SIST EN 1993-1-6:2007/A1:2017

SLOVENSKI STANDARD
SIST EN 1993-1-6:2007/A1:2017
01-september-2017
Evrokod 3 - Projektiranje jeklenih konstrukcij - 1-6. del: Trdnost in stabilnost
lupinastih konstrukcij
Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell
Structures
Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 1-6: Festigkeit und
Stabilität von Schalen
Eurocode 3 - Calcul des structures en acier - Partie 1-6: Résistance et stabilité des
structures en coque
Ta slovenski standard je istoveten z: EN 1993-1-6:2007/A1:2017
ICS:
91.010.30 7HKQLþQLYLGLNL Technical aspects
91.080.13 Jeklene konstrukcije Steel structures
SIST EN 1993-1-6:2007/A1:2017 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 1993-1-6:2007/A1:2017

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SIST EN 1993-1-6:2007/A1:2017


EN 1993-1-6:2007/A1
EUROPEAN STANDARD

NORME EUROPÉENNE

April 2017
EUROPÄISCHE NORM
ICS 91.010.30; 91.080.13
English Version

Eurocode 3 - Design of steel structures - Part 1-6: Strength
and Stability of Shell Structures
Eurocode 3 - Calcul des structures en acier - Partie 1-6 : Eurocode 3 - Bemessung und Konstruktion von
Résistance et stabilité des structures en coque Stahlbauten - Teil 1-6: Festigkeit und Stabilität von
Schalen
This amendment A1 modifies the European Standard EN 1993-1-6:2007; it was approved by CEN on 17 January 2017.

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

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

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1993-1-6:2007/A1:2017 E
worldwide for CEN national Members.

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
Contents Page
European foreword . 4
1 Modifications to the Foreword . 5
2 Modification throughout the whole standard . 5
3 Modification to 1.2, Normative references . 5
4 Modifications to 1.3, Terms and definitions . 5
5 Modifications to 1.4, Symbols . 6
6 Modification to 2.2.5, Linear elastic bifurcation analysis (LBA) . 7
7 Modification to 2.2.6, Geometrically nonlinear elastic analysis (GNA) . 7
8 Modification to 2.2.7, Materially nonlinear analysis (MNA) . 7
9 Modification to 2.2.8, Geometrically and materially nonlinear analysis (GMNA) . 7
10 Modification to 2.2.9, Geometrically nonlinear elastic analysis with imperfections
included (GNIA) . 7
11 Modification to 2.2.10, Geometrically and materially nonlinear analysis with
imperfections included (GMNIA) . 7
12 Modification to 3.3, Geometrical tolerances and geometrical imperfections . 7
13 Modifications to 4.1.1, LS1: Plastic limit . 7
14 Modification to 4.2.2.2,Primary stresses . 8
15 Modification to 4.2.4, Design by global numerical analysis . 8
16 Modification to 5.3, Types of analysis . 8
17 Modification to Clause 6, Plastic limit state (LS1) . 8
18 Modifications to 6.2.1, Design values of stresses . 9
19 Modifications to 6.3, Design by global numerical MNA or GMNA analysis . 9
20 Modification to 8.2, Special definitions and symbols . 10
21 Modifications to 8.5.2, Design resistance (buckling strength) . 10
22 Addition of a new Subclause 8.6, Design using reference resistances . 11
23 Modifications to 8.6.2 (new subclause number: 8.7.2), Design value of resistance . 13
24 Modifications to 8.7.2 (new subclause number: 8.8.2), Design value of resistance . 14
25 Modification to Annex B (normative), Additional expressions for plastic collapse
resistances . 14
26 Modification to C.3.3, Cylinder, pinned: uniform internal pressure with axial loading . 15
27 Modifications to D.1.2.2, Meridional buckling parameters . 15
28 Modification to D.1.3.2, Circumferential buckling parameters . 16
29 Modification to D.1.4.2, Shear buckling parameters . 16
30 Modifications to D.1.5.2, Pressurised meridional buckling parameters . 16
2

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EN 1993-1-6:2007/A1:2017 (E)
31 Modification to D.1.6, Combinations of meridional (axial) compression,
circumferential (hoop) compression and shear. 16
32 Modifications to D.4.2.2, Meridional compression . 17
33 Addition of a new Annex E (normative), Expressions for reference resistance design . 17

3

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
European foreword
This document (EN 1993-1-6:2007/A1:2017) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI.
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 2018, and conflicting national standards shall be
withdrawn at the latest by April 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent
rights.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
4

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
1 Modifications to the Foreword
In the Foreword, in the section “National Annex for EN 1993-1-6”, add the following entries into the list at
the appropriate places:
“
– 6.2.1(6)”;
and
“
– 8.6.3(5);”.
In the Foreword, in the section “National Annex for EN 1993-1-6”, replace:
“
– 8.7.2 (7)
– 8.7.2 (16)
– 8.7.2 (18) (2 times)”
with:
“
– 8.8.2 (9)
– 8.8.2 (18)
– 8.8.2 (20) (2 times)”.
2 Modification throughout the whole standard
Replace “r ” with “R”.
R
3 Modification to 1.2, Normative references
In the list of the parts of EN 1993, replace “Part 1.1 :” with “Part 1.1:2005:”.
4 Modifications to 1.3, Terms and definitions
Replace the whole Entry 1.3.2.1 with:
“
1.3.2.1 plastic failure limit state (LS1)
ultimate limit state where the structure develops zones of yielding in a pattern such that its ability to
resist increased loading is deemed to be exhausted”.
Add a new Entry 1.3.5.3:
“
1.3.5.3 semi-membrane theory analysis
analysis that predicts the behaviour of an unsymmetrically loaded or supported thin-walled cylindrical
shell structure by assuming that only membrane forces and circumferential bending moments satisfy
equilibrium with the external loads”;
and renumber accordingly the former Entry 1.3.5.3 (as 1.3.5.4) and the following definitions in 1.3.5.
5

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
Replace the former Subclause 1.3.5.6 (newly renumbered as 1.3.5.7) with:
“
1.3.5.7 materially nonlinear analysis (MNA)
analysis based on shell bending theory applied to the perfect structure, using the assumption of small
deflections, as in 1.3.5.4, but adopting an ideal elastic plastic material law (idealised perfectly plastic
response after yield)”.
Replace the former Subclause 1.3.5.7 (newly renumbered as 1.3.5.8) with:
“
1.3.5.8 geometrically and materially nonlinear analysis (GMNA)
analysis based on shell bending theory applied to the perfect structure, using the assumptions of
nonlinear large deflection theory for the displacements and a fully nonlinear elastic-plastic-hardening
material law, where appropriate, and in which a bifurcation eigenvalue check is included at each load
level”.
Replace the former Subclause 1.3.5.9 (newly renumbered as 1.3.5.10) with:
“
1.3.5.10 geometrically and materially nonlinear analysis with imperfections included (GMNIA)
analysis with imperfections explicitly included, based on the principles of shell bending theory applied
to the imperfect structure (i.e. the geometry of the middle surface includes unintended deviations from
the ideal shape), including nonlinear large deflection theory for the displacements that accounts fully
for any change in geometry due to the actions on the shell and a fully nonlinear elastic-plastic-
hardening material law, where appropriate
Note 1 to entry: The imperfections may also include imperfections in boundary conditions and residual
stresses. A bifurcation eigenvalue check is included at each load level.”.
5 Modifications to 1.4, Symbols
Delete the NOTE in Paragraph (12).
In Paragraph (12), replace the following line:
“α elastic imperfection reduction factor in buckling strength assessment;”
with:
“α elastic buckling reduction factor in buckling strength assessment;
α geometric reduction factor;
G
α imperfection reduction factor;”.
I
In Paragraph (12), replace the following line:
“χ buckling reduction factor for elastic-plastic effects in buckling strength assessment;”
with:
“χ elastic-plastic buckling reduction factor for elastic-plastic effects in buckling strength
assessment;”.
In Paragraph (12), replace:
“χ overall buckling resistance reduction factor for complete shell;”
ov
with:
6

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
“χ overall elastic-plastic buckling reduction factor for a complete shell;”.
ov
6 Modification to 2.2.5, Linear elastic bifurcation analysis (LBA)
In Paragraph (1), replace “8.6 and 8.7” with “8.7 and 8.8”.
7 Modification to 2.2.6, Geometrically nonlinear elastic analysis (GNA)
In Paragraph (2), replace “8.7” with “8.8”.
8 Modification to 2.2.7, Materially nonlinear analysis (MNA)
In Paragraph (1), replace “8.6 and 8.7” with “8.7 and 8.8”.
9 Modification to 2.2.8, Geometrically and materially nonlinear analysis (GMNA)
Replace Paragraphs (1) and (2) with the following ones:
“(1) The result of a GMNA analysis, analogously to 2.2.7, gives the geometrically nonlinear plastic failure
load of the perfect structure and the plastic strain increment, that may be used for checking the limit
states LS1 and LS2.
(2) Where compression or shear stresses are predominant in some part of the shell, a GMNA analysis
gives the elasto-plastic buckling load of the perfect structure. This perfect shell buckling load should
always be determined when the limit state LS3 is verified using GMNIA analysis, see 8.8.”.
10 Modification to 2.2.9, Geometrically nonlinear elastic analysis with
imperfections included (GNIA)
In Paragraph (1), replace “8.7” with “8.8”.
11 Modification to 2.2.10, Geometrically and materially nonlinear analysis with
imperfections included (GMNIA)
In Paragraph (1), replace “8.7” with “8.8”.
12 Modification to 3.3, Geometrical tolerances and geometrical imperfections
In Paragraph (3), replace twice “8.7” with “8.8”.
13 Modifications to 4.1.1, LS1: Plastic limit
Replace the title itself of Subclause 4.1.1 with “LS1: Plastic failure limit state”.
Replace Paragraph (1) with:
“(1) The limit state of the plastic failure should be taken as the condition in which the capacity of the
structure to resist the actions on it is exhausted by plasticity in the material.
The plastic failure resistance should be distinguished from the plastic reference resistance which is
derived as the plastic collapse load obtained from a mechanism based on small displacement theory
using an ideal elastic-plastic material law.”.
7

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
Replace Paragraph (3) with:
“(3) In the absence of fastener holes, verification at the limit state of tensile rupture may be assumed to
be covered by the check for the plastic failure limit state. However, where holes for fasteners occur, a
supplementary check in accordance with EN 1993-1-1:2005, 6.2 should be carried out.”.
Replace Paragraph (4) with:
“(4) In verifying the plastic failure limit state, plastic or partially plastic behaviour of the structure may
be assumed (i.e. elastic compatibility considerations may be neglected).
NOTE Since the plastic failure limit state includes change of geometry, it may be noted that this limit state
may also capture snap-through buckling, which may occur in the elastic state. The plastic reference resistance
does not include change of geometry, so this apparent anomaly does not occur.”.
14 Modification to 4.2.2.2,Primary stresses
Replace Paragraphs (1) and (2) with:
“(1) The primary stresses should be taken as the stress system required for equilibrium with the
imposed loading. They may be calculated from any realistic statically admissible determinate system.
The plastic failure limit state (LS1) should be deemed to be reached when the primary stress reaches
the yield strength throughout the full thickness of the wall at a sufficient number of points, such that
only the strain hardening reserve or a change of geometry would lead to an increase in the resistance of
the structure.
(2) The calculation of primary stresses should be based on any system of stress resultants, consistent
with the requirements of equilibrium of the structure. It may also take into account the benefits of
plasticity theory. Alternatively, since linear elastic analysis satisfies equilibrium requirements, its
predictions may also be used as a safe representation of the plastic failure limit state (LS1). Any of the
analysis methods given in 5.3 may be applied.”.
15 Modification to 4.2.4, Design by global numerical analysis
In Paragraph (6), replace “8.7” with “8.8”.
16 Modification to 5.3, Types of analysis
In Table 5.2, replace the row:
“
Materially nonlinear analysis (MNA) linear nonlinear perfect
”
with:
“
Materially nonlinear analysis (MNA) linear ideal elastic-plastic perfect
”.
17 Modification to Clause 6, Plastic limit state (LS1)
Replace the title itself with “Plastic failure limit state (LS1)”.
8

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EN 1993-1-6:2007/A1:2017 (E)
18 Modifications to 6.2.1, Design values of stresses
Replace Paragraph (1) with:
“(1) Although stress design is based on an elastic analysis and therefore cannot accurately predict the
plastic failure limit state, it may be used, on the basis of the lower bound theorem, to provide a
conservative assessment of the plastic collapse resistance which is used to represent the plastic failure
limit state, see 4.1.1.”.
Replace Paragraphs (5) and (6) with:
“(5) Where a membrane theory analysis is used, or where a linear bending theory analysis (LA) is used
subject to the conditions defined in (6), the resulting two-dimensional field of stress resultants n ,
x, Ed
n and n may be represented by the equivalent design stress σ obtained from:
θ, Ed xθ, Ed eq, Ed
1
22 2
σ n+−n nn⋅ + 3n (6.1)
eq,Ed x,Ed θ,Ed x,,Ed θθEd x ,Ed
t
(6) Where an LA or GNA analysis is used, and the magnitude of the largest von Mises surface stress
found using Formulae (6.2) to (6.4) exceeds j times the von Mises membrane stress found using
Formula (6.1) at the same location, the equivalent stress should be taken as the value determined using
Formulae (6.2) to (6.4).
2 2 2
σ σ+−σ σσ⋅ + 3τ (6.2)
eq,Ed x,Ed θ,Ed x,,Ed θθEd x ,Ed
in which:
nm nm
x,,Ed x Ed θθ,,Ed Ed
σ ± σ ± (6.3)
x,Ed θ,Ed
2 2
t t
t / 4 t / 4
( ) ( )
nm
xθθ,,Ed x Ed
τ ± (6.4)
xθ,Ed
2
t
t / 4
( )
NOTE 1 Formulae (6.2) to (6.4) give a simplified conservative equivalent stress for design purposes.
NOTE 2 The National Annex may choose the value of j. The recommended value is 3.”.
19 Modifications to 6.3, Design by global numerical MNA or GMNA analysis
Replace Paragraph (1)P with:
“(1)P The design plastic failure resistance shall be determined as a load factor R applied to the
pl
design values F of the combination of actions for the relevant load case.”.
Ed
Replace Paragraph (3) with:
“(3) In an MNA or GMNA analysis based on the design yield strength f , the shell should be subject to
yd
the design values of the load cases detailed in (2), progressively increased by the load ratio R until the
plastic failure condition at the load ratio R is reached.”.
pl
In Paragraph (4), replace “8.7” with “8.8”.
Replace Paragraph (5) with:
9
=
= =
=
=

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
“(5) Where a GMNA analysis is used, if the analysis predicts a maximum load followed by a descending
path, the maximum value should be used to determine the load ratio R . Where a GMNA analysis
GMNA
does not predict a maximum load, but produces a progressively rising action-displacement relationship
without strain hardening of the material, the load ratio R should be taken as no larger than the
GMNA
value at which the maximum von Mises equivalent plastic strain in the structure attains the value
ε =n ⋅(f /E).
mps mps yd
NOTE The National Annex may choose the value of nmps. The value nmps = (66-fyd/15), where fyd is in MPa, is
recommended.”.
Add a new Paragraph (6):
“(6) A GMNA analysis may not be used to establish the plastic reference resistance R , which is used in
pl
Clause 8 as part of the LBA-MNA design method.”.
Renumber accordingly Paragraph (6) (as Paragraph (7)) along with the following paragraphs.
Replace the former Paragraph (6) (new Paragraph (7)) with:
“(7) The characteristic plastic failure resistance R should be taken as either R or R
pl,k MNA GMNA
according to the analysis that has been used.”.
Replace the former Paragraph (7)P (new paragraph (8)P) with:
“(8)P The design plastic failure resistance F shall be obtained from:
Rd
F R ⋅ F
Rk k Ed
F = R ⋅ F (6.7)
Rd d Ed
γγ
M0 M0
”.
20 Modification to 8.2, Special definitions and symbols
Replace Paragraph (1) with:
“(1) Reference should be made to the special definitions of terms concerning buckling in 1.3.7.”.
21 Modifications to 8.5.2, Design resistance (buckling strength)
Replace the first sentence of Paragraph (1) with “The buckling resistance should be represented by the
buckling stresses as defined in 1.3.7.”.
Replace Paragraph (3) with:
“(3) The characteristic buckling stresses should be obtained by multiplying the characteristic yield
strength by the elastic-plastic buckling reduction factors χ:
σχ= f σχ= f τχ= f / 3 (8.12)
x,Rk x yk, θθ,,Rk yk xθτ,Rk yk
Replace Paragraph (4) with:
“(4) The elastic-plastic buckling reduction factors χ , χ and χ should be determined as a function of
x θ τ
the relative slenderness of the shell λ from:
 
λ
 
χχ=−−χ 1 when λλ≤ (8.13)
( )
hh 0
 
λ
 0
10
==

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EN 1993-1-6:2007/A1:2017 (E)
η

λ−λ
0

when (8.14)
χβ1− λ <<λλ
0p

λ −λ
p0

α
χ= when λλ≤ (8.15)
p
2
λ
where:
α is the elastic buckling reduction factor;
β is the plastic range factor;
η is the interaction exponent;
is the squash limit relative slenderness;
λ
0

χ is the hardening limit.
h
”.
In Paragraph (8), replace “8.6.2” with “8.7.2”.
22 Addition of a new Subclause 8.6, Design using reference resistances
Add the following new Subclause 8.6; then have the former Subclauses 8.6 and 8.7 automatically
renumbered as 8.7 and 8.8 and renumber all the formulae in the latter subclauses accordingly:
“
8.6 Design using reference resistances
8.6.1 Principle
(1) Because buckling is not controlled by a single membrane stress at a single location, but depends on
the development of a zone of high stress that may include significant plasticity, the buckling limit state,
within this section, is represented by the design value of the actions, augmented to the point of buckling
and applied to the specific defined conditions.
(2) The influence of membrane and bending effects, of plasticity and geometric imperfections are all
included in the use of the two reference resistances and the buckling parameters.
8.6.2 Design value of actions
(1) The design values of actions should be taken as in 8.1(1)P.
8.6.3 Design value of resistance
(1) The design buckling resistance should be determined from the reference elastic critical resistance
R and the reference plastic resistance R for the geometry and load case, together with the capacity
cr pl
parameters α, β, η, λ and χ as defined in Annex E.
0 h
(2) The plastic reference resistance R may be taken from Annex B. The value of R for a given load
pl pl
case, involving as appropriate the loading P , P , p , F , etc. should be obtained as follows.
n,Ed x,Ed n,Ed Ed
Where there is more than one loading component, the ratios between different loading components
should be retained in fixed proportions, with one nominated as the leading load F . The plastic
Ed
11
=

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EN 1993-1-6:2007/A1:2017 (E)
collapse load should then be determined for the magnitude of the leading load as F . The plastic
R
reference resistance should then be found as the ratio:
F
R
R = (8.24)
pl
F
Ed
(3) The elastic critical reference resistance R is defined in Annex E for specific geometries, load cases,
cr
and boundary conditions and may only be used for these specific cases.
(4) The relative slenderness of the shell should be found as:
R
pl
λ= (8.25)
R
cr
(5) The elastic-plastic buckling reduction factor χ should be determined as a function of the relative
slenderness of the shell λ from:
χ χ− λλ/ χ − 1 when λλ≤ (8.26)
( )( )
h0 h 0
η

λ−λ
0

χβ1− when λ <<λλ (8.27)
0p

λ −λ
p0

α
χ= when λλ≤ (8.28)
p
2
λ
where:
α is the elastic buckling reduction factor;
β is the plastic range factor;
η is the interaction exponent;
is the squash limit relative slenderness;
λ
0

χ is the hardening limit.
h
NOTE The values of these parameters should be taken from Annex E. Where Annex E does not define the
values of these parameters, they may be given by the National Annex.
Formula (8.28) describes the elastic buckling condition, accounting for geometric nonlinearity and
geometric imperfections. In this case, where the behaviour is entirely elastic, the characteristic buckling
resistance may alternatively be determined directly from R = α R .
k cr
(6) The value of the plastic limit relative slenderness λ should be determined from:
p
α
λ = (8.29)
p
1−β
(7) The characteristic resistance of the shell should be determined from:
R =χR (8.30)
k pl
12
=
=

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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
(8) The design resistance of the shell should then be determined from:
(8.31)
RR= /γ
d k M1
8.6.4 Buckling strength verification
(1) The following verification of the resistance of the shell structure to the defined loading should be
undertaken:
R ≥ 1 (8.32)
d
”.
23 Modifications to 8.6.2 (new subclause number: 8.7.2), Design value of
resistance
Replace Paragraph (3) with:
“(3) The plastic reference resistance ratio R (see Figure 8.5) should be obtained by materially non-
pl
linear analysis (MNA) as the plastic limit load under the applied combination of actions. This load ratio
R may be taken as the largest value attained in the analysis, using an ideal elastic-plastic material law.”.
pl
In Paragraph (4), replace the whole Formula (8.24) (to be renumbered as (8.33)):
“
t⋅ f
yk
r = (8.24)
Rpl
2 22
n − n ⋅ nnn++
x,Ed x,,Ed θθEd ,Ed xθ,Ed
with:
t⋅ f
yk,
(8.33)
R =
pl
2 22
n − nn⋅ ++n 3n
x,Ed x,,Ed θθEd ,Ed xθ,Ed
”.
In Paragraph (4), in the NOTE, replace “expression (8.24)” with “Formula (8.33)”.
Replace Paragraph (8) with:
“(8) The overall elastic-plastic buckling reduction factor χ should be determined as
ov
χ = f λ , λ , α β ηχ using 8.5.2(4), in which α is the overall elastic imperfection
( )
ov ov ov,0 ov,,ov ov, ov,h ov
reduction factor, β is the plastic range factor, η is the interaction exponent, χ is the hardening
ov ov ov,h
limit and λ is the squash limit relative slenderness.”.
ov,0
Replace Paragraph (9) with:
“(9) The evaluation of the factors λ , α , β η and χ should take account of the
ov,0 ov ov ov ov,h
,
imperfection sensitivity, geometric nonlinearity and other aspects of the particular shell buckling case.
Conservative values for these parameters should be determined by comparison with known shell
buckling cases (see Annex D) that have similar buckling modes, similar imperfection sensitivity, similar
geometric nonlinearity, similar yielding sensitivity and similar postbuckling behaviour. The value of
α should also take account of the appropriate fabrication tolerance quality class.
ov
13

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Care should be taken in choosing an appropriate value of α when this approach is used on shell
ov
geometries and loading cases where snap-through buckling may occur. Such cases include conical and
spherical caps and domes under external pressure or on supports that can displace radially. The
appropriate value of α should also be chosen with care when the shell geometry and load case
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produce conditions that are highly sensitive to changes of geometry, such as at unstiffened junctions
between cylindrical and conical shell segments under meridional compressive loads (e.g. in chimneys).
The commonly reported elastic shell buckling loads for these special cases are normally based on
geometrically nonlinear analysis applied to a perfect or imperfect geometry, which predicts the snap-
through buckling load. By contrast, the methodology used here adopts the linear bifurcation load as the
reference elastic critical buckling resistance, and this is often much higher than the snap-through load.
The design calculation sha
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