BS_EN1591-1-2001

BRITISH STANDARD BS EN 1591-1:2001

Flanges and their joints — Design rules for gasketed circular flange connections —

Part 1: Calculation method

The European Standard EN 1591-1:2001 has the status of a British Standard

ICS 23.040.60

NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW

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BS EN 1591-1:2001

This British Standard, having been prepared under the direction of the Engineering Sector Committee, was published under the authority of the Standards Committee and comes into effect on 15 September 2001

© BSI 08-2001

ISBN 0 580 38204 4

National foreword

This British Standard is the official English language version of EN 1591-1:2001.

The UK participation in its preparation was entrusted to Technical Committee PSE/2, Jointing materials and their compounds, which has the responsibility to:

A list of organizations represented on this committee can be obtained on request to its secretary.

Cross-referencesThe British Standards which implement international or European publications referred to in this document may be found in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue.A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application.

Compliance with a British Standard does not of itself confer immunity from legal obligations.

— aid enquirers to understand the text;

— present to the responsible European committee any enquiries on the interpretation, or proposals for change, and keep the UK interests informed;

— monitor related international and European developments and promulgate them in the UK.

Summary of pagesThis document comprises a front cover, an inside front cover, the EN title page, pages 2 to 49 and a back cover.

The BSI copyright date displayed in this document indicates when the document was last issued.

Amendments issued since publication

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EUROPEAN STANDARD

NORME EUROPÉENNE

EUROPÄISCHE NORM

EN 1591-1

April 2001

ICS 23.040.60

English version

Flanges and their joints - Design rules for gasketed circularflange connections - Part 1: Calculation method

Brides et leurs assemblages - Règles de calcul desassemblages à brides circulaires avec joint - Partie 1:

Méthode de calcul

Flansche und ihre Verbindungen - Regeln für dieAuslegung von Flanschverbindungen mit runden Flanschen

und Dichtung - Teil 1: Berechnungsmethode

This European Standard was approved by CEN on 8 March 2001.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the officialversions.

CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATIONC OM ITÉ EUR OP ÉEN DE NOR M ALIS AT IONEUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: rue de Stassart, 36 B-1050 Brussels

© 2001 CEN All rights of exploitation in any form and by any means reservedworldwide for CEN national Members.

Ref. No. EN 1591-1:2001 E

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Page 2EN 1591-1:2001

ContentsPage

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Requirement for use of the Calculation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1 Use of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Subscripts and special marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.4 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Calculation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1 Flange parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Bolt parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Gasket parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Internal forces (in the joint) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.1 Applied loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Compliance of the joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Minimum forces necessary for the gasket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4 Internal forces in assembly condition (I = 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.5 Internal forces in subsequent conditions (I = 1, 2, ...) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Checking of the admissibility of the load ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.2 Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.3 Gasket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.4 Integral flange and collar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.5 Blank flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346.6 Loose flange with collar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Annex A (informative) Requirement for limitation of non-uniformity of gasket stress . . . . . . . . . . . . . . . . . 35

Annex B (informative) Dimensions of standard metric bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Annex C (informative) Scatter of bolting-up methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Annex D (informative) Assembly using torque wrench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Annex E (informative) Flange rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Annex F (informative) Diagram of calculation sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Annex G (informative) Joints with spacer seated flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Annex ZA (informative) Clauses of this European Standard addressing essential requirementsor other provisions of the PED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

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Page 3EN 1591-1:2001

Foreword

This European Standard was prepared by the Technical Committee CEN/TC 74 "Flanges and their joints", thesecretariat of which is held by DIN.

This European Standard shall be given the status of a national standard, either by publication of an identical text orby endorsement, at the latest by October 2001, and conflicting national standards shall be withdrawn at the latestby October 2001.

This European Standard has been prepared under a mandate given to CEN by the European Commission and theEuropean Free Trade Association. This European Standard is considered as a supporting standard to otherapplication and product standards which in themselves support an essential safety requirement of a New ApproachDirective and will appear as a normative reference in them.

For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this standard.

EN 1591 consists of two parts:

– EN 1591-1 Flanges and their joints – Design rules for gasketed circular flange connections – Part 1: Calculationmethod

– ENV 1591-2 Flanges and their joints – Design rules for gasketed circular flange connections – Part 2: Gasketparameters

The Calculation method satisfies both leaktightness and strength criteria. The behaviour of the complete flanges-bolts-gasket system is considered. Parameters taken into account include not only basic ones such as:

– fluid pressure;

– material strength values of flanges, bolts and gaskets;

– gasket compression factors;

– nominal bolt load;

but also:

– possible scatter due to bolting up procedure;

– changes in gasket force due to deformation of all components of the joint;

– influence of connected shell or pipe;

– effect of external axial forces and bending moments;

– effect of temperature difference between bolts and flange ring

Calculation for sealing performance is based on elastic analysis of the load/deformation relations between all partsof the flange connection, corrected by a possible plastic behaviour of the gasket material. Calculation for mechanicalresistance is based on (plastic) limit analysis of the flange-shell combination. Both internal and external loads areconsidered. Load conditions covered include initial assembly, hydrostatic test, and all significant subsequentoperating conditions. The calculation steps are broadly as follows:

1) First, the required minimum initial bolt load (to be reached at bolting-up) is determined, so that in anysubsequent specified load condition, the residual force on the gasket will never be less than the minimum meanvalue required for the gasket (value is gasket data from ENV 1591-2, for instance). The determination of this loadis iterative, because it depends on the effective gasket width, which itself depends on the initial bolt load.

2) Then, the internal forces that result from the selected value of initial bolt load are derived for all loadconditions, and the admissibility of combined external and internal forces is checked as follows:

– bolting-up condition: the check is performed against the maximum possible bolt force that may result from thebolting-up procedure;

– test and operating conditions: checks are performed against the minimum necessary forces, to ensure that theconnection will be able to develop these minimum forces without risk of yielding, except in highly localized areas.Higher actual initial bolting results in (limited) plastic deformation in subsequent conditions (test, operation).

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Page 4EN 1591-1:2001

But the checks so defined assure that these deformations will not reduce the bolt force to a value less than theminimum required.

If necessary, the flange rotations may be estimated in all load conditions, using annex E, and the values obtained,compared with the relevant gasket limits which could apply.

Checks for admissibility of loads imply safety factors which are those applied to material yield stress or strength inthe determination of the nominal design stresses used in the Calculation method.

NOTE Where flanges are used to comply with other codes the Calculation method does not specify valuesfor nominal stresses.

Nevertheless, since all significant design parameters are accounted for, the use of low safety factors is madepossible by special use of nominal design stresses:

– for assembly conditions the nominal design stresses have the same values as for the hydraulic pressure tests(normally higher than for operating conditions);

– the nominal design stresses for the bolts are determined by the same rules as relevant for the flange and shellmaterial e.g. same safety factor on yield stress.

The minimum force required on the gasket for leak tightness considerations may be established by two differentways:

1) Use of tabulated gasket factors, for example those given in ENV 1591-2, which are based on industrialexperience and correspond to mainly gas and steam leak rates.

2) Derivation from measured leak rate versus gasket stress data, if available for the gasket, for example as inENV 1591-2. This permits design to be based on any specified maximum leak rate.

The use of this Calculation method is particularly useful for joints where the bolt load is monitored when bolting up.The greater the precision of this, the more benefit can be gained from application of the Calculation method.

In the present stage of development, the Calculation method is not applicable to joints with narrow metal-to-metalcontact (with the exception of joints with spacer seated flanges (see annex G)), or to joints whose rigidity variesappreciably across gasket width.

A chart illustrating the calculation process is given in annex F.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of the followingcountries are bound to implement this European Standard: Austria, Belgium, Czech Republic, Denmark, Finland,France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden,Switzerland and the United Kingdom.

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Page 5EN 1591-1:2001

1 Scope

1.1 General

This European Standard defines a Calculation method for bolted, gasketed, circular flange joints. Its purpose is toensure structural integrity and control of leaktightness. ENV 1591-2 gives values for gasket properties which can beused in the Calculation method.

1.2 Requirement for use of the Calculation method

Where permitted, the Calculation method is an alternative to design validation by other means e.g.

– special testing;

– proven practice;

– use of standard flanges within permitted conditions.

1.3 Validity

1.3.1 Geometry

The Calculation method is applicable to the configurations having:

– flanges whose section is given or may be assimilated to those given in Figures 4 to 12;

– four or more identical bolts uniformly distributed;

– gasket whose section and configuration after loading can be assimilated by one of those given in Figure 3;

– flange dimension which meet the following conditions:

a) 0,2 ≤ bF/eF ≤ 5,0; 0,2 ≤ bL/eL ≤ 5,0

b) eF ≥ max e2; dB0; pB × 3

(0,01...0,10) ×pB/bF

c) cosϕs ≥ 1/(1 + 0,01 ds/es)

NOTE 1 For explanations of symbols see clause 3.

NOTE 2 The condition bF/eF ≤ 5,0 need not to be met for collar in combination with loose flange.

NOTE 3 The condition is for limitation of non-uniformity of gasket pressure dueeF ≥ pB × 3

(0,01...0,10)pB/bF

to spacing of bolts. The values 0,01 and 0,10 are to be applied for soft (non-metallic) and hard (metallic)gaskets respectively. A more precise criterion is given in annex A.

NOTE 4 Attention may need to be given to the effects of tolerances and corrosion on dimensions; referenceshould be made to other codes under which the calculation is made, for example values are given inEN 13445 and EN 13480.

The following configurations are outside the scope of the Calculation method:

– flanges of essentially non-axisymmetric geometry, e.g. split loose flanges, web reinforced flanges;

– flange connections having direct or indirect metal to metal contact between flanges inside and/or outside thegasket, inside and/or outside the bolt circle, except the special case of spacer-seated flanges, which is coveredin annex G.

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Page 6EN 1591-1:2001

1.3.2 Materials

Values of nominal design stresses are not specified in this Calculation method. They depend on other codes whichare applied, for example these values are given in EN 13445 and EN 13480.

Design stresses for bolts are to be determined as for flanges and shells. The model of the gaskets is modelled byelastic behaviour with a plastic correction.

For gaskets in incompressible materials which permit large deformations (for example: flat gaskets with rubber asthe major component), the results given by the Calculation method can be excessively conservative (i.e. requiredbolting load too high, allowable pressure of the fluid too low, required flange thickness too large, etc.) because itdoes not take account of such properties.

1.3.3 Loads

This Calculation method applies to the following load types:

– fluid pressure: internal or external;

– external loads: axial forces and bending moments;

– axial expansion of flanges, bolts and gasket, in particular due to thermal effects.

1.3.4 Mechanical model

The Calculation method is based on the following mechanical model:

a) Geometry of both flanges and gasket is axisymmetric. Small deviations such as those due to a finite numberof bolts, are permitted. Application to split loose flanges or oval flanges is not permitted.

b) The flange ring cross-section (radial cut) remains undeformed. Only circumferential stresses and strains in thering are treated; radial and axial stresses and strains are neglected. This presupposition requires compliance withcondition 1.3.1 a).

c) The flange ring is connected to a cylindrical shell. A tapered hub is treated as being an equivalent cylindricalshell of calculated wall thickness, which is different for elastic and plastic behaviour, but always between theactual minimum and maximum thickness. Conical and spherical shells are treated as being equivalent cylindricalshells with the same wall thickness; differences from cylindrical shell are explicity taken into account in thecalculation formula.

This presupposition requires compliance with 1.3.1 c).

At the connection of the flange ring and shell, the continuity of radial displacement and rotation is accounted forin the calculation.

d) The gasket contacts the flange faces over a (calculated) annular area. The effective gasket width (radial) bGe

may be less than the true width of gasket. This effective width bGe is calculated for the assembly condition (I = 0)and is assumed to be unchanged for all subsequent load conditions (I = 1,2 ...). The calculation of bGe includesthe elastic rotation of both flanges as well as the elastic and plastic deformations of the gasket (approximately)in assembly condition.

e) The modulus of elasticity of the gasket may increase with the compressive stress Q on the gasket. TheCalculation method uses a linear model: EG = E0 + K1 × Q. This is the unloading elasto-plastic secant modulusmeasured between 100 % and 33 % of the highest stress (Q) in assembly conditions.

f) Creep of the gasket under compression is approximated by a creep factor gc (see ENV 1591-2).

g) Thermal and mechanical axial deformations of flanges, bolts and gasket are taken into account.

h) Loading of the flange joint is axisymmetric. Any non-axisymmetric bending moment is replaced by anequivalent axial force, which is axisymmetric according to equation (44).

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Page 7EN 1591-1:2001

i) load changes between load conditions cause internal changes of bolt and gasket forces. These are calculatedwith account taken of elastic deformations of all components. To ensure leaktightness, the required initialassembly force is calculated (see 5.4) to ensure that the required forces on the gasket are achieved under allconditions (see 5.3 and 5.5).

j) load limit proofs are based on limit loads for each component. This approach prevents excessive deformations.The limits used for gaskets, which depend on Qmax are only approximations.

The model does not take account of the following:

k) Bolt bending stiffness and bending strength. This is a conservative simplification. However the tensile stiffnessof the bolts includes (approximately) the deformation within the threaded part in contact with the nut or threadedhole (see equation (34)).

l) Creep of flanges and bolts.

m) Different radial deformations at the gasket (this simplification has no effect for identical flanges).

n) Fatigue proofs (usually not taken into account by codes like this).

o) external torsional moments and external shear loads, e.g. those due to pipework.

2 Normative references

This European Standard incorporates by dated or undated reference, provisions from other publications. Thesenormative references are cited at the appropriate places in the text and the publications are listed hereafter. Fordated references, subsequent amendments to or revisions of any of these publications apply to this EuropeanStandard only when incorporated in it by amendment or revision. For undated references the latest edition of thepublication referred to applies (including amendments).

prEN 1092-1:1997 Flanges and their joints - Circular flanges for pipes, valves, fittings and accessories, PNdesignated - Part 1: Steel flanges

EN 1092-2 Flanges and their joints - Circular flanges for pipes, valves, fittings and accessories, PNdesignated - Part 2: Cast iron flanges

prEN 1092-3:1994 Flanges and their joints - Circular flanges for pipes, valves, fittings and accessories - Part3: Copper alloy and composite flanges, PN designated

prEN 1092-4:1995 Flanges and their joints - Circular flanges for pipes, valves, fittings and accessories, PNdesignated - Part 4: Aluminium alloy flanges

ENV 1591-2 Flanges and their joints - Design rules for gasketed circular flange connections - Part 2:Gasket parameters

3 Notation

3.1 Use of figures

Figures 1 to 12 illustrate the notation corresponding to the geometric parameters. They only show principles and arenot intended to be practical designs. They do not illustrate all possible flange types for which the Calculation methodis valid.

For standard flange types, according to EN 1092, the relevant figures are the following:

Type 01 Figure 8Type 02 Figure 10Type 04 Figure 10Type 05 Figure 9Type 07 Figure 10Type 11 Figure 4Type 12 Figure 11

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Page 8EN 1591-1:2001

Type 13 Figure 12Type 21 Figure 4 to 7

3.2 Subscripts and special marks

3.2.1 Subscripts

A – Additional (FA, MA)

B – Bolt

C – Creep of gasket (gc)

D – Equivalent cylinder (tapered hub + connected shell) for load limit calculation

E – Equivalent cylinder (tapered hub + connected shell) for flexibility calculation

F – Flange

G – Gasket

H – Hub

I – Load condition identifier (taking values 0, 1, 2 ...)

L – Loose flange

M – Moment

P – Pressure

Q – Net axial force due to pressure

R – Net axial force due to external force

S – Shell, shear

T – Shell, modified

X – Weak cross-section

∆ – Symbol for change or difference

av – average

c – calculated

d – design

e – effective

max – maximum

min – minimum

nom – nominal

opt – optimal

req – required

s – non-threaded part of bolt

t – theoretical, torque, thread

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Page 9EN 1591-1:2001

0 – initial bolt-up condition (I = 0, see subscript I)

3.2.2 Special marks

~ – Accent placed above symbols of flange parameters that refers to the second flange of the joint, possiblydifferent from the first

3.3 Symbols

Where units are applicable, they are shown in brackets. Where units are not applicable, no indication is given.

AB – Effective total cross-section area of all bolts [mm2], equation (33)

AF, AL – Gross radial cross-section area (including bolt holes) of flange ring, loose flange [mm2],equations (5), (7), (8)

AGe, AGt – Gasket area, effective, theoretical [mm2], equations (39), (36)

C – Coefficient to account for twisting moment in bolt load ratio, equation (71)

E0 – Compressive modulus of elasticity of the gasket [MPa] at zero compressive stress Q = 0 [MPa](see ENV 1591-2)

EB, EF, EG, EL – Modulus of elasticity of the part designated by the subscript, at the temperature of the part[MPa] (for EG see ENV 1591-2)

FA – Additional external axial force [N], tensile force > 0, compressive force < 0, see Figure 1

FB – Bolt force (sum of all bolts) [N]

FG – Gasket force [N]

FG∆ – Minimum gasket force in assembly condition [N] that guarantees after all load changes tosubsequent conditions the required gasket force, equation (51)

FQ – Axial fluid-pressure force [N], equation (43)

FR – Force resulting from FA and MA [N], equation (44)

I – Load condition identifier, for assembly condition I = 0, for subsequent conditions I = 1, 2, 3, ...

IB – Plastic torsion modulus [mm3] of bolt shanks , equation (71)

π12

× min (dBe; dBs)3

K1 – Rate of change of compressive modulus of elasticity of the gasket with compressive stress,ENV 1591-2

Ks – Systematic error due to the inaccuracy of the bolt tightening method

MA – Additional external moment [N × mm], Figure 1

Mt – Bolt assembly torque [N × mm], annex D

Mt,B – twisting moment [N × mm] applied to bolt shanks as a result of application of the bolt assemblytorque Mt, equations (71) and (D.8) to (D.11)

NR – Number of re-assemblies and re-tightenings during service life of joint, equation (67)

P – Pressure of the fluid [MPa], internal pressure > 0, external pressure < 0 (1 bar = 0,1 MPa)

NOTE P in this standard is equal to the maximum allowable pressure PS according to the PED.

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Page 10EN 1591-1:2001

Q – Mean effective gasket compressive stress [MPa], Q = FG/AGe

QI – Mean effective required gasket compressive stress at load condition I [MPa]

Qmin – Minimum necessary compressive stress in gasket for assembly condition (on the effectivegasket area) [MPa], equation (49), (see ENV 1591-2)

Qmax – Maximum allowable compressive stress in the gasket (depends on the gasket materials,construction, dimensions and the roughness of the flange facings) [MPa], equation (72), seeENV 1591-2 (including safety margins, which are same for all load conditions)

Qmax,Y – Yield stress characteristic of the gasket materials and construction, see Table 1, andENV 1591-2 [MPa]

TB, TF, TG, TL – Temperature (average) of the part designated by the subscript [°C] or [K], equation (45)

TO – Temperature of joint at assembly [°C] or [K] (usually + 20 °C)

U – Axial displacement [mm]; ∆U according to equation (45)

WF, WL, WX – Resistance of the part and/or cross-section designated by the subscript [N × mm], equations(74), (86), (88), (90)

XB, XG – Axial flexibility modulus of bolts, gasket [1/ mm], equations (34), (42)

YG, YQ, YR – Axial compliance of the bolted joint, related to FG, FQ, FR [mm/N], equations (46), (47), (48)

ZF, ZL – Rotational flexibility modulus of flange, loose flange [mm 3], equations (27), (31), (32)

b0 – Width of chamfer (or radius) of a loose flange [mm] see Figure 10, equation (15) such that:d7min = d6+2×b0

bF, bL – Effective width of flange, loose flange [mm], equations (5) to (8)

bGi, bGe, bGt – Gasket width (radial), interim, effective, theoretical [mm], equations (35), (38), Table 1

cF, cM, cS – Correction factors, equations (20), (78), (79)

d0 – Inside diameter of flange ring [mm] and also the outside diameter of central part of blank flange(with thickness e0), in no case greater than inside diameter of gasket [mm], Figures 4 to 12

d1 – Average diameter of hub, thin end [mm], Figures 4, 5, 11 and 12

d2 – Average diameter of hub, thick end [mm], Figures 4, 5, 11 and 12

d3, d3e – Bolt circle diameter, real, effective [mm], Figures 4 to 12

d4 – Outside diameter of flange [mm], Figures 4 to 12

d5, d5t, d5e – Diameter of bolt hole, pierced, blind, effective [mm], Figures 4 to 12

d6 – Inside diameter of loose flange [mm], Figures 10, 12

d7 – Diameter of position of reaction between loose flange and stub or collar [mm], Figure 1,equations (15), (41)

d8 – Outside diameter of collar [mm], Figure 10

d9 – Diameter of a central hole in a blank flange [mm], Figure 9

dB0, dBe, dBs – Diameter of bolt: nominal diameter, effective diameter, shank diameter [mm], Figure 2,Table B.1

dB2, dB3 – Basic pitch diameter, basic minor diameter of thread [mm], see Figure 2

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Page 11EN 1591-1:2001

dGe, dGt – Diameter of gasket, effective, theoretical [mm], Figure 3, Table 1

dG1, dG2 – Inside, outside diameter of theoretical contact area of gasket [mm], Figure 3

dE, dF, dL – Average diameter of part or section designated by the subscript [mm], equations (5) to (8), (10)dS, dX to (12), Figures 4 to 12

e0 – Wall thickness of central plate of blank flange within diameter d0 [mm], Figure 9

e1 – Minimum wall thickness at thin end of hub [mm], Figures 4, 5, 11, 12

e2 – Wall thickness at thick end of hub [mm], Figures 4, 5, 11, 12

eD, eE – Wall thickness of equivalent cylinder for load limit calculations, for flexibility calculations [mm],equations (9), (11), (12), (75)

eF, eL – Effective axial thickness of flange, loose flange [mm], equations (5) to (8)

eFb – Thickness of flange ring at diameter d3 (bolt position) [mm] equation (3)

eFt – Thickness of flange ring at diameter dGe (gasket force position), relevant for thermal expansion[mm], equation (45)

eG – Thickness fo gasket [mm], Figure 3

eP, eQ – Part of flange thickness with (eP), without (eQ) radial pressure loading [mm], Figures 4 to 12,such that eP+eQ = eF

eS – Thickness of connected shell [mm], Figures 4 to 8, 10 to 12

eX – Flange thickness at weak section [mm], Figure 9

fB, fE, fF, fL, fS – Nominal design stress [MPa] of the part designated by the subscript, at design temperature [°C]or [K], as defined and used in pressure vessel codes

gC – Creep factor for gasket, equation (46), see ENV 1591-2

hG, hH, hL – Lever arms [mm], Figure 1, equations (14), (16)

hP, hQ, hR, – Lever arm corrections [mm], equations (13), (21) to (24), (29), (30)hS, hT

jM, jS – Sign number for moment, shear force (+1 or 1), equation (80)

kQ, kR, kM, kS – Correction factors, equation (25), (26), (81)

lB, ls – Bolt axial dimensions [mm], Figure 2, equation (34)

le – le = lB ls

lH – Length of hub [mm], Figures 4, 5, 11, 12, equation (9), (75)

nB – Number of bolts, equations (1), (4), (33), (34)

pB – Pitch between bolts [mm], equation (1)

pt – Pitch of bolt thread [mm], Table B.1

r0, r1 – Radii [mm], Figures 4, 10

r2 – Radius of curvature in gasket cross-section [mm], Figure 3

∆U – Differential axial expansions [mm], equation (45)

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Page 12EN 1591-1:2001

ΘF, ΘL – Rotation of flange, loose flange, due to applied moment [rad], annex E

Ψ – Load ratio of flange ring due to radial force, equation (82)

ΨZ – Particular value of Ψ, equation (74), Table 2

ΦB, ΦF, ΦG, – Load ratio of part and/or cross-section designated by the subscript, to be calculated for all loadΦL, ΦX conditions, equation (71), (72), (73), (85), (87), (89), (91)

Φmax – Reduced maximum allowable load ratio, equation (70)

αB, αF, αG, αL – Thermal expansion coefficient of the part designated by the subscript, averaged between T0 andTB, TF, TG, TL, TS, [K

-1]

β, γ, δ, ϑ – Intermediate variables, equations (9), (17), (18), (19), (41), (70), (75), (77)κ, λ, χ

1+, 1 – Scatter of initial bolt load of a single bolt, above nominal value, below nominal value, annex C

+, – Scatter for the global load of all the bolts above nominal value, below nominal value, equations(60), (61)

π – Numerical constant (π = 3,141593)

ϕG – Angle of inclination of a sealing face [rad or deg], Figure 3, Table 2

ϕS – Angle of inclination of connected shell wall [rad or deg], Figures 6, 7

3.4 Terminology

3.4.1 Flanges

Integral flange: Flange attached to the shell either by welding (e.g. neck weld, see Figures 4 to 7 or slip onweld see Figures 8 and 11) or cast onto the envelope (integrally cast flanges, type 21)

Blank flange: Flat closure, Figure 9

Loose flange: Separate flange ring abutting a collar, Figure 10

Hub: Axial extension of flange ring, usually connecting flange ring to shell, Figures 4, 5

Collar: Abuttment for a loose flange, Figure 10

3.4.2 Loading

External loads: Forces and/or moments applied to the joint by attached equipment, e.g. weight and thermalexpansion of pipes.

3.4.3 Load conditions

Load condition: State with set of applied simultaneous loads; designated by I.

Assembly condition: Load condition due to initial tightening of bolts (bolting up), designated by I = 0

Subsequent condition: Load condition subsequent to assembly condition, e.g. test condition, operating condition,conditions arising during start-up and shut-down; designated by I = 1, 2, 3 ...

3.4.4 Compliances

Compliance: Inverse stiffness (axial), symbol Y, [mm/N]

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Page 13EN 1591-1:2001

Flexibility modulus: Inverse stiffness modulus, excluding elastic constants of material:axial: symbol X, [1/mm] rotational:symbol Z, [1/mm3]

Figure 1 — Loads and lever arms

le = lB ls

Figure 2 — Bolts

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Page 14EN 1591-1:2001

3a 3b 3c

3d 3e 3f

Figure 3 — Gaskets

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Page 15EN 1591-1:2001

Key1 shell2 hub3 ring

Figure 4 — Weld-neck flanges with cylindrical shells (example 1)

Key1 shell2 hub3 ring

Figure 5 — Weld-neck flanges with cylindrical shells (example 2)

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Page 16EN 1591-1:2001

Key1 shell2 ring

Figure 6 — Flanges welded to conical shells

Key1 shell2 ring

Figure 7 — Flanges welded to spherical shells

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Page 17EN 1591-1:2001

Key1 shell2 ring

Figure 8 — Weld-on plate flange

Key1 plate2 ring

Figures 9 — Blank flange

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Page 18EN 1591-1:2001

Key1 shell2 collar3 loose flange

Figure 10 — Loose flanges with collar

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Page 19EN 1591-1:2001

Figure 11 — Hubbed slip-on welded flange

Figure 12 — Hubbed threaded flange

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Page 20EN 1591-1:2001

4 Calculation parameters

The parameters defined in this clause are effective dimensions, areas and stiffness parameters.

4.1 Flange parameters

The formulae given in 4.1 shall be used for each of the two flanges and where applicable, the two collars of a joint.

Specific flange types are treated as follows:

Integral flange: calculated as an equivalent ring with rectangular cross-section, dimensions bF × eF connectedat diameter dE to an equivalent shell of constant wall thickness eE.

Blank flange: calculated as an equivalent ring with rectangular cross-section, dimensions bF × eF, connectedat diameter dE = d0 to a plate of constant thickness e0. It may have a central opening ofdiameter d9. If a nozzle is connected at the opening the nozzle is not taken into account in thecalculation.

Loose flange: calculated as an equivalent ring with rectangular cross-section dimensions bL × eL withoutconnection to a shell.

Screwed flange: calculated as a loose flange with inside diameter equal to load transmission diameter, i.e.average thread diameter.

Collar: The collar is treated in the same way as an integral flange.

In Figures 4 to 12 the equivalent ring is sketched by shaded area.

4.1.1 Flange ring

4.1.1.1 Bolt holes

Pitch between bolts:

pB = π × d3/nB (1)

Effective diameter of bolt hole:

(2)d5e d5 × d5/pB

Diameter of blind holes is assumed to be:

d5 = d5t × l5t/eFb (3)

Effective bolt circle diameter:

d3e = d3 × (1 2/nB2 ) (4)

NOTE 1 pB and p B are equal as well as d3e and d 3e.

NOTE 2 equations (1) to (4) do not apply to collars.

4.1.1.2 Effective dimensions of flange ring

The effective thickness eF or eL used below is the average thickness of the flange ring. It can be obtained by dividingthe cross-section area of the ring AF or AL (including bolt holes) by the actual radial width of this section.

Since there is a large variety of shapes of flange cross-sections, formulae for the calculation of AF or AL are not givenfor specific flange types.

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Page 21EN 1591-1:2001

Integral flange and blank flange (see Figures 4 to 9)

bF = (d4 d0)/2 d5e dF = (d4 + d0)/2 (5)

eF = 2 AF/(d4 do)

bL = dL = eL = 0 (6)

Loose flange with collar (see Figure 10)

For collar:

bF = (d8 d0)/2 dF = (d8 + d0)/2 (7)

eF = 2 AF/(d8 do)

For flange:

bL = (d4 d6)/2 d5e dL = (d4 + d6)/2 (8)

eL = 2 AL/(d4 - d6)

4.1.2 Connected shell

4.1.2.1 Flange with tapered hub

A cylindrical shell (constant wall thickness eS, average diameter dS) integral with a tapered hub is treated as beingan equivalent cylindrical shell of effective wall thickness eE and effective average diameter dE:

(9)eE e1 ×

1 (ß 1) × lH

(ß/3) × d1 × e1 lH

β e2

e1

dE = {min (d1 e1 + eE; d2 + e2 eE) + max (d1 + e1 eE; d2 e2 + eE)}/2 (10)

4.1.2.2 Flange without hub

For a shell (cylindrical or conical or spherical, constant wall thickness es, angle ϕS and diameter dS at junction withflange) directly connected to a flange ring, the effective dimensions are:

eE = eS dE = dS (11)

The equations (11) are not applicable when a nozzle is connected to the central opening of a blank flange. This caseis covered by 4.1.2.3.

4.1.2.3 Blank flange

For a blank flange, the effective dimensions to be used are:

eE = 0 dE = d0 (12)

The equations (12) apply whatever the blank flange configuration (without opening, with opening without nozzle, withopening with nozzle).

4.1.2.4 Collar

The equations which are applicable are those of 4.1.2.1 or 4.1.2.2 depending on whether or not the collar has a hub.

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Page 22EN 1591-1:2001

4.1.3 Lever arms

NOTE When the gasket is of flat type, the parameters hP and hG below can be calculated only when dGe hasbeen determined, i.e. when the calculations given in 4.3.2 have been carried out.

4.1.3.1 All flanges

hP = [(dGe dE)2 × (2 dGe + dE)/6 + 2 eP

2 × dF]/dG

2 e (13)

For blank flanges: ep = 0.

4.1.3.2 Integral flange and blank flange

hG = (d3e dGe)/2 hH = (d3e dE)/2 (14)

hL = 0

NOTE These equations do not apply to collars.

4.1.3.3 Loose flange with collar

d7 min ≤ d7 ≤ d7 max (15)

d7 min = d6 + 2 b0 d7 max = d8

hG = (d7 dGe)/2 hH = (d7 dE)/2 (16)

hL = (d3e d7)/2

As the value of d7 is not known in advance, the following hypotheses can be made:

– for the flexibility calculations (i.e. up to the end of clause 5), take for d7 the value d70 given by equation (41);

NOTE It follows that hG, hN and hL can vary with each iteration necessary to calculate bGe and dGe (see 4.3.2).

– for the calculation of load ratios (clause 5), the most favourable value between d7 min and d7 max can be used,as given in 6.6.

4.1.4 Flexibility-related flange parameters

NOTE When the gasket is of the flat type, the parameter hQ below can be calculated only when dGe hasbeen determined, i.e. when the calculations in 4.3.2 have been carried out.

4.1.4.1 Integral flange and collar

γ = eE × dF/(bF × dE × cosϕs) (17)

(18)ϑ 0,55 cosϕs × dE × eE / eF

λ = 1 eP/eF = eQ/eF (19)

NOTE eP and eQ are defined in Figures 4 to 12 (when eP = eF, eQ = 0).

cF = (1 + γ × ϑ)/{1 + γ × ϑ[4 (1 3 λ + 3 λ2) + 6 (1 2 λ) × ϑ + 6 ϑ2] + 3 γ2 × ϑ4} (20)

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Page 23EN 1591-1:2001

(21)hS 1,1 eF × eE/dE × (1 2 × λ ϑ)/(1 γ × ϑ)

hT = eF (1 - 2 λ γ × ϑ2)/(1 + γ × ϑ) (22)

hQ = {hS × kQ + hT × (2 dF × eP/dE2 0,5 tanϕS)} × (dE/dGe)

2 (23)

hR = hS × kR hT × 0,5 tanϕS (24)

+ 0,85/cosϕs for conical or cylindrical shell

kQ = (25) + 0,35/cosϕS for spherical shell 0,15/cosϕs for conical or cylindrical shell

kR = (26) 0,65/cosϕS for spherical shell

ZF = 3 dF × cF/(π × bF × eF3 )

(27)ZL = 0

4.1.4.2 Blank flange

Diameter ratio:

= d9/dE (28)

NOTE reminder: for a blank flange, dE = d0 (according to equation (12))

hQ = (dE/8) × (1 2) × [0,7 + 3,3 2)/(0,7 + 1,3 2] × (dE/dGe)2 (29)

hR = (dE/4) × (1 2) × (0,7 + 3,3 2)/[(0,7 + 1,3 2) × (1 + 2)] (30)

ZF = 3 dF/{ π × [bF × eF3 + dF × e0

3 × (1 2)/(1,4 + 2,6 2)]}

(31)ZL = 0

4.1.4.3 Loose Flange with collar

For the collar use equations (17) to (27); for the loose flange use the following equation:

ZL = 3 × dL/(π × bL × eL3 ) (32)

4.2 Bolt parameters

The bolt dimensions are shown in Figure 2. Diameters of standard metric series bolts are given in annex B.

4.2.1 Effective cross-section area of bolts

AB = {min (dBe; dBs)}2 × nB × π/4 (33)

4.2.2 Flexibility modulus of bolts

XB = (ls/dB2 s + le/dB

2 e + 0,8/dB0) × 4/(nB × π) (34)

The thickness of washers possibly present in the joint shall be included in lengths ls and le.

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Page 24EN 1591-1:2001

4.3 Gasket parameters

The notation for dimensions of gaskets is given in Figure 3.

ENV 1591-2 gives typical non-mandatory values for material properties. If data for the actual gasket is available, itshould preferably be used.

4.3.1 Theoretical dimensions

bGt = (dG2 dG1)/2 dGt = (dG2 + dG1)/2 (35)

AGt = π × dGt × bGt (36)

NOTE The theoretical gasket width bGt is the maximum which may result from a very high FG.

4.3.2 Effective dimensions

The effective gasket width bGe depends on the force FG applied to the gasket for many types of gasket. The value bGe

is determined iteratively for the assembly condition with FG = FG0 and assumed to be unchanged for subsequentconditions.

NOTE 1 For a flat gasket, the effective gasket width is equal to twice the distance separating the outsidediameter of the sealing face from the point of application of the gasket reaction (i.e. the resultant ofcompressive stress over the gasket width).

The value FG0 used for this determination represents the minimum force which must be reached in assemblycondition, to meet the leak-tightness criteria given in 5.3.

This minimum force is not known when starting the calculation. It will be obtained through the iterative calculationprocess beginning at this point and ending with 5.4, equation (53).

To start calculation, any arbitrary value may be with chosen for FG0. The use of the following realistic value isrecommended.

FG0 = AB × fB0/3 FR0 (37)

where FR0 is as given by 5.1.

Interim gasket width bGi shall be determined from the equations in Table 1, starting with the first approximation givenin this table.

Effective gasket width:

bGe = min {bGi; bGt} (38)

Effective gasket diameter:

The effective gasket diameter dGe is the diameter where the gasket force acts. It is determined from Table 1.

NOTE 2 For flat gaskets, dGe varies with bGe. In that case, bGe is twice the distance between the outsidecontact diameter of the gasket and the effective gasket diameter.

Effective gasket area:

AGe = π × dGe × bGe (39)

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Page 25EN 1591-1:2001

Lever arm: (d3e dGe)/2 for integral flange or blank flange

hG0 = (40) (d70 dGe)/2 for loose flange with collar

d70 = min {max (d7min; (dGe + × d3e)/(1 + ); d7max} (41)

= (ZL × EF0)/(ZF × EL0)

NOTE 3 Equation (41) only applies to loose flanges on a collar.

Equations (38) to (41) are re-evaluated iteratively until the value bGe is constant within the required precision.

NOTE 4 A precision of 5 % is enough. To obtain results almost independent of the operator, a precision of0,1 % is however recommended.

4.3.3 Axial flexibility modulus of gasket

XG = (eG/AGt) × (bGt + eG/2)/(bGe + eG/2) (42)

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Page 26EN 1591-1:2001

Table 1 — Effective gasket geometry

Type Gasket form Formulae

1 Flat gaskets, of lowhardness,composite or puremetallic, materialsFigure 3 a

First approximation: bGi = bGt

More accurate:

bGi

eG/(π × dGe × EGm)

hG0 × ZF/EF0 h G0 × Z F/E F0

FG0

π × dGe × Qmax,y

2

EGm = E0 + 0,5 K1 × FG0/AGe

ZF, Z F according to equation (27) or (31)

In all cases: dGe = dG2 bGe

2 Metal gaskets withcurved surfaces,simple contact,Figures 3 b, 3 c

First approximation:

bGi 6 r2 × cosϕG × bGt × Qmax,y/EG0

More accurate:

bGi

6 r2 × cosϕG × FG0

π × dGe × EG0

FG0

π × dGe × Qmax,y

2

In all cases: dGe = dG0

3 Metal octagonalsection gaskets seeFigure 3 d

In all cases:

bGi = length bGe according to Figure 3 d(Projection of contacting surfaces in axial direction.)

dGe = dGt

4 Metal oval orcircular sectiongaskets, doublecontact see Figures3 e, 3 f

First approximation:

bGi 12 r2 × cosϕG × bGt × Qmax,y/EG0

More accurate:

bGi

12 r2 × cosϕG × FG0

π × dGe × EG0

FG0

π × dGe × Qmax,y

2

In all cases: dGe = dGt

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Page 27EN 1591-1:2001

5 Internal forces (in the joint)

Different load conditions are indicated by the value of indicator "I". Case I = 0 is the assembly condition; highervalues (I = 1,2...) are different test conditions, operating conditions and so on. The number of load conditionsdepends on the application. All potentially critical load conditions shall be calculated.

5.1 Applied loads

5.1.1 Assembly condition (I = 0)

Fluid pressure (internal or external) is zero: P0 = 0.

External loads FA0 and MA0 combine to give a net force FR0 as in equation (44) (load case I = 0).

All temperatures are equal to the initial uniform value T0.

5.1.2 Subsequent conditions (I = 1, 2 ...)

5.1.2.1 Fluid pressure

Internal fluid pressure PI > 0

Unpressurized condition PI = 0 FQI = (π/4) × dG2 e × PI (43)

External fluid pressure PI < 0

NOTE dGe is the location of the forces acting on the gasket and not the location where the leak tightness isachieved. This is conservative, overestimating the load coming from the pressure of the fluid for large gasketwidth.

5.1.2.2 Additional external loads

Additional external loads FAI and MAI combine to give a net force FRI as follows:

Axial tensile force FAI > 0 FRI = FAI±(4/d3e)×MAI (44)

Axial compression force FAI < 0

Select the sign in equation (44) giving the more severe condition.

NOTE In the presence of external moment, the most severe condition may be difficult to foresee because:

– on the side of the joint where the moment induces an additional tensile load (sign + in equation (44)),load limits of flanges or bolts may govern, as well as minimum gasket compression;

– on the side of the joint where the moment induces an additional compression load (sign in equation(44)), load limit of gasket may be decisive.

Therefore, for good practice, it is suggested to consider systematically two load conditions (one for each sign inequation (44)) whenever an external moment is applied, with different indices I being assigned to each case.

5.1.2.3 Thermal loads

Axial thermal expansion relative to the assembly condition (uniform temperature T0) is treated by equation (45).

∆UI = eB × αBI × (TBI T0) eFt × αFI × (TFI T0) eL × αLI × (TLI T0) eG × αGI × (TGI T0) e Ft × α FI × (T FI T0) e L × α LI × (T LI T0) (45)

Herein shall hold: eFt + e Ft + eL + e L + eG = eB

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Page 28EN 1591-1:2001

If washers are present in the joint their thickness shall be included in eFt and e Ft. (It is assumed that their temperatureand thermal expansion coefficient are equal to those of the corresponding flange).

5.2 Compliance of the joint

Lever arms are calculated from 4.1.3. For loose flanges the assumption of equation (41) shall be used.

The following equations apply as follows:

– Equation (46) applies for all load conditions (I = 0, 1, 2 ...), with:

– gC = 1,0 for assembly condition (I = 0), even if gasket characteristics indicate gC < 1,0 at ambient temperature(T ≈ 20 °C);

– Q = FG0/AGe for the calculation of EGI, for all I;

– Equation (47) does not apply for zero fluid pressure cases.

– Equation (48) applies only for load condition where FRI ≠ 0.

YGI = ZF × hG2 /EFI + Z F × h G

2 /E FI + ZL × hL

2 /ELI + Z L × h L

2 /E LI + XB/EBI + XG/(EGI × gCI) (46)

YQI = ZF × hG × (hH hP + hQ)/EFI + Z F × h G × (h H h P + h Q)/E FI + ZL × hL2 /ELI + Z L × h L

2 /E LI + XB/EBI (47)

YRI = ZF × hG × (hH + hR)/EFI + Z F × h G × (h H + h R)/E FI + ZL × hL2 /ELI + Z L × h L

2 /E LI + XB/EBI (48)

NOTE In equations (46) to (48):

– only one term in which the parameters Z and E have the subscript F relates to each integral flange (or blankflange); for the same gasket side (side without , side with ), any term in which Z and E have the subscriptL is not applicable;

– two terms always relate to each loose flange;

– the first relates to the flange itself (term in which Z and E have the subscript L);

– the second relates to its collar (term in which Z and E have the subscript F).

Thus, the six terms of these equations (one for the bolts, one for the gasket, four for the flanges andcollars) only actually exist if a joint has two loose flanges. If there is no loose flange, only four terms exist(one for the bolts, one for the gasket, two for the flanges).

5.3 Minimum forces necessary for the gasket

5.3.1 Assembly condition (I = 0)

Minimum gasket force:

FG0min = AGe × Qmin (49)

5.3.2 Subsequent conditions (I = 1, 2, ...)

Force required to assure leak-tightness and no loss of contact at bolts or nuts due to external compression axial loadon the joint or to negative fluid pressure:

FGImin = max {AGe × QI; (FQI + FRI)} (50)

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Page 29EN 1591-1:2001

5.4 Internal forces in assembly condition (I = 0)

5.4.1 Required forces

To guarantee that the gasket force in subsequent conditions never falls below the value FGImin given by equation (50)the gasket force in the assembly condition shall be at least the following:

FG∆ = maxall I ≠ 0 {FGImin × YGI + [FQI × YQI + (FRI × YRI FR0 × YR0) + ∆UI]}/ YG0 (51)

Taking into account what is also necessary for seating of the gasket (equation (49)), the required gasket force andthe corresponding bolt load are as follows:

FG0req = max {FG0min; FG∆} (52)

FB0req = FG0req + FR0 (53)

If the value FG0req given by equation (52) is higher than the value FG0 assumed up to this step, the calculation mustbe repeated from equation (38), using a higher value for FG0 until:

FG0req ≤ FG0 (54)

On the contrary, if the value FG0 req given by equation (52) is lower than the value FG0 assumed up to this step, thisvalue is acceptable, because it gives a higher approximation of the true FG0req.

The true value FG0req may be found through a number of iterations great enough so that:

FG0 ≈ FG0req (55)

within the required precision.

NOTE A precision of 5 % is enough, with FG0 greater than FG0req. To obtain a result almost independent ofthe operator, a precision of 0,1 % is however recommended.

5.4.2 Accounting for bolt-load scatter at assembly

All bolt-tightening methods involve some degree of inaccuracy. The resulting scatter values for a set of nB bolts are + and , respectively above and below the target value. These are defined by equations (56) to (58). Annex Cgives indicative values 1+ and 1 for single bolts.

When the accuracy of the tightening of one bolt is not influenced by the other bolts, the scatter values +, and

for the total bold load are reasonably expressed in terms of nb, 1+, and 1 as described below.

When the systematic error due to the inaccuracy of the bolt tightening method Ks is known, the following equationdefines values +, and for the global load of all the bolts:

(56a)ε Ks (ε1 Ks)/ nb

(56b)ε Ks (ε1 Ks)/ nb

When the systematic error due to the inaccuracy of the bolt tightening method Ks is not known, a reasonableapproximation of Ks is given by the following equation:

Ks = 0,25 1+ (57a)

or

Ks = 0,25 1 (57b)

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Page 30EN 1591-1:2001

In this case, the following equations follow:

(58a)ε ε1 (1 3/ nb )/4

(58b)ε ε1 (1 3/ nb )/4

The actual force FB0 is limited as follows:

FB0 min ≤ FB0 ≤ FB0 max (59)

where:

FB0 min = FB0 av × (1 ) (60)

FB0 max = FB0 av×(1+ +) (61)

After assembly, the actual bolt force achieved shall be not less than the required minimum bolt force FB0 req:

FB0 min ≥ FB0 req (62)

Consequently the scatter of the bolt-tightening shall be taken account of in the following way.

a) Nominal bolt assembly force, used to define the bolting-up parameters:

– For bolt-tightening methods involving control of bolt-load:

FB0 nom ≥ FB0 req/(1 ) (63)

– For bolt-tightening methods involving no control of bolt-load:

the value to be selected for FB0 nom is the average bolt load FB0 av that can really be expected in practise for themethod used, independently of FB0 req.

The following condition must be met:

FB0 nom = FB0 av ≥ FB0 req/(1 ) where = 0,5 (64)

If not, the bolt-tightening method initially chosen is not valid and must be changed.

NOTE For the common case of manual bolt-tightening, annex C gives an estimate of FB0 av.

b) Maximum forces to be used for load limit calculation (clause 6) in assembly condition:

They shall be based on the nominal bolt assembly force selected according to a) above:

FB0 max = FB0 nom × (1 + +) (65)

FG0 max = FB0 max FR0 (66)

The effective gasket width bGe shall not be recalculated at this stage of the calculation process.

5.5 Internal forces in subsequent conditions (I = 1, 2, ...)

To prevent leakage, the gasket force in all subsequent conditions shall be at least the minimum required FGI min fromequation (50).

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Page 31EN 1591-1:2001

This corresponds to a gasket assembly force equal to FG∆ from equation (51).

If the admissibility of the forces in the connection has been proved for this value of the gasket forces in the assemblyconditions, and in practise a bolt load FB0 (= FG0) > FG∆ + FR0 is applied, plastic deformations may occur in subse-quent load conditions, but global plastic deformation is prevented due to the criteria and admissibility of loads.However, in case of frequent re-assembly (which each of them may generate a bolt load FG∆ + FR0) it is importantto avoid accumulation of the plastic deformations that may occur at start-up after each re-assembly. This is obtainedby checking the load limits of the flange connection, in subsequent conditions, for an assembly gasket force FG0d

possibly higher than FG∆.

FG0d = max {FG∆; (2/3) × (1 10/NR) × FB0 max FR0} (67)

Subsequent gasket force and bolt load for load limit calculations then are

FGI = {FG0d ×Y G0 [FQI × YQI + (FRI × YRI FR0 × YR0) + ∆UI]}/ YGI (68)

FBI = FGI + (FQI + FRI) (69)

NOTE When progressive distortion does not control, i.e. when FG0 d = FG∆ in equation (67), then forces FGI

and FBI defined by equations (68), (69) are those that exist in any condition I ≠ 0 for an initial bolt load equalto the minimum required FB0req.

Then in clause 6 is checked the admissibility of these minimum required forces (in contrary for assemblycondition is checked the admissibility of the maximum possible forces). Actual forces in subsequent conditionsare above the forces defined by equations (68) and (69), due to the scatter of any bolting-up method.

Nevertheless it is valid to waive the extra part of forces due to the amount of FB0 (actual) in excess of FB0 req, sincethis extra part is "passive" ("secondary") forces, i.e. capable of vanishing through plastic deformation.

When progressive distortion controls, the maximum possible initial bolt load FB0 max is used for determinationof a fictitious gasket force (second term in equation (67)), which serves to limit to an acceptable level possibleaccumulation of plastic deformation at each re-assembly.

6 Checking of the admissibility of the load ratio

6.1 General

Loads on the joint system shall be within safe limits at all times. These limits are expressed in calculated load ratios.

Each load ratio Φ ... shall be less than or equal to unity for all conditions (I = 0, 1, 2 ...).

The index I for the load condition is omitted in the following for simplification.

NOTE It is reminded that for bolting-up condition (I = 0), the forces to be considered are the maximumpossible forces (see 5.4.2 b).

For wide flanges a more stringent requirement applies to integral flanges having χ = d4/d0 > 2,0 and loose flangeshaving χ = d4/d6 > 2,0 : Instead of Φ < 1,0 it shall be:

Φ ≤ Φmax = min (70) 1,0; 0,6 1/ [5,25 (χ 1)2]

Nominal design stresses in assembly condition are the same as in test condition.

NOTE Regarding values of nominal design stresses, see 1.3.2.

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Page 32EN 1591-1:2001

6.2 Bolts

Nominal design stress of bolts, shall be determined by the same rules as used for nominal design stress of flangesand shells.

Bolt load ratio:

(71)ΦB 1

fB

FB

AB

2

3

C Mt,B

IB

2

≤ 1

where:

C = 1 in assembly condition, for bolt material with minimum rupture elongation A ≥ 10 %

C = 4/3 in assembly condition, for bolt material with mimimum rupture elongation A < 10 %

C = 0 in all other loading conditions

NOTE 1 In the assembly condition, the value to be considered for the twisting moment Mt,B acting on boltshanks is the maximum possible value (as for the axial force FB, see 6.1), defined as:

Mt,B max = Mt,B nom × (1 + +)

Mt,B nom can be determined according to annex D (informative), for the bolting-up methods involving applicationof the torque to the nut.

With hydraulic tensioners, Mt,B = 0.

NOTE 2 The value C = 1 is based on a plastic limit criterion. Due to this criterion, some limited plasticstrains may occur at periphery of the bolts in assembly condition.

Use of this criterion has been validated by industrial experience, for bolt material with sufficient ductility(A ≥ 10 %).

The value C = 4/3 is based on an elastic limit criterion. Even with sufficiently ductile bolt material, it may beselected if a strict elastic behaviour of the bolts is wished in assembly condition.

NOTE 3 It is recommended to observe a minimum load ratio ΦB0min = 0,3 in assembly condition, becausesmaller initial bolt load is not good practice.

6.3 Gasket

Gasket load ratio:

ΦG = FG/(AGt × Qmax) ≤ 1 (72)

6.4 Integral flange and collar

Load ratio for flange, or collar (for collar Φmax = 1,0):

ΦF = |FG × hG + FQ × (hH hP) + FR × hH|/WF ≤ Φmax (73)

WF = (π/4) × {fF × 2 × bF × eF2 × (1 + 2 × Ψopt × ΨZ ΨZ

2 ) + fE × dE × eD

2 × cM × jM × kM} (74)

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Page 33EN 1591-1:2001

(75)eD e1 ×

1 (ß 1) × lH

4

(ß/3)4 × (d1 × e1)2 l 4

H

fE = min. (fF; fS) (76)

δQ = P × dE/(fE × 2 × eD × cosϕS); δR = FR/(fE × π × dE × eD × cosϕS) (77)

(78)cM

1,33×[1 0,75×(0,5×δ Q δ R)2]×[1 (0,75×δ 2Q 1×δ 2

R)] for conical and cylindrical shell

1,33×[1 0,75×(0,5×δ Q δ R)2]×[1 (0,25×δ 2Q 3×δ 2

R)] for spherical shell

(79)cS

π4

×[ 1 0,75×(0,5×δ Q δ R)2 jS×(0,5×δ R 0,75×δ Q)] for conical and cylindrical shell

π4

×[ 1 0,75×(0,5×δ Q δ R)2 jS×(1,5×δ R 0,25×δ Q)] for spherical shell

jM = sign {FG × hG + FQ × (hH hP) + FR × hH}; jS = ± 1 (80)

1 ≤ kM ≤ + 1; 0 ≤ kS ≤ 1 (81)

(82)

Ψ( js,kM,ks) fE × dE × eD × cosϕS

fF × 2 × bF × eF

×

(0,5 × δ Q δ R) × tanϕS δ Q × 2 × eP/dE jS × kS ×

eD × cM × cS × (1 jS × kM)

dE × cos3ϕS

The values of jS, kM, kS to be used are defined in the calculation sequence described following Table 2.

Ψopt = jM × (2 × eP/eF 1); ( 1 ≤ Ψopt ≤ + 1) (83)

Ψmax = Ψ(+1, +1, +1) Ψ0 = Ψ(0, 0, 0); (84)

Ψmin = Ψ( 1, 1, +1)

The value ΨZ in equation (74) depends on jM and Ψopt as given in Table 2.

Table 2 — Determination of ΨZ

jM Range of Ψopt kM ψZ(jS,kM,kS)

jM = +1

Ψmax ≤ Ψopt kM = + 1 ΨZ = Ψmax

Ψ0 ≤ Ψopt < Ψmax kM = + 1 ΨZ = Ψopt

Ψopt < Ψ0 kM < + 1 ψZ ψ(-1, kM , 1)

jM = 1

Ψopt ≤ Ψmin kM = 1 ΨZ = Ψmin

Ψmin < Ψopt ≤ Ψ0 kM = 1 ΨZ = Ψopt

Ψ0 < Ψopt kM > 1 ψZ ψ( 1, kM , 1)

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Page 34EN 1591-1:2001

The sequence of calculation shall be as follows:

a) Calculate eD from equation (75), ß having previously been calculated by equation (9).

b) Calculate fE, δQ, δR, cM from equations (76) to (78).(If the value in the root giving cM is negative the hub is overloaded).

c) Calculate cS(js = + 1), cS(js = 1), jM, Ψopt, Ψ0, Ψmax, Ψmin from equations (79) to (84).(If Ψmax < 1 or Ψmin > + 1 the ring is overloaded).

d) Determine kM and ΨZ according to Table 2. When that table gives kM < + 1 or kM > 1 or kM without no moreprecision, the value of kM shall be determined so that WF is maximum in equation (74) as calculated at step e)which follows. The value of ΨZ associated with kM is given by equation (82).

e) Calculate WF, ΦF from equations (74), (73).

6.5 Blank flange

Load ratio for blank flange:

ΦF = max { |FB×hG+FQ×(1 3)×dGe/6+FR×(1 )×dGe/2|;

|FB×hG|; |FQ×(1 3)×dGe/6|; |FR×(1 )×dGe/2| /WF ≤ 1,0 (85)

WF = (π/4)×fF×{2×bF×eF2 +d0×(1 )×e0

2 } (86)

If there is a possible critical section where eX < eF (see Figure 9), then calculate additionally the following load ratio:

ΦX = FB × (d3 dX)/(2 WX) ≤ 1,0 (87)

WX = (π/4) × fF × {(d4 2 d5e dX) × eF2 + dX × eX

2 } (88)

6.6 Loose flange with collar

Load ratio for loose flange:

ΦL = FB × hL/WL ≤ Φmax (89)

WL = (π/2) × fL × bL × eL2 (90)

Load ratio for collar can be evaluated arbitrarily from 6.4 (always with Φmax = 1,0) or from equation (91). The morefavourable result (i.e. the smaller of both ΦF values) is valid.

Equation (91) only applies to connections using a flat gasket with (dG2 d7) > 0.

(91)ΦF FQ FR ×hH

(π/4)×dE× fE×min e2E ; e2

F min fF×e2F ; Qmax×(dG2 d7)

2/4

≤ 1,0

The lever arms hG, hH, hL may be determined by variation of the diameter d7 in such a way that equations (89) to (91)and (73) to (84) all give the most favourable result, i.e. max (ΦL; ΦF) is minimum.

In the case of FQ+FR > 0 the most favourable result is generally obtained near d7 min according to equation (15). Inthe assembly condition (with FQ = 0 and FR = 0), in contrast the optimum is near d7 max.

NOTE Diameter d7 may be different depending on the load condition. For the assembly condition (I = 0) theload limit calculations may be performed with a value d7 differing from the value d70 given in equation (41).

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Page 35EN 1591-1:2001

Annex A (informative)

Requirement for limitation of non-uniformity of gasket stress

To limit the non-uniformity of gasket stress due to widely spaced bolts, it is required that:

(A.1)eF ≥ pB ×

3

EGm × bGe

EF × eG

× pB

bF

× 1 (ΦG0 × bGt/bGe)2

10

EGm is given in Table 1, ΦG0 by equation (72) for I = 0 with FG0 = FB0 nom × (1 ) FR0.

For loose flanges eL, bL, EL are used instead of eF, bF, EF.

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Page 36EN 1591-1:2001

Annex B (informative)

Dimensions of standard metric bolts

Table B.1 — Metric bolt diametersDimensions in millimeters

Bolt sizea dB0 dBeb dBsc d

M6 × 1 6 5,06 – 5,3M8 × 1,25 8 6,83 – 7,1M10 × 1,5 10 8,59 – 9,0M12 × 1,75 12 10,36 8,5 10,8M14 × 2e 14 12,12 10,0 12,7f

M16 × 2 16 14,12 12,0 14,7M18 × 2,5e 18 15,65 – 16,3f

M20 × 2,5 20 17,65 15,0 18,3M22 × 2,5e 22 19,65 – 20,3f

M24 × 3 24 21,19 18,0 22,0M27 × 3 27 24,19 20,5 25,0f

M30 × 3,5 30 26,72 23,0 27,7M33 × 3,5e 33 29,72 25,5 30,7f

M36 × 4 36 32,25 27,5 33,4M39 × 4 39 35,25 30,5 36,4f

M42 × 4,5 42 37,78 32,5 39,0M45 × 4,5 45 40,78 35,5 42,0f

M48 × 5 48 43,31 37,5 44,7M52 × 5 52 47,31 41,0 48,7f

M56 × 5,5 56 50,84 44,0 52,4M60 × 5,5e 60 54,84 – 56,4M64 × 6 64 58,37 51,0 60,1M68 × 6e 68 62,37 – 64,1M72 × 6 72 66,37 58,5 68,1M76 × 6e 76 70,37 – 72,1M80 × 6 80 74,37 66,0 76,1M90 × 6 90 84,37 75,0 86,1M100 × 6 100 94,37 84,0 96,1

a For M6 to M64 the pitch pt is that of the normal series (according to ISO 261); up to and including M64 thenominal dimensions conform to EN 24014 and EN 24016.

b The value of dBe corresponds to the following definition:dBe = (dB2 + dB3)/2 (see Figure 2); dBe = dB0 0,9382 × pt

c Diameter of neck for necked-down bolts (dimensions not standardized by EN or ISO).

d Body diameter for rolled thread (approximately equal to the basic pitch diameter dB2 according to ISO 724).

e Non-preferred sizes.

f Dimensions not standardized by EN or ISO.

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Page 37EN 1591-1:2001

Annex C (informative)

Scatter of bolting-up methods

Table C.1 — Indicative values 1 and 1 + for equations (56) to (58) for a single bolt

Bolting up (tightening) method;Measuring method

Factors affecting scatterscatter value a, b, c, d

1 1 +

Wrench:Operator feel or uncontrolled

Friction, Stiffness,Qualification of operator

0,3 µ + 0,5 µ 0,3 µ + 0,5 µ

Impact wrench Friction, Stiffness,Calibration

0,2 µ + 0,5 µ 0,2 µ + 0,5 µ

Torque wrench = Wrench withmeasuring of torque (only)

Friction, Calibration,Lubrication

0,1 µ + 0,5 µ 0,1 µ + 0,5 µ

Hydraulic tensioner;Measuring of hydraulic pressure

Stiffness, Bolt length,Calibration

0,2 0,4

Wrench or hydraulic tensioner;Measuring of bolt elongation

Stiffness, Bolt length,Calibration

0,15 0,15

Wrench; Measuring of turn of nut(nearly to bolt yield)

Stiffness, Friction,Calibration

0,10 0,10

Wrench; Measuring of torque and turnof nut (nearly to bolt yield)

Calibration 0,07 0,07

a Very experienced operators can achieve scatter less than given values (e.g. ε = 0,2 instead of ε = 0,3 withtorque wrench); for inexperienced operators scatter can be greater than shown

b Tabulated scatter values are for a single bolt, the scatter of the total bolt load will be less, for statisticalreasons, see 5.4.2.

c With hydraulic tensioner, ε1 + and ε1 are not equal, due to the fact that an additional load is supplied to thebolt while turning the unit to contact, prior to load transfer to the nut.

d µ is the friction coefficient which can be assumed between bolt and nut.

A rough estimate of average initial bolt force achieved by manual-tightening using standard ring wrenches (withoutadditional lever arm and without hammer impacts):

Average bolt force:

(C.1)FB0av AB × 1 000

dB0

where AB is expressed in [mm2], dB0 in [mm] and FB0av in [N].

NOTE However, such uncontrolled tightening is not recommended.

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Page 38EN 1591-1:2001

Annex D (informative)

Assembly using torque wrench

The nominal torque applied to tighten bolt is:

Mt,nom = kB × FB0nom/nB(D.1)

hence the nominal bolt assembly force is:

FB0nom = nB × Mt,nom/kB(D.2)

The general formula for kB is:

kB = pt/(2π) + µt × dt/(2cosα) + µn × dn/2(D.3)

where:

dn= mean contact diameter under nut or bolt head;dt= mean contact diameter on thread;µn= friction coefficient under nut or bolt head;µt= friction coefficient on thread;pt= thread pitch;α= half thread-angle.

In equation (D.3), the first term is due to inclination of the thread helix angle, the second is due to friction betweenthreads, and the third is due to friction under the nut (or bolt head).

For threads of ISO triangular profile, the expression of kB becomes:

kB = 0,159 pt + 0,577 µt × dB2 + 0,5 µn × dn(D.4)

where dB2 is the mean thread diameter (see Figure 2).

An approximative calculation is possible, making:

µt = µn = µdB2 ≈ 0,9 dB0

dn ≈ 1,3 dB0

where dB0 is the mean thread diameter (see Figure 2).

This leads to the following simplified formula, which gives a good estimate of kB:

kB ≈ 0,16 pt + 1,17 µ × dBO(D.5)

A more rough approximation is given by the following more simple formula:

kB ≈ 1,2 µ × dB0(D.6)

In the formula (D.5) and (D.6), the friction coefficient µ is an average value, which accounts for friction of bolt threadsand nut (or head) face.

The value given below for µ, are typical indicative values, the highest being for austenitic steels.

0,10 to 0,15 for smooth, lubricated surfaces µ = 0,15 to 0,25 for average, "normal" conditions (D.7) 0,20 to 0,35 for rough, dry surfaces

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Page 39EN 1591-1:2001

NOTE Use of simple torque wrench without torque multiplier device is limited to about Mt,nom ≈ 1 000 Nm.

Nominal twisting moment on bolt shanks

This moment is approximately equal to the part of assembly torque due to the friction coefficient on threads. Fromequation (D.1) and (D.4), it writes:

Mt, B nom = (0,159 pt + 0,577 µt × dB2)FB0 nom/nB (D.8)

With the same approximations as for equation (D.5), the following simplified equation is obtained:

Mt, B nom ≈ (0,16 pt + 0,52 µ × dBO)FB0 nom/nB (D.9)

or even simpler:

Mt, B nom ≈ (0,55 µ × dBO)FBOnom/nB (D.10)

NOTE Equation (D.10) amounts to taking:

Mt, B nom = 0,46 Mt, nom (D.11)

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Page 40EN 1591-1:2001

Annex E (informative)

Flange rotations

E.1 General

The flange rotations which can be expected in practice are dependent among other parameters, on the true initialbolt force applied at bolting-up. Also, some (small) plastic deformation may occur, both at bolting-up and insubsequent conditions. Therefore:

– only lower and upper limits to the rotations can be evaluated, assuming successively minimum and maximumpossible values of initial bolt load;

– only the elastic part of the rotations can be calculated.

E.2 Use of flange rotation

If the gasket manufacturer specifies a maximum acceptable value of flange rotation for the gasket, then thecalculated values must be checked to ensure that they are less than the maximum acceptable value.

Measured values of ΘF+Θ F respectively ΘL+Θ L, can be used to control the bolt load during assembly.

E.3 Calculation of flange rotations

The elastic rotation of each flange, or collar may be calculated from the following equation (E.1) and for looseflanges from equation (E.2):

ΘF = (ZF/EF) × {FG × hG + FQ × (hH hP + hQ) + FR × (hH + hR)} (E.1)

ΘL = (ZL/EL) × FB × hL (E.2)

The preceding formulas are applicable to all loading conditions (I = 0, 1, 2 ..), provided use of appropriate values ofEF, EL, FQ, FR, FG and FB for each conditions:

EFI, ELI = same values as elsewhere

FQI, FRI = values according to equations (43) and (44)

FGI, FBI = use minimum possible values of gasket and bolt loads to calculate minimum rotations, respectivelymaximum possible values to calculate maximum rotations.

These values are given by the following equations:

– for bolting up condition (I = 0):

FB0min = FB0nom × (1 ) (E.3)FB0max = FB0nom × (1 + +) (E.4)

FG0min = FB0min FR0 (E.5)FG0max = FB0max FR0 (E.6)

– for subsequent conditions (I ≠ 0):

Minimum and maximum values of FGI, FBI are obtained from the following equations:

FGImin = {FG0min × YG0 [FQI × YQI + (FRI × YRI FR0 × YR0) + ∆UI]}/ YGI (E.7)FGImax = {FG0max × YG0 [FQI × YQI + (FRI × YRI FR0 × YR0) + ∆UI]}/ YGI (E.8)

FBImin = FGImin + (FQI + FRI) (E.9)FBImax = FGImax + (FQI + FRI) (E.10)

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Page 41EN 1591-1:2001

Annex F (informative)

Diagram of calculation sequence

3 PARAMETERS

3.1 First flange and second flange

3.1.1 bF, dF, eF (or bL, dL, eL)1) and b F, d F, e F (or b L, d L, e L)

1)

d3e (d 3e = d3e)

3.1.2 eE, dE and e E, d E

3.1.3 hH, hL and h H, h L

3.1.4 hR and h R

ZF, ZL and Z F, Z L

3.2 Bolts

3.2.1 AB

3.2.2 XB

3.3 Gasket

3.3.1 bGt, dGt, AGt

1) only in the case of loose flanges

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Page 42EN 1591-1:2001

4.4.2 FB0nom, FB0max, FG0max

4.5 Forces in subsequent load conditions

FGI, FBI

5 LOAD LIMITS (to be calculated for each situation I)

5.1 Bolts

ΦB

5.2 Gasket

ΦG

5.3/4/5 First flange and second flange2)

ΦF (or ΦL), possibly ΦX, and Φ F (and Φ L), possibly Φ X

2) for simplicity, possible optimisation of d7 (if the flange is loose) is not shown (see 6.6)

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Page 43EN 1591-1:2001

Annex G (informative)

Joints with spacer-seated flanges

G.1 Introduction

Some gaskets have an outer spacer-ring in the form of a solid metal annulus (or similar 'rigid' material) which islocated between the outer periphery of the sealing element of the gasket and the bolts. Spiral-wound gaskets oftenhave an outer spacer-ring of this type. Such gaskets are used in one of two ways:

1) The bolt load applied at assembly is less than that required to seat the flange faces on the outer spacer ringof the gasket.

2) The bolt load applied at assembly is sufficiently high to seat the flange faces on the outer spacer ring of thegasket.

The design method given in the body of this standard is directly applicable to case 1) but requires modification forcase 2) as described below.

G.2 Behaviour of spacer-seated gaskets

In case 2) the flange faces, being slightly inclined, make initial contact with the outer periphery of the spacer ring andlocal elastic deformations occur at the contacts. At higher loads, there can be yield at the contact over an initiallyindeterminate width. The deformation affects the stiffness of the spacer and the magnitude and location of thereaction forces (and their moments), both at the spacer and at the sealing element. These effects in turn modify theflange rotation, and vice versa. The type of flange facing also affects this behaviour. For a raised face the contactis at the outer periphery of the raised face, but for a flat face the contact is at the outer periphery of the spacer.

An essential complication is that spacer contact may exist after bolting up but not in a subsequent condition withinternal fluid pressure (or even vice versa, e.g. with external pressure).

The most unfavourable feature of spacer seated flanges results from the fact that the gasket force on the sealingelement (FG) has its maximum value at the onset of seating contact and then decreases with increasing bolt load.From this follows an upper limit of the maximum possible internal fluid pressure independent of any load limits. (Thissubstantial limit does not exist for normal flange connections without spacer seating.) Therefore the usual method(given in the body of this standard) to calculate the gasket and bolt load required in assemblage to avoid leakagein all subsequent conditions is not applicable for spacer seated flanges. For a required fluid pressure above theupper limit no bolt load prevents leakage; the flange connection in this case never is acceptable.

Due respect to the above complications, in the following a simplified treatment is presented.

G.3 Simplified treatment

G.3.1 Assumptions

1) The spacer contact is rigid.

2) There is no additional load (FR(I) = 0 and ∆U(I) = 0 for all I)

3) Both flanges are integral flanges (not necessarily equal flanges, but not loose flanges)

G.3.2 Additional notation

EG Unloading compression modulus of gasket (sealing element), equal EG used in the body of this standard [MPa]

EG+ Loading compression modulus of gasket [MPa]

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Page 44EN 1591-1:2001

FSR Force on spacer ring [N]

Y... Compliances of the flange connection, specified by different subscripts [mm/N]

eG(0,0) Thickness of gasket [mm] without force at the begin of assemblage

eG(I) Thickness of gasket [mm] actual in load condition No. I

eSR Thickness of spacer ring [mm] (not variable)

hSR Lever arm between FSR and FB [mm]

ζG Parameter for gasket

η... Parameters for flange connection, specified by different subscripts

For a better visible presentation here the load condition identifier I is written in brackets: (I)

G.3.3 Procedure

– First results are to be calculated with the method given in the body for non-spacer-seated gasket.

– Then the bolt load for the onset of contact between flange and spacer is calculated. This allows to checkwhether or not spacer contact will actually occur in the joint.

– If contact does occur then the second stage of the calculation is carried out to determine the changes of forceson gasket, spacer and bolts during assemblage and subsequent load conditions.

– Then follow two checks for the required thightness and contact conditions. If these checks are not both fulfilledthen a new bolt load in assemblage is to be assumed. In some cases no bolt load in assemblage is appropriateto fulfill all conditions; then the design must be changed.

G.3.4 Calculations

G.3.4.1 Forces in assemblage stage 1 (no spacer contact):

Bolt load for onset of contact between flange and spacer:

(G.1)FB(0 ) eG(0,0) eSR

[(ZF/EF) × hG × (hG hD ) (Z F/E F) × h G × (h G h D ) (XG/EG )](0)

NOTE 1 XG is to be calculated with the actual gasket thickness eG, which has the limitations eSR < eG < eG(0,0).Here may be assumed eG ≈ 0,5 (eG(0,0) + eSR)

NOTE 2 If only values of EG but not of EG+ are known, there are two ways to determine EG+:Either estimate EG+ ≈ (0,05...0,2) EG ≈ 0,1 EG or calculate EG+ = (XG × FGS)/(eG(0,0) eSR), where FGS is the forceto compress the sealing element uniformly between rigid plates to the same thickness as the spacer.

If the actual assemblage bolt load FB(0) fulfills the condition

FB(0) < FB(0*) (G.2)

then in the whole assemblage is not spacer contact. (Within the given simplified treatment then is assumed also nospacer contact in all subsequent conditions.)

Otherwise the joint is spacer seated and may be calculated as follows:

Assemblage stage 1 (no spacer contact) ends at FB(0) = FB(0*).

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Page 45EN 1591-1:2001

G.3.4.2 Forces in assemblage stage 2 (with spacer contact):

Parameter:

(G.3)η0S [(ZF/EF) × (hG hSR) × hSR (Z F/E F) × (h G h SR) × h SR](0)

[(ZF/EF) × (hG hSR)2 (Z F/E F) × (h G h SR)2 (XG/EG )](0)

Forces:

FG(0) = FB(0*) (FB(0) FB(0*)) × η0S (G.4)

FSR(0) = + (FB(0) FB(0*)) × (1 + η0S) (G.4)

G.3.4.3 Compliances

Abbreviation:

hSQ = (hH hP + hQ) (G.6)

Integral flanges having no spacer contact (Subscript N for no contact or for normal; see 5.2):

(G.7)YGN(I) [(ZF/EF(I)) (Z F/E F(I ))] × h 2G (XB /EB(I) ) (XG/EG (I))

(G.8)YQN(I) [(ZF/EF(I)) × hSQ (Z F/E F(I )) × h SQ] × hG (XB /EB(I) )

ηTN = YGN(0)/YGN(I) (Subscript T for temperature effect) (G.9)

ηQN = YQN(I)/YGN(I) (G.10)

Integral flanges with spacer contact (Subscript S for spacer seated):

YGS(I) [(ZF/EF(I)) (Z F/E F(I ))] × (hG hSR)2

(G.11) (XG/EG (I)) × 1 [(ZF/EF(I)) (Z F/E F(I))] × h 2SR /(XB /EB(I))

(G.12)YQG(I) [(ZF/EF(I)) × (hSQ hSR) (Z F/E F(I )) × (h SQ hSR)] × (hG hSR)

YQS(I) [(ZF/EF(I)) × (hG hSQ) (Z F/E F(I )) × (hG h SQ)] × (hG hSR)

(G.13) (XG/EG (I)) × 1 [(ZF/EF(I)) × hSQ (Z F/E F(I)) × h SQ] × hSR/(XB /EB(I))

ηTS = YGS(0)/YGS(I) (G.14)

ηQG = YQG(I)/YGS(I) (G.15)

ηQS = YQS(I)/YGS(I) (G.16)

NOTE Observe the possibilities YQS(I) < 0 and ηQS < 0.

G.3.4.4 Maximum internal fluid pressure

NOTE This subclause may be avoided. The next subclauses contains the same information in a moregeneral way, but it does not clearly show the visible effect of the upper limit.

After spacer contact the gasket force in assemblage decreases. From this follows an upper limit (maximum value)of the fluid pressure which in the best case may apply without leakage. (Without spacer contact such an upper limitdoes not exist. Always additional the applicable fluid pressure is limited by the load carrying capabilities of all partsof the flange connection.)

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Page 46EN 1591-1:2001

This maximum fluid pressure Pmax for spacer seated flange connections depends on the selected assemblage boltload FB(0) and may be calculated as follows:

Parameter:

(G.17)ζG 4 m × bGe

dGe

Forces:

FQ(I)max = min {FQ1; FQ2; FQ3} (G.18)

(G.19)FQ1 FB(0) × ηTN

ηQN ζG

(G.20)FQ2 FB(0 ) (FB(0) FB(0 )) × [(1 η0S) × (ηQN ηQG)/ηQS η0S] × ηTS

ηQN ζG

(G.21)FQ3 FB(0 ) (FB(0) FB(0 )) × η0S × ηTS

ηQG ζG

Pressure:

(G.22)Pmax FQ(I)max/( π4

× d 2Ge )

G.3.4.5 Forces in subsequent conditions

Fluid pressure force FQ(I*) to end the spacer contact:

FQ(I*) = FSR(0)/ηSR(I) (G.23)

if 0 < FQ(I*) /FQ(I) < 1 then

Spacer contact ends during the load change from I = 0 to I > 0.

At the end of the load change the forces are:

FG(I) = FG(0) FQ(I*) × ηQG (FQ(I) FQ(I*)) × ηQN (G.24)

FSR(I) = 0 (G.25)

else (either FQ(I*)/FQ(I) < 0 or FQ(I*)/FQ(I) > 1)

Spacer contact remains to the end of load change in I > 0.

At the end of the load change the forces are:

FG(I) = FG(0) × ηTS FQ(I) × ηQG (G.26)

FSR(I) = FSR(0) × ηTS FQ(I) × ηQS (G.27)

In all cases is valid:

FB(I) = FQ(I) + FG(I) + FSR(I) (G.28)

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Page 47EN 1591-1:2001

G.3.4.6 Conditions for tightness and contact at bolts and nuts

(G.29)FG(I) ≥ AGe × QI

FB(I) ≥ 0 (G.30)

If these conditions are not fulfilled simultaneously, the calculations from equation (G.4) up to here are to be repeatedusing an other value FB(0), which may be greater or smaller than before. In some cases no value FB(0) is appropriateto fulfill all conditions; then the design shall be changed.

G.3.4.7 Final checks

If the conditions (G.29) and (G.30) are met, then the final checks of load limits are to be provided according toclause 6. There in 6.4 [...] ( ) instead of FG × hG (is to be used) [FG × hG + FSR × hSR].

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Page 48EN 1591-1:2001

Annex ZA

(informative)

Clauses of this European Standard addressing essential requirements or other provisions ofthe PED

This European Standard has been prepared under a mandate given to CEN by the European Commission and theEuropean Free Trade Association (EFTA) and supports essential requirements of EU Directive 97/23/EC (PressureEquipment Directive, PED).

Warning Other requirements and other EU Directives may be applicable to the products falling within the scopeof this standard.

The following clauses of this standard are likely to support requirements of Directive 97/23/EC

Compliance with the clauses of this standard provides one means of conforming with the specific essentialrequirements of the Directive concerned and associated EFTA regulations.

Table ZA.1 — Correspondence between this European Standard and Directive 97/23/EC

Clause/subclause

of thisEuropeanStandard

Essential requirements (ER's)of Directive 97/23/EC

Qualifyingremarks/

notes

All clauses

Annex 1, 2: Design:

–

Annex 1, 2.1: To be designed to ensure safety throughout intended life – to incorporate appropriate safety coefficients.

Annex 1, 2.2: To be designed for adequate strength.

Annex 1, 2.2.1: To be designed for loadings appropriate to its intended use.

Annex 1, 2.2.2: To be designed for appropriate strength based on a Calculation method.

Annex 1, 2.2.3(a): Requirements to be met by applying one of the following methods – design by formula.

Annex 1, 2.2.3(b): Design calculations to establish the resistance of equipment, in particular – account to be taken of combinations of temperature & pressure; – maximum stresses & peak stresses to be within safe limits.

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Page 49EN 1591-1:2001

Bibliography

EN 24014:1992Hexagon head bolts. Grades A and B (ISO 4014 : 1988)

EN 24016:1992Hexagon head bolts. Grade C (ISO 4016 : 1988)

ISO 261:1973ISO general purpose metric screw threads – General plan

ISO 724:1978ISO general-purpose metric screw threads – Basic dimensions

CR 13642:1999Flanges and their joints – Design rules for gasketed circular Flange Connections – Background Information

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BS EN 1591-1:2001

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