=
E=
0.378 * ( (3 * E * d * DL) / (sadm) )^0.5
3.0E+09 Pa
L=0. 378⋅
√ 3⋅E⋅d⋅f tot
σ adm
L=

d= #VALUE! m
DL = 0.090 m
sallow = 4.96E+07 Pa
L= #VALUE! m
W= #VALUE! m

PVC
Modulus of elasticity @ 23 ºC Expansion (PVC)
E= 4.3E+05 psi DL = L * l * Dt
E= 3.0E+06 kPa L= 91.4 m
l= 0.000054 m / (ºC * m)
Tensile strength @ 23 ºC Dt = 18.3 ºC
s= 7200 psi DL = 0.090 m
s= 5.0E+04 kPa

Annexes A, B y C
Do not delete these lines

Carbon steel pipes

Carbon steel pipes

dn Sch
in -
1/2 5
1 10
1 20
2 30
2 40
3 60
4 80
5 100
6 120
8 140
10 160
12 STD
14 XS
16 XXS
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
 Rev. cjc. 06.04.2014

DL/ DL/2
2
C D
C

A W B

Esquema de la lira

p/4 *(re^4-ri^4)
m
m Pipe expansion DL
mm The expansion loop will absorb this length
m DL = l * Linst * Dt
m 4
l= 1.29E-05 m/(m*K)
differential Linst = 100 m
operation - tinst Dt = 164.2 K
ºC DL = 0.21 m
ºC DL = 211.27 mm
K DL = 0.211 m
or other materials, www.piping-tools.net
Expansion_loop.xlsm
Carbon steel expansion loop

Length "L" of expansion loop

L = 0.378 * ( (3 * E * d * DL) / (sallow) )^0.5

Elasticy module for carbon steel C < 0.3%

E= 1.93E+11 Pa

Allowable stress for selected material

at its temperature
sallow = 1.379E+08 Pa
Rev. Cjc, 22,01,2013

Pipe dimensions
dn = 10 in
SCH = STD -
de = Pipe_Imp_CS_Dext_dn
de = #VALUE! mm
 d= #VALUE! m

Linear expansion coefficient

Expansion coefficient of selected material
at operation temperature
l= 1.29E-05 m/(m*K)

Pipe installed length

Linst = 100 m
Rev. Cjc, 22,05,2013
Temperature differential
Dt = toperation - tinst
toperation = 174.2 ºC
tinst = 10 ºC
Dt = 164.2 K

Pipe expansion DL
The expansion loop will absorb this length
DL = l * Linst * Dt
l= 1.29E-05 m/(m*K)
Linst = 100 m
Dt = 164.2 K
DL = 0.211 m

Length "L" of expansion loop

L = 0.378 * ( (3 * E * d * DL) / (sallow) )^0.5
E= 1.93E+11 Pa
 d= #VALUE! m
DL = 0.211 m
sallow = 1.38E+08 Pa
ected material L= #VALUE! m
W= #VALUE! m

Total pipe lenght

Ltot = 2*L+W
Ltot = #VALUE! m
Cálculo de lira considerando la flexión en los dos brazos y el giro en los codos

El cálculo de la longitud "L" de los brazos se realiza considerando la condición de que se produzca como máximo un es

El aumento de temperatura produce una extensión de DLinst en la cañería f

Lira
C

La dilatación de la cañería produce una deflexión "DLinst/2"

en el punto "C" del a brazo izquierdo "AC" de la lira.
Lo mismo ocurre en el brazo "BD" de la lira.

En los extremos "C" y "D" de la lira se produce una flecha A

f = DLinst/2 L/2

Esta flecha se debe en parte a una flexión de los brazos

y en parte al giro en los codos en "A" y "B".
Estas dos flechas se deben a la fuerza "P" originada por
la extensión de la cañería. Esta fuerza produce una flecha
"f1" debida a la flexión del brazo y una flecha "f2" debida
al giro del codo.

Viga en voladizo con carga concentrada Una flecha "f2", debida al giro del codo Ecuación diferencial de la curva
en el extremo libre (brazos) de la lira en el punto "A", se agrega a deformada de la viga "A-B" (Figura 2)
la flecha "f1" debida a la flexión del 2
d y
L brazo. La flecha total es f = f1 + f2 EI⋅ =M
P dx 2
A P con
C C D
f1 C M = P⋅L
f
se tiene
Figura 1
2
L Lira EI⋅
d y
= P⋅L
Flecha. [1]. Tabla 8.1, página 218 dx 2
Flecha debida a la flexión de la viga x Intergrando
3 a
∫ EI⋅dx ( dx )⋅dx=∫ P⋅L⋅dx
P⋅L A B d dy
(1)
f 1= m
3⋅E⋅I y
dy
EI⋅ = P⋅L⋅x +c
Fuerza "P" asociada a la flecha f1 Figura 2 dx

3⋅E⋅I⋅f 1 (2) La viga A-B se deforma por momentos dy P⋅L⋅x+ c

P= aplicados en sus dos extremos =
L3 dx E⋅I
La pendiente es luego, y la flecha en el punto C debida al
giro en el codo A es
dy P⋅L P⋅L
2
= ⋅( x−m /2 ) tan ( α )= P⋅L
3
dx E⋅I 4⋅E⋅I f 2=
Pendiente en el codo A (en x = 0) Para el brazo L , la flecha f2 4⋅E⋅I
debida al giro del codo es La flecha total en C es
dy P⋅L⋅0−P⋅L⋅m/2 f2
|x=0 = tan ( α )=
f =f 1 + f 2
dx E⋅I L P⋅L
3
P⋅L
3
f= f +
luego 3⋅E⋅I 2 4⋅E⋅I
dy P⋅L⋅m/ 2 3 3
|x =0 = f2 f=
P⋅L 4 P⋅L
⋅ + ⋅
3
dx E⋅I P⋅L2 3⋅E⋅I 4 4⋅E⋅I 3
= 3
4⋅P⋅L 3⋅P⋅L
3
Definiendo una razón largo/brazo L 4⋅E⋅I f= +
L/m = 2 12⋅E⋅I 12⋅E⋅I
3 7⋅P⋅L3
m= L/2 P⋅L (4) f=
f 2= 12⋅E⋅I
dy P⋅L⋅L/ 4 4⋅E⋅I
|x =0 = La flecha en el punto C debida a la
dx E⋅I
flexión del largo "L" de la lira es
2
dy P⋅L
|x =0 = P⋅L
3 (1)
dx 4⋅E⋅I f 1=
3⋅E⋅I

Esfuerzo máximo Reemplazando f1 Para la lira completa, es decir

considerando la deflexión de los dos
M max (5) 4 brazos, se tiene que
σ max = f 1=(1) ⋅f
I /c 7 f
con c = d/2 f tot =2⋅f f= tot
3⋅E 4 d 2
d σ max = 2 ⋅ ⋅f⋅
L 7 2

√
σ max =M max⋅ (6)
6⋅E⋅d⋅( f tot / 2 )
I⋅2 6 E⋅f ⋅d L=
de (3) σ max = 7⋅σ max
7 L2
M =P⋅L
y reemplazando P de (2) Despejando
L=
√ 6⋅E⋅d⋅f tot
14⋅σ max

√
3⋅E⋅I⋅f 1 6⋅E⋅d⋅f
P= L2 = 3⋅E⋅d⋅f tot
L 3
7⋅σ max L=
7⋅σ max

√
d 6⋅E⋅d⋅f
σ max =P⋅L⋅ (7)
I⋅2 L=
3⋅E⋅I⋅f 1 d
7⋅σ max
σ max = 3 ⋅L⋅
L I⋅2 Relación válida para la deflexión
3⋅E⋅f 1 d de un brazo
σ max = 2 ⋅
L 2
Momento en el codo (punto A)
M max =P⋅L
Reemplazando la fuerza P por (2)
(2)
3⋅E⋅I⋅f 1
M max = ⋅L
L3

Para una viga en cantilever "AC",

el momento inducido en "A" por
una flecha impuesta en el punto "C,
debida a la dilatación de la cañería,
es

3⋅E⋅I⋅f 1
M max =
L2
 Rev. cjc. 30.01.2014

1 de 4

uzca como máximo un esfuerzo de flexión admisible "sadm"

D
C

B
L/2

2 de 4
encial de la curva Para x = m/2
e la viga "A-B" (Figura 2) dy/dx = 0

luego

c=− P⋅L⋅m / 2
(3) Reemplazando en (3)
dy
EI⋅ =P⋅L⋅x−P⋅L⋅m/2
dx
dy
EI⋅ =P⋅L⋅( x−m / 2 )
dx
y
x)⋅dx=∫ P⋅L⋅dx

P⋅L⋅x +c
(4)

⋅L⋅x+ c
E⋅I
 3 de 4
l punto C debida al Relaciones f/f1 y f/f2
3
7⋅P⋅L
f=
12⋅E⋅I
(5) 3
4⋅P⋅L
f 1=
12⋅E⋅I
3⋅P⋅L3
f 2=
12⋅E⋅I
4⋅P⋅L3
f 1 12⋅E⋅I 4
= 3
=
f 7⋅P⋅L 7
12⋅E⋅I
4
f 1= ⋅f
7
3
3⋅P⋅L
f 2 12⋅E⋅I 3
= =
f 7⋅P⋅L3 7
12⋅E⋅I
3
f 2 = ⋅f
7

4 de 4
mpleta, es decir
la deflexión de los dos

f=
f tot
2
L=
1
√7 √ 3⋅E⋅d⋅f tot
σ max

E⋅d⋅( f tot / 2 )
L= 0. 378⋅
√ 3⋅E⋅d⋅f tot
σ max

7⋅σ max Esta es la longitud del brazo de la

lira que, para la expansión dada de
E⋅d⋅f tot la cañería, produce el esfuerzo
⋅σ max máximo admisible "smax"
Ver Hoja Vitaulic. Vitaulic propone
misma ecuación, con la diferencia
E⋅d⋅f tot
que el factor 0.378 es redondeado
7⋅σ max a 0.4 (Hoja 7)
 3 Allowable stress as function of temperature [MPa]
TEMPERATURE °C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Spec & Grade Materi 38 93 149 204 260 316 343 371 399 427 454 482 510 538 566 593 621 649
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 A 53(Type F) Gr.A 110.3 110.3 110.3 110.3 "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A"
2 A 53 - Gr. A 110.3 110.3 110.3 110.3 110.3 102.0 100.0 99.3 73.8 64.1 54.5 44.8 31.0 17.2 11.0 6.9 "NA" "NA"
3 A 53 - Gr. B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2 "NA" "NA" "NA" "NA"
4 A 106 - Gr. A 110.3 110.3 110.3 110.3 110.3 102.0 100.0 99.3 73.8 64.1 54.5 44.8 31.0 17.2 11.0 6.9 "NA" "NA"
5 A106 - Gr. B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2 "NA" "NA" "NA" "NA"
6 A106 - Gr. C 160.6 160.6 160.6 157.9 148.9 135.8 133.8 132.4 102.0 82.7 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
7 API 5L - Gr. A 110.3 110.3 110.3 110.3 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
8 API 5L - Gr. A25 103.4 103.4 100.0 95.1 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
9 API 5L - Gr. B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2 11.0 6.9 "NA" "NA"
10 API 5L - Gr. X42 137.9 137.9 137.9 137.9 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
11 API 5L - Gr. X46 144.8 144.8 144.8 144.8 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
12 API 5L - Gr. X52 151.7 151.7 151.7 151.7 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
13 API 5L - Gr. X56 163.4 163.4 163.4 163.4 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
14 API 5L - Gr. X60 172.4 172.4 172.4 172.4 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
15 API 5L - Gr. X65 177.2 177.2 177.2 177.2 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
16 API 5L - Gr. X70 188.2 188.2 188.2 188.2 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
17 API 5L - Gr. X80 206.8 206.8 206.8 206.8 "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA" "NA"
18 A312 - Gr. TP 304 137.9 137.9 137.9 128.9 120.7 113.1 111.7 110.3 107.6 104.8 102.7 100.7 99.3 95.1 84.1 66.9 53.1 41.4
19 A312 - Gr. TP 304L 115.1 115.1 115.1 108.9 102.0 96.5 94.5 93.1 91.7 89.6 88.3 82.0 68.3 53.8 43.4 35.2 27.6 22.1
20 A312 - Gr. TP 304H 137.9 137.9 137.9 128.9 120.7 113.1 111.7 110.3 107.6 104.8 102.7 100.7 99.3 95.1 84.1 66.9 53.1 41.4
21 A312 - Gr. TP 309 137.9 137.9 137.9 137.9 137.9 132.4 129.6 126.2 124.1 120.7 100.7 95.8 86.2 72.4 58.6 44.8 34.5 26.2
22 A312 - Gr. TP 310 137.9 137.9 137.9 137.9 137.9 132.4 129.6 126.2 124.1 120.7 100.7 95.8 86.2 75.8 49.0 34.5 24.8 17.2
23 A312 - Gr. TP 316 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
24 A312 - Gr. TP 316L 115.1 115.1 115.1 106.9 99.3 93.1 91.0 88.9 86.9 85.5 83.4 81.4 79.3 77.2 74.5 70.3 60.7 44.1
25 A312 - Gr. TP 316H 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
26 A312 - Gr. TP 317 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
27 A312 - Gr. TP 317L 137.9 137.9 137.9 130.3 122.0 115.8 114.5 111.7 108.9 106.9 104.8 "N/A" "N/A" "N/A" "N/A" "N/A" "N/A" "N/A"
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

t= 593 621.0
S= 66.9 53.1
 Table A-1. Basic alowable stresses in tension for metals (Page 157 - 161) de ASME B31.3-2002

ASME B31.3-2002 Table A-1. Basic alowable stresses in tension for metals (Page 157 - 161)

Allowable stress as function of temperature [MPa]

TEMPERATURE °C
Spec Grade 38 93 149 204 260 316 343 371 399 427 454 482 510 538 566 593 621 649
1 A 53 Gr. A 110.3 110.3 110.3 110.3
2 A 53 A 110.3 110.3 110.3 110.3 110.3 102.0 100.0 99.3 73.8 64.1 54.5 44.8 31.0 17.2 11.0 6.9
3 A 53 B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2
4 A 106 A 110.3 110.3 110.3 110.3 110.3 102.0 100.0 99.3 73.8 64.1 54.5 44.8 31.0 17.2 11.0 6.9
5 A106 B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2
6 A106 C 160.6 160.6 160.6 157.9 148.9 135.8 133.8 132.4 102.0 82.7
7 API 5L A 110.3 110.3 110.3 110.3
8 API 5L A25 103.4 103.4 100.0 95.1
9 API 5L B 137.9 137.9 137.9 137.9 130.3 119.3 117.2 113.8 89.6 74.5 60.0 44.8 31.0 17.2 11.0 6.9
10 API 5L X42 137.9 137.9 137.9 137.9
11 API 5L X46 144.8 144.8 144.8 144.8
12 API 5L X52 151.7 151.7 151.7 151.7
13 API 5L X56 163.4 163.4 163.4 163.4
14 API 5L X60 172.4 1482.4 172.4 172.4
15 API 5L X65 177.2 177.2 177.2 177.2
16 API 5L X70 188.2 188.2 188.2 188.2
17 API 5L X80 206.8 206.8 206.8 206.8
18 A312 TP 304 137.9 137.9 137.9 128.9 120.7 113.1 111.7 110.3 107.6 104.8 102.7 100.7 99.3 95.1 84.1 66.9 53.1 41.4
19 A312 TP 304L 115.1 115.1 115.1 108.9 102.0 96.5 94.5 93.1 91.7 89.6 88.3 82.0 68.3 53.8 43.4 35.2 27.6 22.1
20 A312 TP 304H 137.9 137.9 137.9 128.9 120.7 113.1 111.7 110.3 107.6 104.8 102.7 100.7 99.3 95.1 84.1 66.9 53.1 41.4
21 A312 TP 309 137.9 137.9 137.9 137.9 137.9 132.4 129.6 126.2 124.1 120.7 100.7 95.8 86.2 72.4 58.6 44.8 34.5 26.2
22 A312 TP 310 137.9 137.9 137.9 137.9 137.9 132.4 129.6 126.2 124.1 120.7 100.7 95.8 86.2 75.8 49.0 34.5 24.8 17.2
23 A312 TP 316 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
24 A312 TP 316L 115.1 115.1 115.1 106.9 99.3 93.1 91.0 88.9 86.9 85.5 83.4 81.4 79.3 77.2 74.5 70.3 60.7 44.1
25 A312 TP 316H 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
26 A312 TP 317 137.9 137.9 137.9 133.1 123.4 117.2 115.1 112.4 111.0 109.6 108.2 106.9 106.2 105.5 100.0 85.5 67.6 51.0
27 A312 TP 317L 137.9 137.9 137.9 130.3 122.0 115.8 114.5 111.7 108.9 106.9 104.8
 ASME B31.3-2006 Table A-1. Basic alowable stresses in tension for metals ( Carbon steel pipes and tubes. Pag. 140- 144

Allowable stress as function of temperature [ksi]

1 ksi = 6.895 MpaTEMPERATURE °C
38 93 149 204 260 316 343 371 399 427 454 482 510 538 566 593 621
Temperature °F
Material Spec Grade 100 200 300 400 500 600 650 700 750 800 850 900 950 1000 1050 1100 1150
Type F A 53
Gr. A, Type F 16 16 16 16
A 53 A 16 16 16 16 16 14.8 14.5 14.4 10.7 9.3 7.9 6.5 4.5 2.5 1.6 1
A 53 B 20 20 20 20 18.9 17.3 17 16.5 13 10.8 8.7 6.5 4.5 2.5 1.6 1
A 106 A 16 16 16 16 16 14.8 14.5 14.4 10.7 9.3 7.9 6.5 4.5 2.5 1.6 1
A106 B 20 20 20 20 18.9 17.3 17 16.5 13 10.8 8.7 6.5 4.5 2.5 1.6 1
A106 C 23.3 23.3 23.3 22.9 21.6 19.7 19.4 19.2 14.8 12
API 5L A 16 16 16 16 16 14.8 14.5 14.4 10.7 9.3 7.9 6.5 4.5 2.5 1.6 1
Butt weld API 5L A25 15 15 14.5 13.8
API 5L B 20 20 20 20 18.9 17.3 17 16.5 13 10.8 8.7 6.5 4.5 2.5 1.6 1
API 5L X42 20 20 20 20
API 5L X46 21 21 21 21
API 5L X52 22 22 22 22
API 5L X56 23.7 23.7 23.7 23.7
API 5L X60 25 215 25 25
API 5L X65 25.7 25.7 25.7 25.7
API 5L X70 27.3 27.3 27.3 27.3
API 5L X80 30 30 30 30
1 A312 TP 304 20 20 20 18.7 17.5 16.4 16.2 16 15.6 15.2 14.9 14.6 14.4 13.8 12.2 9.7 7.7
2 A312 TP 304L 16.7 16.7 16.7 15.8 14.8 14 13.7 13.5 13.3 13 12.8 11.9 9.9 7.8 6.3 5.1 4
3 A312 TP 304H 20 20 20 18.7 17.5 16.4 16.2 16 15.6 15.2 14.9 14.6 14.4 13.8 12.2 9.7 7.7
4 A312 TP 309 20 20 20 20 20 19.2 18.8 18.3 18 17.5 14.6 13.9 12.5 10.5 8.5 6.5 5
5 A312 TP 310 20 20 20 20 20 19.2 18.8 18.3 18 17.5 14.6 13.9 12.5 11 7.1 5 3.6
6 A312 TP 316 20 20 20 19.3 17.9 17 16.7 16.3 16.1 15.9 15.7 15.5 15.4 15.3 14.5 12.4 9.8
7 A312 TP 316L 16.7 16.7 16.7 15.5 14.4 13.5 13.2 12.9 12.6 12.4 12.1 11.8 11.5 11.2 10.8 10.2 8.8
8 A312 TP 316H 20 20 20 19.3 17.9 17 16.7 16.3 16.1 15.9 15.7 15.5 15.4 15.3 14.5 12.4 9.8
9 A312 TP 317 20 20 20 19.3 17.9 17 16.7 16.3 16.1 15.9 15.7 15.5 15.4 15.3 14.5 12.4 9.8
10 A312 TP 317L 20 20 20 18.9 17.7 16.8 16.6 16.2 15.8 15.5 15.2
 ASME B31.3-2002
Table A-1. Basic alowable stresses in tension for metals (Page 157 - 161)

38

to
Material Spec Grade 100
A 285 G A 134 … 15
A 285 G A 672 A45 15

Butt wel API 5L A25 15

smls API 5L A25 15

Type F A 53 Gr. A 16

A 53 A 16
A 106 A 16
A 135 A 16
A 369 FPA 16
API 5L A 16

A 285 G A 134 16.7

A 285 G A 672 A 50 16.7
285 Gr. B A 134 18.3

A 516 GrA 671 CC60 20

A 515 GrA 671 C860 20
A 515 GrA 672 B60 20
A 516 GrA 672 C60 20

A 53 B 20
A106 B 20
A 333 6 20
A 334 6 20
A 369 FPB 20
A 381 Y35 20
API 5L B 20
 100
API 5L X42 20
API 5L X46 21
API 5L X52 22
API 5L X56 23.7

100
A 516 GrA 671 CC65 21.7
A 515 GrA 671 C865 21.7
A 515 GrA 672 B65 21.7
A 516 GrA 672 C65 21.7

100
A 516 G A 671 CC70 23.1
A 515 G A 671 CB70 23.1
A 515 G A 672 B70 23.1
A 516 G A 672 C70 23.1

A106 C 23.3
API 5L X60 25
API 5L X65 25.7
API 5L X70 27.3
API 5L X80 30
 Table C
ASME B31.3

1
1 2 3 4 5 6
Material -536 -522 -508 -494 -480
(Through 1 2 3 4 5 6
1 3Cr-Mo) - - - - -
2 9Cr-Mo - - - - -
3 18Cr-8Ni - - - - -
4 27Cr - - - - -
5 25Cr-20Ni - - - - -
6 67Ni-30Cu
7 3.5Ni
8 Alloys 1.1E-05 1.2E-05 1.2E-05 1.3E-05 1.4E-05
9 Aluminum - - - - -
10 Iron - - - - -
11 Bronze - - - - -
12 Brass - - - - -
13 70Cu-30Ni - - - - -
14 Ni-Fe-Cr - - - - -
15 Ni-Cr-Fe
Ductile - - - - -
16 Iron - - - - -
 7 8 9 10 11 12 13 14 15 16
-466 -452 -438 -424 -411 -397 -383 -369 -355 -341
7 8 9 10 11 12 13 14 15 16
9.0E-06 9.1E-06 9.2E-06 9.3E-06 9.4E-06 9.5E-06 9.7E-06 9.9E-06 1.0E-05 1.0E-05
8.4E-06 8.5E-06 8.6E-06 8.7E-06 8.8E-06 9.0E-06 9.2E-06 9.3E-06 9.5E-06 9.5E-06
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05
7.7E-06 7.8E-06 7.8E-06 7.9E-06 8.0E-06 8.1E-06 8.3E-06 8.5E-06 8.5E-06 8.6E-06
- - - - - - - - - -
9.9E-06 1.0E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
8.5E-06 8.8E-06 9.0E-06 9.2E-06 9.5E-06 9.8E-06 9.9E-06 1.0E-05 1.0E-05 1.0E-05
1.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05
1.8E-05 1.8E-05 1.8E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 2.0E-05 2.0E-05 2.0E-05
- - - - - - - - - -
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05
- - - - - - - - - -
- - - - - - - - - -
- - - - - 8.4E-06 8.6E-06 8.8E-06 8.9E-06 9.2E-06
 17 18 19 20 21 22 23 24 25 26
-327 -313 -299 -286 -272 -258 -247 -230 -216 -202
17 18 19 20 21 22 23 24 25 26
1.0E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.1E-05 1.1E-05
9.7E-06 9.9E-06 9.9E-06 9.9E-06 1.0E-05 9.8E-06 1.0E-05 1.1E-05 1.1E-05 1.1E-05
1.6E-05 1.6E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-05
8.8E-06 9.0E-06 9.0E-06 9.0E-06 9.0E-06 9.0E-06 9.4E-06 1.0E-05 9.8E-06 9.9E-06
- - - - - - - 1.6E-05 1.6E-05 1.6E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.5E-05 1.5E-05 1.4E-05 1.4E-05 1.4E-05
1.0E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.1E-05 1.1E-05
1.6E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
2.0E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.2E-05 2.3E-05 2.3E-05 2.3E-05
- - - - - - - 1.0E-05 1.0E-05 1.0E-05
1.6E-05 1.7E-05 2.0E-05 1.7E-05 1.6E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.8E-05 1.7E-05 1.8E-05
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.6E-05 1.5E-05 1.5E-05
- - - - - - - 1.4E-05 1.4E-05 1.4E-05
- - - - - - - 1.3E-05 1.3E-05 1.3E-05
9.4E-06 9.6E-06 9.8E-06 9.9E-06 7.7E-06 1.1E-05 1.1E-05 1.0E-05 1.1E-05 1.1E-05
 27 28 29 30 31 32 33 34 35 36
-188 -174 -161 -147 -133 -119 -105 -91 -77 -63
27 28 29 30 31 32 33 34 35 36
1.1E-05 1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
9.9E-06 9.9E-06 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
2.3E-05 2.3E-05 2.3E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-05 2.5E-05
1.0E-05 1.0E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05
1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.2E-05
 Table C-1
Thermal expansion coefficient " l " [m/(m*K)] for metals
Temperatura °C
37 38 39 40 41 42 43 44 45 46
-49 -36 -22 -8 6 20 34 48 62 76
37 38 39 40 41 42 43 44 45 46
1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.7E-05 - -
2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.6E-05 - -
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.8E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05
1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05
- - - - - - - - - -
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
 47 48 49 50 51 52 53 54 55 56
89 103 117 131 145 159 173 187 201 214
47 48 49 50 51 52 53 54 55 56
1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
- - - - - - - - - -
- - - - - - - - - -
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05
1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05
2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.1E-05
- - - - - - - - - -
1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.5E-05 - - - -
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
 57 58 59 60 61 62 63 64 65 66
228 242 256 270 284 298 312 326 339 353
57 58 59 60 61 62 63 64 65 66
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
1.8E-05 1.8E-05 1.8E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.6E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
1.3E-05 1.4E-05 1.4E-05 1.4E-05 - - - - - -
- - - - - - - - - -
- - - - - - - - - -
1.3E-05 1.3E-05 1.3E-05 1.3E-05 - - - - - -
1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 2.0E-05 2.0E-05 2.0E-05 - -
2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 - -
- - - - - - - - - -
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
- - - - - - - - - -
1.3E-05 1.3E-05 1.3E-05 1.3E-05 - - - - - -
 67 68 69 70 71 72 73 74 75 76
367 381 395 409 423 437 451 464 478 492
67 68 69 70 71 72 73 74 75 76
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05
1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05
1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05
1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05
- - - - - - - - - -
- - - - - - - - - -
 77 78 79 80
506 520 534 548
77 78 79 80
- - - -
- - - -
1.9E-05 1.9E-05 1.9E-05 1.9E-05
- - - -
- - - -
- - - -
- - - -
- - - -
- - - -
- - - -
- - - -
- - - -
- - - -
1.8E-05 1.8E-05 1.8E-05 1.8E-05
- - - -
- - - -
 Table B. Young Modulus of Elasticity E [Pa]
Metal Temperature
1 2 3 4 5 6 7 8
1 -200 -129 -73 21 93 149 204
1 2 3 4 5 6 7 8
1 Carbon steel C <= 0.3% 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11 2.0E+11 1.9E+11
2 Carbon steel C => 0.3% 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11
3 Carbon-moly steels 2.1E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11
4 Nickel steels Ni 2% - 9% 2.0E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11
5 Cr-Mo steels Cr 1/2% - 2% 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11 2.0E+11 1.9E+11
6 Cr-Mo steels Cr 2 1/4% - 3% 2.2E+11 2.2E+11 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11
7 Cr-Mo steels Cr 5% - 9% 2.3E+11 2.2E+11 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11
8 Chromium steels Cr 12%, 17%, 27% 2.2E+11 2.1E+11 2.1E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11
Austenitic steels (TP304, 310, 316, 321,
9 347) 2.1E+11 2.0E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11 1.8E+11

Cast iron
Gray cast iron ### ### ### ###

http://www.engineeringtoolbox.com/young-modulus-d_773.html
Mpsi = 6.9E+09 Pa
Elasticity E [Pa]
Temperature (oC)
9 10 11 12 13 14 15 16
260 316 371 427 482 538 593 649 Metal
9 10 11 12 13 14 15 16 3
1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.5E+11 1.4E+11 1.2E+11 "N/A" Carbon steel C <= 0.3%
1.9E+11 1.8E+11 1.7E+11 1.7E+11 1.5E+11 1.4E+11 1.2E+11 1.1E+11 Carbon steel C => 0.3%
1.9E+11 1.8E+11 1.7E+11 1.6E+11 1.5E+11 1.4E+11 1.2E+11 1.1E+11 Carbon-moly steels
1.8E+11 1.7E+11 1.7E+11 1.6E+11 "N/A" "N/A" "N/A" "N/A" Nickel
Cr-Mosteels
steelsNi
Cr2% - 9%
1/2% -
1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.6E+11 1.6E+11 1.5E+11 2%
Cr-Mo steels Cr 2 1/4% -
2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.6E+11 1.6E+11 3%
2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.7E+11 1.6E+11 1.4E+11 1.3E+11 Cr-Mo steels Cr 5% - 9%
Chromium steels Cr 12%,
1.8E+11 1.8E+11 1.8E+11 1.7E+11 1.6E+11 1.5E+11 1.3E+11 1.1E+11 17%, 27%
Austenitic steels (TP304,
1.8E+11 1.7E+11 1.7E+11 1.7E+11 1.6E+11 1.6E+11 1.5E+11 1.5E+11 310, 316, 321, 347)

### ### ### ### Gray cast iron

 Temperature (oC)

-200 -129 -73 21 93 149 204 260 316 371 427

4
31.4 30.8 30.2 29.5 28.8 28.3 27.7 27.3 26.7 25.5 24.2
31.2 30.6 30 29.3 28.6 28.1 27.5 27.1 26.5 25.3 24
31.1 30.5 29.9 29.2 28.5 28 27.4 27 26.4 25.3 23.9
29.6 29.1 28.5 27.8 27.1 26.7 26.1 25.7 25.2 24.6 23
31.6 31 30.4 29.7 29 28.5 27.9 27.5 26.9 26.3 25.5
32.6 32 31.4 30.6 29.8 29.4 28.8 28.3 27.7 27.1 26.3
32.9 32.3 31.7 30.9 30.1 29.7 29 28.6 28 27.3 26.1
31.2 30.7 30.1 29.2 28.5 27.9 27.3 26.7 26.1 25.6 24.7
30.3 29.7 29.1 28.3 27.6 27 26.5 25.8 25.3 24.8 24.1

Cast iron
13.4 13.2 12.9 12.6 12.2 11.7 11 10.2
482 538 593 649
5 6 7 8 9
22.4 20.4 18
22.2 20.2 17.9 15.4
22.2 20.1 17.8 15.3

24.8 23.9 23 21.8

25.6 24.6 23.7 22.5
24.7 22.7 20.4 18.2
23.2 21.5 19.1 16.6
23.5 22.8 22.1 21.2
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipe-expansion-and-support

For expansion "

pipe nominal diameter "dn" (in),
Spiraxsarco graph provides an
expansionloop width "W" (m).

DL =
dn =
Estimated value from Fig. 10.4
W=
ibution/pipe-expansion-and-support.asp

For expansion "DL" (mm), and a

pipe nominal diameter "dn" (in),
Spiraxsarco graph provides an
xpansionloop width "W" (m).

90 mm
273 mm
Estimated value from Fig. 10.4
2.55 m
http://static.victaulic.com/assets/uploads/literature/26.02-SPA.pdf
Vitaulic equation for an expansion loop

Vitaulic equation

H=0. 4⋅
5W =
W=
L
√
L/5
3⋅E⋅d⋅f tot
σ

H= 2*W
H= 2*L/5
H= 0.4 * L

L=0. 378⋅
√ 3⋅E⋅d⋅f tot
σ max
Equation deducted in sheet 2
 E: Elasticity module of material
d: exterior pipe diameter

√ 3⋅E⋅d⋅f tot ftot: total pipe expansion

S: Allowable stress of material
⋅
σ
H=

8⋅
√ 3⋅E⋅d⋅f tot
σ max
ucted in sheet 2
odule of material

ress of material
[1] Elementos de resistencia de materiales
S. Timoshenko, D. H. Young
Ed. Limusa, 1996

[2]

[3]

[4] http://static.victaulic.com/assets/uploads/literature/26.02-SPA.pdf

[5] http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipe-expansion-and-support.asp

[5] F(Simple drive):\Libreria\Piping\Piping Handbook (7th Edition)

[6] http://www.engineeringtoolbox.com/young-modulus-d_773.html
 Microsoft Editor de
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pipe-expansion-and-support.asp
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