EN 1591-1:2024
(Main)Flanges and their joints - Design rules for gasketed circular flange connections - Part 1: Calculation
Flanges and their joints - Design rules for gasketed circular flange connections - Part 1: Calculation
This document defines a calculation method for bolted, gasketed, circular flange joints. Its purpose is to ensure structural integrity and control of leak tightness. It uses gasket parameters based on definitions and test methods specified in EN 13555:2014.
The calculation method is not applicable to joints with a metallic contact out of the sealing face or to joints whose rigidity varies appreciably across gasket width. For gaskets in incompressible materials, which permit large deformations, the results given by the calculation method can be excessively conservative (i.e. required bolting load too high, allowable pressure of the fluid too low, required flange thickness too large, etc.).
Flansche und ihre Verbindungen - Regeln für die Auslegung von Flanschverbindungen mit runden Flanschen und Dichtung - Teil 1: Berechnungsmethode
Dieses Dokument legt eine Berechnungsmethode für Flanschverbindungen mit runden Flanschen, Schrauben und Dichtung fest. Es hat den Zweck, die Festigkeit der Konstruktion sicherzustellen und die Dichtheit zu kontrollieren. Dafür werden Dichtungskennwerte angewendet, die auf Definitionen und Prüfverfahren nach EN 13555:2021 beruhen.
Die Berechnungsmethode ist nicht anwendbar auf Flanschverbindungen mit einem metallischen Dichtflächenkontakt und auf Flanschverbindungen, deren Steifigkeit über die Dichtungsbreite stark schwankt. Bei Dichtungen aus inkompressiblen Werkstoffen, die starke Verformungen zulassen, können die Ergebnisse nach dieser Berechnungsmethode übermäßig konservativ sein (d. h. erforderliche Schraubenkraft zu hoch, zulässiger Mediendruck zu gering, erforderliche Flanschdicke zu groß usw.).
Brides et leurs assemblages - Règles de calcul des assemblages à brides circulaires avec joint - Partie 1: Méthode de calcul
Le présent document définit une méthode de calcul des assemblages à brides circulaires boulonnés avec joint. Son objectif est d'en assurer l'intégrité structurale et la maîtrise de l'étanchéité. Elle utilise des paramètres de joints basés sur les définitions et les modes opératoires d'essais spécifiés dans l'EN 13555:2014:2014.
La méthode de calcul ne s'applique pas aux assemblages à contact métallique en dehors de la face d'étanchéité ni aux assemblages dont la rigidité varie de façon notable sur la largeur du joint. En ce qui concerne les joints en matériau incompressible qui présentent des déformations importantes, les résultats fournis par la méthode de calcul peuvent être excessivement conservateurs (c'est-à-dire effort de boulonnage requis trop élevé, pression admissible de fluide trop faible, épaisseur de bride nécessaire trop importante, etc.).
Prirobnice in prirobnični spoji - Pravila za konstruiranje prirobničnih spojev, sestavljenih iz okroglih prirobnic in tesnil - 1. del: Izračun
Ta dokument določa računsko metodo za prirobnične spoje, sestavljene iz vijakov ter okroglih prirobnic in tesnil. Njegov namen je zagotoviti konstrukcijsko celovitost in nadzor tesnjenja. V dokumentu so uporabljeni parametri tesnil, ki temeljijo na definicijah in preskusnih metodah iz standarda EN 13555:2014.
Računska metoda se ne uporablja za spoje s kovinskim kontaktom zunaj tesnilne površine ali spoje, katerih trdnost se zelo razlikuje glede na širino tesnila. Za tesnila v nestisljivih materialih, ki dopuščajo velike deformacije, so lahko rezultati računske metode preveč konzervativni (tj. previsoka zahtevana obremenitev vijakov, prenizek dovoljeni tlak tekočine, prevelika zahtevana debelina prirobnice itd.).
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-december-2024
Nadomešča:
SIST EN 1591-1:2014
Prirobnice in prirobnični spoji - Pravila za konstruiranje prirobničnih spojev,
sestavljenih iz okroglih prirobnic in tesnil - 1. del: Izračun
Flanges and their joints - Design rules for gasketed circular flange connections - Part 1:
Calculation
Flansche und ihre Verbindungen - Regeln für die Auslegung von Flanschverbindungen
mit runden Flanschen und Dichtung - Teil 1: Berechnung
Brides et leurs assemblages - Règles de calcul des assemblages à brides circulaires
avec joint - Partie 1: Méthode de calcul
Ta slovenski standard je istoveten z: EN 1591-1:2024
ICS:
23.040.60 Prirobnice, oglavki in spojni Flanges, couplings and joints
elementi
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN 1591-1
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2024
EUROPÄISCHE NORM
ICS 23.040.60 Supersedes EN 1591-1:2013
English Version
Flanges and their joints - Design rules for gasketed circular
flange connections - Part 1: Calculation
Brides et leurs assemblages - Règles de calcul des Flansche und ihre Verbindungen - Regeln für die
assemblages à brides circulaires avec joint - Partie 1: Auslegung von Flanschverbindungen mit runden
Méthode de calcul Flanschen und Dichtung - Teil 1: Berechnungsmethode
This European Standard was approved by CEN on 7 July 2024.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a 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 European Standard 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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2024 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1591-1:2024 E
worldwide for CEN national Members.
Contents Page
1 Scope . 7
2 Normative references . 7
3 Terms and definitions, subscripts, special marks and symbols . 7
3.1 Terms and definitions . 7
3.2 Subscripts and special marks . 17
3.2.1 Subscripts . 17
3.2.2 Special marks . 18
3.3 Symbols . 18
4 Requirements for use of the calculation method . 24
4.1 General . 24
4.2 Geometry . 24
4.3 Material . 24
4.4 Loads . 25
5 Calculation parameters . 25
5.1 General . 25
5.2 Flange parameters . 25
5.2.1 General . 25
5.2.2 Flange ring . 26
5.2.3 Connected shell . 27
5.2.4 Flexibility-related flange parameters . 28
5.3 Bolt and washer parameters . 29
5.3.1 General . 29
5.3.2 Effective cross-section area of bolts . 29
5.3.3 Flexibility modulus of bolts . 29
5.3.4 Geometric parameters for washers and contact surfaces . 29
5.3.5 Flexibility modulus of washers . 30
5.4 Gasket parameters . 30
5.4.1 General . 30
5.4.2 Theoretical dimensions . 30
5.4.3 Effective dimensions . 30
5.4.4 Axial flexibility modulus of gasket . 31
5.4.5 Lever arms . 33
6 Forces . 34
6.1 General . 34
6.2 Applied loads . 34
6.2.1 Assembly condition (I = 0) . 34
6.2.2 Subsequent conditions (I = 1, 2 …) . 34
6.3 Compliance of the joint . 35
6.4 Minimum forces necessary for the gasket . 36
6.4.1 Assembly condition (I = 0) . 36
6.4.2 Subsequent conditions (I = 1, 2, ….) . 36
6.5 Internal forces in assembly condition (I = 0) . 37
6.5.1 Required forces . 37
6.5.2 Accounting for bolt-load scatter at assembly . 38
6.6 Internal forces in subsequent conditions (I = 1, 2, …) . 38
7 Load limits . 39
7.1 General . 39
7.2 Bolts . 40
7.3 Gasket . 40
7.4 Integral flange and collar or stub . 41
7.5 Blank flange . 43
7.6 Loose flange on collar/stub. 43
(informative) Dimensions of standard metric bolts . 45
(informative) Tightening . 46
B.1 Scatter of initial bolt load of a single bolt — Indicative values ε and ε for a single
1- 1+
bolt . 46
B.2 Scatter for the global load of all the bolts . 46
B.3 Manual uncontrolled tightening . 47
B.4 Assembly using torque wrench . 47
B.5 Assembly using bolt tensioner . 48
(informative) Flange rotations . 50
C.1 General . 50
C.2 Use of flange rotation . 50
C.3 Calculation of flange rotations . 50
(informative) Use of the calculation method . 52
D.1 Calculation method principle . 52
D.2 Mechanical model . 53
D.3 Required checks . 54
D.4 Calculation sequence . 54
(informative) Gasket/flange face friction coefficients examples . 57
(informative) Checking a specified assembly bolt force . 58
(informative) Sealing gasket parameters when no leakage rate is specified . 59
(informative) Alternative calculation procedure taking into account the plastic
deformation of the gasket in subsequent load conditions procedures (after assembly) . 60
H.1 General . 60
H.2 Calculation procedure. 60
H.2.1 General description . 60
H.2.2 No additional plastic deformation . 61
H.2.3 Additional plastic deformation. 61
H.3 Flat gaskets . 61
H.3.1 Flat gaskets with small or median deformations . 61
H.3.2 Flat gaskets with greater deformations . 63
H.4 Metal gaskets with curved surfaces (Figures 4b), c), e), f)) . 64
H.5 Metal gaskets with octagonal section (Figure 4d)) . 64
(informative) Available, incomplete models for conversion of the leakage rates in
different conditions (based on certain flow models) . 65
I.1 Introduction and warning . 65
I.2 Flow theory fundamentals . 65
I.2.1 Transport modes . 65
I.2.2 Case of gases . 66
I.2.3 Case of liquids: Parallel capillary model . 67
I.3 Factors of influence on the leakage rate of gaskets and gasketed joints. 67
I.3.1 List of identified factors . 67
I.3.2 Limits and restriction of the proposed models . 67
I.3.3 Dependence on pressure . 68
I.3.4 Dependence on temperature . 69
I.3.5 Dependence on the type of fluid . 70
I.3.6 Influence of the gasket thickness . 70
I.3.7 Influence of gasket width . 71
I.3.8 Influence of gasket stress . 71
I.3.9 Influence of other factors . 72
I.3.10 Conclusion on the factors of influence . 72
I.4 Practical application for EN 1591-1 calculations . 72
I.4.1 General . 72
I.4.2 Determination of a trend for the leakage rate for the flange connection in “actual”
from “reference” conditions . 74
I.4.3 Determination of a trend for the leakage rate for the flange connection in “reference”
from “actual” conditions . 75
Annex ZA (informative) Relationship between this European Standard and the essential
requirements of Directive 2014/68/EU aimed to be covered . 77
European foreword
This document (EN 1591-1:2024) has been prepared by Technical Committee CEN/TC 74 “Flanges and
their joints”, the secretariat 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 or by endorsement, at the latest by April 2025, and conflicting national standards shall be withdrawn
at the latest by April 2025.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN 1591-1:2013.
The major changes in comparison with the previous edition include:
— Removal of the possibility to handle gasket creep/relaxation behaviour through additional deflection.
In this new revision, the gasket creep/relaxation behaviour is only treated using the P factor;
QR
— Correction of the lever arms considered for integral flange and collar load ratio calculation (127),
(135);
— Introduction of a reduced maximum allowable value of load ratio for large integral flange and collar
(128) and for large loose flanges (149);
— Possibility to check a bolted flange connection for a specified assembly bolt force value, previously
treated in the body of the document is now defined in a new informative annex (Annex F);
— Update of the Flange/gasket friction factors in Annex E;
— Update of the Annex ZA in accordance with the Directive 2014/68/EU on Pressure Equipment.
This document has been prepared under a standardization request addressed to CEN by the European
Commission. The Standing Committee of the EFTA States subsequently approves these requests for its
Member States.
For the relationship with EU Legislation, see informative Annex ZA, which is an integral part of this
document.
EN 1591 consists of several parts:
— EN 1591-1, Flanges and their joints — Design rules for gasketed circular flange connections — Part 1:
Calculation;
— CEN/TR 1591-2, Flanges and their joints — Design rules for gasketed circular flange connections — Part
2: Gasket parameters;
— CEN/TS 1591-3, Flanges and their joints — Design rules for gasketed circular flange connections — Part
3: Calculation method for metal to metal contact type flanged joint;
— EN 1591-4, Flanges and their joints — Part 4: Qualification of personnel competency in the assembly of
the bolted connections of critical service pressurized systems;
— CEN/TR 1591-5, Flanges and their joints — Design rules for gasketed circular flange connections — Part
5: Calculation method for full face gasketed joints.
The calculation method satisfies both leak tightness 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 forces due to compliance of all components of the joint;
— influence of connected shell or pipe;
— effect of external axial and lateral forces and torsion and bending moments;
— effect of temperature difference between bolts and all clamped components of the flange connection.
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.
Any feedback and questions on this document should be directed to the users’ national standards body. A
complete listing of these bodies can be found on the CEN website.
According to the CEN/CENELEC Internal Regulations, the national standards organisations of the following
countries are bound to announce this Technical Specification: 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, Republic of North
Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the United
Kingdom.
1 Scope
This document defines a calculation method for bolted, gasketed, circular flange joints. Its purpose is to
ensure structural integrity and control of leak tightness. It uses gasket parameters based on definitions
and test methods specified in EN 13555:2021.
The calculation method is not applicable to joints with a metallic contact out of the sealing face or to joints
whose rigidity varies appreciably across gasket width. For gaskets in incompressible materials, which
permit large deformations, the results given by the calculation method can be excessively conservative (i.e.
required bolting load too high, allowable pressure of the fluid too low, required flange thickness too large,
etc.).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
EN 13555:2021, Flanges and their joints — Gasket parameters and test procedures relevant to the design
rules for gasketed circular flange connections
3 Terms and definitions, subscripts, special marks and symbols
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions, subscripts, special marks and
symbols apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
• ISO Online browsing platform: available at https://www.iso.org/obp
• IEC Electropedia: available at http://www.electropedia.org/
For standard flange types, as shown in EN 1092 or EN 1759, the relevant figures are the following:
Type 01 Figure 10
Type 02 Figure 12 (with collar type 35, 36 and 37)
Type 05 Figure 11
Type 11 Figure 6
Type 12 Figure 13
Type 13 Figure 14
Type 21 Figures 6 to 9
NOTE Figure 1 to Figure 14 illustrate the notation corresponding to the geometric parameters. They only show
principles and are not intended to be practical designs. They do not illustrate all possible flange types for which the
calculation method is valid. For further details see 5.2.
3.1.1
flanges
3.1.1.1
integral flange
flange attached to the shell either by welding (e.g. neck weld, see Figure 6 to Figure 9, or slip on welded or
weld-on, see Figure 10 and Figure 13) or cast onto the envelope (integrally cast flanges, type 21)
3.1.1.2
blank or blind flange
flat closure (see Figure 11)
3.1.1.3
loose flange
separate flange ring abutting a collar (see Figure 12)
3.1.1.4
hub
axial extension of flange ring, usually connecting flange ring to shell (see Figure 6 and Figure 7)
3.1.1.5
collar or stub
abutment for a loose flange (see Figure 12)
3.1.2
loading
3.1.2.1
external loads
forces and/or moments applied to the joint by attached equipment, e.g. weight and thermal expansion of
pipes
3.1.3
load conditions
3.1.3.1
load condition
state with set of applied simultaneous loads; designated by I
3.1.3.2
assembly condition
load condition due to initial tightening of bolts (bolting up), designated by I = 0
3.1.3.3
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 .
3.1.4
compliances
3.1.4.1
compliance
inverse stiffness (axial), symbol Y, [mm/N]
3.1.4.2
flexibility modulus:
inverse stiffness modulus, excluding elastic constants of material:
— axial: symbol X, [1/mm]
— rotational: symbol Z, [1/mm ]
Figure 1 — Loads and lever arms
Figure 2 — Washer or spacer
𝑙𝑙 =𝑙𝑙 −𝑙𝑙
𝑒𝑒 𝐵𝐵 𝑠𝑠
Figure 3 — Bolts
Key
a) Flat gaskets, of low hardness, composite or pure metallic, materials
b) and c) Metal gaskets with curved surfaces, simple contact
d) Metal octagonal section gaskets
e) and f) Metal oval or circular section gaskets, double contact
Figure 4 — Gaskets
Key
1 male flange (tongue)
2 female flange (groove)
3 gasket
Figure 5 — Details for tongue and groove facing
Key
1 shell
2 hub
3 ring
Figure 6 — Weld-neck flanges with cylindrical shells (example 1)
Key
1 shell
2 hub
3 ring
Figure 7 — Weld-neck flanges with cylindrical shells (example 2)
Key
1 shell
2 ring
Figure 8 — Flanges welded to conical shells
Key
1 shell
2 ring
Figure 9 — Flanges welded to spherical shells
Key
1 shell
2 ring
Figure 10 — Weld-on plate flange
Key
1 plate
2 ring
Figure 11 — Blank flange
Key
1 shell
2 collar
3 loose flange
Figure 12 — Collar or stub with loose flanges
Figure 13 — Hubbed slip-on welded flange
Figure 14 — Hubbed threaded flange
3.2 Subscripts and special marks
3.2.1 Subscripts
A Additional (F , M )
A A
B Bolt
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, Lateral (F )
LI
M Moment
N Nut
P Fluid pressure
Q Net axial force due to pressure
R Net axial force due to external force
S Shell, Shear
T Shell, modified
TG Torsion (M )
TG
X Flange weakest cross section
W Washer or extension sleeve
∆ Symbol for change or difference
av average
c calculated
e effective
i Interim value
max maximum
min minimum
nom nominal
opt optimal
req required
s non-threaded part of bolt
specified refers to the case of calculation performed for a given (specified) assembly bolt force
(Annex F)
t theoretical, torque, thread
0 assembly 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, possibly different from the first
3.3 Symbols
Where units are applicable, they are shown in brackets. Where units are not applicable, no indication is
given.
A Effective total cross-section area of all bolts [mm ], Formulae (39), (52), (121),
B
(B.3)
A , A Gross radial cross-section area (including bolt holes) of flange ring, loose flange
F L
[mm ], Formulae (8), (11) and (14)
A , A Gasket area, effective, theoretical [mm ], Formulae (51), (54), (126)
Ge Gt
A Effective area for the axial fluid-pressure force [mm ], Formula (88)
Q
E , E , E E Modulus of elasticity of the part designated by the subscript, at the temperature
B F L W
of the part [MPa] Formulae (60), (63), (97) to (100), (C.1), (C.2)
E Modulus of elasticity of the gasket for unloading/reloading at the considered
G
temperature, considering the gasket surface pressure in assembly Q [MPa]
G0
Formulae (56), (64), (65), (67),(68), (72), (73), (98)
F Additional external axial force [N], tensile force > 0, compressive force < 0, see
A
Figure 1, Formulae (90) and (94)
F Bolt force (sum of all bolts) [N] Formulae (106), (109) to (117), (120), (121),
B
(144), (146), (148), (B.4), (B.5), (B.9), (C.2) to (C.4), (C.9), (C.10)
F Gasket force [N] Formulae (52), (55), (63), (73), (105) to (108), (116) to (120),
G
(126), (127), (135), (C.1), (C.5) to (C.8)
F Minimum gasket force in assembly condition [N] that guarantees, the required
G∆
gasket force for all subsequent conditions, Formulae (103), (104)
F Force resulting from the additional radial forces [N], Formulae (91) and (102)
L
F Axial fluid-pressure force [N], Formulae (89), (102), (103), (104), (118), (119),
Q
(120), (127), (135), (144), (151), (C.1), (C.7) to (C.10)
F Force resulting from the additional external loads [N], Formulae (94), (102),
R
(103), (104), (106), (116), (117), (118), (119), (120), (127), (135), (144), (151),
(C.1), (C.5) to (C.10)
F , F , F Additional forces along X, Y and Z-axis at gasket interface [N], Formulae (90) and
X Y Z
(91)
I Load condition identifier, for assembly condition I = 0, for subsequent conditions
I = 1, 2, 3,.
𝜋𝜋
I
B 3
Plastic torsion modulus of bolt shanks �𝐼𝐼 = × min(𝑑𝑑 ;𝑑𝑑 )� [mm ],
𝐵𝐵 𝐵𝐵𝑒𝑒 𝐵𝐵𝑠𝑠
Formula (121)
MA Resulting external bending moment [N × mm], Figure 1, Formulae (92) and
(102)
M Nominal bolt assembly torque [N × mm], Formulae (B.4) and (B.5)
t,nom
M Twisting moment [N × mm] applied to bolt shanks as a result of application of
tB
the nominal bolt assembly force F Formulae (121) and (B.9)
B0,nom
M Additional external torsion moment due to friction, Formula (93) and (102)
TG
N Number of re-assemblies and re-tightenings during service life of joint,
R
Formulae (117), (F.2)
P Pressure of the fluid [MPa], internal pressure > 0, external pressure < 0 (1 bar =
0,1 MPa), Formula (89)
NOTE P in this standard is equivalent to the maximum allowable pressure PS according to the PED.
P Creep relaxation factor which is the ratio of the residual and the original gasket
QR
surface pressure at load conditions [-] Formulae (103), (104), (118), (119), (C.7),
(C.8). (see EN 13555:2021 for more details)
Q Gasket surface pressure in assembly condition [MPa] Formula (55)
G0
Q Gasket surface pressure at assembly prior to the unloading which is necessary
A
for the validity of the corresponding Q in all subsequent conditions [MPa],
Smin (L),I
Formula (101). The lowest acceptable value for Q isQ from EN 13555:2021.
A min (L)
Q Gasket surface pressure required at assembly prior to the unloading when no
0,min
specific leak rate is requested [MPa], replacement of Q in Formula (101),
A
Annex G
Q Minimum level of gasket surface pressure required for tightness class L at
min (L)
assembly (on the effective gasket area) from EN 13555:2021 test results [MPa]
(see 6.4.2 NOTE 1)
Q Minimum level of gasket surface pressure required for tightness class L in service
Smin (L)
conditions (after off-loading) (on the effective gasket area) from EN 13555:2021
test results [MPa], Formula (102)
Q Maximum allowable gasket surface pressure that can be safely imposed upon the
Smax
gasket at the considered temperature without damage [MPa], Formulae (63),
(67), (68), (72), (73), (126) and (151)
T , T , T , T , T Temperature (average) of the part designated by the subscript [°C] or [K],
B F G L W
Formula (95)
T Temperature of joint at assembly [°C] or [K] (usually + 20 °C), Formula (95)
W , W , W Resistance of the part and/or cross-section designated by the subscript
F L X
[N × mm], Formulae (127), (129), (144) to (148), (150)
X , X X Axial flexibility modulus of bolts, gasket, washer [1/ mm], Formulae (40), (41),
B G, w
(47), (48), (61), (97), (98)
Y Y , Y , Y Axial compliance of the bolted joint, related to F , F , F , F [mm/N], Formulae
B, G Q R B G Q R
(97), (98), (99), (100), (103), (104), (118), (119), (C.7), (C.8)
-3
Z , Z Rotational flexibility modulus of flange, loose flange [mm ], Formulae (32),
F L
(36), (33), (37), (38), (60), (63), (97) to (100)
b Width of chamfer (or radius) of a loose flange such that: d = d +2×b [mm],
0 7min 6 0
Figure 12, Formula (83)
b , b Effective width of flange, loose flange [mm], Formulae (5), (6), (9), (12), (23),
F L
(32), (38), (129), (139), (145), (150), see 4.2 d) 1)
b , b , b Gasket width (radial), interim, effective, theoretical [mm], Formulae (49), (51),
Gi Ge Gt
(53), (54), (61) to (63), (66), (67), (68), (70), (72) and (73)
b Contact widths bolt side [mm], Formulae (46) to (48), Figure 2
KB
b Width of a washer [mm], Formulae (42), (47), (48), Figure 2
W
c , c , c , c , c Correction factors [-], Formulae (26), (121) to (125), (133), (134)
A B F M S
d Inside diameter of flange ring [mm] and outside diameter of central part of
blank flange (with thickness e ), in no case greater than inside diameter of
gasket [mm], Figures 6 to 14, Formulae (7) to (9), (22), (128), (145)
d Average diameter of hub, thin end [mm], Figures 6, 7, 13
d Average diameter of hub, thick end [mm], Figures 6, 7, 13
d , d Bolt circle diameter, real, effective [mm], Figures 6 to 14, Formulae (4), (146)
3 3e
d Outside diameter of flange [mm], Figures 6 to 14, Formulae (7), (8), (128),
(147), (149)
d , d , d Diameter of bolt hole, pierced, blind, effective [mm], Figures 6 to 14, Formulae
5 5t 5e
(2), (3), (147)
d Inside diameter of loose flange [mm], Formulae (83), (149), Figures 12, 14
d d d , d Diameter of position of reaction between loose flange and stub or collar, initial,
7, 70, 7min 7max
minimal, maximal [mm], Figure 1, Figure 12, Formulae (59), (82) to (87) and
(151)
d Outside diameter of collar [mm], Formulae (9), (10), (84), Figures 12 and 14
d Diameter of a central hole in a blank flange [mm], Formula (34), Figure 11
d , d , d Diameter of bolt: nominal diameter, effective diameter, shank diameter [mm],
B0 Be Bs
Formulae (39), (40), Figure 3, Table A.1
d , d Basic pitch diameter, basic minor diameter of thread [mm], see Figure 3, Table
B2 B3
A.1, Formula (B.9)
d Maximum possible outside contact diameter between bolt head or nut and
B4
flange or washer [mm], Formula (45), Figure 2
d , d Diameter of gasket, effective, theoretical [mm], Figure 4, Formula (51), (54),
Ge Gt
(57) to (59), (63), (66), (69), (71), (74), (75), (77), (78), (79), (85), (88), (102)
d , d Extreme contact diameters (inside, outside) [mm], Formulae (44) and (45),
K1 K2
Figure 2, 5.3.4.2 NOTE 2
d , d , d Real, theoretical inside, theoretical outside contact diameters [mm], Formulae
G0 G1 G2
(49), (50), (66), (69), (151), Figure 4
d , d , d , d , d Average diameter of part or section designated by the subscript [mm],
E F L S X,
Formulae (6), (7), (10), (13), (20), (22), (24), (27), (32), (34), (35), (36), (38),
(75), (77), (78), (80), (86), (129), (131), (132), (139), (146), (147), (151),
Figures 1, 8, 9, 10, 11
d d d Inside, Mean, Outside diameter of washer [mm], Formulae (42) to (45), Figure
w1, w, w2
1, 2
e Wall thickness of central plate of blank flange within diameter d [mm],
0 0
Formulae (36) and (145), Figure 11
e Lowest wall thickness at thin end of hub or of connected shell [mm], Formulae
(15) to (18), Figures 6, 7, 10, 12, 13, 14
e Wall thickness at thick end of hub [mm], Formulae (17) and (18), Figures 6, 7,
10, 12, 13, 14
e , e Wall thickness of equivalent cylinder for load limit calculations, for flexibility
D E
calculations [mm], Formulae (15), (16), (18), (19), (21), (24), (27), (129),
(131), (132), (139)
e , e Effective axial thickness of flange, loose flange [mm], Formulae (8), (11), (14),
F L
(24), (25), (27), (28), (32), (36), (38), (95), (96), (129), (139), (140), (145),
(147), (150), (151), 4.2 ) 1), Figures 6 to 14
e Thickness of flange ring at diameter d (bolt position) [mm], Formula (3)
Fb 3
e , e Thickness of (integral or loose) flange ring at diameter d (gasket force
Ft Lt Ge
position), relevant for thermal expansion [mm], Formulae (95) and (96),
Figure 5 and Figure 12
e (Q ) Compressed gasket thickness under contact pressure Q [mm], Formulae (61),
G G0 G0
(63),(95), (96), (104), (119), can be obtained from the tests according to EN
13555:2021
e Compressed thickness of gasket after all subsequent conditions (including
G(A)
plastic deformation) [mm], Formulae (104), (119) and Annex H
e Theoretical uncompressed thickness of gasket [mm], Figure 4
Gt
e Nut thickness, Formula (125)
N
e , e Part of flange thickness with (e ), without (e ) radial pressure loading [mm],
P Q P Q
such that e +e = e , Formulae (25) and (139), Figures 6 to 10 and 12 to 14,
P Q F
e Thickness of connected shell [mm], Formula (19), 4.2 d) 2), Figures 6 to 10, 12
S
to 14
e Washer thickness [mm], Formulae (47) and (48), Figure 1
W
e Flange thickness at weak section [mm], Formula (147), Figure 11
X
f , f , f , f , f ,f Nominal design stress [MPa] of the part designated by the subscript, at design
B E F L N , S,
temperature [°C] or [K], as defined and used in pressure vessel codes (see
Formulae (121), (125), (129) to (132), (139), (145), (147), (150) and (151))
h , h , h Lever arms [mm], Figure 1, Formulae (57), (58), (63), (79) to (81) and (85) to
G H L
(87), (97) to (100), (127),(135),(144), (151), (C.1), (C.2)
h , h , h , h , h Lever arm corrections [mm], Formulae (27) to (29), (35), (75), (77), (78), (99),
P Q R S T
(100), (127),(135), (C.1)
j , j Sign number for moment, shear force (+1 or 1), Formulae (135) and (136)
M S
k , k , k , k Correction factors, Formulae (30), (31), (77), (129), (137) to (139), Table 2
Q R M S
l , l Total, effective screws engagment length in threaded hole, Formulae (3) (125),
5 5t
Figures 3, 7, 8 and 9
l , l Bolt axial dimensions [mm], Figure 3, Formulae (95), (96) and (40)
B s
l l = l - l , Formula (40)
e e B S
l Length of hub [mm], Figures 6, 7, 13, Formulae (15), (16)
H
m Tightness factor for subsequent conditions ( I>0 ) [-], (Annex G)
n Number of bolts, Formulae (1), (4), (39), (40), (B.1) to (B.5) and (B.9)
B
p Pitch between bolts [mm], Formula (1)
B
p Pitch of bolt thread [mm], Table A.1, Formulae (B.6), (B.7), (B.9)
t
r , r Radii [mm], Figures 6, 12
0 1
r Radius of curvature in gasket cross-section [mm], Figure 4
T
∆U Differential thermal axial expansions [mm], Formulae (95), (103), (104), (118),
(119), (C.7), (C.8)
Θ , Θ Rotation of flange, loose flange, due to applied moment [rad], Annex C,
F L
Formulae (C.1), (C.2)
Ψ Load ratio of flange ring due to radial force, Formula (139)
Ψ Particular value of Ψ, Formula (129), Table 2
Z
Ф , Ф , Ф , Ф , Ф , Load ratio of part and/or cross-section designated by the subscript, to be
B F G L X
calculated for all load conditions, Formulae (121), (127), (144), (151), (126),
(148), (146)
Ф Maximum allowable value of Ф and Ф Formulae (128), (149)
max F L,
α , α , α , α , α Thermal expansion coefficient of the part designated by the subscript,
B F G L W
-1
averaged between T and T , T , T , T , T [K ], Formula (95)
0 B F G L W
β, γ, δ, ν, κ, λ, x,ϑ Intermediate variables, Formulae (17), (23) to (25), (60), (133), (134)
ε , ε Scatter of initial bolt load of a single bolt, above nominal value, below nominal
1+ 1-
value, Annex B, Table B.1
ε , ε Scatter for the global load of all the bolts above nominal value, below nominal
+ –
value, Annex B, Formulae (B.1), (B.2)
µ Friction factor for bolting, see Annex B, Formula (B.8)
µ Friction factor between the gasket and the flange facing, Table E.1 and Formula
G
(102)
𝜋𝜋 Ratio of the circumference of a circle to its diameter
Diameter ratio as given in Formulae (34) to (36), (144), (145)
ρ
φ Angle of inclination of a sealing face [rad or deg], Figure 4c), 4e), 4f), Formulae
G
(67), (68), (72), (73)
φ Angle of inclination of connected shell wall [rad or deg], Figures 8, 9, Formulae
...
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