SIST EN 13445-3:2009/A2:2014
(Amendment)Unfired pressure vessels - Part 3: Design
Unfired pressure vessels - Part 3: Design
This Part of this European Standard specifies requirements for the design of unfired pressure vessels covered by EN 13445-1:2009 and constructed of steels in accordance with EN 13445-2:2009. EN 13445-5:2009, Annex C specifies requirements for the design of access and inspection openings, closing mechanisms and special locking elements. NOTE This Part applies to design of vessels before putting into service. It may be used for in service calculation or analysis subject to appropriate adjustment.
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Récipients sous pression non soumis à la flamme - Partie 3: Conception
Neogrevane tlačne posode - 3. del: Konstruiranje - Dopolnilo A2
Ta del tega evropskega standarda določa zahteve za konstruiranje neogrevane tlačne posode iz standarda EN 13445-1:2009, ki je izdelana iz jekel v skladu s standardom EN 13445-2:2009. Priloga C k standardu EN 13445-5:2009 določa zahteve za načrtovanje dostopa in odprtin za preglede, zapiralne mehanizme in posebne elemente za zaklepanje. OPOMBA: ta del se uporablja za konstruiranje posode pred zagonom. Uporabi se lahko za izračune med obratovanjem ali analize, ki se ustrezno prilagodijo.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 13445-3:2009/A2:2014
01-julij-2014
1HRJUHYDQHWODþQHSRVRGHGHO .RQVWUXLUDQMH'RSROQLOR$
Unfired pressure vessels - Part 3: Design
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Récipients sous pression non soumis à la flamme - Partie 3: Conception
Ta slovenski standard je istoveten z: EN 13445-3:2009/A2:2013
ICS:
23.020.30 7ODþQHSRVRGHSOLQVNH Pressure vessels, gas
MHNOHQNH cylinders
SIST EN 13445-3:2009/A2:2014 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST EN 13445-3:2009/A2:2014
---------------------- Page: 2 ----------------------
SIST EN 13445-3:2009/A2:2014
EUROPEAN STANDARD
EN 13445-3:2009/A2
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2013
ICS 23.020.30
English Version
Unfired pressure vessels - Part 3: Design
Récipients sous pression non soumis à la flamme - Partie 3: Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Conception
This amendment A2 modifies the European Standard EN 13445-3:2009; it was approved by CEN on 9 November 2013.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for inclusion of this
amendment into the relevant national standard without any alteration. Up-to-date lists and bibliographical references concerning such
national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.
This amendment exists in three official versions (English, French, German). A version in any other language made by translation under the
responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2013 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13445-3:2009/A2:2013 E
worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
Contents Page
Foreword .3
1 Modification to 16.12 .4
16.12 Vertical vessels with skirts .4
16.12.1 Purpose .4
16.12.2 Specific symbols and abbreviations (see Figure 16.12-1, Figure 16.12-2, Figure 16.12-3
and Figure 16.12-4) .4
16.12.3 Connection skirt / shell .5
16.12.4 Design of skirts without and with openings . 17
16.12.5 Design of anchor bolts and base ring for skirts . 20
2 Modification to Clause 22 . 35
22 Static analysis of tall vertical vessels on skirts . 35
22.1 Purpose . 35
22.2 Specific definitions . 36
22.2.1 Tall vertical vessels . 36
22.2.2 Dead loads . 36
22.2.3 Live loads . 36
22.2.4 Wind loads on columns . 36
22.2.5 Earthquake loads on columns . 36
22.2.6 Forces from attached external piping on columns . 36
22.3 Specific symbols and abbreviations . 37
22.4 Loads . 37
22.4.1 Pressures . 37
22.4.2 Dead loads . 37
22.4.3 Live loads . 38
22.4.4 Wind loads . 38
22.4.5 Earthquake loads . 40
22.4.6 Additional loads from attached external piping at nozzles and supports . 40
22.5 Load combinations . 41
Table 22-1 – Load combinations for columns . 42
22.6 Stress analysis of pressure vessel shells and skirts. 43
22.6.1 Cylindrical pressure vessel shells . 43
22.6.2 Conical sections of the pressure vessel . 43
22.6.3 Skirt shell . 43
22.7 Design of joint between skirt and pressure vessel (at dished end or cylindrical shell) . 43
22.8 Design of anchor bolts and base ring assembly . 43
22.9 Foundation loads . 44
Table 22-2 – Data for foundation design . 44
2
---------------------- Page: 4 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
Foreword
This document (EN 13445-3:2009/A2:2013) has been prepared by Technical Committee CEN/TC “Unfired
pressure vessels”, the secretariat of which is held by BSI.
This Amendment to the European Standard EN 13445-3:2009 shall be given the status of a national standard,
either by publication of an identical text or by endorsement, at the latest by June 2014, and conflicting national
standards shall be withdrawn at the latest by June 2014.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive 97/23/EC.
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this document.
This document was submitted to the Formal Vote under reference number EN 13445-3:2009/FprA5.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
3
---------------------- Page: 5 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
1 Modification to 16.12
Delete the existing 16.12 and substitute the following.
16.12 Vertical vessels with skirts
16.12.1 Purpose
This clause gives rules for the design of support skirts for vertical vessels. It deals with the skirt itself and local
stresses in the region where skirt and pressure vessel join and with the design of the base ring.
16.12.2 Specific symbols and abbreviations (see Figure 16.12-1, Figure 16.12-2,
Figure 16.12-3 and Figure 16.12-4)
The following symbols and abbreviations are in addition to those in Clause 4 and 16.3:
a is the lever-arm due to offset of centre-line of shell wall;
e is the analysis thickness of vessel wall;
B
e is the analysis thickness of skirt;
Z
f is the allowable design stress of skirt;
Z
f is the allowable design stress of the ring (Shape A);
T
r is the inside knuckle radius of torispherical end;
R is the inside crown radius of torispherical end;
is the mean shell diameter;
D
B
D is the mean skirt diameter;
Z
is the equivalent force in the considered point (n = p or n = q) in the skirt;
F
Zn
F is the weight of vessel without content;
G
is the vessel weight below section 2-2;
∆F
G
is the weight of content;
F
F
M is the global bending moment, at the height under consideration;
is the moment increase due to change of centre of gravity in cut-out section;
∆ M
P is the hydrostatic pressure;
H
W is the section modulus of ring according to Figure 16.12-1;
α is a stress intensification factor (see equations (16.12-33) to (16.12-36));
γ is the knuckle angle of a domed end (see Figure 16.12-2);
a
γ is part of the knuckle angle (see Figure 16.12-2);
σ is the stress;
Subscripts:
a refers to the external shell surface, i.e. side facing away from central axis of shell;
b refers to bending;
m refers to membrane stress;
4
---------------------- Page: 6 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
i refers to the inside shell surface;
o refers to the outside shell surface;
p is the point in the section under consideration where the global moment causes the greatest
tensile force in the skirt (e.g. side facing the wind = windward side);
q is the point in the section under consideration where the global moment causes the greatest
compressive force in the skirt (e.g. side facing away from the wind = leeward side);
1 is the section 1-1 (see Figures 16.12-1 to 16.12-4);
2 is the section 2-2;
3 is the section 3-3;
4 is the section 4-4;
5 is the section 5-5.
16.12.3 Connection skirt / shell
16.12.3.1 Conditions of applicability
a) For tall vertical vessels, the loads on the skirt shall be determined according to Clause 22.
b) Attention shall be paid to the need to provide inspection openings.
16.12.3.2 Forms of construction
The forms of construction covered in this section are:
a) Structure shape A: Skirt connection via support in cylinder area – Figure 16.12-1;
Cylindrical or conical skirt with angle of inclination ≤ 7° to the
axis;
b) Structure shape B: Frame connection in knuckle area - Figure 16.12-2;
°
Cylindrical or conical stand frame with angle of inclination ≤ 7
to the axis and welded directly onto the domed end in the area
° ° ;
0 ≤ γ ≤ 20
Wall thickness ratio: 0,5 ≤ e /e ≤ 2,25;
B Z
Torispherical end of Kloepper or Korbbogen type (as defined
in 7.2) or elliptical end having an aspect ratio K ≤ 2 (where K
as defined in equation (7.5-18)) and a thickness not less than
that of a Korbbogen-type end of same diameter;
c) Structure shape C: Skirt slipped over vessel shell - Figure 16.12-3;
Cylindrical skirt slipped over vessel shell and welded on
directly
It is assumed that, on either side of the joining seam for a
distance of 3 e , there is no disturbance due to openings, end
B
connections, vessel circumferential welds, etc.;
Note has to be taken of the risk of crevice corrosion.
5
---------------------- Page: 7 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
Outside the above limitations, subclauses 16.12.3.4.1 and 16.12.3.4.2 do not apply. Nevertheless, subclause
16.12.3.4.3 may be used subject to calculate existing stresses by elastic shell theories.
Figure 16.12-1 ― Shape A: Skirt connection with supporting ring
(Membrane forces due to self weight and fluid weight)
6
---------------------- Page: 8 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
Figure 16.12-2 ― Shape B: Skirt connection in knuckle area
(Membrane forces due to self weight and fluid weight)
7
---------------------- Page: 9 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
Figure 16.12-3 ― Shape C: Skipped-over skirt area
(Membrane forces due to self weight and fluid weight)
8
---------------------- Page: 10 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
(a) = Section 1-1 to 5-5 (b) = Section 4-4
Figure 16.12-4 ― Schematic diagram of stand frame - sections
16.12.3.3 Forces and moments
The values F and M at the respective sections n = 1 to n = 4 are determined as a function of the
n n
combination of all the loads to be taken into consideration in this load case (see Figure 16.12-4). Further
checking may be necessary if the wall thickness in the skirt is stepped.
16.12.3.4 Checking at connection areas (sections 1-1, 2-2 and 3-3)
In the connection area, sections 1, 2 and 3 defined in Figure 16.12-1, Figure 16.12-2 and Figure 16.12-3 have
to be checked. Checking is required for the membrane and the total stresses, while only the respective
longitudinal components are being taken into account.
The section force F in the skirt in the region of the joint depends on the position (n), i.e. whether the moment
Z
strengthen (q) or weakens (p) the load component:
9
---------------------- Page: 11 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
M
1
F =−−FF −F+ 4 (16.12-1)
Zp 1 G F
D
Z
M
1
F =−−FF −F− 4 (16.12-2)
Zq 1 G F
D
Z
where
F is the global additional axial force in section 1-1;
1
is the resulting moment due to external loads in section 1-1 above the joint; between the pressure-
M
1
loaded shell and skirt.
16.12.3.4.1 Membrane stresses
The checking procedure for membrane stresses is the same for structural shapes A, B and C. The membrane
stresses at point 1-1 are:
F +∆F +F
PD
m Zp G F
B
σ + (16.12-3)
1p
π De 4e
BBB
F +∆F +F
PD
m Zq G F
B
σ + (16.12-4)
1q
π De 4e
BBB
Check that:
m
σ ≤ f (16.12-5)
1p
m
σ ≤ f (16.12-6)
1q
The minimum required wall thickness in section 1-1 are obtained from next equations:
F +∆F +F
1 PD
m Zp G F
B
e + (16.12-7)
1p
fDπ 4
B
F +∆F +F
1 PD
m Zq G F
B
e + (16.12-8)
1q
fDπ 4
B
The calculation of this wall thickness is necessary for structural shape A.
m m
If σ or σ is a compressive stress, a stability check shall be carried out according to 16.14. This check is
1p 1q
not required if the longitudinal stress component is less than 1,6 times the value of the resulting meridian
membrane compressive stress for a vacuum or partial vacuum load case, provided the latter was checked
according to Clause 8. This applies also to other sections in the cylindrical area of the shell.
Regardless of the check point, the membrane stress in section 2-2 is:
10
=
=
=
=
---------------------- Page: 12 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
FF+∆ PD
m m m
FG B
σσ σ + (16.12-9)
2 2q 2p
π De 4e
BB B
Check that:
m
σ ≤ f (16.12-10)
2
The minimum required wall thickness in section 2-2 is obtained from next equation:
1 ∆+F F PD
m
GF B
e + (16.12-11)
2
fDπ 4
B
The calculation of this wall thickness is necessary for structural shape A.
In section 3-3 of the skirt, the membrane stresses are equal to:
F
m Zp
σ = (16.12-12)
3p
π De
ZZ
F
m Zq
σ = (16.12-13)
3q
π De
ZZ
Check that:
m
σ ≤ f (16.12-14)
3p Z
m
σ ≤ f (16.12-15)
3q Z
The minimum required wall thicknesses in section 3-3 are obtained from next equations:
F
1
m Zp
e = (16.12-16)
3p
fDπ
ZZ
F
1
m Zq
e = (16.12-17)
3q
fDπ
ZZ
The calculation of this wall thickness is necessary for structural shape A.
m m
If σ or σ is a compressive stress, the stability check may also be carried out according to 16.14.
3p 3q
16.12.3.4.2 Bending stresses
a) Structural shape A - Figure 16.12-1
The local bending moment at points p and q is:
M 0,5 D−DF (16.12-18)
( )
p Z B Zp
11
=
=
===
---------------------- Page: 13 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
M 0,5 D−DF (16.12-19)
( )
q Z B Zq
The total section modulus of the support ring at the point n is calculated as follows:
π
2 2 m2 m2 2 m 2
W D+−e D−eh+ 2e−e−e D+ 0,5 e−e D (16.12-20)
( ) ( ) ( )
p Z Z B B B 1p 2 B Z 3p Z
4
π
2 2 m2 m2 2 m 2
W D+−e D−eh+ 2e−e−e D+ 0,5 e−e D (16.12-21)
( ) ( ) ( )
q Z Z B B B 1q 2 B Z 3q Z
4
The factor 0,5 in the third summand allows for the type of transition from the skirt to the connecting ring as
shown in Figure 16.12-1. If the allowable stresses f of the vessel and/or f of the skirt are less than that of the
Z
nd rd
support ring f , the 2 and/or the 3 summand in equations (16.12-20) and (16.12-21) have to be reduced
T
with the respective ratio f / f and/or f / f
T Z T
b) Structural shape B - Figure 16.12-2
The eccentricity a of the shell wall centreline causes a bending moment:
M =aF. (16.12-22)
p Zp
M =aF. (16.12-23)
q Zq
with:
22
a 0,5 e++e 2ee cosγ (16.12-24)
( )
B Z BZ
D +e − De+
BB Z Z
cosγ 1− (16.12-25)
( )
2( re+ )
B
The corresponding bending stresses in sections 1-1 to 3-3 at the outer surface (a):
6M
p
bb
σσa aC (16.12-26)
( ) ( )
1p 2p
2
π De
BB
6M
q
bb
σσa aC (16.12-27)
( ) ( )
1q 2q
2
π De
BB
6M
p
b
σ aC= (16.12-28)
( )
3p
2
π De
ZZ
6M
q
b
σ aC= (16.12-29)
( )
3q
2
π De
ZZ
Within the range 0,5 ≤ e /e ≤ 2,25, the correction factor C can be taken approximately equal to:
B Z
2
(16.12-30)
C = 0,63 - 0,057 (e /e )
B Z
12
==
==
=
=
=
=
=
---------------------- Page: 14 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
This relationship was determined from numerical calculations using the finite element method. Because of the
large number of parameters, a simplification is made which, under certain circumstances, can lead to
significant over-dimensioning, e.g. in the case of “Korbbogen” ends.
In the region of sections 1-1 to 2-2 the above bending stress components are superimposed by the bending
effect caused by the internal pressure in the knuckle.
P+ PD
( ) γ
bb H B
σσpp α−1 (16.12-31)
( ) ( )
12
4e γ
B a
The stress intensification factor α is obtained as follows:
1) calculate the intermediate value y
y = 125 e /D (16.12-32)
B B
°)
2) For Kloepper-type ends (with γ = 45
a
— for e /D > 0,008:
B B
2
α=9,3341−+2,287 7 yy0,33714 (16.12-33)
— for e /D ≤ 0,008:
B B
−−16,1y 1,615 36 y
α= 6,37181× 2,718 28+×3,636 6 2,718 28 + 6,673 6 (16.12-34)
3) °)
for Korbbogen-type ends or elliptical ends which fulfil the requirements of 16.12.3.2 b (with γ = 40
a
— for e /D > 0,008:
B B
α 4,2− 0,2y (16.12-35)
— for e /D ≤ 0,008:
B B
−4,233 5 y
α=1,518 61×+2,718 28 3,994 (16.12-36)
c) Structural shape C - Figure 16.12-3
The eccentricity a off the shell axis causes a bending moment at point n:
M 0,5 D−⋅DF (16.12-37)
( )
p Z B Zn
M 0,5 D−DF⋅ (16.12-38)
( )
q Z B Zq
Resulting bending stresses in section 1-1 and section 2-2:
3M
bb p
σσ (16.12-39)
1p 2p
2
π De
BB
13
==
=
=
=
==
---------------------- Page: 15 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
3M
bb q
σσ (16.12-40)
1q 2q
2
π De
BB
In section 3-3:
6M
b p
σ = (16.12-41)
3p
2
π De
ZZ
6M
b q
σ = (16.12-42)
3q
2
π De
ZZ
Bending stresses caused by pressure are ignored, e.g.:
bb
σσpp 0 (16.12-43)
( ) ( )
12
16.12.3.4.3 Total stresses and strength conditions
The total stresses shall be obtained as follows:
a) Structure shape A
At each point, the strength condition shall be checked as follows:
1) location p : with M from equation (16.12-18) and W from equation (16.12-20)
p p
MW/ ≤ f (16.12-44)
p pT
2) location q: with M from equation (16.12-19) and W from equation (16.12-21)
q q
MW/ ≤ f (16.12-45)
q qT
b) Structure shape B and C
1) the total stresses at point p, section 1-1, are obtained from next equations
- on the inner surface (i)
tot m b b
σ=σσ− ap+σ (16.12-46)
( ) ( )
1pi 1p 1p 1
- on the outer surface (o)
tot m b b
σ=σσ+−apσ (16.12-47)
( ) ( )
1po 1p 1p 1
2) the total stresses at point q, section 1-1, are obtained from next equations
- on the inner surface (i)
tot m b b
σ=σσ−+apσ (16.12-48)
( ) ( )
1qi 1q 1q 1
14
==
==
---------------------- Page: 16 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
- on the outer surface (o)
tot m b b
σ=σσ+−apσ (16.12-49)
( ) ( )
1qo 1q 1q 1
3) The total stresses in section 2-2 at point p are:
- on the inner surface (i)
tot m b b
σ=σσ+ ap+σ (16.12-50)
( ) ( )
2pi 2p 2p 2
- on the outer surface (o)
tot m b b
σ=σσ−−apσ (16.12-51)
( ) ( )
2po 2p 2p 2
4) The total stresses in section 2-2 at point q are:
- on the inner surface (i)
tot m b b
σ=σσ++apσ (16.12-52)
( ) ( )
2qi 2q 2q 2
- on the outer surface (o)
tot m b b
σ=σσ−−apσ (16.12-53)
( ) ( )
2qo 2q 2q 2
5) In section 3-3 the total stresses at point p are:
- on the inner surface (i)
tot m b
σ σσ− (16.12-54)
3pi 3p 3p
- on the outer surface (o)
tot m b
σ σσ+ (16.12-55)
3po 3p 3p
6) In section 3-3 the total stresses at point q are:
- on the inner surface (i)
tot m b
σ σ−σ (16.12-56)
3qi 3q 3q
- on the outer surface (o)
tot m b
σ σσ+ (16.12-57)
3qo 3q 3q
7) In case of ductile materials the total stresses obtained by equations (16.12-46) to (16.12-57) shall
is the design stress in each part:
satisfy next equation where f
s
i) Section 1-1
15
=
=
=
=
---------------------- Page: 17 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
2
m
σ
1
tot 1p
σ ≤−f 3 (16.12-58)
1pi S
1,5 f
2
m
σ
1
tot 1p
σ ≤−f 3 (16.12-59)
1po S
1,5 f
2
m
σ
1
tot 1q
σ ≤−f 3 (16.12-60)
1qi S
1,5 f
2
m
σ
1
tot 1q
σ ≤−f 3 (16.12-61)
1qo S
1,5 f
ii) Section 2-2
2
m
σ
1
tot 2p
σ ≤−f 3 (16.12-62)
2pi S
1,5 f
2
m
σ
1
tot 2p
σ ≤−f 3 (16.12-63)
2po S
1,5 f
2
m
σ
1
tot 2q
σ ≤−f 3 (16.12-64)
2qi S
1,5 f
2
m
σ
1
tot 2q
σ ≤−f 3 (16.12-65)
2qo S
1,5 f
iii) Section 3-3
2
m
σ
1
tot 3p
σ ≤−f 3 (16.12-66)
3pi S
1,5 f
Z
2
m
σ
1
tot 3p
σ ≤−f 3 (16.12-67)
3po S
1,5 f
Z
2
m
σ
1
tot 3q
σ ≤−f 3 (16.12-68)
3qi S
1,5 f
Z
16
---------------------- Page: 18 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
2
m
σ
1
tot 3q
σ ≤−f 3 (16.12-69)
3qo S
1,5 f
Z
16.12.4 Design of skirts without and with openings
16.12.4.1 Specific symbols and abbreviations
d mean diameter of the opening reinforcement (see Figure 16.12-5)
e analysis wall thickness of the skirt wall thickness e
a3 3
e analysis wall thickness of the reinforcement thickness e (see Figure 16.12-5)
t
at
h length of outer part of the opening reinforcement (see Figure 16.12-5)
t
l total length of the opening reinforcement (see Figure 16.12-5)
t
( i index of the opening when more than one opening exist)
y distance between neutral axis and centre of gravity at section 4-4
G
y maximum distance between centre of gravity and outer edge of section 4-4
max
A area of the cross section with openings at section 4-4
4
including analysis wall thicknesses of skirt and nozzles
D mean diameter of the skirt
3
F
vertical compressive force acting in cross section 4-4, see Figure 16.12-4
4
F maximum compressive force according to equation 16.14-2
c,max
with σ according to equation 16.14-20 as defined in Table 22-1
c,all
M bending moment acting in cross section 4-4, see Figure 16.12-4
4
M maximum bending moment according to equation 16.14-3
max
with σ according to equation 16.14-20 as defined in Table 22-1
c,all
W
elastic section modulus of the cross section with openings at section 4-4 including
4
analysis wall thicknesses of skirt and nozzles
δ half angle of the opening, see Figure 16.12-4 (b)
Ψ , Ψ weakening factors of area and elastic section modulus of cross section 4-4
1 2
16.12.4.2 Check of the skirt in regions without openings
For skirts without openings and in regions of skirts where no openings exist the design check shall be
performed as described in 22.6.3.
NOTE Cross sections below regions with openings may be governed because the acting forces and moments are
higher.
16.12.4.3 Check of the skirt in regions with openings
Determine values of F and M acting in cross section 4-4 and F and M with σ for all load cases
4 4 c,max max c,all
defined in Table 22-1.
The check according to equation 16.12-70 shall be performed for the cross section where the largest
weakening effect exists, e.g. where the left term in equation 16.12-70 is maximal.
17
---------------------- Page: 19 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
M +F⋅ y
F
4 4 G
4
+≤1,0 (16.12-70)
Ψ⋅FMΨ ⋅
1 c,max 2 max
with:
A
4
ψ = min {1; }
1
π⋅⋅De
33a
and
4⋅W
4
ψ = min {1; } (16.12-71)
2
2
π⋅⋅De
3
a3
16.12.4.4 Cross section parameter for cross section with one opening
Figure 16.12-5 ― Skirt cross section with one opening
The half angle of the opening δ in radians is determined in equation 16.12-72 and the parameter A , W and
4 4
y of the cross section are given in equations 16.12-73 to 16.12-75.
G
δ= arcsin(dD/ ) (16.12-72)
3
A AA+ (16.12-73)
4 St
with:
A= ()πδ−⋅De⋅
Sa33
and
0,5⋅D⋅e ⋅d− 2⋅⋅le ⋅y
33a t at t
y = (16.12-74)
G
A
4
18
=
---------------------- Page: 20 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
with:
y 0,5⋅D⋅cosδ+−hl0,5⋅
t 3 tt
22 2
Ι +⋅A (y +l /12)−A⋅y
S t tt 4 G
W = (16.12-75)
4
y
max
with:
D
3
3
Ι= [πδ−− sinδ⋅cosδ ]⋅e⋅( )
Sa3
2
and
y max 0,5⋅D⋅cosδ++h y ; 0,5⋅D−y
{ }
max 3 t G 3 G
16.12.4.5 Cross section parameter for cross section with more than one opening
In the general (but seldom) case that more similar-sized openings exist in the section 4-4 (see Figure 16.12-6
with the example of two openings) the parameter A , W and y of the whole cross section shall be calculated
4 4 G
accordingly.
Figure 16.12-6 ― Skirt cross section with two openings
NOTE Whereas the calculation of the section area A is easy done by replacing ΣA instead of A and Σδ instead of
4 ti t
i
δ in formula for A , the calculation of elastic section modulus W requires to find the weakest axis with the corresponding
S 4
distances y and y and second moments of area in this direction using the rules for transforming second moments of
G max
area due to translation and rotation.
In the special (but common) case that one large opening and one or more small openings exist in the section
4-4 the following procedure may be used:
1. Check that the condition 16.12-76 is fulfilled for each of the small openings i:
19
=
=
---------------------- Page: 21 ----------------------
SIST EN 13445-3:2009/A2:2014
EN 13445-3:2009/A2:2013 (E)
A=2⋅⋅l e ≥ A =δ⋅De⋅ (16.12-76)
ti, ti, ati, δ ,i i 33a
in which the limitation: le≤⋅8 is met.
ti,,ati
2. When condition 16.12-76 is not fulfilled then increase the reinforcement area A of the opening in
t,i
question.
3. Apply conditions and equation 16.12-70 to 16.12-75 taking into account the one large opening in section
4-4 only.
16.12.5 Design of anchor bolts and base ring f
...
SLOVENSKI STANDARD
SIST EN 13445-3:2009/oprA5:2012
01-maj-2012
1HRJUHYDQHWODþQHSRVRGHGHO .RQVWUXLUDQMH'RSROQLOR$
Unfired pressure vessels - Part 3: Design
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Récipients sous pression non soumis à la flamme - Partie 3: Conception
Ta slovenski standard je istoveten z: EN 13445-3:2009/prA5
ICS:
23.020.30 7ODþQHSRVRGHSOLQVNH Pressure vessels, gas
MHNOHQNH cylinders
SIST EN 13445-3:2009/oprA5:2012 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST EN 13445-3:2009/oprA5:2012
---------------------- Page: 2 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EUROPEAN STANDARD
DRAFT
EN 13445-3:2009
NORME EUROPÉENNE
EUROPÄISCHE NORM
prA5
March 2012
ICS
English Version
Unfired pressure vessels - Part 3: Design
Récipients sous pression non soumis à la flamme - Partie Unbefeuerte Druckbehälter - Teil 3: Konstruktion
3: Conception
This draft amendment is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 54.
This draft amendment A5, if approved, will modify the European Standard EN 13445-3:2009. If this draft becomes an amendment, CEN
members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for inclusion of this amendment
into the relevant national standard without any alteration.
This draft amendment was established by CEN in three official versions (English, French, German). A version in any other language made
by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has
the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to
provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and
shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13445-3:2009/prA5:2012: E
worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Contents Page
Foreword . 3
1 Modification to 16.12 . 4
2
---------------------- Page: 4 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Foreword
This document (EN 13445-3:2009/prA5:2012) has been prepared by Technical Committee CEN/TC 54
“Unfired pressure vessels”, the secretariat of which is held by BSI.
This document is currently submitted to the CEN Enquiry.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive(s).
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this
document.
3
---------------------- Page: 5 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
1 Modification to 16.12
Delete the existing text of 16.12. and substitute the following:
16.12 Vertical vessels with skirts
16.12.1 Purpose
This clause gives rules for the design of support skirts for vertical vessels. It deals with the skirt itself and
local stresses in the region where skirt and pressure vessel join and with the design of the base ring.
16.12.2 Specific symbols and abbreviations (see Figure 16.12-1 to Figure 16.12-4)
The following symbols and abbreviation are in addition to those in clauses 4 and 16.3:²
a is the lever-arm due to offset of centre-line of shell wall;
e is the thickness of vessel wall;
B
e is the thickness of skirt;
Z
f is the allowable design stress of skirt;
Z
f is the allowable design stress of the ring (Shape A);
T
r is the inside knuckle radius of torispherical end;
R is the inside crown radius of torispherical end;
D is the mean shell diameter;
B
D is the mean skirt diameter;
Z
F is the equivalent force in the considered point (n = p or n = q) in the skirt;
Zn
F is the weight of vessel without content;
G
∆F is the vessel weight below section 2-2;
G
F is the weight of content;
F
M is the global bending moment, at the height under consideration;
∆ M is the moment increase due to change of centre of gravity in cut-out section;
P is the hydrostatic pressure;
H
W is the section modulus of ring according to Figure 16.12-1;
α is a stress intensification factor (see equations 16.12-33 to 16.12-36);
γ is the knuckle angle of a domed end (see Figure 16.12-2);
a
γ is part of the knuckle angle (see Figure 16.12-2);
σ is the stress;
4
---------------------- Page: 6 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Subscripts:
a refers to the external shell surface, i.e. side facing away from central axis of shell;
b refers to bending (superscript);
m refers to membrane stress (superscript);
i refers to the inside shell surface;
o refers to the outside shell surface;
p is the point in the section under consideration where the global moment causes the greatest
tensile force in the skirt (e.g. side facing the wind = windward side);
q is the point in the section under consideration where the global moment causes the greatest
compressive force in the skirt (e.g. side facing away from the wind = leeward side);
1 is the section 1-1 (see Figures 16.12-1 to 16.12-4);
2 is the section 2-2;
3 is the section 3-3;
4 is the section 4-4.
5 is the section 5-5.
16.12.3 Connection skirt/shell
16.12.3.1 Conditions of applicability
a) The load on the skirt shall be determined according to generally accepted practice;
NOTE For tall vertical vessels the loads on the skirt shall be determined according to clause 22.
b) Attention shall be paid to the need to provide inspection openings.
16.12.3.2 Forms of construction
The forms of construction covered in this section are:
a) Structure shape A: skirt connection via support in cylinder area - Figure16.12-1;
o
Cylindrical or conical skirt with angle of inclination ≤ 7 to the axis;
b) Structure shape B: Frame connection in knuckle area - Figure 16.12-2;
°
Cylindrical or conical stand frame with angle of inclination ≤ 7 to the axis and
° ° ;
welded directly onto the domed end in the area 0 ≤ γ ≤ 20
Wall thickness ratio: 0,5 ≤ e /e ≤ 2,25;
B z
Torispherical end of Kloepper or Korbbogen type (as defined in 7.2) or
elliptical end having an aspect ratio K ≤ 2 (where K as defined in equation
(7.5-18)) and a thickness not less than that of a Korbbogen-type end of same
diameter;
c) Structure shape C: skirt slipped over vessel shell - Figure 16.12-3;
5
---------------------- Page: 7 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Cylindrical skirt slipped over vessel shell and welded on directly
It is assumed that, on either side of the joining seam for a distance of 3 e ,
B
there is no disturbance due to openings, end connections, vessel
circumferential welds, etc.;
Note has to be taken of the risk of crevice corrosion.
F = ∆ F
G G
NOTE Outside the above limitations, subclauses 16.12.3.4.1 and 16.12.3.4.2 do not apply. Nevertheless,
subclause 16.12.3.4.3 may be used subject to calculate existing stresses by elastic shell theories.
φ D
B
Figure 16.12-1 ― Shape A: Skirt connection with supporting ring
(Membrane forces due to self weight and fluid weight)
6
---------------------- Page: 8 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Figure 16.12-2 ― Shape B: Skirt connection in knuckle area
(Membrane forces due to self weight and fluid weight)
7
---------------------- Page: 9 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Figure 16.12-3 ― Shape C: Skipped-over skirt area
(Membrane forces due to self weight and fluid weight)
8
---------------------- Page: 10 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
(a) = Section 1-1 to 5-5 (b) = Section 4-4
Figure 16.12-4 ― Schematic diagram of stand frame - sections
16.12.3.3 Forces and moments
The values F and M at the respective sections n=1 to n=4 are determined as a function of the
n n
combination of all the loads to be taken into consideration in this load case (see Figure 16.12-4). Further
checking may be necessary if the wall thickness in the skirt is stepped.
16.12.3.4 Checking at connection areas (sections 1-1, 2-2 and 3-3)
In the connection area, sections 1 to 3 defined in Figure 16.12-1 to 16.12-3 have to be checked. Checking
is required for the membrane and the total stresses, while only the respective longitudinal components
are being taken into account.
9
---------------------- Page: 11 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
The section force F in the skirt in the region of the joint depends on the position (n), i.e. whether the
Z
moment strengthen (q) or weakens (p) the load component:
M
1
F =−F −F −F +4 (16.12-1)
Zp 1 G F
D
Z
M
1
F =−F −F −F −4 (16.12-2)
Zq 1 G F
D
Z
where
F is the global additional axial force in section 1-1;
1
M is the resulting moment due to external loads in section 1-1 above the joint; between the
1
pressure-loaded shell and skirt.
1.1.1.1.1 Membrane stresses
The checking procedure for membrane stresses is the same for structural shapes A, B and C. The
membrane stresses at point 1-1 are:
F +∆F + F
PD
Zp G F
m
B
σ = + (16.12-3)
1p
πD e 4e
B B B
F +∆F + F
PD
Zq G F
m
B
σ = + (16.12-4)
1q
πD e 4e
B B B
check that:
m
σ ≤f (16.12-5)
1p
m
σ ≤f (16.12-6)
1q
The minimum required wall thickness in section 1-1 are obtained from next equations:
F +∆F + F
PD
1 Zp G F
m B
e = +
1p
f πD 4
B
(16.12-7)
F +∆F + F
1 PD
Zq G F
m
B
e = +
1q
f πD 4
B
(16.12-8)
The calculation of this wall thickness is necessary for structural shape A.
m m
If σ or σ is a compressive stress, a stability check shall be carried out according to 16.14. This check
1p 1q
is not required if the longitudinal stress component is less than 1,6 times the value of the resulting
meridian membrane compressive stress for a vacuum or partial vacuum load case, provided the latter
was checked according to clause 8. This applies also to other sections in the cylindrical area of the shell.
Regardless of the check point, the membrane stress in section 2-2 is:
F +∆F PD
m m m
F G B
σ =σ =σ = + (16.12-9)
2 2q 2p
πD e 4e
B B B
10
---------------------- Page: 12 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Check that:
m
σ ≤f (16.12-10)
2
The mathematically necessary wall thickness in section 2-2 is obtained from next equation:
1 ∆F + F PD
m G F B
e = + (16.12-11)
2
f πD 4
B
The calculation of this wall thickness is necessary for structural shape A.
In section 3-3 of the skirt, the membrane stresses are equal to:
F
Zp
m
(16.12-12)
σ =
3p
πD e
Z Z
F
Zq
m
(16.12-13)
σ =
3q
πD e
Z Z
Check that:
m
σ ≤f (16.12-14)
3p Z
m
σ ≤f (16.12-15)
3q Z
The mathematically necessary wall thicknesses in section 3-3 are obtained from next equations:
F
1
m Zp
e = (16.12-16)
3p
f πD
Z Z
F
1
m Zq
e = (16.12-17)
3q
f πD
Z Z
The calculation of this wall thickness is necessary for structural shape A.
m m
If σ or σ is a compressive stress, the stability check may also be carried out according to 16.14.
3p 3q
16.12.3.4.2 Bending stresses
a) Structural shape A - Figure 16.12-1
The local bending moment at points p and q is:
M =0,5()D −D F (16.12-18)
p Z B Zp
M =0,5()D −D F (16.12-19)
q Z B Zq
The total section modulus of the support ring at the point n is calculated as follows:
2 2 2
π
2 2 m m 2 m
W =()D +e −D −e h + 2e −e −e D +0,5 e −e D (16.12-20)
p Z Z B B B 1p 2 B Z 3p Z
4
11
---------------------- Page: 13 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
2 2 2
π
2 2 m m 2 m
W =()D +e −D −e h +2e −e −e D +0,5e −e D (16.12-21)
q Z Z B B B 1q 2 B Z 3q Z
4
The factor 0,5 in the third summand allows for the type of transition from the skirt to the connecting ring as
shown in Figure 16.12-1. If the allowable stresses f of the vessel and/or fZ of the skirt are less then that of
the support ring fT, the 2nd and/or the 3rd summand in equations (16.12-20) and (16.12-21) have to be
reduced with the respective ratio f / fT and/or fZ / fT
b) Structural shape B - Figure 16.12-2
The eccentricity a of the shell wall centreline causes a bending moment at point n:
M =a.F (16.12-22)
p Zp
M =a.F (16.12-23)
q Zq
with
2 2
a=0,5 e +e +2e e cos()γ (16.12-24)
B Z B Z
D +e −D +e
B B Z Z
cos()γ =1− (16.12-25)
2()r+e
B
The corresponding bending stresses in sections 1-1 to 3-3 at the outer surface (a):
6M
p
b b
σ ()a =σ ()a =C (16.12-26)
1p 2p
2
πD e
B B
6M
q
b b
σ ()a =σ ()a = C
1q 2q
2
πD e
B B
(16.12-27)
6M
p
b
σ ()a =C
3p
2
πD e
Z Z
(16.12-28)
6M
q
b
σ ()a =C
3q
2
πD e
Z Z
(16.12-29)
Within the range 0,5 ≤ e /e ≤ 2,25, the correction factor C can be taken approximately equal to:
B z
2 (16.12-30)
C = 0,63 - 0,057 (e /e )
B z
This relationship was determined from numerical calculations using the finite element method. Because of
the large number of parameters, a simplification is made which, under certain circumstances, can lead to
significant over-dimensioning, e.g. in the case of “Korbbogen” ends.
In the region of sections 1-1 to 2-2 the above bending stress components are superimposed by the
bending effect caused by the internal pressure in the knuckle.
()P+P D γ
b b H B
σ ()p =σ ()p = α−1 (16.12-31)
1 2
4e γ
B a
12
---------------------- Page: 14 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
The stress intensification factor is obtained as follows:
α
1) calculate the intermediate value
y
y = 125 e /D (16.12-32)
B B
2) For Kloepper-type ends (with γ = 45°)
a
for e /D > 0,008:
B B
2
α=9,3341−2,2877y+0,33714y (16.12-33)
for e /D ≤ 0,008:
B B
−16,1y −1,61536y
α=6,37181× 2,71828 +3,6366 × 2,71828 +6,6736 (16.12-34)
3) for Korbbogen-type ends or elliptical ends which fulfil the requirements of 16.12.3.2 b
(with γ = 40°)
a
for e /D > 0,008:
B B
α=4,2−0,2y (16.12-35)
for e /D ≤ 0,008:
B B
−4,2335y
α=1,51861× 2,71828 +3,994 (16.12-36)
c) Structural shape C - Figure 16.12-3
The eccentricity a off the shell axis causes a bending moment at point n:
M =0,5()D −D ⋅F (16.12-37)
p Z B Zn
M =0,5()D −D ⋅F (16.12-38)
q Z B Zq
Resulting bending stresses in section 1-1 and section 2-2:
3M
p
b b
σ =σ =
1p 2p
2
πD e
B B
(16.12-39)
3M
b b q
σ =σ = (16.12-40)
1q 2q
2
πD e
B B
In Section 3-3:
6M
p
b
σ = (16.12-41)
3p
2
πD e
Z Z
6M
q
b
σ = (16.12-42)
3q
2
πD e
Z Z
13
---------------------- Page: 15 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Bending stresses caused by pressure are ignored, e.g.:
b b
σ ()p =σ ()p =0 (16.12-43)
1 2
16.12.3.4.3 Total stresses and strength conditions
The total stresses shall be obtained as follows:
a) Structure shape A
At each point, the strength condition shall be checked as follows:
1) location p : with M from equation (16.12-18) and W from equation (16.12-20)
p p
M /W ≤f (16.12-44)
p p T
2) location q: with M from equation (16.12-19) and W from equation (16.12-21)
q q
M /W ≤f (16.12-45)
q q T
b) Structure shape B and C
1) the total stresses at point p, section 1-1, are obtained from next equations
on the inner surface (i)
tot m b b
() ( )
σ =σ −σ a +σ p (16.12-46)
1pi 1p 1p 1
on the outer surface (o)
tot m b b
σ =σ +σ ()a −σ (p) (16.12-47)
1po 1p 1p 1
2) the total stresses at point q, section 1-1, are obtained from next equations
on the inner surface (i)
tot m b b
σ =σ −σ ()a +σ (p) (16.12-48)
1qi 1q 1q 1
on the outer surface (o)
tot m b b
σ =σ +σ ()a −σ (p) (16.12-49)
1qo 1q 1q 1
3) The total stresses in section 2-2 at point p are :
on the inner surface (i)
tot m b b
σ =σ +σ ()a +σ (p) (16.12-50)
2pi 2p 2p 2
on the outer surface (o)
tot m b b
σ =σ −σ ()a −σ (p) (16.12-51)
2po 2p 2p 2
14
---------------------- Page: 16 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
4) The total stresses in section 2-2 at point q are :
on the inner surface (i)
tot m b b
σ =σ +σ ()a +σ (p) (16.12-52)
2qi 2q 2q 2
on the outer surface (o)
tot m b b
σ =σ −σ ()a −σ (p) (16.12-53)
2qo 2q 2q 2
5) In section 3-3 the total stresses at point p are :
on the inner surface (i)
tot m b
σ =σ −σ (16.12-54)
3pi 3p 3p
on the outer surface (o)
tot m b
σ =σ +σ (16.12-55)
3po 3p 3p
6) In section 3-3 the total stresses at point q are :
on the inner surface (i)
tot m b
σ =σ −σ (16.12-56)
3qi 3q 3q
on the outer surface (o)
tot m b
σ =σ +σ (16.12-57)
3qo 3q 3q
7) In case of ductile materials the total stresses obtained by equations (16.12-46) to (16.12-57)
shall satisfy next equation where f is the design stress in each part:
s
a) Section 1-1
2
m
σ
1
1p
tot
σ ≤f 3−
1pi S
1,5 f
(16.12-58)
2
m
σ
1
1p
tot
σ ≤f 3−
1po S
1,5 f
(16.12-59)
2
m
σ
1
1q
tot
σ ≤f 3− (16.12-60)
1qi S
1,5 f
2
m
σ
1
1q
tot
σ ≤f 3− (16.12-61)
1qo S
1,5 f
15
---------------------- Page: 17 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
b) Section 2-2
2
m
σ
1
2p
tot
σ ≤f 3− (16.12-62)
2pi S
1,5 f
2
m
σ
1
2p
tot
σ ≤f 3− (16.12-63)
2po S
1,5 f
2
m
σ
1
tot 2q
σ ≤f 3− (16.12-64)
2qi S
1,5 f
2
m
σ
1
2q
tot
σ ≤f 3− (16.12-65)
2qo S
1,5 f
c) Section 3-3
2
m
σ
1
3p
tot
σ ≤f 3− (16.12-66)
3pi S
1,5 f
Z
2
m
σ
1
3p
tot
σ ≤f 3− (16.12-67)
3po S
1,5 f
Z
2
m
σ
1
3q
tot
σ ≤f 3− (16.12-68)
3qi S
1,5 f
Z
2
m
σ
1
3q
tot
σ ≤f 3− (16.12-69)
3qo S
1,5 f
Z
16.12.4 Design of skirts without and with Openings
As a simplification the check of strength can reliably be provided using the cross section values A and
4
W of the
4
16.12.4.1 Specific symbols and abbreviations
d - mean diameter of the opening reinforcement (see Figure 16.12-5)
e - analysis wall thickness of the skirt wall thickness e
a3 3
e - analysis wall thickness of the reinforcement thickness e (see Figure 16.12-5)
at t
h - length of outer part of the opening reinforcement (see Figure 16.12-5)
t
l - total length of the opening reinforcement (see Figure 16.12-5)
t
( i - index of the opening when more than one opening exist)
y - distance between neutral axis and centre of gravity at section 4-4
G
y - maximum distance between centre of gravity and outer edge of section 4-4
max
16
---------------------- Page: 18 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
A - area of the cross section with openings at section 4-4 including analysis wall thicknesses of
4
skirt and nozzles
D - internal diameter of the skirt
3
F - vertical compressive force acting in cross section 4-4, see Figure 16.12-4
4
F - maximum compressive force according to equation 16.14-2 with σ acc. to equation 16.14-
c,max c,all
20 as defined in Table 22-1
M - bending moment acting in cross section 4-4, see Figure 16.12-4
4
M - maximum bending moment according to equation 16.14-3
max
with σ acc. to equation 16.14-20 as defined in Table 22-1
c,all
W - elastic section modulus of the cross section with openings at section 4-4 including analysis
4
wall thicknesses of skirt and nozzles
δ - half angle of the opening, see Figure 16.12-4 (b)
Ψ , Ψ - weakening factors of area and elastic section modulus of cross section 4-4
1 2
16.12.4.2 Check of the skirt in regions without openings
For skirts without openings and in regions of skirts where no openings exist the design check shall be
performed as described in 22.6.3.
NOTE Cross sections below regions with openings may be governed because the acting forces and moments
are higher.
16.12.4.3 Check of the skirt in regions with openings
Determine values of F and M acting in cross section 4-4 and F and M with σ for all load cases
4 4 c,max max c,all
defined in Table 22-1.
The check according to equation 16.12-70 shall be performed for the cross section where the largest
weakening effect exists, e.g. where the left term in equation 16.12-70 is maximal.
M +F ⋅ y
F
4 4 G
4
+ ≤ 1,0 (16.12-70)
Ψ ⋅F Ψ ⋅M
1 c,max 2 max
A 4 ⋅W
4 4
with: ψ = min {1 ; } and ψ = min {1; } (16.12-71)
2
1 2
π ⋅D ⋅e
π ⋅D ⋅e
3
3 a3
a3
17
---------------------- Page: 19 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
16.12.4.4 Cross section parameter for cross section with one opening
Figure 16.12.5 — Skirt cross section with one opening
The half angle of the opening δ is determined in equation 16.12-72 and the parameter A , W and y of
G
4 4
the cross section are given in equations 16.12-73 to 16.12-75.
δ = arcsin(d/D ) (16.12-72)
3
A = A + A
(16.12-73)
4 S t
A = (π −δ ) ⋅D ⋅e
with:
S 3 a3
A = 2 ⋅ l ⋅ e
and
t t at
0,5 ⋅D ⋅ e ⋅ d − 2 ⋅l ⋅ e ⋅ y
3 a3 t at t
y = (16.12-74)
G
A
4
with: y = 0,5⋅D ⋅ cosδ +h − 0,5⋅l
t 3 t t
2 2 2
Ι + A ⋅ (y +l /12) −A ⋅y
S t t t 4 G
W =
(16.12-75)
4
y
max
3
Ι = [π − δ − sinδ ⋅ cosδ ]⋅e ⋅ (0,5 ⋅D )
with:
S a3 3
and y = max{}0,5 ⋅D ⋅ cosδ +h + y ; 0,5 ⋅D − y
max 3 t G 3 G
16.12.4.5 Cross section parameter for cross section with more than one opening
In the general (but seldom) case that more similar-sized openings exist in the section 4-4 (see Figure
16.12-6 with the example of two openings) the parameter A , W and y of the whole cross section shall
G
4 4
be calculated accordingly.
18
---------------------- Page: 20 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
Figure 16.12.6 — Skirt cross section with two openings
NOTE Whereas the calculation of the section area A is easy done by replacing ΣA instead of A and Σδ
4 ti t
i
instead of δ in formula for A , the calculation of elastic section modulus W requires to find the weakest axis with the
S 4
corresponding distances y and y and second moments of area in this direction using the rules for transforming
G max
second moments of area due to translation and rotation.
In the special (but common) case that one large opening and one or more small openings exist in the
section 4-4 the following procedure may be used:
1. Check that the condition 16.12-76 is fulfilled for each of the small openings i:
A = 2 ⋅l ⋅e ≥ A = δ ⋅D ⋅e (16.12-76)
t,i t,i at,i δ ,i i 3 a3
in which the limitation: l ≤ 8 ⋅ e is met
t,i at,i
2. When condition 16.12-76 is not fulfilled then increase the reinforcement area A of the opening in
t,i
question.
3. Apply conditions and equation 16.12-70 to 16.12-75 taking into account the one large opening in
section 4-4 only.
unpierced shell in the case of a circular non-stiffened opening as long as the resulting stresses are
corrected by applying a weakening factor v .
A
16.12.5 Design of anchor bolts and base ring for skirts
16.12.5.1 Specific symbols and abbreviations
b - radial width of bearing plate
1
b - outer radial width of bearing plate (outer radius of bearing plate minus outer radius of skirt)
2
b - lever arm of bolts (bolt circle radius minus outer radius of skirt)
3
b - width of top plate in circumferential direction
4
b - radial width of top plate or top ring plate (outer radius of top plate minus outer radius of skirt)
5
b - spacing between gussets or support plates with bolts in between for type 2 and 4 version B and
6
type 3 (see figure 16.12-8,16.12-9 and 16.12-10)
19
---------------------- Page: 21 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
b - spacing between gussets or support plates without bolts in between for type 2 and 4 version B
7
and type 3 (see figure 16.12-8,16.12-9 and 16.12-10) but with bolts in between for type 2 and 4
version A
b - spacing between anchor bolts
8
d nominal bolt diameter
B0-
f - nominal design stress for skirt wall as defined in table 22-1 depending from load condition
3
f - nominal design stress for bearing plate as defined in table 22-1 depending from load condition
4
f - nominal design stress for top plate or top ring plate as defined in table 22-1 depending from load
5
condition
f - nominal design stress for gussets or support plate as defined in table 22-1 depending from load
7
condition
f - nominal design stress for anchor bolts as defined in table 22-1 depending from load condition
B
f - allowable concrete compression stress for permanent actions
C
e - nominal wall thickness of the skirt
3
e - analysis wall thickness of the skirt
a3
e - nominal wall thickness of the bearing plate
4
e - analysis wall thickness of the bearing plate
a4
e - nominal wall thickness of the top plates or top ring plate
5
e - analysis wall thickness of the top plates or top ring plate
a5
e - nominal wall thickness of the gussets or support plates
7
e - analysis wall thickness of the gussets or support plates
a7
h - height of the gussets or base ring assembly
1
h - height of the support plates (h =h -e -e )
1S 1S 1 a4 a5
n - number of anchor bolts
B
A - tensile stress area of one bolt
B
D - internal diameter of the skirt
3
D - internal diameter of the bearing plate
4
D - bolt circle diameter
BC
D - mean diameter of bearing ring plate (D =D +b )
CR CR 4 1
E - modulus of elasticity of gussets or support plates
7
F - bolt load on one bolt as defined in 16.12.5.2
B
F - design bolt load on one bolt as defined in 16.12.5.2
B,d
F - load on concrete below whole bearing plate as defined in 16.12.5.2
C
F - design load on concrete below whole bearing plate as defined in 16.12.5.2
C,d
16.12.5.2 Anchor bolt and concrete forces
The maximum anchor bolt forces F and the maximum concrete force F caused by the global axial force
B C
F and the global bending moment M acting in section 5-5 (see Figure 16.12-4) shall be calculated by
5 5
equation (16.12-77) and (16.12-78) respectively:
4 ⋅M
1
5
F = −F ⋅ (16.12-77)
B 5
D n
BC B
4 ⋅M
5
F = + F (16.12-78)
C 5
D
CR
20
---------------------- Page: 22 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
NOTE For tall vertical vessels F and M are defined in Table 22-2 as vertical force F and as bending moment
5 5 V
M respectively for the different load condition status.
B
The required nominal bolt d diameter may be calculated according to equation (16.12-79) or chosen
B0
and then checked by equation (16.12-85):
4 ⋅F
B
d ≥ + ∆ (16.12-79)
B0 B
π ⋅ f
B
0,9382 ⋅P, where P is bolt pitch for metric bolts, see ISO 261
with
∆ =
B
0,9743⋅ P, where P is bolt pitch for UN, UNR bolts, see ASME B1.1
The preloading force FA of the anchor bolts applied during assembly and the associated torque moment
Mt shall be calculated by equation (16.12-80) and (16.12-81) respectively:
F = Φ ⋅A ⋅ f (16.12-80)
A B B,op
f - nominal design stress for anchor bolts for operation condition as defined in 22.3
B,op
Φ assembly factor (recommended value Φ = 0,5)
M = µ ⋅F ⋅d (16.12-81)
t A B0
µ effective friction factor (recommended value µ = 0,2 as combination of friction in the thread and
at the nut)
π
2
A = ⋅d (16.12-82)
B Be
4
d effective bolt diameter = tensile stress diameter of bolt (d = d − ∆ )
Be
Be B0 B
∆ see above
B
The design anchor bolt force F and the design concrete force F are defined by equation (16.12-83)
B,d C,d
and (16.12-84) respectively:
F = max{}F ;F (16.12-83)
B,d A B
F = max{}n ⋅F ; F (16.12-84)
C,d B A C
16.12.5.3 Stress checks for anchor bolts and concrete
The tensile stress check of anchor bolts is given in equation (16.12-85)
F
B,d
σ = ≤ f (16.12-85)
B B
A
B
The compression stress check of the concrete below the base ring bearing plate is given in equation
(16.12-86)
F
C,d
σ = ≤ f = f /1,35 (16.12-86)
C C cd
π ⋅D ⋅b
CR 1
21
---------------------- Page: 23 ----------------------
SIST EN 13445-3:2009/oprA5:2012
EN 13445-3:2009/prA5:2012 (E)
f - allowable concrete compression stress for permanent actions
C
f - allowable concrete compression strength acc. to EN 1992-1-1, 3.16
Cd
with the specifi
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.