SIST EN 1993-1-6:2007/kFprA1:2014
(Amendment)Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell Structures
Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell Structures
- New design method to address a serious omission in the standard, leading to a mismatch with EN 1993-1-1
- Removal of ambiguity concerning plastic resistances and definitions of key parameters
- Resolving uncertainties about the use of GMNIA analyses
- Remedial measures to address mismatch with the stated scope
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 coques
Evrokod 3: Projektiranje jeklenih konstrukcij - 1-6. del: Trdnost in stabilnost lupinastih konstrukcij
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 1993-1-6:2007/kFprA1:2014
01-november-2014
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 coques
Ta slovenski standard je istoveten z: EN 1993-1-6:2007/FprA1
ICS:
91.010.30 7HKQLþQLYLGLNL Technical aspects
91.080.10 Kovinske konstrukcije Metal structures
SIST EN 1993-1-6:2007/kFprA1:2014 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/kFprA1:2014
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SIST EN 1993-1-6:2007/kFprA1:2014
EUROPEAN STANDARD
FINAL DRAFT
EN 1993-1-6:2007
NORME EUROPÉENNE
EUROPÄISCHE NORM
FprA1
August 2014
ICS 91.010.30; 91.080.10
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 Stahlbauten
Résistance et stabilité des structures en coques - Teil 1-6: Festigkeit und Stabilität von Schalen
This draft amendment is submitted to CEN members for unique acceptance procedure. It has been drawn up by the Technical Committee
CEN/TC 250.
This draft amendment A1, if approved, will modify the European Standard EN 1993-1-6:2007. 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, 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: Avenue Marnix 17, B-1000 Brussels
© 2014 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1993-1-6:2007/FprA1:2014 E
worldwide for CEN national Members.
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SIST EN 1993-1-6:2007/kFprA1:2014
EN 1993-1-6:2007/FprA1:2014 (E)
Contents Page
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, .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
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 . 16
33 Modifications to D.4.2.4, Uniform external pressure . 17
2
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EN 1993-1-6:2007/FprA1:2014 (E)
34 Addition of a new Annex E (normative), Expressions for reference resistance design . 17
3
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SIST EN 1993-1-6:2007/kFprA1:2014
EN 1993-1-6:2007/FprA1:2014 (E)
Foreword
This document (EN 1993-1-6:2007/FprA1:2014) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI.
This document is currently submitted to the Unique Acceptance Procedure.
4
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SIST EN 1993-1-6:2007/kFprA1:2014
EN 1993-1-6:2007/FprA1:2014 (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
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 subclauses in 1.3.5.
Replace the former Subclause 1.3.5.6 (newly renumbered as 1.3.5.7) with:
5
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EN 1993-1-6:2007/FprA1:2014 (E)
"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 1.3.5.3, 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
In Paragraph (12), replace the following line:
α
" elastic imperfection reduction factor in buckling strength assessment;"
with:
elastic buckling reduction factor in buckling strength assessment;
α
"
α
G
geometric reduction factor;
α
I
imperfection reduction factor;".
In Paragraph (12), replace the following line:
χ
" buckling reduction factor for elastic-plastic effects in buckling strengths assessment;"
with:
χ
" elastic-plastic buckling reduction factor for elastic-plastic effects in buckling strength
assessment;".
In Paragraph (12) , replace:
χ
ov
" overall buckling resistance reduction factor for complete shell;"
with:
" χ
ov
overall elastic-plastic buckling reduction factor for a complete shell;".
Delete the NOTE in Paragraph (12).
6
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EN 1993-1-6:2007/FprA1:2014 (E)
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,
In Paragraph (2), replace "8.6 and 8.7" with "8.7 and 8.8".
8 Modification to 2.2.7, Materially nonlinear analysis (MNA)
In Paragraph (1), replace "8.7" with "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.".
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 6.2 of EN 1993-1-1:2005 should be carried out.".
7
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EN 1993-1-6:2007/FprA1:2014 (E)
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 non-linear analysis (MNA) linear non-linear perfect
"
with:
"
Materially non-linear analysis (MNA) linear ideal elastic- perfect
plastic
".
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/FprA1:2014 (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 , n and n
x, Ed θ, Ed xθ, Ed
may be represented by the equivalent design stress σ obtained from:
eq, Ed
1
2 2 2
σ = n + n − n ⋅ n + 3n (6.1)
eq, Ed x, Ed θ, Ed
x, Ed θ,Εd xθ, 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 n 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 − σ ⋅σ + 3τ (6.2)
eq, Ed x, Ed θ, Ed
x, Ed θ, Ed xθ, Ed
in which:
n m n m
x,Ed x,Ed θ,Ed θ,Ed
, (6.3)
σ = ± σ = ±
x,Ed θ,Ed
2 2
t (t / 4) t (t / 4)
n m
xθ, Ed xθ, 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 n. 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
pl
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 the
yd
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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EN 1993-1-6:2007/FprA1:2014 (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 does not
GMNA
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 value at which the
GMNA
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 n . The value n = (66 − f /15), where f is
mps mps yd yd
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 according to the
pl,k MNA GMNA
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
R ⋅ F
k Ed
F = F / γ = = R ⋅ F (6.7)".
Rd Rk M0 d Ed
γ
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:
σ = χ f σ = χ f τ = χ f / 3 (8.12)".
x,Rk x yk, θ, Rk θ yk, xθ, Rk τ yk
Replace Paragraph (4) with:
"(4) The elastic-plastic buckling reduction factors χ , χ and χ should be determined as a function of the
x θ τ
relative slenderness of the shell from:
λ
χ = χ − (λ / λ )(χ −1) when λ ≤ λ (8.13)
0 0
h h
10
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EN 1993-1-6:2007/FprA1:2014 (E)
η
λ − λ
0
χ = 1− β when λ < λ < λ (8.14)
0 p
λ − λ
p 0
α
χ = when λ ≤ λ (8.15)
p
2
λ
where:
α is the elastic buckling reduction factor;
β is the plastic range factor;
η is the interaction exponent;
λ is the squash limit relative slenderness;
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 with the following one; 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
cr
the reference plastic resistance R for the geometry and load case, together with the capacity parameters
pl
α, β, η, λ and χ as defined in Annex E.
o h
(2) The plastic reference resistance R may be taken from Annex B. The value of R for a given load case,
pl pl
involving as appropriate the loading P , P , p , F , etc. should be obtained as follows. Where there is
nEd xEd nEd Ed
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 collapse load should then be
Ed
determined for the magnitude of the leading load as F . The plastic reference resistance should then be found
R
as the ratio
11
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EN 1993-1-6:2007/FprA1:2014 (E)
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, and
cr
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 − (λ / λ )(χ −1) when λ ≤ λ (8.26)
0 0
h h
η
λ − λ
0
χ = 1− β when λ < λ < λ (8.27)
0 p
λ − λ
p 0
α
when (8.28)
χ = λ ≤ λ
p
2
λ
where:
α is the elastic buckling reduction factor;
β is the plastic range factor;
η is the interaction exponent;
λ is the squash limit relative slenderness;
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 pl
(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
(8) The design resistance of the shell should then be determined from:
(8.31)
R = R / γ
d k M1
12
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EN 1993-1-6:2007/FprA1:2014 (E)
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) itself with:
"(3) The plastic reference resistance ratio R (see figure 8.5) should be obtained by materially non-linear
pl
analysis (MNA) as the plastic limit load under the applied combination of actions. This load ratio may be
R
pl
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
yk
" r = (8.24)"
Rpl
2 2 2
n − n ⋅ n + n + n
x,Ed x,Ed θ, Ed θ, Ed xθ, Ed
with:
t ⋅ f
y,k
" R = (8.33)".
pl
2 2 2
n − n ⋅ n + n + 3n
x,Ed x,Ed θ, Ed θ, 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 ,η ) using 8.5.2(4), in which is the overall elastic imperfection reduction
α
ov ov ov,0 ov ov ov ov
factor, is the plastic range factor, is the interaction exponent and λ is the squash limit relative
β η
ov ov ov,0
slenderness.".
Replace Paragraph (9) with:
"(9) The evaluation of the factors λ , α , β and η should take account of the imperfection sensitivity,
ov,0 ov ov ov
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
ov
fabrication tolerance quality class.
Care should be taken in choosing an appropriate value of α when this approach is used on shell geometries
ov
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
ov
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).
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SIST EN 1993-1-6:2007/kFprA1:2014
EN 1993-1-6:2007/FprA1:2014 (E)
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 must account for these two sources of reduced resistance by an appropriate choice of the overall
elastic buckling reduction factor α . This choice shall include the effect of both the geometric nonlinearity
ov
(that can lead to snap-through) and the additional strength reduction caused by geometric imperfections.".
Replace Par
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