sutn - Úvoden 13445-3:2002 (e) issue 9 (2004-02) 29 7.5.3 torispherical ends 7.5.3.1 conditions of...
TRANSCRIPT
EN 13445-3:2002 (E)Issue 9 (2004-02)
29
7.5.3 Torispherical ends
7.5.3.1 Conditions of applicability
The following requirements are limited in application to ends for which all the following conditions aremet:
r ≤ 0,2 Di
r ≥ 0,06Di
r ≥ 2e
e ≤ 0,08 De
ea ≥ 0,001 De
R ≤ De
7.5.3.2 Design
The required thickness e shall be the greatest of es, ey and eb, where:
Pz2f
RPe
0,5s
−⋅
⋅= (7.5-1)
( )f
DR Pe i
y0,20,75 +⋅
=β
(7.5-2)
where
ß is found from Figure 7.5-1 or the procedure in 7.5.3.5, replacing e by ey.
and
( )
+=1,5
10,825
i
bib
1110,20,75
r
D
f
PDRe (7.5-3)
where
1,5/tp
b20,R
f = (7.5-4)
except for cold spun seamless austenitic stainless steel, where:
1,5/tp
b20,R1,6
f = (7.5-5)
EN 13445-3:2002 (E)Issue 1 (2002-05)
30
At test conditions the value 1,5 in the equations for fb shall be replaced by 1,05.
NOTE 1 For stainless steel ends that are not cold spun, fb will be less than f.
NOTE 2 The 1,6 factor for cold spun ends takes account of strain hardening.
NOTE 3 It is not necessary to calculate eb if ey > 0,005Di.
NOTE 4 The inside height of a torispherical end is given by
� � � �rDR2DRRh 2/2/ iii ������
7.5.3.3 Rating
For a given geometry Pmax shall be the least of Ps, Py and Pb, where:
a
a
0,5eR
ez2fP
s �
��� (7.5-6)
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
0,010 0,100
β
0,001
r/Di = 0,2r/Di = 0,16r/Di = 0,13r/Di = 0,1r/Di = 0,08r/Di = 0,06
0,75 + 0,2 Di/R) P/f
Figure 7.5-1 — Parameter � for torispherical end – Design
EN 13445-3:2002 (E)Issue 7 (2003-07)
31
)0,2(0,75 i
a
DR
efP
y +⋅
=β
(7.5-7)
where
ß is found from Figure 7.5-2 or the procedure in 7.5.3.5, replacing e by ea.
0,8251,5
0,20,75111
i�
abb
+
=Dr
DR
efP (7.5-8)
NOTE It is not necessary to calculate Pb if ea > 0,005Di.
7.5.3.4 Exceptions
β
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
0,001 0,010 0,100e/R
r/D = 0.2r/D = 0.16r/D = 0.13r/D = 0.1r/D = 0.08r/D = 0.06
Figure 7.5-2 — Parameter ß for torispherical end - rating
It is permissible to reduce the thickness of the spherical part of the end to the value es over a circular
area that shall not come closer to the knuckle than the distance eR ⋅ , as shown in Figure 7.5-3.
Any straight cylindrical flange shall meet the requirements of 7.4.2 for a cylinder, if its length is greater
than eD ⋅i0,2 . When the length is equal or smaller than eD ⋅i0,2 , it may be the same thickness as
required for the knuckle.
EN 13445-3:2002 (E)Issue 9 (2004-02)
32
7.5.3.5 Formulae for calculation of factor ββ
D
D i
e
> e-
R r
> R.e
- > es-
Figure 7.5-3 — Geometry of torispherical end
Y = min(e/R ; 0,04) (7.5-9)
( )YZ /1log10= (7.5-10)
X = r /Di (7.5-11)
})(90{6,2
11,006
4YN
+−= (7.5-12)
For X = 0,06
( )1,88733,2937Z2,2124Z0,3635ZN 230,06 +−+−=β (7.5-13)
For 0,06 < X < 0,1
{ }0,10,06 0,06)(XX)(0,125 βββ −+−= (7.5-14)
For X = 0,1
β 0,13 2= − + − +N Z Z Z( , , , , )0 1833 10383 12943 0 837 (7.5-15)
EN 13445-3:2002 (E)Issue 1 (2002-05)
41
7.6.8.2 Design
Required thicknesses e1 and e2 shall be determined by the following procedure:
Assume values of e1 and e2:
1
2
e
es � (7.6-22)
when s < 1
2
1
)cos(
2sss
���
�� (7.6-23)
when s � 1
� ����
��� �
���
�2cos
11
2ss (7.6-24)
� �0,5
tan0,4
1
cH ���
�
��
e
D(7.6-25)
If
Hc
12
��
���
D
ezfP (7.6-26)
then e1 and e2 are acceptable. If not, repeat with increased values of e1 and/or e2.
NOTE The above procedure does not provide values for e1 and e2 independently. Any values may beselected to suit the needs of the design, for example to obtain a favourable value of l1 or l2.
Provided that the requirements of 7.4.2 and 7.6.4 continue to be met, it is permissible to modify adesign according to the above rule in one of the following ways:
a) Where e1 = e2 a knuckle of the same thickness may be included. l1 and l2 continue to bemeasured from the junction (i.e. the point where the centre lines of cone and cylinder meet).
b) The thickness of the cylinder may be increased near the junction and reduced further awayprovided that the cross-sectional area of metal provided by the cylinder within a distance l1 fromthe junction is not less than l1 e1. In addition, the thickness of the cone may be increased near thejunction and reduced further away provided that the cross-sectional area of metal provided by thecone within a distance l2 from the junction is not less than l2�e2.
EN 13445-3:2002 (E)Issue 9 (2004-02)
42
7.6.8.3 Rating
The maximum permissible pressure for a given geometry shall be:
Hc
1max
2
β⋅⋅⋅
=D
ezfP (7.6-27)
βH is found from equations (7.6-22) to (7.6-25) using e1a and e2a in place of e1 and e2 .
NOTE 1 The procedure for finding e1a and e2a is as provided in the note to 7.6.6.3.
NOTE 2 Analysis thicknesses may exceed the required thickness without leading to any increase in l1 or l2.
7.6.9 Offset cones
This requirement applies to offset cones between two cylinders (see Figure 7.6-5). The cylinders shallhave parallel centre lines offset from each other by a distance no greater than the difference of theirradii. A required thickness shall be calculated in accordance with 7.6.6 for the junction at the largeend. A required thickness shall be calculated in accordance with 7.6.8 for the junction at the small end.The greater of these shall apply to the whole cone. The angle (α) shall be taken as the greatest anglebetween cone and cylinder.
α
1
Figure 7.6-5 — Offset cone
7.7 Nozzles which encroach into the knuckle region
7.7.1 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in 7.5.1:
A is a parameter defined by equation (7.7-4) or (7.7-8);
A1 is a parameter defined by equation (7.7-12) or (7.7-16);
Key
1 Offset of axis
EN 13445-3:2002 (E)Issue 9 (2004-02)
43
B is a parameter defined by equation (7.7-5) or (7.7-9);
B1 is a parameter defined by equation (7.7-13) or (7.7-17);
βK is the weakening factor due to presence of nozzle given by (7.7-10);
di is the inside diameter of the nozzle;
X is a parameter defined by equation (7.7-11) or (7.7-15);
V is a parameter defined by equation (7.7-3) or (7.7-7).
7.7.2 Conditions of applicability
In this sub-clause requirements are given for increasing the thickness of a dished end to compensatefor nozzles which are not entirely within the central area of the head as defined in 9.7.2.4 and aretherefore not covered by clause 9.
The requirements are limited in application to Kloepper and Korbbogen ends for which:
di/De ≤ 0,6 (7.7-1)
and
6,7e
i ≤⋅ De
d (7.7-2)
The nozzle centre line shall lie in the same plane as the centre line of the vessel. The nozzle centreline shall lie between normal to the wall of the end and parallel to the vessel centre line. The location ofthe nozzle shall be such that it does not cross the tangent line between knuckle and cylinder. Nozzlesparallel to the vessel centre line and with outside diameter in line with the outside diameter of thevessel are included in these requirements.
The requirements of 7.7 may also be applied to ellipsoidal ends for which the aspect ratio K ≤ 2. Thethickness of such an ellipsoidal end with a nozzle intruding into the knuckle region shall be as for aKorbbogen end of the same diameter.
The increased thickness required by this clause applies to the whole knuckle region. Welded-oncompensation is not permitted. The thickness of the crown may be reduced provided that therequirements of 7.5.3.4 are met and reinforcement for nozzles in the crown region meets therequirements of clause 9.
When the distance between the edge of the nozzle where it meets the knuckle and the
knuckle/cylinder tan, line is less than re⋅5,2 (measured along the surface) the validity of themethod is in doubt. Unless the design is supported by special analysis or extensive experience,the design pressure shall be multiplied by two in such cases, or in a rating the allowable pressureshall be halved.
7.7.3 Design
For Kloepper type end:
V = log10
f
P000 1 (7.7-3)
A = max (0,5; 0,264 + 0,938V - 0,592V 2 + 0,14V 3) (7.7-4)
EN 13445-3:2002 (E)Issue 9 (2004-02)
44
B = min (4,2; 4,9 - 2,165V + 0,151V 2) (7.7-5)
++=
e
i
e
ik 0,31;max
D
dB
D
dBAβ (7.7-6)
For Korbbogen type end:
V = log10
f
P000 1 (7.7-7)
A = 0,54 + 0,41V - 0,044V 3 (7.7-8)
B = 7,77 - 4,53V + 0,744V 2 (7.7-9)
++=
e
i
e
ik 0,51;max
D
dB
D
dBAβ (7.7-10)
Replace P by Pβk in equation (7.5-2) and in Figure 7.5-1 to arrive at the required thickness. Thesubstitution shall be made before the calculation of β in 7.5.3.5. Equations (7.5-1) and (7.5-3) continueto apply without modification.
NOTE The graphs of Figure 7.7-1 and Figure 7.7-2 are based on the above procedure and give R P
f e as a
function of P/f and di/De.
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2.5
0.001 0.010 0.100
P/f
ef/P
R
d/Di = 0d/Di = 0,1d/D = 0,2
d/Di = 0,6
d/D = 0,3d/Di = 0,4d/Di = 0,5
Figure 7.7-1 — Design ratio for Kloepper ends
EN 13445-3:2002 (E)Issue 9 (2004-02)
45
0.5
1.0
1.5
2.0
2.5
3.0
0.001 0.010 0.100
ef/P
R
P/f
d/Di = 0d/Di = 0,1d/Di = 0,2d/Di = 0,3d/Di = 0,4d/Di = 0,5d/Di = 0,6
Figure 7.7-2 — Design ratio for Korbbogen end
7.7.4 Rating
To determine the maximum permissible pressure corresponding to a given geometry (rating) a trialand error procedure may be adopted. Alternatively the following procedure provides an approximateand always conservative estimate of βk.
For Kloepper type end:
e
a1000 10
log=D
eX (7.7-11)
A1 = 1,07 max(0,71 - X; 0,19X + 0,45) (7.7-12)
EN 13445-3:2002 (E)Issue 9 (2004-02)
46
( )
−+
+31
0,260,1160,241
1min 1,02=
XB );53( X (7.7-13)
++=
e
i1
e
i11k 0,31;max
D
dB
D
dBAβ (7.7-14)
For Korbbogen type end:
e
a000 1 10
log=XD
e(7.7-15)
A1 = 0,8
i
e0,00531,136
1
+
d
D(7.7-16)
B1 = (8,87 - 4,35X + 0,19X 3) (7.7-17)
++++=
e
i1
e
i
e
i11
e
ik 0,51 )1,1(1; )0,1(1max
D
dB
D
d
D
dBA
D
d� (7.7-18)
Replace β by kββ ⋅ in equation (7.5-7). Equations (7.5-6) and (7.5-8) continue to apply without
modification.
7.7.5 Multiple nozzles which encroach into the knuckle region
The requirements for multiple nozzles in clause 9 apply also to nozzles designed to theserequirements if the ligament between adjacent nozzles is entirely within the central area defined in9.7.4. If the connecting line between adjacent nozzles is not entirely within the central area, theligament shall not be less than half the sum of the nozzle bores.
EN 13445-3:2002 (E)Issue 1 (2002-05)
57
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14
12
pr/py
pm/py
KEY
1 - Cylinders and cones
Pm/Py 0 0,25 0,5 0,75 1,0 1,25 1,5 1,75 2,0 2,25 2,5 2,75 3 3,25 3,5
Pr/Py 0 0,125 0,251 0,375 0,5 0,605 0,68 0,72 0,755 0,78 0,803 0,822 0,836 0,849 0,861
Pm/Py 3,75 4,0 4,25 4,5 4,75 5,0 5,25 5,5 5,75 6,0 6,25 6,5 6,75 > 7,0
Pr/Py 0,87 0,879 0,887 0,896 0,905 0,914 0,917 0,923 0,929 0,935 0,941 0,947 0,953 0,959
2 - Spheres and dished ends
ym / PP 0 0,5 1 1,5 2 2,5 3,0 3,5 4 4,5 5,0 5,5 6 > 6,5
yr / PP 0 0,09 0,18 0,255 0,324 0,386 0,435 0,479 0,51 0,533 0,548 0,565 0,56 0,57
Figure 8.5-5 — Values of yr /PP versus ym /PP
EN 13445-3:2002 (E)Issue 9 (2004-02)
58
8.5.3 Stiffened cylinders
8.5.3.1 Introduction
8.5.3 provides a procedure to determine whether a cylinder with specified stiffeners can support thedesign external pressure. All stiffeners shall be designated as either ‘heavy’ or ‘light’. It is permissiblenot to consider small circumferential rings as stiffeners.
NOTE A ‘heavy’ stiffener is usually a girth flange or other major component, but it may be a particularly largeconventional stiffener. A light stiffener is usually a ring (flat bar), tee, angle or I-section. In most practical casesthere will be a number of similar stiffeners uniformly distributed along the cylinder. It is then most economical todesignate all stiffeners as ‘light’ since the calculation of overall collapse pressure takes account of the resistanceof the shell to that mode of failure, but to designate them all as ‘heavy’ leads to a much simpler calculation.
8.5.3.2 Unsupported length
The unsupported lengths of a cylinder with stiffeners shall be in accordance with Table 8.5-1. Thedimensions are shown in Figures 8.5-6, 8.5-7 and 8.5-8.
Table 8.5-1 — Definition of cylinder length
Cylinder with light stiffeners Cylinder with light and heavy stiffeners
For each bay separately For each bay separately
( )L L w h= − +'s " , '1 0 4 (8.5.3-1) ( )L L w hs= − +' " , '1 0 4 (8.5.3-3)
Or or
L L w w= − −"s ' "2 2 (8.5.3-2) L L w w= − −"s ' "2 2 (8.5.3-4)
or
33 "''" s wwLL −−= (8.5.3-5)
For each light stiffener separately For each light stiffener separately
( )L L h Ls s s' "= + +0 4 2, ' / (8.5.3-6) ( )L L h Ls s s' "= + +0 4 2, ' / (8.5.3-8)
Or or
( )L L Ls s s" " '= + / 2 (8.5.3-7) ( )L L Ls s s" " '= + / 2 (8.5.3-9)
For purpose of evaluating β For purpose of evaluating β
L L h hH cyl= + +0 4 0 4, ' , " (8.5.3-10) L L hH H'= +0 4, ' (8.5.3-11)
or
L LH H"= (8.5.3-12)
For each heavy stiffener
( )L L h LsH H H' "= + +0 4 2, ' / (8.5.3-13)
or
( )L L LsH H H" " '= + / 2 (8.5.3-14)
EN 13445-3:2002 (E)Issue 9 (2004-02)
69
( )[ ]⋅+⋅+⋅
⋅ 2 6 6
=
fffw2
3ff
edweed r
weC
i
⋅+⋅⋅+⋅
ffw
ffw
ewed
ewed
3
34(8.5.3-62)
Wf
ewCGs
CGc
wi
e a
e f
r i
Rf
Rs
X c
d
L
Ls or LH
Figure 8.5-14 — External I-shaped stiffener
Wf
ew
CGsCGc
wi
e a
e f
r i
Rf
Rs
X c
d
L
Ls or LH
Figure 8.5-15 — External T-shaped stiffener
Wf
e f
d
L
ew
CGc
Ls or LH
CGs
wi
e a
r i
Rf
Rs
X c
Figure 8.5-16 — External angle stiffener
EN 13445-3:2002 (E)Issue 1 (2002-05)
70
Ls or LH
wi
Wf
Rf
ew
e a
e f
r i
L
dFigure 8.5-17 — Internal T-shaped stiffener
b) If the stiffener is flanged at the edge remote from vessel shell, the stiffener proportions shallconform to the following:
��
��
�
�
�
�� 670
es
ys
esw P
PE, ;
E
e
d
��1,1max (8.5.3-63)
or
��
��
�
�
�
�� 320
es
ys
esf
f
P
PE, ;
E
e
w
��0,5max (8.5.3-64)
8.5.3.8.2 For a flat bar stiffener
ys
es
4 P
Pi �� �� (8.5.3-65)
i� shall be obtained from Table 8.5-4 for internal stiffeners or from Table 8.5-5 for external stiffeners,
using the value of ncyl from Figure 8.5-4.
EN 13445-3:2002 (E)Issue 9 (2004-02)
75
8.6.4 Overall collapse of conical shell and spacing
8.6.4.1 Constant shell thickness, stiffener size and spacing
The requirements for stiffening ring proportions to resist stiffener tripping, given for cylinders in subclause8.5.3.8, apply without modification.
For the design of light stiffeners on cones of constant thickness, as shown in Figure 8.6-3:
( )s
e
L
lEn
R
eEP
⋅
⋅−+
⋅⋅=
3max
2
n
3a
g
R
cos'1cos ααβ(8.6.4-1)
where β shall be determined from figure 8.5-13 with αcos 2 nR
LH instead of R
LH
2 or from equation (8.5.3-
25) with αcosnR instead of R.
nR and maxR shall be as defined in figures 8.6-4 and 8.6-5.
+
+++
⋅
+
⋅
+⋅+⋅=33
22222
2
"
2
'sin
12"
2
"'
2
'' eea
wfsea
sea
wwffe
LL
ellX
L eX
LeX AXAl α
+
+
LL
e eea
2
"
2
'cos
122
3
α (8.6.4-2)
eL' shall be derived from 8.5.3.6.3 with:
⋅
=αcos
2
i
a
R
enx (8.6.4-3)
αcos a
S
⋅⋅=
eR
Lu
i
(8.6.4-4)
where iR is the mean shell radius measured at stiffener i.
To calculate the maximum stress in the stiffeners use:
( )( )fg
f
ys
esfs SSPP
SSP n
R
d E
P
PSS
××−××−
×+
××=
1005.0'2
max
σσ (8.6.4-5)
where
+⋅
+
−
⋅⋅⋅=
N
w e
A
R
R e P
ia
mfaesys
δαα
νασ
2cos
cos
1
21
cos
2max
(8.6.4-6)
EN 13445-3:2002 (E)Issue 8 (2003-11)
76
where
a
cos 28,1
eR⋅= αδ (8.6.4-7)
2f
f'e
Xd += (8.6.4-8)
8.6.4.2 Varying shell thickness, stiffener size or spacing
The minimum shell thickness for any length between planes of substantial support shall be determinedusing the procedure given in 8.6.3.
The requirements for stiffening ring proportions shall apply without modification.
For the design of light stiffeners, either of varying size or spacing or on cones of varying thickness, asshown in Figure 8.6-6, it is permissible to use the method of assessment for stiffened cylinders withequations of 8.6.3 with any of the following.
a) Where the stiffener pitch and size is constant use the minimum thickness anywhere along the lengthof the section under consideration in calculating gP and yP ;
b) Consider each stiffener separately using the appropriate minimum shell thickness and maxR for the
two half bays on either side of the stiffener and β = 0 ;
c) Consider each stiffener separately using the appropriate minimum thickness and Rmax for the two
half bays on either side of the stiffener.
Where n > 2 calculate eP , as in b) and where n = 2 use the following equation:
( ) ∑=
=
⋅
⋅−⋅+⋅⋅=YNi
i i
i
R
L
XI
L
nE
R
eEP
03
C
i2 e,
H
2
n
3
g
sin '
1 cos 2cos
παααβ
(8.6.4-9)
where β shall be determined from figure 8.5-13 with αcos 2 nR
LH instead of R
LH
2 or from equation (8.5.3-
25) with αcosnR instead of R.
8.6.5 Cone-cylinder intersections
8.6.5.1 Planes of substantial support
Where there is no knuckle, the intersection between a cone and a cylinder (at both large and small ends)is a plane of substantial support if °≥ 30α and if ncyl (the mode number for the minimum buckling
pressure obtained from Figure 8.5-4, or found when applying equation 8.5.3-24 when light stiffeners arepresent) does not equal 2 for either cone or cylinder.
When the above conditions are not met (either °< 30α or ncyl = 2), the distance L between planes of
substantial support is the sum of the effective unsupported length(s) of the cylinder or cylinders plus theaxial length of the cone. The thickness of the cone and the small cylinder shall not be less than thecylinder thickness required by 8.5.3.4 and if there are light stiffeners they shall be applied at the pitch andsize determined in 8.6.3.1 to the cone and small cylinder as well as to the large cylinder.
EN 13445-3:2002 (E)Issue 9 (2004-02)
103
where ea,m is the average thickness (obtained considering er and ea and by iterative calculation) along thelength lo :
ea,m = ea,s + (er - ea,s)o
r
l
l(9.5-36.2)
If the width of reinforcing ring lr is greater than lo for reinforcement calculation shall be put lr = lo .
Therefore the effective length l's of shell for calculation of Afs is:
l's = min ( ls ; lo - lr ) (9.5-37)
Moreover:
Afr = er�lr (9.5-38.1)
Apr = 0,5 dir�er (9.5-38.2)
Afs = ec,s�l's (9.5-38.3)
Aps shall be calculated as given in equations (9.5-22) with l's as defined in equation (9.5-37) and witha referred to the external diameter of the reinforcing ring.
If the closure of the opening is located inside the ring (see Figure 9.4-6), the value of area Apr is equal to 0.
9.5.7 Where the nozzle normal to the shell contributes to the reinforcement
9.5.7.1 For a set-on nozzle (see Figure 9.4-7) or set-in nozzle (see Figure 9.4-8), the length of the nozzlecontributing to the reinforcement shall not be greater than lbo calculated as follows:
( ) bbebbo eedl ⋅−= (9.5-39)
For the calculation of value lbo in eq. (9.5-39) the diameter deb of nozzles with elliptical or obround crosssection shall be taken along the smallest dimension of the bore.
For protruding nozzles
l'bi = min (lbi ; 0,5lbo) (9.5-40)
For a set-in nozzle
Afb = eb � (l’b + l’bi + e's) (9.5-41)
For a set-on nozzle
Afb = eb�l’b (9.5-42)
where
l’b = min (lbo ; lb ) (9.5-43)
EN 13445-3:2002 (E)Issue 7 (2003-07)
104
e's is the length of penetration (full or partial) of set-in nozzle into shell wall, but not greater than ea,s.
For both set-in and set-on nozzles,
Apb = 0,5dib�( l'b + ea,s ) (9.5-45)
Afs and Aps shall be calculated as given in 9.5.3.1 and 9.5.3.2 respectively, where Aps is given only by thevalue of As in 9.5.3.2.a),b),c).
For adequate reinforcement either equation (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.7.2 For a butt-welded nozzle, see Figure 9.4-11, adequate reinforcement is provided when eitherequation (9.5-7) or (9.5-11), as appropriate, is satisfied.
9.5.7.3 For a nozzle extruded from the shell see Figures 9.4-11 and 9.4-12. Both Afs and Afb shall bemultiplied by 0,9 to compensate for thinning during manufacturing, if minimum or actual thickness of extrudedpart is not known.
For adequate reinforcement either equation (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
The pressure loaded areas Ap and stress loaded cross-sectional areas Af of nozzles in Figures 9.4-11 and9.4-12 shall be calculated by a suitable method.
9.5.8 Where the nozzle oblique to the shell wall contributes to the reinforcement
9.5.8.1 Oblique nozzles in cylindrical and conical shells
9.5.8.1.1 Where a nozzle is located on a cylindrical or conical shell, its axis is oblique in the transversecross-section (see Figure 9.5-2), and ϕ does not exceed the following value,
ϕ < arcsin (1-δ) (9.5-46)
where
)0,5(2 sa,is
eb
er
d
+=δ (9.5-47)
the reinforcement shall be checked in accordance with 9.5.8.1.3 on both the longitudinal and transversecross-sections. For the check on longitudinal cross-section, ϕ shall be taken equal to zero.
9.5.8.1.2 Where the axis of the nozzle is oblique in the longitudinal cross-section (see Figure 9.5-1) and ϕdoes not exceed 60°, the reinforcement shall be checked in accordance with 9.5.8.1.3 on the longitudinalcross-section only.
9.5.8.1.3 The reinforcement shall be calculated on the side where there is an acute angle between thenozzle wall and the shell wall.
Distance a shall be calculated as given below
i) for cylindrical and conical shells, in the longitudinal cross-section
ϕcos0,5 ebd
a ⋅= (9.5-48)
ii) for cylindrical and conical shells in the transverse cross-section, with rms and δ defined inEquations (9.5-28) and (9.5-29)
a = 0,5 rms � [ arcsin ( δ+sin ϕ ) + arcsin ( δ - sin ϕ )] (9.5-49)
Apb and Afb shall be calculated according to 9.5.7.
EN 13445-3 :2002 (E)Issue 1 (2002-05)
131
10.4.2.2 For an end with a hub, the following conditions shall apply:
a) the inside radius of the hub shall meet the following: r � es and r � 1,3 eaf;
Flat ends which do not meet this shall be treated as ends welded directly to the shell.
b) the hub and adjacent cylinder may be offset, but their wall centre-lines shall not be offset by anamount which is greater than the difference between their nominal thicknesses;
c) a taper hub shall have a slope not exceeding 1:3;
d) where the thickness of the cylindrical shell adjacent to the flat end is uniform (see Figure 10.4-1(a)), lcyl shall be calculated as follows:
ssicyl )(5,0 eeDl �� (10.4-1)
e) where the thickness of the cylindrical shell adjacent to the flat end is tapered (see Figure 10.4-1(b)), a value of lcyl shall be assumed and the mean thickness over that length calculated. Thisthickness shall be inserted into equation (10.4.1) and the required value of lcyl calculated. If lcyl
required is greater than the assumed value, the calculation shall be repeated using a largerassumed value.
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), lcyl is also given by equation (10.4.2).Radius rd shall be at least equal to 0,25es or 5 mm, whichever is greater. The centre of the radius shalllie within the thickness of the flat end and not outside it, see Figure 10.4-3.
10.4.3 Flat end with a hub
The minimum required thickness for a flat end with a hub is given by:
f
PDCe eq1 �� (10.4-3)
The coefficient C1 is given by Figure 10.4-4.
For a uniform thickness shell per Figure 10.4-1 a),
rDD �� ieq (10.4-4)
EN 13445-3:2002 (E)Issue 9 (2004-02)
132
For a tapered shell per Figure 10.4-1 b),
( )2
Fieq
DDD
+= (10.4-5)
The following condition shall be met:
ee ≥af (10.4.6)
NOTE If the parameters P/f and es/Di are outside the limits provided in the graphs for C1 and/or C2 this methodcannot be used. In such cases it is recommended to use Design by Analysis, see Annexes B or C.
10.4.4 Flat ends welded directly to the shell
For normal operating load cases the required thickness for the end is given by the greatest of thefollowing:
⋅⋅=
mini2i1max
f
PDC
f
PDCe , (10.4-7)
where
{ }f f fmin ;= min s (10.4-8)
C1 is given by Figure 10.4-4 using fmin in place of f;
C2 is given by Figure 10.4-5.
When C2 is less than 0,30, only the first term of equation (10.4-7) shall be considered.
NOTE If the parameters P/f and es/Di are outside the limits provided in the graphs for C1 and/or C
2 this
method cannot be used. In such cases it is recommended to use Design by Analysis, see Annexes B or C.
For exceptional load cases and for testing load cases the required thickness for the end shall takeinto account only the first term of equation (10.4-7):
f
PDCe i1 ⋅= (10.4-9a)
In equations (10.4-7) to (10.4-9a), f, fs and P shall be understood as generic symbols valid for alltypes of load conditions (normal, exceptional, testing) and having the following meaning :
— for a normal operating case, f is fd, fs is (fd)s and P is Pd;
— for an exceptional operating case, f is fexp, fs is (fexp)s and P is Pexp;
— for an hydrostatic testing case, f is ftest, fs is (ftest)s and P is Ptest.
EN 13445-3:2002 (E)Issue 9 (2004-02)
141
— for set-in nozzles:
d dAe
= −e2 '
(10.6-6)
where
=
f
fAAA
b;min' (10.6-7)
A is the total area of the reinforcement in mm2, as defined in Figures 10.6-3 and 10.6 -4.
eb is the required thickness of the nozzle cylinder for pressure loading from 7.4.2.
( ) ababi0,8 eedl += (10.6-8)
( ) ababi ''0,8' eedl += (10.6-9)
When equations 10.6-5 and 10.6-6 give a value of the equivalent diameter which is negative, furthercalculation in accordance with 10.6.2.1 is not required.
Figure 10.6-1 — Single opening in a flat end
EN 13445-3 :2002 (E)Issue 1 (2002-05)
142
Figure 10.6-2 — Pair of openings in a flat end
Figure 10.6-3 — Set-on nozzle in a flat end
EN 13445-3:2002 (E)Issue 7 (2003-07)
181
The flange thickness shall be not less than:
( )h
R6
dnCf
Me
⋅−=
π(11.10-6)
Where two flanges of different internal diameters, both designed to the rules of this clause, are to bebolted 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
-
+ - 3 = 21
⋅
⋅
π(11.10-7)
where M1 and M2 are the values of MR calculated for the two flanges.
EN 13445-3:2002 (E)Issue 9 (2004-02)
182
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)
EN 13445-3:2002 (E)Issue 1 (2002-05)
183
Moments and moment arms shall be calculated in accordance with 11.5.3, except that equation(11.5-18) shall be replaced by equation (12.5-4).
B
BRHH
22
Dr
4 =
�
� (12.5-2)
aeh �� /2r (12.5-3)
A
C
HW
e
H
H
B
Gh
e
ae/2
hH
R
D
rh r
G
G
T
T
D
h D
Figure 12-1 — Bolted domed end with narrow face gasket
The moment on the flange in the operating condition is:
rrTTGGDDop hHhHhHhHM �������� (12.5-4)
The assembly condition and operating condition are both design conditions for the purpose ofdetermining nominal design stresses.
The absolute value of Mop shall be used in equation (12.5-6).
EN 13445-3:2002 (E)Issue 9 (2004-02)
184
The following conditions shall be checked:
a) the thickness shall be such that e ���eD;
b) the stress at the assembly condition is:
( )( ) f
eBBA
CBAM≤
⋅−
+2FA3
π(12.5-5)
c) the stress in the operating condition is:
( )( ) f
eBBA
CBAMeBH≤
⋅
++⋅⋅
2
Fopr
-
3
π(12.5-6)
12.5.2 Dome convex to pressure
The required thickness of the spherical dome shall be the greater of the thicknesses from 12.5.1 andclause 8.
Design of the flange shall be in accordance with 12.5.1 except that:
( ) ( ) rrGTTGDDop hHHHHhhHM ⋅−−+−= (12.5-7)
12.6 Bolted domed ends with full face joints
12.6.1 Bolted domed ends with full face joints concave to pressure
NOTE see Figure 12-2 for an illustration of loads and dimensions.
EN 13445-3:2002 (E)Issue 9 (2004-02)
185
dW
e
e/2
a
H
e
R h
H
H H H
h h
h
B
A
G
C
G
D
D
r
1
R
R
G
G T
T
O
b"
r
h D
Figure 12-2 — Bolted domed end with full face gasket
The rules in 12.6 shall only be applied to domed and bolted ends that are bolted to a tubesheet.
The following procedure shall apply to bolted domed ends with soft full face gaskets concave topressure:
a) Apply the rules of 12.5.1 to the spherical dome;
b) Calculate HD, hD, HT, hT, HG and hG using 11.6; eq (11.6-7a) shall be computed using g1=0;
c) Calculate Hr and hr using 12.5.1;
d) Calculate:
hHhHhHhHM rrTTGGDDR ⋅−⋅+⋅+⋅= (12.6-1)
EN 13445-3:2002 (E)Issue 9 (2004-02)
186
e) Complete the calculation for both bolt loads and flange design according to 11.6; eq (11.6-17)shall be computed using g1=0;
f) Increase the thickness e if necessary so that:
( )hr 2dBAefH −−⋅≤ π (12.6-2)
NOTE The limitation on Hr ensures that the flange ring hoop stress is not excessive.
12.6.2 Bolted domed ends with full face joints convex to pressure
The following requirements apply to bolted domed ends with full face joints convex to pressure:
a) the requirements of 11.6.4;
b) for the spherical dome, 12.5.2;
c) equation (12.6-2).
EN 13445-3:2002 (E)Issue 9 (2004-02)
267
efl,a efl,a efl,a ea
a) Flat facing b) Raised facing c) Single tongue and groove
efl,a efl,a
d) Double tongue and groove e) Groove for ring joint
Figure 13.10.4-1 Analysis thicknesses of tubesheet flange extension
13.10.5 Required thickness of tubesheet flange extension
a) The required thickness for assembly condition, Afl,e , is given by:
( ) ( ) A
A
ex
Afl,
f
M
A
DA
e ⋅
−++
=2
11
12
ννπ
(13.10.5-1)
where
2AGC
WM−⋅= (13.10.5-2)
b) The required thickness for operating conditions, efl,op , is given by:
( ) ( )f
M
A
DA
e op
ex
opfl,
⋅
−++
=2
11
12
ννπ
(13.10.5-3)
EN 13445-3:2002 (E)Issue 1 (2002-05)
268
where
� �MD C D G D C D G
b G mC G
Popex2
ex ex2
ex
�
�
���
�
���
�
��
�
�� �
�
���
�
���
�
��
�
�� �
�
��
�
��
�
�
��
�
���
4 2 4
2
42
2
2
(13.10.5-4)
c) The required thickness of the flange tubesheet extension, fle , is given by:
� � � �� � ; max opfl,Afl,fl eee � (13.10.5-5)
d) The analysis thickness of the tubesheet extension, afl,e , shall be at least equal to fle :
flafl, ee � (13.10.5-6)
EN 13445-3:2002 (E)Issue 1 (2005-05)
415
16.14 Global loads
16.14.1 Purpose
Rules are given for determining the minimum thickness of a cylindrical shell subject to acombination of loads in addition to pressure, at sections remote from the area of application oflocal loads and from structural discontinuities.
16.14.2 Specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in clause 4 and 16.3
D is the mean shell diameter;
F is the total axial force carried by shell at transverse section under considerationincluding pressure effects, positive if leading to tensile stresses;
l is the length of template for checking shape deviations;
K is a factor given by equation (16.14-15);
M is the global bending moment carried by shell at tranverse section considered. Itis always positive;
Pe is the (external) calculation pressure;
�e is the elastic limit as defined in 8.4;
w is the deviation from perfect shape;
� is a factor given by equation (16.14-16) or (16.14-17);
� is a factor given by equation (16.14-18) or (16.14-19);
�P is the stress calculated from the pressure;
�c is the maximum longitudinal compressive stress;
�c,all is the maximum permitted compressive longitudinal stress (see clause 16.14.8.1);
�max is the maximum longitudinal stress (positive if tensile), taking account of all loads;
�min is the minimum longitudinal stress (positive if tensile), taking account of all loads;
EN 13445-3:2002 (E)Issue 9 (2004-02)
416
16.14.3 General
The loads to be considered are an axial force (F) and a bending moment (M). Consideration shallbe given to load cases with zero pressure, when considering compressive stresses, to account forpossible loss of pressure during operation.
For the determination of the total axial force (F) two cases shall be distinguished:
1) The end of the cylindrical shell is free, movements not restricted. In this case the total axialforce F is defined as:
PDFF add ⋅⋅+= 2
4
π
where
Fadd is the additional axial force without effect of pressure (Fadd> 0 for tensile, Fadd < 0 forcompression);
P is the calculation pressure (P > 0 internal pressure, P < 0 external pressure)
The pressure component of the axial force is calculated with the mean diameter D toallow for the influence of radial stresses in the cylinder.
2) The movement of the end of cylindrical shell is restricted (e.g. heat exchanger tubes, jacketedwalls). In this case the total axial force may be calculated by means of any statically allowableassumptions (calculations by means of elastic theory are statically allowable but not the mostfavourable solution).
In a vertical vessel (F) also includes the weight of the vessel and its contents (including liquid)above (or below) the point under consideration, depending on whether the vessel support is below(or above) that point.
The moment (M) includes the effect of wind on a vertical vessel or weight for a horizontal vessel.Special consideration is required if there is a significant torque (twisting moment) carried by thecylinder.
16.14.4 Permissible individual loads
The maximum tensile force is:
feDF ⋅⋅= amaxt, π (16.14-1)
The maximum compressive force is:
allc,amaxc, σπ ⋅⋅= eDF (16.14-2)
The maximum bending moment is:
allc,amax σπ ⋅⋅= eDM 2
4 (16.14-3)
EN 13445-3:2002 (E)Issue 9 (2004-02)
565
Table C-3 — Illustration of assessment criteria
Stress Categories
Primary stress
Generalmembrane
stress
Localmembrane
stress
Bendingstress
Secondary
membrane + bending
stressPeak stress
Description
(For practicalexamples,
seeTable C-2)
Primary meanstress calculatedacross the wall
thickness withouttaking into accountdiscontinuities and
stressconcentrations.
Caused only bymechanical loads.
Primary meanstress calculatedacross the wallthickness taking
into account largediscontinuities, but
not stressconcentrations.
Caused only bymechanical loads.
Primary stresscomponent
proportional to thedistance from the
centroid of thesolid wall section.Does not include
discontinuitiesand stress
concentrations.
Caused only bymechanical loads
Self-equilibrating stressnecessary to satisfy the
continuity of thestructure. Occurs at
large discontinuities, butdoes not include stress
concentrations.
Can be caused by bothmechanical loads and
thermal effects.
a) Addition toprimary orsecondarystress becauseof stressconcentration.
b) Certain thermalstresses whichmay causefatigue, but notdistortion.
Symbol Pm PL1) Pb
Q(= Qm + Qb)
F
(σeq)Pm ≤ f
(eq. C.7.2-1) 2)
(σeq)PL ≤ 1,5f
(eq. C.7.2-2)
(∆σeq)P+Q ≤ 3 f
(eq. C.7.3-1)
3)7)
_______ = design loads− − − − − = operating loads
(σeq)P ≤ 1,5 f
(eq. C.7.2-3)2)
assessmentagaintsstatic
loading
Assessment 4) based on :5)
7)
(∆σeq)P+Qor
max (∆σi)or (∆σeq)P+Q+F
6)7)
fatigueassessment
(only ifrequired)
1) PL = Pm does not occur at the point in question.2) In assessment criteria given in equations (C.7.2-1) to (C.7.2-3), the value of the nominal design stress f shall be that
relevant for the loading condition under consideration (normal operation, exceptional operation, proof test), as defined inclause 6.
3) If (∆σeq)P+Q is greater than 3f, see C.7.64) Fatigue assessment shall consider all the applied cycles of various types, each of them being characterised by their own
relevant stress range (see footnotes 5 and 6), mean temperature and mean stress (if relevant). Clause 18 (detailedfatigue assessment) should normally be used.
5) The primary + secondary stress range (named "structural stress range" in clause 18 on detailed fatigue assessment)applies to assessment of welded joints. In that case, either the equivalent stress range (∆σeq)P+Q or the maximum
principal stress range max(∆σi) may be used.6) The primary + secondary + peak stress range, named "total (notch) stress range" in clause 18 on detailed fatigue
assessment, applies to assessment of unwelded parts.7) It should be observed that, depending on the model used, the computer programs usually give directly the primary +
secondary stresses (P + Q) or the primary + secondary + peak stresses (P + Q + F).
EN 13445-3:2002 (E)Issue 9 (2004-02)
566
C.7.2 Limitation of equivalent primary stresses
The equivalent primary membrane stresses shall for all loading conditions satisfy the relationships:
(σeq)Pm ≤ f (C.7.2-1)
(σeq)PL ≤ 1,5 f (C.7.2-2)
(σeq)P ≤ 1,5 f (C.7.2-3)
The value of f to be retained shall be that consistent with the type of loading condition considered(normal operation, exceptional operation, proof test), and shall be taken at the calculation temperatureof that condition.
In addition, the following conditions on the spacing between adjacent regions of local primarymembrane stresses shall be satisfied:
— two adjacent regions of local primary membrane stresses which exceed 1,1 times the nominaldesign stress f shall be at a distance of at least a5,2 eR ⋅ in meridional direction. Here, R is the
mid-surface radius of curvature and ea the wall analysis thickness;
— Discrete regions of local primary membrane stresses, (e.g. those resulting from concentratedloads acting on brackets), where the equivalent membrane stress exceeds 1,1 times the nominaldesign stress f, shall be spaced so that there is no overlapping of these regions.
C.7.3 Limitation of equivalent stress ranges resulting from primary + secondarystresses
The equivalent stress range resulting from variation of primary + secondary stresses between any twonormal operating conditions shall at all points satisfy the relationship:
(∆σeq)P+Q ≤ 3 f (C.7.3-1)
The value of f to be retained shall be that corresponding to loading conditions of normal operatingtype, but as an exception to the corresponding definition given in clause 6, its determination shall bebased on the yield strength of the material only, i.e.:
— for steels other than austenitic steels as per 6.2: Rp0,2/t
— for austenitic steels as per 6.3 or 6.4: Rp1,0/t
and it shall be taken at the following temperature:
t* = 0,75⋅tmax + 0,25⋅tmin (C.7.3-2)
where tmax and tmin are respectively the higher and the lower of the calculation temperatures of thetwo normal operating conditions considered.
C.7.4 Alternative to limitation of equivalent stresses and equivalent stress ranges
Deviations from the preceding limitations of equivalent stresses and equivalent stress ranges arepossible if it is proved by other means that the component meets the required safety margin againstgross plastic deformation and progressive plastic deformation stated in Annex B (e.g. by tests on thecomponent, plastic analysis, or the like).
EN 13445-3:2002 (E)Issue 9 (2004-02)
645
PE is the effective difference pressure in the tubed region [MPa], see J.7.2;
PM is a "pressure" [MPa], representing the resultant bending moment M1 (resultant of active andreactive moments, may be zero) at the outer boundary of the tubed region, see J.8.6;
PQ is a "pressure" [MPa], representing the resultant effective axial force (resultant of active andreactive forces, may be zero) at the outer boundary of the tubed region [MPa], see J.6.3, J.7.6;
PR is a "pressure" [MPa], representing the resultant active axial shear force at the outer boundaryof the tubed region [MPa], see J.6.2, J.7.5;
p is the tube pitch in the tubed region [mm], see Figure J-7;
QA, QI are reactive axial forces per area unit of the tubebundle in the tubed region [N/mm2 = MPa];QA in the outer zone, QI in the inner zone; see J.7.4;
[Qt], [Qc] are the allowable axial forces per area unit of the tubebundle in the tubed region [N/mm2 ];[Qt] for tensiom, [Qc] for compression; see J.7.3;
q is a parameter for the tube support [1], see J.9.3;
ro is the radius of the outermost tubehole centre as shown in Figure 13.7.3-1;
tS, tT are temperature ranges [K] between maximum and minimum temperature for shell (S), tubes(T). For their calculation, the assembly temperature shall be assumed to be +20oC;
u, v, w are auxiliary values [1], used in J.7.6;
xS, xT are relative areas of the tubesheet [1] subject to PS and PT respectively; see J.7.1;
Y is an auxiliary value [1], used in J.7.1;
αS, αT are the thermal expansion coefficients of shell, the tubes [K-1];
β is an auxiliary parameter given by equation (J.10.2-3);
γR is the rigidity factor for the untubed rim, see J.10.3;
∆M1, ∆M2 are ranges of bending moments in the tubesheet [Nmm/mm], used for fatigue check;
∆PF, ∆PS, ∆PT are ranges of pressures [MPa], used for a fatigue check, see J.10.2;
∆S1, ∆S2 are ranges of shear forces in the tubesheet [N/mm], used for fatigue check, see J.10.3;
∆σb1, ∆σb2 are ranges of calculated bending stresses in the tubesheet [Nmm2], used for fatiguecheck, see J.10.3;
∆σlT is the range of calculated longitudinal stress in the tubes [Nmm2], used for fatigue check;
∆σR is the allowable stress range in the tubesheet (plate) [Nmm2], used for fatigue check;
δX is a factor for tube to tubesheet relative strength [1], see J.5.2;
ζ is the force distribution parameter [1] for supported tubesheets; this is the relative radius of theboundary between the reactions QI and QA , see J.7.1.1 and J.7.6.2;
η is the moment distribution parameter [1] for all tubesheets; this is the relative radius of theboundary between constant and variable tangential bending moment in the tubesheet, seeJ.6.3, J.7.1.1 and J.7.6.3;
θ is a factor dependent on the tube pitch [1]; see J.5.1;
ϑ is the relative cross-sectional area of the tubes [1]; see J.7.1;
EN 13445-3:2002 (E)Issue 1 (2002-05)
646
�P is the relative shear strength of the tubesheet [1], see J.5.2;
�A , �C are geometric parameters for tube buckling [1], see J.7.1;
�R , �S are geometric parameters for untubed rims [1], see J.5.1;
�X is the coefficient of friction [1] for the tube-to-tubesheet connection by expansion, see J.7.3;
�* is the tubesheet ligament efficiency in bending (clause 13); it is in this annex replaced by �P ;
�P is the Poissons ratio for the undrilled tubesheet (plate) [1];
�S is the Poissons ratio for the shell [1];
�T is the Poissons ratio for the tubes [1];
�* is the effective Poissons ratio for the drilled tubesheet [1], obtained from subclause 13.7;
� is an active stress general [Nmm2], to be specified by subscripts, see J.7.3, �T(P) ;
[�] is an allowable stress general [Nmm2], to be specified by subscripts, see J.7.5;
�T(P) is an average longitudinal stress in the tubes [MPa], divided by safety factor 1,50, see J.7.3;
�B , �S , �U , �W and �P,t are load ratios [1], see J.2.2 and J.9;
�P is the relative bending strength of the tubesheet [1], see J.5.2;
� is a parameter for the untubed region at the boundary [1], see J.9.3;.
E is the stiffness parameter for the tubed region [1], see J.10.3;
R is the rigity factor for the tubed region [1], see J.10.3.
J.4 General
J.4.1 Conditions of applicability
J.4.1.1 Geometry and materials
The method applies for tubebundles (and some connected components) under the following conditions:
- The whole tubebundle (as the main component of a tubesheet heat exchanger) is axisymmetric.Permitted deviations from the axisymmetry are defined and limited below.
- Each tubesheet (also called "plate", subscript P) has only one central tubed region (nearly circular).Within the tubed region there are permitted small untubed areas, e.g. for pass partitions and tie-rods.The outer boundary of the tubed region needs not to be exact circular, but shall it be approximately.
- The tubesheet thickness eP and the pitch p are the same (constant) for the whole tubed region.For a second tubesheet within the tubebundle the thickness may be different, but again constant.
- Outside the tubed region the plate has an untubed region, beeing not too large.Their outside boundary shall be exact circular, as all other components outside also (with the onlysmall deviations due to the finite number of flange bolts).
- All (inner) tubes have the same cross section dT• eT and are from the same material.
- For tubebundles with two tubesheets all tubes have the same straight lengt LT ; no tie rod is connectedto both tubesheets. (For a tubebundle with only one tubesheet the lengths of the curved tubes may bearbitrary different. If a tubebundle with two tubesheets has curved tubes, it shall be calculated as anU-tube type, where each tubesheet is to be calculated separate.)
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 9 (2004-02)
650
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 Determine the outer tube limit from the tubesheet layout as follows:
d1(o) = 2·ro + dT (J.5.1-1)
J.5.1.1.2 Count the number NI of tubes, which inside an expected compact tubed region do not exist, but(I = ideally) could be inserted to get a equal spaced pitch. In untubed regions due to pass partitions andtie rods where equal spaced pitch is not possible so much tubes NI shall be inserted that the density oftubes ( = tubes per area) is the same as in the tubed region.
First determine the minimum number NImin, which give the smallest compact region with a convexboundary but include no additional tubes outside this boundary.
Then increase NI up to the maximum number NImax, which is defined by the limitation eq.(J.5.1-2), i.e. theabove mentioned compact region is a circle with:
d1(max) ≤ d1(0) . (J.5.1-2)
Figure J-7 shows two small examples how may be counted.
J.5.1.1.3 Calculate by equation (J.5.1-3) the diameters d1 corresponding to the numbers NI :
d1 = d1(min) for NI = NI,min and d1 = d1(max) for NI = NI,max :
Θπ ⋅+⋅⋅= IT
1 2NN
pd (J.5.1-3)
where
Θ = 1,155 for triangular pitch,Θ = 1,000 for square pitch is to be used.
J.5.1.1.4 Check that the condition eq. (J.1.5-2) indeed is met. If not, then NI,max is to be corrected.
Then calculate the following average value:
d1(av) = 0,5·(d1(min) + d1(max)) (J.5.1-4)
J.5.1.1.5 If the following condition eq.(J.5.1-5) is met
d1(max) - d1(min) ≤ min( 1,5·p ; 0,05·d1(av) ) (J.5.1-5)
then d1 = d1(av) is the asked value to be used in all the following calculations.
If condition eq.(J.5.1-5) is not met, then all following calculations should be made minimum two times forthe separate values d1 = d1(min) and d1 = d1(max) , possibly also three or more times with intermediatevalues of d1. Finally valid is the result with the greatest load ratio or the greatest required plate thickness.
NOTE The repeated calculations may be necessary to minimize the incorrectness from calculations for axisymmetriccomponents beeing really non-axisymmetric.
EN 13445-3:2002 (E)Issue 1 (2002-05)
693
Annex P(normative)
Classification of weld details to be assessed using principalstresses
P.1 Weld details and their corresponding classes for use in assessment based on principal stressrange are given in Tables P.1 to P.7.
The fatigue strengths of weld details for which the relevant potential failure mode is by fatiguecracking from the weld toe or weld surface are expressed in terms of the principal stress range on theparent metal surface adjacent to the crack initiation site (see 18.6.2.3.1).
Short or discontinuous welds, where the relevant potential failure is by fatigue cracking from the weldend or weld toe into the parent metal, are assessed on the basis of the maximum principal stressrange, �� , and classified on the basis that the weld is orientated in the least favourable directionwith respect to �� .
Continuous welds (e.g. seams, ring stiffener welds) may be treated differently if the maximumprincipal stress range acts in the direction which is within 45° of the direction of the weld. Then, theweld can be classified as being parallel to the direction of loading with respect to the maximumprincipal stress range and normal to the direction of loading with respect to the minimum principalstress range.
EN 13445-3:2002 (E)Issue 9 (2004-02)
694
Table P.1 — Seam welds
Class
DetailNo.
Joint type Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
1.1 Full penetration buttweld flush ground,including weldrepairs
Fatigue cracks usuallyinitiate at weld flaws
Weld to be proved free fromsurface-breaking flaws andsignificant sub-surface flaws(see EN 13445-5) by non-destructive testing.
90a)
90
71a)
71
1.2 Full penetration buttweld made from bothsides or from one sideon to consumableinsert or temporarynon-fusible backing
Weld to be proved free fromsignificant flaws (see EN13445-5) by non-destructivetesting.
80b)
80b)
80
63b)
63b)
71
1.3
e
Weld to be proved free fromsignificant flaws by non-destructive testing (see EN13445-5).
80b)
80
63b)
63
1.4 Weld to be proved free fromsignificant flaws (see EN13445-5) by non-destructivetesting.
�������
������
80
71
80
63
56
71
a) Use fe instead of few;b) Effect of misalignment to be included in calculated stress, see 18.10.4.
EN 13445-3:2002 (E)Issue 9 (2004-02)
695
Table P.1 — Seam welds (continued)
Class
DetailNo.
Joint type Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
1.5 Full penetration buttwelds made from oneside without backing
Weld to be proved to be fullpenetration and free fromsignificant flaws (see EN 13445-5) by non-destructive testing.
If full penetration can be assured.If inside cannot be visuallyinspected.
80
63b)
40b)
71
40b)
40b)
1.6 Full penetration buttwelds made from oneside onto permanentbacking
(1.6a) Circumferential seams only (see5.7).Backing strip to be continuousand, if attached by welding, tackwelds to be ground out or buriedin main butt weld, or continuousfillet welds are permitted.
Minimum throat = shellthickness. Weld root pass shall beinspected to ensure full fusion tobacking.
Single pass weld.
63
56
40
63
40
40
(1.6b) Circumferential seams only (see5.7).
Backing strip attached withdiscontinuous fillet weld.
63a) 63a)
1.7 Joggle joint Circumferential seams only (see5.7).
Minimum throat = shellthickness.
Weld root pass shall be inspectedto ensure full fusion.
Single pass weld.
63a)
56
40
63a)
40
40
a) Use fe instead of few;
b) Effect of misalignment to be included in calculated stress, see 18.10.4.
EN 13445-3:2002 (E)Issue 9 (2004-02)
696
Table P.2 — Shell to head or tubesheet
For principal stresses acting essentially normal to the weld
ClassDetailNo Joint type
Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
2.1 Welded-on head Head plate must haveadequate through-thicknessproperties to resist lamellartearing.
Full penetration welds madefrom both sides:- as-welded;- weld toes dressed(see 18.10.2.2).
Partial penetration weldsmade from both sides:- refers to fatigue cracking inshell from weld toe- refers to fatigue cracking inweld, based on stress rangeon weld throat
Full penetration welds madefrom one side without back-up weld:- if the inside weld can bevisually inspected and isproved free from weldoverlap and root concavity.- if the inside cannot bevisually inspected.
7180
63
32
63
40
6363
63
32
40
40
2.2 Welded-on headwith relief groove
Full penetration welds
Made from one side withthe inside weld groundflush
Made from one side:- if the inside weld can bevisually inspected and isproved free from weldoverlap and rootconcavity.- if the inside cannot bevisually inspected.
80
63
40
63
40
EN 13445-3:2002 (E)Issue 9 (2004-02)
697
Table P.2 — Shell to head or tubesheet (continued)
For principal stresses acting essentially normal to the weld
ClassDetailNo Joint type
Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
2.3 Set-in head (a)
(b)
(c)
Full penetration weldmade from both sides:refers to fatigue crackingfrom weld toe in shell:
- as-welded;- weld toes dressed (see18.10.2.2).
Partial penetration weldsmade from both sides:- refers to fatigue crackingin weld, based on weldthroat stress range;- refers to fatigue failure inshell;- refers to fatigue failure inhead.
Full penetration weldmade from one side.
7180
32
71
63
56
6363
32
71
63
40
EN 13445-3:2002 (E)Issue 9 (2004-02)
698
Table P.3 — Branch connections
Class
DetailNo.
Joint type Sketch of detail Comments Testinggroup1 or 2
Testinggroup
3
3.1 Crotch corner
Crack radiates from corner.Sketches show plane of crack.
Assessment by the method forunwelded parts based onequivalent stress is the normalapproach. However, simplifiedassessment, using class 100,according to annex Q, stillbased on equivalent stress, isallowedfew = 1.
100 100
3.2 Weld toe in shell Full penetration welds:- as-welded;- weld toes dressed(see 18.10.2.2).
Partial penetration welds
7180
63
6371
63
EN 13445-3:2002 (E)Issue 9 (2004-02)
699
Table P.3 — Branch connections (continued)
Class
DetailNo.
Joint type Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
3.3 Stressed weld metal Continuous weld stressedalong its length
Weld metal stressed normal toits length
Based on stress range parallel toweld on weld cross-sectionfew = 1.
Full penetration weld
Partial penetration weld
Based on stress range on weldthroat. few = 1.
71
71
32
71
71
32
3.4 Weld toe in branch As-welded;
Weld toes dressed(see 18.10.2.2)en = branch thickness inEquation 18.10-6
71
80
63
71
EN 13445-3:2002 (E)Issue 9 (2004-02)
700
Table P.4 — Jackets
For principal stresses acting essentially normal to the weld
ClassDetailNo Joint type
Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
4.1 Jacket connectionweld with shapedsealer ring
Full penetration weld to beproved free from significantflaws (see EN 13445-5) bynon-destructive testing
Welded from one side:- multi-pass weld with rootpass inspected to ensure fullfusion:
- single pass weld.- in all cases
Welded from both sides orfrom one side with back-upweld.
63
40
71
40
56
EN 13445-3:2002 (E)Issue 9 (2004-02)
701
Table P.5 — Attachments
Class for use with:
Structuralequivalent stress
range
Nominalequivalent stress
rangeDetailNo. Joint type Sketch of detail Comments
Testinggroup1 or 2
Testinggroup 3
Testinggroup1 or 2
Testinggroup 3
5.1 Attachmentof any shapewith an edgefillet or bevel– butt weldedto the surfaceof a stressedmember, withweldscontinuousaround theends or not Stresses acting essentially
parallel to weld
Stresses acting essentiallynormal to weld
For details withwelds continuousaround ends, oneclass increase ifweld toes dressed(see 18.10.2.2).
L ≤ 160 mm
L > 160 mm
few = 1.
One classincrease if weldtoes dressed (see18.10.2.2)
t ��55 mm
t > 55 mm
few = 1
71
71
71
71
71
71
71
71
56
50
56
50
56
50
56
50
5.2 Attachmentof any shapewith surfacein contactwith stressedmember, withweldscontinuousaround endsor not
For details withwelds continuousaround ends, oneclass increase ifweld toes dressed(see 18.10.2.2)
L ���������
w �������
L > 160 mm,w �������
L > 160 mm,w > 55 mm
71
71
71
71
71
71
56
50
45
56
50
45
EN 13445-3:2002 (E)Issue 9 (2004-02)
702
Table P.5 — Attachments (continued)
Class for use with:
Structuralequivalent
stress range
Nominalequivalent stress
rangeDetailNo.
Joint typeSketch of detail Comments
Testinggroup1 or 2
Testinggroup 3
Testinggroup1 or 2
Testinggroup 3
5.3 Continuousstiffener
Stresses acting essentiallyparallel to weld :
Stresses acting essentiallynormal to weld
Based on stressrange parallel toweld in stiffener.few = 1.
Full penetrationweld.
Partialpenetrationweld.
For fullpenetrationwelds, one classincrease if weldtoes dressed(see 18.10.2.2).
t ≤ 55 mm
t > 55 mm
80
71
71
71
71
71
71
71
80
71
56
50
71
71
56
50
EN 13445-3:2002 (E)Issue 9 (2004-02)
703
Table P.6 — Supports
For principal stresses acting essentially normal to the weldClass
DetailNo
Joint type Sketch of detail CommentsTestinggroup1 or 2
Testinggroup 3
6.1 Support on eitherhorizontal or verticalvessel
As-welded;
Weld toe in shelldressed (see 18.10.2.2)
71
80
71
80
6.2 Trunnion support As-welded;
Weld toe in shelldressed (see 18.10.2.2)
71
80
71
80
6.3 Saddle support As-welded;
Weld toe in shelldressed (see 18.10.2.2)
71
80
71
80
6.4 Skirt support Welded from both sides:
As-welded;
Weld toe in shelldressed (see 18.10.2.2).
Welded from one side.
71
80
56
71
80
56
6.5 Leg support (with orwithout reinforcingpad) with fillet weldto vessel continuousall around.
ab
a) Refers to fatiguecracking in the shell.
b) Refers to fatiguecracking in the leg.
80
71
80
71
EN 13445-3:2002 (E)Issue 9 (2004-02)
704
Table P.7 — Flanges and pads
For principal stresses acting essentially normal to the weld
ClassDetail
NoJoint type
Sketch of detail CommentsTestinggroup1 or 2
Testinggroup 3
7.1 Full penetration buttwelded neck flange orcompensation flangewith welding lug.
Weld to be proved free fromsurface-breaking andsignificant sub-surface flaws(see EN 13445-5) by non-destructive testing.
Weld made from both sidesor from one side with back-up weld or onto consumableinsert or temporary backing.
Weld made from one side:
- if full penetration can beassured;- if the inside cannot bevisually inspected.
80
63
40
63
40
7.2 Welded flange a
ab
a
Full penetration welds:
a) as-welded;
weld toes dressed(see 18.10.2.2).
Partial penetration welds:
a) refers to fatigue crackingfrom weld toe;b) refers to fatigue cracking inweld, based on stress range onweld throat.
71
80
63
32
63
63
63
32
EN 13445-3:2002 (E)Issue 9 (2004-02)
705
Table P.7 — Flanges and pads (continued)
For principal stresses acting essentially normal to the weld
ClassDetailNo Joint type
Sketch of detail Comments Testinggroup1 or 2
Testinggroup 3
7.3 Set-in flange or pad Full penetration weld:- as-welded- weld toes dressed(see 18.10.2.2).Fillet welded from both sides:- refers to fatigue crackingfrom weld toe- refers to fatigue cracking inweld, based on stress range onweld throat .
7180
63
32
6363
63
32
7.4 Set-in flange or pad,welded from bothsides a
b
a) refers to fatigue crackingfrom weld toea) refers to fatigue cracking inweld, based on stress range onweld throat .b) based on hoop stress inshell at weld root.
few = 1.
63
32
71
63
32
71
EN 13445-3:2002 (E)Issue 1 (2002-05)
706
Annex Q(normative)
Simplified procedure for the fatigue assessment ofunwelded zones
A simplified procedure for the fatigue assessment of unwelded steel is permissible using theclass 90 design data for welded components, independently of material static strength orsurface finish. The data are used in conjunction with equation 18.10-12, with fw replaced by fu.
If the applied stress is partly compressive, it is permissible to assume that the relevant valueof ��eq is the sum of the tensile component and 60 % of the compressive component. Thus,for mean stress � eq the correction factor fu becomes f f fe t c� �* / Keff in which:
cf = - 2
125,�
�
eq
R�
�
�
��
�
�
��
(Q-1)
fe is given in 18.11.1.2 and ft* in 18.10.5.2.