SIST EN 13445-3:2014/oprA14:2019
(Amendment)Unfired pressure vessels - Part 3: Design
Unfired pressure vessels - Part 3: Design
Amends clause 9
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Récipients sous pression non soumis à la flamme - Partie 3 : Conception
Nekurjene tlačne posode - 3. del: Konstruiranje - Dopolnilo A14
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 13445-3:2014/oprA14:2019
01-september-2019
Neogrevane (nekurjene) tlačne posode - 3. del: Konstruiranje - Dopolnilo A14
Unfired pressure vessels - Part 3: Design
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Récipients sous pression non soumis à la flamme - Partie 3 : Conception
Ta slovenski standard je istoveten z: EN 13445-3:2014/prA14
ICS:
23.020.32 Tlačne posode Pressure vessels
SIST EN 13445-3:2014/oprA14:2019 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN 13445-3:2014/oprA14:2019
DRAFT
EUROPEAN STANDARD
EN 13445-3:2014
NORME EUROPÉENNE
EUROPÄISCHE NORM
prA14
July 2019
ICS 23.020.30
English Version
Unfired pressure vessels - Part 3: Design
Récipients sous pression non soumis à la flamme - Unbefeuerte Druckbehälter - Teil 3: Konstruktion
Partie 3 : Conception
This draft amendment is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 54.
This draft amendment A14, if approved, will modify the European Standard EN 13445-3:2014. If this draft becomes an
amendment, CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for
inclusion of this amendment into the relevant national standard without any alteration.
This draft amendment was established by CEN in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC
Management Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13445-3:2014/prA14:2019 E
worldwide for CEN national Members.
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Contents Page
European foreword . 3
1 Modification to Clause 9, Openings in shells . 4
2
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European foreword
This document (EN 13445-3:2014/prA14:2019) has been prepared by Technical Committee CEN/TC 54
“Unfired pressure vessels”, the secretariat of which is held by BSI.
This document is currently submitted to the CEN Enquiry.
This document has been prepared under a standardization request given to CEN by the European
Commission and the European Free Trade Association, and supports essential requirements of
EU Directive(s).
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of
EN 13445-3:2014.
3
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1 Modification to Clause 9, Openings in shells
Replace the whole Clause 9 with the following one:
"
9 Openings in shells
9.1 Purpose
The design method specified in this clause is applicable to circular, elliptical or obround openings in
dished ends or cylindrical, conical or spherical shells under internal or external pressure.
This clause is applicable to openings, nozzles and reinforcing plates in dished ends which are
completely located inside the central area limited by a radius equal to 0,4D as shown in Figure 9.5-4.
e
For different locations (i.e. nozzles in knuckle regions) the relevant design rules are given in Clause 7.
Design for non-pressure loads is covered by Clause 16.
9.2 Specific definitions
The following definitions apply in addition to those in Clause 3.
9.2.1
ligament check
evaluation of the reinforcement between two adjacent openings
9.2.2
opening
reinforcing ring or a nozzle, through penetration of the shell which may or may not be fitted with a
reinforcing plate
9.2.2.1
obround opening
opening with an obround shape, given by two semicircles connected by two parallel straight lines
9.2.3
overall check
evaluation of the reinforcement in the cross-section including the walls on each side of each opening
and the lengths of adjacent shell
9.2.4
reinforcement
loaded cross-sectional area of metal considered to provide resistance to the pressure at an opening
9.2.5
reinforced opening
opening where the reinforcement includes a contribution from the shell, from a nozzle, a reinforcing
plate or a reinforcing ring
9.2.6
reinforcing plate
plate which is fillet welded to the shell and contributes to the reinforcement
9.2.7
reinforcing ring
set-in ring which contributes to the reinforcement
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9.2.8
set-in nozzle
nozzle which passes through the shell and is welded to it on the inside and outside of the shell
(see Figure 9.4-8)
9.2.9
set-on nozzle
nozzle which is welded only to the outside of the shell (see Figure 9.4-7)
9.2.10
shell
cylinder, sphere, cone or dished end
9.2.11
shell discontinuity
junction between any two of the following: cylinder, cylinder on a different axis, cone, dished head,
spherical end, flange or flat head
9.2.12
small opening
isolated opening which satisfies the condition of Formula (9.5-18)
9.3 Specific symbols and abbreviations
9.3.1 General
The following symbols, subscripts and abbreviations apply in addition to those in Clause 4.
9.3.2 Subscripts
The following subscripts apply to the symbols listed in 9.3.3.
a refers to the analysis thickness of a component;
b refers to a nozzle or branch;
c refers to the mean value of a dimension;
e refers to the outside or external dimension;
i refers to the inside or internal dimension;
L refers to a ligament check;
O refers to an overall check;
o refers to a possible maximum or minimum value; among different values;
p refers to a reinforcing plate;
r refers to a reinforcing ring;
s refers to the shell;
w refers to the area of fillet weld which may be taken into account for reinforcement;
φ refers to additional pressure loaded area for an oblique nozzle connection;
1 refers to the first of two adjacent openings;
2 refers to the second of two adjacent openings.
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9.3.3 Symbols
Symbol Description Unit
a Distance taken along the mid-thickness of the shell between the centre mm
of an opening and the external edge of a nozzle or ring; or, if no nozzle
or ring is present, a is the distance between the centre of the hole and its
bore.
a , a Values of a on the ligament side of the opening (Figures 9.6–2 and 9.6– mm
1 2
3).
a’ , a’ Values of a on the opposite side of the opening to the ligament mm
1 2
(see Figure 9.6–5).
2
Af Stress loaded cross-sectional area effective as reinforcement. mm
2
Af Af of the shell contained along the length L (see Figures 9.6–1 to 9.6–4). mm
Ls b
Af Af of the shell contained along the length L (see Figures 9.6–5 to 9.6–
Os b1
2
mm
6).
Af Cross-sectional area of fillet weld between nozzle (or plate) and shell
w
2
mm
(see 9.5.2.3.3 and Figures 9.4–4 and 9.5–1).
2
Ap Pressure loaded area. mm
2
Ap Ap of the shell for the length L (see Figures 9.6–1 to 9.6–4). mm
Ls b
2
Ap Ap of the shell for the length L (see Figures 9.6–5 to 9.6–6). mm
Os b1
Ap Additional pressure loaded area for oblique nozzle connection, function
φ
2
mm
of angle φ (see Figures 9.5–1 to 9.5–3).
d Diameter (or maximum width) of an opening on shell without nozzle. mm
d External diameter of a nozzle fitted in a shell. mm
eb
d Internal diameter of a nozzle fitted in a shell. mm
ib
d Internal diameter of a reinforcing plate. mm
ip
d External diameter of a reinforcing ring. mm
er
d Internal diameter of a reinforcing ring. mm
ir
d Internal diameter of extruded opening. mm
ix
D Mean diameter of a cylindrical shell at the junction with another mm
c
component.
De External diameter of a cylindrical or spherical shell, the cylindrical part mm
of a torispherical or an elliptical dished end, a conical shell at the centre
of an opening.
D Internal diameter of a cylindrical or spherical shell, the cylindrical part mm
i
of a torispherical or an elliptical dished end, a conical shell at the centre
of an opening.
e Minimum required thickness of a cylindrical shell at the junction with mm
1
another component (see Figures 9.7–6 and 9.7–10).
e Minimum required thickness of a conical shell at the junction with a mm
2
cylindrical shell (see Figures 9.7–6 and 9.7–10).
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Symbol Description Unit
e Effective thickness of nozzle (or mean thickness within the external mm
b
length l or internal length l ) taken into account for reinforcement
bo bio
calculation.
e Analysis thickness of nozzle (or mean analysis thickness within the mm
a,b
length lb external or internal by the shell).
e Average thickness along the length l for reinforcing rings mm
a,m o
(see Formula (9.5–48)).
e Assumed shell thickness of shell wall (see Formula (9.5–2) for checking mm
c,s
of reinforcement of an opening. The thickness may be assumed by
designer between the minimum required shell thickness e and the shell
analysis thickness e . This assumed thickness shall then be used
a,s
consistently in all requirements.
For e the shell analysis thickness may be used always, but sometimes it
c,s
may be advantageous to use a smaller assumed value to obtain smaller
distances from adjacent shell discontinuities.
e Effective thickness of reinforcing plate taken into account for mm
p
reinforcement calculation.
e Analysis thickness of reinforcing plate. mm
a,p
er Effective thickness of reinforcing ring taken into account for mm
reinforcement calculation.
e Analysis thickness of reinforcing ring. mm
a,r
e Analysis thickness of shell wall or mean analysis thickness within the mm
a,s
length l' and excluding the thickness of the reinforcing pad if fitted.
s
e's Length of penetration of nozzle into shell wall for set-in nozzles with mm
partial penetration.
f Nominal design stress of the nozzle material. MPa
b
f Nominal design stress of the reinforcing plate material. MPa
p
f Nominal design stress of shell material. MPa
s
h Inside height of a dished end, excluding cylindrical skirt. mm
k Reduction factor for l (used for overall check in 9.6.4). _
so
l Length of nozzle extending outside the shell. mm
b
l' Effective length of nozzle outside the shell for reinforcement. mm
b
l Length of nozzle extending inside the shell (i.e.: protruding nozzle). mm
bi
l’ Effective length of nozzle inside the shell for reinforcement. mm
bi
l Maximum length of nozzle outside the shell for reinforcement. mm
bo
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Symbol Description Unit
l Length of cylindrical shell given by Formula (9.7–3) and used in the mm
cyl
strength assessment of a junction (see Figure 9.7–6) between a cylinder
and:
— the small end of a conical shell with same axis;
— a spherical shell convex towards the cylinder;
— a cylindrical shell with convergent axis.
l Length of conical shell given by Formula (9.7–7) and used in the mm
con
strength assessment of a junction between the small end of a cone and a
cylindrical shell, (see Figure 9.7–6).
l Distance between the centre line of a shell butt-weld and the centre of mm
n
an opening near or crossing the butt-weld.
l Maximum length of ring and shell wall in reinforcing rings for mm
o
reinforcement.
l Width of reinforcing plate. mm
p
l Width of reinforcing plate between two adjacent openings (Figure 9.6– mm
pi
5).
l’ Effective width of reinforcing plate for reinforcement. mm
p
l Width of reinforcing ring. mm
r
l’r Effective width of reinforcing ring for reinforcement. mm
l Length of shell, from the edge of an opening or from the external mm
s
diameter of a nozzle, to a shell discontinuity.
l’ Effective length of shell for opening reinforcement. mm
s
l Maximum length of shell contributing to opening reinforcement, taken mm
so
on the mean surface of the shell wall.
L Centre-to-centre distance between two openings or nozzles taken on the mm
b
mean surface of the shell (see Figure 9.6–2).
L Length of cross sectional area of shell including the whole section of two mm
b1
adjacent openings taken on the surface of the shell.
r Inside radius of curvature of the shell at the opening centre. mm
is
R Inside radius of a hemispherical end or of the crown of a torispherical mm
end.
w Distance between an opening and a shell discontinuity (see Figures 9.7– mm
1 to 9.7–11).
w Required minimum value for w. mm
min
w Minimum value for w which has no influence on l from shell mm
p s
discontinuities.
α Half apex angle of a conical shell. degrees
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Symbol Description Unit
θ For a nozzle having a longitudinal weld, angle between the plane degrees
containing the nozzle axis and the longitudinal weld line, and the plane
containing the nozzle axis and the shell generatrix passing through the
centre of the opening.
φ Obliquity angle in the longitudinal or transversal cross-section, degrees
measured between the normal to the wall at the opening centre and the
projection of the nozzle axis on the considered cross-section.
φ Projection of φ in the plane in which L lies for ligament check of radians
e b
multiple openings.
Φ Angle between the centre-to-centre line of two openings or nozzles and degrees
the generatrix of a cylindrical or conical shell (0° ≤ Φ ≤ 90°)
(see Figure 9.6–1).
— for isolated openings, angle between shell generatrix and axis of
Ω degrees
major diameter
— for adjacent openings, angle between the plane containing the
opening centres and the axis of major diameter.
9.4 General
9.4.1 Opening
A shell containing an opening shall be adequately reinforced in the area adjacent to the opening. This is
to compensate for the reduction of the pressure bearing section. The reinforcement shall be obtained by
one of the following methods:
a) increasing the wall thickness of the shell above that required for an unpierced shell
(see Figures 9.4-1 and 9.4-2);
b) using a reinforcing plate (see Figures 9.4-3 and 9.4-4);
c) using a reinforcing ring (see Figures 9.4-5 and 9.4-6);
d) increasing the wall thickness of the nozzle (see Figures 9.4-7 and 9.4-8) above that required for the
membrane pressure stress;
e) using a combination of the above (see Figures 9.4-9 to 9.4-13).
9.4.2 Reinforcement
The dimensions of the reinforcement area at an opening shall be assumed and the design shall be
verified by the method laid down in the following subclauses.
The method is based on ensuring that the reactive force provided by the material is greater than, or
equal to, the load from the pressure. The former is the sum of the product of the average membrane
stress in each component and its stress loaded cross-sectional area (see Figures 9.4-1 to 9.4-13). The
latter is the sum of the product of the pressure and the pressure loaded cross-sectional areas. If the
reinforcement is insufficient, it shall be increased and the calculation repeated.
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Reinforcement and strength may vary around the axis of an opening. Reinforcement shall be shown to
be sufficient in all planes.
9.4.3 Design
The design method is applicable when the opening is located at a minimum distance from a shell
discontinuity. Rules for determining this minimum distance are given in 9.7.
9.4.4 Elliptical or obround openings
Elliptical or obround openings resulting from a circular nozzle oblique to the shell wall shall be
calculated according to 9.5.2.4.5.
For all other elliptical or obround openings the ratio between the major and minor diameter shall not
exceed 2.
9.4.4.1 Elliptical or obround openings reinforced by increased shell wall thickness,
reinforcing plate or reinforcing ring (see 9.4.1 a), b) or c)):
In cylindrical or conical shells the diameter d of the opening for reinforcing calculations shall be taken:
— along the generatrix of the shell for isolated openings;
— in the plane containing the centres of the openings.
In spherical shells and dished ends the diameter d of the opening shall be taken:
— along the largest dimension of the bore (major axis) for isolated openings;
— in the plane containing the centres of the openings.
9.4.4.2 Openings reinforced by elliptical or obround nozzles normal to the shell wall
(see 9.4.1 d)):
In cylindrical or conical shells the diameter d of the opening shall be calculated as follows:
d ()dd+
2 max min max 2
dd= ⋅(sin ΩΩ+⋅ ⋅cos ) (9.4-1)
min
dd2⋅
min min
where
d and d are the minor and major diameter of the opening, and
min max
Ω is:
— for isolated openings, the angle between the shell generatrix passing through
the centre of the opening and the axis of the major diameter.
— for adjacent openings, and for each of the two openings, the angle between the
shortest line lying on the surface of the shell passing through the centres of the
two openings, and the line resulting on the shell from the intersection of the
plane defined by the nozzle axis and the axis of the major diameter of any
nozzle cross section under consideration.
In spherical shells and dished ends the diameter d of the opening shall be calculated as follows:
dd+
min max
dd ⋅() (9.4-2)
max
2⋅ d
min
10
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where
d and d are defined above.
min max
The diameter for the calculation of value l in Formula (9.5-75) is defined in 9.5.2.4.4.1.
bo
For nozzles with elliptical or obround cross-section the pressure produces not only membrane stresses,
but also bending stresses in the circumferential direction. Thus the attached shell wall on one side and
the attached flange or circular pipe on the other side have to support the nozzle if its wall thickness has
been determined using only membrane stresses. The nozzle loads the shell and it is possible that the
diameter which applies for the elliptical or obround nozzle is larger than the major axis.
9.4.4.3 For elliptical or obround nozzles not normal to the shell wall 9.4.4.2 is not applicable,
therefore 9.4.4.1 shall be used without contribution of nozzle wall for reinforcing calculations.
9.4.5 Limitations on diameter
9.4.5.1 Shell reinforced openings
Shell reinforced openings without a nozzle shall satisfy the following condition:
d
≤ 0,5 (9.4-3)
2r
is
9.4.5.2 Openings with reinforcing plates
Where an opening is fitted with a reinforcing plate without the presence of a nozzle, the condition of the
Formula (9.4-3) shall be satisfied. Reinforcing plates are normally situated on the external surface of the
shell, but they may be situated also on the internal surface or on both surfaces.
In case of high mean wall temperature for the shell (more than 250 °C) or in the presence of severe
temperature gradients through the shell, the use of reinforcing plates shall be avoided; if it is necessary
then the material of the reinforcing plate shall be of the same quality of shell material, and special
measures and warnings shall be taken to avoid thermal stress concentrations.
9.4.5.3 Openings in dished ends
For openings in hemispherical ends and dished ends, the ratio d / D shall not exceed 0,6. Therefore, if
e
the opening is reinforced by a nozzle or a reinforcing ring d / D and d / D shall not exceed 0,6.
ib e ir e
9.4.5.4 Openings with nozzles
For openings in cylindrical shells reinforced by nozzles the ratio d / (2r ) shall not exceed 1.0
ib is
(see Figures 9.4-14 and 9.4-15).
9.4.6 Effective thickness for nozzles
9.4.6.1 In fatigue applications where fatigue is assessed using Clause 17 and if the opening is a
critical area (as defined in 17.2)
The ratio e /e shall not exceed the value taken from the graph in Figure 9.4-14 and the value of e
b
b a,s
. Nozzle thickness in excess of that calculated using Figure 9.4-14
shall never exceed the value of ea,b
shall not be included in the reinforcement calculation.
Furthermore the ratio e /e shall not exceed the value taken from the graph in Figure 9.4-15.
a,b a,s
NOTE 1 e is the effective thickness of the nozzle, to be used for the verification of the reinforcement; e is the
b a,b
analysis thickness of this nozzle; the ratio e /e limits the contribution of the nozzle to the resistance of the
b a,s
opening; the ratio e /e limits the analysis thickness of the nozzle, and thus its manufacturing thickness, in order
a,b a,s
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to limit the stresses which can occur due to great thickness differences and to avoid the fatigue problems which
can result.
NOTE 2 When fatigue is assessed using Clause 18, no limitation to the thickness ratio is necessary because in
that case more accurate stresses are used for fatigue calculations.
9.4.6.2 In creep applications (i.e.: when the calculation temperature is situated in the creep
range)
The effective thickness e may be taken equal to the analysis thickness e of the nozzle.
b a,b
However the ratio e /e shall not exceed the value taken from the graph in Figure 9.4-15.
a,b a,s
9.4.6.3 In applications without creep and without fatigue assessment using Clause 17 (i.e.: when
the calculation temperature is situated out of the creep range and the opening is not a critical
area as defined in 17.2)
The effective thickness e may be taken equal to the analysis thickness e of the nozzle and no
b a,b
limitations apply to the ratio e .
a,b/ea,s
9.4.7 Nozzles to shell connections
Nozzles are usually of the following forms: welded (set-in, set-on, protruding nozzles) or extruded or
screwed.
For welded nozzles the cross sectional area of the nozzle can always be taken in account for
reinforcement of the opening, provided weld dimensions are in accordance with Tables A-6 and A-8 of
Annex A of this standard.
For nozzles extruded from the shell the cross sectional area of the nozzle shall be taken in account for
reinforcement provided the requirements of 9.5.2.4.4.2 are applied.
For screwed nozzles the cross sectional area of the nozzle shall not be taken in account for
reinforcement of the opening.
9.4.8 Distance between a nozzle and a shell butt-weld
The distance between the centre line of a shell butt-weld (longitudinal or circumferential) and the
centre of an opening shall be either less than d / 6 or greater than the value l given by:
ib n
l = min (0,5 d + 2e ; 0,5 d + 40) (9.4-4)
n eb a,s eb
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Figure 9.4-1 — Cylindrical shell with isolated opening and increased wall thickness
Figure 9.4-2 — Spherical shell or dished end with isolated opening and increased wall thickness
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Figure 9.4-3 — Cylindrical shell with isolated opening and reinforcing plate
Figure 9.4-4 —Spherical shell or dished end with isolated opening and reinforcing plate
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Figure 9.4-5 — Cylindrical shell with isolated opening and reinforcing ring, with external blind
flange B
Figure 9.4.6— Spherical shell or dished end with isolated opening and reinforcing ring, with
internal blind flange B
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Figure 9.4-7 — Cylindrical shell with isolated opening and set-on nozzle
Figure 9.4-8 — Spherical shell or dished end with isolated opening and set-in nozzle
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Figure 9.4-9 — Cylindrical shell with isolated opening, increased wall thickness and set-in nozzle
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NOTE The various lengths and areas shown for the case of a nozzle with a reinforcing plate in a sphere also
applies to the case of a nozzle with a reinforcing plate in a cylinder.
Figure 9.4-10 — Spherical shell or dished end with isolated opening and shell, nozzle and
reinforcing plate
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Figure 9.4-11 — Cylindrical shell with isolated opening and a butt-weld nozzle (see X) or an
extruded shell (see Y)
Figure 9.4-12 — Spherical shell or dished end with isolated opening extruded from the shell,
with internal blind flange B
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Figure 9.4-13 — Conical shell with isolated opening. Combined reinforcement from shell and
nozzle
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Figure 9.4-14 — Limitation of effective thickness ratio for nozzles, for the calculation
Figure 9.4-15 — Limitation of actual thickness ratio for nozzles, for the manufacturing
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9.5 Isolated openings
9.5.1 Limitations
An opening is considered isolated if the following condition is satisfied:
L ≥ a + a + l + l (9.5-1)
b 1 2 so1 so2
where
a and a are shown in Figures 9.6–1 to 9.6–4, and l and l are calculated according to:
1 2 so1 so2
l ()2re+⋅ e (9.5-2)
so is cs,,cs
where
e is the assumed shell thickness to be taken as is explained in 9.3.3; normally the value of shell
c,s
analysis thickness e may be taken, but this may be conservative and sometimes it may be
a,s
advantageous to use a smaller assumed value for e to obtain smaller minimum distances
c,s
from adjacent shell discontinuities;
r is given by:
is
— for cylindrical or spherical shells
D
e
(9.5–3)
re−
is a,s
2
— for hemispherical or torispherical ends
r = R (9.5–4)
is
— for elliptical ends
2
0,44D
i
(9.5–5)
rD+ 0,02
is i
2h
— for conical shells:
D
e
r − e
(9.5–6)
is a,s
2 cosa
9.5.2 Reinforcement rules
9.5.2.1 General formula and its derivates
9.5.2.1.1 The general formula for the reinforcement of an isolated opening is given by:
(Af + Af ) (f - 0,5P) + Af (f - 0,5P) + Af (f - 0,5P) ≥ P (Ap + Ap + 0,5 Ap ) (9.5-7)
s w s p op b ob s b φ
where
f = min (f ; f ) (9.5-8)
ob s b
f = min (f ; f ) (9.5-9)
op s p
Where a reinforcing ring is fitted, Af and Ap shall be substituted for Af and Ap .
r r b b
9.5.2.1.2 For all reinforced openings except small openings and those reinforced by a ring, the
Formula (9.5-7) applies; in particular:
22
=
=
=
=
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SIST EN 13445-3:2014/oprA14:2019
EN 13445-3:2014/prA14:2019 (E)
a) Where either f or f is not greater than f, the reinforcement shall be determined from
b p s
Formula (9.5-7)
and P shall be obtained as follows
max
(Aφ + Aφ ) ⋅⋅φ + Aφ φ + Aφ ⋅ φ
s w b ob p op
s
P = (9.5-10)
max
(Ap +Ap +0,5Ap ) + 0,5 (Aφ +Aφ +Aφ +Aφ )
s b s w bp
φ
b) Where f and f are both greater than f , the reinforcement shall be determined from:
b p s
(Af + Af + Af + Af ) · (f - 0,5P) ≥ P (Ap + Ap + 0,5Ap ) (9.5-11)
s w p b s s b φ
()Aφ + Aφ ++Aφ Aφ ⋅ φ
s w bp
s
P = (9.5-12)
max
(Ap + Ap + 0,5Ap )+ 0,5(Aφ + Aφ ++Aφ Aφ )
s b φ s w bp
9.5.2.1.3 For an opening with a reinforcing ring:
a) where f is less than f , the following shall apply
r s
(Af + Af ) · (f - 0,5P) + Af · (f - 0,5P) ≥ P (Ap + Ap + 0,5Ap ) (9.5-13)
s w s r or s r φ
and P is given by
max
(Aφ + Aφ )⋅⋅φ + Aφ φ
s w r or
s
P = (9.5-14)
max
(Ap + Ap + 0,5Ap ) + 0,5(Aφ +
...
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