expansion loop
TRANSCRIPT
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 temperature
4 Lambda. Coefficient of linear expansion of some of the most common materials.
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
Routine for the expansion loop calculation
Deduction of the expansion loop equation
Allowable stress for the material as functiuon of temperature
Coefficient of linear expansion of some of the most common materials.
Elasticity modules of materials at different temperatures
Spiraxsarco Chart for expansion loops sizing
Vitaulic equation for expansion loops sizing
Expansion loopSteel 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 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: dn = 10 in Elasticity module
SCH = 40 Elasticity module of selected material
100 m at operation temperature
10 ºC
174.2 °C Material type, to obtain "E"
Allowable stress E = 1.93E+11 Pa
Allowable stress of selected material Auxiliary data
at operation temperature
137.9 MPa dn = 10 in
Linear expansion coefficient SCH = 40 -
Expansion coefficient of selected material Pipe_Imp_CS_Dint_dn_sch
at operation temperature #VALUE! mm
Pipe_Imp_CS_Dext_dn
1.29E-05 m/(m*K) #VALUE! mm
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 = 1.93E+11 Pad = #VALUE! m
0.211 m
1.38E+08 Pa L = #VALUE! m
W = #VALUE! m
Expansion loop of PVC schedule 80 Length "L" of expansion loop
The pipe will expand with respect to its length "Linst", due to the temperature rise Dt = tmax - tinst
Linst =
tinst =
toperation =
Pipe dimensions (Note 1)
sallow =
di =
di =
de =
l = de =
0.378 * ( (3 * E * d * DL) / (sallow) )^0.5
DL =
sallow =
L=0.378⋅√ 3⋅E⋅d⋅f totσ adm
Length "L" of expansion loop
L =E = 3.0E+09 Pad = #VALUE! m
0.090 m
4.96E+07 Pa L = #VALUE! m
W = #VALUE! m
PVCModulus of elasticity @ 23 ºC Expansion (PVC)
E = 4.3E+05 psiE = 3.0E+06 kPa L =
Tensile strength @ 23 ºC7200 psi
5.0E+04 kPa
Annexes A, B y CDo not delete these lines
Carbon steel pipes
Carbon steel pipesdn Schin -
1/2 51 101 202 302 403 604 805 1006 1208 140
10 16012 STD14 XS16 XXS18202224262830
0.378 * ( (3 * E * d * DL) / (sadm) )^0.5
DL =
sallow =
DL =
l =Dt =
s = DL =s =
L=0.378⋅√ 3⋅E⋅d⋅f totσ adm
323436384042444648
Rev. cjc. 06.04.2014
Esquema de la lira
Polar inertia moment
I =
#VALUE! m
#VALUE! m
#VALUE! mm The expansion loop will absorb this length
#VALUE! m
I = #VALUE! 1.29E-05 m/(m*K)
Temperature differential 100 m
164.2 K
174.2 ºC 0.21 m
10 ºC 211.27 mm
164.2 K 0.211 m
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
Length "L" of expansion loop
Rev. Cjc, 22,01,2013
Length "L" of expansion loop
t = tmax - tinst
p/4 *(re^4-ri^4)
de =
re = Pipe expansion DL
di =
ri = DL = l * Linst * Dt
m4 l =
Linst =
Dt = toperation - tinst Dt =
toperation = DL =
tinst = DL =
Dt = DL =
L =
DL/2 DL/2
A
L
C
B
DC
W
L=0.378⋅√ 3⋅E⋅d⋅f totσ adm
Rev. Cjc, 22,05,2013
Expansion (PVC)
91.4 m0.000054 m / (ºC * m)
18.3 ºC0.090 m
L * l * Dt
L =
L=0.378⋅√ 3⋅E⋅d⋅f totσ adm
Expansion_loop.xlsmCarbon steel expansion loop Temperature differential
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
The expansion loop will absorb this length
Allowable stress for selected material at its temperature
1.379E+08 Pa
Pipe dimensionsdn = 10 in
SCH = STD - Length "L" of expansion loop
Pipe_Imp_CS_Dext_dn
#VALUE! mm E =
www.piping-tools.net
Dt =
toperation =
tinst =
Dt =
Pipe expansion
DL =l =
sallow = Linst =Dt =DL =
de = L = 0.378 * ( (3 * E * d * DL) / (sallow) )^0.5
de =
d = #VALUE! m d =
Linear expansion coefficientExpansion coefficient of selected material L =at operation temperature W =
1.29E-05 m/(m*K)
Total pipe lenghtPipe installed length Ltot =
100 m Ltot =
DL =
sallow =
l =
Linst =
Temperature differential
174.2 ºC
10 ºC
164.2 K
The expansion loop will absorb this length
1.29E-05 m/(m*K)
100 m164.2 K0.211 m
Length "L" of expansion loop
1.93E+11 Pa
toperation - tinst
Pipe expansion DL
l * Linst * Dt
L = 0.378 * ( (3 * E * d * DL) / (sallow) )^0.5
#VALUE! m0.211 m
1.38E+08 Pa#VALUE! m#VALUE! m
Total pipe lenght2 * L + W
#VALUE! m
Cálculo de lira considerando la flexión en los dos brazos y el giro en los codos
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
Esta flecha se debe en parte a una flexión de los brazosy en parte al giro en los codos en "A" y "B".Estas dos flechas se deben a la fuerza "P" originada porla extensión de la cañería. Esta fuerza produce una flecha
al giro del codo.
Viga en voladizo con carga concentradaen el extremo libre (brazos) de la lira en el punto "A", se agrega a
la flecha "f1" debida a la flexión del
brazo. La flecha total es
Figura 1
Flecha. [1]. Tabla 8.1, página 218Flecha debida a la flexión de la viga
(1)
Figura 2
(2) La viga A-B se deforma por momentosaplicados en sus dos extremos
La pendiente es luego,
El cálculo de la longitud "L" de los brazos se realiza considerando la condición de que se produzca como máximo un esfuerzo de flexión admisible "sadm"
El aumento de temperatura produce una extensión de DLinst en la cañería
La dilatación de la cañería produce una deflexión "DLinst/2"
f = DLinst/2
"f1" debida a la flexión del brazo y una flecha "f2" debida
Una flecha "f2", debida al giro del codo
f = f1 + f2
Fuerza "P" asociada a la flecha f1
f1
LP
f
A
L
m
Lira
A
B
P
x
y
a
CC
Lira
DC
f 1=P⋅L3
3⋅E⋅I
P=3⋅E⋅I⋅f 1L3
Pendiente en el codo A (en x = 0) debida al giro del codo es
luego
Definiendo una razón largo/brazoL/m = 2 m = L/2 (4)
La flecha en el punto C debida a la flexión del largo "L" de la lira es
(1)
Esfuerzo máximo
(5) (1)
con c = d/2
(6)
de (3)
y reemplazando P de (2) Despejando
(7)
Relación válida para la deflexiónde un brazo
Momento en el codo (punto A)
Reemplazando la fuerza P por (2)(2)
Para el brazo L , la flecha f2
Reemplazando f1
dydx
|x=0=P⋅L⋅0−P⋅L⋅m /2
E⋅I
dydx
|x=0=P⋅L⋅m /2E⋅I
dydx
|x=0=P⋅L⋅L/ 4E⋅I
dydx
|x=0=P⋅L2
4⋅E⋅I
tan(α )= P⋅L2
4⋅E⋅I
tan(α )=f 2L
f 2L= P⋅L2
4⋅E⋅I
Mmax=3⋅E⋅I⋅f 1L3
⋅L
σmax=Mmax
I /c
σmax=M max⋅dI⋅2
L2=6⋅E⋅d⋅f7⋅σmax
L=√ 6⋅E⋅d⋅f7⋅σmax
dydx
=P⋅LE⋅I
⋅(x−m /2 )
Mmax=P⋅L
f 1=47⋅f
f 2=P⋅L3
4⋅E⋅I
f 1=P⋅L3
3⋅E⋅I
M=P⋅L
P=3⋅E⋅I⋅f 1L3
σmax=P⋅L⋅dI⋅2
σmax=3⋅E⋅I⋅f 1L3
⋅L⋅dI⋅2
σmax=3⋅E⋅f 1L2
⋅d2
σmax=3⋅EL2
⋅47⋅f⋅d2
σmax=67E⋅f⋅dL2
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
Mmax=3⋅E⋅I⋅f 1L3
⋅L
Mmax=3⋅E⋅I⋅f 1L2
Rev. cjc. 30.01.2014
1 de 4
2 de 4
Ecuación diferencial de la curva Para x = m/2 deformada de la viga "A-B" (Figura 2) dy/dx = 0
luego
con(3) Reemplazando en (3)
se tiene
Intergrando
(4)
3 de 4
y la flecha en el punto C debida al Relaciones f/f1 y f/f2
El cálculo de la longitud "L" de los brazos se realiza considerando la condición de que se produzca como máximo un esfuerzo de flexión admisible "sadm"
f
A
C
B
L
L/2
DC
f
EI⋅d2 ydx2
=M
M=P⋅L
EI⋅d2 ydx2
=P⋅L
c=−P⋅L⋅m /2
EI⋅dydx
=P⋅L⋅x−P⋅L⋅m /2
∫EI⋅ ddx ( dydx )⋅dx=∫P⋅L⋅dx
EI⋅dydx
=P⋅L⋅x+c
dydx
=P⋅L⋅x+cE⋅I
EI⋅dydx
=P⋅L⋅( x−m /2 )
giro en el codo A es
(5)
La flecha total en C es
4 de 4
Para la lira completa, es decir considerando la deflexión de los dosbrazos, se tiene que
Esta es la longitud del brazo de lalira que, para la expansión dada dela cañería, produce el esfuerzo
Ver Hoja Vitaulic. Vitaulic propone misma ecuación, con la diferenciaque el factor 0.378 es redondeadoa 0.4 (Hoja 7)
máximo admisible "smax"
f=f tot2
L=√ 6⋅E⋅d⋅(f tot /2 )7⋅σmax
L=√ 6⋅E⋅d⋅f tot14⋅σmax
L=√ 3⋅E⋅d⋅f tot7⋅σmax
L= 1√7 √ 3⋅E⋅d⋅f totσmax
L=0.378⋅√ 3⋅E⋅d⋅f totσmax
f tot=2⋅f
f=f 1+ f 2
f=P⋅L3
3⋅E⋅If 2+
P⋅L3
4⋅E⋅I
f=P⋅L3
3⋅E⋅I⋅44+P⋅L
3
4⋅E⋅I⋅33
f=4⋅P⋅L3
12⋅E⋅I+3⋅P⋅L
3
12⋅E⋅I
f=7⋅P⋅L3
12⋅E⋅I
f=7⋅P⋅L3
12⋅E⋅I
f 1=4⋅P⋅L3
12⋅E⋅I
f 2=3⋅P⋅L3
12⋅E⋅I
f 1f
=
4⋅P⋅L3
12⋅E⋅I7⋅P⋅L3
12⋅E⋅I
=47
f 1=47⋅f
f 2f
=
3⋅P⋅L3
12⋅E⋅I7⋅P⋅L3
12⋅E⋅I
=37
f 2=37⋅f
f 2=P⋅L3
4⋅E⋅I
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 Materia 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 19 201 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 41.419 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 22.120 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 41.421 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 26.222 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 17.223 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 51.024 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 44.125 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 51.026 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 51.027 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 = 593 621.0S = 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 6491 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 6.93 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 6.95 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 110.3 110.3 110.3 110.38 API 5L A25 103.4 103.4 100.0 95.19 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 137.9 137.9 137.9 137.911 API 5L X46 144.8 144.8 144.8 144.812 API 5L X52 151.7 151.7 151.7 151.713 API 5L X56 163.4 163.4 163.4 163.414 API 5L X60 172.4 1482.4 172.4 172.415 API 5L X65 177.2 177.2 177.2 177.216 API 5L X70 188.2 188.2 188.2 188.217 API 5L X80 206.8 206.8 206.8 206.818 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 41.419 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 22.120 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 41.421 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 26.222 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 17.223 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 51.024 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 44.125 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 51.026 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 51.027 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 metal 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 621Temperature °F
Material Spec Grade 100 200 300 400 500 600 650 700 750 800 850 900 950 1000 1050 1100 1150Type F A 53Gr. 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 1A 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 1A106 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 1A106 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 1API 5L X42 20 20 20 20 API 5L X46 21 21 21 21API 5L X52 22 22 22 22API 5L X56 23.7 23.7 23.7 23.7API 5L X60 25 215 25 25API 5L X65 25.7 25.7 25.7 25.7API 5L X70 27.3 27.3 27.3 27.3API 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 7.72 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 43 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 7.74 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 55 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 3.66 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 9.87 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 8.88 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 9.89 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 B31.3-2002Table A-1. Basic alowable stresses in tension for metals (Page 157 - 161)
38
toMaterial Spec Grade 100A 285 Gr A 134 … 15A 285 Gr A 672 A45 15
Butt wel API 5L A25 15smls API 5L A25 15
Type F A 53 Gr. A 16
A 53 A 16A 106 A 16A 135 A 16A 369 FPA 16API 5L A 16
A 285 Gr A 134 16.7A 285 Gr A 672 A 50 16.7
285 Gr. B A 134 18.3
A 516 Gr A 671 CC60 20A 515 Gr A 671 C860 20A 515 Gr A 672 B60 20A 516 Gr A 672 C60 20
A 53 B 20A106 B 20A 333 6 20A 334 6 20A 369 FPB 20A 381 Y35 20API 5L B 20
100API 5L X42 20API 5L X46 21API 5L X52 22API 5L X56 23.7
100A 516 Gr A 671 CC65 21.7A 515 Gr A 671 C865 21.7A 515 Gr A 672 B65 21.7A 516 Gr A 672 C65 21.7
100A 516 GR A 671 CC70 23.1A 515 GR A 671 CB70 23.1A 515 GR A 672 B70 23.1A 516 GR A 672 C70 23.1
A106 C 23.3
API 5L X60 25API 5L X65 25.7API 5L X70 27.3API 5L X80 30
Table CASME B31.3
Table C-1
1 Temperatura °C1 2 3
Material -536 -522
1 2 31 - -2 - -3 - -4 - -5 25Cr-20Ni - -67 3.5Ni8 1.1E-05 1.2E-059 Aluminum - -
10 - -11 Bronze - -12 Brass - -13 70Cu-30Ni - -14 - -15 - -16 - -
Thermal expansion coefficient " l " [m/(m*K)] for metals
3Cr-Mo)9Cr-Mo18Cr-8Ni27Cr
67Ni-30Cu
Alloys
Iron
Ni-Fe-CrNi-Cr-FeIron
Table C-1
Temperatura °C4 5 6 7 8 9 10 11
-508 -494 -480 -466 -452 -438 -424 -4114 5 6 7 8 9 10 11- - - 9.0E-06 9.1E-06 9.2E-06 9.3E-06 9.4E-06- - - 8.4E-06 8.5E-06 8.6E-06 8.7E-06 8.8E-06- - - 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- - - - - - - -
9.9E-06 1.0E-05 1.0E-05 1.1E-05 1.1E-058.5E-06 8.8E-06 9.0E-06 9.2E-06 9.5E-06
1.2E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05- - - 1.8E-05 1.8E-05 1.8E-05 1.9E-05 1.9E-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 1.5E-05- - - 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05- - - - - - - -- - - - - - - -- - - - - - - -
Thermal expansion coefficient " l " [m/(m*K)] for metals
Table C-1
Temperatura °C12 13 14 15 16 17 18 19
-397 -383 -369 -355 -341 -327 -313 -29912 13 14 15 16 17 18 19
9.5E-06 9.7E-06 9.9E-06 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.1E-059.0E-06 9.2E-06 9.3E-06 9.5E-06 9.5E-06 9.7E-06 9.9E-06 9.9E-061.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.5E-058.1E-06 8.3E-06 8.5E-06 8.5E-06 8.6E-06 8.8E-06 9.0E-06 9.0E-06
- - - - - - - -1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-059.8E-06 9.9E-06 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.1E-051.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.9E-05 1.9E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.1E-05 2.1E-05
- - - - - - - -1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.7E-05 2.0E-051.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.2E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05
- - - - - - - -- - - - - - - -
8.4E-06 8.6E-06 8.8E-06 8.9E-06 9.2E-06 9.4E-06 9.6E-06 9.8E-06
Thermal expansion coefficient " l " [m/(m*K)] for metals
Table C-1
Temperatura °C20 21 22 23 24 25 26 27
-286 -272 -258 -247 -230 -216 -202 -18820 21 22 23 24 25 26 27
1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.1E-05 1.1E-05 1.1E-059.9E-06 1.0E-05 9.8E-06 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-051.5E-05 1.5E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-059.0E-06 9.0E-06 9.0E-06 9.4E-06 1.0E-05 9.8E-06 9.9E-06 9.9E-06
- - - - 1.6E-05 1.6E-05 1.6E-05 1.6E-051.2E-05 1.2E-05 1.5E-05 1.5E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-051.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 1.1E-05 1.1E-05 1.2E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-052.1E-05 2.1E-05 2.1E-05 2.2E-05 2.3E-05 2.3E-05 2.3E-05 2.3E-05
- - - - 1.0E-05 1.0E-05 1.0E-05 1.0E-051.7E-05 1.6E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.8E-05 1.7E-05 1.8E-05 1.8E-051.4E-05 1.4E-05 1.4E-05 1.5E-05 1.6E-05 1.5E-05 1.5E-05 1.5E-05
- - - - 1.4E-05 1.4E-05 1.4E-05 1.4E-05- - - - 1.3E-05 1.3E-05 1.3E-05 1.3E-05
9.9E-06 7.7E-06 1.1E-05 1.1E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05
Thermal expansion coefficient " l " [m/(m*K)] for metals
Table C-1
Temperatura °C28 29 30 31 32 33 34 35
-174 -161 -147 -133 -119 -105 -91 -7728 29 30 31 32 33 34 35
1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-059.9E-06 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-05 1.0E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-052.3E-05 2.3E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-05 2.4E-051.0E-05 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-051.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-051.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-051.5E-05 1.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.6E-051.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-051.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05
Thermal expansion coefficient " l " [m/(m*K)] for metals
Table C-1
Temperatura °C36 37 38 39 40 41 42 43
-63 -49 -36 -22 -8 6 20 3436 37 38 39 40 41 42 43
1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-051.1E-05 1.1E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.8E-05 1.8E-05 1.8E-051.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-051.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-052.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-05 2.5E-051.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-051.8E-05 1.8E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.8E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.6E-05 - - - - - - -1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.3E-05
Thermal expansion coefficient " l " [m/(m*K)] for metals
Table C-1
Temperatura °C44 45 46 47 48 49 50 51
48 62 76 89 103 117 131 14544 45 46 47 48 49 50 51
1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-051.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.5E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-051.7E-05 - - - - - - -2.6E-05 - - - - - - -1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.9E-05 1.9E-05 1.9E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05 2.0E-05
- - - - - - - -1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.7E-051.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.5E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05
Table C-1
Temperatura °C52 53 54 55 56 57 58 59
159 173 187 201 214 228 242 25652 53 54 55 56 57 58 59
1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-05 1.4E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-051.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-051.6E-05 1.6E-05 1.6E-05 1.6E-05 1.6E-05 1.7E-05 1.7E-05 1.7E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05
- - - - - - - - - - - - - - - -
1.2E-05 1.2E-05 1.2E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-051.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-052.0E-05 2.0E-05 2.0E-05 2.0E-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-051.5E-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
Table C-1
Temperatura °C60 61 62 63 64 65 66 67
270 284 298 312 326 339 353 36760 61 62 63 64 65 66 67
1.4E-05 1.4E-05 1.4E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-051.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-051.4E-05 - - - - - - -
- - - - - - - - - - - - - - - -
1.3E-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 - - -
- - - - - - - -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 - - - - - - -
Table C-1
Temperatura °C68 69 70 71 72 73 74 75
381 395 409 423 437 451 464 47868 69 70 71 72 73 74 75
1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-05 1.5E-051.3E-05 1.3E-05 1.3E-05 1.3E-05 1.3E-05 1.4E-05 1.4E-05 1.4E-051.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-05 1.2E-051.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-05 1.7E-051.7E-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 1.8E-05 1.8E-05 1.8E-05 1.8E-05 - - - - - - - - - - - - - - - -
Table C-1
Temperatura °C76 77 78 79 80
492 506 520 534 54876 77 78 79 80
1.5E-05 - - - -1.4E-05 - - - -1.9E-05 1.9E-05 1.9E-05 1.9E-05 1.9E-051.2E-05 - - - -1.7E-05 - - - -1.8E-05 - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1.8E-05 1.8E-05 1.8E-05 1.8E-05 1.8E-05 - - - - - - - - - -
Table B. Young Modulus of Elasticity E [Pa]Metal
1 2 3 4 51 -200 -129 -73 211 2 3 4 5
1 Carbon steel C <= 0.3% 2.2E+11 2.1E+11 2.1E+11 2.0E+112 Carbon steel C => 0.3% 2.2E+11 2.1E+11 2.1E+11 2.0E+113 Carbon-moly steels 2.1E+11 2.1E+11 2.1E+11 2.0E+114 Nickel steels Ni 2% - 9% 2.0E+11 2.0E+11 2.0E+11 1.9E+115 Cr-Mo steels Cr 1/2% - 2% 2.2E+11 2.1E+11 2.1E+11 2.0E+11
6 Cr-Mo steels Cr 2 1/4% - 3% 2.2E+11 2.2E+11 2.2E+11 2.1E+117 Cr-Mo steels Cr 5% - 9% 2.3E+11 2.2E+11 2.2E+11 2.1E+11
8 Chromium steels Cr 12%, 17%, 27% 2.2E+11 2.1E+11 2.1E+11 2.0E+11
9 Austenitic steels (TP304, 310, 316, 321, 347) 2.1E+11 2.0E+11 2.0E+11 2.0E+11
Cast ironGray cast iron 1.3E+01
http://www.engineeringtoolbox.com/young-modulus-d_773.htmlMpsi = 6.9E+09 Pa
Table B. Young Modulus of Elasticity E [Pa]
6 7 8 9 10 11 12 13 14
93 149 204 260 316 371 427 482 538
6 7 8 9 10 11 12 13 142.0E+11 2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.5E+11 1.4E+112.0E+11 1.9E+11 1.9E+11 1.9E+11 1.8E+11 1.7E+11 1.7E+11 1.5E+11 1.4E+112.0E+11 1.9E+11 1.9E+11 1.9E+11 1.8E+11 1.7E+11 1.6E+11 1.5E+11 1.4E+111.9E+11 1.8E+11 1.8E+11 1.8E+11 1.7E+11 1.7E+11 1.6E+11 "N/A" "N/A"2.0E+11 2.0E+11 1.9E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.6E+11
2.1E+11 2.0E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+112.1E+11 2.0E+11 2.0E+11 2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.7E+11 1.6E+11
2.0E+11 1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.8E+11 1.7E+11 1.6E+11 1.5E+11
1.9E+11 1.9E+11 1.8E+11 1.8E+11 1.7E+11 1.7E+11 1.7E+11 1.6E+11 1.6E+11
Cast iron1.3E+01 1.3E+01 1.3E+01 1.2E+01 1.2E+01 1.1E+01 1.0E+01
Temperature (oC)
Table B. Young Modulus of Elasticity E [Pa]
Metal
15 16
593 649 -200 -129 -7315 16 3 4
1.2E+11 "N/A" Carbon steel C <= 0.3% 31.4 30.8 30.21.2E+11 1.1E+11 Carbon steel C => 0.3% 31.2 30.6 301.2E+11 1.1E+11 Carbon-moly steels 31.1 30.5 29.9"N/A" "N/A" Nickel steels Ni 2% - 9% 29.6 29.1 28.5
1.6E+11 1.5E+11 Cr-Mo steels Cr 1/2% - 2% 31.6 31 30.4
1.6E+11 1.6E+11 Cr-Mo steels Cr 2 1/4% - 3% 32.6 32 31.41.4E+11 1.3E+11 Cr-Mo steels Cr 5% - 9% 32.9 32.3 31.7
1.3E+11 1.1E+11 31.2 30.7 30.1
1.5E+11 1.5E+11 30.3 29.7 29.1
Cast iron Cast ironGray cast iron
Chromium steels Cr 12%, 17%, 27%
Austenitic steels (TP304, 310, 316, 321, 347)
21 93 149 204 260 316 371 427 482
4
29.5 28.8 28.3 27.7 27.3 26.7 25.5 24.2 22.429.3 28.6 28.1 27.5 27.1 26.5 25.3 24 22.229.2 28.5 28 27.4 27 26.4 25.3 23.9 22.227.8 27.1 26.7 26.1 25.7 25.2 24.6 2329.7 29 28.5 27.9 27.5 26.9 26.3 25.5 24.8
30.6 29.8 29.4 28.8 28.3 27.7 27.1 26.3 25.630.9 30.1 29.7 29 28.6 28 27.3 26.1 24.7
29.2 28.5 27.9 27.3 26.7 26.1 25.6 24.7 23.2
28.3 27.6 27 26.5 25.8 25.3 24.8 24.1 23.5
Cast iron13.4 13.2 12.9 12.6 12.2 11.7 11 10.2
Temperature (oC)
538 593 649
4 5 6 7 8 920.4 1820.2 17.9 15.420.1 17.8 15.3
23.9 23 21.8
24.6 23.7 22.522.7 20.4 18.2
21.5 19.1 16.6
22.8 22.1 21.2
Cast iron
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipe-expansion-and-support.asp
pipe nominal diameter "dn" (in),Spiraxsarco graph provides anexpansionloop width "W" (m).
90 mmdn = 273 mm
Estimated value from Fig. 10.4W = 2.55 m
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipe-expansion-and-support.asp
For expansion "DL" (mm), and a
DL =
http://static.victaulic.com/assets/uploads/literature/26.02-SPA.pdfVitaulic equation for an expansion loop
L=0.378⋅√ 3⋅E⋅d⋅f totσmax
Vitaulic equation
5W = LW = L/5
H = 2*WH = 2 * L / 5H = 0.4 * L
Equation deducted in sheet 2
H =
H=0. 4⋅√ 3⋅E⋅d⋅f totσ
L=0.378⋅√ 3⋅E⋅d⋅f totσmax
E: Elasticity module of materiald: exterior pipe diameterftot: total pipe expansion S: Allowable stress of material
[1] Elementos de resistencia de materialesS. Timoshenko, D. H. YoungEd. 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
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipe-expansion-and-support.asp
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