Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements

(1) EN 1993-1-5 gives design requirements of stiffened and unstiffened plates which are subject to inplane
forces.
(2) Effects due to shear lag, in-plane load introduction and plate buckling for I-section girders and box
girders are covered. Also covered are plated structural components subject to in-plane loads as in tanks and
silos. The effects of out-of-plane loading are outside the scope of this document.
NOTE 1: The rules in this part complement the rules for class 1, 2, 3 and 4 sections, see EN 1993-1-1.
NOTE 2: For the design of slender plates which are subject to repeated direct stress and/or shear and also
fatigue due to out-of-plane bending of plate elements (breathing) see EN 1993-2 and EN 1993-6.
NOTE 3: For the effects of out-of-plane loading and for the combination of in-plane effects and out-of-plane
loading effects see EN 1993-2 and EN 1993-1-7.
NOTE 4: Single plate elements may be considered as flat where the curvature radius r satisfies:
t
a
r
2
³ (1.1)
where a is the panel width
t is the plate thickness

Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 1-5: Plattenförmige Bauteile

1.1   Anwendungsbereich von prEN 1993 1 5
(1)   Dieses Dokument enthält Regelungen für die Tragwerksplanung von nominell ebenen und in ihrer Ebene belasteten Blechen mit oder ohne Steifen.
(2)   Diese Regelungen gelten für Blechträger mit I-Querschnitt und Kastenträger, bei denen ungleichmäßige Spannungsverteilungen infolge Schubverzerrungen sowie Beulen unter Längsspannungen, Schubspannungen und Querlasten auftreten. Sie gelten auch für ebene Bleche aller anderen Bauteile, z. B. von Tankbauwerken und Silos, soweit Lasten und Beanspruchungen in der Ebene der Bauteile wirken. Die Wirkungen von Lasten quer zur Bauteilebene werden in diesem Dokument nicht behandelt.
ANMERKUNG 1   Die Regelungen in diesem Teil ergänzen die Regelungen für Querschnitte der Querschnittsklassen 1, 2, 3 und 4, siehe EN 1993 1 1.
ANMERKUNG 2   Regelungen zu schlanken Platten mit wechselnden Längsspannungen und/oder Schubspannungen, die zu Ermüdung durch wechselnde Biegung aus der Plattenebene („Blechatmen“) führen können, sind in EN 1993 2 und EN 1993 6 angegeben.
ANMERKUNG 3   Regelungen zur Wirkung von Lasten quer zur Plattenebene und zur Kombination von Lastwirkungen in der Ebene und aus der Ebene sind EN 1993 2 und EN 1993 1 7 zu entnehmen.
(3)   Einzelne Blechfelder werden als nominell eben angesehen, wenn für den Krümmungsradius r in der Richtung senkrecht zur Druckrichtung gilt:
Bild 1.1...
1.2   Annahmen
(1)   Sofern nicht spezifisch angegeben, gelten EN 1990, EN 1991 (alle Teile) und EN 1993 1 1.
(2)   Die in EN 1993 1 5 angegebenen Bemessungsverfahren sind anwendbar, wenn
-   die Qualität der Ausführung den Festlegungen nach EN 1090 2 entspricht; und
-   die verwendeten Baustoffe und Produkte den Festlegungen nach den maßgebenden Teilen von EN 1993 (alle Teile) oder nach den maßgebenden Baustoffproduktspezifikationen entsprechen.

Eurocode 3 - Calcul des structures en acier - Partie 1-5: Plaques planes

1.1   Domaine d'application du prEN 1993-1-5
(1) Le présent document fournit les règles de calcul structural pour des plaques nominalement plates, raidies et non raidies, qui sont soumises à des charges dans le plan.
(2) Les effets du traînage de cisaillement, de l'application de charges dans le plan et du voilement des plaques pour les poutres en I à âme pleine et les poutres-caissons sont couverts. Les plaques planes soumises à des charges dans le plan telles que celles exercées dans les réservoirs et les silos, sont également couvertes. Les effets des charges hors du plan ne sont pas traités.
NOTE 1   Les règles définies dans la présente partie complètent les règles applicables aux sections de classe 1, 2, 3 et 4, voir l'EN 1993-1-1.
NOTE 2   Pour le calcul des plaques élancées sur lesquelles s'exercent des contraintes normales et/ou de cisaillement répétées et qui sont soumises à la fatigue due à la flexion hors plan de leurs éléments constitutifs (respiration), voir l'EN 1993-2 et l'EN 1993-6.
NOTE 3   Pour les effets des charges exercées hors du plan et pour la combinaison des effets desdites charges et des charges exercées dans le plan, voir l'EN 1993-2 et l'EN 1993-1-7.
(3) Les plaques simples peuvent être considérées comme planes lorsque le rayon de courbure r, dans le sens perpendiculaire à la compression, satisfait :
Figure 1.1...
1.2   Hypothèses
(1) Sauf indication contraire, l'EN 1990, l'EN 1991 (toutes les parties) et l'EN 1993-1-1 s'appliquent.
(2) Les méthodes de calcul données dans l'EN 1993-1-5 sont applicables si :
-   la qualité de l'exécution est telle que spécifiée dans l'EN 1090-2 ; et
-   les matériaux et produits de construction sont tels que spécifiés dans les parties pertinentes de l'EN 1993 (toutes les parties) ou dans les spécifications de matériaux et de produits appropriées.

Evrokod 3 - Projektiranje jeklenih konstrukcij - 1-5. del: Elementi pločevinaste konstrukcije

General Information

Status
Not Published
Public Enquiry End Date
30-May-2022
Technical Committee
Current Stage
4020 - Public enquire (PE) (Adopted Project)
Start Date
15-Mar-2022
Due Date
02-Aug-2022
Completion Date
02-Jun-2022

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SLOVENSKI STANDARD
oSIST prEN 1993-1-5:2022
01-maj-2022
Evrokod 3 - Projektiranje jeklenih konstrukcij - 1-5. del: Elementi pločevinaste
konstrukcije
Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements
Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 1-5: Plattenförmige
Bauteile
Eurocode 3 - Calcul des structures en acier - Partie 1-5: Plaques planes
Ta slovenski standard je istoveten z: prEN 1993-1-5
ICS:
91.010.30 Tehnični vidiki Technical aspects
91.080.13 Jeklene konstrukcije Steel structures
oSIST prEN 1993-1-5:2022 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN 1993-1-5:2022

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oSIST prEN 1993-1-5:2022


DRAFT
EUROPEAN STANDARD
prEN 1993-1-5
NORME EUROPÉENNE

EUROPÄISCHE NORM

March 2022
ICS 91.010.30; 91.080.13 Will supersede EN 1993-1-5:2006
English Version

Eurocode 3 - Design of steel structures - Part 1-5: Plated
structural elements
Eurocode 3 - Calcul des structures en acier - Partie 1-5: Eurocode 3 - Bemessung und Konstruktion von
Plaques planes Stahlbauten - Teil 1-5: Plattenförmige Bauteile
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 250.

If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations
which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard 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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, 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
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 1993-1-5:2022 E
worldwide for CEN national Members.

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Contents Page
European foreword . 4
0 Introduction . 5
1 Scope . 8
2 Normative references . 9
3 Terms and definitions . 9
3.1 Terms . 9
3.2 Sign convention . 10
3.3 Symbols . 10
4 Basis of design . 11
4.1 General rules . 11
4.2 Partial factors . 12
4.3 Effective width models for global analysis . 12
4.4 Plate buckling effects on uniform members . 13
4.5 Reduced stress method . 14
4.6 Design assisted by finite element analysis . 14
4.7 Non-uniform members . 14
4.8 Members with corrugated webs . 14
5 Shear lag in member design . 14
5.1 General. 14
5.2 Elastic shear lag . 14
5.3 Shear lag at the ultimate limit state . 18
6 Plate buckling effects due to direct stresses at the ultimate limit state . 19
6.1 General. 19
6.2 Resistance to direct stresses . 20
6.3 Effective cross-section . 20
6.4 Plate elements without longitudinal stiffeners . 22
6.5 Stiffened plate elements with longitudinal stiffeners . 27
6.6 Interpolation between plate and column buckling . 32
6.7 Verification . 37
7 Resistance to shear. 39
7.1 General. 39
7.2 Design resistance . 40
7.3 Contribution from the web . 41
7.4 Contribution from flanges . 43
7.5 Verification . 44
8 Resistance to patch loading . 44
8.1 General. 44
8.2 Design resistance . 45
8.3 Length of stiff bearing . 45
8.4 Reduction factor χ . 45
F
8.5 Effective loaded length . 46
8.6 Verification . 47
9 Interaction . 47
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9.1 Interaction between shear force, bending moment and axial force . 47
9.2 Interaction between transverse force, bending moment and axial force . 48
9.3 Interaction between transverse force, bending moment and shear force . 48
10 Flange induced buckling . 49
11 Stiffeners and detailing . 50
11.1 General . 50
11.2 Direct stresses . 50
11.3 Shear . 55
11.4 Transverse loads . 57
12 Reduced stress method . 57
12.1 General . 57
12.2 Buckling verification . 58
12.3 Plate slenderness . 59
12.4 Reduction factors . 60
13 Plate girders with corrugated webs . 63
13.1 General . 63
13.2 Ultimate limit state . 64
Annex A (informative) Calculation of critical stresses for stiffened plates . 69
A.1 Use of this informative annex. 69
A.2 Scope and field of application . 69
A.3 Equivalent orthotropic plate for plates with at least three longitudinal stiffeners . 69
A.4 Equivalent orthotropic plate for plates with one or two longitudinal stiffeners . 70
A.5 Shear buckling coefficients . 70
A.6 Buckling coefficient for patch loading . 71
Annex B (informative) Non-uniform members . 72
B.1 Use of this informative annex. 72
B.2 Scope and field of application . 72
B.3 General . 72
B.4 Interaction of plate buckling and lateral torsional buckling . 72
Bibliography . 73

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European foreword
This document (prEN 1993-1-5:2022) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI. CEN/TC 250 is responsible for all
Structural Eurocodes and has been assigned responsibility for structural and geotechnical matters by
CEN.
This document is currently submitted to the CEN Enquiry.
This document will supersede EN 1993-1-5:2006 and its amendments and corrigenda.
The first generation of EN Eurocodes was published between 2002 and 2007. This document forms part
of the second generation of the Eurocodes, which have been prepared under Mandate M/515 issued to
CEN by the European Commission and the European Free Trade Association.
The Eurocodes have been drafted to be used in conjunction with relevant execution, material, product
and test standards, and to identify requirements for execution, materials, products and testing that are
relied upon by the Eurocodes.
The Eurocodes recognize the responsibility of each Member State and have safeguarded their right to
determine values related to regulatory safety matters at national level through the use of National
Annexes.
4

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0 Introduction
0.1 Introduction to the Eurocodes
The Structural Eurocodes comprise the following standards generally consisting of a number of Parts:
— EN 1990, Eurocode: Basis of structural and geotechnical design
— EN 1991, Eurocode 1: Actions on structures
— EN 1992, Eurocode 2: Design of concrete structures
— EN 1993, Eurocode 3: Design of steel structures
— EN 1994, Eurocode 4: Design of composite steel and concrete structures
— EN 1995, Eurocode 5: Design of timber structures
— EN 1996, Eurocode 6: Design of masonry structures
— EN 1997, Eurocode 7: Geotechnical design
— EN 1998, Eurocode 8: Design of structures for earthquake resistance
— EN 1999, Eurocode 9: Design of aluminium structures
— New parts are under development, e.g. Eurocode for design of structural glass
0.2 Introduction to EN 1993 (all parts)
EN 1993 (all parts) applies to the design of buildings and civil engineering works in steel. It complies with
the principles and requirements for the safety and serviceability of structures, the basis of their design
and verification that are given in EN 1990 – Basis of structural design.
EN 1993 (all parts) is concerned only with requirements for resistance, serviceability, durability and fire
resistance of steel structures. Other requirements, e.g. concerning thermal or sound insulation, are not
covered.
EN 1993 is subdivided in various parts:
EN 1993-1, Design of Steel Structures — Part 1: General rules and rules for buildings;
EN 1993-2, Design of Steel Structures — Part 2: Steel bridges;
EN 1993-3, Design of Steel Structures — Part 3: Towers, masts and chimneys;
EN 1993-4, Design of Steel Structures — Part 4: Silos and tanks;
EN 1993-5, Design of Steel Structures — Part 5: Piling;
EN 1993-6, Design of Steel Structures — Part 6: Crane supporting structures;
EN 1993-7, Design of steel structures — Part 7: Design of sandwich panels.
EN 1993-1 in itself does not exist as a physical document, but comprises the following 14 separate parts,
the basic part being EN 1993-1-1:
EN 1993-1-1, Design of Steel Structures — Part 1-1: General rules and rules for buildings;
EN 1993-1-2, Design of Steel Structures — Part 1-2: Structural fire design;
5

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EN 1993-1-3, Design of Steel Structures — Part 1-3: Cold-formed members and sheeting;
NOTE Cold formed hollow sections supplied according to EN 10219 are covered in EN 1993-1-1.
EN 1993-1-4, Design of Steel Structures — Part 1-4: Stainless steels;
EN 1993-1-5, Design of Steel Structures — Part 1-5: Plated structural elements;
EN 1993-1-6, Design of Steel Structures — Part 1-6: Strength and stability of shell structures;
EN 1993-1-7, Design of Steel Structures — Part 1-7: Strength and stability of planar plated structures
transversely loaded;
EN 1993-1-8, Design of Steel Structures — Part 1-8: Design of joints;
EN 1993-1-9, Design of Steel Structures — Part 1-9: Fatigue strength of steel structures;
EN 1993-1-10, Design of Steel Structures — Part 1-10: Selection of steel for fracture toughness and through-
thickness properties;
EN 1993-1-11, Design of Steel Structures — Part 1-11: Design of structures with tension components made
of steel;
EN 1993-1-12, Design of Steel Structures — Part 1-12: Additional rules for steel grades up to S960;
EN 1993-1-13, Design of Steel Structures — Part 1-13: Beams with large web openings;
EN 1993-1-14, Design of Steel Structures — Part 1-14: Design assisted by finite element analysis.
All subsequent parts EN 1993-1-2 to EN 1993-1-14 treat general topics that are independent from the
structural type such as structural fire design, cold-formed members and sheeting, stainless steels, plated
structural elements, etc.
All subsequent parts numbered EN 1993-2 to EN 1993-7 treat topics relevant for a specific structural
type such as steel bridges, towers, masts and chimneys, silos and tanks, piling, crane supporting
structures, etc. EN 1993-2 to EN 1993-7 refer to the generic rules in EN 1993-1 and supplement, modify
or supersede them.
0.3 Introduction to prEN 1993-1-5
prEN 1993-1-5 gives design requirements for unstiffened and stiffened plates that are subject to in-plane
forces. It also covers plated structural elements like I-section girders or box girders, as well as plated
components used in tanks and silos.
0.4 Verbal forms used in the Eurocodes
The verb “shall" expresses a requirement strictly to be followed and from which no deviation is permitted
in order to comply with the Eurocodes.
The verb “should” expresses a highly recommended choice or course of action. Subject to national
regulation and/or any relevant contractual provisions, alternative approaches could be used/adopted
where technically justified.
The verb “may" expresses a course of action permissible within the limits of the Eurocodes.
The verb “can" expresses possibility and capability; it is used for statements of fact and clarification of
concepts.
0.5 National Annex for prEN 1993-1-5
National choice is allowed in this standard where explicitly stated within notes. National choice includes
the selection of values for Nationally Determined Parameters (NDPs).
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The national standard implementing prEN 1993-1-5 can have a National Annex containing all national
choices to be used for the design of buildings and civil engineering works to be constructed in the relevant
country.
When no national choice is given, the default choice given in this standard is to be used.
When no national choice is made and no default is given in this standard, the choice can be specified by a
relevant authority or, where not specified, agreed for a specific project by appropriate parties.
National choice is allowed in prEN 1993-1-5 through notes to the following:
4.6(2) 6.4.1(10) 7.1(2)
National choice is allowed in prEN 1993-1-5 on the application of the following informative annexes:
Annex A Annex B

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1 Scope
1.1 Scope of prEN 1993-1-5
(1) This document provides rules for structural design of stiffened and unstiffened nominally flat plates
which are subject to in-plane forces.
(2) Effects due to shear lag, in-plane load introduction and plate buckling for I-section girders and box
girders are covered. Also covered are plated structural components subject to in-plane loads as in tanks
and silos. The effects of out-of-plane loading are outside the scope of this document.
NOTE 1 The rules in this part complement the rules for class 1, 2, 3 and 4 sections, see EN 1993-1-1.
NOTE 2 For the design of slender plates which are subject to repeated direct stress and/or shear and also fatigue
due to out-of-plane bending of plate elements (“breathing”), see EN 1993-2 and EN 1993-6.
NOTE 3 For the effects of out-of-plane loading and for the combination of in-plane effects and out-of-plane
loading effects, see EN 1993-2 and EN 1993-1-7.
(3) Single plate elements are considered as nominally flat where the curvature radius r in the direction
perpendicular to the compression satisfies:
2
b
r≥ (1.1)
t
where
b is the panel width;
t is the plate thickness.

Figure 1.1 — Definition of plate curvature
1.2 Assumptions
(1) Unless specifically stated, EN 1990, EN 1991 (all parts) and EN 1993-1-1 apply.
(2) The design methods given in EN 1993-1-5 are applicable if
— the execution quality is as specified in EN 1090-2 and
— the construction materials and products used are as specified in the relevant parts of EN 1993 (all
parts) or in the relevant material product specifications.
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2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
NOTE See the Bibliography for a list of other documents cited that are not normative references, including
those referenced as recommendations (i.e. through ‘should’ clauses) and permissions (i.e. through ‘may’ clauses).
EN 1090-2:2018, Execution of steel structures and aluminium structures — Part 2: Technical requirements
for steel structures
EN 1990, Eurocode: Basis of structural and geotechnical design
EN 1991 (all parts), Eurocode 1: Actions on structures
prEN 1993-1-1:2020, Eurocode 3: Design of steel structures — Part 1-1: General rules and rules for
buildings
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
Terms
3.1.1
plate
structural element that, in general, has two large dimensions a and b and a uniform much smaller
dimension t, and is shaped such that the two large dimensions lie in a single plane
3.1.2
elastic critical stress
stress in a component at which the component becomes unstable when using small deflection elastic
theory of a perfect structure
3.1.3
membrane stress
stress at mid-plane of the plate
3.1.4
gross cross-section
total cross-sectional area of a member but excluding discontinuous longitudinal stiffeners
3.1.5
effective cross-section and effective width
gross cross-section or width reduced for the effects of plate buckling or shear lag or both
Note 1 to entry: To distinguish between their effects the word “effective” is clarified as follows:
p
— “effective “ denotes effects of plate buckling
s
— “effective “ denotes effects of shear lag
— “effective“ denotes effects of plate buckling and shear lag
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3.1.6
plated structure
structure built up from nominally flat plates which are connected together
Note 1 to entry: The plates can be stiffened or unstiffened.
3.1.7
stiffener
flat plate or prismatic section attached to a plate to resist buckling or to strengthen the plate
Note 1 to entry: A stiffener is denoted:
— longitudinal if its direction is parallel to the member constituted of the assembled plates;
— transverse if its direction is perpendicular to the member constituted of the assembled plates.
3.1.8
stiffened plate
plate with transverse or longitudinal stiffeners or both
3.1.9
subpanel
unstiffened plate portion surrounded by flanges and/or stiffeners
3.1.10
hybrid girder
girder with flanges and web(s) made of different steel grades
3.1.11
direct stresses
normal stresses acting in the direction of the longitudinal axis of the member
3.1.12
patch loading
local introduction of in-plane forces
 Sign convention
Unless otherwise stated, compression is taken as positive.
 Symbols
For the purposes of this document, the symbols in EN 1990, EN 1993-1-1 and the following apply.
A total gross cross-sectional area of all the longitudinal stiffeners of a stiffened plate
sℓ
without contributing plating;
A gross cross-sectional area of one transverse stiffener;
st
A effective cross-sectional area;
eff
p
A effective cross-sectional area;
c,eff
p
A effective cross-sectional area for local buckling;
c,eff,loc
a length of a stiffened or unstiffened plate;
b width of a stiffened or unstiffened plate;
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b gross width of the flange outstand or half the width of an internal element;
0
b gross width of the compression zone corresponding to A ;
g c,eff
s
b effective width for elastic shear lag;
eff
F design transverse force;
Ed
h clear web depth between flanges;
w
L effective length for resistance to transverse forces;
eff
M design plastic moment of resistance of the cross-section consisting of the effective area
f,Rd
of the flanges only;
Mf,Rk characteristic plastic moment of resistance of the cross-section consisting of the
effective area of the flanges only;
M design plastic moment of resistance of the cross section consisting of the effective area
f,eff,Rd
of the flanges and the fully effective web irrespective of its section class;
M design value of the plastic moment resistance (irrespective of cross-section class);
pl,Rd
M design bending moment;
Ed
N design axial force;
Ed
t thickness of the plate;
V design shear force including shear from torque;
Ed
W effective elastic section modulus;
eff
s
β effective width factor for shear lag;
Additional symbols are defined where they first occur.
4 Basis of design
General rules
Basic requirement
(1) The design of steel plated structures elements shall be in accordance with the general rules given in
EN 1990 and EN 1991 (all parts) and the specific design provisions for steel structures given in
EN 1993-1-1.
(2) Steel structures designed according to this document shall be executed according to EN 1090-2 with
construction materials and products used as specified in the relevant parts of EN 1993 or in the relevant
material and product specifications.
(3) The effects of shear lag and plate buckling shall be taken into account at the ultimate, serviceability
and fatigue limit states.
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Partial factors
(1) The partial factors as defined in EN 1993-1-1 should be applied to the characteristic values of the
following resistances:
— Resistance to direct stresses γ
M0
— Resistance to shear γ
M1
— Resistance to patch loading γ
M1
— Resistance of transverse stiffeners γ
M1
— Resistance according to the reduced stress method γ
M1
— Resistance of compression flanges of girder with corrugated webs where γ
M1
lateral torsional buckling governs
(2) Partial factors γ and γ have the value assigned to them in the National Annex to the relevant parts
M0 M1
of EN 1993-1 to EN 1993-6.
Effective width models for global analysis
(1) The effects of shear lag and of plate buckling on the stiffness of members and joints shall be taken into
account in the global analysis.
(2) The effects of shear lag of flanges in global analysis may be taken into account by the use of an
s s
effective width. For simplicity this effective width may be assumed to be uniform over the length of the
sp
...

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