Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell Structures

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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

Evrokod 3 - Projektiranje jeklenih konstrukcij - 1-6. del: Trdnost in stabilnost lupinastih konstrukcij

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Published
Publication Date
25-Apr-2017
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
26-Apr-2017
Completion Date
26-Apr-2017

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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

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

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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.
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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”.
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.

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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;
α imperfection reduction factor;”.
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;”
with:
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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;”.
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.”.
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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)”.
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SIST EN 1993-1-6:2007/A1:2017
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
22 2
σ n+−n nn⋅ + 3n (6.1)
eq,Ed x,Ed θ,Ed x,,Ed θθEd x ,Ed

(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
( ) ( )
xθθ,,Ed x Ed
τ ± (6.4)
xθ,Ed
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

design values F of the combination of actions for the relevant load case.”.
Replace Paragraph (3) with:

“(3) In an MNA or GMNA analysis based on the design yield strength f , the shell should be subject to

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.”.
In Paragraph (4), replace “8.7” with “8.8”.
Replace Paragraph (5) with:
= =
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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

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:
F R ⋅ F
Rk k Ed
F = R ⋅ F (6.7)
Rd d Ed
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:
 
 
χχ=−−χ 1 when λλ≤ (8.13)
( )
hh 0
 
 0
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SIST EN 1993-1-6:2007/A1:2017
EN 1993-1-6:2007/A1:2017 (E)
λ−λ
when (8.14)
χβ1− λ <<λλ
λ −λ
χ= when λλ≤ (8.15)
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;
χ is the hardening limit.
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

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

reference resistance should then be found as the ratio:
R = (8.24)

(3) The elastic critical reference resistance R is defined in Annex E for specific geometries, load cases,

and boundary conditions and may only be used for these specific cases.
(4) The relative slenderness of the shell should be found as:
λ= (8.25)

(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
λ−λ
χβ1− when λ <<λλ (8.27)
λ −λ
χ= when λλ≤ (8.28)
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;
χ is the hardening limit.

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:

λ = (8.29)
1−β
(7) The characteristic resistance of the shell should be determined from:
R =χR (8.30)
k pl
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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)
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-

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.”.

In Paragraph (4), replace the whole Formula (8.24) (to be renumbered as (8.33)):
t⋅ f
r = (8.24)
Rpl
2 22
n − n ⋅ nnn++
x,Ed x,,Ed θθEd ,Ed xθ,Ed
with:
t⋅ f
yk,
(8.33)
R =
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

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.

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EN 1993-1-6:2007/A1:2017 (E)

Care should be taken in choosing an appropriate value of α when this approach is used on shell

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

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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