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Figure 9.4-7 Cylindrical shell with isolated opening and set-on nozzle
Figure 9.4-8 Spherical shell or dished end with isolated opening and set-in nozzle
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Figure 9.4-9 Cylindrical shell with isolated opening, increased wall thickness and set-in nozzle
NOTE The various lengths and areas shown for the case of a nozzle with a reinforcing plate in a sphere also applies to the case of a nozzle with a reinforcing plate in a cylinder.
Figure 9.4-10 Spherical shell or dished end with isolated opening and shell, nozzle and reinforcing plate
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b) On a conical shell connected at its smaller diameter with a cylindrical shell having the same axis, the distance w, as shown in Figure 9.7-10, shall satisfy the following condition
w > wmin = lcon (9.7-6)
where
lcon = αcoseD 2c ⋅ (9.7-7)
9.7.2.3 Openings in domed and bolted ends
For openings in domed and bolted ends, the distance w of the edge of the opening from the flange, taken as shown in Figure 9.7-11, shall satisfy the following condition
w > wmin = max )e;e)er(,( s,as,cs,cis 3220 ⋅+ (9.7-8)
9.7.2.4 Openings in elliptical and torispherical ends
For dished ends the value w is the distance along the meridian between edge of the opening (outside diameter of nozzle or pad) and the point on the dished end which is determined by the distance of De/10 shown in Figure 9.5-4 (i.e. the distance wmin = 0 ).
9.7.2.5 Openings in hemispherical ends
On a hemispherical end connected to a cylindrical shell, a flange or a tubesheet, the distance w as shown in Figures 9.7-12 to 9.7-14 shall satisfy the following condition:
( )( )sa,sc,sc,ismin 3 ;22,0max eeerww ⋅+=≥ (9.7-8a)
9.7.3 Rules regarding wp
When the distance w of an opening from a discontinuity, as shown in Figures 9.7-1 to 11, is lower than the value wp defined in a), b), c) as below, the shell length ls available for reinforcement to take in account for equation (9.5-26) and others similar is reduced to the following values:
a) for discontinuities indicated in 9.7.2.1 (a), 9.7.2.2 (a), 9.7.2.3 and 9.7.2.4
w < wp = lso (9.7-9)
ls = w (9.7-10)
b) for discontinuities indicated in 9.7.2.1 (b) and (c)
w < wp = lso + wmin (9.7-11)
ls = w - wmin (9.7-12)
c) for discontinuities indicated in 9.7.2.2.(b)
w < wp = lso + lcon (9.7-13)
ls = w - lcon (9.7-14)
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Figure 9.7-1 Opening in a cylindrical shell, close to the junction with a domed end
Figure 9.7-2 Opening in a cylindrical shell, close to the junction with the larger diameter of aconical reducer
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Flat ends which do not meet these conditions shall be treated as ends welded directly to the shell.
10.4.2.3 For a flat end welded directly to the shell (see Figure 10.4-2), lcyl is given by:
l D e ecyl i s s= +( ) (10.4-2)
10.4.2.4 For a flat end with a relief groove (see Figure 10.4-3), the following conditions shall apply:
a) lcyl is also given by equation (10.4-2);
b) radius rd shall be at least equal to 0,25es or 5 mm, whichever is greater;
c) the centre of the radius shall lie within the thickness of the flat end and not outside it, and the distance hw of the end-to-shell weld to the outside surface of the end shall be greater than (e - 2mm), see Figure 10.4-3.
10.4.3 Flat ends with a hub
The minimum required thickness for a flat end with a hub is given by:
f
PDCe eq1 ⋅= (10.4-3)
When the distance from the inside surface of the flat portion of the end to the end-to-shell weld is larger than lcyl + r, the coefficient C1 is given by Figure 10.4-4 or by :
+
+=
i
s
i
si11 7,11 299,0, 40825,0
De
DeD
AMAXC (10.4-4)
where :
( )
+
−=si
s111 2
1eD
eBBA (10.4-5)
( )( )3si
2ssi
4
si
i2
si
s1
243
16331
eDeeD
fP
eDD
eDe
PfB
+
+−
+
+
+
−= (10.4-6)
When this distance is lower than lcyl + r , then the coefficient C1 is still given by Figure 10.4-4 but using P/f instead of P/fmin . For a uniform thickness shell per Figure 10.4-1 a),
rDD −= ieq (10.4-7)
For a tapered shell per Figure 10.4-1 b),
( )
2Fi
eqDD
D+
= (10.4-8)
The following condition shall be met:
ee ≥af (10.4-9)
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10.4.4 Flat ends welded directly to the shell
10.4.4.1 The minimum required thickness for the end is given, for a normal operating case, by the greatest of the following:
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅=
mini2i1max
fP
DCfP
DCe , (10.4-10)
where
{ }f f fmin ;= min s (10.4-11)
C1 is given:
− either by Figure 10.4-4
− or by equation (10.4-4) calculated with the A1 value derived from equations (10.4-5) and (10.4-6) using fmin instead of f.
C2 is given by Figure 10.4-5.
Instead of reading C2 on Figure 10.4-5, the term min
i2 fPDC ⋅ may also be calculated directly by means of the
method given in 10.4.6
NOTE The Equation 10.4-10 is valid only for values of P/f up to 0,1 (see Figures 10.4-4 and 10.4-5). For values of P/f below 0,01 the value of 0,01 may be taken. For values of P/f above 0,1, it is recommended to use design by analysis, see Annex B or C.
When C2 is less than 0,30, only the first term of equation (10.4-10) shall be considered.
10.4.4.2 For an exceptional operating case and for a hydrostatic testing case the calculation of e shall take into account only the first term of equation (10.4-10):
f
PDCe i1 ⋅= (10.4-12)
10.4.4.3 In equations (10.4-10) to (10.4-12), f, fs and P shall be understood as generic symbols valid for all types of load cases (normal, exceptional, testing) and having the following meaning:
— for a normal operating case, f is fd, sf is sd )(f and P is Pd;
— or an exceptional operating case, f is fexp, sf is (fexp)s and P is Pexp;
— for an hydrostatic testing case, f is ftest, sf is (ftest)s and P is Ptest.
10.4.4.4 For a normal operating case, the minimum required thickness of the end may alternatively be calculated using equation (10.4-12) instead of (10.4-10), provided a simplified assessment of the fatigue life of the flat end to shell junction is performed according to Clause 17. In performing this assessment:
— the following stress index value shall be used :
⎟⎟⎠
⎞⎜⎜⎝
⎛=
2max,
1max,3PP
η (10.4-13)
where Pmax,1 is the maximum permissible pressure derived from equation (10.4-12) for the analysis thickness ea;
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C
P/f
0,0025
e I D =s i
0,0030,004
0,0050,0065
0.42
0.40
0.38
0.36
0.34
0.32
0.300,001 0,01 0,1
0,0080,01
0,01250,015
0,020,025
0,03
0,040,05
0,0650,08
1
min
Figure 10.4-4 — Values of coefficient C1
NOTE 1 Where P/fmin is lower than the value corresponding to the point of intersection between the es/Di curve and the bottom curve (dotted line), C1 is the value defined by the horizontal line passing through this point. NOTE 2 There are cases where P/f shall be used instead of P/fmin , see 10.4.3.
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Figure 10.4-5 — Values of coefficient C2
10.4.6 Direct calculation of the term with coefficient C2 in equation 10.4-10
a) calculate successively the following quantities :
si
i
eDDg+
= (10.4-16)
( )si
s4
2112eD
eH
+−= ν (10.4-17)
( )1
43
ssi
2imin −+
−=eeD
DPf
J (10.4-18)
( )
( )213
22
ν
ν
−
⋅−=
gU (10.4-19)
421 2 ggf −= (10.4-20)
( ) ( ) ⎥⎦
⎤⎢⎣
⎡+
−++⎟⎟⎠
⎞⎜⎜⎝
⎛−
⋅=
si
s
s
i 111243
eDeJ
eDUA νν (10.4-21)
( ) HggHJe
DUB ⎥
⎦
⎤⎢⎣
⎡⋅−−⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⋅= ν2
23
83 2
s
i (10.4-22)
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h
D i
Figure 10.6-1 — Single opening in a flat end
k
D i
Figure 10.6-2 — Pair of openings in a flat end
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Figure 10.6-3 — Set-on nozzle in a flat end
eab
e'ab
de
eb
e
Al
l'
Figure 10.6-4 — Set-in nozzle in a flat end
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11.4.2 Use of standard flanges without calculation
Flanges that conform to an European Standard for pipework flanges may be used as pressure vessel components without any calculation, provided all the following conditions are fulfilled:
a) Under normal operating conditions, the calculation pressure does not exceed the rating pressure given in the tables of the relevant European Standard, for the flange and material under consideration for the calculation temperature.
b) Under testing conditions or exceptional conditions, the calculation pressure does not exceed 1,5 times the rating pressure given in the same tables, at appropriate temperature.
c) The gasket is one of those permitted by Table 11.4-1 for the relevant PN or Class series.
d) The bolts are of a strength category (see Table 11.4-2) at least equal to the minimum required by Table 11.4-1 as a function of the gasket type used in the connection.
e) The vessel is subjected to loadings of predominantly non-cyclic nature, see 5.4.2.
f) The difference between mean temperatures of bolts and flange does not exceed 50 °C in any condition.
g) The bolt and flange materials have coefficients of thermal expansion at 20 °C that differ by more than 10 % (e.g. austenitic steel flanges with ferritic steel bolts) but the calculation temperature is < 120 °C, or the bolt and flange materials have coefficients of thermal expansion at 20 °C which do not differ by more than 10 %.
11.4.3 Bolting
11.4.3.1 Bolts
There shall be at least four bolts.
The bolts shall be equally spaced. Flanges with unequally spaced bolts can be calculated as flanges with equally spaced bolts provided in all the following subparagraphs the bolt area AB to be used for comparison with ABmin is decreased in respect of the actual bolt area by replacing the actual bolt number n with an equivalent bolt number nEQ obtained from the following equation:
maxBEQ
Cnδπ
= (11.4-1)
where δBmax is the maximum bolt pitch; in equation (11.5-20) the value of δB shall also be replaced by δBmax. nEQ need not to be an integer.
In the case of small diameter bolts it may be necessary to use torque spanners or other means for preventing the application of excessive load on the bolt.
Special means may be required to ensure that an adequate preload is obtained when tightening bolts of nominal diameter greater than 38 mm.
Bolt nominal design stresses for determining the minimum bolt area in 11.5.2 shall be:
for carbon and other non-austenitic steels, the lesser of Rp0,2/3 measured at design temperature and Rm/4 measured at room temperature;
for austenitic stainless steel, Rm/4 measured at design temperature.
11.4.3.2 Nuts
The nuts shall have specifies proof load values not less than the minimum proof load values of the screws on which they are mounted.
Nuts with standard thread pitch (i.e. coarse pitch) fulfil this requirement if they have :
a height not less than 0,8dn,
a yield strength or class of quality not less than that of the screws.
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When these conditions are not met, the height of the nuts shall not be less than:
nutp,
screwp,n8,0
RR
d ⋅
Note : pR is p0,2R for non-austenitic steels, p1,0R for austenitic steels.
11.4.3.3 Threaded holes
The engagement length of screws in threaded holes of a component shall not be less than:
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅ n
componentp,
screwp,n 8,0 ; 8,0max d
RR
d
Note : pR is p0,2R for non-austenitic steels, p1,0R for austenitic steels.
Table 11.4-1 — Gaskets for standard flanges
PN designated
series1)
Class designated
series1) Gasket type
Minimum bolt strength category required (see Table 11.4-2)
2,5 to 16 - — Non-metallic flat gasket with or without jacket
Low strength
— Non-metallic flat gasket with or without jacket
Low strength
25 150 — Spiral-wound metal with filler — Corrugated metal jacketed with filler Medium strength — Corrugated metal with or without filler — Non-metallic flat gasket with or without
jacket Low strength
40 - — Spiral-wound metal with filler — Corrugated metal jacketed with filler Medium strength — Corrugated metal with or without filler — Flat metal jacketed with filler High strength — Grooved or solid flat metal — Non-metallic flat gasket with or without
jacket Low strength
63 300 — Spiral-wound metal with filler — Corrugated metal jacketed with filler Medium strength — Corrugated metal with or without filler — Flat metal jacketed with filler
— Grooved or solid flat metal High strength — Metal ring joint
100 600 — Non-metallic flat gasket with or without jacket
— Spiral-wound metal with filler Medium strength — Corrugated metal jacketed with filler — Corrugated metal with or without filler — Flat metal jacketed with filler — Grooved or solid flat metal High strength — Metal ring joint 1) The PN (or Class) values presented in this table are restricted to those existing in EN Standards on Steel Flanges, up to PN 100 (or Class 600).
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Table 11.4-2 — Bolt strength categories
Low strength Medium strength High strength R
Rp,bolt
p,flange ≥ 1 ≥ 1,4 ≥ 2,5
NOTE Rp is Rp0,2 for non-austenitic steels, Rp1,0 for austenitic steels. If Rp1,0 is not known, use Rp0,2 for both bolt and flange.
The assembly condition and operating condition are both normal design conditions for the purpose of determining nominal design stresses.
These allowable stresses may be multiplied by 1,5 for testing or exceptional conditions.
NOTE These stresses are nominal in so far as they may have to be exceeded in practice to provide against all conditions that tend to produce a leaking joint. However there is sufficient margin to provide a satisfactory closure without having to overload or repeatedly tighten the bolts.
11.4.4 Flange construction
A distinction is made between flanges in which the bore of the flange coincides with the bore of the shell (for example welded joints F1, F2, F3 and F5 as shown in annex A Table A.7) and those with a fillet weld at the end of the shell (for example welded joint F4) in which the two bores are different. They are known as smooth bore (see Figure 11.5-1) and stepped bore (see Figure 11.5-2) respectively.
A further distinction is made between the slip-on hubbed flange (see Figure 11.5-3), in which a forged flange complete with taper hub is slipped over the shell and welded to it at both ends, and other types of welded construction.
Any fillet radius between flange and hub or shell shall be not less than 0,25g0 and not less than 5 mm.
Hub flanges shall not be made by machining the hub directly from plate material without special consideration.
Fillet welds shall not be used for design temperatures above 370 °C.
11.4.5 Machining
The bearing surface for the nuts shall be parallel within 1° to the flange face. Any back facing or spot facing to accomplish this shall not reduce the flange thickness nor the hub thickness below design values. The diameter of any spot facing shall be not less than the dimension across corners of the nut plus 3 mm. The radius between the back of the flange and the hub or shell shall be maintained.
The surface finish of the gasket contact face should be in accordance with the gasket manufacturers' recommendations or be based on experience.
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11.4.6 Gaskets
The values of the gasket factors m and y should normally be provided by the gasket manufacturer butsuggested values are given in annex H.
Suggested minimum values of w, the assembly width, are also given in annex H.
NOTE Asbestos containing gaskets are forbidden in most European countries.
11.5 Narrow face gasketed flanges
11.5.1 General
.
G
B
A C
e
h
W
g0
g1
hD
hG
hT
HD
HTHG
Figure 11.5-1 — Narrow face flange - smooth bore
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11.5.4 Flange stresses and stress limits
11.5.4.1 Flange stresses
11.5.4.1.1 Flange stresses calculation
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
++
= ;1
0,56 2
max b
bF
med
Cδ
(11.5-20)
K = A/B (11.5-21)
00 Bgl = (11.5-22)
( )( ) ( )11,94481,0472
1)(10
log8,5524612
2
T−+
−+=
KK
KKβ (11.5-23)
( )( ) 1)(11,36136
1)(10
log8,5524612
2
U−−
−+=
KK
KKβ (11.5-24)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+
−=
1
)(10
log5,71690,66845
1
12
2
Y K
KK
Kβ (11.5-25)
Flange stresses shall be determined from the moment, M, as follows:
For the assembly condition,
B
CMM F
A= (11.5-26)
For the operating condition,
B
CMM F
op= (11.5-27)
a) Integral method
βF βV and ϕ are given by Equations 11.5-27a to 11.5-27c or are found from Figures 11.5-4 to 11.5-6:
( )( )CAC
Eβ
341
2
6
1
13
+
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−=
/F
v
(11.5-27a)
where A, C and E6 are coefficients obtained from Equations in 11.5.4.1.2.
For flanges with cylindrical hub, βF = 0,908920.
( ) ( )3412
4
113 AC
Eβ
+⎥⎥⎦
⎤
⎢⎢⎣
⎡ −=
/νν
(11.5-27b)
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where A, C and E4 are coefficients obtained from Equations in 11.5.4.1.2.
For flanges with cylindrical hub, βV = 0,550103.
AC+
=1
36ϕ (11.5-27c)
where A and C36 are coefficients obtained from Equations in 11.5.4.1.2.
0,5
0,6
0,7
0,8
0,9
1 1,5 2 2,5 3 3,5 4 4,5 5
0,100,200,250,300,350,400,45
0,50
0,60
0,70
0,80
0,901,00
1,251,50
2,00
h = hl Bg 00
0,908920
β F
g1/g0 Figure 11.5-4 — Value of βF (integral method factor)
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0
0,1
0,2
0,3
0,5
0,4
0,6
1 1,5 2 2,5 3 53,5 4 4,5
g / g1 0
0,100,120,140,160,180,20
0,250,300,350,400,450,500,600,700,800,901,001,251,502,00
h = hl Bg0 0
0,550103
β V
Figure 11.5-5 — Value of βv (integral method factor)
Figure 11.5-6 — Value of ϕ (hub stress correction factor)
= 1 (minimum) = 1 for hubs of uniform thickness (g /g = 1)
1 0
ϕ
ϕϕ
1 1,5 2 3 4 5
1
1,5
2
2,5
3
4
5
6
789
10
1,20
1,10
0,90
1,00
0,80
0,70
0,60
0,500,450,40
0,30
0,20
0,10
0,35
0,25
0,15
0,050
g /g1 0
15
20
25
h hl Bg00
1,30
=
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⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅⋅
⋅+
⋅+⋅
=200U
V3
0T
0F
gle
lle
β
βββ
λ (11.5-28)
The longitudinal hub stress:
21
H = g
M
λ
ϕσ (11.5-29)
The radial flange stress:
02
0Fr
)(1,333
le
Mle
λ
βσ
+= (11.5-30)
The tangential flange stress:
11
2
2
r2Y
−
+−
⋅=
KK
eM σβσθ (11.5-31)
b) Loose method
The tangential flange stress:
2Y
e
M⋅=β
σθ (11.5-32)
The radial stress in flange and longitudinal stress in hub are
0Hr == σσ (11.5-33)
c) Loose hubbed flange method
βFL and βVL are given by Equations 11.5-33a and 11.5-33b or are found from Figures 11.5-7 and 11.5-8 respectively :
( )CA
vC
AACACACβ
34/1
2
242118
FL1
)1(3
36059
21023
841121
63
+
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
⎟⎠
⎞⎜⎝
⎛ +−⎟
⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ +
= (11.5-33a)
where A, C, C18, C21 and C24 are coefficients obtained from Equations in 11.5.4.1.2.
( ) ( )34/12
182124
VL
113
23
541
ACv
CCC
β
+⎥⎥⎦
⎤
⎢⎢⎣
⎡ −
−−−= (11.5-33b)
where A, C, C18, C21 and C24 are coefficients obtained from Equations in 11.5.4.1.2.
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0,40,50,60,70,80,91,0
1,5
2
3
4
56789
10
15
20
2,00
1,50
1,000,900,800,700,600,500,450,400,350,300,25
0,200,180,160,140,120,100,090,080,070,060,05
g / g1 0
h = hl Bg0
1,0 1,5 2,0 3,0 4,0 5,0
β FL
Figure 11.5-7 — Value of βFL (loose hub flange factor)
0,010,020,030,040,08
0,10,2
0,20,30,40,60,8
1
23468
10
2030406080
100
2,00
1,50
1,000,900,800,700,60
0,500,450,400,350,30
0,25
0,200,180,160,14
0,120,10
1,0 1,5 2,0 3,0 4,0 5,0
g / g1 0
βVL
h = hl Bg0 0
Figure 11.5-8 — Value of βVL (loose hub flange factor)
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡+
+=
200U
VL3
0T
0FL
gle
lle
β
βββ
λ (11.5-34)
The longitudinal hub stress:
EN 13445-3:2002 (E) Issue 31 (2008-06)
21
H g
M
λσ = (11.5-35)
The radial flange stress:
02
0FLr
)(1,333
le
Mle
⋅⋅
+⋅=
λ
βσ (11.5-36)
The tangential flange stress:
1
12
2
r2Y
−
+−
⋅=
K
K
e
Mσ
βσθ (11.5-37)
11.5.4.1.2 Coefficients for flange stresses calculations
10
1 −=ggA (11.5-37a)
4
0
2)1(48 ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
lhvC (11.5-37b)
1231
1AC += (11.5-37c)
33617
425
2AC += (11.5-37d)
3602101
3AC += (11.5-37e)
CAAC 31
504059
36011
4+
++= (11.5-37f)
CAAC
3
5)1(
10085
901 +
++= (11.5-37g)
CAC 1
504017
1201
6 ++= (11.5-37h)
CAAAAC 1
1435150225120
123251
2772215 32
7 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37i)
CAAAAC 1
773513216566
45045128
693031 32
8 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37j)
CAAAAC 1
842511719842
73920653
30240533 32
9 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37k)
CAAAAC 1
849124319842
7043
378029 32
10 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++−+= (11.5-37l)
CAAAAC 1
8410457242
6652801763
604831 32
11 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37m)
163a
EN 13445-3:2002 (E) Issue 31 (2008-06)
CAAAAC 1
3854215619888
30030071
29251 32
12 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37n)
CAAAAC 1
70311122
1663200937
831600761 32
13 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37o)
CAAAAC 1
70717122
332640103
415800197 32
14 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++−+= (11.5-37p)
CAAAAC 1
210415186
55440097
831600233 32
15 ⎟⎟⎠
⎞⎜⎜⎝
⎛ +++++= (11.5-37q)
( )12221
287
23283382127116 ......... CCCCCCCCCCCCCCCC ++−++= (11.5-37r)
( )[ ]16
921242837139831382127417
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37s)
( )[ ]16
10212528371410831482127518
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37t)
( )[ ]16
11212628371511831582127619
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37u)
( )[ ]16
241218139232133384129120
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37v)
( )[ ]16
241218139232133384129120
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37w)
( )[ ]16
25121814102321433851210121
1..........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37x)
( )[ ]16
26121815112321533861211122
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37y)
( )[ ]16
1322198473284392137123
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37z)
( )[ ]16
142211085732853102147124
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37aa)
( )[ ]16
152211186732863112157125
1...........C
CCCCCCCCCCCCCCCCCC ++−++= (11.5-37ab)
4/1
26 4⎟⎠
⎞⎜⎝
⎛−=CC (11.5-37ac)
2617172027 .125 CCCCC +−−= (11.5-37ad)
2619192228 .121 CCCCC +−−= (11.5-37ae)
2/1
29 4⎟⎠
⎞⎜⎝
⎛−=CC (11.5-37af)
163b
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4/3
30 4⎟⎠
⎞⎜⎝
⎛−=CC (11.5-37ag)
301731 .2
3 CCAC −= (11.5-37ah)
301932 .21 CCC −= (11.5-37ai)
⎟⎠
⎞⎜⎝
⎛ +−+= 2927322830
2931283226
33 ..2...
2. CCCCCCCCCCC (11.5-37aj)
2618211834 .121 CCCCC −−+= (11.5-37ak)
301835 .CCC = (11.5-37al)
( )33
293432293528361....
CCCCCCCC −= (11.5-37am)
33292735
3430293134
352637
1..2...
2.
CCCCCCCCCCCC ⎟
⎠
⎞⎜⎝
⎛ −−+= (11.5-37an)
37191836171 .. CCCCCE ++= (11.5-37ao)
37222136202 .. CCCCCE ++= (11.5-37ap)
37252436233 .. CCCCCE ++= (11.5-37aq)
1010152
1233 1233637
4EEECCE ++
−++
= (11.5-37ar)
⎟⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ ++⎟
⎠
⎞⎜⎝
⎛ +=
21023
841121
63
3215AEAEAEE (11.5-37as)
⎟⎠
⎞⎜⎝
⎛ ++−−−⎟⎠
⎞⎜⎝
⎛ ++−=C
ACACAACEE 1
120601
724013
361207
373656 (11.5-37at)
11.5.4.2 Stress limits
The assembly condition and operating condition are both normal design conditions for the purpose of determining nominal design stresses.
Nominal design stresses f shall be obtained in accordance with clause 6, except that for austenitic steels as per 6.4 the nominal design stress for normal operating load cases is given by 6.4.1 a) only, and for testing load cases by 6.4.2 a).
fH shall be the nominal design stress of the shell except for welding neck or slip-on hubbed construction where it is the nominal design stress of the flange.
If B ≤ 1 000 mm then k = 1,0.
If B ≥ 2 000 mm then k = 1,333.
For values of B between 1 000 mm and 2 000 mm:
⎟⎠⎞
⎜⎝⎛
+=000 2
13
2 Bk (11.5-38)
164
EN 13445-3:2002 (E) Issue 31 (2008-06)
181
The flange thickness shall be not less than:
( )h
R6dnCf
Me
⋅−=
π (11.10-6)
where dh is the diameter of bore holes.
Where two flanges of different internal diameters, both designed to the rules of this clause, are to be bolted together to make a joint, the following additional requirements apply:
a) value of MR to be used for both flanges shall be that calculated for the smaller internal diameter;
b) the thickness of the flange with the smaller bore shall be not less than:
( )( )BABf
BAMMe
- + 2 - 13
= ⋅
⋅
π (11.10-7)
where M1 and M2 are the values of MR calculated for the two flanges.
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12 Bolted domed ends
12.1 Purpose
This clause specifies requirements for the design of bolted domed ends, with either full face or narrowface gaskets, and with the dome either convex or concave to pressure. The rules provided in thisclause for the narrow face gasket design are well established but Annex G provides a modernalternative - see NOTE 1 of 11.1.
12.2 Specific definitions
The following definition applies in addition to those in 11.2.
12.2.1bolted domed endcover or blind flange consisting of a flange and a dome of constant radius of curvature
12.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in 11.3:
a is distance from top of flange to the mid-thickness line of the dome where it meets the flange;
eD is required thickness of spherical dome section;
fD is design stress for dome section;
Hr is radial component of membrane force developed in dome, acting at edge of flange;
hr is the axial distance from mid-surface of dome section at edge to center of flange ring cross-section,as given by equation (12.5-3);
R is inside radius of curvature of dome.
12.4 General
Relevant parts of 11.4 also apply to flanges designed in accordance with clause 12.
12.5 Bolted domed ends with narrow face gaskets
12.5.1 Dome concave to pressure
NOTE See Figure 12-1 for an illustration of loads and dimensions.
Bolt loads and areas and gasket loads shall be calculated in accordance with 11.5.2.
The required thickness of the spherical dome section shall be:
e = P R
fDD
56
⋅(12.5-1)
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14.3 Specific symbols and abbreviations
The following symbols apply in addition to those listed in clause 4.
A is the cross sectional metal area of one convolution, given by equation (14.5.2-7) or (14.6.3-7);
C C Cp f d, , are coefficients used for U-shaped convolutions, see Figures 14.5.2-1, 2 and 3;
21 and CC are coefficients given by equations (14.5.2-8) and (14.5.2-9) or (14.6.3-8) and (14.6.3-9), used to determine the coefficients C C Cp f d, , ;
cD is the mean diameter of collar, given by equation (14.5.2-2) or (14.6.3-2) or (14.7.3-2);
Di is the inside diameter of bellows convolution and end tangents, see Figure 14.1-1;
Dm is the mean diameter of bellows convolution, given by equation (14.5.2-3) or (14.6.3-3) or (14.7.3-3);
Eb is the modulus of elasticity of bellows material at design temperature;
Ec is the modulus of elasticity of collar material at design temperature;
Eo is the modulus of elasticity of bellows material at room temperature;
e is the bellows nominal thickness, given by equation (14.5.2-1) or (14.6.3-1) or (14.7.3-1); For single ply bellows: e e= p ;
ec is the collar thickness, see Figure 14.1-1;
ep is the nominal thickness of one ply;
*e is the bellows thickness, corrected for thinning during forming, given by equation (14.5.2-5) or (14.6.3-5) or (14.7.3-5);
ep* is the thickness of one ply, corrected for thinning during forming, given by equation (14.5.2-4) or
(14.6.3-4) or (14.7.3-4);
f is the nominal design stress of bellows material at design temperature;
fc is the nominal design stress of collar material at design temperature;
Kb is the bellows axial rigidity, given by equation (14.5.7-1, 14.6.8-1 or 14.7.8-1);
k is the factor considering the stiffening effect of the attachment weld and the end convolution on the pressure capacity of the end tangent, given by equation (14.5.2-6) or (14.6.3-6);
cL is the collar length, see Figure 14.1-1;
tL is the end tangent length, see Figure 14.1-1;
N is the number of convolutions;
alwN is the allowable number of fatigue cycles;
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speN is the specified number of fatigue cycles;
np is the number of plies;
P is the calculation pressure;
q is the convolution pitch, given by equation (14.5.2-10);
ri is the internal radius of torus at the crest and root of U-shaped convolutions, see Figure 14.5.1-1;
ds is the strain caused by deformation during manufacturing, see 14.5.2.2;
w is the convolution height, see Figure 14.1-1;
α is the in-plane instability stress interaction factor, given by equation (14.5.2-12);
δ is the in-plane stress instability stress ratio, given by equation (14.5.2-11);
Δq is the total equivalent axial displacement range per convolution, given by 14.10.5;
νb is the Poisson's ratio of the bellows material;
( )σ P is a stress depending on P;
( )qΔσ is a stress depending on qΔ ;
eqσ is the total stress range due to cyclic displacement;
Main subscripts:
b for bellows
c for collar
m for membrane or meridional
p for ply
r for reinforced
t for end tangent
θ for circumferential
No subscript is used for the bellows convolutions.
14.4 Conditions of applicability
14.4.1 Geometry
14.4.1.1 An expansion bellows comprises one or more identical convolutions. Each convolution is axisymmetric.
14.4.1.2 Each convolution may have one or more plies of equal thickness and made of same material.
14.4.1.3 Bellows including a cylindrical end tangent of length Lt , with or without collar (see Figure 14.1-1): if the thickness of the tangent is less than the cylindrical shell to which the bellows is welded, Lt shall be such that:
it DeLL c ⋅≤− 5,0
In this formula , Lc = 0 if the bellow is without collar.
14.4.1.4 The number of plies shall be such that:
5≤pn
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Table 14.7.3-1 — Coefficients B1, B2, B3
∗pm
261,6eDr
B1
B2
B3
0 1,0 1,0 1,0 1 1,1 1,0 1,1 2 1,4 1,0 1,3 3 2,0 1,0 1,5 4 2,8 1,0 1,9 5 3,6 1,0 2,3 6 4,6 1,1 2,8 7 5,7 1,2 3,3 8 6,8 1,4 3,8 9 8,0 1,5 4,4 10 9,2 1,6 4,9 11 10,6 1,7 5,4 12 12,0 1,8 5,9 13 13,2 2,0 6,4 14 14,7 2,1 6,9 15 16,0 2,2 7,4 16 17,4 2,3 7,9 17 18,9 2,4 8,5 18 20,3 2,6 9,0 19 21,9 2,7 9,5 20 23,3 2,8 10,0
14.7.4 Stresses due to internal pressure
14.7.4.1 End tangent
The circumferential membrane stress due to pressure:
( ) ( )( )
2i w b
θ,ti w b c c c
12
D e L EP P
e D e L E D E Aσ
⎡ ⎤+= ⎢ ⎥
+ +⎢ ⎥⎣ ⎦ (14.7.4-1)
shall comply with:
( )θ,t t P fσ ≤
14.7.4.2 Collar
The circumferential membrane stress due to pressure:
( ) ( )2c w c
θ,ci w b c c c
12
D L EP Pe D e L E D E A
σ⎡ ⎤
= ⎢ ⎥+ +⎣ ⎦ (14.7.4-2)
shall comply with:
( )θ,c cP fσ ≤
14.7.4.3 Bellows convolutions
The following formulae are used to determine the bellows convolutions:
a) The circumferential membrane stress due to pressure:
( )θ *2rP Pe
σ = (14.7.4-3)
shall comply with:
( )P fθσ ≤
EN 13445-3:2002 (E) Issue 15 (2005-07)
b) The meridionial membrane stress due to pressure:
( ) mm,m *
m 2D rr
P Pe D r
σ −
= − (14.7.4-4)
shall comply with:
( )m,m P fσ ≤
14.7.5 Instability due to internal pressure
14.7.5.1 Column instability
The allowable internal design pressure to avoid column instability, s,cP , is given by:
bs,c 0,15
KP
Nrπ
= (14.7.5-1)
The internal pressure P shall not exceed cs,P :
cs,PP ≤
14.7.5.2 In-plane instability
Toroidal bellows are not subject to in-plane instability
14.7.6 External pressure design
14.7.6.1 Stresses due to external pressure
The rules of 14.7.4 shall be applied, taking P as the absolute value of the external pressure and using Ac in the equations.
When the expansion bellows is submitted to vacuum, the design shall assume that only the internal ply resists the pressure. The pressure stress equations of 14.7.4. shall be applied with np = 1.
14.7.6.2 Instability due to external pressure
Instability due to external pressure is not covered by the present rules.
14.7.7 Fatigue evaluation
14.7.7.1 Calculation of stresses due to the total equivalent axial displacement range ∆q of each convolution
The following formulae are used to determine the stresses due to the total equivalent axial displacement range of ∆q of each convolution.
a) The meridional membrane stress, ( )m,m qσ ∆ , is given by:
( ) ( )2*b p 1
m,m 334,3
E e Bq q
rσ ∆ = ∆ (14.7.7-1)
b) The meridional bending stress, ( )m,b qσ ∆ , is given by:
( )*
b p 2m,b 25,72
E e Bq q
rσ ∆ = ∆ (14.7.7-2)
14.7.7.2 Calculation of the total stress range due to cyclic displacement
The total stress range due to cyclic displacement, eqσ , is given by:
( ) ( ) ( )eq m,m m,m m,b3 P q qσ σ σ σ= + ∆ + ∆ (14.7.7-3)
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EN 13445-3:2002 (E) Issue 15 (2005-07)
14.9.2.2 Convolutions welds
14.9.2.2.1 Circumferential welds at root or crest of convolutions
This subclause deals with convolutions circumferentially welded at their crest and/or root as covered in 14.5.9.
Circumferential weld joints of convolutions shall be subjected to 100 % non-destructive examination in accordance with requirements of EN 13445-5:2002.
14.9.2.2.2 Longitudinal welds
This clause applies to bellows manufactured out of cylinders that are convoluted after longitudinal butt welding.
These longitudinal butt welds shall be subjected to:
100% visual examination before forming the convolutions of the bellows;
non-destructive examination in accordance with Table 14.9.2-1 after forming the convolutions of the bellows.
For bellows fabricated in series, at least 10 % of the bellows, but not less than one, shall be subjected to non-destructive examination. Samples shall be taken throughout the production run during manufacture.
Table 14.9.2-1 — Non-destructive examination for longitudinal butt welds of bellows without circumferential welds
Bellows forming method
Hydraulic, elastomer forming or similar method
Rolling DN
ep
mm
Single ply Multiply Single ply Multiply
= 1,5 — — PTa
outside PTa
tight ply = 300
> 1,5 PTa
outside — PTa
outside PTa
tight ply
= ep, max — — PTa
outside PTa
tight ply > 300
> ep, max PT
outside PTa
tight ply PT
outside PTa
tight ply
( ) ( )[ ]mm4;087,0minmax, ip De = PT=Penetrant Testing
a The test shall be performed on the longitudinal welds at the outside crest and the inside root of the convolutions, to the maximum extent possible considering physical accessibility.
14.9.2.3 Radiographic examination
When radiographic examination is performed, the requirements of EN 13445-5:2002, 6.6.3.2 apply, with the following modifications to EN 13445-5:2002, Table 6.6.4-1:
gas porosity and pores:
maximum pore diameter: p 4,0 e ;
maximum number of pores: 5 per 100 mm;
elongated cavity: not permitted;
inclusion: not permitted;
lack of fusion and lack of penetration: not permitted;
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EN 13445-3:2002 (E) Issue 31 (2008-06)
300
⎯ maximum undercut for short imperfections: 01, pe .·A smooth transition is required;
⎯ shrinkage groove for short imperfections: 01, pe .·A smooth transition is required.
14.9.3 Pressure test
Expansion bellows shall be tested in accordance with EN 13445-5:2002, 10.2.3.
However, the designer shall consider the possibility of instability of the bellows due to internal pressure if the test pressure exceeds:
( ) ( )t,s s,c s,i1,5 ;P Max P P⎡ ⎤= ⎣ ⎦ (14.9.3-1)
where Ps,c and Ps,i shall be calculated at room temperature.
In this case, the designer shall either:
a) specify special precautions to be taken during the test; or
b) redesign the bellows to satisfy the test condition.
NOTE For reinforced and toroidal bellows, use s,i 0P = in equation (14.9.3-1).
14.9.4 Leak test
When a leak test is performed, EN 13445-5:2002, Annex D applies.
14.10 Bellows subjected to axial, lateral or angular displacements 14.10.1 General
The purpose of this subclause is to determine the equivalent axial displacement of an expansion bellows subjected at its ends to:
— an axial displacement from the neutral position: x in extension (x > 0), or in compression (x < 0);
— a lateral deflection from the neutral position: y (y > 0);
— an angular rotation from the neutral position: θ (θ > 0).
14.10.2 Axial displacement
When the ends of the bellows are subjected to an axial displacement x (see Figure 14.10.2-1), the equivalent axial displacement per convolution is given by:
xN
q ⋅=Δ1
x (14.10.2-1)
Where x shall be taken: - positive for extension (x > 0)
- negative for compression (x < 0)
Values of x in extension and compression may be different.
The corresponding axial force Fx applied to the ends of the bellows is given by:
xKF ⋅= bx (14.10.2-2)
EN 13445-3:2002 (E)Issue 1 (2002-05)
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������������ �����������������������������������������������
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16.4 Local loads on nozzles in spherical shells
16.4.1 Purpose This clause provides a method for the design of a spherical shell with a nozzle subjected to local loads and internal pressure.
16.4.2 Additional specific symbols and abbreviations The following symbols and abbreviations are in addition to those in clause 4 and sub-clause 16.3: R is mean shell radius at the nozzle; d is mean nozzle diameter; di is inside nozzle diameter; de is outside nozzle diameter; d2 is outside diameter of a reinforcing plate; ec is analysis thickness of the combined shell and reinforcing plate; eeq is equivalent shell thickness; eb is nozzle thickness; fb is allowable design stress of nozzle material; FZ is axial nozzle force (positive when force is tensile or radially outwards); Fz,max is maximum allowable axial force on the nozzle; L is width of the reinforcing plate; MB is bending moment in the nozzle at the junction with the shell; MB,max is maximum allowable bending moment in the nozzle at the shell junction; scf scf scfP Z Mand , are stress factors due to pressure, nozzle axial load and moment respectively;
EN 13445-3:2002 (E) Issue 31 (2008-06)
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Figure 16.4-3 ― Stress factor in sphere for internal pressure (flush nozzle)
Figure 16.4-4 ― Stress factor in sphere for internal pressure (protruding nozzle)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.01 0.10 1.00 10.00
50/ .ee cb =
250/ .ee cb =
0.1/ =cb ee
0.0/ =cb ee
sλ
pscf
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.01 0.10 1.00 10.00
0.0/ =cb ee250/ .ee cb =
50/ .ee cb =
0.1/ =cb ee
sλ
pscf
EN 13445-3:2002 (E) Issue 31 (2008-06)
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Figure 16.4-5 ― Stress factor in sphere for moment loading (flush nozzle)
Figure 16.4-6― Stress factor in sphere for moment loading (protruding nozzle)
0.00
1.00
2.00
3.00
0.10 1.00 10.00
scf M
.00/ ee cb =
50/ .ee cb =
250/ ee cb =
1.0/ ee cb =
sλ
0.00
1.00
2.00
3.00
0.10 1.00 10.00
scf M
sλ
e b / e c = 0.0
e b / e c = 0.25
e b / e c = 1.0
e b / e c = 0.5
EN 13445-3:2002 (E) Issue 31 (2008-06)
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Figure 16.4-7 ― Stress factor in sphere for thrust loading (flush nozzle)
Figure 16.4-8 : Maximum stress in sphere for thrust loading (protruding nozzle)
Figure 16.4-8 ― Stress factor in sphere for thrust loading (protruding nozzle)
0.0
1.0
2.0
3.0
4.0
0.1 1.0 10.0
sλ
scf Z
e b / e c = 0.5
e b / e c = 0.0
e b / e c = 0.25
e b / e c = 1.0
0.0
1.0
2.0
3.0
4.0
0.1 1.0 10.0
sλ
scf Z
eb / ec = 0.5
eb / ec = 0.0
eb / ec = 0.25
eb / ec = 1.0
F
F
EN 13445-3:2002 (E)Issue 1 (2002-05)
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16.5 Local loads on nozzles in cylindrical shells
16.5.1 Purpose
This clause provides a method for the design of a cylindrical shell with a nozzle subjected to localloads and under internal pressure.
16.5.2 Additional specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in clause 4 and 16.3:
R is mean shell radius at the nozzle;
D is the mean shell diameter at the opening;
di is the inside nozzle diameter;
de is the outside nozzle diameter;
d is the mean nozzle diameter;
d2 is the external diameter of a reinforcing plate;
ec is the combined analysis thickness of the shell and reinforcing plate;
eeq is the equivalent shell thickness;
eb is the nozzle analysis thickness;
fb is the allowable stress of nozzle material;
FZ is the axial nozzle force (figure16.5-1);
FZ,max is the maximum allowable axial nozzle force;
L is the width of the reinforcing plate;
MX is the circumferential moment applied to the nozzle (figure 16.5-1);
MY is the longitudinal moment applied to the nozzle (figure 16.5-1);
MX,max is the maximum allowable circumferential moment applied to the nozzle;
MY,max is the maximum allowable longitudinal moment applied to the nozzle;
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a0 to a4 are the coefficients of the polynomials;
C1 to C4 are factors;
λC is a parameter applicable to nozzles in cylinders;
Φ is a load ratio;
σP is the stress range due to pressure;
σFZ is the stress range due to axial nozzle load;
σMX is the stress range due to circumferential moment;
σMy is the stress range due to longitudinal moment;
σT is the thermal stress due to temperature difference through the wall thickness;
16.5.3 Conditions of applicability
The following conditions apply:
a) 0.001 ≤ ea / D ≤ 0.1 ;
b) λCc
= ≤d
De10 ;
NOTE outside this range, effects of torsional moment are significant.
c) distances to any other local load in any direction shall be not less than ceD ⋅ ;
d) nozzle thickness shall be maintained over a distance of: bedl ⋅≥ .
16.5.4 Summary of design procedure
The design procedure is as follows:
1) calculate the basic dimensions ec and L from the following:
- at the nozzle outside diameter, when a reinforcing plate is fitted:
e e effc a= + ⋅
2
2 1min ;
- at the outside edge (d = d2) of a reinforcing plate, or when no reinforcing plate is fitted:
e ec a=
EN 13445-3:2002 (E) Issue 31 (2008-06)
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The width L of the reinforcing pad is given by:
( )L d d= −0 5. 2 e
2) calculate the maximum allowable individual loads (see 16.5.5);
3) check the load ratios and the interaction of the loads (see 16.5.6);
4) if no reinforcing plate or if a reinforcing plate is applied with )( 2a eeDL +≥ go to step 6;
5) calculate the maximum allowable individual loads at the edge of the reinforcing plate (d = d2 ; ec = ea and eb / ec ≥ 0.5 ) and check the load ratios and the interaction of the loads;
6) calculate the equivalent shell thickness eeq (see 16.5.7.2) and check the combined stress range (see 16.5.7);
7) check the nozzle strength (see 16.5.8);
8) if stresses or load ratios are excessive, increase the shell or nozzle thickness, or reduce the loads
and return to step 1. NOTE Step 6 has to be made only at the nozzle edge.
16.5.5 Maximum allowable individual loads 16.5.5.1 To determine the maximum allowable values of pressure, axial load and bending moment, which may be independently applied to a nozzle the following procedure shall be applied. 16.5.5.2 Determine λC thus:
λCc
=d
D e …(16.5-1)
16.5.5.3 Calculate permissible pressure Pmax from the general equation for reinforcement of isolated openings given in clause 9. It is reproduced from 9.5.2 for convenience and the notation is in 9.3.
( ) )(5,05,0.)(
Pbwsbs
oppobbswsmax AfAfAfAfApApAp
fAffAffAfAfP
++++++
⋅+⋅++=
ϕ
…(16.5-2)
16.5.5.4 Determine the allowable axial nozzle load FZ,max from the following:
12cmaxZ, CefF ⋅⋅= …(16.5-3)
in which C1 is either read from figure 16.5-2 or calculated from:
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ ⋅+⋅+⋅+⋅+⋅= 81,1;max 4
C43C3
2C2C101 λλλλ aaaaaC …(16.5-4)
and coefficients ao to a4 are given in table 16.5-1.
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16.5.5.5 Determine the allowable circumferential moment MX,max from:
22cmaxX, 4
CdefM ⋅⋅⋅= …(16.5-5)
in which C2 is either read from figure 16.5-3 or calculated from:
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ ⋅+⋅+⋅+⋅+= 90,4; max 4
C43C3
2C2C102 λλλλ aaaaaC …(16.5-6)
and coefficients ao to a4 are taken from table 16.5-2. 16.5.5.6 Determine the allowable longitudinal moment MY,max from
32cmaxY, 4
CdefM ⋅⋅⋅= …(16.5-7)
in which C3 is either read from figure 16.5-4 or calculated from:
⎥⎦⎤
⎢⎣⎡ ⎟
⎠⎞⎜
⎝⎛ ⋅+⋅+⋅+⋅+= 90,4; max 4
C43C3
2C2C103 λλλλ aaaaaC …(16.5-8)
and coefficients ao to a4 are given in table 16.5-3. If the thickness ratio eb/ec is situated between 0.2 and 0.5, the factor C3 is obtained by linear interpolation (fig. 16.5-4). NOTE The curves of figures 16.5-2 to 16.5-4 are derived from WRCB No. 297 - see [5] in Annex L, while the allowable loads are based on a maximum stress concentration factor of 2,25. 16.5.6 Combination of external loads and internal pressure 16.5.6.1 To determine the effects of the combination of pressure, axial load and bending moments, acting simultaneously the following procedure shall be applied: 16.5.6.2 Calculate the individual load ratios as follows:
ΦPmax
=P
P …(16.5-9)
ΦZZ
Z,max=
FF
…(16.5-10)
ΦBX
X,max
Y
Y,max=
⎛
⎝⎜⎜
⎞
⎠⎟⎟ +
⎛
⎝⎜⎜
⎞
⎠⎟⎟
MM
MM
2 2
…(16.5-11)
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16.5.6.3 Check that each individual load ratio is limited as follows:
ΦP ≤ 10, …(16.5-12)
ΦZ ≤ 10, …(16.5-13)
ΦB ≤ 10, …(16.5-14)
16.5.6.4 Check that the interaction of all the loads meets the following:
max PZ Z
PZ B| | ; | | ; | , | ,
ΦΦ Φ
ΦΦ Φ
C C4 4
220 2 10+ −
+ ≤ …(16.5-15)
Factor C4 shall equal 1,1 where nozzle connections are attached to a piping system designed withdue allowance for expansion, thrusts, etc. It shall equal 1,0 for ring reinforcements or rigidattachments. It shall not exceed 1,10.
NOTE In equation (16.5-15) a circular interaction with the bending moment load is accepted on the grounds ofa conservative estimate of the stress concentration factor in WRCB No. 297 (see ref [5] in Annex L).
16.5.7 Stress ranges and their combination
16.5.7.1 From the minimum and maximum values of the pressure and local loads, determine thefollowing load ranges:
( ) ( )∆P P P= −max ; min ;0 0 …(16.5-16)
( ) ( )∆F F FZ Z Zmax min= −; ;0 0 …(16.5-17)
( ) ( )∆M M MX X Xmax min= −; ;0 0 …(16.5-18)
( ) ( )∆M M MY Y Ymax min= −; ;0 0 …(16.5-19)
16.5.7.2 At the nozzle edge only, calculate the equivalent shell thickness eeq . This is equal to ec
unless a reinforcing ring of width )( 2a eeDL +< is used, in which case eeq is given by:
( )e e
e L
D e ee
ffeq a
2
a 22
2min min= ++
.; . ;1 …(16.5-20)
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16.10 Vertical vessels on bracket supports
16.10.1 General This clause gives rules for the design of vertical cylindrical or conical shells supported by brackets
16.10.2 Additional specific symbols and abbreviations (see Figure 16.10-1) The following symbols and abbreviation are in addition to those in clause 4 and 16.3
a1 is the distance from centre of load to shell or reinforcing plate; a1eq is the equivalent lever arm; b1 is the flange width of bracket; b2 is the width of reinforcing plate; b3 is the height of reinforcing plate; Deq is the equivalent calculation diameter (see 16.6.3); FVi is the vertical force acting in the leg at bracket i; FH is the horizontal force acting at the base of the legs; FHi is the horizontal force acting at the base of leg i; g is the distance between webs of bracket; h is the vertical distance from the centre of the bracket to the base of the leg (see Figure 16.10-1a); h1 is the height of bracket; h2 is the depth of bracket; MA is the global moment at the centre-point of the cross section at the base of the legs; n is the number of brackets;
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16.10.3 Conditions of applicability
The following conditions shall apply:
a) 0,001 � en / Deq � 0,05 (with Deq from 16.6.3);
b) For bracket supports type A, B and C (Figure 16.10-1)
0,2 � g / h1 � 1,0 ;
c) For bracket supports type D (Figure 16.10-1)
0,5 � b1 / h1 � 1,5 ;
d) If a reinforcing plate is applied:
e2 � en ;b3 � 1,5 h1 ;b2 � 0,6 b3 ;
e) The bracket is connected to a cylindrical or a conical shell;
f) The local bracket force Fi acts parallel to the shell axis.
NOTE 1 Application of more than 3 brackets requires special care during assembly toguarantee a nearly equal loading of all brackets
NOTE 2 Special considerations should be given to the stability of the vessel in the case where n = 2
16.10.4 Applied forces
The applied vertical force Fvi on the brackets is obtained from:
� �� �F
Fn
M
n D a e eiV
A
i a
� �� � �
4
2 1 2
(16.10-1)
The horizontal force at each leg:
FFniHH� (16.10-2)
NOTE A better estimation for FHi may be obtained using : F FI
Ii
i
H Hxxi
xxi
��
, where Ixxi is the
2nd area moment of the cross section of the considered leg for an axis normal to FH and Ixxii�
is the sum over all legs.
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16.10.5 Load limits of the shell
To obtain the load limit of the shell the following procedure shall be followed:
1) Determine the type of bracket : type A, B, C or D (see Figure 16.10-1); 2) If a reinforcing plate is applied then go to step 6; 3) Determine the parameters �, K16, �1 and �2 :
a) for brackets type A, B and C:
� � h D e1 / eq a (16.10-3)
K162
1
0 36 0 40 0 02�
� �, , ,� �
(16.10-4)
�1 = min {0,08 � ; 0,30} (16.10-5)
�2 = see equation (16.6-8) with �m = �my from equation (16.6-11)
b) for bracket type D:
� � b D e1 / eq a (16.10-6)
K162
1
0 36 0 86�
�, , �
(16.10-7)
�1 = min {0,08 � ; 0,30} (16.10-8)
�2 = see equation (16.6-8) with �m = �mx from equation (16.6-9) or equation (16.6-10)
4) With the appropriate values of �1 and �2 , calculate the allowable bending limit stress �b,all from equation (16.6-6);
5) Calculate the equivalent lever arm and the resulting maximum allowable bracket load :
a aF h
Fi
i1 1,eq
H
V� �
. (16.10-9)
� �Fe h
K ag hi,max
b,all a
1,eq�
�
�
�
�
�� �
� . .
..min ; , /
21
1611 0 5 (16.10-10)
Go to step 9
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6) Bracket with a reinforcing plate : determine the parameters λ, K17, υ1 and υ2
λ = b D e3 / eq a (16.10-11)
K17 =+ +
1
0 36 0 50 0 50 2, , ,λ λ (16.10-12)
υ1 = min {0,08 λ ; 0,40} (16.10-13) υ2 = see equation (16.6-8) with σm = σmy from equation (16.6-11)
7) With the appropriate values of υ1 and υ2 , calculate the allowable bending limit stress σb,all from
equation (16.6-6); 8) Calculate the equivalent lever arm and the maximum allowable bracket load
a a eF h
F1 1 2,eqHi
vi= + +
. (16.10-14)
Fe b
K ai,maxb,all a
1eq=⎛
⎝⎜⎜
⎞
⎠⎟⎟
σ . ..
23
17 (16.10-15)
The design procedure normally assumes the use of similar material in shell and reinforcing plate. Where this is not the case and provided that f2 < f , the thickness e2 shall be reduced by the ratio f2 / f in equation (16.10-12).
9) Check that
F FiV i,max≤ (16.10-16)
Legend 1 centre of the bracket NOTE centre of the bracket means the location of the horizontal neutral axis of bracket joint to shell or reinforcing plate.
Figure 16.10-1a — Explanation of h
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Fi is the force on the leg;
n is the number of legs;
� is the angle of tangent to the dished end at the leg junction;
x is the distance between the axis of the semi-ellipsoidal head and the centre of thesupporting leg;
� is the angle between leg axis and vertical axis;
� is a geometric parameter;
16.11.3 Conditions of applicability
The following conditions shall apply :
a) 0,001 � en / Deq � 0,05 (with Deq from 16.6.3);
b) if a reinforcing plate is applied:
e2 � en ;d3 � 1,6 d2 ;
c) External pressure is excluded;
d) Apropriate steps must be taken to ensure that movement of the legs does not produce additionalbending stresses in the shell;
e) On torispherical ends the supporting legs shall be located in the central spherical part;
f) On elliptical ends the supporting legs shall be located within 0 � x � 0.4 Di ;
g) Application of more than four legs is not recommended;
h) A global moment can be allowed only if the number of legs is > 2 and if the supporting legs are
fixed at the foundation. Furthermore the following requirement shall be met: FM
d�
4
4 ;
NOTE Application of four legs requires special care during assembly to guarantee a nearly equal loading of alllegs.
16.11.4 Applied force
The applied local force Fi on the legs is obtained from:
FFn
Mn di � �4
4 (16.11-1)
16.11.5 Load limits for the shell
To define the load limit of the shell and the maximum allowable force Fi,max and Pmax the followingprocedure shall be applied:
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1) Determine the parameter
λ =d
D eeff
eq a (16.11-2)
where deff = d2 for supporting legs without reinforcing plate; = d3 for supporting legs with reinforcing plate; Deq see 16.6.3
2) Calculate the maximum allowable force Fi,max
( ) ( )22amaxi, 91,06,382,1
coscos λλ
βαβ
++−
⋅⋅= efF (16.11-3)
3) Obtain the maximum allowable pressure Pmax
Pmax is to be defined for a spherical shell (see clause 7). When the end is elliptical, then the diameter of this spherical shell shall be taken as equal to twice Deq obtained from equation 16.6-4, where x = d4.
4) Check that
FF
i
i,max≤ 10, (16.11-4)
5) Check that
0,14/
maxmaxi,
2effi ≤+
⋅⋅−PP
FdPF π
(16.11-5)
Any support legs shall be checked for buckling. In this check the legs should be considered as:
a) hinged at the base plate, and
b) free to move laterally, but not free to rotate at the vessel.
The same results will be obtained for legs both sides hinged with a calculation length twice the actual length of the legs.
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16.13.6 Total equivalent force F The equivalent force F is equal to
Fn
Md
G= +⎛
⎝⎜
⎞
⎠⎟
1 47s
(16.13-1)
In case of uniform support of the ring F is equal to
F Md
G= +4
7 (16.13-2)
16.13.7 Allowable section values for rings For type I integral and loose ring supports the allowable stress of the ring is fT, while for type II integral ring supports the allowable reduced stress of the ring becomes equal to:
f f P h dA fT T
T T
* = −⎛
⎝⎜
⎞
⎠⎟1
21 (16.13-3)
NOTE Box section or U-section rings are considered type II, when the width b is larger then the height h (see Table 16.13-2)
The allowable section values in the ring are obtained by multiplying the allowable unit quantities from Table 16.13-2 with the allowable stress or the allowable reduced stress
M f m or f mt,max T t T t= * (16.13-4)
M f m or f mb,max T b T b= * (16.13-5)
t*TTTmax qforqfQ = (16.13-6)
16.13.8 Load-bearing capacity of ring The allowable force as a single load on the support is obtained as the minimum value of the allowable bending moment load and the allowable transverse force load:
FM
d Z ZMM
QS,maxb,max
b,max
T,max
max=
+⎛
⎝⎜⎜
⎞
⎠⎟⎟
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥
min ;4
2
4 02
12
2
π (16.13-7)
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If the support is uniform
FM
dS,maxb,max�
4
4
�
� � (16.13-8)
The values for Z0 and Z1 may be taken from the following Table. However those values lead toconservative results. A more accurately estimation of the allowable forces is obtained by using thevalues Z0 and Z1 from Figures 16.13-3 to 16.13-6
�������������� ���������ZO and Z1
nS Z0 Z1
23468
1,81,92,12,73,5
1,10,70,70,70,7
The lever arm ratios � and � are calculated by next equations, with diameters as shown in Figure 16.13-1
� � � � �0 2 0 27 5 4, / ,� d d d (16.13-9)
� � � � �0 2 0 26 5 4, / ,� d d d (16.13-10)
For externally fitted rings:
d d e t5 3 4 02� � � (16.13-11)
For internally fitted rings:
d d e t5 3 4 02� (16.13-12)
For closed cross sections t0 shall be taken from Table 16.13-2;For open ring cross section t0 = 0 ;
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Table A-2 — Pressure bearing welds - Circumferential welds in cylinders, cones and dished ends (continued)
Ref Type of joint Design requirements Applicable weld testing
group
Fatigue class 1)
Lamellar tearing
susceptibility 2)
Corrosion 3)
prEN 1708-1
C 26
see C 10 NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
see § 5.7.4.2 testing group 4
- A S -
C 27
NOT ALLOWED
C 28
see C 4 NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
see § 5.7.4.2
see Table 18.4 detail n° 1.6
A S -
C 29
see C 4 NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
see § 5.7.4.2 testing group 4
not allowed A S -
C 30
NOT ALLOWED
C 31
NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
4 - B N -
C 32
A = circumferential weld l e e> 2 1 2min ( , ) see C 35 L left side R right side Pressure applied on either side NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
4 - B S on L side N on R side
9.1.2
C 33
A = plug weld l e e> 2 1 2min ( , ) see C 35 L left side R right side Pressure applied on either side NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
4 - B S on L side N on R side
9.1.2
1), 2), 3) see Table A-1
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Table A-2 — Pressure bearing welds - Circumferential welds in cylinders, cones and dished ends (concluded)
Ref Type of joint Design requirements Applicable weld testing
group
Fatigue class 1)
Lamellar tearing
susceptibility 2)
Corrosion 3)
prEN 1708-1
C 34
l e e> 2 1 2min ( , ) see C 35 L left side R right side Pressure applied on either side NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
4 - B N -
C 35
l e e> 2 1 2min ( , )
if the weld is at the end of a shell, minimum distance between the weld and the end shall be 5 mm. L left side R right side Pressure applied on either side NOT ALLOWED FOR DBA-DR AND CREEP DESIGN
4 - B S on L side N on R side
9.1.1
C 36
NOT ALLOWED
C 37
NOT ALLOWED
C 38
NOT ALLOWED
1), 2), 3) see Table A-1
EN 13445-3:2002 (E) Issue 31 (2008-06)
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B.9.5.4.3 Action cycles without plastification
Action cycles, which interrupt long creep periods, are considered to be without plastification, if the maximum von Mises' equivalent stress of the response of the model, described below, to the cyclic actions and with initial conditions, described below, does not exceed the short-term design material strength parameter, described below:
a) The constitutive law of the model shall be linear-elastic with material parameters for a temperature given in B.7.5.2.
b) The initial stress distribution shall be the one obtained like in the determination of the limit action B.9.5.3.3.3 for a reference time, required for the determination of the material strength parameters in B.9.5.3.3.2 given by the total creep period.
c) The short-term design material strength parameter, with which the maximum equivalent stress is compared, shall be the minimum specified values of
⎯ cp0,2/TR for ferritic steels,
⎯ cp1,0/TR for austenitic steels,
where cT is the respective temperature at each point and each time.
B.9.5.4.4 Design checks
Design checks are required for normal operating load cases only
a) Partial safety factors for actions, combination rules, material strength parameters, reference temperature and reference time for creep periods, shall be as for the CR-DC, in B.9.4.3.
b) Partial safety factors Rγ shall be 1,0.
B.9.6 Creep and cyclic fatigue (CFI)
B.9.6.1 Principle
For each point of the structure, the sum of the design value of the creep damage indicator, see B.9.5.3, and the design value of the fatigue damage indicator (for cyclic actions), see B.8.5, shall not exceed unity.
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Annex C(normative)
Design by analysis � Method based on stress categories
C.1 Purpose
This annex gives rules concerning design by analysis using stress classification. It applies to pressurevessels in all testing groups.
The method described, known as "stress analysis", involves the interpretation of stresses calculatedon an elastic basis at any point in a part of a vessel, and then verification of their admissibility bymeans of appropriate assessment criteria.
It applies to pressure vessels in all testing groups.
It may be used:
— as an alternative to design-by-formula (see 5.4.1);
— as a complement to design-by-formula for:
— cases not covered by that route;
— cases involving superposition of environmental actions;
— exceptional cases where the manufacturing tolerances given in EN 13445-4:2002, clause 5 areexceeded.
In the last item, any deviation beyond tolerance limits shall be clearly documented.
— as an alternative to the design-by-analysis direct route, according to Annex B.
It may be used for a component or even a part of a component.
In all cases, all relevant requirements of this annex shall be fulfilled for that component or part.
The minimum thickness for pressure loading only, shall not be less than required by (7.4-1) or (7.4-2)for cylindrical shells, (7.4-4) or (7.4-5) for spherical shells, (7.5-1) for dished ends and (7.6-2) or (7.6-3)for conical shells.
Fatigue failure is not covered by this annex. When required, fatigue assessment shall be performedaccording to clause 18 or clause 17, as relevant.
Failure by elastic or elastic-plastic instability (buckling) is not covered by this annex. When the analysisreveals significant compression stresses, the risk for buckling shall be assessed separately.
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NOTE 9 Parameter Q0,min serves, in part, a similar purpose to ´y´ in ASME and other design codes (including
BS 5500 and CODAP) but differs as follows:a) Due to the different ways in which the effective gasket width is calculated in the ASME Code and in thismethod, the value of Q0,min is not the same as that of y.b) Q0,min also serves to define the lower limit of validity of empirical formulae where used to calculate gasket
properties.
NOTE 10 Qmax is used in the following way: Given a maximum possible area Agt and with an adjustment forplastic yield, based on maximum possible gasket width bGt and initial gasket thickness eG0 , the maximum
permitted gasket force FG is subject to the condition: � �F A Q b eG Gt max Gt G0� � � � �1 20/ ( ) (see
equations (G.7-4), (G.7-5)) (G.9-6)
G.9.3 Tables for gasket properties (Subclause essential edited)
All tabulated gasket properties are informative only. (See G.9.1). Application of other validated valuesis permitted.
NOTE 1 The theoretically possible absolute minimum mI = 0,5 is not applicable for practical purposes,
because some safety against failure is necessary.
NOTE 2 The mayority of tabulated mI values is intended to correspond to a nitrogen gas leak rate of about
1 ml/min (at standard ambient temperature and pressure) for a fluid pressureP = 40 bar, gasket outside diameter dG2 = 90 mm, and gasket inside diameter dG1 = 50 mm.
NOTE 3 There are only a few types of gaskets for which thermal expansion coefficients �G have been
measured, and that are not given in Tables G.9-1 to G.9-6.If no values �G are available, calculation with the assumption �G � �F or an other logical estimation of �G isacceptable, because normally the effect of �G is very small.
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Table G.9-1 ― Non-metallic flat gaskets (soft), also with metal insertion
t Q0,min Qmax E0 K1 mΙ gC Gasket type and material °C Mpa Mpa Mpa
0...20 0,5 28 200 10 0,9 0,9 100 18 200 10 0,9 0.9
Rubber 1)
150 12 200 10 0,9 0.9 0...20 10 50 600 20 1,3 0,9 100 35 500 20 1,3 0,7
PTFE
200 20 400 20 1,3 0,5 0…20 12 150 500 40 1,3 1,0 100 150 1 500 35 1,3 0,9
Expanded PTFE (ePTFE)
200 150 2 500 30 1,3 0,8 0...20 10 100 1 26 1,3 1,0 100 100 1 26 1,3 1,0 200 95 1 26 1,3 1,0
Expanded graphite without metal insertion
300 90 1 26 1,3 1,0 0...20 15 150 1 31 1,3 1,0 100 145 1 31 1,3 1,0 200 140 1 31 1,3 1,0
Expanded graphite with perforated metal insertion
300 130 1 31 1,3 1,0 0...20 10 100 1 28 1,3 0,9 100 90 1 28 1,3 0,9 200 80 1 28 1,3 0,9
Expanded graphite with adhesive flat metal insertion
300 70 1 28 1,3 0,9 0…20 15 270 1 33 1,3 1,0 100 250 1 33 1,3 1,0 200 230 1 33 1,3 1,0
Expanded grafite and metallic sheets laminated in thin layers withstanding high stresses 300 210 1 33 1,3 1,0
0...20 40 100 500 20 1,6 - 100 90 500 20 1,6 -
Non-asbestos fibre with binder, eG < 1mm
200 70 500 20 1,6 - 0...20 35 80 500 20 1,6 - 100 70 500 20 1,6 -
Non-asbestos fibre with binder, eG ≥ 1mm
200 60 500 20 1,6 - 1) Gasket thickness eG used in calculation shall be the thickness under load.
NOTE A dash indicates no values available.
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Table G.9-2 ― Grooved steel gaskets with soft layers on both sides
Gasket type t Q0,min Qmax E0 K1 mΙ gC
and material °C Mpa Mpa Mpa
0...20 10 350 16 000 0 1,3 0,9 100 330 16 000 0 1,3 0,8 200 290 16 000 0 1,3 0,7
PTFE layers on soft steel or soft iron
300 250 16 000 0 1,3 0,6 0...20 10 500 16 000 0 1,3 0,9 100 480 16 000 0 1,3 0,8 200 450 16 000 0 1,3 0,7
PFTE layers on stainless steel
300 420 16 000 0 1,3 0,6 0...20 15 350 16 000 0 1,3 1,0 100 330 16 000 0 1,3 1,0 200 290 16 000 0 1,3 1,0
Graphite layers on soft steel or soft iron
300 250 16 000 0 1,3 1,0 0...20 15 400 16 000 0 1,3 1,0 100 390 16 000 0 1,3 1,0 200 360 16 000 0 1,3 1,0 300 320 16 000 0 1,3 1,0 400 270 16 000 0 1,3 0,9
Graphite layers on low alloy heat resistant steel
500 220 16 000 0 1,3 0,8 0...20 15 500 16 000 0 1,3 1,0 100 480 16 000 0 1,3 1,0 200 450 16 000 0 1,3 1,0 300 420 16 000 0 1,3 1,0 400 390 16 000 0 1,3 0,9
Graphite layers on stainless steel
500 350 16 000 0 1,3 0,8 0...20 125 600 20 000 0 1,8 1,0 100 570 20 000 0 1,8 1,0 200 540 20 000 0 1,8 1,0 300 500 20 000 0 1,8 1,0 400 460 20 000 0 1,8 1,0 500 400 20 000 0 1,8 0,9
Silver layers on heat resistant stainless steel
600 250 20 000 0 1,8 0,8
NOTE The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0 may be used for the calculation in this Annex.
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Table G.9-3 ― Spiral wound gaskets with soft filler
t Q0,min Qmax E0 K1 mΙ gC Gasket type and material °C Mpa Mpa Mpa
0...20 20 110 6 000 0 1,6 0,9 100 100 6 000 0 1,6 0,8 200 90 6 000 0 1,6 0,7
PTFE filler, one side ring-supported
300 80 6 000 0 1,6 0,6 0...20 20 180 6 000 0 1,6 0,9 100 170 6 000 0 1,6 0,8 200 160 6 000 0 1,6 0,7
PFTE filler, both sides ring-supported
300 150 6 000 0 1,6 0,6 0...20 20 110 8 000 0 1,6 1,0 100 110 8 000 0 1,6 1,0 200 100 8 000 0 1,6 1,0 300 90 8 000 0 1,6 1,0
Graphite filler, one side ring-supported
400 80 8 000 0 1,6 0,9 0...20 50 300 10 000 0 1,6 1,0 100 280 10 000 0 1,6 1,0 200 250 10 000 0 1,6 1,0 300 220 10 000 0 1,6 1,0
Graphite filler, both sides ring-supported
400 180 10 000 0 1,6 0,9
NOTE 1 Modern philosophy is to use 2 rings: centering ring and outer ring. NOTE 2 The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0 may be used for the calculation in this Annex.
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Table G.9-4 ― Solid metal gaskets
Gasket type and t Q0,min Qmax E0 K1 mΙ gC material °C Mpa Mpa Mpa
0…20 50 100 70 000 0 2,0 1,0 100 85 65 000 0 2,0 0,9 200 60 60 000 0 2,0 0,8
Aluminium (Al) (soft)
300 20 50 000 0 2,0 0,7 0…20 100 210 115 000 0 2,0 1,0 100 190 110 000 0 2,0 1,0 200 155 105 000 0 2,0 1,0 300 110 95 000 0 2,0 0,9
Copper (Cu) or brass (soft)
(400) 50 85 000 0 2,0 0,7 0...20 175 380 210 000 0 2,0 1,0 100 340 205 000 0 2,0 1,0 200 280 195 000 0 2,0 1,0 300 220 185 000 0 2,0 1,0 400 160 175 000 0 2,0 0,9
Iron (Fe) (soft)
(500) 100 165 000 0 2,0 0,7 0...20 200 440 210 000 0 2,0 1,0 100 410 205 000 0 2,0 1,0 200 360 195 000 0 2,0 1,0 300 300 185 000 0 2,0 1,0 400 220 175 000 0 2,0 0,9
Steel (soft)
(500) 140 165 000 0 2,0 0,7 0...20 225 495 210 000 0 2,0 1,0 100 490 205 000 0 2,0 1,0 200 460 195 000 0 2,0 1,0 300 420 185 000 0 2,0 1,0 400 370 175 000 0 2,0 1,0
Steel, low alloy, heat resistant
500 310 165 000 0 2,0 0,9 0...20 250 550 200 000 0 2,0 1,0 100 525 195 000 0 2,0 1,0 200 495 188 000 0 2,0 1,0 300 460 180 000 0 2,0 1,0 400 425 170 000 0 2,0 0,9 500 370 160 000 0 2,0 0,8
Stainless steel
(600) 300 150 000 0 2,0 0,7 0...20 300 660 210 000 0 2,0 1,0 100 630 205 000 0 2,0 1,0 200 600 200 000 0 2,0 1,0 300 560 194 000 0 2,0 1,0 400 510 188 000 0 2,0 1,0 500 445 180 000 0 2,0 0,9
Stainless steel, heat resistant
600 360 170 000 0 2,0 0,8
NOTE 1 The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0 may be used for the calculation in this Annex.
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Table G.9-5 ― Covered metal-jacketed gaskets
t Q0,min Qmax E0 K1 mΙ gC Gasket type and material °C Mpa Mpa Mpa
0...20 10 150 1 69 1,3 1,0 100 150 1 69 1,3 0,9 200 150 1 69 1,3 0,8
Stainless steel jacket with expanded PTFE filler and covering
(300) 150 1 69 1,3 0,7 0...20 10 150 1 69 1,3 1,0 100 150 1 69 1,3 0,9 200 150 1 69 1,3 0,8
Nickel alloy jacket with expanded PTFE filler and covering
(300) 150 1 69 1,3 0,7 0...20 20 300 1 48 1,3 1,0 100 300 1 48 1,3 1,0 200 300 1 48 1,3 1,0 300 300 1 48 1,3 1,0 400 300 1 48 1,3 1,0
Soft iron or soft steel jacket with graphite filler and covering
(500) 300 1 48 1,3 1,0 0...20 20 300 1 48 1,3 1,0 100 300 1 48 1,3 1,0 200 300 1 48 1,3 1,0 300 300 1 48 1,3 1,0 400 300 1 48 1,3 1,0
Low alloy steel (4 % to 6 % chrome) or stainless steel jacket with graphite filler and covering
500 300 1 48 1,3 1,0
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Table G.9-6 ― Metal-jacketed gaskets
t Q0,min Qmax E0 K1 mΙ gC Gasket type and material °C MPa MPa MPa
0...20 50 135 500 25 1,6 1,0 100 120 800 25 1,6 1,0 200 90 1 100 25 1,6 1,0
Aluminium (soft) jacket with graphite filler
(300) 60 1 400 25 1,6 1,0 0...20 60 150 600 25 1,8 1,0 100 140 900 25 1,8 1,0 200 130 1 200 25 1,8 1,0 300 120 1 500 25 1,8 1,0
Copper or brass (soft) jacket with graphite filler
(400) 100 1 800 25 1,8 1,0 0...20 80 180 800 25 2,0 1,0 100 170 1 100 25 2,0 1,0 200 160 1 400 25 2,0 1,0 300 150 1 700 25 2,0 1,0 400 140 2 000 25 2,0 1,0
Soft iron or soft steel jacket with graphite filler
(500) 120 2 300 25 2,0 1,0 0...20 100 250 800 25 2,2 1,0 100 240 1 100 25 2,2 1,0 200 220 1 400 25 2,2 1,0 300 200 1 700 25 2,2 1,0 400 180 2 000 25 2,2 1,0
Low alloy steel (4 % to 6 % chrome) or stainless steel jacket with graphite filler
500 140 2 300 25 2,2 1,0
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G.10 Bibliography
[1] prEN 1591-1, Flanges and their joints. Design rules for gasketed circular flange connections.Part 1: Calculation method.
[2] CR 13642, Flanges and their joints. Design rules for gasketed circular flange connections.Background information (to prEN 1591).
[3] Wesstrom, D.B.; Bergh, S.E., "Effect of Internal Pressure on Stresses and Strains in Bolted-Flanged Connections"; Transactions of the ASME, July 1951, pp.553-568
[4] Richtlinienkatalog Festigkeitsberechnungen (RKF), Behälter und Apparate; Teil 1, BR-A13,"Behälter- und Apparateelemente. Flanschverbindungen"; Institut für Chemieanlagen,Dresden 1971; VEB Komplette Chemieanlagen Dresden, 1979;
[5] DIN 2505, "Berechnung von Flanschverbindungen"; Entwurf November 1972;Entwurf April 1990.
[6] TGL 20360, "Flanschverbindungen. Berechnung auf Festigkeit und Dichtigkeit";Februar 1977
[7] TGL 32903/13, "Behälter und Apparate. Festigkeitsberechnung. Flanschverbindungen";Dezember 1983.
[8] Wölfel, J.; Räbisch, W., "Berechnung und Standardisierung von Flanschverbindungen";Chemische Technik, Leipzig, 1975, S.470-478.
[9] Wölfel, J., "Berechnung der Dichtigkeit und Festigkeit von Flanschverbindungen";Maschinenbautechnik, Berlin, 1985, S.244-247.
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hp = [(dGe – dE)2 · (2 · dGe + dE)/6 + 2 · eP2 · dF]/dGe
2 (GA.5-70)
For blind flanges:
eP = 0 (GA.5-71)
GA.5.4.1 Integral flange and blind flange (see Figures GA.3-4 to GA.3-9)
Lever arms (equal for all load cases (all Ι)):
hG = (d3e – dGe)/2 (GA.5-72)
hH = (d3e – dE)/2 (GA.5-73)
hL = 0 (GA.5-74)
GA.5.4.2 Loose flange with stub or collar (see Figure GA.3-10)
GA.5.4.2.1 Load transfer diameter d7
d7,min ≤ d7 ≤ d7,max (GA.5-75)
d7min = d6 + 2 · b0 (GA.5-76)
d7,max = d8 (GA.5-77)
Assemblage:
d7(0) = min{ max[d7,min; (dGe + κ · d3e)/(1 + κ) ]; d7,max} (GA.5-78)
κ = (ZL · EF(0))/(ZF · EL(0)) (GA.5-79)
Subsequent load cases:
d7(Ι) = d7,min + 2 · x(Ι)· hV (GA.5-80)
hV = (d7,max – d7,min)/2 (GA.5-81)
The variable x(Ι) (0 ≤ x(Ι) ≤ 1) shall be determined in GA.7.
GA.5.4.2.2 Lever arms
hG(Ι) = (d7(Ι) – dGe)/2 = hG(x=0) + x(Ι) · hV (G.5-82)
hH(Ι) = (d7(Ι) – dE)/2 = hH(x=0) + x(Ι) · hV (G.5-83)
hL(Ι) = (d3e(Ι) – d7)/2 = hL(x=0) – x(Ι) · hV (G.5-84)
GA.6 Forces
GA.6.0 General
The following calculations are to be made for assemblage and for all subsequent load conditions. All potentially critical load conditions shall be calculated. For selection and numbering of these conditions GA.4.3.3 gives some information.
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GA.6.1 Loads
GA.6.1.1 Fluid pressure P(Ι)
Internal pressure is defined by P(Ι) > 0, external pressure by P(Ι) < 0. Axial fluid pressure force:
FQ(Ι) = P(Ι) · AQ (GA.6-1)
GA.6.1.2 External loads
There exists maximum 6 components of additional external loads: FX(Ι), FY(Ι), FZ(Ι); MX(Ι), MY(Ι), MZ(Ι). Axial tensile force is defined by FA(Ι) = FZ(Ι) > 0, axial compressive force by FA(Ι) < 0. (Definitions correspond to those of P(Ι).) The signs of the other external loads here are not important.
Shearing forces and bending moments are related to the mid-plane of the gasket. Only their resultants FS(Ι) and MB(Ι) are of interest:
FS(Ι) = { FX(Ι)2 + FY(Ι)
2 }1/2 (GA.6-2)
MB(Ι) = {MX(Ι)2 + MY(Ι)
2}1/2 (GA.6-3)
The axial force FA(Ι) = FZ(Ι) and the bending moment MB(Ι) are combined to an equivalent resulting net force FR(Ι) as follows:
FR(Ι) = FA(Ι) ± MB(Ι) · 4/d3e (GA.6-4)
When an external bending moment occurs, the most severe case may be difficult to predict. On the side of the joint where the moment induces an additional tensile load (sign + in Equation (GA.6-4)) the load limits of the flange or bolts may govern, or minimum gasket compression. On the side where the moment induces a compressive load (sign – in Equation (GA.6-4)) the load limit of the gasket may govern. Therefore two load conditions (one for each sign in Equation (GA.6-4), using different indices Ι for each case) shall be systematically checked whenever an external bending moment is applied.
GA.6.1.3 Thermal loads
Different thermal expansions produce the following differences of axial displacement:
ΔUT(Ι) = IB · αB(Ι) · (tB(Ι) – t0) – eG(A) · αG(Ι) · (tG(Ι) – t0) + ..
- eFt(1) · αF(1,Ι) · (tF(1,Ι) – t0) – eL(1) · αL(1,Ι) · (tL(1,Ι) – t0) – eW(1) · αW(1,Ι) · (tW(1,Ι) – t0) + ..
- eFt(2) · αF(2,Ι) · (tF(2,Ι) – t0) – eL(2) · αL(2,Ι) · (tL(2,Ι) – t0) – eW(2) · αW(2,Ι) · (tW(2,Ι) – t0) + .. (GA.6-5)
In this equation necessary shall be (calculate lB correspondingly):
IB = eG(A) + eFt(1) + eFt(2) + eL(1) + eL(2) + eW(1) + eW(2) (GA.6-6)
GA.6.1.4 Assembly condition (Ι=0)
Fluid pressure (internal or external) is zero; therefore P(0) = 0.
External loads FS(0) (shearing force) and MZ(0) (torsional moment) shall be zero. A resulting axial force FR(0) may exist. (General caution is necessary if bending is not very small!).
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Table GA.9.3 — Spiral wound gaskets with soft filler
Gasket Mechanical parameters (depending on temperature) Type and material (limit cG) Temp αG μG C0 C1 K0 K1 QR
Tightness parameters (presented without influence of temperature) °C 10-6
∗ K-1 - MPa - MPa - MPa
PTFE filler, one side ring supported -100 14,5 0,10 170 20 500 25 120
(cG = 1) 0 .. 40 15,0 0,10 160 20 400 25 120
QA0 = 10 MPa 100 15,5 0,10 150 20 300 25 120
QA1 = 10; M1 = 6; N1 = 2; (TP)1mx = 1 200 16,0 0,12 140 20 200 25 110
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 16,5 0,14 130 20 100 25 100 PTFE filler, both sides ring supported -100 14,5 0,10 250 25 600 30 250
(cG = 1) 0 .. 40 15,0 0,10 250 25 500 30 250
QA0 = 10 MPa 100 15,5 0,10 240 25 400 30 250
QA1 = 10; M1 = 6; N1 = 2; (TP)1mx = 108 200 16,0 0,12 220 25 300 30 240
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 16,5 0,14 180 25 200 30 200 Graphite filler, one side ring supported -100 14,5 0,10 190 25 620 40 150
(cG = 1) 0 .. 40 15,0 0,10 180 25 600 40 150
QA0 = 10 MPa 100 15,5 0,10 180 25 580 40 150
QA1 = 10; M1 = 4; N1 = 2; (TP)1mx = 107 200 16,0 0,12 170 25 560 40 140
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 16,5 0,14 160 25 540 40 130
400 17,0 0,16 150 25 520 40 120
500 17,5 0,18 130 25 500 40 100 Graphite filler, both sides ring supported -100 14,5 0,10 290 30 820 60 300
(cG = 1) 0 .. 40 15,0 0,10 280 30 800 60 300
QA0 = 10 MPa 100 15,5 0,10 270 30 780 60 280
QA1 = 10; M1 = 4; N1 = 2; (TP)1mx = 107 200 16,0 0,12 250 30 760 60 260
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 16,5 0,14 230 30 740 60 240
400 17,0 0,16 210 30 720 60 220
500 17,5 0,18 190 30 700 60 200
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Table GA.9.4 — Solid metal gaskets
Gasket Mechanical parameters (depending on temperature) Type and material (limit cG) Temp αG μG C0 C1 K0 K
1
QR
Tightness parameters (presented without influence of temperature) °C 10-6
∗ K-1 - MPa - MPa - MPa
Aluminium (Al), soft -100 22,4 0,12 65 000 -480 75 000 0 100
(cG > 1) 0 .. 40 23,0 0,14 60 000 -480 70 000 0 100
QA0 = 30 MPa 100 23,8 0,16 55 000 -520 65 000 0 90
QA1 = 30; M1 = 8; N1 = 2; (TP)1mx = 1 200 24,6 0,18 50 000 -760 60 000 0 60
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 25,2 0,20 40 000 -920 50 000 0 40
(400) (26) 0,22 20 000 -….. 30 000 0 20 Copper (Cu), soft, Brass (soft) -100 17,0 0,12 110 000 -380 120 000 0 210
(cG > 1) 0 .. 40 17,6 0,14 105 000 -380 115 000 0 210
QA0 = 60 MPa 100 18,4 0,16 100 000 -460 110 000 0 180
QA1 = 60; M1 = 8; N1 = 2; (TP)1mx = 1 200 19,2 0,18 95 000 -540 105 000 0 150
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 300 20,0 0,20 85 000 -620 95 000 0 120
400 (21) 0,22 75 000 -760 85 000 0 90 Iron (Fe), soft 0 .. 40 (12,) 0,10 200 000 -420 210 000 0 380
(cG > 1) 100 0,12 195 000 -480 205 000 0 340
QA0 = 80 MPa 200 0,14 185 000 -560 195 000 0 280
QA1 = 80; M1 = 8; N1 = 2; (TP)1mx = 1 300 0,16 175 000 -640 185 000 0 240
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 400 (12,) 0,18 165 000 -760 175 000 0 200 Steel, soft 0 .. 40 10,6 0,10 200 000 -340 210 000 0 440
(cG > 1) 100 11,2 0,12 200 000 -380 205 000 0 410
QA0 = 100 MPa 200 12,0 0,14 190 000 -420 195 000 0 360
QA1 = 100; M1 = 8; N1 = 2; (TP)1mx = 1 300 12,8 0,16 180 000 -500 185 000 0 300
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 400 13,6 0,18 170 000 -660 175 000 0 230
(500) 14,4 0,20 160 000 -880 165 000 0 170 Steel, low alloy, heat resistant 0 .. 40 10,8 0,10 200 000 -280 210 000 0 500
(cG > 1) 100 11,4 0,12 195 000 -280 205 000 0 490
QA0 = 120 MPa 200 12,2 0,14 185 000 -300 195 000 0 460
QA1 = 120; M1 = 8; N1 = 2; (TP)1mx = 1 300 12,8 0,16 175 000 -320 185 000 0 420
QA2 = ; M2 = ; N2 = ; (TP)2mx = - 400 13,4 0,18 165 000 -340 175 000 0 370
500 14,0 0,20 155 000 -400 165 000 0 310
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DJ is the inside diameter of the expansion bellows [mm]; see sublause 13.5;
dC, dS are the inside diameters of the channel (C), of the shell (S), [mm];
d0, d0,e is the tubehole diameter [mm], d0 is the real value, d0,e is the effective value;
d1 is the outside diameter of the tubed region to be used in the calculation [mm], see J.5.1;
d1(av) is the average of ( )min1d and ( )max1d , [mm], see J.5.1.1.4;
d1(max) is the maximum value of 1d , [mm], see J.5.1.1.2;
d1(min) is the minimum value of 1d , [mm], see J.5.1.1.3;
d2 is the true outside diameter [mm] over which PS and PT act;
d3, d3,e is the bolt pitch circle diameter [mm]; d3 for the real value, d3,e for the effective value;
dGC, dGS are the effective gasket diameters [mm] for channel side (C), shell side (S);
dK is the diameter for compensation of axial forces [mm]; for floating heads this is the diameter of the sliding face at a packed gland or an O-ring seal; for expansion bellows this is the mean inside diameter of the bellows: dK = DJ + hJ ;
dT is the tube outside diameter [mm];
EP, ET are the elastic moduli of the tubesheet (P = plate), of the tubes (T), [MPa];
EC, ES are the elastic moduli of the channel (C), of the shell (S), [MPa];
E* is the effective elastic modulus of the tubesheet [MPa], see Figures 13.7.6-1, 13.7.6-2;
eC is the analysis thicknesses of the channel adjacent to the tubesheet [mm];
eF is the average thickness of a flange like part of the tubesheet [mm], see Figures J-10 to J-13;
eP is the analysis thickness of the tubesheet (plate) [mm] in the tubed region and the untubed rim;
eP,red is a possibly reduced thickness of the tubesheet (plate) at its outer periphery [mm]; eP,red ≤ eP ;
eS is the analysis thicknesses of the shell adjacent to the tubesheet [mm];
eS,av is the average thicknesses of the shell over the total length LT [mm];
eT is the tube thickness [mm];
eU is the analysis thickness of the tubesheet in its greatest untubed region [mm]; normally eU = eP ;
FB is the total force applied by the bolts (total force for one flange connection) [N], see Annex G;
FG,C, FG,S are the total gasket reaction forces [N], channel side (C), shell side (S);
[Ft], [Fc] are the allowable total axial forces in the shell [N], [Ft] for tension, [Fc] for compression, see J.7.5;
FR is the total axial force acting on tubebundle and shell [N], see J.7.5;
FW is the total weight acting as a force on a tubesheet [N], see J.9.4;
fC is the nominal design stress for the channel adjacent to the tubesheet [MPa];
fF is the nominal design stress for the flange like part of tubesheet (plate) [MPa]; normally fF = fP ;
fP is the nominal design stress for the tubesheet (plate) [MPa];
fS is the nominal design stress for the shell adjacent to the tubesheet [MPa];
fT is the nominal design stress for the tubes [MPa];
fT,t is the allowable longitudinal stress for the tubes in tension [MPa]; see J.7.3;
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fT,c is the allowable longitudinal stress for tubes in compression [MPa]; see J.7.3;
fX is the calculated design stress for the tube-to-tubesheet connection [MPa]; see J.7.3;fX,E and fX,W are special values of fX ;
H1, H2, H3 are factors (compliances) used in the fatigue design [1], see Figure J-15;
hJ is the inside height of the expansion bellows [mm]; see sublause 13.5;
Ke1, Ke2, Ke3 are effective stress-strain concentration factors [1] used in the fatigue design, see J.10;
L1 , L2 , L3 are loading parameters [1], used in the calculation of a load ratio, see J.9.1;
LT is the true total length of the tubes [mm]; in Figure J-9 shown between outer faces oftubesheets;
lA is the length of tubes [mm] between the first tubesheet and the first supporting baffle,see Figure J-9;
lB is the length of tubes [mm] between two adjacent supporting baffles, see Figure J-9. If alongone tube more than one lB exist, all lB are presupposed to be equal;
lC is the length of tubes [mm] between the last supporting baffle and the second tubesheet,see Figure J-9;
lR is a characterisitc length of the tubebundle [mm], used for fatigue design, see J.10.3;
lT,K is the buckling length of tubes [mm], see J.7.1;
lX is the length of the strength attachement between tube and tubesheet [mm], see J.5.2.1;
M1 is the resultant bending moment [Nmm/mm] at the diameter d1 ;
M2 is the resultant bending moment [Nmm/mm] at the diameter d2 ;
MA is the active bolt load bending moment [Nmm/mm] at the diameter d2 , see J.8.1;
MB is the active fluid pressure bending moment [Nmm/mm] at the diameter d2 , see J.8.2;
MC is the reactive bending moment [Nmm/mm] from connected components, see J.8.3;
MD is the reactive bending moment [Nmm/mm] limitation at the diameter d2 , see J 8.4;
NB is the number of baffles [1]; NB,t is the true total number, NB,e is the effective number;
NC is the number of load cycles [1];.
NI Number of ideal possible, not real existing tubes (general) [1]; see J.5.1;
NI,min minimum possible value of NI = number of extra tubes which, positioned on same tubepitch, would occupy the area taken up by the pass-partitions and the tiee-rods; see J.5.1;
NI,max maximum possible value of NI = number of extra tubes which, positioned on same tubepitch, would fill the total untubed area within the outer tube limit; see J.5.1;
NT is the number of real existing tubes [1]; in a U-tube type the number of tubeholes [1];
nB is the number of bolts [1] in a flange connection;
PA, PI are the resultants of active and reactive axial forces per area unit in the tubebundle in thetubed region [N/mm2 = MPa] ; PA in the outer zone, PI in the inner zone; see J.7.6;
PD is the direct difference between tube side and shell side fluid pressure [MPa], see J.6.2, J.7.2;
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- The parameters met the following conditions:
The width of the untubed rim should be not too large:
λR,max ≤ 0,30 (J.4.1-1)
The geometry should be approximately axisymmetric:
λR,min/λR,max ≥ 0,20 (J.4.1-2)
The tubed region may be calculated as a homogeneous weakened plate:
NT ≥ 20 (J.4.1-3)
For vertical tubebundles its weight may be covered by the tube bending:
{ }2TTT 100030 LfN ⋅⋅≤ (J.4.1-4)
The tubesheet thickness should be not too small and not too large:
0,005 ≤ eP/d1 ≤ 0,50 (J.4.1-5)
With some caution the method may be used also outside of the given conditions.
J.4.1.2 Loads
The method applies to the following loads:
- Fluid pressures tube side (PT) and shell side (PS), both arbitrary internal or external;
- Boundary moments at the outside boundary of tubesheets;
- Weight of the vertical tubebundle;
- Axial thermal expansion (to be calculated only for tubebundles with fixed tubesheets without expansion bellows).
J.4.2 Mechanical model
The method is based on the following mechanical model:
- The main component of a tubesheet heat exchanger is always one tubebundle, in general located within a vessel. The vessel around of and connected to the tubebundle in general may be subdivided into one shell and two channels at the ends of the shell (possibly only one channel and one head), including vessel flanges, nozzles and support elements also. The given method calculates the strength of the tubebundle as complete as necessary. If required are taken into account some properties of the vessel, which includes their check also. But there are not given all necessary proofs for the whole vessel.
- The tubebundle in general consists of two tubesheets (possibly only one), a large number of (inner) tubes and (normally) some baffles. The given method calculates the strength of the tubesheets and the tubes, including their joints.
- The baffles are treated to be supports against buckling of the inner tubes. There should be taken into account, that in general not all tubes are supported by all baffles. The distances between the baffles and to the tubesheets need not to be equal. The thickness of the baffles may be small; their strength in general is not critical and is not calculated in the given method.
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- The calculation model for the tubed region of the tubesheet is a weakened quasi-homogeneous flatplate, supported by reaction forces (or reaction moments) per plate area unit from the tubes.Therefore, if the number of tubes is too small, the results becomes inaccurate. The tube reactionspossibly may be equal zero or negative also.
For the first untubed rim around the tubed region (average width bR, loaded by both fluid pressures)the model is the same plate, but not weakened and not supported.
Outside the first untubed rim in general is a second untubed rim (true width bS , loaded by one fluidpressure only), which is treated as a part of a "flange" ring (true width bF, average thickness eF ).
These rings are calculated as flange rings, to get (as possible) correct boundary moments. But thewidth of the rings should not be too large and they should be at least approximately axisymmetric.
- The additional effect of weight for vertical tubebundles is calculated taking account for bending oftubes, which normally for these kind of loading is sufficient to cover the whole effect. Only for very longtubebundles and/or low strength of the tubes these assumption is not met.
- The required flange bolt loads and gasket forces are to be taken from a separate calculation, e.g. fromAnnex G or from clause 11. (Some special effects for flanged tubebundles in these methods are notrespected; therefore some inaccuracies remain.)
- All strength calculations (except fatigue assessment subclause J.10) are based on the limit loadanalysis (therefore progressive), using the static method (therefore either exact or conservative).
- All calculation models (except proofs for limit load of untubed regions, subclause J.9.3) areaxisymmetric.
J.4.3 Calculation method
J.4.3.1 Required checks
All tubesheets shall be checked against bending within the tubed region and at its boundary; see J.9.1.
All tubesheets shall be checked against shear at the boundary of the tubed region; see J.9.2.
Thin tubesheets also shall be checked against the local loading on untubed regions; see J.9.3.
Thin tubesheets in vertical tubebundles additional shall be checked for the effect of weight; see J.9.4.
Fixed tubesheet heat exchangers without expansion bellows also shall be checked for cyclic loading byJ.10 Fatigue asessment.
Fixed tubesheet heat exchangers with expansion bellows are not to be checked by J.10, but theirexpansion bellows requires checks by clause 14.
All required flange bolt loads and gasket diameters are to be determined from an adequate calculation fortubesheet-flange-connections. As long such special calculation method is not available, the required datashall be determined either based on clause 11 or based on annex G.
For the gasket diameters dGC and dGS the following is valid:
Clause 11: dGC and dGS shall be taken as the value of G on the channel and shell gaskets respectively.
Annex G: dGC and dGS shall be taken as the value of dGe on the channel and shell gaskets respectively.
EN 13445-3:2002 (E)Issue 1 (2002-05)
649
J.4.3.2 Load cases to be calculated
J.4.3.2.1 Load limit calculations (J.5 to J.9) shall be provided
- for all types of tubebundles
- using all real possible combinations of design pressures and additional design loads.
NOTE 1 A restriction to one calculation for the absolute maximum �PT - PS� in general is not sufficient.
NOTE 2 Observe the real possible design loads (not normal acting operating loads) are to be used.
J.4.3.2.2 Fatigue asessment (J.10) shall be provided
- for fixed tubesheets without expansion bellows only
- using all normal simultaneously acting operating pressures, additional loads and temperatures .
NOTE 3 In many cases it is sufficient to calculate for the worst load change only, which is given by the highestvalue ��PF� from eqation (J.10.2-2). But in other cases with different comparable load changes, especially ifslightely higher load values are connected with only slightely lower numbers of load cycles, it may be necessaryto calculate several times and to check the acceptance by subclause 17.7.
NOTE 4 Observe the normal acting operating loads (not real possible design loads) are to be used.
J.4.3.3 Working with the method
J.4.3.3.1 Basic rules
The calculation shall be made in the corroded condition. Several iterations may be required.
Where the two tubesheets in a tubebundle differ in dimension, material or edge support condition,separate calculations shall be made for each tubesheet.
The calculation starts with J.5.1. At least in J.5.2 a value shall be assumed for the tubesheet thicknesseP. Then - depending on the heat exchanger type - either subclause J.6 or subclause J.7 is to be used.Clauses J.8 and J.9 always are to be applied.
NOTE Many calculations within J.5 to J.7 are independent of eP ; however it is to be observed, that lX and eF may tobe changed if eP is changed; also fP and FB may depend on eP. Therefore, to be safe, it is recommended after eachchange of eP to repeat the calculations starting from J.5.2.
J.4.3.3.2 Main conclusions
If the calculated total load ratio �P,t is less than 1,0, the result is acceptable; but the real requiredtubesheet thickness may be less than the assumed and the calculation should be repeated using asmaller eP.
If the calculated total load ratio �P,t is greater than 1,0, the result is not acceptable, the assumedtubesheet thickness eP must be increased and the calculation is to be repeated.
J.4.3.3.3 Additional rules
If for tubebundles with fixed tubesheets without expansion bellows the fatigue criteria are govern, thedesign shall be based on subclause J.10 Fatigue asessment. In these cases not only a greater tubesheetthickness may lead to acceptable results, e.g. a less stiff design in some cases also may be a sufficientbetter design.
EN 13445-3:2002 (E) Issue 31 (2008-06)
J.5 Parameters for all types
J.5.1 Diameters and widths
J.5.1.1 Outside diameter d1 of tubed region
J.5.1.1.1 General
The procedure for calculating 1d is given below.
NOTE Upper and lower limits for 1d can be established by considering the space within the tubed area which is available
for additional tubes. 1d is calculated from the limits.
J.5.1.1.2 Maximum diameter ( )max1d
Determine ( )max1d as follows:
( ) To drd += 2max1 (J.5.1-1)
NOTE If an isolated tube or small group of tubes lies outside the main tubed region (by a distance of more than one pitch) it should be ignored when determining or and NT.
J.5.1.1.3 Minimum diameter ( )min1d
J.5.1.1.3.1 Defining trapezoidal areas
Draw the tangent lines to the outside tubes to enclose the tubed region within a polygon. The positions of the tie rods shall be ignored.
NOTE 1 An example is shown in Figures J-7(a) and J-7(b).
NOTE 2 For simplicity, where two tangent lines have nearly equal slopes, they can be replaced by a single tangent line if this line lies outside the centres of any tubes it crosses (i.e. it cuts less than half tube sections). (See area of height 7b in Figure J-7(b).)
Divide the tubed region into (perforated or un-perforated) trapezoidal areas by drawing straight lines parallel to the tube rows.
Where the intersection of the tangent lines which form the polygon lies closer to the tube centreline, the construction line shall be through the tube centres (see Figure J-7(b)). Where the intersection of the tangent lines which form the polygon lies closer to the tangent line than to the tube centreline, the construction line shall be the tangent to the tube row (see Figure J-7(b)). This also applies when the intersection is mid-way between the tube centre line and the tube tangent line. Extend the construction lines to the enclosing polygon to form trapezoidal areas. Denote the heights of the trapezoidal areas by jb (j = 1,2, ..,) and widths by jc (j = 0, 1, 2, .,).
J.5.1.1.3.2 Determination of ( )minRA
Determine ( )minRA by one of the following three methods.
(a) Tube counting
Determine the total number of potential extra tubes ( )minIN as follows.
Calculate the tube pitches bp and cp as follows:
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EN 13445-3:2002 (E) Issue 31 (2008-06)
On triangular pitch:
ppb 0,866= (J.5.1-2)
and
ppc = (J.5.1-3)
On square pitch:
ppb = (J.5.1-4)
and
ppc = (J.5.1-5)
For each tube row, count all unfilled positions within the row. For unfilled positions at the ends of the row, multiples of half a tube may be added when the tangent line lies inside the centre of the potential extra tube. This gives
( )rIN for each row.
NOTE An example of this is shown in Figure J-7(c).
For a pass partition zone where the distance between the adjacent tube rows equals an integral number of tube pitches, count all the potential extra tube positions to obtain )(kIN for that zone.
NOTE Area of height 3b in Figure J-7(b) is one where the distance between the adjacent tube rows equals an integral number of tube pitches.
For a pass partition zone or other untubed area, with arbitrary distances to the adjacent tube rows, calculate )(kIN for that zone as follows:
( )[ ]( )
cb
pkpkbpkkI pp
ccpbN
⋅
++= −
2,,1, (J.5.1-6)
In Equation J.5.1-6, pk,b is the distance between the centrelines of adjacent tube rows and bp is the
corresponding (vertical) pitch; p,-kc 1 and pk,c are the (upper and lower) widths of the trapezoidal area respectively;
and cp is the corresponding (horizontal) pitch, see Figure J-7(b). The calculated number ( )kIN for each partition zone of this type shall be rounded up to the nearest half tube.
NOTE The area of height p,b5 in Figure J-7(b) is an untubed area with an arbitrary distance between the adjacent tube
rows.
( )minIN is the sum of all the potential extra tubes from the rows, ( )rIN , and all the potential extra tubes from the
pass partition zones, ( )kIN . In extreme cases (where the layout is fully packed) ( )minIN may equal zero.
Calculate area ( )minRA as follows:
( )( ) cbITR ppNNA ⋅⋅+= min(min) (J.5.1-7)
(b) Calculation of all the trapezoidal areas
650a
EN 13445-3:2002 (E) Issue 31 (2008-06) Calculate the values of Jb and Jc for each of the trapezoidal areas (see FigureJ-7(b)) as follows:
⎯ in the perforated zones, the heights Jb are to be calculated as the nearest multiple of bp and 2Td .
The widths Jc are similarly to be calculated as the nearest multiple of cp and 2Td . In case of doubt,
always assume the smaller value.
⎯ for any pass partition zones, the height of the zone, whether or not it is an exact multiple of bp , is inserted in Equation J.5.1-8.
Calculate ( )minRA to include all perforated and un-perforated areas as follows:
( ) ( ) ( ){ } ( )∑=
=− ⋅+⋅=⋅++⋅++⋅+⋅=
max
11332221110(min) 5,0.....5,0
jj
jjjjR bccbccbccbccA (J.5.1-8)
(c) Measurement of area
Measure area ( )minRA
NOTE This could be done by computer or other device.
J.5.1.1.3.3 Calculation of ( )min1d
Calculate ( )min1d from ( )minRA as follows:
( ) π(min)
min14 RA
d = (J.5.1-9)
NOTE If ( )min1d exceeds ( )max1d , the calculation is incorrect and should be checked.
J.5.1.1.4 Average diameter ( )avd1
Calculate ( )avd1 as follows:
( )( ) ( )[ ]
2max1min1
1dd
d av+
= (J.5.1-10)
J.5.1.1.5 Calculation of outside diameter d1
Compare the calculated diameter difference and the allowable diameter tolerance as follows:
( ) ( ) ( )min1max1 ddd act −=Δ (J.5.1-11)
( ) ( ){ }avall dpd 103,0;0,1min=Δ (J.5.1-12)
If the following condition is met:
( ) ( )allact dd ΔΔ ≤ (J.5.1-13)
in all following calculations, put
( )avdd 11 = (J.5.1-14)
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EN 13445-3:2002 (E) Issue 31 (2008-06)
If the condition Equation (J.5.1-13) is not met, calculate M as follows:
( )( )
1+⎟⎟⎠
⎞⎜⎜⎝
⎛=
all
act
dd
IntegerMΔΔ
(J.5.1-15)
where
( )( ) ⎟
⎟⎠
⎞⎜⎜⎝
⎛
all
actdd
IntegerΔΔ
is the integer below or equal to the value of ( )( ) ⎟
⎟⎠
⎞⎜⎜⎝
⎛
all
act
ddΔΔ
.
Make all subsequent calculations M times with values of 1d given by:
( )( ) ( )( )( )1
min1max1min11 −
−+=
Mdd
ndd (J.5.1-16)
where ( )1210 −= Mn ...,,
The result with the greatest load ratio, and hence the greatest required tube plate thickness, shall be taken as the required tube sheet thickness.
NOTE The repeated calculations are necessary to minimize the error from calculations for which assume symmetry on components which are non-axisymmetric.
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EN 13445-3:2002 (E) Issue 31 (2008-06)
Key
1 tie rod
Figure J-7(a) ― Construction of the polygon surrounding the tubed area
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EN 13445-3:2002 (E) Issue 31 (2008-06)
Key
1 pass partition with a height which equals multiple tube pitches
2 pass partition with an arbitary height
Note The equations to calculate the dimensions in Figure J-7(d) are:
Area 1 2
80T
cdpc += ; bpb =1
Area 2 2
111T
cdpc += ;
232
Tb
dpb +=
Area 3
+=
22142
Tc
dpc ; bpb 23 =
Area 4
+=
22143
Tc
dpc ; bpb 24 =
Area 5
+=
22134
Tc
dpc ; pb bpb ,55 +=
Area 6
+=
22115
Tc
dpc ; 26T
bdpb +=
Area 7
+=
2296
Tc
dpc ; bpb 27 = ;
2
47T
cdpc +=
Figure J-7(b) — Construction of trapezoidal areas
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EN 13445-3:2002 (E) Issue 31 (2008-06)
Figure J-7(c) — Tube calculation method
651b
EN 13445-3:2002 (E)Issue 12 (2004-11)
661
[PSe] is the allowable external fluid pressure for the shell; [PSc] = Pe,max(Subclause 16.14)
[σSxt ] is the allowable longitudinal tensile stress in the shell; [σSxt ] = fS[σSxc] is the allowable longitudinal compressive stress in the shell; [σSxc] = σc,all(Subclause 16.14)
J.7.6 Govern pressure representing the resultant effective axial force
J.7.6.1 Resultants of active and reactive axial forces per area unit in the tubebundle
PI = PE + QI (J.7.6-1)
PA = PE + QA (J.7.6-2)
NOTE: If the strength of the tubes is large enough to give the optimum support for the tubesheets,then is PI = 0. Also if this optimum is not realized, the tubebundle may have an acceptable gooddesign.
J.7.6.2 Force distribution parameter
The force distribution parameter ζ shall be calculated thus:
ζ2 = (PA - PR)/(PA - PI) (J.7.6-3)
A necessary minimum requirement for the tubebundle strength is:
0 ≤ ζ2 ≤ 1 (J.7.6-4)
If this requirement is not met, the tubebundle is unable to bear the active loadings and must beredesigned.
J.7.6.3 Govern pressure
J.7.6.3.1 The govern resultant effective axial force is represented by the pressure PQ ; it depends on theforce distribution parameter ζ and the moment distribution parameter η.PQ and η are to be determined simultaneously by the following algorithm:
First calculate:
2
22min
12
1A
PPPP
dPef
⋅⋅⋅⋅⋅
=ϕκ
η (J.7.6-5)
J.7.6.3.2 Special case PI > 0 and ζ > ηmax
Calculate:
η2max = η2
min·PA/PI (J.7.6-6)
If indeed ζ > ηmax then the following results are to be used, and the calculation is to be continued in J.8;otherwise is to be continued in J.7.6.3.3.
2maxmax ηηη == (J.7.6-7)
PQ = (PA - PI )·{1 - ζ2 + ζ2·lnζ2 } + PI (J.7.6-8)
EN 13445-3:2002 (E) Issue 31 (2008-06)
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J.7.6.3.3 Other cases:
Calculate the following auxiliary parameters
u = ζ2·⏐PI/PA⏐ (J.7.6-9)
v = η2min - u (J.7.6-10)
Assume a starting value w = 1,5 and calculate:
( )[ ] ( )[ ] wv/wuv/wuv ⋅⋅+⋅−+⋅−+= 2222 22 ζζη (J.7.6-11)
Determine more precise
w = 2·(η/ζ + 1)/(η/ζ + 2) (J.7.6-12)
and calculate η2 from eq.(J.7.6-11) again.
NOTE: Equations (J.7.6-11) and (J.7.6.12) may be treated as an iterative cycle up to an any precision; but the proposed algorithm without repetition of e.q.(J.7.6-12) is sufficient precise for practical purposes.
If η2 < 1,0 then use η as determined and calculate
PQ = (PA - PI )·{1 - 3·ζ2 + 2·ζ3/η + ζ2·lnη2 } + PI (J.7.6-13)
else (η2 ≥ 1,0) , put
η = 1,0 (J.7.6-14)
and calculate
PQ = (PA - PI )·{1 - 3·ζ2 + 2·ζ3 } + PI (J.7.6-15)
J.8 Edge bending moments
Figures J-10 to J-13 show (schematic simplified) four essential different edge configurations, each with two variants ( bS > 0 channel side; bS < 0 shell side). These Figures are refered in the following determination for MA , MB , MC , MD .
J.8.1 MA = active bolt load bending moment
Edge configuration per Figure J-10: Both sides integral (no gasket):
MA = 0 (J.8.1-1)
Edge configuration per Figure J-11: Both sides flanged (two gaskets)
MA = -FB·bS/(π·d2) (J.8.1-2)
EN 13445-3:2002(E) Issue 31 (2008-06)
665
Edge configuration per Figure J-12: Channel flanged (one gasket):
MA = +FB·(d3e - dGC)/(2·π·d2) (J.8.1-3)
Edge configuration per Figure J-13: Shell flanged (one gasket):
MA = -FB·(d3e - dGS)/(2·π·d2) (J.8.1-4)
where
d3e = d3·(1 - 2/nB2) …(J.8.1-5)
J.8.2 MB = active fluid pressure bending moment
For all cases ⏐λS⏐ < 0,05 simple MB = 0 may be assumed. More precise:
All edge configurations with bS > 0, λS > 0:
MB = +PT·(d2 + 2·bS)·bS/4 (J.8.2-1)
All edge configurations with bS < 0, λS < 0:
MB = +{PS·(d2 - 2·bS) + (PD - PR)·d12/d2
}·bS/4 (J.8.2-2)
J.8.3 MC = reactive bending moment from connected components
Edge configuration per Figure J-10: Both sides integral (no gasket):
2
S
SS2S
2S
2
C
CT2C
2C
2
F2
FFC 4
344
34
24 ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⋅
⋅−⋅+⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅
⋅−⋅+⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅⋅
⋅=
edPfe
edPfe
dbefM (J.8.3-1)
Edge configuration per Figure J-11: Both sides flanged (two gaskets):
⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅⋅
⋅=
2
F2
FFC
24 d
befM (J.8.3-2)
Edge configuration per Figure J-12: Channel flanged (one gasket):
2
S
SS2S
2S
2
F2
FFC 4
34
24 ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⋅
⋅−⋅+⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅⋅
⋅=
edPfe
dbefM (J.8.3-3)
Edge configuration per Figure J-13: Shell flanged (one gasket):
2
C
CT2C
2C
2
F2
FFC 4
34
24 ⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅⋅
⋅−⋅+⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅⋅
⋅=
edPfe
dbefM (J.8.3-4)
NOTE If the terms under the radical sign (for both the channel C and the shell S) are negative then the cylindrical shells of the channel or the shell are overloaded already by the pressures PT or PS alone.
J.8.4 MD = reactive bending moment limitation by the tubesheet
For all edge configurations the same limitation is valid:
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅⋅⋅
−⋅⋅
=2
redP,P
2R2
redP,PD 2
14 ef
dPefM (J.8.4-1)
EN 13445-3:2002 (E)Issue 2 (2002-06)
666
NOTE If the whole tubesheet has the same constant thickness, then is valid eP,red = eP .
J.8.5 Resultant optimum edge bending moment
The resultant bending moment M2 (in the tubesheet per circular length unit at the diameter d2 )may vary within the range M2,min ≤ M2 ≤ M2,max . Due to small plastic deformations the real valueM2 approximates a value M2,opt , being optimum for the limit load. These values are calculatedas follows:
M2,max = min{ MA + MB + MC ; +MD } (J.8.5-1)
M2,min = max{ MA + MB - MC ; -MD } (J.8.5-2)
( ) ( ) ( )
+⋅⋅+⋅++⋅
⋅+⋅
−= 3/12218 R
2RDRR
P
Q
R
21
opt2, λλλλ
PPk
PdM (J.8.5-3)
M2 = max{ M2,min ; min( M2,opt ; M2,max )} (J.8.5-4)
Herein the modified strength parameter kP is defined as follows:
kP = κP·(1 - lnη2) (J.8.5-5)
NOTE: Observe, that due to η2 ≤ 1,0 always is lnη2 ≤ 0 and kP ≥ κP.
J.8.6 Pressure representing the moment
PM = M2·8·(1 + λR)/d1
2 + PR·λR + PD·λR
2·(1 + λR/3) (J.8.6-1)
J.9 Limit load conditions for all tubesheets
J.9.1 Bending within the tubed region
Calculate the required loading parameters and then the load ratio for bending ΦB .
( ) PP
Q1 2
3
ϕ∗+∗
=k
PL (J.9.1-1)
( )( ) RPP
RMRMQ
2 1
)2(3
λϕλλ
+⋅+
⋅+−⋅+⋅=
k
PPPL (J.9.1-2)
RP
MQQ3
6
λϕ +⋅++
=PPP
L (J.9.1-3)
( ) 0,112
;;max2
PP
21
321B ≤⋅⋅
⋅=ef
dLLLΦ (J.9.1-4)
J.9.2 Shear at the boundary of the tubed region
The load ratio for shear at the boundary of the tubed region is to be calculated thus:
0,12 PPP
1Rs ≤
⋅⋅⋅⋅
=Φef
dP
ϕ (J.9.2-1)
EN 13445-3:2002 (E) Issue 31 (2008-06)
683
Annex M (informative)
In service monitoring of vessels operating in fatigue or creep
M.1 Purpose
This annex gives guidance on the monitoring of vessels which operate in either fatigue or creep.
M.2 Fatigue operation
The operator should record in a suitable fashion the number of load cycles occurring and a plan should be prepared for the inspection of the vessel throughout its life. Typically, a pressure vessel operating in fatigue should be internally and if necessary externally inspected (by VT, RT, UT, PT, etc. as relevant) at a period not later than 20 % of the allowable fatigue life. Surface inspection is generally more relevant than volumetric inspection.
NOTE 1 This time corresponds to 20 % of the allowable number of cycles when the design stress range spectrum includes only one type of cycle. For more complex loading spectra, it corresponds to the time when a total fatigue damage index of 0,2 (see definition in Clauses 17 or 18) has been reached.
NOTE 2 The records may indicate a need for sooner inspection than originally laid down.
For pressure vessels subject to cyclic loading, in-service inspections are of particular importance for early detection of incipient damage. The internal inspections should be supplemented by non-destructive tests on highly loaded locations especially by surface crack tests and ultrasonic tests. For monitoring inaccessible areas, an ultrasonic test from the outside surface of the vessel may be appropriate.
NOTE 3 Fatigue crack growth generally occurs exponentially and if an incipient crack has appeared after ten units of time, at constant loading, it is likely to become through-wall in one further unit.
If the operating conditions deviate from those assumed in the calculation according to Clauses 17 or 18 to cause greater cyclic loading, or if damage of the vessel wall is to be expected before the end of the next inspection interval owing to other operating influences, the inspection intervals should be shortened.
Conversely, if no incipient cracks are detected during regular inspections, the vessel may be operated further up to the next inspection in the interval laid down or agreed, even if the allowable lifetime as calculated according to Clauses 17 or 18 has been reached or has been exceeded.
NOTE 4 Longer inspection intervals may possibly result from calculations according to Clause 18 (Detailed assessment of fatigue life) rather than from Clause 17 (Simplified fatigue assessment).
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M.3 Measures to be taken when the calculated allowable fatigue lifetime has been reached
If the allowable fatigue lifetime for a component has been reached (i.e. if the allowable number of cycles has been reached or if the total fatigue damage index according to Clauses 17 or 18 has reached the value 1, non-destructive tests should be performed as completely as possible concentrating on the highly stressed locations.
If no cracks are detected in the non-destructive tests conducted in the inspection intervals and in the test above, continued operation may be allowed.
If cracks or crack-like defects or other more extensive damage are found, the component or the structural element concerned should be replaced, unless continued operation appears admissible by virtue of appropriate measures.
The following design, manufacturing and process-related measures can be considered with regard to continued operation:
a) Removal of cracks by grinding. Possible reduction in wall thickness should be assessed by special analysis.
b) Grinding the welds to remove all notches. c) Elimination of deformation restraints, e.g. replacement of cracked rigid braces by flexible
connections. d) Change in mode of operation. e) Repairs by welding.
M.4 Operation in the creep range
A plan should be prepared for the inspection of the vessel throughout its life. NOTE TRD 508, chapter 2.2 [1], ECCC recommendations Part 2 [2] and CTI-R5 section 5 [3] give guidance on monitoring in the creep range.
Typically, a vessel should be internally and if necessary externally inspected (by VT, RT, UT, PT, etc. as relevant) at a period not later than 50 % of the allowed lifetime. Internal inspections should be supplemented by non-destructive tests on creep critical locations.
Replica testing may provide a means for monitoring creep damage. A suitable region should be selected on the most vulnerable component. A replica test should be made before the vessel enters service and at appropriate intervals during service.
Measurement of diameter may also give guidance on creep accumulation.
Measurement of hardness may indicate the material condition before and after service.
EN 13445-3:2002 (E) Issue 31 (2008-06)
684a
Where lifetime monitoring is provided, higher stresses are permitted and there is no check on creep strain if the design is made by design by formulae according to Clause 19. This permits a thinner vessel but an appropriate in-service inspection programme is highly recommended, including check of creep deformations and replicas.
If the operating conditions deviate from those assumed in the design, the inspection intervals should be modified.
M.5 Measures to be taken when the calculated allowable creep lifetime has been reached
If the allowed lifetime for a component has been reached, non-destructive tests should be performed as completely as possible concentrating on the highly stressed locations.
If no evidence of damage is shown by the non-destructive tests conducted at the inspection intervals and in the test above, continued operation may be allowed.
If cracks or crack-like defects or other more extensive damage are found, the component should be replaced, unless continued operation appears admissible by virtue of appropriate measures, such as:
a) Removal of cracks by grinding.
b) Removal of damaged locations by grinding.
c) Elimination of deformation restraints.
d) Change in mode of operation.
e) Repairs by welding.
M.6 Bibliography
[1] Technische Regeln für Dampkessel 508, Chapter 2.2, 1986
[2] European Creep Collaborative Committee Recommendations, Part 2, Vol. 6 and Vol. 9
[3] ComitatoTermotecnico Italiano - R5:2005, section 5, Milan
