# 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

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### 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.

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SIST EN 13445-3:2009/A2:2014

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

=

=

=

=

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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

=

=

===

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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

==

==

=

=

=

=

=

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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

==

=

=

=

==

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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

==

==

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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

=

=

=

=

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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

=

=

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

**...**

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