PREAMBLE (NOT PART OF THE STANDARD)

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END OF PREAMBLE (NOT PART OF THE STANDARD)

EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM

EN 1999-1-1:2007+A1

June 2009

ICS 91.010.30; 91.080.10

Supersedes ENV 1999-1-1:1998

English Version

Eurocode 9: Design of aluminium structures - Part 1-1: General structural rules

Eurocode 9: Calcul des structures en aluminium - Partie 1-1: Règles générales Eurocode 9: Bemessung und Konstruktion von Aluminiumtragwerken - Teil 1 - 1: Allgemeine Bemessungsregeln

This European Standard was approved by CEN on 18 September 2006.

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. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Management Centre or to any CEN member.

This European Standard 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 Management Centre has the same status as the official versions.

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

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Management Centre: rue de Stassart, 36 B-1050 Brussels

© 2007 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.

Ref. No. EN 1999-1-1:2007: E

1

Contents

Page
Foreword 7
1 General 11
  1.1 Scope 11
    1.1.1 Scope of EN 1999 11
    1.1.2 Scope of EN 1999-1-1 11
  1.2 Normative references 12
    1.2.1 General references 12
    1.2.2 References on structural design 12
    1.2.3 References on aluminium alloys 13
    1.2.4 References on welding 15
    1.2.5 Other references 15
  1.3 Assumptions 16
  1.4 Distinction between principles and application rules 16
  1.5 Terms and definitions 16
  1.6 Symbols 17
  1.7 Conventions for member axes 27
  1.8 Specification for execution on the work 27
2 Basis of design 29
  2.1 Requirements 29
    2.1.1 Basic requirements 29
    2.1.2 Reliability management 29
    2.1.3 Design working life, durability and robustness 29
  2.2 Principles of limit state design 29
  2.3 Basic variables 30
    2.3.1 Actions and environmental influences 30
    2.3.2 Material and product properties 30
  2.4 Verification by the partial factor method 30
    2.4.1 Design value of material properties 30
    2.4.2 Design value of geometrical data 30
    2.4.3 Design resistances 30
    2.4.4 Verification of static equilibrium (EQU) 31
  2.5 Design assisted by testing 31
3 Materials 32
  3.1 General 32
  3.2 Structural aluminium 32
    3.2.1 Range of materials 32
    3.2.2 Material properties for wrought aluminium alloys 33
    3.2.3 Material properties for cast aluminium alloys 37
    3.2.4 Dimensions, mass and tolerances 37
    3.2.5 Design values of material constants 37
  3.3 Connecting devices 38
    3.3.1 General 38
    3.3.2 Bolts, nuts and washers 38
    3.3.3 Rivets 39
    3.3.4 Welding consumables 40
    3.3.5 Adhesive 42
4 Durability 42
5 Structural analysis 43
  5.1 Structural modelling for analysis 43
    5.1.1 Structural modelling and basic assumptions 43
    5.1.2 Joint modelling 43
    5.1.3 Ground-structure interaction 43
  5.2 Global analysis 43 2
    5.2.1 Effects of deformed geometry of the structure 43
    5.2.2 Structural stability of frames 44
  5.3 Imperfections 45
    5.3.1 Basis 45
    5.3.2 Imperfections for global analysis of frames 45
    5.3.3 Imperfection for analysis of bracing systems 49
    5.3.4 Member imperfections 52
  5.4 Methods of analysis 52
    5.4.1 General 52
    5.4.2 Elastic global analysis 52
    5.4.3 Plastic global analysis 52
6 Ultimate limit states for members 53
  6.1 Basis 53
    6.1.1 General 53
    6.1.2 Characteristic value of strength 53
    6.1.3 Partial safety factors 53
    6.1.4 Classification of cross-sections 53
    6.1.5 Local buckling resistance 58
    6.1.6 HAZ softening adjacent to welds 59
  6.2 Resistance of cross-sections 61
    6.2.1 General 61
    6.2.2 Section properties 62
    6.2.3 Tension 63
    6.2.4 Compression 64
    6.2.5 Bending moment 64
    6.2.6 Shear 66
    6.2.7 Torsion 67
    6.2.8 Bending and shear 69
    6.2.9 Bending and axial force 69
    6.2.10 Bending, shear and axial force 71
    6.2.11 Web bearing 71
  6.3 Buckling resistance of members 71
    6.3.1 Members in compression 71
    6.3.2 Members in bending 75
    6.3.3 Members in bending and axial compression 77
  6.4 Uniform built-up members 80
    6.4.1 General 80
    6.4.2 Laced compression members 82
    6.4.3 Battened compression members 83
    6.4.4 Closely spaced built-up members 85
  6.5 Un-stiffened plates under in-plane loading 85
    6.5.1 General 85
    6.5.2 Resistance under uniform compression 86
    6.5.3 Resistance under in-plane moment 87
    6.5.4 Resistance under transverse or longitudinal stress gradient 88
    6.5.5 Resistance under shear 88
    6.5.6 Resistance under combined action 89
  6.6 Stiffened plates under in-plane loading 89
    6.6.1 General 89
    6.6.2 Stiffened plates under uniform compression 90
    6.6.3 Stiffened plates under in-plane moment 92
    6.6.4 Longitudinal stress gradient on multi-stiffened plates 92
    6.6.5 Multi-stiffened plating in shear 93
    6.6.6 Buckling load for orthotropic plates 93
  6.7 Plate girders 96
    6.7.1 General 96
    6.7.2 Resistance of girders under in-plane bending 96
    6.7.3 Resistance of girders with longitudinal web stiffeners 97 3
    6.7.4 Resistance to shear 98
    6.7.5 Resistance to transverse loads 102
    6.7.6 Interaction 105
    6.7.7 Flange induced buckling 106
    6.7.8 Web stiffeners 106
  6.8 Members with corrugated webs 108
    6.8.1 Bending moment resistance 108
    6.8.2 Shear force resistance 108
7 Serviceability Limit States 110
  7.1 General 110
  7.2 Serviceability limit states for buildings 110
    7.2.1 Vertical deflections 110
    7.2.2 Horizontal deflections 110
    7.2.3 Dynamic effects 110
    7.2.4 Calculation of elastic deflection 110
8 Design of joints 111
  8.1 Basis of design 111
    8.1.1 Introduction 111
    8.1.2 Applied forces and moments 111
    8.1.3 Resistance of joints 111
    8.1.4 Design assumptions 112
    8.1.5 Fabrication and execution 112
  8.2 Intersections for bolted, riveted and welded joints 112
  8.3 Joints loaded in shear subject to impact, vibration and/or load reversal 113
  8.4 Classification of joints 113
  8.5 Connections made with bolts, rivets and pins 113
    8.5.1 Positioning of holes for bolts and rivets 113
    8.5.2 Deductions for fastener holes 116
    8.5.3 Categories of bolted connections 117
    8.5.4 Distribution of forces between fasteners 119
    8.5.5 Design resistances of bolts 120
    8.5.6 Design resistance of rivets 122
    8.5.7 Countersunk bolts and rivets 123
    8.5.8 Hollow rivets and rivets with mandrel 123
    8.5.9 High strength bolts in slip-resistant connections 123
    8.5.10 Prying forces 125
    8.5.11 Long joints 125
    8.5.12 Single lap joints with fasteners in one row 126
    8.5.13 Fasteners through packings 126
    8.5.14 Pin connections 126
  8.6 Welded connections 129
    8.6.1 General 129
    8.6.2 Heat-affected zone (HAZ) 129
    8.6.3 Design of welded connections 129
  8.7 Hybrid connections 136
  8.8 Adhesive bonded connections 136
  8.9 Other joining methods 136
Annex A [normative] – Execution classes 137
Annex B [normative] - Equivalent T-stub in tension 140
  B.1 General rules for evaluation of resistance 140
  B.2 Individual bolt-row, bolt-groups and groups of bolt-rows 144
Annex C [informative] - Materials selection 146
  C.1 General 146
  C.2 Wrought products 146
    C.2.1 Wrought heat treatable alloys 146 4
    C.2.2 Wrought non-heat treatable alloys 149
  C.3 Cast products 150
    C.3.1 General 150
    C.3.2 Heat treatable casting alloys EN AC-42100, EN AC-42200, EN AC-43000 and EN AC-43300 150
    C.3.3 Non-heat treatable casting alloys EN AC-44200 and EN AC-51300 150
    C.3.4 Special design rules for castings 150
  C.4 Connecting devices 152
    C.4.1 Aluminium bolts 152
    C.4.2 Aluminium rivets 152
Annex D [informative] – Corrosion and surface protection 153
  D.1 Corrosion of aluminium under various exposure conditions 153
  D.2 Durability ratings of aluminium alloys 153
  D.3 Corrosion protection 154
    D.3.1 General 154
    D.3.2 Overall corrosion protection of structural aluminium 154
    D.3.3 Aluminium in contact with aluminium and other metals 155
    D.3.4 Aluminium surfaces in contact with non-metallic materials 155
Annex E [informative] - Analytical models for stress strain relationship 160
  E.1 Scope 160
  E.2 Analytical models 160
    E.2.1 Piecewise linear models 160
    E.2.2 Continuous models 162
  E.3 Approximate evaluation of εu 165
Annex F [informative] - Behaviour of cross-sections beyond the elastic limit 166
    F.1 General 166
    F.2 Definition of cross-section limit states 166
    F.3 Classification of cross-sections according to limit states 166
    F.4 Evaluation of ultimate axial load 167
    F.5 Evaluation of ultimate bending moment 168
Annex G [informative] - Rotation capacity 170
Annex H [informative] - Plastic hinge method for continuous beams 172
Annex I [informative] - Lateral torsional buckling of beams and torsional or torsional-flexural buckling of compressed members 174
  I.1 Elastic critical moment and slenderness 174
    I.1.1 Basis 174
    I.1.2 General formula for beams with uniform cross-sections symmetrical about the minor or major axis 174
    I.1.3 Beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections 179
    I.1.4 Cantilevers with uniform cross-sections symmetrical about the minor axis 180
  I.2 Slenderness for lateral torsional buckling 182
  I.3 Elastic critical axial force for torsional and torsional-flexural buckling 184
  I.4 Slenderness for torsional and torsional-flexural buckling 185
Annex J [informative] - Properties of cross sections 190
  J.1 Torsion constant It 190
  J.2 Position of shear centre S 190
  J.3 Warping constant Iw 190
  J.4 Cross section constants for open thin-walled cross sections 194
  J.5 Cross section constants for open cross section with branches 196
  J.6 Torsion constant and shear centre of cross section with closed part 196
Annex K [informative] - Shear lag effects in member design 197 5
  K.1 General 197
  K.2 Effective width for elastic shear lag 197
    K.2.1 Effective width factor for shear lag 197
    K.2.2 Stress distribution for shear lag 198
    K.2.3 In-plane load effects 199
  K.3 Shear lag at ultimate limit states 200
Annex L [informative] - Classification of joints 201
  L.1 General 201
  L.2 Fully restoring connections 202
  L.3 Partially restoring connections 202
  L.4 Classification according to rigidity 202
  L.5 Classification according to strength 203
  L.6 Classification according to ductility 203
  L.7 General design requirements for connections 203
  L.8 Requirements for framing connections 203
    L.8.1 General 203
    L.8.2 Nominally pinned connections 204
    L.8.3 Built-in connections 205
Annex M [informative] - Adhesive bonded connections 206
  M.1 General 206
  M.2 Adhesives 206
  M.3 Design of adhesive bonded joints 207
    M.3.1 General 207
    M.3.2 Characteristic strength of adhesives 207
    M.3.3 Design shear stress 208
  M.4 Tests 208
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Foreword

This European Standard (EN 1999-1-1:2007) has been prepared by Technical Committee CEN/TC250 « 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 November 2007, and conflicting national standards shall be withdrawn at the latest by March 2010.

This European Standard supersedes ENV 1999-1-1: 1998.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard:

Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom.

Background of the Eurocode programme

In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.

Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works, which in a first stage would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them.

For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980s.

In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement1 between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products – CPD – and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).

The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts:

EN 1990 Eurocode 0: Basis of structural 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

1 Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89).

7

Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.

Status and field of application of Eurocodes

The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes:

The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents2 referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standard3. Therefore, technical aspects, arising from the Eurocodes work, need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving a full compatibility of these technical specifications with the Eurocodes.

The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.

National Standards implementing Eurocodes

The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National annex (informative).

The National Annex (informative) may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e. :

Links between Eurocodes and product harmonised technical specifications (ENs and ETAs)

There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works4. Furthermore, all the information accompanying the CE Marking of the

2According to Art. 3.3 of the CPD, the essential requirements (ERs) should be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for hENs and ETAGs/ETAs.

3According to Art. 12 of the CPD the interpretative documents should :

  1. give concrete form to the essential requirements by harmonising the terminology and the technical bases and indicating classes or levels for each requirement where necessary ;
  2. indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g. methods of calculation and of proof, technical rules for project design, etc. ;
  3. serve as a reference for the establishment of harmonised standards and guidelines for European technical approvals.

    The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.

4 See Art.3.3 and Art. 12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.

8

construction products which refer to Eurocodes should clearly mention which Nationally Determined Parameters have been taken into account.

Additional information specific to EN 1999-1-1

EN 1999 is intended to be used with Eurocodes EN 1990 – Basis of Structural Design, EN 1991 – Actions on structures and EN 1992 to EN 1999, where aluminium structures or aluminium components are referred to.

EN 1999-1-1 is the first part of five parts of EN 1999. It gives generic design rules that are intended to be used with the other parts EN 1999-1 -2 to EN 1999-1 -5.

The four other parts EN 1999-1-2 to EN 1999-1-5 are each addressing specific aluminium components, limit states or type of structures.

EN 1999-1-1 may also be used for design cases not covered by the Eurocodes (other structures, other actions, other materials) serving as a reference document for other CEN TC’s concerning structural matters.

EN 1999-1-1 is intended for use by

Numerical values for partial factors and other reliability parameters are recommended as basic values that provide an acceptable level of reliability. They have been selected assuming that an appropriate level of workmanship and quality management applies.

9

National annex for EN 1999-1-1

This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 1999-1-1 should have a National Annex containing all Nationally Determined Parameters to be used for the design of aluminium structures to be constructed in the relevant country.

National choice is allowed in EN 1999-1-1 through clauses:

10

1 General

1.1 Scope

1.1.1 Scope of EN 1999

  1. P EN 1999 applies to the design of buildings and civil engineering and structural works in aluminium. 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.
  2. EN 1999 is only concerned with requirements for resistance, serviceability, durability and fire resistance of aluminium structures. Other requirements, e.g. concerning thermal or sound insulation, are not considered.
  3. EN 1999 is intended to be used in conjunction with:
  4. EN 1999 is subdivided in five parts:

    EN 1999-1-1 Design of Aluminium Structures: General structural rules.

    EN 1999-1-2 Design of Aluminium Structures: Structural fire design.

    EN 1999-1-3 Design of Aluminium Structures: Structures susceptible to fatigue.

    EN 1999-1-4 Design of Aluminium Structures: Cold-formed structural sheeting.

    EN 1999-1-5 Design of Aluminium Structures: Shell structures.

1.1.2 Scope of EN 1999-1-1

  1. EN 1999-1-1 gives basic design rules for structures made of wrought aluminium alloys and limited guidance for cast alloys Image (see section 3 and Annex C). Image

    NOTE Minimum material thickness may be defined in the National Annex. The following limits are recommended – if not otherwise explicitly stated in this standard:

  2. The following subjects are dealt with in EN 1999-1-1:

    Section 1: General

    Section 2: Basis of design

    Section 3: Materials

    Image footnote deleted Image

    11

    Section 4: Durability

    Section 5: Structural analysis

    Section 6: Ultimate limit states for members

    Section 7: Serviceability limit states

    Section 8: Design of joints

    Annex A Execution classes
    Annex B Equivalent T-stub in tension
    Annex C Materials selection
    Annex D Corrosion and surface protection
    Annex E Analytical models for stress strain relationship
    Annex F Behaviour of cross section beyond elastic limit
    Annex G Rotation capacity
    Annex H Plastic hinge method for continuous beams
    Annex I Lateral torsional buckling of beams and torsional or flexural-torsional buckling of compression members
    Annex J Properties of cross sections
    Annex K Shear lag effects in member design
    Annex L Classification of connections
    Annex M Adhesive bonded connections
  3. Sections 1 to 2 provide additional clauses to those given in EN 1990 “Basis of structural design”.
  4. Section 3 deals with material properties of products made of structural aluminium alloys.
  5. Section 4 gives general rules for durability.
  6. Section 5 refers to the structural analysis of structures, in which the members can be modelled with sufficient accuracy as line elements for global analysis.
  7. Section 6 gives detailed rules for the design of cross sections and members.
  8. Section 7 gives rules for serviceability.
  9. Section 8 gives detail rules for connections subject to static loading: bolted, riveted, welded and adhesive bonded connections.

1.2 Normative references

  1. This European Standard incorporates by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only if incorporated in it by amendment or revision. For undated references the latest edition of the publication referred to applies (including amendments).

1.2.1 General references

prEN 1090-1: Execution of steel structures and aluminium structures – Part 1: Requirements for conformity assessment of structural components

Image EN 1090-3Image: Execution of steel structures and aluminium structures – Part 3: Technical requirements for aluminium structures

1.2.2 References on structural design

Image footnote deleted Image

EN 1990 Basis of structural design 12
EN 1991 Actions on structures – All parts

Image Text deleted Image

EN 1999-1-2 Design of aluminium structures - Part 1-2: Structural fire design
EN 1999-1-3 Design of aluminium structures - Part 1-3: Structures susceptible to fatigue
EN 1999-1-4 Design of aluminium structures - Part 1-4: Cold-formed structural sheeting
EN 1999-1-5 Design of aluminium structures - Part 1-5: Shell structures

1.2.3 References on aluminium alloys

Image Text deleted Image

Image 1.2.3.1 Technical delivery conditions
EN 485-1 Aluminium and aluminium alloys - Sheet, strip and plate - Part 1: Technical conditions for inspection and delivery
EN 586-1 Aluminium and aluminium alloys - Forgings - Part 1: Technical conditions for inspection and delivery
EN 754-1 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 1: Technical conditions for inspection and delivery
EN 755-1 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles - Part 1: Technical conditions for inspection and delivery Image

Image Text deleted Image

EN 28839 Fasteners - Mechanical properties of fasteners - Bolts, screws, studs and nuts made from non-ferrous metals
EN ISO 898-1 Mechanical properties of fasteners made of carbon steel and alloy steel - Part 1: Bolts, screws and studs
EN ISO 3506-1 Mechanical properties of corrosion-resistant stainless-steel fasteners - Part 1: Bolts, screws and studs
Image 1.2.3.2 Dimensions and mechanical properties
EN 485-2 Aluminium and aluminium alloys - Sheet, strip and plate - Part 2: Mechanical properties
EN 485-3 Aluminium and aluminium alloys - Sheet, strip and plate - Part 3: Tolerances on shape and dimensions for hot-rolled products
EN 485-4 Aluminium and aluminium alloys - Sheet, strip and plate - Part 4: Tolerances on shape and dimensions for cold-rolled products Image 13
Image EN 508-2 Roofing products from metal sheet - Specifications for self supporting products of steel, aluminium or stainless steel - Part 2: Aluminium
EN 586-2 Aluminium and aluminium alloys - Forgings - Part 2: Mechanical properties and additional property requirements
EN 586-3 Aluminium and aluminium alloys - Forgings - Part 3: Tolerances on dimension and form
EN 754-2 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 2: Mechanical properties
EN 754-3 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 3: Round bars, tolerances on dimension and form
EN 754-4 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 4: Square bars, tolerances on dimension and form
EN 754-5 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 5: Rectangular bars, tolerances on dimension and form
EN 754-6 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 6: Hexagonal bars, tolerances on dimension and form
EN 754-7 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 7: Seamless tubes, tolerances on dimension and form
EN 754-8 Aluminium and aluminium alloys - Cold drawn rod/bar and tube - Part 8: Porthole tubes, tolerances on dimension and form
EN 755-2:2008 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles - Part 2: Mechanical properties
EN 755-3 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 3: Round bars, tolerances on dimension and form
EN 755-4 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 4: Square bars, tolerances on dimension and form
EN 755-5 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 5: Rectangular bars, tolerances on dimension and form
EN 755-6 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 6: Hexagonal bars, tolerances on dimension and form
EN 755-7 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 7: Seamless tubes, tolerances on dimension and form
EN 755-8 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 8: Porthole tubes, tolerances on dimension and form
EN 755-9 Aluminium and aluminium alloys - Extruded rod/bar, tube and profiles- Part 9: Profiles, tolerances on dimension and form Image

Image Text deleted Image

Image 1.2.3.3 Aluminium alloy castings
EN 1559-1 Founding - Technical conditions of delivery - Part 1: General
EN 1559-4 Founding - Technical conditions of delivery - Part 4: Additional requirements for aluminium alloy castings Image 14
Image EN 1371-1 Founding - Liquid penetrant inspection - Part I: Sand, gravity die and low pressure die castings
EN 12681 Founding - Radiographic examination
EN 571-1 Non destructive testing - Penetrant testing - Part 1: General principles
EN 13068-1 Non-destructive testing - Radioscopic testing - Part 1: Quantitative measurement of imaging properties
EN 13068-2 Non-destructive testing - Radioscopic testing - Part 2: Check of long term stability of imaging devices
EN 13068-3 Non-destructive testing - Radioscopic testing - Part 3: General principles of radioscopic testing of metallic materials by X- and gamma rays
EN 444 Non-destructive testing - General principles for radiographic examination of metallic materials by X- and gamma-rays Image

Image Text deleted Image

Image EN 1706 Aluminium and aluminium alloys - Castings - Chemical composition and mechanical properties Image

1.2.4 References on welding

Image Text deleted Image

Image EN 1011-4:2000 Welding – Recommendations for welding of metallic materials – Part 4: Arc welding of aluminium and aluminium alloys Image

Image Text deleted Image

1.2.5 Other references

Image Text deleted Image

Image ISO 8930 General principles on reliability for structures - List of equivalent terms
ISO 11003-1 Adhesives -- Determination of shear behaviour of structural adhesives -- Part l: Torsion test method using butt-bonded hollow cylinders
ISO 11003-2 Adhesives -- Determination of shear behaviour of structural adhesives -- Part 2: Tensile test method using thick adherents
prEN ISO 1302 Geometrical Product Specification (GPS) - Indication of surface texture in technical product documentation. Image 15
Image EN ISO 4287 Geometral Product Specifications (GSP) - Surface texture: Profile method - Terms, definitions and surface texture parameters
EN ISO 4288 Geometrical Product Specification (GPS) - Surface texture - Profile method: Rules and procedures for the assessment of surface texture. Image

1.3 Assumptions

  1. In addition to the general assumptions of EN 1990 the following assumptions apply:

1.4 Distinction between principles and application rules

  1. The rules in EN 1990 1.4 apply.

1.5 Terms and definitions

  1. The definitions in EN 1990 1.5 apply.
  2. The following terms are used in EN 1999-1-1 with the following definitions:

1.5.1
frame

the whole or a portion of a structure, comprising an assembly of directly connected structural members, designed to act together to resist load; this term refers to both moment-resisting frames and triangulated frames; it covers both plane frames and three-dimensional frames

1.5.2
sub-frame

a frame that forms part of a larger frame, but is be treated as an isolated frame in a structural analysis

1.5.3
type of framing

terms used to distinguish between frames that are either:

1.5.4
global analysis

the determination of a consistent set of internal forces and moments in a structure, which are in equilibrium with a particular set of actions on the structure

1.5.5
system length

distance in a given plane between two adjacent points at which a member is braced against lateral displacement, or between one such point and the end of the member

1.5.6
buckling length

length of an equivalent uniform member with pinned ends, which has the same cross-section and the same elastic critical force as the verified uniform member (individual or as a component of a frame structure).

16

1.5.7
shear lag effect

non uniform stress distribution in wide flanges due to shear deformations; it is taken into account by using a reduced “effective” flange width in safety assessments

1.5.8
capacity design

design based on the plastic deformation capacity of a member and its connections providing additional strength in its connections and in other parts connected to the member.

1.6 Symbols

  1. For the purpose of this standard the following apply.

    Additional symbols are defined where they first occur.

    NOTE Symbols are ordered by appearance in EN 1999-1-1. Symbols may have various meanings.

    Section 1 General

    x - x axis along a member
    y - y axis of a cross-section
    z - z axis of a cross-section
    u - u major principal axis (where this does not coincide with the y-y axis)
    v - v minor principal axis (where this does not coincide with the z-z axis)

    Section 2 Basis of design

    Pk nominal value of the effect of prestressing imposed during erection
    Gk nominal value of the effect of permanent actions
    Xk characteristic values of material property
    Xn nominal values of material property
    Rd design value of resistance
    Rk characteristic value of resistance
    γM general partial factor
    γMi particular partial factor
    γMf partial factor for fatigue
    η conversion factor
    ad design value of geometrical data

    Section 3 Materials

    fo characteristic value of 0,2 % proof strength
    fu characteristic value of ultimate tensile strength
    foc characteristic value of 0,2 % proof strength of cast material
    fuc characteristic value of ultimate tensile strength of cast material
    A50 elongation value measured with a constant reference length of 50 mm, see EN 10 002
    Image, elongation value measured with a reference length Image, see EN 10 002
    A0 original cross-section area of test specimen
    fo,haz 0,2 % proof strength in heat affected zone, HAZ
    fu,haz ultimate tensile strength in heat affected zone, HAZ
    ρo,haz = fo,haz / fo , ratio between 0,2 % proof strength in HAZ and in parent material
    ρu,haz = fu,haz / fu , ratio between ultimate strength in HAZ and in parent material
    BC buckling class 17
    np exponent in Ramberg-Osgood expression for plastic design
    E modulus of elasticity
    G shear modulus
    v Poissoir’s ratio in elastic stage
    α coefficient of linear thermal expansion
    ρ unit mass

    Section 5 Structural analysis

    αcr factor by which the design loads would have to be increased to cause elastic instability in a global mode
    FEd design loading on the structure
    Fcr elastic critical buckling load for global instability mode based on initial elastic stiffness
    HEd design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal loads
    VEd total design vertical load on the structure on the bottom of the storey
    δH,Ed horizontal displacement at the top of the storey, relative to the bottom of the storey
    h storey height, height of the structure
    Image non dimensional slenderness
    NEd design value of the axial force
    ϕ global initial sway imperfection
    ϕ0 basic value for global initial sway imperfection
    αh reduction factor for height h applicable to columns
    αm reduction factor for the number of columns in a row
    m number of columns in a row
    e0 maximum amplitude of a member imperfection
    L member length
    e0,d design value of maximum amplitude of an imperfection
    MRk characteristic moment resistance of the critical cross section
    NRk characteristic resistance to normal force of the critical cross section
    q equivalent force per unit length
    δq in-plane deflection of a bracing system
    qd equivalent design force per unit length
    MEd design bending moment
    k factor for eo,d

    Section 6 Ultimate limit states for members

    γM1 partial factor for resistance of cross-sections whatever the class is
    γM1 partial factor for resistance of members to instability assessed by member checks
    γM2 partial factor for resistance of cross-sections in tension to fracture
    b width of cross section part
    t thickness of a cross-section part
    β width-to-thickness ratio b/t
    η coefficient to allow for stress gradient or reinforcement of cross section part
    Ψ stress ratio
    σcr elastic critical stress for a reinforced cross section part
    σcr0 elastic critical stress for an un-reinforced cross section part
    R radius of curvature to the mid-thickness of material 18
    D diameter to mid-thickness of tube material
    β1, β2, β3 limits for slenderness parameter
    ε Image, coefficient
    z1 distance from neutral axis to most severely stressed fibre
    z2 distance from neutral axis to fibre under consideration
    C1, C2 Constants
    ρc reduction factor for local buckling
    bhaz extent of HAZ
    T1 interpass temperature
    α2 factor for bhaz

    6.2 Resistance of cross sections

    σx,Ed design value of the local longitudinal stress
    σy,Ed design value of the local transverse stress
    τEd design value of the local shear stress
    NEd design normal force
    My,Ed design bending moment, y-y axis
    Mz,Ed design bending moment, z-z axis
    NRd design values of the resistance to normal forces
    My,Rd design values of the resistance to bending moments, y-y axis
    Mz,Rd design values of the resistance to bending moments, z-z axis
    s staggered pitch, the spacing of the centres of two consecutive holes in the chain measured parallel to the member axis
    p spacing of the centres of the same two holes measured perpendicular to the member axis
    n number of holes extending in any diagonal or zig-zag line progressively across the member or part of the member
    d diameter of hole
    Ag area of gross cross-section
    Anet net area of cross-section
    Aeff effective area of cross-section
    Nt,Rd design values of the resistance to tension force
    No,Rd design value of resistance to general yielding of a member in tensions
    Nu,Rd design value of resistance to axial force of the net cross-section at holes for fasteners
    Nc,Rd design resistance to normal forces of the cross-section for uniform compression
    MRd design resistance for bending about one principal axis of a cross-section
    Mu,Rd design resistance for bending of the net cross-section at holes
    Mo,Rd design resistance for bending to general yielding
    α shape factor
    Wel elastic modulus of the gross section (see 6.2.5.2)
    Wnet elastic modulus of the net section allowing for holes and HAZ softening, if welded
    Wpl plastic modulus of gross section
    Weff effective elastic section modulus, obtained using a reduced thickness teff for the class 4 parts
    Wel,haz effective elastic modulus of the gross section, obtained using a reduced thickness ρo,hazt for the HAZ material 19
    Wpl,haz effective plastic modulus of the gross section, obtained using a reduced thickness ρo,hazt for the HAZ material
    Weff,haz effective elastic section modulus, obtained using a reduced thickness ρct for the class 4 parts or a reduced thickness ρo,hazt for the HAZ material, whichever is the smaller
    α3,u shape factor for class 3 cross section without welds
    α3,w shape factor for class 3 cross section with welds
    VEd design shear force
    VRd design shear resistance
    Av shear area
    ηv factor for shear area
    hw depth of a web between flanges
    tw web thickness
    Ae the section area of an un-welded section, and the effective section area obtained by taking a reduced thickness ρo,hazt for the HAZ material of a welded section
    TEd design value of torsional moment
    TRd design St. Venant torsion moment resistance
    WT,pl plastic torsion modulus
    Tt,Ed design value of internal St. Venant torsional moment
    Tw,Ed design value of internal warping torsional moment
    τt,Ed design shear stresses due to St. Venant torsion
    τw,Ed design shear stresses due to warping torsion
    σw,Ed design direct stresses due to the bimoment BEd
    BEd bimoment
    VT,Rd reduced design shear resistance making allowance for the presence of torsional moment
    fo,V reduced design value of strength making allowance for the presence of shear force
    Mv,Rd reduced design value of the resistance to bending moment making allowance for the presence of shear force

    6.3 Buckling resistance

    NRd resistance of axial compression force
    My,Rd bending moment resistance about y-y axis
    Mz,Rd bending moment resistance about z-z axis
    η0, γ0, ξ0, Ψ exponents in interaction formulae
    ɷ0 factor for section with localized weld
    ρ reduction factor to determine reduced design value of the resistance to bending moment making allowance of the presence of shear force
    Nb,Rd design buckling resistance of a compression member
    K factor to allow for the weakening effect of welding
    χ reduction factor for relevant buckling mode
    ϕ value to determine the reduction factory χ
    α imperfection factor
    Image limit of the horizontal plateau of the buckling curves
    Ncr elastic critical force for the relevant buckling mode based on the gross cross sectional properties
    i radius of gyration about the relevant axis, determined using the properties of the gross cross-section
    Image relative slenderness
    Image relative slenderness for torsional or torsional-flexural buckling 20
    Ncr elastic torsional-flexural buckling force
    k buckling length factor
    Mb,Rd design buckling resistance moment
    χLT reduction factor for lateral-torsional buckling
    ϕLT value to determine the reduction factor χLT
    αLT imperfection factor
    Image non dimensional slenderness for lateral torsional buckling
    Mcr elastic critical moment for lateral-torsional buckling
    Image plateau length of the lateral torsional buckling curve
    ηc, γc, ξc, Ψc exponents in interaction formulae
    ɷx, ɷx,LT factors for section with localized weld
    Image relative slenderness parameters for section with localized weld
    xs distance from section with localized weld to simple support or point of contra flexure of the deflection curve for elastic buckling from an axial force

    6.4 Uniform built-up compression members

    Lch buckling length of chord
    h0 distance of centrelines of chords of a built-up column
    a distance between restraints of chords
    α angle between axes of chord and lacings
    imin minimum radius of gyration of single angles
    Ach area of one chord of a built-up column
    Nch,Ed design chord force in the middle of a built-up member
    Image design value of the maximum moment in the middle of the built-up member
    Ieff effective second moment of area of the built-up member
    SV shear stiffness of built-up member from the lacings or battened panel
    n number of planes of lacings
    Ad area of one diagonal of a built-up column
    d length of a diagonal of a built-up column
    Av area of one post (or transverse element) of a built-up column
    Ich plane second moment of area of a chord
    Ibl plane second moment of area of a batten
    μ efficiency factor
    iy, iz radius of gyration (y-y axis and z-z axis)

    6.5 Un-stiffened plates under in-plane loading

    v1 reduction factor for shear buckling
    kτ buckling coefficient for shear buckling

    6.6 Stiffened plates under in-plane loading

    c elastic support from plate
    lw half wave-length in elastic buckling
    χ reduction factor for flexural buckling of sub-unit
    Ieff second moment of area off effective cross section of plating for in-plane bending
    yst distance from centre of plating to centre of outermost stiffener
    Bx bending stiffness of orthotropic plate in section x = constant 21
    By bending stiffness of orthotropic plate in section y = constant
    H torsional stiffness of orthotropic plate
    IL second moment of area of one stiffener and adjacent plating in the longitudinal direction
    IxT torsional constant of one stiffener and adjacent plating in the longitudinal direction
    a half distance between stiffeners
    t1, t2 thickness of layers in orthotropic plate
    s developed width of stiffeners and adjacent plate
    τcr,g shear buckling stress for orthotropic plate
    ϕ, ηh factors

    6.7 Plate girders

    bf Flange width
    hw web depth = clear distance between inside flanges
    bw depth of straight portion of a web
    tw web thickness
    tf flange thickness
    Ist second moment of area of gross cross-section of stiffener and adjacent effective parts of the web plate
    b1, b2 distances from stiffener to inside flanges (welds)
    ac half wave length for elastic buckling of stiffener
    ρv factor for shear buckling resistance
    η factor for shear buckling resistance in plastic range
    λw slenderness parameter for shear buckling
    Vw,Rd shear resistance contribution from the web
    Vf,Rd shear resistance contribution from the flanges
    kτ,st contribution from the longitudinal stiffeners to the buckling coefficient kτ
    kτ1 buckling coefficient for subpanel
    c factor in expression for Vf,Rd
    Mf,Rd design moment resistance of a cross section considering the flanges only
    Af1, Af2 cross section area of top and bottom flange
    FEd design transverse force
    FRd design resistance to transverse force
    Leff effective length for resistance to transverse force
    ly effective loaded length for resistance to transverse force
    χF reduction factor for local buckling due to transverse force
    ss length stiff bearing under transverse force
    λF slenderness parameter for local buckling due to transverse force
    kF buckling factor for transverse force
    γs relative second moment of area of the stiffener closest to the loaded flange
    Is1 second moment of area of the stiffener closest to the loaded flange
    m1, m2 parameters in formulae for effective loaded length
    le parameter in formulae for effective loaded length
    MN,Rd reduced moment resistance due to presence of axial force
    Aw cross section area of web
    Afc cross-section area of compression flange
    k factor for flange induced buckling 22
    r radius of curvature
    hf distance between centres of flanges

    6.8 members with corrugated webs

    b1, b2 flange widths
    t1, t2 flange thicknesses
    ρz reduction factor due to transverse moments in the flanges
    Mz transverse bending moment in the flanges
    ρc,g reduction factor for global buckling
    λc,g slenderness parameter for global buckling
    τcr,g shear buckling stress for global buckling
    ρc,1 reduction factor for local buckling
    λc,1 slenderness parameter for local buckling
    τcr,1 shear buckling stress for local buckling
    a0, a1, a2, a3, amax widths of corrugations

    Section 7 Serviceability limit state

    Iser effective section moment of area for serviceability limit state
    Ieff section moment of area for the effective cross-section at the ultimate limit state
    σgr maximum compressive bending stress at the serviceability limit state based on the gross cross section

    Section 8 Design of connections

    γM3γM7 partial safety factors
    γMw partial safety factor for resistance of welded connection
    γMp partial safety factor for resistance of pin connection
    γMa partial safety factor for resistance of adhesive bonded connection
    γMser partial safety factor for serviceability limit state
    Image Text deleted Image
    e1e4, edge distances
    p, p1, p2 spacing between bolt holes
    d diameter of fastener
    d0 hole diameter
    Veff,1,Rd design block tearing resistance for concentric loading
    Veff,2,Rd design block tearing resistance for eccentric loading
    Ant net area subject to tension
    Anv net area subject to shear
    A1 area of part of angle outside the bolt hole
    β2, β3 reduction factors for connections in angles 23
    Fv,Ed design shear force per bolt for the ultimate limit state
    Fv,Ed,ser design shear force per bolt for the serviceability limit state
    Fv,Rd design shear resistance per bolt
    Fb,Rd design bearing resistance per bolt
    Fs,Rd,ser design slip resistance per bolt at the serviceability limit state
    Fs,Rd design slip resistance per bolt at the ultimate limit state
    Ft,Ed design tensile force per bolt for the ultimate limit state
    Ft,Rd design tension resistance per bolt
    Nnet,Rd design resistance of section at bolt holes
    Bt,Rd design tension resistance of a bolt-plate assembly
    fub characteristic ultimate strength of bolt material
    fur characteristic ultimate strength of rivet material
    A0 cross section area of the hole
    A gross cross section of a bolt
    As tensile stress area of a bolt
    k2 factor for tension resistance of a bolt
    dm mean of the across points and across flats dimensions of the bolt head or the nut or if washers are used the outer diameter of the washer, whichever is smaller;
    tp thickness of the plate under the bolt head or the nut;
    Fp,C preloading force
    μ slip factor
    n number of friction interfaces
    βLf reduction factor for long joint
    Lj distance between the centres of the end fasteners in a long joint
    βp reduction factor for fasteners passing through packings
    a, b plate thickness in a pin connection
    c gap between plates in a pin connection
    fw characteristic strength of weld metal
    σ normal stress perpendicular to weld axis
    σ normal stress parallel to weld axis
    τ, τ shear stress parallel to weld axis
    τ shear stress perpendicular to weld axis
    γMw partial safety factor for welded joints
    Lw total length of longitudinal fillet weld
    Lw,eff effective length of longitudinal fillet weld
    a effective throat thickness
    σhaz design normal stress in HAZ, perpendicular to the weld axis
    τhaz design shear stress in HAZ
    fv,haz characteristic shear strength in HAZ

    Annex A Execution classes

    U utilization grade

    Annex B Equivalent T-stub in tension

    Fu,Rd tension resistance of a T-stub flange
    Bu tension resistance of a bolt-plate assembly
    B0 conventional bolt strength at elastic limit 24
    As stress area of bolt
    Ieff effective length
    emin minimum edge distance
    m distance from weld toe to centre of bolt

    Annex C Materials selection

    σeq,Ed equivalent design stress for castings
    σx,Ed design stress in x-axis direction for castings
    σy,Ed design stress in y-axis direction for castings
    τxy,Ed design shear stress for castings
    σRd design resistance for castings
    γMo,c , γMu,c partial factors for yields strength and ultimate strength castings respectively
    γM2,co , γM2,cu partial factors for yields strength and ultimate strength for bearing resistance of bolts, rivets in castings
    γMp,co , γMp,cu partial factors for yields strength and ultimate strength for bearing resistance of pins in castings

    Annex E Analytical model for stress-strain relationship

    The symbols are defined in the Annex

    Annex F Behavior of cross-sections beyond elastic limit

    α0 geometrical shape factor
    α5 , α10 generalized shape factors corresponding to ultimate curvature values χu = 5χe1 and χu = 10χe1
    αM ,red correction factor for welded class 1 cross section

    Annex G Rotation capacity

    χu ultimate bending curvature
    χe1 elastic bending curvature (= χ0.2)
    ξ ductility factor
    Mo elastic bending moment corresponding to the attainment of the proof stress fo
    m, k numerical parameters
    R rotation capacity
    θp, θel and θu, plastic rotation, elastic rotation and maximum plastic rotation corresponding to ultimate curvature χu

    Annex H Plastic hinge method for continuous beams

    η parameter depending on geometrical shape factor and conventional available ductility of the material
    αξ shape factor α5 or α10
    a, b, c coefficients in expression for η

    Annex I Lateral torsional buckling of beams and torsional or flexural-torsional buckling of compression members

    It torsion constant
    Iw warping constant
    Iz second moment of area of minor axis
    kz end condition corresponding to restraints against lateral movement
    kw end condition corresponding to rotation about the longitudinal axis
    ky end condition corresponding to restraints against movement in plane of loading 25
    Kwt non-dimensional torsion parameter
    ϛg relative non-dimensional coordinate of the point of load application
    ϛj relative non-dimensional cross section mono-symmetry parameter
    μcr relative non-dimensional critical moment
    za coordinate of the point of load application related to centroid
    zs coordinate of the shear centre related to centroid
    zg coordinate of the point of load application related to shear centre
    zj mono-symmetry constant
    c depth of a lip
    ψf mono-symmetry factor
    hf distance between centrelines of flanges
    hs distance between shear centre of upper flange and shear centre of bottom flange
    Ifc second moment of area of the compression flange about the minor axis of the section
    Ift second moment of area of the tension flange about the minor axis of the section
    C1, C2, C3, C1,1, C12 coefficients in formulae for relative non-dimensional critical moment
    Ncr,y, Ncr,z , Ncr,T elastic flexural buckling load (y-y and z-z axes) and torsional buckling load
    is polar radius of gyration
    αyw, αzw coefficients in equation for torsional and torsional-flexural buckling
    k, λt coefficients in formula for relative slenderness parameter Image
    λ0, s, X coefficients to calculate λt

    Annex J Properties of cross sections

    β, δ, γ fillet or bulb factors
    bsh width of flat cross section parts
    α fillet or bulb factor; angle between flat section parts adjacent to fillets or bulbs
    D diameter of circle inscribed in fillet or bulb

    NOTE Notations for cross section constants given in J.4 and are not repeated here

    Annex K Shear lag effects in member design

    beff effective width for shear lag
    βS effective width factor for shear lag
    K notional width-to-length ratio for flange
    Ast area of all longitudinal stiffeners within half the flange width
    ast,1 relative area of stiffeners = area of stiffeners divided by centre to centre distance of stiffeners
    se loaded length in section between flange and web
    Image b0 width of outstand or half width of internal cross-section part
    Le points of zero bending moment Image

    Annex L Classification of joints

    F load, generalized force force
    Fu ultimate load, ultimate generalized force
    v generalized deformation
    vu deformation corresponding to ultimate generalized force

    Annex M Adhesive bonded connection

    fv,adh characteristic shear strength values of adhesives
    τ average shear stress in the adhesive layer
    γMa material factor for adhesive bonded joint
26

1.7 Conventions for member axes

  1. In general the convention for member axes is:
    x-x - along the member
    y-y - axis of the cross-section
    z-z - axis of the cross-section
  2. For aluminium members, the conventions used for cross-section axes are:
  3. The symbols used for dimensions and axes of aluminium sections are indicated in Figure 1.1.
  4. The convention used for subscripts, which indicate axes for moments is: “Use the axis about which the moment acts.”

    NOTE All rules in this Eurocode relate to principal axis properties, which are generally defined by the axes y-y and z-z for symmetrical sections and by the u-u and v-v axis for unsymmetrical section such as angles.

1.8 Specification for execution of the work

  1. A specification for execution of the work should be prepared that contains all necessary technical information to carry out the work. This information should include execution class(es), whether any non-normative tolerances in Image EN 1090-3 should apply, complete geometrical information and of materials to be used in members and joints, types and sizes of fasteners, weld requirements and requirements for execution of work. EN 1090-3 Image contains a checklist for information to be provided. 27

    Figure 1.1 - Definition of axes for various cross-sections

    Figure 1.1 - Definition of axes for various cross-sections

    28

2 Basis of design

2.1 Requirements

2.1.1 Basic requirements

  1. P The design of aluminium structures shall be in accordance with the general rules given in EN 1990.
  2. P The supplementary provisions for aluminium structures given in this section shall also be applied.
  3. P The basic requirements of EN 1990 section 2 shall be deemed to be satisfied where limit state design is used in conjunction with the partial factor method and the load combinations given in EN 1990 together with the actions given in EN 1991.
  4. The rules for resistances, serviceability and durability given in the various parts of EN 1999 should be applied.

2.1.2 Reliability management

  1. Where different levels of reliability are required, these levels should be achieved by an appropriate choice of quality management in design and execution, according to EN 1990, Image EN 1090-3 Image.
  2. Aluminium structures and components are classified in execution classes, see Annex A of this standard.
  3. The execution should be carried out in accordance with prEN 1090-1 and Image EN 1090-3. The information, which EN 1090-3 Image requires to be included in the execution specification, should be provided.

    NOTE Options allowed by prEN 1090 may be specified in a National Annex to EN 1999-1-1 to suit the reliability level required.

2.1.3 Design working life, durability and robustness

  1. Depending on the type of action affecting durability and the design working life (see EN 1990) aluminium structures should as applicable be

    NOTE 1 Recommendarions for the design for corrosion are given in Annex C and Annex D

    NOTE 2 Requirements for fatigue, see EN 1999-1-3

2.2 Principles of limit state design

  1. The resistances of cross sections and members specified in this EN 1999-1-1 for the ultimate limit states as defined in EN 1990 are based on simplified design models of recognised experimental evidence.
  2. The resistances specified in this EN 1999-1-1 may therefore be used where the conditions for materials in section 3 are met.
29

2.3 Basic variables

2.3.1 Actions and environmental influences

  1. Actions for the design of aluminium structures should be taken from EN 1991. For the combination of actions and partial factors of actions see Annex A to EN 1990

    NOTE The National Annex may define actions for particular regional or climatic or accidental situations.

  2. The actions to be considered in the erection stage should be obtained from EN 1991-1-6.
  3. Where the effects of predicted absolute and differential settlements need be considered best estimates of imposed deformations should be used.
  4. The effects of uneven settlements or imposed deformations or other forms of prestressing imposed during erection should be taken into account by their nominal value Pk as permanent action and grouped with other permanent actions Gk to a single action (Gk + Pk).
  5. Fatigue loading not defined in EN 1991 should be determined according to EN 1999-1-3.

2.3.2 Material and product properties

  1. Material properties for aluminium and other construction products and the geometrical data to be used for design should be those specified in the relevant ENs, ETAGs or ETAs unless otherwise indicated in this standard.

2.4 Verification by the partial factor method

2.4.1 Design value of material properties

  1. P For the design of aluminium structures characteristic value X k or nominal values X n of material property shall be used as indicated in this Eurocode.

2.4.2 Design value of geometrical data

  1. Geometrical data for cross sections and systems may be taken from product standards or drawings for the execution according to Image EN 1090-3 Image and treated as nominal values.
  2. Design values of geometrical imperfections specified in this standard comprise

2.4.3 Design resistances

  1. For aluminium structures equation (6.6c) or equation (6.6d) of EN 1990 applies:

    Image

    where:

    Rk is the characteristic value of resistance of a cross section or member determined with characteristic or nominal values for the material properties and cross sectional dimensions
    γM is the global partial factor for the particular resistance

    NOTE For the definition of η1 , ηi , X k1 , X ki ad see EN 1990.

30

2.4.4 Verification of static equilibrium (EQU)

  1. The reliability format for the verification of static equilibrium in Table 1.2 (A) in Annex A of EN 1990 also applies to design situations equivalent to (EQU), e.g. for the design of holding down anchors or the verification of up lift of bearings of continuous beams.

2.5 Design assisted by testing

  1. The resistances RK in this standard have been determined using Annex D of EN 1990.
  2. In recommending classes of constant partial factors γMi the characteristic values Rk were obtained from

    Rk = Rd · γMi     (2.2)

    where:

    Rd are design values according to Annex D of EN 1990
    γMi are recommended partial factors.

    NOTE 1 The numerical values of the recommended partial factors γMi have been determined such that Rk represents approximately the 5 %-fractile for an infinite number of tests.

    NOTE 2 For characteristic values of fatigue strength and partial factors γMf for fatigue see EN 1999-1-3.

  3. Where resistances Rk for prefabricated products are determined by tests, the procedure referred in (2) should be followed.
31

3 Materials

3.1 General

  1. The material properties given in this section are specified as characteristic values. They are based on the minimum values given in the relevant product standard.
  2. Other material properties arc given in the ENs listed in 1.2.1.

3.2 Structural aluminium

3.2.1 Range of materials

  1. This European standard covers the design of structures fabricated from aluminium alloy material listed in Table 3. la for wrought alloys conforming to the ENs listed in 1.2.3.1. For the design of structures of cast aluminium alloys given in Table 3.1 b, see 3.2.3.1.

    NOTE Annex C gives further information for the design of structures of cast aluminium alloys.

    Table 3.1a - Wrought aluminium alloys for structures
    Alloy designation Form of product Durability rating 3)
    Numerical Chemical symbols
    EN AW-3004 EN AW-AlMn 1Mg 1 SH, ST, PL A
    EN AW-3005 EN AW-AlMn 1Mg0,5 SH, ST, PL A
    EN AW-3103 EN AW-Al Mn 1 SH, ST, PL, ET, EP, ER/B A
    EN AW-5005 / 5005A EN AW-AlMg1(B) / (C) SH, ST, PL A
    EN AW-5049 EN AW-AlMg2Mn0,8 SH, ST, PL A
    EN AW-5052 EN AW-Al Mg2,5 SH, ST, PL, ET2), EP2), ER/B, DT A
    EN AW-5083 EN AW-Al Mg4,5Mn0,7 SH, ST, PL, ET2), EP2), ER/B, DT, FO A1)
    EN AW-5454 EN AW-Al Mg3Mn SH, ST, PL, ET2), EP2), ER/B A
    EN AW-5754 EN AW-Al Mg3 SH, ST, PL, ET2), EP2), ER/B, DT, FO A
    EN AW-6060 EN AW-Al MgSi ET,EP,ER/B,DT B
    EN AW-6061 EN AW-Al MglSiCu SH, ST,PL,ET,EP,ER/B,DT B
    EN AW-6063 EN AW-Al Mg0,7Si ET, EP, ER/B,DT B
    EN AW-6005A EN AW-Al SiMg(A) ET, EP, ER/B B
    EN AW-6082 EN AW-Al SilMgMn SH, ST, PL, ET, EP, ER/B, DT, FO B
    EN AW-6106 EN AW-AlMgSiMn EP B
    EN AW-7020 EN AW-Al Zn4,5Mg1 SH, ST, PL, ET, EP, ER/B, DT C
    EN AW-8011A EN AW-AlFeSi SH, ST, PL B
    Key:
         SH - Sheet (EN 485)
         ST - Strip (EN 485)
         PL - Plate (EN 485)
         ET - Extruded Tube (EN 755)
         EP - Extruded Profiles (EN 755)
         ER/B - Extruded Rod and Bar (EN 755)
         DT - Drawn Tube (EN 754)
         FO - Forgings (EN 586)
         1) See Annex C: C2.2.2(2)
         2) Only simple, solid (open) extruded sections or thick-walled tubes over a mandrel (seamless)
         3) See 4, Annex C and Annex D
    32
    Table 3.1b - Cast aluminium alloys for structures
    Alloy designation Durability rating1)
    Numerical Chemical symbols
    EN AC-42100 EN AC-Al Si7Mg0,3 B
    EN AC-42200 EN AC-Al Si7Mg0,6 B
    EN AC-43000 EN AC-Al Si10Mg(a) B
    EN AC-43300 EN AC-AlSi9Mg B
    EN AC-44200 EN AC-Al Si 12(a) B
    EN AC-51300 EN AC-Al Mg5 A
    1) see 4, Annex C and Annex D

    NOTE 1 For other aluminium alloys and temper than those listed, see the National Annex.

    NOTE 2 For advice on the selection of aluminium alloys see Annex C.

3.2.2 Material properties for wrought aluminium alloys

  1. Characteristic values of the 0,2% proof strength fo and the ultimate tensile strength fu for wrought aluminium alloys for a range of tempers and thicknesses are given in Table 3.2a for sheet, strip and plate products; Table 3.2b for extruded rod/bar, extruded tube and extruded profiles and drawn tube and Table 3.2c for forgings. The values in Table 3.2a, b and c, as well as in Table 3.3 and Table 3.4 (for aluminium fasteners only) are applicable for structures subject to service temperatures up to 80°C.

    NOTE Product properties for electrically welded tubes according to EN 1592-1 to 4 for structural applications are not given in this standard. The National Annex may give rules for their application. Buckling class B is recommended.

  2. For service temperatures between 80°C and 100°C reduction of the strength should be taken in account.

    NOTE 1 The National Annex may give rules for the reduction of the characteristic values to be applied. For temperatures between 80°C and 100°C the following procedure is recommended:

    All characteristic aluminium resistance values (fo, fu, fo,haz and fu,haz) may be reduced according to

    XkT = [1 - k100(T - 80) / 20] Xk     (3.1)

    where:

    Xk is the characteristic value of a strength property of a material
    XkT is the characteristic strength value for the material at temperature T between 80°C and 100 °C
    T is the highest temperature the structure is operating
    k100 = 0,1 for strain hardening alloys (3xxx-alloys, 5xxx-alloys and EN AW 8011 A)
    k100 = 0,2 for precipitation hardening material (6xxx-alloys and EN AW-7020)

    At 100°C generally Buckling Class B is applicable for all aluminium alloys. For temperatures between 80°C and 100°C interpolation between Class A and Class B should be done.

    NOTE 2 Between 80°C and 100°C the reduction of the strength values is recoverable, e.g. the materials regain its strength when the temperature is dropping down. For temperatures over 100°C also a reduction of the elastic modulus and additionally time depending, not recoverable reductions of strength should be considered.

  3. Characteristic values for the heat affected zone (0,2% proof strength fo,haz and ultimate tensile strength fu,haz) are also given in Table 3.2a to 3.2c and also reduction factors (see 6.1.6), buckling class (used in 6.1.4 and 6.3.1) and exponent in Ramberg-Osgood expression for plastic resistance. 33
    Table 3.2a - Characteristic values of 0,2% proof strength fo, ultimate tensile strength fu (unwelded and for HAZ), min elongation A, reduction factors ρo,haz and ρu,haz in HAZ, buckling class and exponent np for wrought aluminium alloys - Sheet, strip and plate
    Alloy EN-AW Temper 1) Thickness mm 1) fo 1) fu A50 1) 6)

    %
    fo,haz 2) fu,haz 2) HAZ-factor2) BC
    4)
    np
    1),5)
    N/mm2 N/mm2 ρo,haz1) ρu,haz
    3004 H14 | H24/H34 ≤6 | 3 180 | 170 220 1 | 3 75 155 0,42 | 0,44 0,70 B 23 | 18
    H16 | H26/H36 ≤ 4 | 3 200 | 190 240 1 | 3 0,38 | 0,39 0,65 B 25 | 20
    3005 H14 | H24 ≤6 | 3 150 | 130 170 1 | 4 56 115 0,37 | 0,43 0,68 B 38 | 18
    H16 | H26 ≤4 | 3 175 | 160 195 1 | 3 0,32 | 0,35 0,59 B 43 | 24
    3103 H14 | H24 ≤ 25 | 12,5 120 | 110 140 2 | 4 44 90 0,37 | 0,40 0,64 B 31 | 20
    H16 | H26 ≤4 145 | 135 160 1 | 2 0,30 | 0,33 0,56 B 48 | 28
    5005/5005A O/H111 ≤ 50 35 100 15 35 100 1 1 B 5
    H12 | H22/H32 ≤ 12,5 95 | 80 125 2 | 4 44 100 0,46 | 0,55 0,80 B 18 | 11
    H14 | H24/H34 ≤ 12,5 120 | 110 145 2 | 3 0,37 | 0,40 0,69 B 25 | 17
    5052 H12 | H22/H32 ≤ 40 160 | 130 210 4 | 5 80 170 0,50 | 0,62 0,81 B 17 | 10
    H14 | H24/H34 ≤ 25 180 | 150 230 3 | 4 0,44 | 0,53 0,74 B 19 | 11
    5049 O/H111 ≤ 100 80 190 12 80 190 1 1 B 6
    H14 | H24/H34 ≤ 25 190 | 160 240 3 | 6 100 190 0,53 | 0,63 0,79 B 20 | 12
    5454 O / H111 ≤ 80 85 215 12 85 215 1 1 B 5
    H14 | H24/H34 ≤ 25 220 | 200 270 2 | 4 105 215 0,48 | 0,53 0,80 B 22 | 15
    5754 0/H111 ≤ 100 80 190 12 80 190 1 1 B 6
    H14 | H24/H34 ≤ 25 190 | 160 240 3 | 6 100 190 0,53 | 0,63 0,79 B 20 | 12
    5083 0/H111 ≤ 50 125 275 11 125 275 1 1 B 6
    50<t≤80 115 270 14 3) 115 270 B
    H12 | H22/H32 ≤ 40 250 | 215 305 3 | 5 155 275 0,62 | 0,72 0,90 B 22 | 14
    H14 | H24/H34 ≤ 25 280 | 250 340 2 | 4 0,55 | 0,62 0,81 A 22 | 14
    6061 T4 / T451 ≤ 12,5 110 205 12 95 150 0,86 0,73 B 8
    T6 / T651 ≤ 12,5 240 290 6 115 175 0,48 0,60 A 23
    T651 12,5<t≤80 240 290 6 3)
    6082 T4 / T451 ≤ 12,5 110 205 12 100 160 0,91 0,78 B 8
    T61/T6151 ≤12,5 205 280 10 125 185 0,61 0,66 A 15
    T6151 12,5<t≤100 200 275 12 3) 0,63 0,67 A 14
    T6/T651 ≤ 6 260 310 6 0,48 0,60 A 25
    6<t≤12,5 255 300 9 0,49 0,62 A 27
    T651 12,5<t≤100 240 295 7 3) 0,52 0,63 A 21
    7020 T6 ≤ 12,5 280 350 7 205 280 0,73 0,80 A 19
    T651 ≤ 40 9 3)
    8011A H14 | H24 ≤ 12,5 110 | 100 125 2 | 3 37 85 0,34 | 0,37 0,68 B 37 | 22
    H16 | H26 ≤ 4 130 | 120 145 1 | 2 0,28 | 0,31 0,59 33 | 33

    1) If two (three) tempers are specified in one line, tempers separated by “|” have different technological values but separated by “/” have same values. (The tempers show differences for fo , A and np.).
    2) The HAZ-values are valid for MIG welding and thickness up to 15mm. For TIG welding strain hardening alloys (3xxx, 5xxx and 8011 A) up to 6 mm the same values apply, but for TIG welding precipitation hardening alloys (6xxx and 7xxx) and thickness up to 6 mm the HAZ values have to be multiplied by a factor 0,8 and so the ρ-factors. For higher thickness - unless other data are available - the HAZ values and ρ-factors have to be further reduced by a factor 0,8 for the precipitation hardening alloys (6xxx and 7xxx) and by a factor 0,9 for the strain hardening alloys (3xxx, 5xxx and 8011A). These reductions do not apply in temper O.
    3) Based on Image, not A50.
    4) BC = buckling class, see 6.1.4.4, 6.1.5 and 6.3.1.
    5) n-value in Ramberg-Osgood expression for plastic analysis. It applies only in connection with the listed fo-value.
    6) The minimum elongation values indicated do not apply across the whole range of thickness given, but mostly to the thinner materials. In detail see EN 485-2.

    34
    Table 3.2b - Characteristic values of 0,2% proof strength fo and ultimate tensile strength fu (unwelded and for HAZ), min elongation A, reduction factors ρo,haz and ρu,haz in HAZ, buckling class and exponent np for wrought aluminium alloys - Extruded profiles, extruded tube, extruded rod/bar and drawn tube
    Image Alloy EN-AW Product form Temper Thickness t mm 1) 3) fo 1) fu 1) A 5) 2) fo,haz 4) fu,haz 4) HAZ-factor4) BC
    6)
    np
    7)
    N/mm2 % N/mm2 ρo,haz ρu,haz
    5083 ET, EP,ER/B O/H111, F, H112 t ≤ 200 110 270 12 110 270 1 1 B 5
    DT H12/22/32 t ≤ 10 200 280 6 135 270 0,68 0,96 B 14
    H14/24/34 t ≤ 5 235 300 4 0,57 0,90 A 18
    5454 ET, EP,ER/B O/H111 F/H 112 t25 85 200 16 85 200 1 1 B 5
    5754 ET, EP,ER/B O/H 111 F/H 112 t25 80 180 14 80 180 1 1 B 6
    DT H14/ H24/H34 t ≤ 10 180 240 4 100 180 0,56 0,75 B 16
    6060 EP,ET,ER/B T5 t5 120 160 8 50 80 0,42 0,50 B 17
    EP 5 < t ≤ 25 100 140 8 0,50 0,57 B 14
    ET,EP,ER/B T6 t15 140 170 8 60 100 0,43 0,59 A 24
    DT t ≤ 20 160 215 12 0,38 0,47 A 16
    EP,ET,ER/B T64 t15 120 180 12 60 100 0,50 0,56 A 12
    EP,ET,ER/B T66 t3 160 215 8 65 110 0,41 0,51 A 16
    EP 3 < t ≤ 25 150 195 8 0,43 0,56 A 18
    6061 EP,ET,ER/B T4 t25 110 180 15 95 150 0,86 0,83 B 8
    DT t20 110 205 16 0,73 B 8
    EP,ET,ER/B T6 t25 240 260 8 115 175 0,48 0,67 A 55
    DT t20 240 290 10 0,60 A 23
    6063 EP,ET,ER/B T5 t3 130 175 8 60 100 0,46 0,57 B 16
    EP 3 < t ≤ 25 110 160 7 0,55 0,63 B 13
    EP,ET,ER/B T6 t25 160 195 8 65 110 0,41 0,56 A 24
    DT t ≤ 20 190 220 10 0,34 0,50 A 31
    EP,ET,ER/B T66 t10 200 245 8 75 130 0,38 0,53 A 22
    EP 10 < t ≤ 25 180 225 8 0,42 0,58 A 21
    DT t ≤ 20 195 230 10 0,38 0,57 A 28
    6005A EP/O, ER/B T6 t5 225 270 8 115 165 0,51 0,61 A 25
    5 < t ≤ 10 215 260 8 0,53 0,63 A 24
    10 < t ≤ 25 200 250 8 0,58 0,66 A 20
    EP/H, ET T6 t ≤ 5 215 255 8 0,53 0,65 A 26
    5 < t10 200 250 8 0,58 0,66 A 20
    6106 EP T6 t ≤ 10 200 250 8 95 160 0,48 0,64 A 20 Image 35
    6082 EP, ET, ER/B T4 t25 110 205 14 100 160 0,91 0,78 B 8
    Image EP T5 t ≤ 5 230 270 8 125 185 0,54 0,69 B 28
    EP Image
    ET
    T6 t ≤ 5 250 290 8 125 185 0,50 0,64 A 32
    5 < t15 260 310 10 0,48 0,60 A 25
    ER/B T6 t ≤ 20 250 295 8 0,50 0,63 A 27
    20 < t ≤ 150 260 310 8 0,48 0,60 A 25
    DT T6 t ≤ 5 255 310 8 0,49 0,60 A 22
    5 < t ≤ 20 240 310 10 0,52 0,60 A 17
    7020 EP,ET,ER/B T6 t15 290 350 10 205 280 0,71 0,80 A 23
    EP,ET,ER/B T6 15 < t < 40 275 350 10 0,75 0,80 A 19
    DT T6 t ≤ 20 280 350 10 0,73 0,80 A 18
    Key: EP - Extruded profiles
    EP/H - Extruded hollow profiles
    ER/B - Extruded rod and bar
    EP/O - Extruded open profiles
    ET - Extruded tube
    DT - Drawn tube

    1): Where values are quoted in bold greater thicknesses and/or higher mechanical properties may be permitted in some forms see ENs and prENs listed in 1.2.1.3. In this case the Rp0,2 and Rm values can be taken as fo and fu. If using such higher values the corresponding HAZ-factors ρ have to be calculated acc. to expression (6.13) and (6.14) with the same values for fo,haz and fu,haz.
    2): Where minimum elongation values are given in bold, higher minimum values may be given for some forms or thicknesses.
    3): According to Image EN 755-2:2008 Image: following rule applies: “if a profile cross-section is comprised of different thicknesses which fall in more than one set of specified mechanically property values, the lowest specified value should be considered as valid for the whole profile cross-section.” Exception is possible and the highest value given may be used provided the manufacturer can support the value by an appropriate quality assurance certificate.
    4) The HAZ-values are valid for MIG welding and thickness up to 15mm. For TIG welding strain hardening alloys Image (3xxx and 5xxx) Image up to 6 mm the same values apply, but for TIG welding precipitation hardening alloys (6xxx and 7xxx) and thickness up to 6 mm the HAZ values have to be multiplied by a factor 0,8 and so the ρ-factors. For higher thickness - unless other data are available - the HAZ values and ρ-factors have to be further reduced by a factor 0,8 for the precipitation hardening alloys (6xxx and 7xxx) alloys and by a factor 0,9 for strain hardening alloys (3xxx, 5xxx and 8011A). These reductions do not apply in temper O.
    5) Image
    6) BC = buckling class, see 6.1.4.4, 6.1.5 and 6.3.1.
    7) n-value in Ramberg-Osgood expression for plastic analysis. It applies only in connection with the listed fo-value (= minimum standardized value).
    Image Text deleted Image
    Table 3.2c - Characteristic values of 0,2% proof strength fo, ultimate tensile strength fu (unwelded and for HAZ), minimum elongation A and buckling class for wrought aluminium alloys - Forgings
    Alloy EN-AW Temper Thickness up to mm Direction fo fu fo,haz 1) fu,haz 1) A 3)
    %
    Buckling class
    N/mm2
    5754 H112 150 Longitudinal (L) 80 180 80 180 15 B
    5083 H112 150 Longitudinal (L) 120 270 120 270 12 B
    Transverse (T) 110 260 110 260 10 B
    6082 T6 100 Longitudinal (L) 260 310 125 2) 185 2) 6 A
    Transverse (T) 250 290 5 A
    1) ρo,haz; ρu,haz to be calculated according to expression (6.13) and (6.14)
    2) For thicknesses over 15 mm (MIG-welding) or 6 mm (TIG-welding) see table 3.2.b footnote 4).
    3) Image
    36

3.2.3 Material properties for cast aluminium alloys

3.2.3.1 General
  1. EN 1999-1-1 is not generally applicable to castings.

    NOTE 1 The design rules in this European standard are applicable for gravity cast products according to Table 3.3 if the additional and special rules and the quality provisions of Annex C. C.3.4 are followed.

    NOTE 2 The National Annex may give rules for quality requirements for castings.

3.2.3.2 Characteristic values
  1. Image The characteristic values of the 0,2% proof strength fo and the ultimate tensile strength fu for sand and permanent mould cast aluminium to be met by the caster or the foundry in each location of a cast piece are given in Table 3.3. The listed values are 70% of the values of EN 1706:1998, which are only valid for separately cast test specimens (see 6.3.3.2 of EN 1706:1998).

    NOTE The listed values for A50 in Table 3.3 are 50 % of the elongation values of EN 1706:1998. which are only valid for separately cast test specimens (see 6.3.3.2 of EN 1706:1998) Image

    Table 3.3 - Characteristic values of 0,2% proof strength fo and ultimate tensile strength fu for cast aluminium alloys – Gravity casting
    Alloy Casting process Temper fo (foc)
    N/mm2
    fu (fuc)
    N/mm2
    A50 1)
    %
    EN AC-42100 Permanent mould T6 147 203 2,0
    Permanent mould T64 126 175 4
    EN AC-42200 Permanent mould T6 168 224 1,5
    Permanent mould T64 147 203 3
    EN AC-43000 Permanent mould F 63 126 1,25
    EN AC-43300 Permanent mould T6 147 203 2,0
    Sand cast T6 133 161 1,0
    Permanent mould T64 126 175 3
    EN AC-44200 Permanent mould F 56 119 3
    Sand cast F 49 105 2,5
    EN AC-51300 Permanent mould F 70 126 2,0
    Sand cast F 63 112 1,5
    1) For elongation requirements for the design of cast components, see C.3.4.2(1).

3.2.4 Dimensions, mass and tolerances

  1. The dimensions and tolerances of structural extruded products, sheet and plate products, drawn tube, wire and forgings, should conform with the ENs and prENs listed in 1.2.3.3.
  2. The dimensions and tolerances of structural cast products should conform with the ENs and prENs listed in 1.2.3.4.

3.2.5 Design values of material constants

  1. The material constants to be adopted in calculations for the aluminium alloys covered by this European Standard should be taken as follows:
    - modulus of elasticity E = 70 000 N/mm2;
    - shear modulus G = 27 000 N/mm2;
    - Poisson’s ratio v = 0,3;
    - coefficient of linear thermal expansion α = 23 × 10-6 per °C;
    - unit mass ρ = 2 700 kg/m3.
  2. For material properties in structures subject to elevated temperatures associated with fire see EN 1999-1-2.
37

3.3 Connecting devices

3.3.1 General

  1. Connecting devices should be suitable for their specific use.
  2. Suitable connecting devices include bolts, friction grip fasteners, solid rivets, special fasteners, welds and adhesives.

    NOTE For adhesives, see Annex M

3.3.2 Bolts, nuts and washers

3.3.2.1 General
  1. Bolts, nuts and washers should conform with existing ENs, prENs and ISO Standards. For load bearing joints bolts and rivets according to Table 3.4 should be used.
  2. The minimum values of the 0,2% proof strength fo and the ultimate strength fu to be adopted as characteristic values in calculations, are given in Table 3.4.
  3. Aluminium bolts and rivets should be used only for connections of category A (bearing type, see Table 8.4).

    NOTE 1 Presently no EN-standard, which covers all requirements for aluminium bolts, exists. The National Annex may give provisions for the use of aluminium bolts. Recommendations for the use of the bolts listed in Table 3.4 are given in Annex C.

    NOTE 2 Presently no EN-standard, which covers all requirements for solid aluminium rivets, exists. Recommendations for the use of the solid rivets listed in Table 3.4 are given in Annex C.

  4. Selftapping and selfdrilling screws and blind rivets may be used for thin-walled structures. Rules are given in EN 1999-1-4. 38
    Table 3.4 - Minimum values of 0,2 % proof strength fo and ultimate strength fu for bolts and solid rivets
    Material Type of fastener Alloy Numerical designation: EN AW-. Alloy Chemical designation: EN AW- Temper or grade Diameter fo 7)
    N/mm2
    fu 7)
    N/mm2
    Aluminium alloy Solid Rivets 1) 5019 AlMg5 H111 ≤20 110 250
    H14,H34 ≤18 210 300
    5754 AlMg3 H111 ≤20 80 180
    H14/H34 ≤18 180 240
    6082 AlSi1MgMn T4 ≤20 110 205
    T6 ≤20 240 300
    Bolts 2) 5754 AlMg3 4) ≤10 230 270
    (AL1) 3) 10<d≤20 180 250
    5019 AlMg5 4) ≤14 205 310
    (AL2) 3) 14<d≤36 200 280
    6082 AlSi1MgMn 4) ≤6 250 320
    (AL3) 3) 14<d≤36 260 310
    Steel Bolts 5)     4.6 ≤39 240 400
    5.6 ≤39 300 500
    6.8 ≤39 480 600
    8.8 ≤39 640 800
    10.9 ≤39 900 1000
    Stainless Steel Bolts 6) A2, A4   50 ≤39 210 500
    A2, A4   70 ≤39 450 700
    A2, A4   80 ≤39 600 800
    1) see 3.3.2.1 (3) Image text deleted Image
    2) see 3.3.2.1 (3) Image text deleted Image
    3) Material designation according to EN 28839
    4) No grade designation in EN 28839
    5) Grade according to EN ISO 898-1
    6) Designation and grade according to EN ISO 3506-1
    7) The given values for solid rivets are the lesser values of EN 754 (drawn rods) or EN 1301 (drawn wire) of which solid rivets are manufactured by cold forming. For the 0,2-proof stress EN 1301 defines indeed only typical values, but the above given values can all be regarded as on the safe side. Anyway for the design of connections of category A (bearing mode) the ultimate strength value is the basis for the calculation of the bearing capacity of a bolt or a rivet.
3.3.2.2 Preloaded bolts
  1. Bolts of class 8.8 and 10.9 may be used as preloaded bolts with controlled tightening, provided they conform to the requirements for preloaded bolts in existing ENs, prENs and ISO Standards.

    NOTE The National Annex may give rules for bolts not according to these standards, to be used for preloading application.

3.3.3 Rivets

  1. The material properties, dimensions and tolerances of aluminium alloy solid and hollow rivets should conform to ENs, prENs or ISO Standards (if and when they are available). 39
  2. The minimum guaranteed values of the 0,2% proof strength fo and the ultimate strength fu to be adopted as characteristic values in calculations, are given in Table 3.4.

3.3.4 Welding consumables

  1. All welding consumables should conform to ENs, prENs or ISO Standards (if available) listed in 1.2.2.

    NOTE prEN(WI 121 127 and WI 121 214) are in preparation.

  2. The selection of welding filler metal for the combination of alloys being joined should be made from prEN 1011 -4 Table B.2 and B.3 in conjunction with the design requirements for the joint, see 8.6.3.1. Guidance on the selection of filler metal for the range of parent metals given in this European Standard is given in Tables 3.5 and 3.6.
    Table 3.5 - Alloy grouping used in Table 3.6
    Filler metal grouping Alloys
    Type 3 3103
    Type 4 4043A, 4047A1)
    Type 5 5056A, 5356 / 5356A, 5556A / 5556B, 5183 / 5183A
    1) 4047A is specifically used to prevent weld metal cracking in joints. In most other cases, 4043A is preferable.
    40
    Table 3.6 - Selection of filler metals (see Table 3.5 for alloy types)
    Parent metal combination 1)
    1st Part 2nd Part
      Al-Si castings Al-Mg castings 3xxx series alloys 5xxx- series alloys except 5083 5083 6xxx-series alloys 7020
    7020 NR2) Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 4
    Type 5
    Type 5
    Type 5
    5556A
    Type 5
    5556A
    Type 5
    Type 5
    Type 4
    5556A
    Type 5
    Type 44)
    6xxx-series alloys Type 4
    Type 4
    Type 4
    Type 5
    Type 5
    Type 5
    Type 4
    Type 4
    Type 4
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 4
    Type 4
     
    5083 NR2) Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    5556A
    Type 5
    Type 5
       
    5xxx- series alloys except 5083 NR2) Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 5
    Type 53)

    Type 5
         
    3xxx series alloys Type 4
    Type 4
    Type 4
    Type 5
    Type 5
    Type 5
    Type 3
    Type 3
    Type 3
           
    Al-Mg castings NR2) Type 5
    Type 5
    Type 5
             
    Al-Si castings Type 4
    Type 4
    Type 4
               
    1) In each box the filler metal for the maximum weld strength is shown in the top line; in the case of 6xxx series alloys and EN-AW 7020, this will be below the fully heat treated parent metal strength. The filler metal for maximum resistance to corrosion is shown in the middle line. The filler metal for avoidance of persistent weld cracking is shown on the bottom line.
    2) NR = Not recommended. The welding of alloys containing approximately 2% or more of Mg with Al-Si filler metal, or vice-versa is not recommended because sufficient Mg2Si precipitate is formed at the fusion boundaries to embrittle the weld. Where unavoidable see prEN 1011-4.
    3) The corrosion behaviour of weld metal is likely to be better if its alloy content is close to that of the parent metal and not markedly higher. Thus for service in potentially corrosive environments it is preferable to weld EN-AW 5454 with 5454 filler metal. However, in some cases this may only be possible at the expense of weld soundness, so that a compromise will be necessary.
    4) Only in special cases due to the lower strength of the weld and elongation of the joint.
41

3.3.5 Adhesives

NOTE Recommendations for adhesive bonded connections are given in Annex M

4 Durability

  1. The basic requirements for durability are given in EN 1990.

    NOTE For aluminium in contact with other material, recommendations are given in Annex D.

  2. Under normal atmospheric conditions, aluminium structures made of alloys listed in Tables 3.1a and 3.1.b can be used without the need for surface protection to avoid loss of load-bearing capacity.

    NOTE Annex D gives information on corrosion resistance of aluminium and guidelines for surface protection of aluminium, as well as information on conditions for which a corrosion protection is recommended.

  3. Components susceptible to corrosion and subject to aggressive exposure, mechanical wear or fatigue should be designed such that inspection, maintenance and repair can be carried out satisfactorily during the design life. Access should be available for service inspection and maintenance.
  4. The requirements and means for execution of protective treatment undertaken off-site and on-site are given in Image EN 1090-3 Image.
  5. The excecution specification should describe the extent, type and execution procedure for a selected protective treatment.
42

5 Structural analysis

5.1 Structural modelling for analysis

5.1.1 Structural modelling and basic assumptions

  1. Analysis should be based upon calculation models of the structure that are appropriate for the limit state under consideration.
  2. The calculation model and basic assumptions for the calculations should reflect the structural behaviour at the relevant limit state with appropriate accuracy and reflect the anticipated type of behaviour of the cross sections, members, joints and bearings.

5.1.2 Joint modelling

  1. The effects of the behaviour of the joints on the distribution of internal forces and moments within a structure, and on the overall deformations of the structure, may generally be neglected, but where such effects are significant (such as in the case of semi-continuous joints) they should be taken into account.
  2. To identify whether the effects of joint behaviour on the analysis need be taken into account, a distinction may be made between three joint models as follows:

    NOTE Recommendations for the various types of joints are given in Annex L.

5.1.3 Ground-structure interaction

  1. Account should be taken of the deformation characteristics of the supports where significant.

    NOTE EN 1997 gives guidance for calculation of soil-structure interaction.

5.2 Global analysis

5.2.1 Effects of deformed geometry of the structure

  1. The internal forces and moments may generally be determined using either:
  2. P The effects of the deformed geometry (second-order effects) shall be considered if they increase the action effects significantly or modify significantly the structural behaviour.
  3. First order analysis may be used for the structure, if the increase of the relevant internal forces or moments or any other change of structural behaviour caused by deformations can be neglected. This condition may be assumed to be fulfilled, if the following criterion is satisfied:

    Image

    where:

    αcr is the factor by which the design loading would have to be increased to cause elastic instability in a global mode 43
    FEd is the design loading on the structure
    Fcr is the elastic critical buckling load for global instability mode based on initial elastic stiffness.

    NOTE The national Annex may give a different criterion for the limit of αcr for neglecting the influence of second order effects.

  4. The effects of shear lag and of local buckling on the stiffness should be taken into account if this significantly influences the global analysis.

    NOTE Recommendations how to allow for shear lag are given in Annex K.

  5. The effects on the global analysis of the slip in bolt holes and similar deformations of connection devices like studs and anchor bolts on action effects should be taken into account, where relevant and significant.

5.2.2 Structural stability of frames

  1. If according to 5.2.1 the influence of the deformation of the structure has to be taken into account. (2) to (6) should be applied to consider these effects and to verify the structural stability.
  2. The verification of the stability of frames or their parts should be carried out considering imperfections and second order effects.
  3. According to the type of frame and the global analysis, second order effects and imperfections may be accounted for by one of the following methods:
    1. both totally by the global analysis,
    2. partially by the global analysis and partially through individual stability checks of members according to 6.3,
    3. for basic cases by individual stability checks of equivalent members according to 6.3 using appropriate buckling lengths according to the global buckling mode of the structure.
  4. Second order effects may be calculated by using an analysis appropriate to the structure (including step-by-step or other iterative procedures). For frames where the first sway buckling mode is predominant first order elastic analysis should be carried out with subsequent amplification of relevant action effects (e.g. bending moments) by appropriate factors.
  5. In accordance with 5.2.2(3) a) and b) the stability of individual members should be checked according to the following:
    1. If second order effects in individual members and relevant member imperfections (see 5.3.4) are totally accounted for in the global analysis of the structure, no individual stability check for the members according to 6.3 is necessary.
    2. If second order effects in individual members or certain individual member imperfections (e.g. member imperfections for flexural and/or lateral torsional buckling, see 5.3.4) are not totally accounted for in the global analysis, the individual stability of members should be checked according to the relevant criteria in 6.3 for the effects not included in the global analysis. This verification should take account of end moments and forces from the global analysis of the structure, including global second order effects and global imperfections (see 5.3.2) where relevant and may be based on a buckling length equal to the system length, see Figure 5.1 (d), (e), (f) and (g).
  6. Where the stability of a frame is assessed by a check with the equivalent column method according to 6.3 the buckling length values should be based on a global buckling mode of the frame accounting for the stiffness behaviour of members and joints, the presence of plastic hinges and the distribution of compressive forces under the design loads. In this case internal forces to be used in resistance checks are calculated according to first order theory without considering imperfections, see Figure 5.1 (a), (b) and (c).
44

5.3 Imperfections

5.3.1 Basis

  1. P Appropriate allowances shall be considered to cover the effects of imperfections, including residual stresses and geometrical imperfections such as lack of verticality, lack of straightness, lack of flatness, lack of fit and any unspecified eccentricities present in joints of the unloaded structure.

    NOTE Geometrical imperfections Image in accordance with the essential tolerances given in EN 1090-3 are considered in the resistance formulae, the buckling curves and the γM-values Image in EN 1999.

  2. Equivalent geometric imperfections, see 5.3.2 and 5.3.3, should be used, with values which reflect the possible effects of all type of imperfections. In the equivalent column method according to 5.3.4 the effects are included in the resistance formulae for member design.
  3. The following imperfections should be taken into account:
    1. global imperfections for frames and bracing systems
    2. local imperfections for individual members

5.3.2 Imperfections for global analysis of frames

  1. The assumed shape of global imperfections and local imperfections may be derived from the elastic buckling mode of a structure in the plane of buckling considered.
  2. Both in and out of plane buckling including torsional buckling with symmetric and asymmetric buckling shapes should be taken into account in the most unfavourable direction and form.
  3. For frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members. The imperfections may be determined from:
    1. global initial sway imperfections, see Figure 5.1(d):

      ϕ = ϕ0αhαm     (5.2)

      where:

      ϕ0 is the basic value: ϕ0 = 1 / 200
      αh is the reduction factor for height h applicable to columns:
      Image
      h is the height of the structure in meters
      αm is the reduction factor for the number of columns in a row: Image
      m is the number of columns in a row including only those columns which carry a vertical load NEd not less than 50% of the average value of the column in the vertical plane considered.
      45

      Figure 5.1 - Equivalent buckling length and equivalent sway imperfections

      Figure 5.1 - Equivalent buckling length and equivalent sway imperfections

    2. relative initial local bow imperfections of members for flexural buckling

      e0 / L     (5.3)

      where L is the member length

      NOTE The values e0/L may be chosen in the National Annex. Recommended values are given in Table 5.1.

      Table 5.1 - Design values of initial bow imperfection e0 / L
      Buckling class
      acc. to Table 3.2
      elastic analysis plastic analysis
      e0/L e0/L
      A 1/300 1/250
      B 1/200 1/150
  4. For building frames sway imperfections may be disregarded where

    HEd ≥ 0,15 VEd     (5.4)

    where:

    HEd is the design value of the horizontal force

    VEd is design value of the vertical force.

  5. For the determination of horizontal forces to floor diaphragms the configuration of imperfections as given in Figure 5.2 should be applied, where ϕ is a sway imperfection obtained from expression (5.2) assuming a single storey with height h, see (3) a).46

    Figure 5.2 - Configuration of sway imperfections ϕ for horizontal forces on floor diaphragms

    Figure 5.2 - Configuration of sway imperfections ϕ for horizontal forces on floor diaphragms

  6. When performing the global analysis for determining end forces and end moments to be used in member checks according to 6.3 local bow imperfections may be neglected. However, for frames sensitive to second order effects local bow imperfections of members additionally to global sway imperfections (see 5.2.1(3)) should be introduced in the structural analysis of the frame for each compressed member where the following conditions are met:

    where:

    NEd is the design value of the compression force

    Image is the in-plane relative slenderness calculated for the member considered as hinged at its ends

    NOTE Local bow imperfections are taken into account in member checks, see 5.2.2 (3) and 5.3.4.

  7. The effects of initial sway imperfection and bow imperfections may be replaced by systems of equivalent horizontal forces, introduced for each column, see Figure 5.2 and Figure 5.3. 47

    Figure 5.3 - Replacement of initial imperfections by equivalent horizontal forces

    Figure 5.3 - Replacement of initial imperfections by equivalent horizontal forces

  8. These initial sway imperfections should apply in all relevant horizontal directions, but need only be considered in one direction at a time.
  9. Where, in multi-storey beam-and-column building frames, equivalent forces are used they should be applied at each floor and roof level.
  10. The possible torsional effects on a structure caused by anti-symmetric sways at the two opposite faces, should also be considered, see Figure 5.4.

    Figure 5.4 - Translational and torsional effects (plan view)

    Figure 5.4 - Translational and torsional effects (plan view)

  11. As an alternative to (3) and (6) the shape of the elastic critical buckling mode ηcr of the structure or of the verified member may be applied as a unique global and local imperfection. The equivalent geometrical imperfection may be expressed in the form:

    Image

    where:

    Image

    48
    Image and m denotes the cross-section where Image reaches its maximum in the case of uniform normal force and uniform cross-section; Image
      α is the imperfection factor for the relevant buckling curve, see Table 6.6;
      Image is the relative slenderness of the structure;
      Image is the limit given in Table 6.6;
      χ is the reduction factor for the relevant buckling curve, see 6.3.1.2;
      Ncr,m = αcrNEd,m is the value of axial force in cross-section m when the elastic critical buckling was reached;
      αcr is the minimum force amplifier for the axial force configuration NEd in members to reach the elastic critical buckling;
      MRk,m is the characteristic moment resistance of the cross-section m according to (6.25) 6.2.5.1;
      NRk,m is the characteristic normal force resistance of the cross-section m according to (6.22) 6.2.4;
         Image Image is the bending moment due to ηcr at the cross-section m; Image
      Image is the second derivative of ηcr (x)

    NOTE 1 For calculating the amplifier αcr the members of the structure may be considered to be loaded by axial forces NEd only that result from the first order elastic analysis of the structure for the design loads.

    NOTE 2 The ration Image may be replaced by Image

    where:

    Image |ηcr|max is the maximum value of the amplitude of the buckling. mode of the structure (arbitrary value may be taken); Image
    Image |ηII|max is the maximum deflection of the structure calculated using second order analysis (symbolised by II) for the structure with the imperfection in the shape of the elastic critical buckling mode ηcr with maximum amplitude |ηcr|max ; Image
    Image is the bending moment in cross-section m calculated as given for |ηII|max.

    The bending moments in the structure due to ηinit (x) with allowing for second order effects may be then calculated from:

    Image

    NOTE 3 Formula (5.6) is based on the requirement that the imperfection ηinit having the shape of the elastic buckling mode ηcr, should have the same maximum curvature as the equivalent uniform member.

5.3.3 Imperfection for analysis of bracing systems

  1. In the analysis of bracing systems which are required to provide lateral stability within the length of beams or compression members the effects of imperfections should be included by means of an equivalent geometric imperfection of the members to be restrained, in the form of an initial bow imperfection:

    e0 = αmL/500     (5.9)

    49

    where:

    L is the span of the member and

    Image

    in which m is the number of members to be restrained.

  2. For convenience, the effects of the initial bow imperfections of the members to be restrained by a bracing system, may be replaced by the equivalent stabilising force as shown in Figure 5.5:

    Image

    where:

    δq is the inplane deflection of the bracing system due to q0 plus any external loads calculated from first order analysis.

    NOTE 1 δq may be taken as 0 if second order theory is used.

    NOTE 2 As δq in (5.11) depends on q0, it results in an iterative procedure.

  3. Where the bracing system is required to stabilise the compression flange of a beam of constant height, the force NEd in Figure 5.5 may be obtained from:

    NEd = MEd / h     (5.12)

    where:

    MEd is the maximum moment in the beam
    h is the overall depth of the beam.

    NOTE Where a beam is subjected to external compression, this should be taken into account.

  4. At points where beams or compression members are spliced, it should also be verified that the bracing system is able to resist a local force equal to αmNEd / 100 applied to it by each beam or compression member which is spliced at that point, and to transmit this force to the adjacent points at which that beam or compression member is restrained, see Figure 5.6.
  5. For checking for the local force according to clause (4), any external loads acting on bracing systems should also be included, but the forces arising from the imperfection given in (1) may be omitted.
50

Figure 5.5 - Equivalent stabilising force

Figure 5.5 - Equivalent stabilising force

Figure 5.6 - Bracing forces at splices in compression members

Figure 5.6 - Bracing forces at splices in compression members

51

5.3.4 Member imperfections

  1. The effects of imperfections of members described in 5.3.1(1) are incorporated within the formulas given for buckling resistance for members, see section 6.3.1.
  2. Where the stability of members is accounted for by second order analysis according to 5.2.2(5)a) for compression members imperfections Image e0 Image according to 5.3.2(3)b) or 5.3.2(5) or (6) should be considered.
  3. For a second order analysis taking account of lateral torsional buckling of a member in bending the imperfections may be adopted as Image ke0, where e0 Image is the equivalent initial bow imperfection of the weak axis of the profile considered. In general an additional torsional imperfection need not to be allowed for.

    NOTE The National Annex may choose the value of k. The value k = 0,5 is recommended.

5.4 Methods of analysis

5.4.1 General

  1. The internal forces and moments may be determined using either
    1. elastic global analysis
    2. plastic global analysis.

    NOTE For finite element model (FEM) analysis see EN 1993-1-5.

  2. Elastic global analysis may be used in all cases.
  3. Plastic global analysis may be used only where the structure has sufficient rotation capacity at the actual location of the plastic hinge, whether this is in the members or in the joints. Where a plastic hinge occurs in a member, the member cross sections should be double symmetric or single symmetric with a plane of symmetry in the same plane as the rotation of the plastic hinge and it should satisfy the requirements specified in 5.4.3. Where a plastic hinge occurs in a joint the joint should either have sufficient strength to ensure the hinge remains in the member or should be able to sustain the plastic resistance for a sufficient rotation.

    NOTE 1 Information on rotation capacity is given in Annex G.

    NOTE 2 Only certain alloys have the required ductility to allow sufficient rotation capacity, see 6.4.3(2).

5.4.2 Elastic global analysis

  1. Elastic global analysis is based on the assumption that the stress-strain behaviour of the material is linear, whatever the stress level is.

    NOTE For the choice of a semi-continuous joint model see 5.1.2.

  2. Internal forces and moments may be calculated according to elastic global analysis even if the resistance of a cross section is based on its plastic resistance.
  3. Elastic global analysis may also be used for cross sections, the resistances of which are limited by local buckling.

5.4.3 Plastic global analysis

  1. Plastic global analysis should not be used for beams with transverse welds on the tension side of the member at the plastic hinge locations.

    NOTE For plastic global analysis of beams recommendations are given in Annex H.

  2. Plastic global analysis should only be used where the stability of members can be assured, see 6.3.
52

6 Ultimate limit states for members

6.1 Basis

6.1.1 General

  1. P Aluminium structures and components shall be proportioned so that the basic design requirements for the ultimate limit state given in Section 2 are satisfied. The design recommendations are for structures subjected to normal atmospheric conditions.

6.1.2 Characteristic value of strength

  1. Resistance calculations for members are made using characteristic value of strength as follows:

    fo is the characteristic value of the strength for bending and overall yielding in tension and compression

    fu is the characteristic value of the strength for the local capacity of a net section in tension or compression

  2. The characteristic value of the 0,2% proof strength fo and the ultimate tensile strength fu for wrought aluminium alloys are given in 3.2.2.

6.1.3 Partial safety factors

  1. The partial factors γM as defined in 2.4.3 should be applied to the various characteristic values of resistance in this section as follows:
    Table 6.1 - Partial safety factors for ultimate limit states
    resistance of cross-sections whatever the class is: γM1
    resistance of members to instability assessed by member checks:
    resistance of cross-sections in tension to fracture: γM2
    resistance of joints: See Section 8

    NOTE 1 Partial factors γMi may be defined in the National Annex. The following numerical values are recommended:

    γM1 = 1,10

    γM2 = 1,25

    NOTE 2 For other recommended numerical values see EN 1999 Part 1-2 to Part 1-5. For structures not covered by EN 1999 Part 1-2 to Part 1-5 the National Annex may give information.

6.1.4 Classification of cross-sections

6.1.4.1 Basis
  1. The role of cross-section classification is to identify the extent to which the resistance and rotation capacity of cross-sections is limited by its local buckling resistance.

    NOTE See also Annex F.

6.1.4.2 Classification
  1. Four classes of cross-sections are defined, as follows:
  2. In Class 4 cross-sections effective thickness may be used to make the necessary allowances for reduction in resistance due to the effects of local buckling, see 6.1.5.
  3. The classification of a cross-section depends on the width to thickness ratio of the parts subject to compression.
  4. Compression parts include every part of a cross-section that is either totally or partially in compression under the load combination considered.
  5. The various compression parts in a cross-section (such as web or a flange) can, in general, be in different classes. A cross-section is classified according to the highest (least favourable) class of its compression parts.
  6. The following basic types of thin-walled part are identified in the classification process:
    1. flat outstand parts;
    2. flat internal parts;
    3. curved internal parts.

These parts can be un-reinforced, or reinforced by longitudinal stiffening ribs or edge lips or bulbs (see Figure 6.1).

Figure 6.1 - Types of cross-section parts

Figure 6.1 - Types of cross-section parts

6.1.4.3 Slenderness parameters
  1. The susceptibility of an un-reinforced flat part to local buckling is defined by the parameter β, which has the following values:
    1. flat internal parts with no stress gradient or
      flat outstands with no stress gradient or peak compression at toe     β = b/t     (6.1)
    2. internal parts with a stress gradient that results in a neutral axis at the Image centre Image     β = 0,40 b/t     (6.2)
    3. internal parts with stress gradient and outstands with peak compression at root     β = η b/t     (6.3)

    where:

    b is the width of a cross-section part 54
    t is the thickness of a cross-section
    η is the stress gradient factor given by the expressions:

    η = 0,70 + 0,30Ψ     (l ≥ Ψ ≥ −l) ,     (6.4)

    η = 0,80/(1 − Ψ)     (Ψ < −1) , see Figure 6.2     (6.5)

    where

    Ψ is the ratio of the stresses at the edges of the plate under consideration related to the maximum compressive stress. In general the neutral axis should be the elastic neutral axis, but in checking whether a section is class 1 or 2 it is permissible to use the plastic neutral axis.

    NOTE All cross section parts are considered simply supported when calculating the parameters β even if the cross section parts are elastically restrained or clamped.

    Figure 6.2 - Flat internal parts under stress gradient, values of η. For internal parts or outstands (peak compression at root) use curve A. For outstands (peak compression at toe) use line B.

    Figure 6.2 - Flat internal parts under stress gradient, values of η. For internal parts or outstands (peak compression at root) use curve A. For outstands (peak compression at toe) use line B.

  2. When considering the susceptibility of a reinforced flat part to local buckling, three possible buckling modes should be considered, as shown in Figure 6.3. Separate values of β should be found for each mode. The modes are:
    a) Mode 1: the reinforced part buckles as a unit, so that the reinforcement buckles with the same curvature as the part. This mode is often referred to as distortional buckling.
    b) Mode 2: the sub-parts and the reinforcement buckle as individual parts with the junction between them remaining straight.
    c) Mode 3: this is a combination of Modes 1 and 2 in which sub-part buckles are superimposed on the buckles of the whole part. This is indicated in Figure 6.3(c).

    Figure 6.3 - Buckling modes for flat reinforced parts

    Figure 6.3 - Buckling modes for flat reinforced parts

    55
  3. Values of β are found as follows:
    1. Mode l, uniform compression, standard reinforcement:
      When the reinforcement is a single-sided rib or lip of thickness equal to the part thickness t,

      Image

      where η is given in expressions (6.7a), (6.7b) or (6.7c), or is read from Figure 6.4(a), (b) or (c). In this figure the depth c of the rib or lip is measured to the inner surface of the plate.

      Image

    2. Mode 1, uniform compression, non-standard reinforcement:
      With any other single shape of reinforcement, the reinforcement is replaced by an equivalent rib or lip equal in thickness to the part (t). The value of c for the equivalent rib or lip is chosen so that the second moment of area of the reinforcement about the mid-plane of the plate part is equal to that of the non-standard reinforcement about the same plane. An alternative method is given in 6.6.
    3. Mode 1, uniform compression, complex reinforcement:
      For unusual shapes of reinforcement not amenable to the analysis described above,

      Image

      σcr is the elastic critical stress for the reinforced part assuming simply supported edges
      σcr0 is the elastic critical stress for the unreinforced part assuming simply supported edges.
    4. Mode 1, stress gradient:

      The value of β is found from the expression (6.8), where σcr and σcr0 now relate to the stress at the more heavily compressed edge of the part.

    5. Mode 2:

      The value of β is found separately for each sub-part in accordance with Image 6.1.4.3(1) Image

  4. The susceptibility of a uniformly compressed shallow curved unreinforced internal part to local buckling is defined by β, where:

    Image

    R is radius of curvature to the mid-thickness of material
    b is developed width of the part at mid-thickness of material
    t is thickness.

    The above treatment is valid if R/b > 0,1 b/t. Sections containing more deeply curved parts require special study or design by testing.

  5. The susceptibility of a thin-walled round tube to local buckling, whether in uniform compression or in bending is defined by β, where: 56

    Image

    D = diameter to mid-thickness of tube material.

    Figure 6.4 - Values of η for reinforced cross section parts

    Figure 6.4 - Values of η for reinforced cross section parts

6.1.4.4 Classification of cross-section parts
  1. The classification of parts of cross-sections is linked to the values of the slenderness parameter as β follows:
    Parts in beams Parts in struts
    ββ1 : class 1 ββ2 : class 1 or 2
    β1 < ββ2 : class 2 β2 < ββ3 : class 3
    β2 < ββ3 : class 3 β3 < β : class 4
    β3 < β : class 4  
    57
  2. Values of β1, β2 and β3 are given in Table 6.2.
    Table 6.2 - Slenderness parameters β1 / ε , β2 / ε and β3 / ε
    Material classification according to Table 3.2 Internal part Outstand part
    β1 / ε β2 / ε β3 / ε β1 / ε β2 / ε β3 / ε
    Class A, without welds 11 16 22 3 4,5 6
    Class A, with welds 9 13 18 2,5 4 5
    Class B, without welds 13 16,5 18 3,5 4,5 5
    Class B, with welds 10 13,5 15 3 3,5 4
    Image
  3. In the Table 6.2, a cross-section part is considered with welds if it contains welding at an edge or at any point within its width. However, a cross-sections part may be considered as without welds if the welds are transversal to the member axis and located at a position of lateral restraint.

    NOTE In a cross-section part with welds the classification is independent of the extent of the HAZ.

  4. When classifying parts in members under bending, if the parts are less highly stressed than the most severely stressed fibres in the section, a modified expression Image may be used. In this expression, z1 is the distance from the elastic neutral axis of the effective section to the most severely stressed fibres, and z2 is the distance from the elastic neutral axis of the effective section to the part under consideration. z1 and z2 should be evaluated on the effective section by means of an iterative procedure (minimum two steps).

6.1.5 Local buckling resistance

  1. Local buckling in class 4 members is generally allowed for by replacing the true section by an effective section. The effective section is obtained by employing a local buckling factor ρc to factor down the thickness. ρc is applied to any uniform thickness class 4 part that is wholly or partly in compression. Parts that are not uniform in thickness require a special study.
  2. The factor ρc is given by expressions (6.11) or (6.12), separately for different parts of the section, in terms of the ratio β / ε , where β is found in 6.1.4.3, ε is defined in Table 6.2 and the constants C1 and C2 in Table 6.3. The relationships between ρc and β / ε are summarised in Figure 6.5.

    ρc = 1,0     if ββ3     (6.11)

    Image

    Table 6.3 - Constants C1 and C2 in expressions for ρc
    Material classification according to Table 3.2 Internal part Outstand part
    C1 C2 C1 C2
    Class A, without welds 32 220 10 24
    Class A, with welds 29 198 9 20
    Class B, without welds 29 198 9 20
    Class B, with welds 25 150 8 16
  3. For flat outstand parts in unsymmetrical cross-sections (Figure 6.1), ρc is given by the above expressions for flat outstand in symmetrical sections, but not more than 120/(β / ε)2. 58
  4. For reinforced cross-section parts: Consider all possible modes of buckling, and take the lower value of ρc. In the case of mode 1 buckling the factor ρc should be applied to the area of the reinforcement as well as to the basic plate thickness. See also 6.7. For reinforced outstand cross section part use curve for outstands, otherwise curve for internal cross section part.
  5. For the determination of ρc in sections required to carry biaxial bending or combined bending and axial load, see notes in 6.3.3(4).

    Figure 6.5 - Relationship between ρc and β / ε for outstands, internal parts and round tubes

    Figure 6.5 - Relationship between ρc and β / ε for outstands, internal parts and round tubes

6.1.6 HAZ softening adjacent to welds

6.1.6.1 General
  1. P In the design of welded structures using strain hardened or artificially aged precipitation hardening alloys the reduction in strength properties that occurs in the vicinity of welds shall be allowed for.
  2. Exceptions to this rule, where there is no weakening adjacent to welds, occur in alloys in the O-condition; or if the material is in the F condition and design strength is based on O-condition properties.
  3. For design purposes it is assumed that throughout the heat affected zone (HAZ) the strength properties are reduced on a constant level.

    NOTE 1 The reduction affects the 0.2% proof strength of the material more severely than the ultimate tensile strength. The affected region extends immediately around the weld, beyond which the strength properties rapidly recover to their full unwelded values.

    NOTE 2 Even small welds to connect a small attachment to a main member may considerably reduce the resistance of the member due to the presence of a HAZ. In beam design it is often beneficial to locate welds and attachments in low stress areas, i.e. near the neutral axis or away from regions of high bending moment.

    NOTE 3 For some heat treatable alloys it is possible to mitigate the effects of HAZ softening by means of artificial ageing applied after welding.

6.1.6.2 Severity of softening
  1. The characteristic value of the 0,2 % proof strengths fo,haz and the ultimate strength fa,haz in the heat affected zone are listed in Table 3.2. Table 3.2 also gives the reduction factors

    Image

    59

    NOTE Values for other alloys and tempers must be found and defined by testing. If general values are wanted, testing series are necessary to allow for the fact that material from different manufactures of semi products may vary in chemical composition and therefore may show different strength values after welding. In some cases it is also possible to derive strength values from values of well-known alloys by interpolation.

    Figure 6.6 - The extent of heat-affected zones (HAZ)

    Figure 6.6 - The extent of heat-affected zones (HAZ)

  2. The values of fo,haz and Image fu,haz Image in Table 3.2 are valid from the following times after welding, providing the material has been held at a temperature not less than 10°C:

    NOTE 1 If the material is held at a temperature below 10°C after welding, the recovery time will be prolonged. Advice should be sought from manufacturers.

    NOTE 2 The severity of softening can be taken into account by the characteristic value of strength fo,haz and fu,haz, in the HAZ (Table 3.2) as for the parent metal, or by reducing the assumed cross-sectional area over which the stresses acts with the factors ρo,haz and ρu,haz (Table 3.2). Thus the characteristic resistance of a simple rectangular section affected by HAZ softening can be expressed as A fu,haz = (ρu,haz A) fu if the design is dominated by ultimate strength or as A fo,haz = (ρo,haz A) fo if the design is dominated by the 0,2% proof strength.

6.1.6.3 Extent of HAZ
  1. The HAZ is assumed to extend a distance bhaz in any direction from a weld, measured as follows (see Figure 6.6).
    1. transversely from the centre line of an in-line butt weld;
    2. transversely from the point of intersection of the welded surfaces at fillet welds;
    3. transversely from the point of intersection of the welded surfaces at butt welds used in corner, tee or cruciform joints;
    4. in any radial direction from the end of a weld.
  2. The HAZ boundaries should generally be taken as straight lines normal to the metal surface, particularly if welding thin material. However, if surface welding is applied to thick material it is permissible to assume a curved boundary of radius bhaz, as shown in Figure 6.6. 60
  3. For a MIG weld laid on unheated material, and with interpass cooling to 60°C or less when multi-pass welds are laid, values of bhaz are as follows:
    0 < t ≤ 6 mm: bhaz = 20 mm
    6 < t ≤ 12 mm: bhaz = 30 mm
    12 < t ≤ 25 mm: bhaz = 35 mm
    t > 25 mm: bhaz = 40 mm
  4. For thickness > 12 mm there may be a temperature effect, because interpass cooling may exceed 60°C unless there is strict quality control. This will increase the width of the heat affected zone.
  5. The above figures apply to in-line butt welds (two valid heat paths) or to fillet welds at T-junctions (three valid heat paths) in Image 6xxx and 7xxx series alloys, and in 3xxx and 5xxx series Image alloys in the work-hardened condition.
  6. For a TIG weld the extent of the HAZ is greater because the heat input is greater than for a MIG weld. TIG welds for in-line butt or fillet welds in 6xxx, 7xxx Image and work-hardened 3xxx and 5xxx series Image alloys, have a value of bhaz given by:
    0 < t ≤ 6 mm: bhaz = 30 mm
  7. If two or more welds are close to each other, their HAZ boundaries overlap. A single HAZ then exists for the entire group of welds. If a weld is located too close to the free edge of an outstand the dispersal of heat is less effective. This applies if the distance from the edge of the weld to the free edge is less than 3bhaz. In these circumstances assume that the entire width of the outstand is subject to the factor ρo,haz.
  8. Other factors that affect the value of bhaz are as follows:
    1. Influence of temperatures above 60°C

      When multi-pass welds are being laid down, there could be a build-up of temperature between passes. This results in an increase in the extent of the HAZ. Image If the interpass temperature T1(°C) is between 60°C and 120°C, it is conservative for 6xxx, 7xxx and work-hardened 3xxx and 5xxx series alloys to multiply bhaz by a factor α2 as follows: Image

      - 6xxx alloys Image and work-hardened 3xxx and 5xxx series Image alloys: α2 = 1 + (T1 − 60)/120;
      - 7xxx alloys: α2 = 1 + 1,5(T1 − 60)/120.

      If a less conservative value of α2 is desired, hardness tests on test specimens will indicate the true extent of the HAZ. A temperature of 120°C is the maximum recommended temperature for welding aluminium alloys.

    2. Variations in thickness

      If the cross-section parts to be joined by welds do not have a common thickness t, it is conservative to assume in all the above expressions that t is the average thickness of all parts. This applies as long as the average thickness does not exceed 1,5 times the smallest thickness. For greater variations of thickness, the extent of the HAZ should be determined from hardness tests on specimens.

    3. Variations in numbers of heat paths

      If the junctions between cross-section parts are fillet welded, but have different numbers of heat paths (n) from the three designated at (5) above, multiply the value of bhaz by 3/n.

6.2 Resistance of cross-sections

6.2.1 General

  1. P The design value of an action effect in each cross-section shall not exceed the corresponding design resistance and if several action effects act simultaneously the combined effect shall not exceed the resistance for that combination.
  2. Shear lag effects should be included by an effective width. Local buckling effects should be included by an effective thickness, see 6.1.5. As an alternative, equivalent effective width may also be used. 61

    NOTE For the effect of shear lag. see Annex K

  3. The design values of resistance depend on the classification of the cross-section.
  4. Verification according to elastic resistance may be carried out for all cross-sectional classes provided the effective cross-sectional properties are used for the verification of class 4 cross-sections.
  5. For the resistance the following yield criterion for a critical point of the cross-section may be used unless other interaction formulae apply, see 6.2.7 to 6.2.10.

    Image

    where:

    σx,Ed is the design value of the local longitudinal stress at the point of consideration
    σz,Ed is the design value of the local transverse stress at the point of consideration
    τEd is the design value of the local shear stress at the point of consideration
    C ≥ 1 is a constant, see NOTE 2

    NOTE 1 The verification according to 6.2.1(5) can be conservative as it only partially allow for plastic stress distribution, which is permitted in elastic design. Therefore it should only be performed where the interaction on the basis of resistances cannot be performed.

    NOTE 2 The constant C in criterion (6.15) may be defined in the National Annex. The numerical value C = 1,2 is recommended.

6.2.2 Section properties

6.2.2.1 Gross cross-section
  1. The properties of the gross cross-section (Ag) should be found by using the nominal dimensions. Holes for fasteners need not be deducted, but allowance should be made for larger openings. Splice materials and battens should not be included.
6.2.2.2 Net area
  1. The net area of a cross-section (Anet) should be taken as the gross area less appropriate deductions for holes, other openings and heat affected zones.
  2. For calculating net section properties, the deduction for a single fastener hole should be the Image text deleted Image cross-sectional area of the hole in the plane of its axis. For countersunk holes, appropriate allowance should be made for the countersunk portion.
  3. Provided that the fastener holes are not staggered, the total area to be deducted for the fastener holes should be the maximum sum of the sectional areas of the holes in any cross-section perpendicular to the member axis (see failure plane 1 in Figure 6.7).

    NOTE The maximum sum denotes the position of the critical failure line.

  4. Where the fastener holes are staggered, the total area to be deducted for fastener holes should be the greater of (see Figure 6.7):
    1. the deduction for non-staggered holes given in (3)
    2. a deduction taken as ∑td − ∑tbs where bs is the lesser of

      s2 /(4p) or 0,65s   (6.16)

      62

      where:

      d is the diameter of hole
      s is staggered pitch, the spacing of the centres of two consecutive holes in the chain measured parallel to the member axis
      p is the spacing of the Image centres Image of the same two holes measured perpendicular to the member axis
      t is the thickness (or effective thickness in a member containing HAZ material).

      Figure 6.7 - Staggered holes and critical fracture lines 1, 2 and 3

      Figure 6.7 - Staggered holes and critical fracture lines 1, 2 and 3

      Figure 6.8 - Angles with holes in both legs

      Figure 6.8 - Angles with holes in both legs

  5. Image In an angle or other member with holes in more than one plane, the spacing p should be measured along the centre Image of thickness of the material (see Figure 6.8).
6.2.2.3 Shear lag effects
  1. The effect of shear lag on the buckling and rupture resistance of flanges should be taken into account.

    NOTE Recommendations for the effect of shear lag are given in Annex K.

6.2.3 Tension

  1. P The design value of the tensile force NEd shall satisfy:

    Image

    Image NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected.Image

  2. The design tension resistance of the cross-section Nt,Rd should be taken as the lesser of No,Rd and Nu,Rd where:
    a) general yielding along the member: No,Rd = Agfo / γM1 (6.18)
    b) local failure at a section with holes: Nu,Rd = 0,9Anet fu / γM2 (6.19a)
    c) local failure at a section with HAZ: Nu,Rd = Aeff fu / γM2 (6.19b)

    where:

    63

    Ag is either the gross section or a reduced cross-section to allow for HAZ softening due to longitudinal welds. In the latter case Ag is found by taking a reduced area equal to ρo,haz times the area of the HAZ, see 6.1.6.2

    Anet is the net section area, with deduction for holes and a deduction if required to allow for the effect of HAZ softening in the net section through the hole. The latter deduction is based on the reduced thickness of ρu,hazt.

    Aeff is the effective area based on the reduced thickness of ρu,hazt.

  3. For angles connected through one leg Image see 8.5.2.3 Image. Similar consideration should also be given to other types of sections connected through outstands such as T-sections and channels.

Image (4) Image For staggered holes, see 6.2.2.2.

6.2.4 Compression

  1. P The design value of the axial compression force NEd shall satisfy:

    Image

    Image NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected.Image

  2. The design resistance for uniform compression Nc,Rd should be taken as the lesser of Nu,Rd and Nc,Rd where :
    a) in sections with unfilled holes Nu,Rd = Anet fu / γM2 (6.21)
    b) other sections Nc,Rd = Aeff fo / γM1 (6.22)

    in which:

    Anet is the net section area, with deductions for unfilled holes and HAZ softening if necessary. See 6.2.2.2. For holes located in reduced thickness regions the deduction may be based on the reduced thickness, instead of the full thickness.
    Aeff is the effective section area based on reduced thickness allowing for local buckling and HAZ softening but ignoring unfilled holes.

6.2.5 Bending moment

6.2.5.1 Basis
  1. P The design value of the bending moment M Ed at each cross section shall satisfy

    Image

    Image NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected. Image

  2. The design resistance for bending about one principal axis of a cross section M Rd is determined as the lesser of Mu,Rd and Image Mo,Rd Image where:

    Mu,Rd = Wnet fu / γM2 in a net section and     (6.24)

    Image Mo,Rd = αWel fo / γM1 at each cross-section     (6.25) Image

    where:

    α is the shape factor, see Table 6.4

    Wel is the elastic modulus of the gross section (see 6.2.5.2)

    64

    Wnet is the elastic modulus of the net section allowing for holes and HAZ softening, if welded (see 6.2.5.2). The latter deduction is based on the reduced thickness of ρu,hazt.

    Table 6.4 - Values of shape factor α
    Cross-section class Without welds With longitudinal welds
    1 Wpl / Wel *) Wpl, haz / Wel *)
    2 Wpl / Wel Wpl,haz / Wel
    3 α3,u α3,w
    4 Weff / Wel Weff,haz / Wel
    *) NOTE These formulae are on the conservative side. For more refined value, recommendations are given in Annex F

    In Table 6.4 the various section moduli W and α3,u , α3,w are defined as:

    Wpl plastic modulus of gross section
    Weff effective elastic section modulus, obtained using a reduced thickness teff for the class 4 parts (see 6.2.5.2)
    Wel,haz effective elastic modulus of the gross section, obtained using a reduced thickness ρo,hazt for the HAZ material (see 6.2.5.2)
    Wpl,haz effective plastic modulus of the gross section, obtained using a reduced thickness ρo,hazt for the HAZ material (see 6.2.5.2)
    Weff,haz effective elastic section modulus, obtained using a reduced thickness ρct for the class 4 parts or a reduced thickness ρo,hazt for the HAZ material, whichever is the smaller (see 6.2.5.2)

    α3,u = 1 or may alternatively be taken as:

    Image

    α3, w = Wel,haz / Wel or may alternatively be taken as:

    Image

    where:

    The critical part is determined by the lowest value of Image β2 / β Image

  3. Refer to 6.2.8 for combination of bending moment and shear force.
  4. In addition, the resistance of the member to lateral-torsional buckling should also be verified, see 6.3.2.
6.2.5.2 Design cross section
  1. The terminology used in this section is as follows: 65
    1. net section includes the deduction for holes and includes the allowance for reduced material strength taken in the vicinity of the welds to allow for HAZ softening, if welded.
    2. effective section includes the allowance for HAZ softening and local buckling, but with no reduction for holes. See Figure 6.9.
  2. In items a) and b) above the allowance for reductions in material strength should generally be taken as follows for the various parts in the section:
    1. Class 4 part free of HAZ effects. A value teff = ρct is taken for the compressed portion of the cross-section part, where ρc is found as in 6.1.5. Application of an effective section can result in an iteration procedure. See 6.7.
    2. Class 1, 2 or 3 parts subject to HAZ effects. A value ρo,hazt is taken in the softened portions of the cross-section part, where ρo,haz and the extent of the softening are as given in 6 1.6.2 and 6.1.6.3.
    3. Class 4 part with HAZ effects. The allowance is taken as the lesser of that corresponding to the reduced thickness teff and that corresponding to the reduced thickness in the softened part, ρo,hazt and as teff in the rest of the compressed portion of the cross-section part. See Figure 6.9.
    4. In the case of reinforced cross-section parts (see 6.1.4.3(2)), ρc should be applied to the area of the reinforcement as well as to the basic plate thickness.
    5. For a welded part in a Class 3 or 4 section a more favourable assumed thickness may be taken as follows:
      • - HAZ softening is ignored in any material at distance less than ρo,haz z1 from the elastic neutral axis of the gross section, where z1 is the distance from there to the furthest extreme fibres of the section.
      • - For HAZ material, at a distance z (> ρo,haz z1) from the neutral axis, ρo,haz may be replaced by a value ρzy determined as ρzy = ρo,haz + 1 − z / z1.

        Figure 6.9 - Effective thickness in class 4 cross-section with welds

        Figure 6.9 - Effective thickness in class 4 cross-section with welds

6.2.6 Shear

  1. P The design value of the shear force VEd at each cross-section shall satisfy:

    Image

    where:

    VRd is the design shear resistance of the cross-section.

  2. For non-slender sections, hw / tw < 39ε , see 6.5.5(2) 66

    Image

    where Av is the shear area, taken as:

    1. For sections containing shear webs

      Image

      where:

      hw is the depth of the web between flanges.
      bhaz is the total depth of HAZ material occurring between the clear depth of the web between flanges. For sections with no welds, ρo,haz = 1. If the HAZ extends the entire depth of the web panel bhaz = hw − ∑ d
      tw is the web thickness
      d is the diameter of holes along the shear plane
      n is the number of webs.
    2. For a solid bar and a round tube

      Av = ηvAe     (6.31)

      where:

      ηv = 0,8 for a solid bar
      ηv = 0,6 for a round tube
      Ae is the full section area of an unwelded section, and the effective section area obtained by taking a reduced thickness ρo,hazt for the HAZ material of a welded section.
  3. For slender webs and stiffened webs, see 6.7.4 - 6.7.6.
  4. Where a shear force is combined with a torsional moment, the shear resistance VRd should be reduced as specified in 6.2.7(9).

6.2.7 Torsion

6.2.7.1 Torsion without warping
  1. P For members subjected to torsion for which distortional deformations and warping torsion may be disregarded the design value of the torsional moment TEd at each cross-section shall satisfy:

    Image

    where:

    Image is the design St. Venants torsion moment resistance of the cross-section in which WT,pl is the plastic torsion modulus.

    Note 1 If the resultant force is acting through the shear centre there is no torsional moment due to that loading.

    Note 2 Formulae for the shear centre for some frequent cross-sections are given in Annex J

  2. For the calculation of the resistance TRd of hollow sections with slender cross section parts the design shear strength of the individual parts of the cross-section should be taken into account according to 6.7.4 or 6.7.5.
67
6.2.7.2 Torsion with warping
  1. For members subjected to torsion for which distortional deformations may be disregarded but not warping torsion the total torsional moment at any cross-section should be considered as the sum of two internal effects:

    TEd = Tt,Ed + Tw,Ed     (6.33)

    where:

    Tt,Ed is the internal St. Venants torsion moment;
    Tw,Ed is the internal warping torsion moment.
  2. The values of Tt,Ed and Tw,Ed at any cross-section may be determined from TEd by elastic analysis, taking account of the section properties of the member, the condition of restraint at the supports and the distribution of the actions along the member,

    NOTE No expression for resistance TRd can be given in this case

  3. The following stresses due to torsion should be taken into account:

    NOTE Cross section constants are given in Annex J.

  4. For elastic resistance the yield criterion in 6.2.1(5) may be applied.
  5. For determining the moment resistance of a cross-section due to bending and torsion only, torsion effects BEd should be derived from elastic analysis, see (3).
  6. As a simplification, in the case of a member with open cross section, such as I or H, it may be assumed that the effect of St. Venant torsion moment can be neglected.
6.2.7.3 Combined shear force and torsional moment
  1. P For combined shear force and torsional moment the shear force resistance accounting for torsional effects shall be reduced from VRd to VT,Rd and the design shear force shall satisfy:

    Image

    in which VT,Rd may be derived as follows:

6.2.8 Bending and shear

  1. Where a shear force is present allowance should be made for its effect on the moment resistance.
  2. If the shear force VEd is less than half the shear resistance VRd its effect on the moment resistance may be neglected except where shear buckling reduces the section resistance, see 6.7.6.
  3. Otherwise the reduced moment resistance should be taken as the design resistance of the cross-section, calculated using a reduced strength

    fo,V = fo (1 − (2VEd / VRd − 1)2)     (6.38)

    where VRd is obtained from 6.2.6.

  4. In the case of an equal-flanged I-section classified as class 1 or 2 in bending, the resulting value of the reduced moment resistance Mv,Rd is:

    Image

    where h is the total depth of the section and hw is the web depth between inside flanges.

  5. In the case of an equal-flanged I-section classified as class 3 in bending, the resulting value of Mv,Rd is given by expression (6.39) but with the denominator 4 in the second term replaced by 6:
  6. Image For sections classified as class 4 in bending or affected by HAZ softening, see 6.2.5.
  7. Where torsion is present VRd in expression (6.38) is replaced by VT,Rd , see 6.2.7, but fo, V = fo for VEd ≤ 0,5VT,Rd
  8. For the interaction of bending, shear force and transverse loads see 6.7.6. Image

6.2.9 Bending and axial force

6.2.9.1 Open cross-sections
  1. For doubly symmetric cross-sections (except solid sections, see 6.2.9.2) the following two criterions should be satisfied:

    Image

    Image

    where:

    η0 = 1,0 or may alternatively be taken as Image but 1 ≤ η0 ≤ 2     (6.42a)

    69

    γ0 = 1,0 or may alternatively be taken as Image but 1 ≤ γ0 ≤ 1,56     (6.42b)

    ξ0 = 1,0 or may alternatively be taken as Image but 1 ≤ ξ0 ≤ 1,56     (6.42c)

    NEd is the design values of the axial compression or tension force

    My,Ed and Mz,Ed are the bending moments about the y-y and z-z axis

    NRd = Aeff fo / γM1, see 6.2.4

    My,Rd = αyWy,el fo / γM1

    Mz,Rd = αzWz,el fo / γM1

    αy, αz are the shape factors for bending about the y and z axis, with allowance for local buckling and HAZ softening from longitudinal welds, see 6.2.5.

    ω0 = 1 for sections without localized welds or holes. Otherwise, see 6.2.9.3.

    NOTE For classification of cross section, see 6.3.3(4).

  2. Criterion (6.41) may also be used for mono-symmetrical cross-sections with Image (but 1 ≤ η0 ≤ 2,0) and γ0 = ξ0 = 1, where αy = max (αy1, αy2), see Figure 6.10, if the axial force and the bending moment give stresses with the same sign in the larger flange and αy = min (αy1, αy2) if the axial force and the bending moment give stresses with the same sign in the smaller flange.

    Figure 6.10 - Shape factor for a mono-symmetrical class 1 or 2 cross-section

    Figure 6.10 - Shape factor for a mono-symmetrical class 1 or 2 cross-section

6.2.9.2 Hollow sections and solid cross-sections
  1. Hollow sections and solid cross-sections should satisfy the following criterion:

    Image

    where ψ = 1,3 for hollow sections and ψ = 2 for solid cross-sections. Alternatively ψ may be taken as αyαz but 1 ≤ ψ ≤ 1,3 for hollow sections and 1 ≤ ψ ≤ 2 for solid cross-sections.

6.2.9.3 Members containing localized welds
  1. If a section is affected by HAZ softening with a specified location along the length and if the softening does not extend longitudinally a distance greater than the least width of the member, then the limiting stress should be taken as the design ultimate strength ρu,haz fu / γM2 of the reduced strength material.

    ωo = (ρu,haz fu / γM2) / (fo / γM1)     (6.44)

    NOTE This includes HAZ effects due to the welding of temporary attachments.

  2. If the softening Image extends Image longitudinally a distance greater than the least width of the member the limiting stress should be taken as the strength ρo,haz fo for overall yielding of the reduced strength material, thus

    ωo = ρo,haz     (6.45)

70

6.2.10 Bending, shear and axial force

  1. Where shear and axial force are present, allowance should be made for the effect of both shear force and axial force on the resistance of the moment.
  2. Provided that the design value of the shear force VEd does not exceed 50% of the shear resistance VRd no reduction of the resistances defined for bending and axial force in 6.2.9 need be made, except where shear buckling reduces the section resistance, see 6.7.6.
  3. Where VEd exceeds 50% of VRd the design resistance of the cross-section to combinations of moment and axial force should be reduced using a reduced yield strength

    (1 – ρ) fo     (6.46)

    for the shear area where:

    ρ = (2VEd/ VRd – 1)2     (6.47)

    and VRd is obtained from 6.2.6(2).

    NOTE Instead of applying reduced yield strength, the calculation may also be performed applying an effective plate thickness.

6.2.11 Web bearing

  1. This clause concerns the design of webs subjected to localised forces caused by concentrated loads or reactions applied to a beam. For un-stiffened and longitudinally stiffened web this subject is covered in 6.7.5.
  2. For transversely stiffened web, the bearing stiffener, if fitted, should be of class 1 or 2 section. It may be conservatively designed on the assumption that it resists the entire bearing force, unaided by the web, the stiffener being checked as a strut (see 6.3.1) for out-of-plane column buckling and local squashing, with lateral bending effects allowed for if necessary (see 6.3.2). See also 6.7.8.

6.3 Buckling resistance of members

6.3.1 Members in compression

  1. Members subject to axial compression may fail in one of three ways:
    a) flexural (see 6.3.1.1 to 6.3.1.3)
    b) torsional or flexural torsional (see 6.3.1.1 and 6.3.1.4)
    c) local squashing (see 6.2.4)

    NOTE Check a) should always be made. Check b) is generally necessary but may be waived in some cases. Check c) is only necessary for struts of low slenderness that are significantly weakened locally by holes or welding.

6.3.1.1 Buckling Resistance
  1. P A compression member shall be verified against both flexural and torsional or torsional-flexural buckling as follows:

    Image

    where:

    NEd is the design value of the compression force
    Nb,Rd design buckling resistance of the compression member
  2. The design buckling resistance of a compression member Nb,Rd should be taken as: 71

    Nb,Rd = Kχ Aeff fo / γM1     (6.49)

    where:

    χ is the reduction factor for the relevant buckling mode as given in 6.3.1.2.
    K is a factor to allow for the weakening effects of welding. For longitudinally welded member K is given in Table 6.5 for flexural buckling and K = 1 for torsional and torsional-flexural buckling. In case of transversally welded member K = ωx Image according to 6.3.3.3. k = 1 if there are no welds. Image
    Aeff is the effective area allowing for local buckling for class 4 cross-section. For torsional and torsional-flexural buckling see Table 6.7.
    Aeff = A for class 1, 2 or 3 cross-section
6.3.1.2 Buckling curves
  1. For axial compression in members the value of χ for the appropriate value of Image should be determined from the relevant buckling curve according to:

    Image

    where:

    Image

    α is an imperfection factor
    Image is the limit of the horizontal plateau
    Ncr is the elastic critical force for the relevant buckling mode based on the gross cross-sectional properties

    Image NOTE In a member with a local weld the slenderness parameter Image according to 6.3.3.3 (3)should be used for the section with the weld Image

  2. The imperfection factor α and limit of horizontal plateau Image corresponding to appropriate buckling curve should be obtained from Table 6.6 for flexural buckling and Table 6.7 for torsional or torsional-flexural buckling.
  3. Values of the reduction factor χ for the appropriate relative slenderness Image may be obtained from Figure 6.11 for flexural buckling and Figure 6.12 for torsional or torsional-flexural buckling.
  4. For slenderness Image or for Image the buckling effects may be ignored and only cross-sectional check apply.
    Table 6.5 - Values of K factor for member with longitudinal welds
    Class A material according to Table 3.2 Class B material according to Table 3.2
    Image
    with A1 = AAhaz (1 − ρo,haz)
    in which Ahaz = area of HAZ
    k = 1 if Image ≤ 0,2
    Image
    if Image > 0,2
    Table 6.6 - Values of α and Image for flexural buckling
    Material buckling class according to Table 3.2 α Image
    Class A 0,20 0,10
    Class b 0,32 0,00
    72

    Figure 6.11 - Reduction factor χ for flexural buckling

    Figure 6.11 - Reduction factor χ for flexural buckling

    Table 6.7 - Values of α, Image and Aeff for torsional and torsional-flexural buckling
    Cross-section α Image Aeff
    General1)

    Composed entirely of radiating outstands 2)
    0,35

    0,20
    0,4

    0,6
    Aeff 1)

    A 2)
    1. For sections containing reinforced outstands such that mode 1 would be critical in terms of local buckling (see 6.1.4.3(2)), the member should be regarded as “general” and Aeff determined allowing for either of both local buckling and HAZ material.
    2. For sections such as angles, tees and cruciforms, composed entirely of radiating outstands, local and torsional buckling are closely related. When determining Aeff allowance should be made, where appropriate, for the presence of HAZ material but no reduction should be made for local buckling i,e. ρc = 1.

    Figure 6.12 - Reduction factor χ for torsional and torsional-flexural buckling

    Figure 6.12 - Reduction factor χ for torsional and torsional-flexural buckling

6.3.1.3 Slenderness for flexural buckling
  1. Image The relative slenderness Image is given by:

    Image

    where:

    Lcr is the buckling length in the buckling plane considered Image 73
    Image i is the radius of gyration about the relevant axis, determined using the properties of gross cross-section.
  2. The buckling length Lcr. should be taken as kL, where L is the length between points of lateral support; for a cantilever, L is its length. The value of k, the buckling length factor for members, should be assessed from knowledge of the end conditions. Unless more accurate analysis is carried out, Table 6.8 should be used.

    NOTE The buckling length factors k are increased compared to the theoretical value for fixed ends to allow for various deformations in the connection between different structural parts.

    Table 6.8 - Buckling length factor k for members
    End conditions k
    1. Held in position and restrained in direction at both ends 0,7
    2. Held in position at both ends and restrained in direction at one end 0,85
    3. Held in position at both ends, but not restrained in direction 1,0
    4. Held in position at one end, and restrained in direction at both ends 1,25
    5. Held in position and restrained in direction at one end, and partially restrained in direction but not held in position at the other end 1,5
    6. Held in position and restrained in direction at one end, but not held in position or restrained at the other end 2,1 Image
6.3.1.4 Slenderness for torsional and torsional-flexural buckling
  1. For members with open cross-sections account should be taken of the possibility that the resistance of the member to either torsional or torsional-flexural buckling could be less than its resistance to flexural buckling

    NOTE The possibility of torsional and torsional-flexural buckling may be ignored for the following:

    1. hollow sections
    2. doubly symmetrical I-sections
    3. sections composed entirely of radiating outstands, e.g. angles, tees, cruciforms, that are classified as class 1 and 2 in accordance with 6.1.4
  2. The relative slenderness Image for torsional and torsional-flexural buckling should be taken as:

    Image

    where:

    Aeff is the cross-section area according to Table 6.7
    Ncr is the elastic critical load for torsional buckling, allowing for interaction with flexural buckling if necessary (torsional-flexural buckling)

    NOTE Values of Ncr and Image are given in Annex I.

6.3.1.5 Eccentrically connected single - bay struts
  1. Providing the end attachment prevents rotation in the plane of the connected part and no deliberate bending is applied, the following types of eccentrically connected strut may be designed using a simplified approach. This represents an alternative to the general method for combined bending and compression of 6.3.3:
    1. single angle connected through one leg only;
    2. back to back angles connected to one side of a gusset plate;
    3. single channel connected by its web only;
    4. Image single Image tee connected by its flange only. 74
  2. Where flexural buckling using 6.3.1.1 out of the plane of the attached part(s) is checked, the eccentricity of loading should be ignored and the value of Nb,Rd should be taken as 40% of the value for centroidal loading.
  3. The value for a) should be that about the axis parallel to the connected part(s). For torsional buckling no change to the method of 6.3.1.1 and 6.3.1.4 is necessary.

6.3.2 Members in bending

  1. The following resistances should normally be checked:
    1. bending (see 6.2.5), including, where appropriate, allowance for coincident shear (see 6.2.8);
    2. shear (see 6.2.6 and 6.2.8);
    3. web bearing (see 6.7.5);
    4. lateral torsional buckling (see 6.3.2.1).
  2. Due account should be taken of the class of cross-section (see 6.1.4), the presence of any heat affected zones (see 6.1.5) and the need to allow for the presence of holes (see 6.2.5).
  3. For members required to resist bending combined with axial load reference is made to 6.3.3.
  4. Biaxial bending combined with axial load is covered under 6.2.9 and 6.3.3. If there is no axial force the term with N Ed should be deleted.
6.3.2.1 Buckling resistance

NOTE Lateral torsional buckling need not be checked in any of the following circumstances:

  1. bending takes place about the minor principal axis and at the same time the load application is not over the shear centre;
  2. the member is fully restrained against lateral movement throughout its length;
  3. the relative slenderness Image (see 6.3.2.3) between points of effective lateral restraint is less than 0,4.
  1. P A laterally unrestrained member subject to Image major Image axis bending shall be verified against lateral-torsional buckling as follows:

    Image

    where:

    MEd is the design value of the bending moment
    Mb,Rd is the design buckling resistance moment.
  2. The design buckling resistance moment of laterally un-restrained member should be taken as:

    Mb,Rd = χLT αWel,y fo / γM1     (6.55)

    where:

    Wel,y is the elastic section modulus of the gross section, without reduction for HAZ softening, local buckling or holes.
    α is taken from Table 6.4 subject to the limitation αWpl,y/Wel,y.
    χLT is the reduction factor for lateral torsional buckling (see 6.3.2.2).
6.3.2.2 Reduction factor for lateral torsional buckling
  1. The reduction factor for lateral torsional buckling χLT for the appropriate relative slenderness Image should be determined from: 75

    Image

    where

    Image
    αLT is an imperfection factor
    Image is the relative slenderness
    Image is the limit of the horizontal plateau
    Mcr is the elastic critical moment for lateral-torsional buckling.
  2. The value of αLT and Image should be taken as:

    αLT = 0,10 and Image = 0,6 for class 1 and 2 cross-sections

    αLT = 0,20 and Image = 0,4 for the class 3 and 4 cross-sections.

  3. Values of the reduction factor χLT for the appropriate relative slenderness Image may be obtained from Figure 6.13
  4. For slenderness Image or for M Ed Image the buckling effects may be ignored and only cross-sectional check apply.

    Figure 6.13 - Reduction factor for lateral-torsional buckling

    Figure 6.13 - Reduction factor for lateral-torsional buckling

6.3.2.3 Slenderness
  1. The relative slenderness parameter Image should be determined from

    Image

    where:

    α is taken from Table 6.4 subject to the limitation αWpl,y / Wel,y.
    Mcr is the elastic critical moment for lateral-torsional buckling.
  2. Mcr is based on gross cross sectional properties and takes into account the loading conditions, the real moment distribution and the lateral restraints.

    NOTE Expressions for Mcr for certain sections and boundary conditions are given in Annex I.1 and approximate values of Image for certain I-sections and channels are given in Annex 1.2.

76
6.3.2.4 Effective Lateral Restraints
  1. Bracing systems providing lateral restraint should be designed according to 5.3.3.

    NOTE Where a series of two or more parallel members require lateral restraint, it is not adequate merely to tie the compression flanges together so that they become mutually dependent. Adequate restraint will be provided only by anchoring the ties to an independent robust support, or by providing a triangulated bracing system. If the number of parallel members exceeds three, it is sufficient for the restraint system to be designed to resist the sum of the lateral forces derived from the three largest compressive forces only.

6.3.3 Members in bending and axial compression

  1. Unless second order analysis is carried out using the imperfections as given in 5.3.2, the stability of uniform members should be checked as given in the following clause, where a distinction is made for:
  2. Two checks are in general needed for members that are susceptible to torsional deformations:
  3. For calculation of the resistance NRd, My,Rd and Mz,Rd due account of the presence of HAZ-softening from longitudinal welds should be taken. (See 6.2.4 and 6.2.5). The presence of localized HAZ-softening from transverse welds and the presence of holes should be taken care of according to 6.3.3.3 and 6.3.3.4 respectively.
  4. All quantities in the interaction criterion should be taken as positive.

    NOTE 1 Classification of cross-sections for members with combined bending and axial forces is made for the loading components separately according to 6.1.4. No classification is made for the combined state of stress.

    NOTE 2 A cross-section can belong to different classes for axial force, major axis bending and minor axis bending. The combined state of stress is taken care of in the interaction expressions. These interaction expressions can be used for all classes of cross-section. The influence of local buckling and yielding on the resistance for combined loading is taken care of by the capacities in the denominators and the exponents, which are functions of the slenderness of the cross-section.

    NOTE 3 Section check is included in the check of flexural and lateral-torsional buckling if the methods in 6.3.3.1 and 6.3.3.5 are used.

6.3.3.1 Flexural buckling
  1. For a member with open doubly symmetric cross-section (solid sections, see (2)), one of the following criterions should be satisfied:
  2. For solid cross-sections criterion (6.60) may be used with the exponents taken as 0,8 or

    ηc = 2χ     but ηc ≥ 0,8     (6.61d)

    ξc = l,56 χ     but ξc ≥ 0,8     (6.61e)

  3. Hollow cross-sections and tubes should satisfy the following criterion:

    Image

    where ψc = 0,8 or may alternatively be taken as l,3 χy or l,3 χz depending on direction of buckling, but ψc ≥ 0,8. χmin = min(χy,χz)

  4. For other open monosymmetrical cross sections, bending about either axis, expression (6.59) may be used with ξyc, My,Ed, My,Rd and χy replaced by ξzc, M z,Ed, Mz,Rd and χz
  5. The notations in the criterions (6.59) to (6.62) are:

    NEd is the design value of the axial compressive force

    My,Ed, Mz,Ed are the design values of bending moment about the y- and z-axis. The moments are calculated according to first order theory

    NRd = A fo / γM1 or Aeff fo/ γM1 for class 4 cross-sections. For members with longitudinal welds but without localized welds NRd = k A fo / γM1 or k Aeff fo / γM1, see 6.3.1.

    χy and χz are the reduction factor for buckling in the z-x plane and the y-x plane, respectively

    M y,Rd = αy Wy fo / γM1 bending moment capacity about the y-axis

    M z,Rd = αz Wz fo / γM1 bending moment capacity about the z-axis

    αy, αz are the shape factors, but αy and az should not be taken larger than 1,25. See 6.2.5 and 6.2.9.1(1)

6.3.3.2 Lateral-torsional buckling
  1. Members with open cross-section symmetrical about major axis, centrally symmetric or doubly symmetric cross-section, the following criterion should satisfy:

    Image

    where:

    NEd design value of axial compression force
    My,Ed is bending moment about the y-axis. In the case of beam-columns with hinged ends and in the case of members in non-sway frames, My,Ed is moment of the first order. For members in frames free to sway, My,Ed is bending moment according to second order theory.
    Mz,Ed bending moment about the z-axis. Mz,Ed is bending moment according to first order theory
    NRd = Afo / γM1 or Aeff fo / γM1 for class cross-sections. For members with longitudinal welds but without localized welds NRd = KAfo / γM1 or KAeff fo / γM1, see 6.3.1. 78
    χz is the reduction factor for buckling when one or both flanges deflects laterally (buckling in the x-y plane or lateral-torsional buckling) based on (6.68a) in section with localized weld
    My,Rd = αy Wy,el fo / γM1 = bending moment capacity for y-axis bending
    Mz,Rd = αz Wz,el fo / γM1 = bending moment capacity for z-axis bending
    αy, αz are the shape factors but αy and αz should not be taken larger than l ,25. See 6.2.5 and 6.2.9.1(1)
    χLT is the reduction factor for lateral-torsional buckling
    ηc = 0,8 or alternatively η0 χz but ηc ≥ 0,8
    γc = γ0
    ξzc = 0,8 or alternatively ξ0 χz but ξzc ≥ 0,8
    where η0, γ0 and ξ0 are defined according to the expression in 6.2.9.1.
    ωx, ω0 and ωxLT = HAZ-softening factors, see 6.3.3.3 or factors for design section, see 6.3.3.5.
  2. The criterion for flexural buckling, see 6.3.3.1, should also be satisfied.
6.3.3.3 Members containing localized welds
  1. The value of ωx, ω0 and ωxLT for a member subject to HAZ softening, should generally be based on the ultimate strength of the HAZ softened material. It could be referred to the most unfavourable section in the bay considered. If such softening occurs only locally along the length, then ωx, ω0 and ωxLT in the expressions in 6.3.3.1 and 6.3.3.2 are:

    Image

    Where ρu,haz is the reduction factor for the heat affected material according to 6.1.6.2.

  2. However, if HAZ softening occurs close to the ends of the bay, or close to points of contra flexure only, ωx and ωxLT may be increased in considering flexural and lateral-torsional buckling, provided that such softening does not extend a distance along the member greater than the least width (e.g. flange width) of the section.

    Image

    Image

    Image

    where:

    χ = χy or χz depending on buckling direction
    χLT is the reduction factor for lateral-torsional buckling of the beam-column in bending only
    xs is the distance from the localized weld to a support or point of contra flexure for the deflection curve for elastic buckling of axial force only, compare Figure 6.14.
    lc is the buckling length.
  3. Calculation of χ (χy or χz) and χLT the section with the localized weld should be based on the ultimate strength of the heat affected material for the relative slenderness parameters

    Image

    79

    Image

  4. If the length of the softening region is larger than the least width (e.g. flange width) of the section, then the factor ρu,haz for local failure in the expressions for ωx , ωxLT , Image should be replaced by the factor ρo,haz for overall yielding.
  5. If the localized softening region covers a part of the cross-section (e.g. one flange) then the whole cross-section is supposed to be softened.
6.3.3.4 Members containing localized reduction of cross-section
  1. Members containing localized reduction of cross-section, e.g. bolt holes or flange cut-outs, should be checked according to 6.3.3.3 by replacing ρu,haz in ωx and ωxLT with Anet / Ag where Anet is net section area, with reduction of holes and Ag gross section area.
6.3.3.5 Unequal end moments and/or transverse loads
  1. For members subjected to combined axial force and unequal end moments and/or transverse loads, different sections along the beam-column should be checked. The actual bending moment in the studied section is used in the interaction expressions. ωx and ωxLT should be:

    Image

    Image

    where xs is the distance from the studied section to a simple support or point of contra flexure of the deflection curve for elastic buckling of axial force only, see Figure 6.14.

  2. Image For end moments MEd,1 > MEd,2 only, the distance xs can be calculated from

    Image

    Figure 6.14 - Buckling length lc and definition of x s (= x A or x B)

    Figure 6.14 - Buckling length lc and definition of xs (= xA or xB) Image

6.4 Uniform built-up members

6.4.1 General

  1. Uniform built-up compression members with hinged ends that are laterally supported should be designed with the following model, see Figure 6.15. 80
    1. The member may be considered as a column with a bow imperfection e0 = L / 500
    2. The elastic deformations of lacings or battenings, see Figure 6.15, may be considered by continuous (smeared) shear stiffness Sv of the column.

      NOTE For other end conditions appropriate modifications may be performed.

  2. The model of a uniform built-up compression member applies if:
    1. the lacings or battenings consist of equal modules with parallel chords;
    2. the minimum number of modules in a member is three.

      NOTE This assumption allows the structure to be regular and smearing the discrete structure to a continuum.

  3. The design procedure is applicable to built-up members with lacings in two directions, see Figure 6.16.
  4. The chords may be solid members or may themselves be laced or battened in the perpendicular plane.

    Figure 6.15 - Uniform built-up columns with lacings and battenings

    Figure 6.15 - Uniform built-up columns with lacings and battenings

    Figure 6.16 - Lacings on four sides and buckling length LC h of chords

    Figure 6.16 - Lacings on four sides and buckling length Lch of chords

  5. Checks should be performed for chords using the design chord forces Nch,Ed from compression forces NEd and moments MEd at mid span of the built-up member.81
  6. For a member with two identical chords the design force Nch,Ed should be determined from:

    Image

    where:

    Image

    Ncr = π2 EIeff / L2 is the critical force of the effective built-up member
    NEd is the design value of the compression force to the built-up member
    MEd is the design value of the maximum moment in the middle of the built-up member considering second order effects
    Image is the design value of the maximum moment in the middle of the built-up member without second order effects
    h0 is the distance between the centroids of chords
    Ach is the cross-sectional area of one chord
    Ieff is the effective second moment of area of the built-up member, see 6.4.2 and 6.4.3
    Sv is the shear stiffness of the lacings or battened panel, see 6.4.2 and 6.4.3
  7. The checks for the lacings of laced built-up members or for the frame moments and shear forces of the battened panels of battened built-up members should be performed for the end panel taking account of the shear force in the built-up member:

    Image

6.4.2 Laced compression members

6.4.2.1 Resistance of components of laced compression members
  1. The chords and diagonal lacings subject to compression should be designed for buckling.

    NOTE Secondary moments may be neglected.

  2. P For chords the buckling verification shall be performed as follows:

    Image

    where:

    Nch,Ed is the design compression force in the chord at mid-length of the built-up member according to 6.4.1(6)

    Nb,Rd is the design value of the buckling resistance of the chord taking the buckling length Lch from Figure 6.16.

  3. The shear stiffness Sy of the lacings should be taken from Figure 6.17.
  4. The effective second order moment of area of laced built-up members may be taken from (6.77) with μ = 0. Then :

    Image

    82

    Figure 6.17 - Shear stiffness of lacings of built-up members

    Figure 6.17 - Shear stiffness of lacings of built-up members

6.4.2.2 Constructional details
  1. Single lacing system in opposite faces of the built-up members with two parallel laced planes should be corresponding systems as shown in Figure 6.18(a), arranged so that one is shadow of the other.
  2. If the single lacing systems on opposite faces of a built-up member with two parallel laced planes are mutually opposed in direction as shown in Figure 6.18(b), the resulting torsional effects in the member should be taken into account.
  3. Tie panels should be provided at the ends of lacing systems, at points where the lacing is interrupted and at joints with other members.

    Figure 6.18 - Single lacing system on opposite faces of a built-up member with two parallel laced planes

    Figure 6.18 - Single lacing system on opposite faces of a built-up member with two parallel laced planes

6.4.3 Battened compression members

6.4.3.1 Resistance of components of battened compression members
  1. The chords and the battens and their joints to the chords should be checked for the actual moments and forces in an end panel and at mid-span as indicated in Figure 6.19.

    NOTE For simplicity the maximum chord forces Nch,Ed may he combined with the maximum shear force VEd.

    83

    Figure 6.19 - Moments and forces in an end panel of a battened built-up members

    Figure 6.19 - Moments and forces in an end panel of a battened built-up members

  2. The shear stiffness Sv should be taken as follows:

    Image

  3. The effective second moment of area of battened built-up members may be taken as:

    Image

    where:

    Ich is in plane second moment of area of one chord
    Ib is in plane second moment of area of one batten
    μ is efficiency factor from Table 6.9
    Table 6.9 - Efficiency factor μ
    criterion efficiency factor μ
    λ ≥ 150 0
    75 < λ < 150 μ = 2 − λ / 75
    λ ≤ 150 1,0
    Where Image
84
6.4.3.2 Constructional details
  1. Battens should be provided at each end of a member.
  2. Where parallel planes of battens are provided, the battens in each plane should be arranged opposite each other.
  3. Battens should also be provided at intermediate points where loads are applied or lateral restraint is supplied.

6.4.4 Closely spaced built-up members

  1. Built-up compression members with chords in contact or closely spaced and connected through packing plates, see Figure 6.20, or star battened angle members connected by pairs of battens in two perpendicular planes, see Figure 6.21 should be checked for buckling as a single integral member ignoring the effect of shear stiffness (Sv = ∞), if the conditions in Table 6.10 are met.

    Figure 6.20 - Closely spaced built-up members

    Figure 6.20 - Closely spaced built-up members

    Table 6.10 - Maximum spacing for interconnection in closely spaced built-up or star battened angle members
    Type of built-up member Maximum spacing between interconnection *)
    Members according to Figure 6.20 in contact or connected through packing by bolts or Welds 15imin
    Members according to Figure 6.21 in contact or connected by pair of battens and by bolts of welds 70imin

    *) centre-to-centre distance of interconnections

    imin is the minimum radius of gyration of one chord or one angle

  2. The shear forces to be transmitted by the battens should be determined from 6.4.3.1(1).
  3. In the case of unequal-leg angles, see Figure 6.21, buckling about the y-y axis may be verified with:

    iy ≅ 0,87i0     (6.78)

    where i0 is the radius of gyration of the built-up member about the 0-0 axis.

    Figure 6.21 - Star-battened angle members

    Figure 6.21 - Star-battened angle members

6.5 Un-stiffened plates under in-plane loading

6.5.1 General

  1. In certain types of structure un-stiffened plates can exist as separate components under direct stress, shear stress, or a combination of the two. The plates are attached to the supporting structure by welding, riveting, 85 bolting or bonding, and the form of attachment can affect the boundary conditions. Thin plates must be checked for the ultimate limit states of bending under lateral loading, buckling under edge stresses in the plane of the plate, and for combinations of bending and buckling. The design rules given in this section only refer to rectangular plates. For slender beam webs, see 6.7.

Figure 6.22 - Unstiffened plates

Figure 6.22 - Unstiffened plates Image

6.5.2 Resistance under uniform compression

  1. A rectangular plate under uniform end compression is shown in Figure 6.22. The length of the plate in the direction of compression = a, and the width across the plate = b. The thickness is assumed to be uniform, and equal to t. The plate can be supported on all four edges, where the support conditions are hinged, elastically restrained or fixed, or it can be free along one longitudinal edge.
  2. The susceptibility of the unstiffened plate to buckling is defined by the parameter β, where β = b/t. The classification of the cross-section is carried out in the same way as that described in 6.1.4, where plates with longitudinal edges simply supported, elastically restrained, or completely fixed are taken to correspond to “internal parts”, and plates with one longitudinal edge free correspond to “outstands”. Thus
    ββ2 class 1 or 2
    β2ββ3 class 3
    β3 < β class 4

    where values of β2 and β3 are given in Table 6.2.

  3. P The design value of the compression force NEd shall satisfy

    Image

    where NRd is the lesser of

    No,Rd = Aeff f o / γM1 (overall yielding and local buckling) and (6.80)
    N u,Rd = Anet f u / γ M2 (local failure) (6.81)

    where:

    Aeff is the effective area of the cross-section taking account of local buckling for class 4 cross-sections and HAZ softening of longitudinal welds
    Anet is the area of the least favourable cross-section taking account of unfilled holes and HAZ softening of transverse or longitudinal welds if necessary
  4. Aeff for class 4 cross-section is obtained by taking a reduced thickness to allow for buckling as well as for HAZ softening, but with the presence of holes ignored. Aeff is generally based on the least favourable cross-section, taking a thickness equal to the lesser of ρct and ρo,hazt in HAZ regions, and ρct elsewhere. In this check HAZ softening due to welds at the loaded edges may be ignored. 86

    The factor ρc is found from the more favourable of the following treatments:

    1. Calculate ρc from 6.1.5(2) or read from Figure 6.5, using the internal part expressions for plates that are simply supported, elastically restrained, or fixed along longitudinal edges, and the outstand part expressions for plates with one longitudinal free edge.
    2. Take ρc = χ, where χ is the column buckling reduction factor from 6.3.1. In calculating χ take a slenderness parameter Image Image equal to 3,5 a/t, which corresponds to simple support at the loaded edges. For restrained loaded edges a lower value of Image Image can be used at the discretion of the designer.

6.5.3 Resistance under in-plane moment

  1. If a pure in-plane moment acts on the ends (width = b) of a rectangular unstiffened plate (see Figure 6.22) the susceptibility to buckling is defined by the parameter β, where β = 0,40 b/t. The classification of the cross-section is carried out in the same way as described in section 6.5.2.
  2. P The design value of the bending moment MEd shall satisfy

    Image

    where the design bending moment resistance MRd is the lesser of Mo,Rd and Image Mu,Rd Image according to (3) and (4).

  3. The design bending moment resistance Mo,Rd for overall yielding and local buckling is as follows:

    Image Class 1 and 2 cross-sections Image

    Mo,Rd = W p1 f o / γ M1     (6.83)

    Class 3 cross-sections

    Image

    Class 4 cross-sections

    Mo,Rd = W eff f o / γ M1     (6.85)

    where

    W pl and Wel are the plastic and elastic moduli for the gross cross-section or a reduced cross-section to allow for HAZ softening from longitudinal welds, but with the presence of holes ignored
    W eff is the elastic modulus for the effective cross-section obtained by taking a reduced thickness to allow for buckling as well as HAZ softening from longitudinal welds if required, but with the presence of holes ignored. See 6.2.5.2.
    β is the slenderness factor for the most critical part in the section
    β2 and β3 are the class 2 and class 3 limiting values of β for that part
    Image text deleted Image
  4. The design bending moment resistance Mu,Rd for local failure at sections with holes or transverse welds is:

    Mu,Rd = Wnet f u / γM2     (6.86)

    where

    Wnet is the section modulus allowing for holes and taking a reduced thickness ρu,hazt in any region affected by HAZ softening. See 6.2.5.1 (2).

87

6.5.4 Resistance under transverse or longitudinal stress gradient

  1. Image If the applied actions at the end of a rectangular plate result in a transverse stress gradient, the stresses are transferred into an axial force and a bending moment treated separately according to 6.5.2 and 6.5.3. The load combination is then treated as in 6.5.6. Image
  2. If the applied compression or in-plane bending moment varies longitudinally along the plate (i.e. in the direction of the dimension a), the design moment resistance for class 1, 2 or 3 cross-sections at any cross-section should not be less than the action arising at that section under factored loading. For class 4 cross-sections the yielding check Image should be performed Image at every cross-section, but for the buckling check it is permissible to compare the design compressive or moment resistance with the action arising at a distance from the more heavily loaded end of the plate equal to 0,4 times the elastic plate buckling half wavelength.

6.5.5 Resistance under shear

  1. A rectangular plate under uniform shear forces is shown in Figure 6.22. The thickness is assumed to be uniform and the support conditions along all four edges are either simply supported, elastically restrained or fixed.
  2. The susceptibility to shear buckling is defined by the parameter β, where β = b/t and b is the shorter of the side dimensions. For all edge conditions the plate in shear is classified as slender or non-slender as follows:
    β ≤ 39ε non-slender plate
    β > 39ε slender plate

    where:

    Image

  3. The design value of the shear force VEd at each cross-section should satisfy

    VEdVRd     (6.87)

    where VRd is the design shear resistance of the cross-section based on the least favourable cross-section as follows.

    1. non-slender plate (β ≤ 39ε):

      Image

      where Anet is the net effective area allowing for holes, and taking a reduced thickness Image ρo,hazt Image in any area affected by HAZ softening. If the HAZ extends around the entire perimeter of the plate the reduced thickness is assumed to extend over the entire cross-section. In allowing for holes, the presence of small holes may be ignored if their total cross-sectional area is less than 20% of the total cross-sectional area bt.

    2. slender plate (β > 39ε):

      Values of VRd for both yielding and buckling should be checked. For the yielding check use a) above for non-slender plates. For the buckling check:

      Image

      where:

      Image but not more than ImageImage and v1 ≤ 1,0 Image

      kτ = 5,34 + 4,00(b/a)2 if a /b ≥ 1

      88

      kτ = 4,00 + 5,34(b/a)2 if a/b < 1

      NOTE These expressions do not take advantage of tension field action, but if it is known that the edge supports for the plate are capable of sustaining a tension field, the treatment given in 6.7.3 can be employed.

6.5.6 Resistance under combined action

  1. A plate subjected to combined axial force and in-plane moment under factored loading should be given a separate classification for the separate actions in accordance with 6.5.2. In so doing, the value of β should be based on the pattern of edge stress produced if the force (NEd) and the moment (MEd) act separately.
  2. If the plate is class 4, each individual resistance, Nc,Rd and Image Mo,Rd Image should be based on the specific type of action considered.
  3. If the combined action is axial force and in-plane moment, the following Image condition Image should be satisfied:

    Image

  4. ImageIf the combined action includes the effect of a coincident shear force, VEd, then VEd may be ignored if it does not exceed 0,5VRd (see 6.5.8). If VEd > VRd the following condition should be satisfied:

    Image

6.6 Stiffened plates under in-plane loading

6.6.1 General

  1. The following rules concern plates, supported on all four edges and reinforced with one or two, central or eccentric longitudinal stiffeners, or three or more equally spaced longitudinal stiffeners or corrugations (see Figure 6.23). Also general rules for orthotropic plating (Figure 6.23(c), (d) and (e) and clause 6.6.6) are given. Rules for extruded profiles with one or two open stiffeners are given in 6.1.4.3.
  2. The stiffeners may be unsupported on their whole length or else be continuous over intermediate transverse stiffeners. The dimension L should be taken as the spacing between the supports. An essential feature of the design is that the longitudinal reinforcement, but not transverse stiffening, is “sub-critical”, i.e. it can deform with the plating in an overall buckling mode.
  3. The resistance of such plating to longitudinal direct stress in the direction of the reinforcement is given in 6.6.2 to 6.6.4, and the resistance in shear is given in 6.6.5. Interaction between different effects may be allowed for in the same way as for un-stiffened plates (see 6.7.6). The treatments are valid also if the cross-section contains parts that are classified as slender. 89

    Figure 6.23 - Stiffened plates and types of stiffeners

    Figure 6.23 - Stiffened plates and types of stiffeners

  4. If the structure consists of flat plating with Image longitudinal stiffeners, the resistance to transverse direct stress may be taken the same as for an unstiffened plate. With corrugated structure it is negligible. Orthotropic plating may have considerable resistance to transverse in-plane direct stress Image.

6.6.2 Stiffened plates under uniform compression

  1. P General

    The cross-section shall be classified as compact or slender in accordance with 6.1.4, considering all the component parts before carrying out either check.

    The design value of the compression force NEd shall satisfy

    Image

    where NRd is the lesser of Nu,Rd and Nc,Rd according to (2) and (3).

  2. Yielding check

    The entire section should be checked for local squashing in the same way as for a strut (see 6.3). The design resistance Nu,Rd should be based on the net section area Anet for the least favourable cross-section, taking account of Image text deleted Image HAZ softening if necessary, and also any unfilled holes.

    N u,Rd = Anet f u / γM2     (6.92)

    90
  3. Column check

    The plating is regarded as an assemblage of identical column sub-units, each containing one centrally located stiffener or corrugation and with a width equal to the pitch Image 2a Image. The design axial resistance Nc,Rd is then taken as:

    Nc,Rd = Aeff χ f o / γM 1     (6.93)

    where:

    χ is the reduction factor for flexural buckling
    Aeff is the effective area of the cross-section of the plating allowing for local buckling and HAZ softening due to longitudinal welds. HAZ softening due to welds at the loaded edges or at transverse stiffeners may be ignored in finding Aeff. Also unfilled holes may be ignored.

    The reduction factor χ should be obtained from the appropriate column curve relevant to column buckling of the sub-unit as a simple strut out of the plane of the plating.

  4. The relative slenderness parameter Image in calculating χ is

    Image

    where

    Ncr = the elastic orthotropic buckling load based on the gross cross-section

  5. For a plate with open stiffeners:

    Image

    where c is the elastic support from the plate according to expressions (6.97), (6.98) or (6.99) and Iy is the second moment of area of Image all stiffeners and plating within the width b Image with respect to y-axes in Figure 6.23f.

  6. For a cross-section part with one central or eccentric stiffener (Figure 6.23(f)):

    Image

    where t is the thickness of the plate, b is the overall width of the plate and b1 and b2 are the width of plate parts on both sides of the stiffener.

  7. For a cross-section part with two symmetrical stiffeners located a distance b1 from the longitudinal supports (Figure 6.23(g)):

    Image

  8. For a multi-stiffened plate with open stiffeners (Figure 6.23(c), (b) (h) and (i)) with small torsional stiffness

    Image

  9. For a multi-stiffened plate with closed or partly closed stiffeners (Figure 6.23 (e) and (j))

    Ncr is the elastic orthotropic buckling load. See 6.6.6.

    91
  10. The half-wavelength in elastic buckling, used if the applied action varies in the direction of the stiffener or corrugations (see 6.6.4(3)) is

    Image

6.6.3 Stiffened plates under in-plane moment

  1. General

    Two checks should be performed, a yielding check (see 6.6.3(3)) and a column check (see 6.6.3(4)).

  2. Section classification and local buckling

    The cross-section should be classified as Classes 2, 3 and 4 (see 6.1.4) when carrying out either check. For the purpose of classifying individual parts, and also when determining effective thicknesses for slender parts, Image it should generally be assumed Image that each part is under uniform compression taking η = 1 in 6.1.4.3. However, in the case of the yielding check only, it is permissible to base η on the actual stress pattern in parts comprising the outermost region of the plating, and to repeat this value for the corresponding parts further in. This may be favourable if the number of stiffeners or corrugations is small.

  3. Yielding check

    The entire cross-section of the plating should be treated as a beam under in-plane bending (see 6.2.5). The design moment resistance MRd should be based on the least favourable cross-section, taking account of local buckling and HAZ softening if necessary, and also any holes.

  4. Column check

    The plating is regarded as an assemblage of column sub-units in the same general way as for axial compression (see 6.6.2(3)), the design moment resistance Image Mo,Rd Image being taken as follows

    Image

    where:

    Image χ is the reduction factor for flexural buckling of sub-unit
    Ieff is the second moment of area of the effective cross-section of the plating for in-plane bending
    yst is the distance from centre of plating to centre of outermost stiffener

    The reduction factor χ Image should be determined in the same way as for uniform compression (see 6.6.2(3)).

6.6.4 Longitudinal stress gradient on multi-stiffened plates

  1. General

    Cases where the applied action NEd or MEd on a multi-stiffened plate varies in the direction of the stiffeners or corrugations are described in 6.6.4(2) and 6.6.4(3).

  2. Yielding check

    The design resistance at any cross-section should be not less than the design action effect arising at that section.

    92
  3. Column check

    For the column check it is sufficient to compare the design resistance with the design action effect arising at a distance 0,4lw from the more heavily loaded end of a panel, where lw is the half wavelength in elastic buckling according to 6.6.2(10).

6.6.5 Multi-stiffened plating in shear

  1. A yielding check (see (2)) and a buckling check (see (3)) should be performed. The methods given in 6.6.5(2) and (3) are valid provided the stiffeners or corrugations, as well as the actual plating, are as follows:
    1. effectively connected to the transverse framing at either end;
    2. continuous at any transverse stiffener position.
  2. Yielding check: The design shear force resistance VRd is taken as the same as that for a flat unstiffened plate of the same overall aspect (L × b) Image text deleted Image in accordance with 6.5.5(2).
  3. Buckling check: The design shear force resistance is found from 6.8.2. In order to calculate the resistance the following values should be used (Note difference in coordinate system, x and v in Figure 6.23 are z and x in Figure 6.33):

    By = Et3 /10,9 for a flat plate with stiffeners, otherwise see 6.6.6(1)

    Image Bx = EIy / b where Iy is the second moment of area of stiffeners Image and plating within the width b about a centroidal axis parallel to the plane of the plating

    hw is the buckling length l which may be safely taken as the unsupported length L (see Figure 6.23). If L greatly exceeds b, a more favourable result may be obtained by putting Vo,cr equal to the elastic orthotropic shear buckling force. No allowance for HAZ softening needs to be made in performing the buckling check.

6.6.6 Buckling load for orthotropic plates

  1. For an orthotropic plate under uniform compression the procedure in 6.6.2 may be used. The elastic orthotropic buckling load Ncr for a simply supported orthotropic plate is given by

    Image

    Expressions for Bx, By and H for different cross-sections are given in Table 6.1 1 where the expressions Image (6.104) to (6.110) Image are given below. (Indexes x and y indicates rigidity in section x = constant and y = constant, respectively).

    Table 6.11, Case No. 2:

    Image

    where

    93

    Image

    Table 6.11, Case No. 5:

    Image

    where:

    Image

    Image

    94
    Table 6.11 - Flexural and torsional rigidity of orthotropic plates
    Case No Cross-section Bx (corresponds to EIy) By (corresponds to EIx) H
    1 Image Image Image Image
    2 Image Image Eq.(6.104) Eq.(6.105)
    3 Image Image Image Image
    4 Image Image Image Image
    5 Image Image Eq.(6.109) Eq.(6.110)
    6 Image Image 0 Image

    IL is the second moment of area of one stiffener and adjacent plating within 2a.

    It is the torsional constant of the same cross-section.

    Figure 6.24 - Cross-section notations of closed stiffener

    Figure 6.24 - Cross-section notations of closed stiffener

  2. The shear force resistance for an orthotropic plate with respect to global buckling can for ϕ ≤ 1 calculated according to 6.8.2(3) where:

    Image

    kτ = 3,25 − 0,567ϕ + 1,92ϕ2 + (1,95 + 0,1ϕ + 2,75ϕ2) ηh     (6.112)

    Image

    Bx , By and H are given in Table 6.11 and A is cross section area in smallest section for y = constant (A = Lt for cases 1, 2 and 3 in Table 6.11 and A = L(t1 + t2) for 4 and 5. Not applicable to case 6).

    95

    For originally ϕ > 1 interchange subscripts x and y and widths b and L in (6.111) and (6.113) and use A = bt.

6.7 Plate girders

6.7.1 General

  1. A plate girder is a deep beam with a tension flange, a compression flange and a web plate. The web is usually slender and may be reinforced transversally with bearing and intermediate stiffeners. It can also be reinforced by longitudinal stiffeners.
  2. Webs buckle in shear at relatively low applied loads, but considerable amount of post-buckled strength can be mobilized due to tension field action. Plate girders are sometimes constructed with transverse web reinforcement in the form of corrugations or closely-spaced transverse stiffeners.
  3. Plate girders can be subjected to combinations of moment, shear and axial loading, and to local loading on the flanges. Because of their slender proportions they may be subjected to lateral torsional buckling, unless properly supported along their length.
  4. The rules for plate girders given in this Standard are generally applicable to the side members of box girders.

    Failure modes and references to clauses with resistance expressions are given in Table 6.12.

    Table 6.12 - Buckling modes and corresponding clause with resistance expressions
    Buckling mode Clause
    Web buckling by compressive stresses 6.7.2 and 6.7.3
    Shear buckling 6.7.4 and 6.8
    Interaction between shear force and bending moment 6.7.6
    Buckling of web because of local loading on flanges 6.7.5
    Flange Induced web buckling 6.7.7
    Torsional buckling of flange (local buckling) 6.1.5
    Lateral torsional buckling 6.3.2

6.7.2 Resistance of girders under in-plane bending

  1. A yielding check and a buckling check should be made, and for webs with continuous longitudinal welds the effect of the HAZ should be investigated. The HAZ effect caused by the welding of transverse stiffeners may be neglected and small holes in the web may be ignored provided they do not occupy more than 20 % of the cross-sectional area of the web. The web depth between flanges is hw and the distance between the weld toes of the flanges is bw.
  2. P For the yielding check, the design value of the moment, MEd at each cross-section shall satisfy

    MEdMo,Rd     (6.115)

    where Mo,Rd, for any class cross-section, is the design moment resistance of the cross-section that would apply if the section were designated class 3. Thus,

    Mo,Rd = Wnet fo / γM1     (6.116)

    where Wnet is the elastic modulus allowing for holes and taking a reduced thickness ρo,hazt in regions adjacent to the flanges which might be affected by HAZ softening (see 6.1.6.2).

  3. In applying the buckling check it is assumed that transverse stiffeners comply with the requirements of the effective stiffener section given in 6.7.8. It is also assumed that the spacing between adjacent transverse stiffeners is greater than half the clear depth of the web between flange plates. If this is not the case, refer to 6.8 for corrugated or closely stiffened webs. 96
  4. For each bay of the girder of length a between transverse stiffeners, the moment arising under design load at a distance 0,4 a from the more heavily stressed end should not exceed the design moment resistance, Image Mo,Rd Image for that bay, where:

    Image Mo,Rd = W eff f o / γM1     (6.117)Image

    Weff is the effective elastic modulus obtained by taking a reduced thickness to allow for buckling as well as HAZ softening, but with the presence of holes ignored. The reduced thickness is equal to the lesser of ρo,hazt and ρct in HAZ regions, and ρct elsewhere, see 6.2.5.

  5. The thickness is reduced in any class 4 part that is wholly or partly in compression (bc in Figure 6.25). The stress ratio Ψ used in 6.1.4.3 and corresponding width bc may be obtained using the effective area of the compression flange and the gross area of the web, see Figure 6.25(c), gravity centre G1.
  6. If the compression edge of the web is nearer to the neutral axis of the girder than in the tension flange, see Figure 6.25(c), the method in 6.1.4.3 may be used.

    This procedure generally requires an iterative calculation in which Ψ is determined again at each step from the stresses calculated on the effective cross-section defined at the end of the previous step.

    Figure 6.25 - Plate girder in bending

    Figure 6.25 - Plate girder in bending

6.7.3 Resistance of girders with longitudinal web stiffeners

  1. Plate buckling due to longitudinal compressive stresses may be taken into account by the use of an effective cross-section applicable to class 4 cross-sections.
  2. The effective cross-section properties should be based on the effective areas of the compression parts and their locations within the effective cross-section.
  3. In a first step the effective areas of flat compression sub panels between stiffeners should be obtained using effective thicknesses according to 6.1.5. See Figure 6.26.
  4. Overall plate buckling, including buckling of the stiffeners, is considered as flexural buckling of a column consisting of the stiffeners and half the adjacent part of the web. If the stresses change from compression to tension within the sub panel, one third of the compressed part is taken as part of the column. See Figure 6.26(c).
  5. The effective thicknesses of the different parts of the column section are further reduced in a second step with a reduction factor χ obtained from the appropriate column curve relevant for column buckling of the column as a simple strut out of the plane of the web.
  6. The relative slenderness parameter Image in calculating χ is

    Image

    where

    97

    Ast,eff is the effective area of the column from the first step, see Figure 6.26c. Ncr is the elastic buckling load given by the following expression:

    Image

    Image

    Image

    where:

    Ist is second moment of area of the gross cross-section of the stiffener and adjacent part of web (see (7)) about an axis through its centroid and parallel to the plane of the web
    b1 and b2 are distances from longitudinal edges to the stiffener (b1 + b2 = bw).
    ac is the half wave length for elastic buckling of stiffener
  7. For calculation of Ist the column consists of the actual stiffener together with an effective width 15tw of the web plate on both sides of the stiffener. See Figure 6.26(d1) and (d2).
  8. In case of two longitudinal stiffeners, both in compression, the two stiffeners are considered as lumped together, with an effective area and a second moment of area equal to the sum of those of the individual stiffeners. The location of the lumped stiffener is the position of the resultant of the axial forces in the stiffeners. If one of the stiffeners is in tension the procedure will be conservative.

    Figure 6.26 - Stiffened web of plate girder in bending

    Figure 6.26 - Stiffened web of plate girder in bending

6.7.4 Resistance to shear

  1. This section gives rules for plate buckling effects from shear force where the following criteria are met:
    1. panels are rectangular and flanges are parallel within an angle not greater than 10°;
    2. stiffeners if any are provided in the longitudinal and /or transverse direction;
    3. open holes or cut outs are small and limited to diameters d that satisfies d / hw ≤ 0,05 where hw is the width of the plate;
    4. members are uniform. 98
  2. P A plate girder in shear shall be verified against buckling as follows:

    Image

    where:

    VEd is the design value of the shear force
    VRd is the design resistance for shear, see 6.7.4.1 or 6.7.4.2.
6.7.4.1 Plate girders with web stiffeners at supports
  1. This section gives rules for plate buckling effects from shear force where stiffeners are provided at supports only.
  2. Plates with Image should be checked for resistance to shear buckling.

    NOTE For η see Table 6.13, for hw and tw see Figure 6.27.

  3. For webs with transverse stiffeners at supports only, the design resistance VRd for shear should be taken as

    Image

    in which ρv is a factor for shear buckling obtained from Table 6.13 or Figure 6.28.

    Table 6.13 - Factor ρv for shear buckling
    Ranges of λw Rigid end post Non-rigid end post
    λw ≤ 0,83/η
    0,83/η < λw < 0,937
    0,937 ≤ λw
    η
    0,83/λw
    2/3(1,66 + λw)
    η
    0,83/λw
    0,83/λw
    Image η = 0,7 + 0,35 fuw / fow but not more than 1,2 where than 1,2 where fow is the strength for overall yielding and fuw Image is the ultimate strength of the web material

    Figure 6.27 - End-stiffeners

    Figure 6.27 - End-stiffeners

    Figure 6.27 shows various end supports for girders:

    1. no end post, see 6.7.5, type c); 99
    2. rigid end posts, see 6.7.8.1. This case is also applicable for panels not at the end of the girder and at an intermediate support of a continuous girder;
    3. non-rigid end posts, see 6.7.8.2;
    4. bolted connection, see 6.7.8.2, to be classified as non-rigid in resistance calculation.

      Figure 6.28 - Factor ρv for shear buckling

      Figure 6.28 - Factor ρv for shear buckling

  4. The slenderness parameter λw in Table 6.13 and Figure 6.28 is

    Image

6.7.4.2 Plate girders with intermediate web stiffeners
  1. This section gives rules for plate buckling effects from shear force where web stiffeners are provided in the longitudinal and/or transverse direction
  2. Plates with Image should be checked for resistance to shear buckling and should be provided with transverse stiffeners at the supports.

    NOTE For η see Table 6.13, for hw and tw see Figure 6.29 and for kτ see (6)

  3. For beams with transverse and longitudinal stiffeners the design resistance for shear buckling VRd is the sum of the contribution Vw,Rd of the web and Vf,Rd of the flanges.

    VRd = Vw,Rd + Vf,Rd     (6.124)

    in which Vw,Rd includes partial tension field action in the web according to (4) and Vf,Rd is an increase of the tension field caused by local bending resistance of the flanges according to (10).

  4. The contribution from the web to the design resistance for shear should be taken as:

    Image

    where ρv is the factor for shear buckling obtained from Table 6.13 or Figure 6.28.

  5. The slenderness parameter λw is

    Image

    100

    in which kτ is the minimum shear buckling coefficient for the web panel. Rigid boundaries may be assumed if flanges and transverse stiffeners are rigid, see 6.7.8.3. The web panel is then the panel between two adjacent transverse stiffeners.

  6. The second moment of area of the longitudinal stiffeners should be reduced to 1/3 Image of its value Image when calculating kτ. Formulae for kτ taking this into account are given in (7) and (8).
  7. For plates with rigid transverse stiffeners and without longitudinal stiffeners or more than two longitudinal stiffeners, the shear buckling coefficient kτ in (5) is:

    kτ = 5,34 + 4,00(bw/a)2 + kτst if a/bw ≥ 1     (6.127)

    kτ = 4,00 + 5,34(bw/a)2 + kτst if a/bw < 1     (6.128)

    where:

    Image

    a is the distance between transverse stiffeners. See Figure 6.29.

    Ist is the second moment of area of the longitudinal stiffener with regard to the z-axis. See Figure 6.29(b). For webs with two or more equal stiffeners, not necessarily equally spaced, Ist Image is the second moment of area of all individual stiffeners. Image

  8. The expression (6.129) also applies to plates with one or two longitudinal stiffeners, if the aspect ratio a/bw ≥ 3. For plates with one or two longitudinal stiffeners and an aspect ratio a/bw < 3 the shear buckling coefficient should be taken from:

    Image

  9. For webs with longitudinal stiffeners the relative slenderness parameter λw should be taken not less than

    Image

    where kτ1 and bw1 refers to the sub-panel with the largest slenderness parameter λw of all subpanels within the webpanel under consideration. To calculate kτ1 the expression in 6.7.4.2(7) may be used with kτst = 0.

  10. If the flange resistance is not completely utilized in withstanding the bending moment (MEd < Mf,Rd, curve (1) in Figure 6.32) the shear resistance contribution Vf,Rd from the flanges may be included in the shear buckling resistance as follows:

    Image

    in which bf and tf are taken for the flange leading to the lowest resistance,

    bf being taken as not larger than 15tf on each side of the web

    Mf,Rd is the design moment resistance of the cross section considering of the effective flanges only

    Image

    101

    Figure 6.29 - Web with transverse and longitudinal stiffeners

    Figure 6.29 - Web with transverse and longitudinal stiffeners

  11. If an axial force NEd is present, the value of Mf,Rd should be reduced by a factor

    Image

    where Af1 and Af2 are the areas of the top and bottom flanges.

  12. Image Image If MEdMf,Rd then Vf,Rd = 0. For further interaction, see 6.7.6.

6.7.5 Resistance to transverse loads

6.7.5.1 Basis
  1. The resistance of the web of extruded beams and welded girders to transverse forces applied through a flange may be determined from the following rules, provided that the flanges are restrained in the lateral direction either by their own stiffness or by bracings.
  2. A load can be applied as follows:
    1. Load applied through one flange and resisted by shear forces in the web. See Figure 6.30(a).
    2. Load applied to one flange and transferred through the web to the other flange, see Figure 6.30(b)
    3. Load applied through one flange close to an un-stiffened end, see Figure 6.30(c).
  3. For box girders with inclined webs the resistance of both the web and flange should be checked. The internal forces to be taken into account are the components of the external load in the plane of the web and flange respectively.
  4. P The resistance of the web to transverse forces applied through a flange shall be verified as follows:

    Image

    where:

    FEd is the design transverse force;

    FRd is the design resistance to transverse forces, see 6.7.5.2;

  5. The interaction of the transverse force, bending moment and axial force should be verified using 6.7.6.2.
102
6.7.5.2 Design resistance
  1. For un-stiffened or stiffened webs the design resistance FRd to local buckling under transverse loads should be taken as

    FRd = Leff tw fow / γM1     (6.134)

    where:

    fow is the characteristic value of strength of the web material.

    Leff is the effective length for resistance to transverse loads, which should be determined from

    Leff = χFly     (6.135)

    where:

    ly is the effective loaded length, see 6.7.5.5, appropriate to the length of stiff bearings ss, see 6.7.5.3

    χF is the reduction factor due to local buckling, see 6.7.5.4.

6.7.5.3 Length of stiff bearing

Figure 6.30 - Load applications and buckling coefficients

Figure 6.30 - Load applications and buckling coefficients

  1. The length of stiff bearing, ss, on the flange is the distance over which the applied load is effectively distributed and it may be determined by dispersion of load through solid material at a slope of 1:1, see Figure 6.31. However, ss should not be taken as larger than bw.
  2. If several concentrated loads are closely spaced (ss for individual loads > distance between loads), the resistance should be checked for each individual load as well as for the total load with ss as the centre-to-centre distance between the outer loads.

    Figure 6.31 - Length of stiff bearing

    Figure 6.31 - Length of stiff bearing

6.7.5.4 Reduction factor χF for resistance
  1. The reduction factor χF for resistance should be obtained from:

    Image but not more than 1,0     (6.136)

    where:

    103

    Image

    Image

    ly is effective loaded length obtained from 6.7.5.5.

  2. For webs without longitudinal stiffeners the factor kF should be obtained from Figure 6.30
  3. For webs with longitudinal stiffeners kF should be taken as

    Image

Where:

b1 is the depth of the loaded sub-panel taken as the clear distance between the loaded flange and the stiffener

Image

where Is1 is the second moment of area (about z-z axis) of the stiffener closest to the loaded flange including contributing parts of the web according to Figure 6.29. Equation (6.140) is valid for 0,05 ≤ b1 / hw ≤ 0,3 and loading according to type (a) in Figure 6.30.

6.7.5.5 Effective loaded length
  1. The effective loaded length ly should be calculated using the two dimensionless parameters m1 and m2 obtained from

    Image

    where bf is the flange width, see Figure 6.31. For box girders, bf in expression (6.141) is limited to 15tf on each side of the web.

  2. For cases (a) and (b) in Figure 6.30, ly should be obtained using:

    Image

  3. For case (c) in Figure 6.30, ly should be obtained as the smaller of the values obtained from the equations (6.143), (6.144) and (6.145). However, ss in (6.143) should be taken as zero if the structure that introduces the force does not follow the slope of the girder, see Figure 6.31.

    Image

    104

    Image

6.7.6 Interaction

6.7.6.1 Interaction between shear force, bending moment and axial force
  1. Provided that the flanges can resist the whole of the design value of the bending moment and axial force in the member, the design shear resistance of the web need not be reduced to allow for the moment and axial force in the member, except as given in 6.7.4.2(10).
  2. If MEd > Mf,Rd the following two expressions (corresponding to curve (2) and (3) in Figure 6.32) should be satisfied:

    Image

    Image MEdMo,Rd Image

    where:

    Image Mo,Rd is the design bending moment resistance according to 6.7.2 (4). Image
    Mf,Rd is the design bending moment resistance of the flanges only Image(= min(Afl · hffo/γMl, Af2 · hffo/γM1).Image
    Mpl,Rd is the plastic design bending moment resistance
  3. If an axial force NEd is also applied, then Mpl,Rd should be replaced by the reduced plastic moment resistance MN,Rd given by

    Image

    where Af1, Af2 are the areas of the flanges.

    Figure 6.32 - Interaction of shear force resistance and bending moment resistance

    Figure 6.32 - Interaction of shear force resistance and bending moment resistance

6.7.6.2 Interaction between transverse force, bending moment and axial force
  1. If the girder is subjected to a concentrated force acting on the compression flange in conjunction with bending moment and axial force, the resistance should be verified using 6.2.9, 6.7.5.1 and the following interaction expression

    Image

    105

    where:

    Image Mo, Rd is the design bending moment resistance according to 6.7.2 (4). Image
    Nc,Rd is the design axial force resistance, see 6.3.1.1.
  2. If the concentrated force is acting on the tension flange the resistance according to 6.7.5 should be verified and in addition also 6.2.1(5)

6.7.7 Flange induced buckling

  1. To prevent the possibility of the compression flange buckling in the plane of the web, the ratio bw/tw of the web should satisfy the following expression

    Image

    where:

    Aw is the cross section area of the web
    Afc is the cross section area of the compression flange
    Imagefof is the 0,2% proof strength of the flange material Image

    The value of the factor k should be taken as follows:

    - plastic rotation utilized k = 0,3
    - plastic moment resistance utilized k = 0,4
    Image - elastic moment of resistance utilized k = 0,55 Image
  2. If the girder is curved in elevation, with the compression flange on the concave face, the ratio bw / tw for the web should satisfy the following criterion:

    Image

    in which r is the radius of curvature of the compression flange.

  3. If the girder is provided with transverse web stiffeners, the limiting value of bw / tw may be increased by the factor 1 + (bw / a)2.

6.7.8 Web stiffeners

6.7.8.1 Rigid end post
  1. The rigid end post (see Figure 6.27) should act as a bearing stiffener resisting the reaction from bearings at the girder support, and as a short beam resisting the longitudinal membrane stresses in the plane of the web.
  2. A rigid end post may comprise of one stiffener at the girder end and one double-sided transverse stiffener that together form the flanges of a short beam of length hf , see Figure 6.27(b). The strip of web plate between the stiffeners forms the web of the short beam. Alternatively, an end post may be in the form of an inserted section, connected to the end of the web plate.
  3. Image The double-sided transverse stiffener may act as a bearing stiffener resisting the reaction at the girder support (see 6.2.11).
  4. The stiffener at the girder end should have a cross-sectional area of at least Image where e is the centre to centre distance between the stiffeners and e > 0,1hf, see Figure 6.27(b). Image 106
  5. Image If an end post is the only means of providing resistance against twist at the end of a girder, the second moment of area of the end-post section about the centre-line of the web (Iep) should satisfy: Image

    Image

    where:

    tf   is the maximum value of flange thickness along the girder

    REd   is the reaction at the end of the girder under design loading

    WEd   is the total design loading on the adjacent span.

6.7.8.2 Non-rigid end post and bolted connection
  1. A non-rigid end post may be a single double-sided stiffener as shown in Figure 6.27(c). It may act as a bearing stiffener resisting the reaction at the girder support (see 6.2.11).
  2. The shear force resistance for a bolted connection as shown in Figure 6.27(c) may be assumed to be the same as for a girder with a non-rigid end post provided that the distance between bolts is p < 40tw.
6.7.8.3 Intermediate transverse stiffeners
  1. Intermediate stiffeners that act as rigid supports of interior panels of the web should be checked for strength and stiffness.
  2. Other intermediate transverse stiffeners may be considered flexible, their stiffness being considered in the calculation of kτ in 6.7.4.2.
  3. Intermediate transverse stiffeners acting as rigid supports for web panels should have a minimum second moment of area Ist:

    Image

    The strength of intermediate rigid stiffeners should be checked for an axial force equal to VEdρvbwtwfv / γM1 where ρv is calculated for the web panel between adjacent transverse stiffeners assuming the stiffener under consideration removed. In the case of variable shear forces the check is performed for the shear force at distance 0,5hw from the edge of the panel with the largest shear force.

6.7.8.4 Longitudinal stiffeners
  1. Longitudinal stiffeners may be either rigid or flexible. In both cases their stiffness should be taken into account when determining the relative slenderness λw in 6.7.4.2(5).
  2. If the value of λw is governed by the sub-panel then the stiffener may be considered as rigid.
  3. The strength should be checked for direct stresses if the stiffeners are taken into account for resisting direct stress.
6.7.8.5 Welds
  1. The web to flange welds may be designed for the nominal shear flow VEd / hw if VEd does not exceed ρvhwtwfo/(Image). For larger values the weld between flanges and webs should be designed for the shear flow ηtwfo/(Image) unless the state of stress is investigated in detail.
107

6.8 Members with corrugated webs

  1. For plate girders with trapezoidal corrugated webs, see Figure 6.33, the bending moment resistance is given in 6.8.1 and the shear force resistance in 6.8.2.

    NOTE 1 Cut outs are not included in the rules for corrugated webs.

    NOTE 2 For transverse loads the rules in 6.7.7 can be used as a conservative estimate.

6.8.1 Bending moment resistance

  1. The bending moment resistance may be derived from:

    Image

    where fo,r = ρzfo includes the reduction due to transverse moments in the flanges

    Image

    Mz is the transverse bending moment in the flange

    χLT is the reduction factor for lateral torsional buckling according to 6.3.2.

    NOTE The transverse moment Mz may result from the shear flow introduction in the flanges as indicated in Figure 6.33(d).

    Figure 6.33 - Corrugated web

    Figure 6.33 - Corrugated web

6.8.2 Shear force resistance

  1. The shear force resistance V Rd may be taken as

    Image

    where ρc is the smallest of the reduction factors for local buckling ρc,l, reduction factor for global buckling ρc,g and HAZ softening factor ρo,haz:

    108
  2. The reduction factor ρc,l for local buckling may be calculated from:

    Image

    where the relative slenderness λc,l for trapezoidal corrugated webs may be taken as

    Image

    with amax as the greatest width of the corrugated web plate panels, a0, a1 or a2, see Figure 6.33.

  3. The reduction factor ρc,g for global buckling should be taken as

    Image

    where the relative slenderness λc,g may be taken as

    Image

    where the value τcr,g may be taken from:

    Image

    where:

    Image

    2a is length of corrugation, see Figure 6.33

    a0, a1 and a2 are widths of folded web panels, see Figure 6.33

    Ix is second moment of area of one corrugation of length 2a, see Figure 6.33.

    NOTE Equation (6.162) applies to plates with hinged edges.

  4. The reduction factor ρo,haz in HAZ is given in 6.1.6.
109

7 Serviceability Limit States

7.1 General

  1. P Image An aluminium Image structure shall be designed and constructed such that all relevant serviceability criteria are satisfied.
  2. The basic requirements for serviceability limit states are given in 3.4 of EN 1990.
  3. Any serviceability limit state and the associated loading and analysis model should be specified for a project.
  4. Where plastic global analysis is used for the ultimate limit state, plastic redistribution of forces and moments at the serviceability limit state may occur. If so, the effects should be considered.

    NOTE The National Annex may give further guidance.

7.2 Serviceability limit states for buildings

7.2.1 Vertical deflections

  1. With reference to EN 1990 – Annex A1.4 limits for vertical deflections according to Figure A1.1 in EN 1990 should be specified for each project and agreed with the owner of the construction work.

    NOTE The National Annex may specify the limits.

7.2.2 Horizontal deflections

  1. With reference to EN 1990 – Annex A1.4 limits for horizontal deflections according to Figure A1.2 in EN 1990 should be specified for each project and agreed with the owner of the construction work.

    NOTE The National Annex may specify the limits.

7.2.3 Dynamic effects

  1. With reference to EN 1990 – Annex A1.4.4 the vibrations of structures on which the public can walk should be limited to avoid significant discomfort to users, and limits should be specified for each project and agreed with the owner of the construction work.

    NOTE The National Annex may specify limits for vibration of floors.

7.2.4 Calculation of elastic deflection

  1. The calculation of elastic deflection should generally be based on the properties of the gross cross-section of the member. However, for slender sections it may be necessary to take reduced section properties to allow for local buckling (see section 6.7.5). Due allowance of effects of partitioning and other stiffening effects, second order effects and changes in geometry should also be made.
  2. For class 4 sections the following effective second moment of area Iser, constant along the beam may be used

    Image

    where:

    Igr is the second moment of area of the gross cross-section
    Ieff is the second moment of area of the effective cross-section at the ultimate limit state, with allowance for local buckling, Image see 6.2.5.2 Image
    σgr is the maximum compressive bending stress at the serviceability limit state, based on the gross cross-section (positive in the formula).
  3. Deflections should be calculated making also due allowance for the rotational stiffness of any semi-rigid joints, and the possible recurrence of local plastic deformation at the serviceability limit state.
110

8 Design of joints

8.1 Basis of design

8.1.1 Introduction

  1. P All joints shall have a design resistance such that the structure remains effective and is capable of satisfying all the basic design requirements given in 2.
  2. The partial safety factors γM for joints should be applied to the characteristic resistance for the various types of joints.

    NOTE Numerical values for γM may be defined in the National Annex. Recommended values are given in Table 8.1

    Image Table 8.1 - Recommended partial factors γM for joints
    Resistance of members and cross-section γM1 and γM2 see 6.1.3
    Resistance of bold connections γM2 = 1,25
    Resistance of rivet connections
    Resistance of plates in bearing
    Resistance of pin connections γMp = 1,25
    Resistance of welded connections γMw = 1,25
    Slip resistance, see 8.5.9.3
    - for serviceability limit states
    - for ultimate limit states
    γMs,ser = 1,1
    γMs,ult = 1,25
    Resistance of adhesive bonded connections γMa ≥ 3,0
    Resistance of pins at serviceability limit state γMp,ser = 1,0 Image
  3. Joints subject to fatigue should also satisfy the rules given in EN 1999-1-3.

8.1.2 Applied forces and moments

  1. The forces and moments applied to joints at the ultimate limit state should be determined by global analysis conforming to 5.
  2. These applied forces and moments should include:

    NOTE For the effect of connection flexibility, see Annex L.

8.1.3 Resistance of joints

  1. The resistance of a joint should be determined on the basis of the resistances of the individual fasteners, welds and other components of the joint. 111
  2. Linear-elastic analysis should generally be used in the design of the joint. Alternatively non-linear analysis of the joint may be employed provided that it takes account of the load deformation characteristics of all the components of the joint.
  3. If the design model is based on yield lines such as block shear i.e., the adequacy of the model should be demonstrated on the basis of physical tests.

8.1.4 Design assumptions

  1. Joints may be designed by distributing the internal forces and moments in whatever rational way is best, provided that:
    1. the assumed internal forces and moments are in equilibrium with the applied forces and moments;
    2. Image each part Image in the joint is capable of resisting the forces or stresses assumed in the analysis;
    3. the deformations implied by this distribution are within the deformation capacity of the fasteners or welds and of the connected parts, and
    4. the deformations assumed in any design model based on yield lines are based on rigid body rotations (and in-plane deformations) which are physically possible.
  2. In addition, the assumed distribution of internal forces should be realistic with regard to relative stiffness within the joint. The internal forces will seek to follow the path with the greatest rigidity. This path should be clearly identified and consistently followed throughout the design of the joint.
  3. Residual stresses and stresses due to tightening of fasteners and due to ordinary accuracy of fit-up need not usually be allowed for.

8.1.5 Fabrication and execution

  1. Ease of fabrication and execution should be considered in the design of all joints and splices.
  2. Attention should be paid to:
  3. Attention should also be paid to the requirements for:

Requirements to execution of aluminium structures are given in Image EN 1090-3 Image

8.2 Intersections for bolted, riveted and welded joints

  1. Members meeting at a joint should usually be arranged with their centroidal axes intersecting at a point.
  2. Any kind of eccentricity in the nodes should be taken into account, except in the case of particular types of structures where it has been demonstrated that it is not necessary.
112

8.3 Joints loaded in shear subject to impact, vibration and/or load reversal

  1. Image Where a joint loaded in shear is subject to frequent impact or significant vibration either welding, preloaded bolts, injection bolts or other types of bolts, which effectively prevent movement and loosening of fastener, should be used.
  2. Where slipping is not acceptable in a joint because it is subject to reversal of shear load (or for any other reason), preloaded bolts in a slip-resistant connection (category B or C as appropriate, see 8.5.3), fitted bolts or welding should be used.
  3. For wind and/or stability bracings, bolts in bearing type connections (category A in 8.5.3) may be used. Image

8.4 Classification of joints

NOTE Recommendations for classification of joints are given in Annex L.

8.5 Connections made with bolts, rivets and pins

8.5.1 Positioning of holes for bolts and rivets

  1. The positioning of holes for bolts and rivets should be such as to prevent corrosion and local buckling and to facilitate the installation of the bolts or rivets.
  2. In case of minimum end distances, minimum edge distances and minimum spacings no minus tolerances are allowed.
  3. The positioning of the holes should also be in conformity with the limits of validity of the rules used to determine the design resistances of the bolts and rivets.
  4. Minimum and maximum spacing, end and edge distances are given in Table 8.2. 113
    Table 8.2 - Minimum, regular and maximum spacing, end and edge distances
    1 2 3 4 5
    Distances and spacings, see Figures 8.1 and 8.2 Minimum Regular distance Maximum1) 2) 3)
    Structures made of aluminium according to Table 3.1a
    Aluminium exposed to the weather or other corrosive influences Aluminium not exposed to the weather or other corrosive influences
    End distance e1 1,2d0 6) 2,0d0 4t + 40 mm The larger of 12t or 150 mm
    Edge distance e2 1,2d0 6) 1,5d0 4t + 40 mm The larger of 12t or 150 mm
    End distance e3 for slotted holes 4)      Slotted holes are not recommended.
         Slotted holes of category A see Image 8.5.1(5) Image – (10)
    Edge distance e4 for slotted holes 4)      Slotted holes are not recommended.
         Slotted holes of category A see Image 8.5.1(5) Image – (10)
    Compression members (see Figure 8.2): Spacing p1 2,2d0 2,5d0 Compression members: The smaller of 14t or 200 mm Compression members: The smaller of 14t or 200 mm
    Tension members (see Figure 8.3):

    Spacing p1, p1,0, p1,i
    2,2d0 2,5d0 Outer lines:
    The smaller of 14t or 200 mm
    Inner lines:
    The smaller of 28t or 400
    mm
    1,5 times the values of column 4
    Spacing P2 5) 2,4d0 3,0d0 The smaller of 14t or 200 mm The smaller of 14t or 200 mm
    1. Maximum values for spacings, edge and end distances are unlimited, except in the following cases:
      • - for compression members in order to avoid local buckling and to prevent corrosion in exposed members and:
      • - for exposed tension members to prevent corrosion.
    2. The local buckling resistance of the plate in compression between the fasteners should be calculated according to Image 6.3 Image Image Text deleted Image by using 0,6 p1 as buckling length. Local buckling between the fasteners need not to be checked if p1/t is smaller than 9ε. The edge distance should not exceed the maximum to satisfy local buckling requirements for an outstand part in the compression members, see 6.4.2 - 6.4.5. Image Text deleted Image
    3. t is the thickness of the thinner outer connected part.
    4. Slotted holes are not recommended, slotted holes of category A see 8.5.1 (5)
    5. For staggered rows of fasteners a minimum line spacing p2 = 1,2d0 may be used, if the minimum distance between any two fasteners in a staggered row is p1 = 2,4d0, see Figure 8.2
    6. The minimum values of e1 and e2 should be specified with no minus deviation but only plus deviations.
    114

    Figure 8.1 - Symbols for spacing of fasteners

    Figure 8.1 - Symbols for spacing of fasteners

    Figure 8.2 - Staggered spacing - compression

    Figure 8.2 - Staggered spacing – compression

    Figure 8.3 - Spacing in tension member

    Figure 8.3 - Spacing in tension member

    Figure 8.4 - Slotted holes

    Figure 8.4 - Slotted holes

  5. Slotted holes are not recommended. However, slotted holes may be used in connections of the category A with loads only perpendicular to the direction of the slotted hole.
  6. The length between the extreme edges of a slotted hole in the direction of the slot should be either 1,5(d + 1 mm) (short slotted hole) or 2,5(d + 1 mm) (long slotted hole) but not larger.
  7. The width of the hole perpendicular to the slot, i.e. in the direction of the load, should be not greater than d + 1 mm.
  8. The distance e3 between the edge of the hole and the end of the member in the direction of the load should be greater than 1 ,5(d + 1 mm), the distance e4 between the edge of the hole and the edge of the member perpendicular to the direction of the load should be greater than d + 1 mm.
  9. The distance p3 between the edges of two adjacent holes in the direction of the load and the distance p4 between the edges of two adjacent holes perpendicular to the direction of the load should be greater than 2(d + 1 mm).
  10. Bolts in slotted holes according to category A should be verified according to Table 8.5, see 8.5.5.
  11. For oversized holes the rules in (8), (9) and (10) apply.
  12. Image Oversized holes in bolted connections of Category A may be used if the following conditions are met:
115

8.5.2 Deductions for fastener holes

8.5.2.1 General
  1. For detailed rules for the design of members with holes see 6.3.4.
8.5.2.2 Design for block tearing resistance
  1. Block tearing consists of failure in shear at the row of bolts along the shear face of the hole group accompanied by tensile failure along the line of bolt holes on the tension face of the bolt group. Figure 8.5 shows block tearing.
  2. For a symmetric bolt group subject to concentric loading the design block tearing resistance, Veff,1,Rd is given by:

    Veff,1,Rd = fu Ant / γM2 + (1 / √3)fo Anv / γM1     (8.1)

    where:

    Ant is net area subjected to tension;

    Anv is net area subjected to shear.

  3. For a bolt group subject to eccentric loading the design block shear tearing resistance Veff,2,Rd is given by:

    Veff,2,Rd = 0,5 fu Ant / γM2 + (1 / √3)fo Anv / γM1     (8.2)

Figure 8.5 - Block tearing

Figure 8.5 - Block tearing

8.5.2.3 Angles and angles with bulbs
  1. In the case of unsymmetrical or unsymmetrically Image connected members under tension and compression Image bulbs, the eccentricity of fasteners in end connections and the effects of the spacing and edge distances of the bolts should be taken into account when determining the design resistances.
  2. Angles and angles with bulbs connected by a single row of bolts, see Figure 8.6, may be treated as concentrically loaded and the design ultimate resistance of the net section determined as follows:
116

Figure 8.6 - Connection of angles

Figure 8.6 - Image Connection of angles Image

Image

where:

β2 and β3 are reduction factors dependent on the pitch p1 as given in Table 8.3 for intermediate values p1 the values of β may be determined by linear interpolation.

Anet is the net area of the angle. For an unequal-leg angle connected by its smaller leg, Anet should be taken as equal to the net section area of an equivalent equal-leg angle of leg size equal to that of the smaller leg.

Image Text deleted Image

Table 8.3 - Reduction factors β2 and β3
Pitch p1 ≤ 2,5 d0 ≥ 5,0 d0
β2 for 2 bolts 0,4 0,7
β3 for 3 bolts or more 0,5 0,7

8.5.3 Categories of bolted connections

8.5.3.1 Shear connections
  1. The design of a bolted connection loaded in shear should conform to one of the following categories, see Table 8.4. 117
    Table 8.4 - Categories of bolted connections
    Shear connections
    Category Criteria Remarks
    A; bearing type Fv,EdFv,Rd
    Fv,EdFb,Rd
    ΣFv,EdNnet,Rd
    No preloading required.
    All grades from 4.6 to 10.9
    Nnet,Rd = 0,9Anetfu / γM2
    B; slip resistant at serviceability Fv,Ed,serFs,Rd,ser
    Fv,EdFv,Rd
    Fv,EdFb,Rd
    ΣFv,EdNnet,Rd
    ΣFv,Ed,serNnet,Rd,ser
    Preloaded high strength bolts.
    No slip at the serviceability limit state.
    Nnet,Rd = 0,9Anetfu / γM2
    Nnet,Rd,ser = Anetfo / γM1
    C; slip resistant at ultimate Fv,EdFs,Rd
    Fv,EdFb,Rd
    ΣFv,EdNnet,Rd
    Image ΣFv,EdNnet,Rd,ser Image
    Preloaded high strength bolts.
    No slip at the ultimate limit state.
    Nnet,Rd = 0,9Anetfu/M2
    Nnet,Rd,ser = Anetfo/M1
    Tension connections
    Category Criterion Remarks
    D; non-preloaded Ft,EdFt,Rd
    Ft,EdBp,Rd
    Bolt class from 4.6 to 10.9.
    E; preloaded Ft,EdFt,Rd
    Ft,EdBp,Rd
    Preloaded 8.8 or 10.9 bolts.
    Key: Fv,Ed design shear force per bolt for the ultimate limit state
    Fv,Ed,ser design shear force per bolt for the serviceability limit state
    Fv,Rd design shear resistance per bolt
    Fb,Rd design bearing resistance per bolt
    Fs,Rd,ser design slip resistance per bolt at the serviceability limit state
    Fs,Rd design slip resistance per bolt at the ultimate limit state
    Ft,Ed design tensile force per bolt for the ultimate limit state
    Ft,Rd design tension resistance per bolt
    Anet net area, see 6.2.2.2 (tension members only)
    Bp,Rd design resistance for punching resistance, see Table 8.5.
  2. Category A: Bearing type

    In this category protected steel bolts (ordinary or high strength type) or stainless steel bolts or aluminium bolts or aluminium rivets should be used. No preloading and special provisions for contact surfaces are required.

    Image Text deleted Image

  3. Category B: Slip-resistant at serviceability limit state

    In this category preloaded high strength bolts with controlled tightening in conformity with Image EN 1090-3 Image should be used. Slip should not occur at the serviceability limit state. The combination of actions to be considered should be selected from 2.3.4 depending on the load cases where resistance to slip is required. The design serviceability shear load should not exceed the design slip resistance, obtained from 8.5.9.

    ImageText deleted Image

  4. Category C: Slip resistant at ultimate limit state 118

    In this category preloaded high strength bolts with controlled tightening in conformity with Image EN 1090-3 Image should be used. Slip should not occur at the ultimate limit state. Image Text deleted Image

  5. In addition, at the ultimate limit state the design plastic resistance of the net section at bolt holes Nnet,Rd should be taken as:

    Nnet,Rd = 0,9Anetfu / γM2     (8.6)

8.5.3.2 Tension connections
  1. The design of a bolted connection loaded in tension should conform with one of the following categories, see Table 8.4.
  2. Category D: Connections with non-preloaded bolts
    In this category bolts from class 4.6 up to and including class 10.9 or aluminium bolts or stainless steel bolts should be used. No preloading is required. This category should not be used where the connections are frequently subjected to variations of tensile loading. However, they may be used in connections designed to resist normal wind loads.
  3. Category E: Connections with preloaded high strength bolts
    In this category preloaded high strength bolts with controlled tightening in conformity with Image EN 1090-3 Image should be used. Such preloading improves fatigue resistance. However, the extent of the improvement depends on detailing and tolerances.
  4. For tension connections of both categories D and E no special treatment of contact surfaces is necessary, except where connections of category E are subject to both tension and shear (combination E-B or E-C).

8.5.4 Distribution of forces between fasteners

  1. The distribution of internal forces between fasteners due to the bending moment at the ultimate limit state should be proportional to the distance from the centre of rotation and the distribution of the shear force should be equal, see Figure 8.7(a), in the following cases:
  2. In other cases the distribution of internal forces between fasteners due to the bending moment at the ultimate limit state may be assumed plastic and the distribution of the shear force may be assumed equal, see Figure 8.7(b).
  3. In a lap joint, the same bearing resistance in any particular direction should be assumed for each fastener up to a maximum length of max L = 15 d, where d is the nominal diameter of the bolt or rivet. For L > 15 d see 8.5.11.
119

Figure 8.7 - Example of distribution of loads between fasteners (five bolts)

Figure 8.7 - Example of distribution of loads between fasteners (five bolts)

8.5.5 Design resistances of bolts

  1. The design resistances given in this clause apply to standard manufactured steel bolts, stainless steel bolts and aluminium bolts according to Table 3.4 which conform, including corresponding nuts and washers, to the reference standards listed in Image EN 1090-3 Image. For aluminium bolts the additional requirements of C.4.1 should be followed.
  2. P At the ultimate limit state the design shear force Fv,Ed on a bolt shall not exceed the lesser of:
  3. P At the ultimate limit state the design tensile force Ft,Ed, inclusive of any force due to prying action, shall not exceed the design tension resistance Bt,Rd of the bolt-plate assembly.
  4. Bolts subject to both shear force and tensile force should in addition be verified as given in Table 8.5.
  5. P The design tension resistance of the bolt-plate assembly Bt,Rd shall be taken as the smaller of the design tension resistance Ft,Rd of the bolt given in Table 8.5 and the design punching shear resistance of the bolt head and the nut in the plate, Bp,Rd obtained from Table 8.5. 120
    Table 8.5 - Design resistance for bolts and rivets
    Failure mode Bolts Rivets
    Shear resistance per shear plane: Image
    • - where the shear plane passes through the threaded portion of the bolt (A is the tensile stress area of the bolt AS):
    • - for steel bolts with classes 4.6, 5.6 and 8.8: αv = 0,6
    • - for steel bolts with classes 4.8, 5.8, 6.8 and 10.9, stainless steel bolts and aluminium bolts: αv = 0,5
    Image
    fur = characteristic ultimate strength of the rivet material
    A0 = cross sectional area of the hole
    - where the shear plane passes through the unthreaded portion of the bolt (A is the gross cross section of the bolt): αv = 0,6
    fub = characteristic ultimate strength of the bolt material
    Bearing resistance 1) 2) 3) 4) 5) 6) Image
    where αb is the smallest of αd Image or 1,0; but ≤ 0,66 for slotted holes in the direction of the load transfer: (8.12)
    • - for end bolts: Image for inner bolts Image     (8.13 and 8.14)

    perpendicular to the direction of the load transfer:
    • - for edge bolts: k1 is the smallest of Image
    • - for inner bolts: k1 is the smallest of Image
    fu is the characteristic ultimate strength of the material of the connected parts
    fub is the characteristic ultimate strengths of the bolt material
    d is the bolt diameter
    d0 is the hole diameter
    e1, e2, p1, p2 see Figure 8.1 5)
    Tension resistance Image
    where
    • k2 = 0,9 for steel bolts,
    • k2 = 0,50 for aluminium bolts and
    • k2 = 0,63 for countersunk steel bolts,
    Image
    For solid rivets with head dimensions according to Annex C, Figure C.1 or greater on both sides.
    Punching shear resistance Bp,Rd = 0,6 π dm tp fu / γM2     (8.19)
    where:
    dm is the mean of the across points and across flats dimensions of the bolt head or the nut or if washers are used the outer diameter of the washer, whichever is smaller;
    tp is the thickness of the plate under the bolt head or the nut;
    fu characteristic ultimate strength of the member material.
    Combined shear and tension Image 121
    1. The bearing resistance Fb,Rd for bolts
      • - in oversized holes according to Image EN 1090-3 Image is 0,8 times the bearing resistance for bolts in normal holes,
      • - in short slotted holes, where the longitudinal axis of the slotted hole is perpendicular to the direction of the force transfer and the length of the slotted hole is not more than 1,5 times the diameter of the round part of the hole, is 0,80 times the bearing resistance for bolts in round, normal holes.
      • - in long slotted holes, where the longitudinal axis of the slotted hole is perpendicular to the direction of the force transfer and the length of the slotted hole is between 1,5 times the hole diameter and 2,5 times the hole diameter of the round part of the hole, is 0,65 times the bearing resistance for bolts in round, normal holes.
    2. For countersunk bolts:
      • - the bearing resistance Fb,Rd should be based on a plate thickness t equal to the thickness of the connected plate minus half the depth of the countersinking,
    3. In addition to bearing resistance, the net section resistance needs to be checked
    4. If the load on a bolt is not parallel to the edge, the bearing resistance may be verified separately for the bolt load components parallel and normal to the end.
    5. Aluminium bolts should not be used in connections with slotted holes.
    6. For slotted holes replace d0 by (d + 1 mm), e1 by (e3 + d/2), e2 by (e4 + d/2), p1 by (p3 + d) and p2 by (p4 + d) where p3, p4, e3 and e4 are found in Figure 8.4.
  6. The design resistances for tension and for shear through the threaded portion given in Table 8.5 are restricted to bolts with rolled threads. Image For bolts with cut threads, the relevant values from Table 8.5 should be reduced by multiplying them by a factor of 0,85. Image
  7. Image (7) The values for design shear resistance Fv,Rd given in Table 8.5 apply only where the bolts are used in holes with nominal clearances not exceeding those for standard holes as specified in EN 1090-3. For oversized holes and slotted holes Fv, RD is reduced by a factor of 0,7. Image

8.5.6 Design resistance of rivets

  1. Riveted connections should be designed to transfer forces in shear and bearing. The design resistances in this clause apply to aluminium rivets acc. to Table 3.4. The additional requirements of C.4.2 should be followed
  2. P At the ultimate limit state the design shear force Fv,Ed on a rivet shall not exceed the lesser of:
  3. Tension in aluminium rivets should be limited to exceptional cases (see Table 8.5).
  4. P At the ultimate limit state the design tension force Ft,Ed on a rivet shall not exceed the design ultimate tension resistance Ft, Rd as given in Table 8.5.
  5. Rivets subject to both shear and tensile forces should in addition satisfy the requirement for combined shear and tension as given in Table 8.5.

    Image Text deleted Image

  6. As a general rule, the grip length of a rivet should not exceed 4,5d for hammer riveting and 6,5d for press riveting. 122
  7. Single rivets should not be used in single lap joints.

8.5.7 Countersunk bolts and rivets

  1. Connections with countersunk bolts or rivets made from steel should be designed to transfer forces in shear and bearing.
  2. P At the ultimate limit state the design shear force Fv,Ed on a countersunk bolt or rivet made from steel shall not exceed the lesser of:
  3. Tension in a countersunk bolt made from steel should be designed to transfer tension force Ft,Ed. It should be limited to exceptional cases (see Table 8.5).
  4. P At the ultimate limit state the design tension force Ft,Ed on a countersunk bolt made from steel shall not exceed the design ultimate tension resistance Ft,Rd as given in Table 8.5.
  5. Bolts and rivets subject to both shear and tensile forces should in addition satisfy the requirement for combined shear and tension as given in Table 8.5.
  6. The angle and depth of countersinking should conform with Image EN 1090-3 Image.

    Image Text deleted Image

  7. As a general rule, the grip length of a countersunk bolt or rivet should not exceed 4,5 d for hammer riveting and 6,5 d for press riveting.
  8. Single countersunk bolts or rivets should not be used in single lap joints.

8.5.8 Hollow rivets and rivets with mandrel

  1. For the design strength of hollow rivets and rivets with mandrel, see EN 1999-1-4.

8.5.9 High strength bolts in slip-resistant connections

8.5.9.1 General
  1. Slip resistant connections should only be used if the proof strength of the material of the connected parts is higher than 200 N/mm2.
  2. The effect of extreme temperature changes and/or long grip lengths which may cause a reduction or increase of the friction capacity due to the differential thermal expansion between aluminium and bolt steel cannot be ignored.
8.5.9.2 Ultimate limit state
  1. P It is possible to take the slip resistance as ultimate or serviceability limit state, see 8.5.3.1, but, besides, at the ultimate limit state the design shear force, Fv,Ed on a high strength bolt shall not exceed the lesser of:
8.5.9.3 Slip resistance / Shear resistance
123
  1. The design slip resistance of a preloaded high-strength bolt should be taken as:

    Image

    where:

    Fp,C is the preloading force, given in 8.5.9.4.
    μ is the slip factor, see 8.5.9.5 and
    n is the number of friction interfaces.
  2. For bolts in standard nominal clearance holes, the partial safety factor for slip resistance γMs should be taken as γMs,ult for the ultimate limit state and γMs,ser for the serviceability limit state where γMs,ult and γMs,ser are given in 8.1.1.

    If the slip factor μ is found by tests the partial safety factor for the ultimate limit state may be reduced by 0,1.

  3. Slotted or oversized holes are not covered by these clauses
8.5.9.4 Preloading
  1. For high strength bolts grades 8.8 or 10.9 with controlled tightening, the preloading force Fp,C to be used in the design calculations, should be taken as:

    Fp,C = 0,7 fub AS     (8.22)

8.5.9.5 Slip factor
  1. The design value of the slip factor μ is dependent on the specified class of surface treatment. The value of μ for grit blasting to achieve a roughness value Ra 12,5, see EN ISO 1302 and EN ISO 4288, without surface protection treatments, should be taken from Table 8.6.
    Table 8.6 - Slip factor of treated friction surfaces
    Total joint thickness mm Slip factor μ
    12 ≤ Σt < 18
    18 ≤ Σt < 24
    24 ≤ Σt < 30
    30 ≤ Σt
    0,27
    0,33
    0,37
    0,40

    NOTE Experience show that surface protection treatments applied before shot blasting lead to lower slip factors.

  2. The calculations for any other surface treatment or the use of higher slip factors should be based on specimens representative of the surfaces used in the structure using the procedure set out in Image EN 1090-3 Image.
8.5.9.6 Combined tension and shear
  1. If a slip-resistant connection is subjected to an applied tensile force Ft in addition to the shear force Fv tending to produce slip, the slip resistance per bolt should be taken as follows:

    Category B: Slip-resistant at serviceability limit state

    Image

    Category C: Slip-resistant at ultimate limit state

    124

    Image

8.5.10 Prying forces

  1. Where fasteners are required to carry an applied tensile force, they should be proportioned to also resist the additional force due to prying action, where this can occur, see Figure 8.8.

    Figure 8.8 - Prying forces (Q)

    Figure 8.8 - Prying forces (Q)

  2. The prying forces depend on the relative stiffness and geometrical proportions of the parts of the connection, see Figure 8.9.

    Figure 8.9 - Effect of details on prying forces

    Figure 8.9 - Effect of details on prying forces

  3. If the effect of the prying force is taken advantage of in the design of the end plates, then the prying force should be allowed for in the analysis. See Annex B.

8.5.11 Long joints

  1. Where the distance Lj between the centres of the end fasteners in a joint, measured in the direction of the transfer of force (see Figure 8.10), is more than 15 d, the design shear resistance Fv,Rd of all the fasteners calculated as specified in 8.5.5 or 8.5.6 as appropriate should be reduced by multiplying it by a reduction factor βLf, given by:

    Image

    125

    but 0,75 ≤ βLf ≤ 1,0.

    Figure 8.10 - Long joints

    Figure 8.10 - Long joints

  2. This provision does not apply where there is a uniform distribution of force transfer over the length of the joint, e.g. the transfer of shear force from the web of a section to the flange.

8.5.12 Single lap joints with fasteners in one row

  1. A single rivet or one row of rivets should not be used in single lap joints.
  2. The bearing resistance Fb,Rd determined in accordance with 8.5.5 should be limited to:

    Fb,Rdfu d t / γM2      (8.26)

    Figure 8.11 - Single lap joint with one row of bolts

    Figure 8.11 - Single lap joint with one row of bolts

  3. In the case of high strength bolts, grades 8.8 or 10.9, appropriate washers should be used for single lap joints of flats with only one bolt or one row of bolts (normal to the direction of load), even where the bolts are not preloaded.

8.5.13 Fasteners through packings

  1. Where bolts or rivets transmitting load in shear and bearing pass through packings of total thickness tp greater than one-third of the nominal diameter d, the design shear resistance Fv,Rd calculated as specified in 8.5.5 or 8.5.6 as appropriate, should be reduced by multiplying it by a reduction factor βp given by:

    Image

  2. (2 For double shear connections with packings on both sides of the splice, tp should be taken as the thickness of the thicker packing.
  3. Any additional fasteners required due to the application of the reduction factor βp may optionally be placed in an extension of the packing.

8.5.14 Pin connections

8.5.14.1 Image General
  1. Pin connections where rotation is required should be designed according to 8.5.14.2 - 8.5.14.3.
  2. Pin connections in which no rotation is required may be designed as single bolted connections, provided that the length of the pin is less than 3 times the diameter of the pin, see 8.5.3. For all other cases the method in 8.5.14.3 should be followed. Image
126
8.5.14.2 Pin holes and pin plates
  1. Image The geometry of plates in pin connections should be in accordance with the dimensional requirements, see Figure 8.12.

    Figure 8.12 - Geometrical requirements for pin ended members

    Figure 8.12 - Geometrical requirements for pin ended members

  2. P At the ultimate limit state the design force FEd in the plate shall not exceed the design resistance given in Table 8.7.
  3. Pin plates provided to increase the net area of a member or to increase the bearing resistance of a pin should be of sufficient size to transfer the design force from the pin into the member and should be arranged to avoid eccentricity. Image
8.5.14.3 Design of pins
  1. Image Pins should not be loaded in single shear, so one of the members to be joined should have a fork end, or clevis. The pin retaining system, e.g. spring clip, should be designed to withstand a lateral load not less than 10% of the total shear load of the pin.
  2. The bending moments in a pin should be calculated as indicated in Figure 8.13.
  3. At the ultimate limit state the design forces and moments in a pin should not exceed the relevant design resistances given in Table 8.7.
  4. If the pin is intended to be replaceable (multiple assembling and disassembling of a structure), in addition the provisions given in 8.5.14.2 and 8.5.14.3 the contact bearing stress should satisfy:

    σh,Edfh,Rd     (8.28a)

    where:

    Image

    fh,Rd = 2,5 fo/γM6,ser

    where:

    d is the diameter of the pin Image

127
Image d0 is the diameter of the pin hole
FEd,ser is the design value of the force to be transferred in bearing under the characteristic load combination for serviceability limit state
Ep, Epl is the elastic modulus of the pin and the plate material respectively.
Table 8.7 - Design resistances for pin connections
Criterion Resistance
Shear of the pin

If the pin is intended to be replaceable this requirement should also be satisfied
Fv,Rd = 0,6 A fupMp               ≥Fv,Ed

Fv,Rd, ser = 0,6 A fop/γM6,ser      ≥Fv,Ed,ser
Bearing of the plate and the pin

If the pin is intended to be replaceable this requirement should also be satisfied
Fb,Rd = 1,5 t d fo,minM1          ≥Fb,Ed

Fb,Rd = 0,6 t d f0/γM6,ser           ≥Fb,Ed,ser
Bending of the pin

If the pin is intended to be replaceable this requirement should also be satisfied
MRd = 1,6 WelfopM1               ≥MRd

MRd = 0,8 Wel fop/γM6,ser          ≥MEd,ser
Combined shear and bending of the pin (MEd/MRd)2 + (Fv,Rd)2 ≤ l,0
d is the diameter of the pin
fo,min is the lower of the design strengths of the pin and the connected part
fup is the ultimate tensile strength of the pin
fop is the yield strength of the pin
t is the thickness of the connected part
A is the cross sectional area of a pin.

Figure 8.13 - Actions and action effects on a pin

Figure 8.13 - Actions and action effects on a pin

128

8.6 Welded connections

8.6.1 General

  1. In the design of welded joints consideration should be given both to the strength of the welds and to the strength of the HAZ.
  2. The design guidance given here applies to:
  3. If - in case of primary load bearing members - the above conditions are not fulfilled special test pieces should be welded and tested, which should be agreed upon by the contracting parties.
  4. If for secondary or non load-bearing members a lower quality level has been specified lower design strength values should be used.

8.6.2 Heat-affected zone (HAZ)

  1. For the following classes of alloys a heat-affected zone should be taken into account (see also Image 6.1.6 Image):
  2. The severity and extent (dimensions) of HAZ softening given in Image 6.1.6 Image should be taken into account. Both severity and extent are different for TIG and MIG welding. For TIG welding a higher extent (larger HAZ area) and more severe softening due to the higher heat-input should be applied.
  3. The characteristic strengths fu,haz for the material in the HAZ are given in Table 3.2. The characteristic shear strength in the HAZ is defined as: fv,haz = fv,haz / Image

8.6.3 Design of welded connections

  1. For the design of welded connections the following should be verified:
  2. The deformation capacity of a welded joint can be improved if the design strength of the welds is greater than that of the material in the HAZ.
8.6.3.1 Characteristic strength of weld metal
  1. For the characteristic strength of weld metal (fw) the values according to Table 8.8 should be used, provided that the combinations of parent metal and filler metal as given in 3.3.4, are applied.
  2. In welded connections the strength of the weld metal is usually lower than the strength of the parent metal except for the strength in the HAZ. 129
    Table 8.8 - Characteristic strength values of weld metal fw
    Characteristic strength Filler metal Alloy
    3103 5052 5083 5454 6060 6005A 6061 6082 7020
    fw [N/mm2] 5356 - 170 240 220 160 180 190 210 260
      4043A 95 - - - 150 160 170 190 210
    1. For alloys EN AW-5754 and EN AW-5049 the values of alloy 5454 can be used;
      • for EN AW-6063, EN AW-3005 and EN AW-5005 the values of alloy 6060 can be used;
      • for EN AW-6106 the values of alloy 6005A can be used;
      • for EN AW-3004 the values of alloy 6082 can be used;
      • for EN AW-8011 A a value of 100 N/mm2 for filler metal Type 4 and Type 5 can be used.
    2. Image If filler metals 5056,5356A, 5556A/5556B, 5183/5183A are used Image then the values for 5356 have to be applied.
    3. If filler metals 4047A or 3103 are used then the values of 4043A have to be applied.
    4. For combinations of different alloys the lowest characteristic strength of the weld metal has to be used.
  3. The characteristic strength of weld metal should be distinguished according to the filler metal used. The choice of filler metal has a significant influence on the strength of the weld metal.
8.6.3.2 Design of butt welds
8.6.3.2.1 Full Penetration Butt Welds
  1. Full penetration butt welds should be applied for primary load-bearing members.
  2. The effective thickness of a full penetration butt weld should be taken as the thickness of the connected members. With different member thicknesses the smallest member thickness should be taken as weld thickness.
  3. Reinforcement or undercut of the weld within the limits as specified should be neglected for the design.
  4. The effective length should be taken as equal to the total weld length if run-on and run-off plates are used. Otherwise the total length should be reduced by twice the thickness t.
8.6.3.2.2 Partial Penetration Butt Welds
  1. Partial penetration butt welds should only be used for secondary and non load-bearing members.
  2. For partial penetration butt welds an effective throat section te should be applied (see Figure 8.21).
8.6.3.2.3 Design Formulae for Butt Welds
  1. For the design stresses the following applies:
  2. Residual stresses and stresses not participating in the transfer of load need not be included when checking the resistance of a weld. Image Text deleted Image

    Figure 8.14 - Butt weld subject to normal stresses

    Figure 8.14 - Butt weld subject to normal stresses

    Figure 8.15 - Butt weld subject to shear stresses

    Figure 8.15 - Butt weld subject to shear stresses

8.6.3.3 Design of fillet welds
  1. For the design of fillet welds the throat section should be taken as the governing section.
  2. The throat section should be determined by the effective weld length and the effective throat thickness of the weld.
  3. The effective length should be taken as the total length of the weld if:
  4. Image If the length of the weld is less than 8 times the throat thickness the resistance of the weld should not be taken into account. If the stress distribution along the length of the weld is not constant, see Figure 8.16b, and the length of the weld exceeds 100 times the throat thickness the effective weld length of longitudinal welds should be taken as:

    Lw,eff = (1,2 - 0,2 Lw/100 a)Lw with Lw ≥ 100 a     (8.32)Image

    131

    Image where:

    Lw,eff =effective length of longitudinal fillet welds
    Lw =total length longitudinal fillet welds
    a =effective throat thickness, see Figure 8.17.

    NOTE With non-uniform stress distributions and thin, long welds the deformation capacity at the ends may be exhausted before the middle part of the weld yields: thus the connection fails by a kind of zipper-effect.

    Figure 8.16 - Stress Distributions in Joints with Fillet Welds

    Figure 8.16 - Stress Distributions in Joints with Fillet Welds Image

  5. The effective throat thickness a has to be determined as indicated in Figure 8.17 (a the height of the largest triangle which can be inscribed within the weld).
  6. If the qualification specimens show a consistent, positive root penetration, for design purposes the following may be assumed:
  7. The forces acting on a fillet weld should be resolved into stress components with respect to the throat section, see Figure 8.18. These components are:
    - a normal stress σ perpendicular to the throat section;
    - a normal stress σ parallel to the weld axis;
    - a shear stress τ acting on the throat section perpendicular to the weld axis;
    - a shear stress τ acting on the throat section parallel to the weld axis.
  8. Residual stresses and stresses not participating in the transfer of load need not be included when checking the resistance of a fillet weld. This applies specifically to the normal stress τ parallel to the axis of a weld. 132

    Figure 8.18 - Stresses σ⊥,τ⊥,σ∥, and σ∥, acting on the throat section of a fillet weld.

    Figure 8.18 - Stresses σ, τ, σ, and τ, acting on the throat section of a fillet weld.

  9. The design resistance of a fillet weld should fulfil:

    Image

    where:

    fw is the characteristic strength of weld metal according to Table 8.8;
    γMw is the partial safety factor for welded joints, see 8.1.1.
  10. For two frequently occurring cases the following design formulas, derived from formula (8.33), should be applied:
8.6.3.4 Design resistance in HAZ
  1. The design of a HAZ adjacent to a weld should be taken as follows:
    1. Tensile force perpendicular to the failure plane (see Figure 8.21):
      • - HAZ butt welds:

        Image Image at the toe of the weld (full cross section) for full penetration welds and effective throat section te for partial penetration welds; Image     (8.38)

      • - HAZ fillet welds:

        Image at the fusion boundary and at the toe of the weld (full cross section).     (8.39)

      where:

      σhaz,Ed design normal stress perpendicular to the weld axis;
      Image Text deleted Image
      fu,haz characteristic strength HAZ, see 8.6.2;
      γMw Image partial safety factor Image for welded joints, see 8.1.1.
    2. Shear force in failure plane:
      • - HAZ butt welds: 134

        Image Image at the toe of the weld (full cross section) for full penetration welds and effective throat section te for partial penetration welds Image     (8.40)

      • - HAZ fillet welds:

        Image Image at the fusion boundary and at the toe Image of the weld (full cross section)     (8.41)

      where:

      τhaz,Ed shear stress parallel to the weld axis;
      fv,haz characteristic shear strength HAZ, see 8.6.2;
      γMw Image partial safety factor Image for welded joints, see 8.1.1;.
    3. Combined shear and tension:
      • - HAZ butt welds:

        Image Image at the toe of the weld (full cross section) for full penetration welds and effective throat section te for partial penetration welds Image     (8.42)

      • - HAZ fillet welds:

        Image at the fusion boundary and at the toe of the weld (full cross section)     (8.43)Image

        Symbols see 8.6.3.4a) and b).

        Figure 8.21 - Failure planes in HAZ adjacent to a weld

        Figure 8.21 - Failure planes in HAZ adjacent to a weld

  2. The above design guidance about HAZ is dealing with welded connections as such. In 6.3 and 6.5 design guidance is given for the effect of HAZ on the structural behaviour of members.
8.6.3.5 Design of connections with combined welds
  1. For the design of connections with combined welds one of the two following methods should be applied(see also 8.1.4):
    - Method 1: The loads acting on the joint are distributed to the respective welds that are most suited to carry them.
    - Method 2: The welds are designed for the stresses occurring in the adjacent parent metal of the different parts of the joint.
  2. Applying one of the above methods the design of connections with combined welds is reduced to the design of the constituent welds.
  3. With method 1 it has to be checked whether the weld possesses sufficient deformation capacity to allow for such a simplified load distribution. Besides, the assumed loads in the welds should not give rise to overloading of the connected members. 135
  4. With method 2 the above problems do not exist, but sometimes it may be difficult to determine the stresses in the parent metal of the different parts of the joint.
  5. Assuming a simplified load distribution, like described as method l, is the most commonly applied method. Since the actual distribution of loads between the welds is highly indeterminate, such assumptions have been found to be an acceptable and satisfactory design practice. However, these assumptions rely on the demonstrated ability of welds to redistribute loads by yielding.
  6. Residual stresses and other stresses not participating in the transfer load need not be considered for the design. For instance, stresses due to minor eccentricities in the joint need not be considered.

8.7 Hybrid connections

  1. If different forms of fasteners are used to carry a shear load or if welding and fasteners are used in combination, the designer should verify that they act together.
  2. In general the degree of collaboration may be evaluated through a consideration of the load-displacement curves of the particular connection with individual kind of joining, or also by adequate tests of the complete hybrid connection.
  3. In particular normal bolts with hole clearance should not collaborate with welding.
  4. Preloaded high-strength bolts in connections designed as slip-resistant at the ultimate limit state (Category C in 8.5.3.1) may be assumed to share load with welds, provided that the final tightening of the bolts is carried out after the welding is complete. The total design load should be given as the sum of the appropriate design resistance of each fastener with its corresponding γM -value.

8.8 Adhesive bonded connections

NOTE Recommendations for adhesive bonded connections are given in Annex M.

8.9 Other joining methods

  1. Rules for the design of mechanical fasteners are given in EN 1999-1-4
  2. Other joining methods, which are not covered by the design rules in this standard, may be used provided that appropriate tests in accordance with EN 1990 are carried out in order:
  3. Examples of other joining methods are:

    NOTE The National Annex may give provisions for other joining methods.

136

Image Annex A – Reliability differentiation

[informative]

A.1 Introduction

  1. EN 1990 gives in its section 2 basic requirements to ensure that the structure achieves the required reliability. Its Annex B introduces consequence classes and reliability classes and gives guidelines for the choice of consequence class for the purpose of reliability differentiation. Consequence classes for structural components are divided in three levels noted CCi (i = 1,2 or 3)
  2. The consequence class and the associated reliability class for a structure or component have implications for the requirements for the design and execution of the structure, and in particular to requirements to design supervision and to inspection of execution.
  3. This annex is a guide for the application of the various parts of EN 1999 and for drafting the execution specification required by EN 1090-3.

A.2 Design provisions for reliability differentiation - Design supervision levels

  1. The guidance in EN 1990, Annex B for reliability differentiation provides:

    NOTE The National Annex may give rules for the application of consequence classes and reliability classes and for the connection between them and requirements for design supervision. Recommendations are given in EN 1990 Annex B.

A.3 Execution provisions for reliability differentiation – Execution classes

  1. Execution classes are introduced in order to differentiate in requirements to structures and their components for reliability management of the execution work, in accordance with EN 1990, clause 2.2 and its informative Annex B.
  2. Aluminium structures are classified in 4 execution classes denoted EXC1, 2, 3 and 4, where class 4 has the most stringent requirements.

    NOTE EN 1990 recommends three consequence classes and three reliability classes. EN 1990 does, however, not include structures subject to fatigue that is covered in EN 1999-1-3.

  3. The execution class may apply to the whole structure, to a part of a structure, to one or more components or to specific details. A structure may include more than one execution class.
  4. It is a condition that the execution of structures and structural components is undertaken according to EN 1090-3 following the rules for the various execution classes given in EN 1090-3.

A.4 Governing factors for choice of execution class

  1. The execution class should be selected based on the following three conditions:
    1. the consequences of a structural failure, either human, economical or environmental;
    2. the type of loading, i.e. whether the structure is subject to predominantly static loading or a significant fatigue loading; Image 137
    3. Image the technology and procedures to be used for the work connected with the requirements for the quality level of the component.
  2. For considerations of the conditions under (a.) by use of consequence classes, see A. 1.
  3. The type of uncertainty in exposure and actions (b.) and the complexity in work execution (c.) represent hazards that can impose flaws in the structure leading to its malfunction during use. To consider such hazards service categories and production categories are introduced, see Table A.1 and A.2.
    Table A.1: Criteria for service category
    Category Criterion
    SC1 Structures subject to quasi static actions a)
    SC2 Structures subject to repeated actions of such intensity that the inspection regime specified for components subject to fatigue is required. b)
    a)Guidance is given in EN 1999-1-3 whether a component or structure may be regarded as subject to quasi static actions and classified in category SC1.
    b) Service category SC2 should be used for cases not covered by SC1.
    Table A.2: Criteria for production category
    Category Criterion
    PC1 Non welded components
    PC2 Welded components

    NOTE 1 The determination of the execution class for a structure/component should be taken jointly by the designer and the owner of the construction works, following national provisions in the place of use for the structure. EN 1090-3 requires that the execution class is defined in the execution specification.

    NOTE 2 EN 1090-3 gives rules for the execution of work including rules for inspection. The inspection includes in particular rules for welded structures with requirements for quality level, allowable size and kind of weld defects, type and extent of inspection, requirements to supervision and competence of welding supervisors and welding personnel, in relation to the execution class.

    Table A.3 gives recommendations for selection of execution class based on the above criteria. In case that no execution class has been specified, it is recommended that execution class EXC2 applies.

A.5 Determination of execution class

  1. The recommended procedure for determination of the execution class is the following:
    1. Determination of consequence class, expressed in terms of predictable consequences of a failure or collapse of a component, see EN 1990;
    2. determination of service category and production category, see Table A.1 and A.2;
    3. determination of execution class from the results of the operations a) and b) in accordance with the recommended matrix in Table A.3. Image
    138
    Image Table A.3 Determination of execution class
    Consequence class CC1 CC2 CC3
    Service category SC1 SC2 SC1 SC2 SC1 SC2
    Production category PC1 EXC1 EXC1 EXC2 EXC3 EXC3 a) EXC3 a)
    PC2 EXC1 EXC2 EXC2 EXC3 EXC3 a) EXC4
    a) EXC4 should be applied to special structures or structures with extreme consequences of a structural failure also in the indicated categories as required by national provisions.

A.6 Utilization grades

  1. Utilization grades are used to determine requirements to the amount of inspection and to the acceptance criteria for welds, see EN 1090-3.
  2. The utilization grade U for structures and components subject to predominantly static loading is defined by

    Image

    where:

    Ek is the characteristic action effect;
    Rk is the characteristic resistance.

    For combined actions U is given by the interaction formulae.

  3. The utilization grade for structures and components subject to fatigue loads is defined in EN 1999-1-3. Image
139

Annex B - Equivalent T-stub in tension

[normative]

B.1 General rules for evaluation of resistance

  1. In bolted connections an equivalent T-stub may be used to model the resistance of the basic components of several structural systems (for instance beam-to-column joints), rather then as a stand alone connection as indicated in Figure 8.8.
  2. The possible modes of failure of the flange of an equivalent T-stub may be assumed to be similar to those expected to occur in the basic component that it represents, see Figure B.1.
  3. The total effective length ∑leff of an equivalent T-stub should be such that the resistance of its flange is equivalent to that of the basic joint component that it represents, see Figure B.5.

    NOTE The effective length of an equivalent T-stub is a notional length and does not necessarily correspond to the physical length of the basic joint component that it represents.

    Figure B.1 - T-stub as basic component of other structural systems

    Figure B.1 - T-stub as basic component of other structural systems

  4. In cases where prying forces may develop, see 8.5.10 of EN 1999-1-1, the tension resistance of a T-stub flange Fu,Rd should be taken as the smallest value for the four possible failure modes (see Figure B.2) and has to be determined as follows (generally in bolted beam-to-column joints or beam splices it may be assumed that prying forces will develop):
  5. In case where prying forces may not develop (failure mode 3), the tension resistance of a T-stub flange Fu,Rd should be taken as the smallest value, determined as follows:
  6. Methods for determination effective lengths leff for the individual bolt-rows and the bolt-group, for modeling basic components of a joint as equivalent T-stub flanges, are given in:

    where the dimension emin and m are as indicated in Figure B.3, while the factor α of Table B.2 is given in Figure B.4.

142
Table B.1 - Effective length for unstiffened flanges
Bolt-row location Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows
Circular patterns leff,cp Non-circular patterns leff,np Circular patterns leff,cp Non-circular patterns leff,cp
Inner bolt-row m 4m + 1,25e 2p P
End bolt-row The smaller of: 2πm πm + 2e1 The smaller of: 4m + l,25e
2m + 0,625e + e1
The smaller of: πm + p 2e1 + p The smaller of: 2m + 0,625e + 0,5p e1 + 0,5p
Mode 1: leff, 1 = leff,nc but leff, lleff,cp Σleff,1 = Σlleff,nc but Σleff,1 ≤ Σleff,cp
Mode 2: leff, 1 = leff,nc Σleff,l = Σleff,nc
Image NOTE See figures 8.1 to 8.4. Image
Table B.2 - Effective length for stiffened flanges
Bolt-row location Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows
Circular patterns leff,cp Non-circular patterns leff,cp Circular patterns leff,cp Non-circular patterns leff,cp
Bolt-row adjacent to a stiffener m αm πm + p 0,5p + αm − (2m + 0,625e)
Other inner bolt-row 2πm 4m + 1,25e 2p P
Other end bolt-row The smaller of: 2πm

πm + 2e1

The smaller of: 4m + l,25e

2m + 0,625e + e1

The smaller of: πm + p
2e1 + p
The smaller of: 2m + 0,625e + 0,5p
End bolt row adjacent to a stiffener The smaller of 2πm

πm + 2e1

e1 + αm − (2m + 0,625e) not relevant not relevant
Mode 1: leff, 1 = leff,nc but leff, lleff,cp Σleff,1 = Σlleff,nc but Σleff,1 ≤ Σleff,cp
Mode 2: leff, 1 = leff,nc Σleff,l = Σleff,nc
143

Figure B.4 - Values of factor α for the effective length for stiffened flanges

Figure B.4 - Values of factor α for the effective length for stiffened flanges

B.2 Individual bolt-row, bolt-groups and groups of bolt-rows

Although in an actual T-stub flange the forces at each bolt-row are generally equal, if an equivalent T-stub flange is used to model a basic component in a joint, allowance should be made for the forces are generally different at each bolt-row.

When modeling a basic joint component by equivalent T-stub flanges, if necessary more than one equivalent T-stub may be used, with the bolt-rows divided into separate bolt-groups corresponding to each equivalent T-stub flange (see Figure B.1).

  1. The following conditions should be satisfied:
    1. the force at each bolt-row should not exceed the resistance determined considering only that individual bolt-row;
    2. the total force on each group of bolt row, comprising two or more adjacent bolt-row within the same bolt-group, should not exceed the resistance of that group of bolt-row.
  2. Accordingly, when obtaining the tension resistance of the basic component represented by an equivalent T-stub flange, the following parameters should generally be determined:
    1. the maximum resistance of an individual bolt-row, determined considering only that bolt-row, see Figure B.5(a);
    2. the contribution of each bolt-row to the maximum resistance of two or more adjacent bolt-row within a bolt-group, determined considering only those bolt-rows, see Figure B.5(b).
  3. In the case of an individual bolt-row Σleff should be taken as equal to the effective length leff given in Table B.1 and Table B.2 for that bolt-row as an individual bolt-row.
  4. In the case of a group of bolt-rows Σleff should be taken as equal to the effective length leff given in Table B.1 and Table B.2 for each relevant bolt-row as part of a bolt group.
144

Figure B.5 - Equivalent T-stub for individual bolt-rows and groups of bolt-rows.

Figure B.5 - Equivalent T-stub for individual bolt-rows and groups of bolt-rows.

145

Annex C - Materials selection

[informative]

C.1 General

  1. The choice of a suitable aluminium or aluminium alloy material for any application in the structural field is determined by a combination of factors; strength, durability, physical properties, weldability, formability and availability both in the alloy and the particular form required. The wrought and cast alloys are described below subdivided into heat treatable and non-heat treatable alloys.
  2. The properties and characteristics of these alloys may be compared in general terms in Table C.1 for wrought aluminium alloys and Table C.2 for casting alloys. Properties and characteristics may vary with temper of the alloy.
  3. If connections are to be made to other metals, specialist advice should be sought on the protective measures necessary to avoid galvanic corrosion.

C.2 Wrought products

C.2.1 Wrought heat treatable alloys

  1. Within the 6xxx series alloys, the alloys EN AW-6082, EN AW-6061, EN AW-6005A, EN AW-6106, EN AW-6063 and EN AW-6060 are suitable for structural applications. These alloys have durability rating B. Within the 7xxx series alloys, the alloy EN AW-7020 is suitable for general structural applications and has durability rating C.
C.2.1.1 Alloys EN AW-6082 and EN AW-6061
  1. EN AW-6082 is one of the most widely used heat treatable alloy and often the principal structural alloy for welded and non-welded applications. It is a high strength alloy available in most forms; solid and hollow extrusions, tube, plate, sheet and forging, and finds increasing use in components exposed to the marine environment. EN AW-6061 is also a widely used heat treatable alloy for welded and non-welded applications available in solid and hollow extrusions and tube. Both alloys are used normally in the fully heat-treated condition EN AW-6082-T6 and EN AW-6061-T6.
  2. The choice of these alloys as a structural material is based on a favourable combination of properties; high strength after heat treatment, good corrosion resistance, good weldability by both the MIG and TIG processes good formability in the T4 temper and good machining properties. Loss of strength in the heat-affected zone (HAZ) of welded joints should be considered. Strength can be recovered to a limited degree by post weld natural ageing. If used in extrusions it is generally restricted to thicker less intricate shapes than with the other 6xxx series alloys. AW-6082 is a common alloy for extrusions, plate and sheet from stock. The alloy may be riveted using alloys EN AW-6082, EN AW-5754 or EN AW-5019 in O or harder tempers, filler metals for welding are specified in prEN 1011 -4.
C.2.1.2 Alloys EN AW-6005A
  1. EN AW-6005A alloy which is also recommended for structural applications, is available in extruded forms only and combines medium strength with the ability to be extruded into shapes more complex than those obtainable with EN AW-6082 or EN AW-6061. This is particularly true for thin-walled hollow shapes. Like EN AW-6082 and EN AW-6061, the alloys are readily welded by the TIG and MIG processes and have similar loss of strength in the HAZ in welded joints. Filler metals for welding these alloys are specified in prEN 1011-4.
  2. The corrosion resistance of welded and unwelded components is similar or better than EN AW-6082. The machining properties are similar to those of EN AW-6082.
146
Table C.1 - Comparison of general characteristics and other properties for structural alloys
Alloy EN-Designation Form and temper standardised for Strength Durability rating a) Weldability Decorative anodising
Sheet, strip and plate Extruded products Cold drawn products Forgings
Bar / rod Tube Profile Tube
EN AW-3004 Image - - - -   III/IV A I I
EN AW-3005 Image - - - -   III/IV A I I
EN AW-3103 Image Image Image Image Image   III/IV A I II
EN AW-5005 Image Image Image Image Image   III/IV A I I
EN AW-5049 Image - - - -   II/III A I I/II
EN AW-5052 Image Image Image x) Image x) Image     A I I/II
EN AW-5083 Image Image Image x) Image x) Image Image I/II A I I/II
EN AW-5454 Image Image Image x) Image x) -   II/III A I I/II
EN AW-5754 Image Image Image x) Image x) Image Image II/III A I I/II
EN AW-6060 - Image Image Image Image   II/III B I I
EN AW-6061 - Image Image Image Image   II/III B I II/III
EN AW-6063 - Image Image Image Image   II/III B I I/II
EN AW-6005A - Image Image Image -   II B I II/III
EN AW-6106 - - - Image -   II/III B I I/II
EN AW-6082 Image Image Image Image Image Image I/II B I II/III
EN AW-7020 Image Image Image Image Image   I C I II/III
EN AW-8011A Image - - - - - III/IV B II III/IV
Key: Image Standardised in a range of tempers; Availability of semi products from stock to be checked for each product and dimension
-1 Not standardised
x) Simple, solid sections only (seamless products over mandrel)
I Excellent
II Good
III Fair
IV Poor
NOTE These indications are for guidance only and each ranking is only applicable in the column concerned and may vary with temper
a) See Table 3.1a.
147
Table C.2 - Comparison of casting characteristics and other general properties
Casting alloy Form of casting Castability Strength Durability rating Decorative anodising Weld-ability
Designation Sand Chill or permanent mould
EN AC-42100   II II/III B IV II
EN AC-42200   II II B IV II
EN AC-43300 I II B V II
EN AC-43000   I/II IV B V II
EN AC-44200 I IV B V II
EN AC-51300 III IV A I II
Key: I Excellent
II Good
III Fair
IV Poor
V Not recommended
Indicates the casting method recommended for load bearing parts for each alloy.
NOTE 1 These indications are for guidance only and each ranking is only applicable in the column concerned.
NOTE 2 The properties will vary with the condition of the casting.
C.2.1.3 Alloys EN AW-6060, EN AW-6063 and EN AW 6106
  1. EN AW-6060, EN AW-6063 and EN AW-6106 are recommended for structural applications and are available in extruded and cold drawn products only. They are used if strength is not of paramount importance and has to be compromised with appearance where they offer good durability and surface finish and the ability to be extruded into thin walled and intricate shapes. The alloys are particularly suited to anodising and similar finishing processes. Like other 6xxx series alloys they are readily weldable by both MIG and TIG processes and lose strength in welded joints in the HAZ. Filler metals for welding these alloys are specified in prEN 1011-4.
C.2.1.4 Alloys EN AW-7020
  1. EN AW-7020 alloys are recommended for structural applications for welded and non-welded applications. It is a high strength alloy available in solid and hollow extrusions; plate and sheet and tube. This alloy is not as easy to produce in complicated extrusions as 6xxx series alloys and is not readily available. It is used normally in the fully heat treated condition EN AW-7020 T6. It has better post weld strength than the 6xxx series due to its natural ageing property. This alloy and others in the 7xxx series of alloys are however sensitive to environmental conditions and its satisfactory performance is as dependent on correct methods of manufacture and fabrication as on control of composition. Due to the susceptibility of exfoliation corrosion, material in T4 temper should only be used in the fabrication stage provided the structure could be artificially aged after completion. If not heat-treated after welding, the need for protection of the HAZ should be checked according to D.3.2. If a material in the T6 condition is subjected to any operations which induce cold work such as bending, shearing or punching etc., the alloy may be made susceptible to stress corrosion cracking. It is essential therefore that there be direct collaboration between the designer and the manufacturer on the intended use and the likely service conditions.
148

C.2.2 Wrought non-heat treatable alloys

  1. Within the 5xxx series alloys, the alloys EN AW-5049, EN AW-5052 EN AW-5454 and EN AW-5754 and EN AW-5083 are recommended for structural applications all have durability rating A. Other non-heat treatable alloys considered for less stressed structural applications are EN AW- 3004, EN AW-3005, EN AW 3103 and EN AW-5005 again with durability rating A.
C.2.2.1 EN AW- 5049, EN AW-5052, EN AW-5454 and EN AW-5754
  1. EN AW-5049; EN AW-5052, EN AW-5454 and EN AW-5754 are suitable for welded or mechanically joined structural parts subjected to moderate stress. The alloys are ductile in the annealed condition, but loose ductility rapidly with cold forming. They are readily welded by MIG and TIG processes using filler metals specified in prEN 1011-4 and offer very good resistance to corrosive attack, especially in a marine atmosphere. Available principally as rolled products their reduced magnesium content also allows only simple extruded solid shapes.
  2. The alloys can be easily machined in the harder tempers. EN AW-5754 is the strongest 5xxx series alloy offering practical immunity to intergranular corrosion and stress corrosion.
C.2.2.2 EN AW-5083
  1. EN AW-5083 is the strongest non-heat treatable structural alloy in general commercial use, possessing good properties in welded components and good corrosion resistance. It is ductile in the soft condition with good forming properties but looses ductility with cold forming, and can become hard with low ductility.
  2. EN AW-5083 may in all tempers (Hx), especially in H32 and H34 tempers, be susceptible to intergranular corrosion, which under certain circumstances, may develop into stress corrosion cracking under sustained loading. Special tempers such as H1 16 have been developed to minimise this effect. Nevertheless the use of this alloy is not recommended where the material is to be subjected to further heavy cold working and/or where the service temperature is expected to be above 65° C. In such cases the alloy EN AW-5754 should be selected instead.
  3. If the service conditions for the alloy/temper to be used are such that there is a potential for stress corrosion cracking, the material should be checked in a stress corrosion test prior to its delivery. The conditions for the test should be agreed between the parties concerned, taking the relevant service conditions and the material properties of the actual alloy/temper into account.
  4. EN AW-5083 is fitted to be welded with the MIG and the TIG processes applying filler metals specified in prEN 1011-4. If strain hardened material is welded, the properties in the HAZ will revert to the annealed temper. The alloy is available as plate, sheet, simple solid shape extrusions, seamless tube, drawn tube and forging. Due to the high magnesium content it is difficult to extrude. Consequently it is limited to delivery in relatively thick-walled simple solid profiles and seamless hollow profiles with one hollow space (tubes).
  5. EN AW 5083 has good machining properties in all tempers.
C.2.2.3 EN AW-3004, EN AW-3005, EN AW-3103 and EN AW 5005
  1. EN AW-3004, EN AW-3005, EN AW-3103 and EN AW 5005 are available and used preferably in sheet and plate forms. These alloys are slightly stronger and harder than “commercially pure” aluminium with high ductility, weldability and good corrosion resistance.
C.2.2.4 EN AW-8011A
  1. EN AW-8011A belongs to the AlFeSi group and has a long tradition used preferably as material for packaging. Due to its advantages in fabrication EN AW-8011A finds more and more application in building industry especially for facades.
149

C.3 Cast products

C.3.1 General

  1. The casting materials of Table 3.3 may be used for load carrying parts under the provision that special design rules and quality requirements given in C.3.4 are observed.
  2. Six foundry alloys are recommended for structural applications, four heat treatable alloys EN AC-42100, EN AC-42200, EN AC-43000 and EN AC-43300 plus two non-heat treatable alloys, EN AC-44200 and EN AC-51300. These alloys are described below. The alloys will normally comply with the requirements for elongation given in C.3.4.3. Due to the low Cu content they also have good corrosion resistance.

C.3.2 Heat treatable casting alloys EN AC-42100, EN AC-42200, EN AC-43000 and EN AC-43300

  1. EN AC-42100, EN AC-42200, EN AC-43000 and EN AC-43300 are all alloys in the Al-Si-Mg system and are responsive to heat treatment. All are suitable for sand and chill or permanent mould castings but are not normally used for pressure die castings except by using advanced casting methods. The highest strength is achieved with EN AC-42200-T6 but with a lower ductility than EN AC-42100.
  2. EN AC-43300 exhibits the best foundry castability with fair resistance to corrosion, good machinability and weldability. Foundry castability of alloys EN AC-42100 and EN AC-42200 is good, with good resistance to corrosion and machinability.

C.3.3 Non-heat treatable casting alloys EN AC-44200 and EN AC-51300

  1. Image EN AC-44200 Image and EN AC-51300 alloys are suitable for sand and chill or permanent mould castings but not recommended for pressure die castings. Alloy EN AC-44200 possesses excellent foundry castability, but EN AC-51300 has fair castability and is only suitable for more simple shapes. EN AC-51300 has the highest strength, has excellent resistance to corrosion and is machinable. The EN AC-51300 alloy may be decoratively anodised.

C.3.4 Special design rules for castings

C.3.4.1 General design provisions
  1. The special design rules are applicable to cast parts which have geometry and applied actions where buckling cannot occur. The cast component should not be formed by bending or welded or machined with sharp internal corners.
  2. The design of load carrying parts of casts in temper and casting method as listed in Table 3.3 should be done on the basis of linear elastic analysis by comparing the equivalent design stress

    Image

    with the design strength σRd, where σRd is the lesser of foc/γMo,c and fuc/γMu,c

    NOTE Partial factors γMo,c and γMu,c may he defined in the National Annex. The following numerical values are recommended for buildings:

    γMo,c = 1,1 and γMu,c = 2,0

  3. The design bearing resistance of bolts and rivets should be taken as the lesser value from the following two expressions, based on equation (8.11) of Table 8.5:

    Fb,Rd = k1αb fucdt/γM2,cu     (C.2)

    Fb,Rd = k1αbfocdt/γM2,co     (C.3)

    NOTE Partial factors γM2,cu and γM2,co may be defined in the National Annex. The following numerical values are recommended for buildings:

    γM2,cu = γMu,c = 2,0 and γM2,co = γMo,c = 1,1

    150
  4. The design bearing resistance for the plate material of pin connections Fb,Rd should be taken as the lesser value from the following two expressions, based on Table 8.7:

    Fb,Rd = 1,5 fucdt/γMp,cu     (C.4)

    Fb,Rd = 1,5 focdt/γMp,co     (C.5)

    NOTE Partial factors γMp,co and γMp,cu may be defined in the National Annex. The following numerical values are recommended for buildings:

    γMp,co = γMp = 1,25 and γMp,cu = γMu,c = 2,0

  5. The specification for the cast part should include the following information:
    1. areas with tension stresses and utilization of the design resistance of more than 70 % (areas H);
    2. areas with tension stresses and utilization of the design resistance between 70 and 30 % (areas M);
    3. areas with compressive stresses and utilization of the design resistance between 100 and 30 % (areas M);
    4. areas with utilization of the design resistance of less than 30 % (areas N);
    5. the location and direction where the sampling for the material test should be made. The location should be identical or close to the location with the highest stresses of the component. If there are various areas with high stresses, sampling should be executed at more than one location;
    6. all tests to be performed and any test conditions deviating from EN 1706, qualification procedures and qualification requirements;
    7. the required minimum values for strength and elongation.
C.3.4.2 Quality requirements, testing and quality documentation
  1. To check the mechanical properties of each area specified as having high strain two test specimens should betaken from the batch. In some cases also areas with difficult casting conditions should be specified as areas to betested. The test results for ultimate strength and yield strength should not be less than the values in Table 3.3. Deviating from Table 3.3, the As-elongation Image should not be less than 2 %. If sand casting is used it is allowed to thicken the cast part in the areas with the highest stresses or where the test specimens should be taken so that these can be taken without the casting being destroyed.
  2. The following requirements apply to limitation of internal defects:
    1. Cracks in the cast parts are not allowed.
    2. For porosity the limiting values are:
      • - H-areas: 4 %
      • - M-areas: 6 %
      • - N-areas: 8 %

      The diameter of pores should be less than 2 mm.

    3. Each casting should be subject to penetrant testing for exterior cracks and to radiation test for interior defects using image intensifier unless otherwise specified. The amount of inspection may be reduced if the cast parts are subject to only compressive stresses. The following standards specify the test procedures: EN 1371-1 in combination with EN 571 for the penetrant testing and prEN 13068 (radiology) Image EN 12681 Image (radiography) in combination with EN 444 for carrying out the radiation test.
  3. Test procedures and delivery details regarding the test and the quality requirements of EN 1559-1 and EN 1559-4 should be agreed and given in written specifications for the tests. Repair welding is only allowed to repair minor casting defects. The manufacturer should inform about any need for and the result of such repair.
  4. The supplier of cast products should confirm all required material properties and the tests executed to fulfil the specified requirements by an inspection certificate 3.1.B in accordance with EN 10204.
151

C.4 Connecting devices

C.4.1 Aluminium bolts

  1. In lack of EN standards for aluminium bolts, the aluminium bolts given in Table 3.4 should only be used if the bolt manufacturer certifies that the bolts are produced and tested according to EN 28839 with regard to mechanical properties and that geometrical tolerances correspond to those for steel bolts according to EN 24014 or EN 24017. If the use of bolts with threads manufactured by cutting is not allowed it should be stated in the specification. All requirements for the bolts should be given in the specification. The bolt manufacturer should confirm that the material properties and the tests executed to check this by issuing an inspection certificate 3.1.B according to EN 10204.

C.4.2 Aluminium rivets

  1. In lack of EN standards for aluminium rivets, the solid aluminium rivets listed in Table 3.4 should only be used if the manufacturer certifies that they are produced of drawn round bar material according to EN 754 or drawn round wire material according to EN 1301 and expressly that the strength values of the rivet also fulfil the values of these standards.
  2. The following requirements concerning the geometry should be observed: Depth of head ≥ 0,6d; diameter of head ≥ 1,6d, radius ≥ 0,75d, no countersunk (d = nominal diameter of the solid shaft; see also Figure C.1). The requirements defined here should be inserted in the design specification and in all drawings with the remark that all procurement has to be done accordingly.
  3. The manufacturer of the rivets has to confirm all required material properties and tests to be executed fulfilling the specified requirement by an inspection certificate 3.1.B according to EN 10204.

Figure C.1 - Minimum head dimensions of solid shaft rivets (no countersunk)

Figure C.1 - Minimum head dimensions of solid shaft rivets (no countersunk)

152

Annex D – Corrosion and surface protection

[informative]

D.1 Corrosion of aluminium under various exposure conditions

  1. This annex gives information on corrosion tendency of aluminium alloys and recommendations for selection and protection of aluminium alloys dependant on the various exposure conditions.
  2. The corrosion resistance of aluminium alloys is attributable to the protective oxide film which forms on the surface of the metal immediately on exposure to air. This film is normally invisible, relatively inert and as it forms naturally on exposure to air or oxygen, and in many complex environments containing oxygen; the protective film is thus self sealing.
  3. In mild environments an aluminium surface will retain its original appearance for years, and no protection is needed for most alloys. In moderate industrial conditions there will be a darkening and roughening of the surface. As the atmosphere becomes more aggressive such as in certain strongly acidic or strongly alkaline environments, the surface discoloration and roughening will be worse with visible white powdery surface oxides and the oxide film may itself be soluble. The metal ceases to be fully protected and added protection is necessary. These conditions may also occur in crevices due to high local acid or alkaline conditions, but agents having this extreme effect are relatively few in number.
  4. In coastal and marine environments the surface will roughen and acquire a grey, stone-like, appearance, and protection of some alloys is necessary. Where aluminium is immersed in water special precautions may be necessary.
  5. Where surface attack does occur corrosion time curves for aluminium and aluminium alloys usually follow an exponential form, with an initial loss of reflectivity after slight weathering. After this there is very little further change over very extensive periods. On atmospheric exposure, the initial stage may be a few months or two to three years, followed by little, if any, further change over periods of twenty, thirty or even eighty years. Such behaviour is consistent for all external freely exposed conditions and for all internal or shielded conditions, except where extremes of acidity or alkalinity can develop. Tropical environments are in general no more harmful to aluminium than temperate environments, although certain 5xxx-alloys are affected by long exposure to high ambient temperatures, particularly if in marine environment.
  6. Generally the structure should be designed according to known practice for avoiding corrosion. The possibility of galvanic corrosion and crevice corrosion should be evaluated and avoided due to proper design. All parts should be well drained.
  7. If a decorative appearance of aluminium is required to be kept for a long time the suitable surface treatments are organic coatings (liquid coating, powder coating) and anodic oxidation. The excecution specification should define the detail requirements. Deviations of colour appearance should be taken in account and should agreed and defined e.g. by limit samples. Differences in appearance may occur by different lots of semi-products, by different lots of coating material and by different coaters. For the selection of suitable surface treatments the different behaviours of the systems concerning repairability, weathering resistance and cleanability should be taken in account. Specifications for anodic oxidation are given in EN 12373-1

D.2 Durability ratings of aluminium alloys

  1. The aluminium alloys listed in Tables 3.1a and 3.1b are categorised into three durability ratings; A, B and C in descending order of durability. These ratings are used to determine the need and degree of protection required. In structures employing more than one alloy, including filler metals in welds, the classification should be in accordance with the lowest of their durability ratings.
  2. For advice on the durability rating of aluminium alloys see Annex C.
  3. Table D.1 gives recommendation for corrosion protection for the three classes of durability ratings.
153

D.3 Corrosion protection

D.3.1 General

  1. The excecution specification should describe type and amount of protective treatment. The type of corrosion protection should be adapted to the corrosion mechanism as surface corrosion, galvanic induced corrosion, crevice corrosion and corrosion due to contamination by other building materials. Crevice corrosion can occur in any type of crevice, also between metal and plastic. Special building conditions may provoke corrosion e.g. if a copper roof is installed over aluminium elements.
  2. For the selection of a suitable corrosion protection the following item should be taken in account: Damages on organic coatings are to a certain degree repairable. Anodised parts have to be handled very carefully in transport and erection. Therefore protecting foils should be used.
  3. Anodic oxidation and organic coating under many circumstances are equivalent, under special conditions the one or other surface treatment is doubtless to prefer, depending on corrosive agents and the environment that influence the corrosion effects. In case of corrosion protection in combination with decorative aspects, see D.3.2(7). Specifications for anodic oxidation should be based on the EN 12373-1.
  4. Passivation is a short-term protection or for mild conditions.

D.3.2 Overall corrosion protection of structural aluminium

  1. The need to provide overall corrosion protection to structures constructed from the alloys listed in Tables 3.1a and 3.1b if exposed to various environments is given in Table D.1. The methods of providing corrosion protection are given in Image EN 1090-3Image. For the protection of sheet used in roofing and siding see Image EN 508-2 Image.
  2. In selecting the appropriate column of Table D.1 for a given exposure, a presence of localities within a region that have ‘microclimates’ significantly different from the environmental characteristics of the region as a whole should be evaluated. A region designated ‘rural’ may have local environments more closely resembling an industrial atmosphere at sites close to and down wind of factories. Similarly, a site near the sea but close to shore installations may, with the appropriate prevailing winds, have the characteristics of an industrial, rather than marine, atmosphere. The environment is not necessarily the same for a structure inside a building as for one outside.
  3. The occurrence of corrosion depends not only on the susceptibility of the material and the global conditions, but in practice more on the period of time during which moisture may be present in conjunction with entrapped dirt and corrosive agents. Areas of members, or structural details, where dirt is trapped or retained are more critical than areas where rain, and wind driven rain, cleans the surface and drying occurs quickly. This means that sheltered ledges should be avoided and that pockets in which water can remain should be eliminated or provided with effective draining devices.
  4. In assessing the need and level of protection required the design life history of the structure should be considered. For short life structures less stringent measures or no protection may be acceptable. Where planned inspection and maintenance will reveal the onset of corrosion at an early stage, so allowing remedial action to be taken, the initial level of protection provided may be permitted to be relaxed. Whereas, where inspection is impractical and evidence of corrosion attack will not be revealed, the initial level of protection must be higher. Therefore the need for protection in those cases marked (P) on Table D.1 should be established in conjunction with the engineer, manufacturer and if necessary a corrosion specialist.
  5. Because of these factors, localised conditions of increased severity may result. It is advisable to study the precise conditions prevailing at the actual site before deciding on the appropriate environment column of Table D.1.154
    Table D.1 - Recommendations for corrosion protection for various exposure conditions and durability ratings
    Alloy durability rating Material thickness mm Protection according to the exposure
    Atmospheric Immersed
    Rural Industrial/urban Marine Freshwater Sea water
    Moderate Severe Non-industrial Moderate Severe    
    A All 0 0 (Pr) 0 0 (Pr) 0 (Pr)
    B < 3 0 0 (Pr) (Pr) (Pr) (Pr) Pr Pr
    ≥ 3 0 0 0 0 0 (Pr) (Pr) Pr
    C All 0 0 2) (PD 2) 0 2) 0 2) (Pr) 2) (Pr) 1) NR
    0 Normally no protection necessary
    Pr Protection normally required except in special cases, see D.3.2
    (Pr) The need for protection depends on if there are special conditions for the structure, see D.3.2. In case there is a need it should be stated in the specification for the structure
    NR Immersion in sea water is not recommended
    1) For 7020, protection only required in Heat Affected Zone (HAZ) if heat treatment not applied after welding
    2) If heat treatment of 7020 after welding is not applied, the need to protect the HAZ should be checked with respect to conditions, see D.3.2.
    NOTE For the protection of sheet used in roofing and siding see Image EN 508-2Image.
  6. Where hollow sections are employed consideration should be given to the need to protect the internal void to prevent corrosion arising from the ingress of corrosive agents. Because of the difficulty of painting such sections, chemical conversion coatings may be of benefit. Where the internal void is sealed effectively or if no water can congregate inside the section, internal protection is not necessary.

D.3.3 Aluminium in contact with aluminium and other metals

  1. Consideration should be given to contacting surfaces in crevices and contact with certain metals or washings from certain metals which may cause electrochemical attack of aluminium. Such conditions can occur within a structure at joints. Contact surfaces and joints of aluminium to aluminium or to other metals and contact surfaces in bolted, riveted, welded and high strength friction grip bolted joints should be given additional protection to that required by Table D.1 as defined in Table D.2. Details of the corrosion protection procedure required are given Image EN 1090-3Image. For the protection of metal to metal contacts including joints for sheet used in roofing and siding see Image EN 508-2 Image.
  2. Where pre-painted or protected components are assembled, an additional sealing of the contact surfaces should be defined in the excecution specification including type and procedure of the sealing. Requirements should consider expected life of the structure, the exposure and the protection quality of the pre-protected components.

D.3.4 Aluminium surfaces in contact with non-metallic materials

D.3.4.1 Contact with concrete, masonry or plaster
  1. Aluminium in contact with dense compact concrete, masonry or plaster in a dry unpolluted or mild environment should be coated in the contacting surface with a coat of bituminous paint, or a coating providing the same protection. In an industrial or marine environment the contacting surface of the aluminium should be coated with at least two coats of heavy-duty bituminous paint; the surface of the 155 contacting material should preferably be similarly painted. Submerged contact between aluminium and such materials is not recommended, but if unavoidable, separation of the materials is recommended by the use of suitable mastic or a heavy duty damp course layer.
  2. Lightweight concrete and similar products require additional consideration if water or rising damp can extract a steady supply of aggressive alkali from the cement. The alkali water can then attack aluminium surfaces other than the direct contact surfaces.
D.3.4.2 Embedment in concrete
  1. The aluminium surfaces should be protected with at least two coats of bituminous paint or hot bitumen, and the coats should extend at least 75 mm above the concrete surface.
  2. Where the concrete contains chlorides (e.g. as additives or due to the use of sea-dredged aggregate), at least two coats of plasticised coal-tar pitch should be applied in accordance with the manufacturer’s instructions and the finished assembly should be over-painted locally with the same material, after the concrete has fully set, to seal the surface. Care should be taken where metallic contact occurs between the embedded aluminium parts and any steel reinforcement.
D.3.4.3 Contact with timber
  1. In an industrial, damp or marine environment the timber should be primed and painted.
  2. Some wood preservatives may be harmful to aluminium. The following preservatives are generally accepted as safe for use with aluminium without special precautions:
  3. The following preservatives should only be used in dry situations and where the aluminium surface in contact with the treated timber has a substantial application of sealant:
  4. The following preservatives should not be used in association with aluminium:
  5. Oak, chestnut and western red cedar, unless well seasoned, are likely to be harmful to aluminium, parti-cularly where these are through fastenings.
D.3.4.4 Contact with soils
  1. The surface of the metal should be protected with at least two coats of bituminous paint, hot bitumen, or plasticised coal tar pitch. Additional wrapping-tapes may be used to prevent mechanical damage to the coating.
D.3.4.5 Immersion in water
  1. Where aluminium parts are immersed in fresh or sea water including contaminated water, the aluminium should preferably be of durability rating A, with fastenings of aluminium or corrosion-resisting steel or fastened by welding. Tables D.1 and D.2 give the protection requirements for fresh water and sea water immersion.
  2. Data on the oxygen content, pH number, chemical or metallic, particularly copper content and the amount of movement of the water should be obtained as these factors may affect the degree of protection required.
D.3.4.6 Contact with chemicals used in the building industry
  1. Fungicides and mould repellents may contain metal compounds based on copper, mercury, tin and lead which, under wet or damp conditions could cause corrosion of the aluminium. The harmful effects may be countered by protecting the contacting surfaces which may be subject to washing or seepage from the chemicals.156
  2. Some cleaning materials can affect (pH < 5 and pH > 8) the surface of the aluminium. Where such chemicals are used to clean aluminium or other materials in the structure, care should be taken to ensure that the effects will not be detrimental to the aluminium. Often quick and adequate water rinsing will suffice, while in other situations temporary measures may be necessary to protect the aluminium from contact with the cleaners.
D.3.4.7 Contact with insulating materials used in the building industry

Products such as glass fibre, polyurethane and various insulation products may contain corrosive agents which can be extracted under moist conditions to the detriment of the aluminium. Insulating materials should be tested for compatibility with aluminium under damp and saline conditions. Where there is doubt a sealant should be applied to the associated aluminium surfaces.

157
Table D.2 - Additional protection at metal-to-metal contacts to take precautions against crevice and galvanic effects
Metal to be joined to aluminium Bolt or rivet material Protection according to exposure
Atmospheric Marine Immersed
Rural Industrial urban Non industrial Industrial Fresh water Sea water
Dry, unpolluted Mild Moderate Severe Moderate Severe
(M) (B/R) M B/R M B/R M B/R M B/R M B/R M B/R M B/R M B/R M B/R
Aluminium Aluminium 0 0 0 0 0/X 0 X
a
1 0/X (1) 0/X
a
(1) X
a
z
1 X 1 X 1
Stainless steel 0 0 0 1 (1) l (1) l 1 2
Zinc-coated steel 0 (2) (1) (2) 1(2) (1) (2) (1) (2) 1(2) l 2 1 2
Zinc-coated steel

Painted steel

Aluminium 0 0 0 0 0/X
a
0 X
a
z
1 0/X
a
(1) 0/X
a
(1) X
a
z
1 X
z
1 Y
(Z)
z
1 2
Stainless steel 0 0 0 1 (1) (1) 1 l 1 2
Zinc-coated steel 0 (2) (2) 1 (2) (1) (2) 1 (2) 1 (2) l 2 1 2
Stainless steel Aluminium 0 0 0 0 0/X
a
0 X
a
z
1 0/X
a
(1) 0/X
a
(1) X
a
1 Y
(X)
(Z)
1 Y
(Z)
1 2
Stainless steel 0 0 0 1 0 (1) 1 l 1 2
Zinc-coated steel 0 (2) (2) 1 (2) (1) (2) (1) (2) 1(2) l 2 1 2

NOTE 1 The overall protection of aluminium parts should to be decided acc. to Table D. 1.
NOTE 2 Items in () should have a evaluation taking D.3.2 into account.
NOTE 3 For the protection of sheet used in roofing or siding see Image EN 508-2 Image
NOTE 4 For stainless steels see also EN 1993-1-4.

Image Legend:

M = metal, B = bolt, R = rivet,

Treatments applied to the contact areas of structural members Image

Procedure 0

A treatment is usually unnecessary for causes of corrosion

Procedure 0/X

Treatment depends on structural conditions. Small contact areas and areas which dry quickly may be assembled without sealing (see procedure X)

158

Procedure X

Both contact surfaces should be assembled so that no crevices exist where water can penetrate. Both contact surfaces, including bolt and rivet holes should, before assembly, be cleaned, pre-treated and receive one priming coat, see Image EN 1090-3 Image, or sealing compound, extending beyond the contact area. The surfaces should be brought together while priming coat is still wet. Where assembling pre-painted or protected components sealing of the contact surfaces might be unnecessary, dependant on the composition of the paint or protection system employed, the expected life and the environment.

Procedure Y

Full electrical insulation between the two metals and all fixings should be ensured by insertion of non-absorbent, non-conducting tapes, gaskets and washers to prevent metallic contact between the materials. The use of additional coating or sealants may be necessary.

Procedure Z

Where procedure Y is required and the load transfer through the point precludes the use of insulating materials, the joint should be assembled without the use of insulating materials, with the whole joint assembly completely sealed externally to prevent moisture ingress to elements of the joint. Procedures should be established by agreement between the parties involved.

Treatment applied to bolts and rivets

Procedure 0

No additional treatment is usually necessary.

Procedure 1

Inert washers or jointing compound should be applied between the bolt heads, nuts, washers and connected materials to seal the joint and to prevent moisture entering the interface between components and fixings. Care should be employed to ensure that load transfer through the joint is not adversely affected by the washers or jointing compounds.

Procedure 2

(1) Where the joint is not painted or coated for other reasons, the heads of bolts, nuts and rivets and the surrounding areas as noted below, should be protected with at least one priming coat (see Image EN 1090-3 Image;), care being taken to seal all crevices. (2) Where zinc-coated bolts are used, the protection on the aluminium side of the joint is not necessary. (3) Where aluminium bolts or rivets are used, the protection on the aluminium side of the joint is not necessary (4) Where stainless steel bolts are used in combination with aluminium and zinc-coated steel parts, the surrounding zinc-coated area of the joint should be similarly protected

Further treatments

Procedure a

If not painted for other reasons it may be necessary to protect the adjacent metallic parts of the contact area by a suitable paint coating in cases where dirt may be entrapped or where moisture retained.

Procedure z

Additional protection of zinc-coated structural parts as a whole may be necessary

159

Annex E - Analytical models for stress strain relationship

[informative]

E.1 Scope

  1. This Annex provides the models for the idealization of the stress-strain relationship of aluminium alloys. These models are conceived in order to account for the actual elastic-hardening behaviour of such materials.
  2. The proposed models have different levels of complexity according to the accuracy required for calculation.

    NOTE The notations in this Annex E are specific to the different models and do not necessarily comply with those in 1.6.

E.2 Analytical models

  1. The analytical characterization of the stress (σ) - strain (ε) relationship of an aluminium alloy can be done by means of one of the following models:
  2. The numerical parameters, which define each model, should be calibrated on the basis of the actual mechanical properties of the material. These should be obtained through appropriate tensile test or, as an alternative, on the bases of the nominal values given, for each alloy, in Section 3.

E.2.1 Piecewise linear models

  1. These models are based on the assumption that material σ-ε law is described by means of a multi linear curve, each branch of it representing the elastic, inelastic and plastic, with or without hardening, region respectively.
  2. According to this assumption, the characterization of the stress-strain relationship may generally be performed using either:
E.2.1.1 Bi-linear model
  1. If a bi-linear model with hardening is used (Figure E.1a), the following relationships may be assumed:

    σ = for Image 0 ≤ εεpImage     (E.1)

    σ = fp + E1 (εεp) for εp < εεmax     (E.2)

    where:

    fp = conventional elastic limit of proportionality
    εp = strain corresponding to the stress fp
    εmax = strain corresponding to the stress fmax
    E = elastic modulus
    E1 = hardening modulus
  2. In case the “Elastic-Perfectly plastic” model is assumed (Figure E.1b), the material remains perfectly elastic until the elastic limit stress fp. Plastic deformations without hardening (E1 = 0) should be considered up to εmax.
  3. In the absence of more accurate evaluation of the above parameters the following values may be assumed for both models of Figures E.1a) and b):
    fp = nominal value of fo (see Section 3)
    Image fmax = nominal value of fu (see Figure E.1a and Section 3) or fp (see Figure E.1b)Image
    εmax = 0,5 εu
    Imageεu = nominal value of ultimate strain (see E.3)Image
    εp = fo/E
    E1 = (fufo)/(0,5 εuεp)
160
E.2.1.2 Three-linear model
  1. If three-linear model with hardening is used (Figure E.2a), the following relationships may be assumed:

    σ = for Image 0≤ εεpImage     (E.3)

    σ = fp + E1 (ε - εp) for εp < εεe     (E.4)

    σ = fe + E2 (ε - εe) for εp < εεmax     (E.5)

    where:

    Imagefp = conventional elastic limit of proportionality (see E.2.1.2(3)) Image
    Image fe = conventional limit of elasticity (see E.2.1.2(3))Image
    εp = strain corresponding to the stress fp
    εe = strain corresponding to the stress fe
    εmax = strain corresponding to the stress fmax
    E = elastic modulus
    E1 = first hardening modulus
    E2 = second hardening modulus
  2. In case the “Perfectly plastic” model is assumed (Figure E.2b), plastic deformations without hardening (E2 = 0) should be considered for strain ranges from εe to εmax.

    Figure E.1 - Bi-linear models

    Figure E.1 - Bi-linear models

    Figure E.2 - Three-linear models

    Figure E.2 - Three-linear models

  3. Image In the absence of more accurate evaluation of the above parameters the following values may be assumed for both models of Figures E.2a) and E.2b):
    fp = f0,01
    fe = nominal value of fo (see Section 3)
    fmax = nominal value of fu (see Figure E.2a and Section 3) of fe (See Figure E.2b)
    εu = nominal value of ultimate strain (see E.3)
    εmax = 0,5 εu
    εp = f0,01/E
    E1 = (fefp/(εe − εp)
    E2 = (fmaxfe)/(εmaxεe) in Figure E.2a) Image
161

E.2.2 Continuous models

  1. These models are based on the assumption that the material σ-ε law is described by means of a continuous relationship representing the elastic, inelastic and plastic, with or without hardening, region respectively.
  2. According to this assumption, the characterization of the stress-strain relationship may generally be performed using either:
E.2.2.1 Continuous models in the form σ = σ(ε)
  1. If a σ = σ(ε) law is assumed, it is convenient to identify three separate regions which can be defined in the following way (see Figure E.3a):
  2. In each region the behavior of the material is represented by means of different stress versus strain relationships, which have to ensure continuity at their limit points. According to this assumption, the characterization of the stress-strain relationship may be expressed as follows (Figures E.3b):

    Image

    σ = Eε     (E.6)

    Image

    Image

    Image

    Image

    where:

    Image fe = conventional limit of elasticity Image
    fmax = tensile strength at the top point of σ - ε curve
    εe = strain corresponding to the stress fe Image
    εmax = strain corresponding to the stress fmax
    E = elastic modulus
  3. In the absence of more accurate evaluation of the above parameters the following values may be assumed:
    fe = nominal value of fo (see Section 3)
    fmax = nominal value of fu (see Section 3)
    εmax = 0,5 εu
    Image εu = nominal value of ultimate strain (see E.3) Image162
    E = nominal value of elastic modulus (see Section 3)

Figure E.3 - Continuous models in the form σ = σ(ε)

Figure E.3 - Continuous models in the form σ = σ(ε)

E.2.2.2 Continuous models in the form ε = ε (σ)
  1. For materials of round-house type, as aluminium alloys, the Ramberg-Osgood model may be applied to describe the stress versus strain relationship in the form ε = ε (σ). Such model may be given in a general form as follows (see Figure E.4a):

    Image

    where:

    Image fe = conventional limit of elasticity Image
    εo,e = residual strain corresponding to the stress fe
    n = exponent characterizing the degree of hardening of the curve
  2. In order to evaluate the n exponent, the choice of a second reference stress fx, in addition to the conventional limit of elasticity fe, is required. Assuming (Figure E.4b):
    fx = second reference stress
    εo,x = residual strain corresponding to the stress fx

    The exponent n is expressed by:

    Image

  3. Image As conventional limit of elasticity Image, the proof stress fo evaluated by means of 0,2% offset method may be assumed, i.e.:

    fe = fo

    εo,e = 0,002

    and the model equation become:

    Image

    163

    Figure E.4 - Continuous models in the form ε = ε(σ)

    Figure E.4 - Continuous models in the form ε = ε(σ)

  4. The choice of the second reference point (fx - εo,x) should be based on the strain range corresponding to the phenomenon under investigation. The following limit cases may be considered:
    1. if the analysis concerns the range of elastic deformations, the proof stress evaluated by means of 0,1% offset method may be assumed as the second reference point (see Figure E.4c), giving:

      fx = f0,1

      εo,x = 0,001

      and, therefore,

      Image

    2. if the analysis concerns the range of plastic deformations, the tensile stress at the top point of the σ-ε curve may be assumed as the second reference point (see Figure E.4d), giving:

      fx = fmax

      εo,x - εo,max = residual strain corresponding to the stress fmax

      and, therefore,

      Image

  5. Based on extensive tests, the following values may be assumed instead of the ones given in E.2.2.2(4):

    Image

    164

    where:

    1. elastic range (fx = fp, εp = 0,000001)

      Image

      where the proportional limit fp only depends on the value of the fo yield stress:

      Image

      Image fp = f0,2 / 2 if f0,2 ≤ 160 N/mm2     (E.17) Image

    2. plastic range (fx = fu)

      Image

E.3 Approximate evaluation of εu

According to experimental data the values of εu for the several alloys could be calculated using an analytical expression obtained by means of interpolation of available results. This expression, which provides an upper bound limit for the elongation at rupture, can be synthesised by the following expressions:

Image

Image εu = 0,08 if fo ≥ 400 N/mm2     (E.20)Image

NOTE This formulation can be used to quantify the stress-strain model beyond the elastic limit for plastic analysis purposes but it is not relevant for material ductility judgement.

165

Annex F - Behaviour of cross-sections beyond the elastic limit

[informative]

F.1 General

  1. This Annex provides the specifications for estimating the post-elastic behaviour of cross-sections according to the mechanical properties of the material and the geometrical features of the section.
  2. The actual behaviour of cross-sections beyond elastic limit should be considered in whichever type of inelastic analysis, including the simple elastic analysis if redistributions of internal actions are allowed for (see 5.4). In addition, suitable limitation to the elastic strength should be considered also in elastic analysis if slender sections are used.
  3. The choice of the generalized force-displacement relationship for the cross-sections should be consistent with the assumptions for the material law and with the geometrical features of the section itself (see F.3).
  4. The reliability of the assumptions on behaviour of cross-sections can be checked on the basis of tests.

F.2 Definition of cross-section limit states

  1. The behaviour of cross-sections and the corresponding idealization to be used in structural analysis should be related to the capability to reach the limit states listed below, each of them corresponding to a particular assumption on the state of stress acting on the section.
  2. Referring to the global behaviour of a cross-section, regardless of the internal action considered (axial load, bending moment or shear), the following limit states can be defined:
  3. Elastic buckling limit state is related to the strength corresponding to the onset of local elastic instability phenomena in the compressed parts of the section.
  4. Elastic limit state is related to the strength corresponding to the attainment of the conventional elastic limit fo of material in the most stressed parts of the section.
  5. Plastic limit state is related to the strength of the section, evaluated by assuming a perfectly plastic behaviour for material with a limit value equal to the conventional elastic limit fo, without considering the effect of hardening.
  6. Collapse limit state is related to the actual ultimate strength of the section, evaluated by assuming a distribution of internal stresses accounting for the actual hardening behaviour of material. Since, under this hypothesis, the generalized force-displacement curve is generally increasing, the collapse strength refers to a given limit of the generalized displacement (see F.5).

F.3 Classification of cross-sections according to limit states

  1. Cross-sections can be classified according to their capability to reach the above defined limit states. Such a classification is complementary to that presented at 6.1.4 and may be adopted if the section capabilities for getting into the plastic range need to be specified. In such a sense, referring to a generalized force F versus displacement D relationship, cross-sections can be divided as follows (see Figure F. 1): 166

    Figure F.1 - Classification of cross-sections

    Figure F.1 - Classification of cross-sections

  2. Ductile sections (Class 1) develop the collapse resistance as defined in F.2(6) without having local instability in the section. The full exploitation of the hardening properties of material is allowed until the ultimate value of deformation, depending on the type of alloy, is reached.
  3. Compact sections (Class 2) are capable of developing the plastic limit resistance as defined in F.2(5). The full exploitation of the hardening properties of material is prevented by the onset of plastic instability phenomena.
  4. Semi-compact sections (Class 3) are capable of developing the elastic limit resistance only, as defined in F.2(4), without getting into inelastic range owing to instability phenomena. Only small plastic deformations occur within the section, whose behaviour remains substantially brittle.
  5. Both serviceability and ultimate behaviour of slender sections (Class 4) are governed by the occurring of local buckling phenomena, which cause the ultimate strength of the cross-section to be determined by the elastic buckling limit state, as defined in F.2(3). No plastic deformations are allowed within the section, whose behaviour is remarkably brittle.

F.4 Evaluation of ultimate axial load

  1. The load-bearing resistance of cross-sections under axial compression may be evaluated with reference to the above mentioned limit states, by means of the following practical rules.
  2. The value of axial load for a given limit state can be expressed by the generalized formula:

    NEd = αN,j A f d     (F.1)

    where:

    fd = fo / γM1 the design value of 0,2% proof strength, see 6.1.2
    A the net cross sectional area
    αN,j a correction factor, given in Table F. 1, depending on the assumed limit state.
    167
    Table F.1 - Ultimate Axial Load
    Axial load Limit State Section class Correction factor
    Nu Collapse Class 1 αN,1 = f1 / fd
    Npl Plastic Class 2 αN,1 = 1
    Nel Elastic Class 3 αN,1 = 1
    Nred Elastic buckling Class 4 αN,4 = Aeff / A

    where Aeff is the effective cross sectional area, evaluated accounting for local buckling phenomena (see 6.2.4).

    ft = fu / γM2 the design value of ultimate strength, see 6.1.2

  3. The ultimate load bearing resistance of a section under axial load, evaluated according to the above procedure, does not include the overall buckling phenomena, which should be evaluated according to 6.3.1.
  4. If welded sections are involved, a reduced value Arec of the net cross sectional area should be used, which should be evaluated according to 6.3.1.

F.5 Evaluation of ultimate bending moment

  1. The load-bearing resistance of cross-sections under bending moment can be evaluated with reference to the above mentioned limit states, by means of the following rules.
  2. The value of bending moment for a given limit state can be expressed by the generalized formula:

    MRd = αM,j Welfd     (F.2)

    where:

    fd = foM1 the design value of 0,2 % proof strength, see 6.1.2
    Wel the elastic section modulus
    αM,j a correction factor, given in Table F.2, depending on the assumed limit state.
    Table F.2 - Ultimate Bending Moment
    Bending moment Limit state Section class Correction factor
    Mu Collapse Class 1 Image(depending on the alloy - see Annex (G)
    Mpl Plastic Class 2 αM,2 = α0 = Wpl/Wel
    Mel Elastic Class 3 αM,3 = 1
    Mred Elastic buckling Class 4 αM,4 = Weff/Wel(see 6.2.5)

    where:

    n = np is the exponent of Ramberg-Osgood law representing the material behaviour in plastic range (see Annex E)
    α5 and α10, are the section generalized shape factors corresponding respectively to ultimate curvature168
    values χu = 5χel and 10χel,χel being the elastic limit curvature (See Annex G)
    α0 the geometrical shape factor
    Wpl is the section plastic modulus
    Weff is the effective section resistance modulus evaluated accounting for local buckling phenomena (see 6.2.5).
  3. If welded sections are involved, reduced values Weff,haz and Wpl,haz of section resistance and plastic modulus should be used, evaluated by accounting for HAZ (See 6.2.5).
  4. The evaluation of the correction factor αM,j for a welded section of class 1 may be done by means of the following formula:

    Image

    where:

    Ψ = αM,1 / αM,2 being the correction factors for unwelded sections of class 1 and 2, respectively.

169

Annex G - Rotation capacity

[informative]

  1. The provisions given in this Annex G apply to class 1 cross-sections in order to define their nominal ultimate resistance. The provisions may also be used for the evaluation of the ultimate resistance of class 2 and class 3 sections, provided it is demonstrated that the rotation capacity is reached without local buckling of the sections
  2. If no reliance can be placed on the ductility properties or if no specific test can be performed on the material, the ultimate values of Mu should be referred to a conventional ultimate bending curvature given by:

    χu = ξχel     (G.1)

    where

    ξ is a ductility factor depending on the type of alloy and χel conventionally assumed equal to the elastic bending curvature χ0,2, which corresponds to the attainment of the proof stress fo in the most stressed fibres.

  3. From the ductility point of view the common alloys can be subdivided into two groups (see also Annex H):
  4. The evaluation of elastic and post-elastic behaviour of the cross-section may be done through the moment-curvature relationship, written in the Ramberg-Osgood form:

    Image

    where:

  5. The stable part of the rotation capacity R is defined as the ratio between the plastic rotation at the collapse limit state θp = θu - θel to the limit elastic rotation θel (Figure G.I):

    Image

    where

    Θu is the maximum plastic rotation corresponding to the ultimate curvature χu.

    170

    Figure G.1 - Definition of rotation capacity

    Figure G.1 - Definition of rotation capacity

  6. The rotation capacity R may be calculated through the approximate formula:

    Image

    with m and k: defined before.

    The value of αM,j is given in Table F.2 for the different behavioural classes.

  7. If the material exponent n is known (see Annex H), an approximate evaluation of α5 and α10 can be done through the formulas:

    Image

    Image

    α0 = Wpl/W being the geometrical shape factor.

    In the absence of more refined evaluations, the value n = np should be assumed (Annex H).

171

Annex H - Plastic hinge method for continuous beams

[informative]

  1. The provisions given in this Annex H apply to cross-sections of class 1 in structures where collapse is defined by a number of cross-sections that are reaching an ultimate strain. The provisions may be used also for structures with cross-sections of class 2 and class 3 provided that the effect of local buckling of the sections is taken into account for determination of the load bearing capacity and the available ductility of the component. See also Annex G
  2. The concentrated plasticity method of global analysis, hereafter referred to as “plastic hinge method”, commonly adopted for steel structures, may be applied to aluminium structures as well, provided that the structural ductility is sufficient to enable the development of full plastic mechanisms. See (3), (4) and (5).
  3. Plastic hinge method should not be used for members with transverse welds on the tension side of the member at the plastic hinge location.
  4. Adjacent to plastic hinge locations, any fastener holes in tension flange should satisfy

    Af,net 0,9 fu / γM2Af fo / γM1     (H.1)

    for a distance each way along the member from the plastic hinge location of not less than the greater of:

    Af is the area of the tension flange and Af,net is the net area in the section with fastener holes.

  5. These rules arc not applicable to beams where the cross section vary along their length.
  6. If applying the plastic hinge method to aluminium structures both ductility and hardening behaviour of the alloy have to be taken into account. This leads to a correction factor η of the conventional yield stress, see (10).
  7. With regard to ductility, two groups of alloys are defined, depending on whether the conventional curvature limits 5χe and 10χe are reached or not (see also Annex G):
  8. Assuming an elastic- (or-rigid-) perfectly plastic law for the material (see Annex G), the ultimate bending moment of a given cross section at plastic hinge location is conventionally calculated as a fully plastic moment given by:

    Mu = α0ηfoWel     (H.2)

    where:

    η is the previously defined correction factor;
    Wel is the section elastic modulus.
  9. Assuming a hardening law for the material (see Annex G), the ultimate bending moment of a given cross section at plastic hinge location is conventionally calculated in the following way: 172

    Mu = αξηfoWel     (H.3)

    where, in addition to η and Wel previously defined, the index ξ is equal to 5 or 10 depending on the alloy ductility features set out in (4) (for the definition of α5 and α10 refer to Annex F and G):

  10. The correction coefficient η is fitted in such a way that the plastic hinge analysis provides the actual ultimate load bearing capacity of the structure, according to the available ductility of the alloy. In general, η is expressed by:

    Image

    where np is the alloy Ramberg-Osgood hardening exponent evaluated in plastic range (see 3.2.2). For structures made of beams in bending, the coefficients a, b and c of equation Image H.4 Image are provided in Table H.1. Values of the correction coefficient η are shown in Figure H.1.

  11. The global safety factor evaluated through plastic hinge methods applied with η < 1 should be not higher than that evaluated through a linear elastic analysis. If this occurs the results of elastic analysis should be used.

Figure H.1 - Values of the correction coefficient η

Figure H.1 - Values of the correction coefficient η

Table H.1 - Values of coefficients a, b and c.
Coefficients of the law: Image α0 = l,4 – 1,5 α0 = 1,1 – 1,2
Brittle alloys (χu = 5χe) Ductile alloys (χu = 10χe) Brittle alloys (χu = 10χe) Ductile alloys (χu = 10χe)
a 1,20 1,18 1,15 1,13
b 1,00 1,50 0,95 1,70
c 0,70 0.75 0.66 0,81
173

Annex I - Lateral torsional buckling of beams and torsional or torsional-flexural buckling of compressed members

[informative]

I.1 Elastic critical moment and slenderness

I.1.1 Basis

  1. The elastic critical moment for lateral-torsional buckling of a beam of uniform symmetrical cross-section with equal flanges, under standard conditions of restraint at each end and subject to uniform moment in plane going through the shear Image centre Image is given by:

    Image

    where:

    Image

    It is the torsion constant
    Iw is the warping constant
    Iz is the second moment of area about the minor axis
    L is the length of the beam between points that have lateral restraint
    v is the Poisson ratio
  2. The standard conditions of restraint at each end are:

I.1.2 General formula for beams with uniform cross-sections symmetrical about the minor or major axis

  1. In the case of a beam of uniform cross-section which is symmetrical about the minor axis, for bending about the major axis the elastic critical moment for lateral-torsional buckling is given by the general formula:

    Image

    where relative non-dimensional critical moment μcr is

    Image

    non-dimensional torsion parameter is Image

    relative non-dimensional coordinate of the point of load application related to shearImagecentreImageImage

    relative non-dimensional cross-section mono-symmetry parameter Image

    174

    where:

    C1, C2 and C3 are factors depending mainly on the loading and end restraint conditions (See Table I.1 and I.2)

    kz and kw are buckling length factors

    zg = za - zs

    Image

    za is the coordinate of the point of load application related to centroid (see Figure I.1)
    zs is the coordinate of the shear Image centre Image related to centroid
    zg is the coordinate of the point of load application related to shear Image centre Image.

    NOTE 1 See I.1.2 (7) and (8) for sign conventions and I.1.4 (2) for approximations for zj.

    NOTE 2 zj = 0 (yj = 0) for cross sections with y-axis (z-axis) being axis of symmetry.

    NOTE 3 The following approximation for zj can be used:

    Image

    where:

    c is the depth of a lip
    hf is the distance between Image centrelines Image of the flanges.

    Image

    Ifc is the second moment of area of the compression flange about the minor axis of the section
    Ift is the second moment of area of the tension flange about the minor axis of the section
    hs is the distance between the shear centre of the upper flange and shear centre of the bottom flange (Su and Sb in Figure I.1).

    For an I-section with unequal flanges without lips and as an approximation also with lips:

    Image

  2. The buckling length factors kz (for lateral bending boundary conditions) and kw (for torsion boundary condition) vary from 0,5 for both beam ends fixed to 1,0 for both ends simply supported, with 0,7 for one end fixed (left or right) and one end simply supported (right or left).
  3. The factor kz refers to end rotation on plan. It is analogous to the ratio Lcr/L for a compression member.
  4. The factor kw refers to end warping. Unless special provision for warping fixity of both beam ends (kw = 0,5) is made, kw should be taken as 1,0. 175

    Figure I.1 - Notation and sign convention for beams under gravity loads (Fz) or for cantilevers under uplift loads (- Fz)

    Figure I.1 - Notation and sign convention for beams under gravity loads (Fz) or for cantilevers under uplift loads (- Fz)

  5. Values of C1, C2 and C3 are given in Tables I.1 and I.2 for various load cases, as indicated by the shape of the bending moment diagram over the length L between lateral restraints. Values are given in Table I.1 corresponding to various values of kz and in Table I.2 also corresponding to various values of kw.
  6. For cases with kz = 1,0 the value of C1 for any ratio of end moment loading as indicated in Table I.1, is given approximately by:

    C1 = (0.310 + 0.428Ψ + 0.262Ψ2)-0.5     (I.6)

  7. The sign convention for determining z and zj, see Figure I.1, is:
  8. The sign convention for determining zg is: 176
    Table I.1 - Values of factors C1 and C3 corresponding to various end moment ratios Ψ, values of buckling length factor kz and cross-section parameters Ψf and kwt.
    End moment loading of the simply supported beam with buckling length factors ky = 1 for major axis bending and kw = 1 for torsion
    Loading and support conditions.

    Cross-section monosymmetry factor Ψf
    Bending moment diagram.

    End moment ratio Ψ.
    kz2) Values of factors
    Cl1) C3
    C1,0 C1,1 Image Image Image Image
    M-
    -side
    ΨM-
    -side
    Image Image 1,0 1,000 1,000 1,000
    0,7L 1,016 1,100 1,025 1,000
    0,7R 1,016 1,100 1,025 1,000
    0,5 1,000 1,127 1,019
    Image 1,0 1,139 1,141 1,000
    0,7 L 1,210 1,313 1,050 1,000
    0,7R 1,109 1,201 1,000
    0,5 1,139 1,285 1,017
    Image 1,0 1,312 1,320 1,150 1,000
    0,7L 1,480 1,616 1,160 1,000
    0,7R 1,213 1,317 1,000
    0,5 1,310 1,482 1,150 1,000
    Image 1,0 1,522 1,551 1,290 1,000
    0,7L 1,853 2,059 1,600 1,260 1,000
    0,7R 1,329 1,467 1,000
    0,5 1,516 1,730 1,350 1,000
    Image 1,0 1,770 1,847 1,470 1,000
    0,7L 2,331 2,683 2,000 1,420 1,000
    0,7R 1,453 1,592 1,000
    0,5 1,753 2,027 1,500 1,000
    Image 1,0 2,047 2,207 1,65 1,000 0,850
    0,7L 2,827 3,322 2,40 1,550 0,850 -0,30
    0,7R 1,582 1,748 1,38 0,850 0,700 0,20
    0,5 2,004 2,341 1,75 1,000 0,650 -0,25
    Image 1,0 2,331 2,591 1,85 1,000 1,3-1,2Ψf -0,70
    0,7L 3,078 3,399 2,70 1,450 1-1,2Ψf -1,15
    0,7R 1,711 1,897 1,45 0,780 0,9 - 0,75Ψf -0,53
    0,5 2,230 2,579 2,00 0,950 0,75 - Ψf -0,85
    Image 1,0 2,547 2,852 2,00 1,000 0,55 - Ψf -1,45
    0,7L 2,592 2,770 2,00 0,850 0,23 - 0,9Ψf -1,55
    0,7R 1,829 2,027 1,55 0,700 0,68 - Ψf -1,07
    0,5 2,352 2,606 2,00 0,850 0,35 - Ψf -1,45
    Image 1,0 2,555 2,733 2,00 -Ψf -2,00
    0,7L 1,921 2,103 1,55 0,380 -0,580 -1,55
    0,7R 1,921 2,103 1,55 0,580 -0,380 -1,55
    0,5 2,223 2,390 1,88 0,125-0,7Ψf -0,125-0,7Ψf -1,88
    1) C1 = C1,0 + (C1,1- C1,0)κwtC1,1 , (C1 = C1,0 for κwt = 0, C1 = C1,1 for κwt ≥ 1)
    2) 0,7 L = left end fixed, 0,7R = right end fixed
    177
    Table I.2 - Values of factors C1, C2 and C3 corresponding to various transverse loading cases, values of buckling length factors ky, kz, kw , cross-section monosymmetry factor Ψf and torsion parameter κwt.
    Loading and support conditions Buckling length factors Values of factors
    ky kZ kw C11) C2 C3
    C1,0 C1,1 Image Image Image Image Image Image
    Image 1 1 1 1,127 1.132 0,33 0,459 0,50 0,93 0,525 0,38
    1 l 0,5 1,128 1,231 0,33 0,391 0,50 0,93 0,806 0,38
    1 0,5 1 0,947 0,997 0,25 0,407 0,40 0,84 0,478 0,44
    1 0,5 0,5 0,947 0,970 0,25 0,310 0,40 0,84 0,674 0,44
    Image 1 1 1 1,348 1,363 0,52 0,553 0,42 1,00 0,411 0,31
    1 1 0,5 1,349 1,452 0,52 0,580 0,42 1,00 0,666 0,31
    1 0,5 1 1,030 1,087 0,40 0,449 0,42 0,80 0,338 0,31
    1 0,5 0,5 1,031 1,067 0,40 0,437 0,42 0,80 0,516 0,31
    Image 1 1 1 1,038 1,040 0,33 0,431 0,39 0,93 0,562 0,39
    1 1 0,5 1,039 1.148 0,33 0,292 0,39 0,93 0,878 0,39
    1 0,5 1 0,922 0,960 0,28 0,404 0,30 0,88 0,539 0,50
    1 0,5 0,5 0,922 0,945 0,28 0,237 0,30 0,88 0,772 0,50
      Ψf = -1 -0,5 ≤ Ψf ≤ 0,5 Ψf = 1 Ψf = -1 -0,5 ≤ Ψf ≤ 0,5 Ψf = 1
    Image 0,5 1 1 2,576 2,608 1,00 1,562 0,15 1,00 -0,859 -1,99
    0,5 0,5 1 1,490 1,515 0,56 0,900 0,08 0,61 -0,516 -1,20
    0,5 0,5 0,5 1,494 1,746 0,56 0,825 0,08 0,61 0,002712 -1,20
    Image 0,5 1 1 1,683 1,726 1,20 1,388 0,07 1,15 -0,716 -1,35
    0,5 0,5 1 0,936 0,955 0,69 0,763 0,03 0,64 -0,406 -0,76
    0,5 0,5 0,5 0,937 1,057 0,69 0,843 0,03 0,64 -0,0679 -0,76
    1) C1 = C1,0 + (C1,1 - C1,0)κwtC1,1 , (C1 = C1,0 for κwt = 0, C1 = C1,1 for κwt ≥ 1).
    2) Parameter Ψf refers to the middle of the span.
    3) Values of critical moments Mcr refer to the cross section, where Mmax is located
178

I.1.3 Beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections

  1. For beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections loaded perpendicular to the major axis in the plane going through the shear centre, Figure I.2, zj = 0, thus

    Image

  2. For end-moment loading C2 = 0 and for transverse loads applied at the shear centre zg = 0. For these cases:

    Image

  3. If also κwt = 0: µcr = C1/kz

    Figure I.2 - Beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections

    Figure I.2 - Beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections

  4. For beams supported on both ends (ky = 1, kz = 1, 0,5 ≤ kw ≤ 1) or for beam segments laterally restrained on both ends, which are under any loading (e.g. different end moments combined with any transverse loading), the following value of factor C1 may be used in the above two formulas given in I.1.3 (2) and (3) to obtain approximate value of critical moment:

    Image

    where

    Mmax is maximum design bending moment,

    Mo,25, Mo,75 are design bending moments at the quarter points and

    Mo,5 is design bending moment at the midpoint of the beam or beam segment with length equal to the distance between adjacent cross-sections which are laterally restrained.

  5. Factor C1 defined by (I.9) may be used also in formula (I.7), but only in combination with relevant value of factor C2 valid for given loading and boundary conditions. This means that for the six cases in Table I.2 with boundary condition ky = 1, kz = 1, 0,5 ≤ kw ≤ 1, as defined above, the value C = 0,5 may be used together with (I.9) in (I.7) as an approximation.
  6. In the case of continuous beam the following approximate method may be used. The effect of lateral continuity between adjacent segments are ignored and each segment is treated as being simply supported laterally. Thus the elastic buckling of each segment is analysed for its in-plane moment distribution (formula (I.9) for C1 may be used) and for an buckling length equal to the segment length L. The lowest of critical moments computed for each segment is taken as the elastic critical load set of the continuous beam. This method produces a lower bound estimate.
179

I.1.4 Cantilevers with uniform cross-sections symmetrical about the minor axis

  1. In the case of a cantilever of uniform cross-section, which is symmetrical about the minor axis, for bending about the major axis the elastic critical moment for lateral-torsional buckling is given by the formula (I.2), where relative non-dimensional critical moment µcr is given in Table I.3 and I.4. In table I.3 and I.4 non-linear interpolation should be used.
  2. The sign convention for determining zj and zg is given in I.1,2(7) and (8).
    Table I.3 - Relative non-dimensional critical moment µcr for cantilever (ky = kz = kw = 2) loaded by concentrated end load F.
    Loading and support conditions Image Image Image
    -4 -2 -1 0 1 2 4
    Image 0 4 0,107 0,156 0,194 0,245 0,316 0,416 0,759
    2 0,123 0,211 0,302 0,463 0,759 1,312 4,024
    0 0,128 0,254 0,478 1,280 3,178 5,590 10,730
    -2 0,129 0,258 0,508 1,619 3,894 6,500 11,860
    -4 0,129 0,258 0,511 1,686 4,055 6,740 12,240
    0,5 4 0,151 0,202 0,240 0,293 0,367 0,475 0,899
    2 0,195 0,297 0,393 0,560 0,876 1.528 5,360
    0 0,261 0,495 0,844 1,815 3,766 6,170 11,295
    -2 0,329 0,674 1,174 2,423 4,642 7,235 12,595
    -4 0,364 0,723 1,235 2,529 4,843 7,540 13,100
    1 4 0,198 0,257 0,301 0,360 0,445 0,573 1,123
    2 0,268 0,391 0,502 0,691 1,052 1,838 6,345
    0 0,401 0,750 1,243 2,431 4,456 6,840 11,920
    -2 0,629 1,326 2,115 3,529 5,635 8,115 13,365
    -4 0,777 1,474 2,264 3,719 5,915 8,505 13,960
    2 4 0,335 0,428 0,496 0,588 0,719 0,916 1,795
    2 0,461 0,657 0,829 1,111 1,630 2,698 7,815
    0 0,725 1,321 2,079 3,611 5,845 8,270 13,285
    -2 1,398 3,003 4,258 5,865 7,845 10,100 15,040
    -4 2,119 3,584 4,760 6,360 8,385 10,715 15,825
    4 4 0,845 1,069 1,230 1,443 1,739 2,168 3,866
    2 1,159 1,614 1,992 2,569 3,498 5,035 10,345
    0 1,801 3,019 4,231 6,100 8,495 11,060 16,165
    -2 3,375 6,225 8,035 9,950 11,975 14,110 18,680
    -4 5,530 8,130 9,660 11,375 13,285 15,365 19,925
    a) For zj = 0, zg = 0 and κwt0 ≤ 8: µcr = 1,27 + 1,14 κwt0 + 0,017Image.
    b) For zj = 0, -4 ≤ ζg ≤ 4 and κwt ≤ 4, µcr may be calculated also from formulae (I.7) and (I.8), where the following approximate values of the factors C1, C2 should be used for the cantilever under tip load F:
    C1 = 2,56 + 4,675 κwt - 2,62Image + 0,5Image,     if κwt ≤ 2
    C1 = 5,55     if κwt > 2
    C2 = 1,255 + 1,566κwt - 0,931Image + 0,245Image - 0,024Image,     if ζg ≥ 0
    C2 = 0,192 + 0,585 κwt - 0,054Image - (0,032 +0,102 κwt -0,013Image) ζg ,if ζg <0
    180
    Table I.4 - Relative non-dimensional critical moment µcr for cantilever (ky = kz = kw = 2) loaded by uniformly distributed load q
    Loading and support conditions Image Image Image
    -4 -2 -1 0 1 2 4
    Image 0 4 0,113 0,173 0,225 0,304 0,431 0,643 1,718
    2 0,126 0,225 0,340 0,583 1,165 2,718 13,270
    0 0,132 0,263 0,516 2,054 6,945 12,925 25,320
    -2 0,134 0,268 0,537 3,463 10,490 17,260 30,365
    -4 0,134 0,270 0,541 4,273 12,715 20,135 34,005
    0,5 4 0,213 0,290 0,352 0,443 0,586 0,823 2,046
    2 0,273 0,421 0,570 0,854 1,505 3,229 14,365
    0 0,371 0,718 1,287 3,332 8,210 14,125 26,440
    -2 0,518 1,217 2,418 6,010 12,165 18,685 31,610
    -4 0,654 1,494 2,950 7,460 14,570 21,675 35,320
    1 4 0,336 0,441 0,522 0,636 0,806 1,080 2,483
    2 0,449 0,663 0,865 1,224 1,977 3,873 15,575
    0 0,664 1,263 2,172 4,762 9,715 15,530 27,735
    -2 1,109 2,731 4,810 8,695 14,250 20,425 33,075
    -4 1,623 3,558 6,025 10,635 16,880 23,555 36,875
    2 4 0,646 0,829 0,965 1,152 1,421 1,839 3,865
    2 0,885 1,268 1,611 2,185 3,282 5,700 18,040
    0 1,383 2,550 4,103 7,505 12,770 18,570 30,570
    -2 2,724 6,460 9,620 13,735 18,755 24,365 36,365
    -4 4,678 8,635 11,960 16,445 21,880 27,850 40,400
    4 4 1,710 2,168 2,500 2,944 3,565 4,478 8,260
    2 2,344 3,279 4,066 5,285 7,295 10,745 23,150
    0 3,651 6,210 8,845 13,070 18,630 24,625 36,645
    -2 7,010 13,555 17,850 22,460 27,375 32,575 43,690
    -4 12,270 18,705 22,590 26,980 31,840 37,090 48,390
    a) For zj = 0, zg = 0 and κwt0 ≤ 8: µcr = 2,04 + 2,68 κwt0 + 0,021Image.
    b) For zj = 0, −4 ≤ ζg ≤ 4 and κwt ≤ 4, µcr may be calculated also from formulae (I.7) and (I.8), where the following approximate values of the factors C1, C2 should be used for the cantilever under uniform load q:
    C1 = 4,11 + 11.2 κwt − 5,65 Image + 0,975 Image,     if κwt ≤ 2
    C1 = 12     if κwt > 2
    C2 = 1,661 + 1,068 κwt − 0,609 Image + 0,153 Image − 0,014 Image,     if ζg ≥ 0
    C2 = 0,535 + 0,426 κwt − 0,029 Image − (0,061 + 0,074 κwt − 0,0085 Image) ζg ,if ζg < 0
181

I.2 Slenderness for lateral torsional buckling

  1. The general relative slenderness parameter ImageLT for lateral-torsional buckling is given by:

    Image

    where:

    α is the shape factor taken from Table 6,4.

  2. Alternatively, for I- sections and channels covered by Table I.5, the value of ImageLT may be obtained from:

    Image

    where:

    Image

    Lcr,z is the buckling length for lateral torsional buckling

    iz is the minor axis radius of gyration of the gross section

    h is the overall section depth

    t2 is the flange thickness (t2 = t for Case 2 and 4 in Table I.5)

    X and Y are coefficients obtained from Table I.5. For lipped channel (profile 18 in Table I.8) X = 0,95 and Y = 0,071. For all Cases it is conservative to take X = 1,0 and Y = 0,05.

  3. If the flange reinforcement to an I-section or channel is not of the precise form shown in Table I.5 (simple lips), it is still permissible to obtain ImageLT using the above expression, providing X and Y are taken as for an equivalent simple lip having the same internal depth c, while iz is calculated for the section with its actual reinforcement.
  4. Normally Lcr,z = 1,0L, where L is actual distance between points of lateral support to the compression flange. If at these points the both flanges of the segment ends are restrained against rotation about z-axis, the length L may be reduced by the factor 0,5 in the case of theoretical full restraints, by the factor 0,7 in the case of practically achieved full restraints and by the factor 0,85 in the case of partial restraints. Such values of the buckling lengths should be increased by the factor 1,2 if the beams with the cross-sections given in Table I.5 are under transverse destabilizing load applied at top flange level. For beam that is free to buckle over its whole length, the absence of end-post can be allowed for by further increasing Lcr,z by an amount 2h above the value that would otherwise apply. Simplified procedure in I.2(2) and (3) should not be used in the case of cantilever beams if appropriate value of Lcr,z taking into account all type of cantilever restraints and destabilizing effect of transverse loads is not known. 182
    Table I.5 - Lateral-torsional buckling of beams, coefficients X and Y
    Image 1,5 ≤ h / b ≤ 4,5
    1 ≤ t2 / t1 ≤ 2
    X = 0,90 − 0,03h / b + 0,04t2 / t1
    Image
    Image 1,5 ≤ h / b ≤ 4,5
    1 ≤ c / b ≤ 0,5
    X = 0,94 − (0,03 − 0,07c / b) h /b − 0,3c / b
    Y = 0,05 − 0,06c / h
    Image 1,5 ≤ h / b ≤ 4,5
    1 ≤ t2 / t1 ≤ 2
    X = 0,95 − 0,03h / b + 0,06t2 / t1
    Image
    Image 1,5 ≤ h / b ≤ 4,5
    0 ≤ c / b ≤ 0,5
    X = 1,01 − (0,03 − 0,06c / b) h /b − 0,3c / b
    Y = 0,07 − 0,10c / h
183

I.3 Elastic critical axial force for torsional and torsional-flexural buckling

  1. The elastic critical axial force Ncr for torsional and torsional-flexural buckling of a member of uniform cross-section, Image under various conditions at its ends and subject to uniform axial force in the gravity centre Image is given by:

    Image

    where:

    Image

    Image

    Image

    Image It, Iw, Iz, ky, kz, kw and G see I.1,1. Image

    L is the length of the member between points that have lateral restraint.

    Image

    ys and zs are the coordinates of the shear Image centre Image related to centroid

    αyw (ky, kw) and αzw (kz, kw) depend on the combinations of bending with torsion boundary conditions, see Table I.6, where symbols for torsion boundary conditions are explained in Table I.7

    Table I.6 - Values of αyw or αzw for combinations of bending and torsion boundary conditions
    Bending boundary condition k y or k z Torsion boundary condition, kw
    Image

    1,0
    Image

    0,7
    Image

    0,7
    Image

    0,5
    Image

    2,0
    Image

    2,0
    Image

    1,0
    Image

    1,0
    Image

    2,0
    Image 1,0 1 0,817 0,817 0,780 a) a) a) a) a)
    Image 0,7 0,817 1 a) 0,766 a) a) a) a) a)
    Image 0,7 0,817 a) 1 0,766 a) a) a) a) a)
    Image 0,5 0,780 0,766 0,766 1 a) a) a) a) a)
    Image 2,0 a) a) a) a) 1 a) a) a) a)
    Image 2,0 a) a) a) a) a) 1 a) a) a)
    Image 1,0 a) a) a) a) a) a) 1 a) a)
    Image 1,0 a) a) a) a) a) a) a) 1 a)
    Image 2,0 a) a) a) a) a) a) a) a) 1
    a) conservatively, use αyw = 1 and αzw = 1
    184
    Table I.7 - Torsion boundary conditions in Table I.6
    Symbol in Table I.6 Deformation of member end Torsion boundary condition
    Image Image Rotation restrained, warping free
    Image Image Rotation restrained, warping restrained
    Image Image Rotation free, warping free
    Image Image Rotation free, warping restrained
  2. For cross-sections symmetrical about the z-axis ys = 0 and the solution to equation (I.13) is:

    Ncr,1 = Ncr,y     (flexural buckling)     (I.18)

    Image

  3. For doubly symmetrical cross sections ys = 0 and zs = 0 and the solution to equation (I.13) is:

    Ncr,1 = Ncr,y, Ncr,2 = Ncr,z (flexural buckling) and Ncr,3 = Ncr,T (torsional buckling)

  4. Slenderness based on approximate formulae for certain cross sections are given in I.4(2).

I.4 Slenderness for torsional and torsional-flexural buckling

  1. The general expression for relative slenderness parameter ImageT for torsional and torsional-flexural buckling is:

    Image

    where

    Aeff is the effective area for torsional or torsional-flexural buckling, see 6.3.1.2, Table 6.7

    Ncr is the elastic critical load for torsional buckling, allowing for interaction with flexural buckling if necessary (torsional-flexural buckling). See I.3.

  2. Alternatively, for sections as given in Table I.8

    Image

    where k is read from Figure 1,3 or given by the expression:

    Image

    in which X > 0 and s are found in Table I.8.

    185

    λt is found as follows:

    1. for angles, tees, cruciforms λt = λ0     (I.23)
    2. for channels, top-hats Image

    Table I.8 contains expressions for λ0 and Y and also for s and X (needed in expression (I.22) and for Figure I.3).

    In expression (I.24) the quantity λy should be taken as the effective slenderness for column buckling about axis y-y (as defined in Table I.8, Cases 15 to 18).

    Figure I.3 - Torsional buckling of struts, interaction factor k

    Figure I.3 - Torsional buckling of struts, interaction factor k

    For the definition of s, see Table I.8

    186
    Table I.8 - Torsional buckling parameters for struts
    Image ρ ≤ 5
    See Note 3 for ρ
    λ0 = 5b / t − 0,6ρ1,5(b / t)0,5
    s = λu / λ0
    X = 0,6
    Image ρ ≤ 5
    1 ≤ δ ≤ 2,5
    See Note 3 for ρ
    λ0 = 5b / t − 0,6ρ1,5(b / t)0,5 − −(δ – 1)[2(δ − 1)2 − 1,5ρ]
    s = λu / λ0
    X = 0,6
    Image b / t = 20
    ri / t = 2
    δ = 3
    β ≈ 4
    See Note 3 for ri
    λ0 = 66
    s = λu / λ0
    X = 0,61
    (Equal legs)
    Image ρ ≤ 5
    0,5 ≤ b / h ≤ 1
    See Note 3 for ρ
    Image
    Image ρ ≤ 5
    0,5 ≤ b / h ≤ 1
    1 ≤ δ ≤ 2,5
    See Note 3 for ρ
    Image
    Image h / t = 20
    b / t = 15
    ri / t = 2
    δ = 3, β ≈ 4
    See Note 3 for ri
    λ0 = 57
    s = 1,4λu / λ0
    X = 0,6
    (Unequal lags, equal bulbs)
    Image ρ ≤ 3,5
    See Note 3 for ρ
    λ0 = 5,1b / tρ1,5(b / t)0,5
    X = 1 187
    Image ρ ≤ 5
    0,5 ≤ h / b ≤ 2
    See Note 3 for ρ
    Image
    s = λz / λ0
    X = 1,1 – 0,3h / b
    Image ρ ≤ 5
    0,5 ≤ h / b ≤ 2
    1 ≤ δ ≤ 2,5
    See Note 3 for ρ
    Image
    s = λz / λ0
    X = 1,1 – 0,3h / b
    Image Shape of angles as Case 3. λ0 = 70
    s = λz / λ0
    X = 0,83
    Image Shape of angles as Case 6. λ0 = 60
    s = λz / λ0
    X = 0,76
    Image Shape of angles as Case 6. λ0 = 63
    s = λz / λ0
    X = 0,89
    Image ρ ≤ 3,5
    0,5 ≤ h / b ≤ 2
    See Note 3 for ρ
    λ0 = (1,4 + 1,5b / h + 1,1h / b)h / tρ1,5(h / t)0,5
    s = λz / λ0
    X = 1,3 − 0,8h / b + 0,2(h / b)2
    Image h / t = 25
    b / h = 1,2
    ri / t = 0,5
    See Note 3 for ri
    λ0 = 65
    s = λz / λ0
    X = 0,78 188
    Image 1 ≤ h / b ≤ 3
    1 ≤ t2 / t1 ≤ 2
    λ0 = (b / t2)(7 + 1,5(h / b)t2 / t1)
    s = λy / λt
    X = 0,38h / b − 0,04(h / b)2
    Y = 0,14 − 0,02h / b − 0,02t2 / t1
    Image 1 ≤ h / b ≤ 3
    c / b ≤ 0,4
    λ0 = (b / t)(7 + 1,5h / b + 5c / b)
    s = λy / λt
    X = 0,38h / b − 0,04(h / b)2 − 0,25c / b
    Image
    Image 1 ≤ h / b ≤ 3
    c / b ≤ 0,4
    λ0 = (b / t)(7 + 1,5h / b + 5c / b)
    s = λy / λt
    X = 0,38h / b − 0,04(h / b)2
    Image
    Image h / t = 32
    b / h = 0,5
    ri / t = 2
    See Note 3 for ri
    λ0 = 126
    s = λy / λt
    X = 0,59
    Y = 0,104
    1) The sections are generally of uniform thickness t, except Cases 14 and 15
    2) λu, λy or λz is the slenderness for flexural buckling about u, y or z axis
    3) ρ is a factor depending on the amount of material at the root of the section as follows:
    Image

    4) The values given for λ0, X and Y are only valid within the limits shown. In the case of back-to-back angles (Cases 8 to 12) the expressions ceases to apply if the gap between the angles exceeds 2t.
    189

Annex J - Properties of cross sections

[informative]

J.1 Torsion constant It

  1. For an open thin-walled section composed solely of flat plate parts, each of uniform thickness, and reinforced with fillets and/or bulbs, the value of the torsion constant It is given by

    It = ∑bsht3 / 3 − 0,105∑t4 + ∑(β + δ γ)4t4     (J.I)

    in which the first sum concerns flat plates, second term is applied to free ends of flat plates without bulbs only and last sum concerns fillets or bulbs and:

    t = thickness of flat cross-section parts

    β, δ and γ are fillet or bulb factors, see Figure J.I, Case 3 to 11

    bsh = width of flat cross-section parts, measured to the edge of the shaded area in Figure J.1 in the case of a flat cross-section part abutting a fillet or bulb.

  2. For Case 1 and 2 in Figure J.1, with different thickness t1 and t2

    It = ∑bt3 / 3 − 0,105∑ t4 + ∑ α D4     (J.1a)

    in which α and δ are fillet factors and D is diameter of inscribed circle, see Figure J.1.

  3. For a simple rectangular cross-section with any b/t ratio ≥ 1

    Image

  4. For closed cross sections It is found in J.6.

J.2 Position of shear centre S

  1. Figure J.2 gives the position of the shear centre for a number of cross-sections. See J.4 and J.5 for open thin-walled cross sections and J.6 for mono-symmetrical closed cross sections.

J.3 Warping constant Iw

  1. Values of the warping constant Iw for certain types of cross-section may be found as follows:
    1. for sections composed entirely of radiating outstands e.g. angles, tees, cruciforms, Iw may conservatively be taken as zero or

      Iw = ∑ b3t3 / 36     (J.3)

      where b is the width and t is thickness of outstand cross-section parts, see L-section and T-section in Figure J.2.

    2. For simple rectangular cross-section with any b/t ratio ≥ 1

      Image

    3. for the specific types of section illustrated in Figure J.2 values of Iw may be calculated using the expression given there.
    4. formulae for section constants, including shear Image centre Image position and warping constant Iw , for open thin- walled cross sections are given in J.4 and J.5.
190

Figure J.1 - Torsion constant factors for certain fillets and bulbs

Figure J.1 - Torsion constant factors for certain fillets and bulbs

191

Figure J.1 - Torsion constant factors for certain fillets and bulbs (continued)

Figure J.1 - Torsion constant factors for certain fillets and bulbs (continued)

192

Figure J.2 - Shear-centre position S and warping constant Iw for certain thin-walled sections

Figure J.2 - Shear-centre position S and warping constant Iw for certain thin-walled sections

193

J.4 Cross section constants for open thin-walled cross sections

Figure J.3 - Cross section nodes

Figure J.3 - Cross section nodes

  1. Divide the cross section into n parts. Number the parts 1 to n.
    Insert nodes between the parts. Number the nodes 0 to n.
    Part i is then defined by nodes i - 1 and i.
    Give nodes, co-ordinates and (effective) thickness.

    Nodes and parts j = 0..n     i = 1..n

    Area of cross section parts

    Image

    Cross section area

    Image

    First moment of area with respect to y-axis and coordinate for gravity centre

    Image

    Second moment of area with respect to original y-axis and new y-axis through gravity centre

    Image

    First moment of area with respect to z-axis and gravity centre

    Image

    Second moment of area with respect to original z-axis and new z-axis through gravity centre

    Image

    Product moment of area with respect of original y- and z-axis and new axes through gravity centre

    Image

    Principal axis

    Image

    Image

    Image

    Sectorial co-ordinates

    ω0 = 0     ω0i = yi−1 · ziyi · zi−1     ωi = ωi−1 + ω0i     (J.15)

    Mean of sectorial coordinate

    194

    Image

    Sectorial constants

    Image

    Image

    Image

    Shear centre

    Image

    Warping constant

    Iw = Iωω + zsc · Iysc · I     (J.21)

    Torsion constant

    Image

    Sectorial co-ordinate with respect to shear centre

    ωsj = ωjωmean + zsc ·(yjygc) − ysc · (zjzgc)     (J.23)

    Maximum sectorial co-ordinate and warping modulus

    Image

    Distance between shear centre and gravity centre

    ys = yscygc     zs = zsczgc     (J.25)

    Polar moment of area with respect to shear centre

    Image

    Non-symmetry factors zj and yj according to Annex I

    Image

    Image

    where the coordinates for the centre of the cross section parts with respect to shear Image centre Image are

    Image

    NOTE Zj = 0 (yj = 0) for cross sections with y-axis (z-axis) being axis of symmetry, see Figure J.3.

    195

J.5 Cross section constants for open cross section with branches

Figure J.4 - Nodes and parts in a cross section with branches

Figure J.4 - Nodes and parts in a cross section with branches

  1. In cross sections with branches, formulae in J.4 can be used. However, follow the branching back (with thickness t = 0) to the next part with thickness t ≠ 0, see branch 3 - 4 - 5 and 6 - 7 in Figure J.4.

J.6 Torsion constant and shear ImagecentreImage of cross section with closed part

Figure J.5 - Cross section with closed part

Figure J.5 - Cross section with closed part

  1. For a symmetric or non-symmetric cross section with a closed part, Figure J.5, the torsion constant is given by

    Image

    where

    Image

    Image

    196

Annex K - Shear lag effects in member design

[informative]

K.1 General

  1. Shear lag in flanges may be neglected provided that b0 < Le /50 where the flange width b0 is taken as the outstand or half the width of an internal cross section part and Le is the length between points of zero bending moment, see K.2.1(2).

    NOTE The National Annex may give rules where shear lag in flanges may be neglected at ultimate limit states. b0 < Le / 25 is recommended for support regions, cantilevers and region with concentrated load. For sagging bending regions b0 < Le / 15 is recommended.

  2. Where the above limit is exceeded the effect of shear lag in flanges should be considered at serviceability and fatigue limit state verifications by the use of an effective width according to K.2.1 and a stress distribution according to K.2.2. For effective width at the ultimate limit states, see K.3.
  3. Stresses under elastic conditions from the introduction of in-plane local loads into the web through flange should be determined from K.2.3.

K.2 Effective width for elastic shear lag

K.2.1 Effective width factor for shear lag

  1. The effective width beff for shear lag under elastic condition should be determined from:

    beff = βs b0     (K.1)

    where the effective factor βs is given in Table K.1.

    NOTE This effective width may be relevant for serviceability limit states.

  2. Provided adjacent internal spans do not differ more than 50% and cantilever span is not larger than half the adjacent span the effective length Le may be determined from Figure K.1. In other cases Le should be taken as distance between adjacent points of zero bending moment.

    Figure K.1 - Effective length Le for continuous beam and distribution of effective width

    Figure K.1 - Effective length Le for continuous beam and distribution of effective width

    197

    Figure K.2 - Definitions of notations for shear lag

    Figure K.2 - Definitions of notations for shear lag

    Table K.1 - Effective width factor βs
    K Location for verification βs
    K ≤ 0,02   βs = 1,0
    0,02 < K ≤ 0,70 sagging bending Image
    hogging bending Image
    K > 0,70 sagging bending Image
    hogging bending Image
    All K end support βS,0 = (0,55 + 0,025 / K)βs,1 but βs,0βs,1
    All K cantilever βs = βs,2 at support and at the end
    k = α0b0 / Le with Image
    in which Ast is the area of all longitudinal stiffeners within the width b0 and other symbols as defined in Figure K.1 and Figure K.2.

K.2.2 Stress distribution for shear lag

  1. The distribution of longitudinal stresses across the plate due to shear lag should be obtained from Figure K.3. 198

    Figure K.3 - Distribution of longitudinal stresses across the plate due to shear lag

    Figure K.3 - Distribution of longitudinal stresses across the plate due to shear lag

K.2.3 In-plane load effects

  1. The elastic stress distribution in a stiffened or unstiffened plate due to the local introduction of in-plane forces (see Figure K.4) should be determined from:

    Image

    where ast,1 is the gross-sectional area of the smeared stiffeners per unit length, i.e. the area of the stiffener divided by the centre-to-centre distance.

    Figure K.4 - In-plane load introduction

    Figure K.4 - In-plane load introduction

    NOTE The stress distribution may be relevant for the fatigue verification.

199

K.3 Shear lag at ultimate limit states

  1. At ultimate limit states shear lag effects may be determined using one of the following methods:
    1. elastic shear lag effects as defined for serviceability and fatigue limit states;
    2. interaction of shear lag effects with geometric effects of plate buckling;
    3. elastic-plastic shear lag effects allowing for limited plastic strains.

    NOTE 1 The National Annex may choose the method to be applied. Method a) is recommended.

    NOTE 2 The geometric effects of plate buckling on shear lag may be taken into account by first reducing the flange width to an effective width as defined for the serviceability limit states, then reducing the thickness to an effective thickness for local buckling basing the slenderness β on the effective width for shear lag.

    NOTE 3 The National Annex may give rules for elastic-plastic shear lag effects allowing for limited plastic strains.

200

Annex L - Classification of joints

[informative]

L.1 General

  1. The following definitions apply:

    Connection: Location at which two members are interconnected and assembly of connection elements and - in case of a major axis joint - the load introduction into the column web panel.

    Joint: Assembly of basic components that enables members to be connected together in such a way that the relevant internal forces and moment can be transferred between them. A beam-to-column joint consists of a web panel and either one connection (single sided joint configuration) or two connections (double sided joint configuration).

    A “Connection” is defined as the system, which mechanically fastens a given member to the remaining part of the structure. It should be distinguished from the term “joint”, which usually means the system composed by the connection itself plus the corresponding interaction zone between the connected members (see Figure L.1).

    Figure L.1 - Definition of “connection” and “joint”

    Figure L.1 - Definition of “connection” and “joint”

  2. Structural properties (of a joint): Its resistance to internal forces and moments in the connected members, its rotational stiffness and its rotation capacity.
  3. In the following the symbols “F” and “V” refer to a generalized force (axial load, shear load or bending moment) and to the corresponding generalized deformation (elongation, distortion or rotation), respectively. The subscripts “e” and “u” refer to the elastic and ultimate limit state, respectively.
  4. Connections may be classified according to their capability to restore the behavioural properties (rigidity, strength and ductility) of the connected member. With respect to the global behaviour of the connected member, two main classes are defined (Figure. L.2):
  5. With respect to the single behavioural property of the connected member, connections may be classified according to (Figures L.2.b)-d)):
  6. The types of connection should conform with the member design assumptions and the method of global analysis.
201

L.2 Fully restoring connections

  1. Fully restoring connections are designed to have properties at least equal to those of the connecting members in terms of ultimate strength, elastic rigidity and ductility. The generalized force-displacement curve of the connection lies above those of the connected members.
  2. The existence of the connection may be ignored in the structural analysis.

L.3 Partially restoring connections

  1. The behavioural properties of the connection do not reach those of the connected member, due to its lack of capability to restore either elastic rigidity, ultimate strength or ductility of the connected member. The generalized force-displacement curve may in some part fall below the one of the connected member.
  2. The existence of such connections must be considered in the structural analysis.

    Figure L.2.a) - d) - Classification of connections

    Figure L.2.a) - d) - Classification of connections

L.4 Classification according to rigidity

  1. With respect to rigidity, joints should be classified as (Figure L.2.b):

    depending on whether the initial stiffness of the jointed member is restored or not, regardless of strength and ductility.

202

L.5 Classification according to strength

  1. With respect to strength, connections can be classified as (Figure L.2.c):

    depending on whether the ultimate strength of the connected member is restored or not, regardless of rigidity and ductility.

L.6 Classification according to ductility

  1. With respect to ductility, connections can be classified as (Figure L.2.d):

    depending on whether the ductility of the connection is higher or lower than that of the connected member, regardless of strength and rigidity.

  2. Ductile connections have a ductility equal or higher than that of the connected member; elongation or rotation limitations may be ignored in structural analysis.
  3. Semi-ductile connections have a ductility less than the one of the connected member, but higher than its elastic limit deformation; elongation or rotation limitations must be considered in inelastic analysis.
  4. Brittle connections have a ductility less than the elastic limit deformation of the connected member; elongation or rotation limitations must be considered in both elastic and inelastic analysis.

L.7 General design requirements for connections

  1. The relevant combinations of the main behavioural properties (rigidity, strength and ductility) of connections give rise to several cases (Figure L.3).

    In Table L.1 they are shown with reference to the corresponding requirements for methods of global analysis (see 5,2.1).

L.8 Requirements for framing connections

L.8.1 General

  1. With respect to the moment-curvature relationship, the connection types adopted in frame structures can be divided into:
  2. The types of connections should conform with Table L.1 in accordance with the method of global analysis(see 5.2.1) and the member design assumptions (Annex F). 203

    Figure L.3 - Main connection types

    Figure L.3 - Main connection types

L.8.2 Nominally pinned connections

  1. A nominally pinned connection should be designed in such a way to transmit the design axial and shear forces without developing significant moments which might adversely affect members of the structure.
  2. Nominally pinned connections should be capable of transmitting the forces calculated in design and should be capable of accepting the resulting rotations.
  3. The rotation capacity of a nominally pinned connection should be sufficient to enable all the necessary plastic hinges to develop under the design loads. 204
    Table L.1 - General design requirements
    Method of global analysis (see 5.2.1) Type of connection which must be accounted for Type of connection which may be ignored
    ELASTIC Semi-rigid connections (full or partial strength, ductile or non-ductile with or without restoring of member elastic strength)

    Partial strength connections (rigid or semi-rigid, ductile or non-ductile) without restoring of member elastic strength
    Fully restoring connections

    Rigid connections (full or partial strength, ductile or non-ductile) with restoring of member elastic strength

    Partial strength connections (rigid, ductile or non-ductile) with restoring of member elastic strength
    PLASTIC

    (rigid-plastic elastic-plastic inelastic-plastic)
    Partial strength connections (rigid or semi-rigid ductile or non-ductile) without restoring of member elastic strength Fully restoring connections

    Partial strength, ductile connections (rigid or semi-rigid) with restoring of member elastic strength

    Full strength connections
    HARDENING (rigid-hardening elastic-hardening genetically inelastic) Partially restoring connections Fully restoring connections

L.8.3 Built-in connections

  1. Built-in connections allow for the transmission of bending moment between connected members, together with axial and shear forces. They can be classified according to rigidity and strength as follows (see L.4 and L.5):
  2. A rigid connection should be designed in such a way that its deformation has a negligible influence on the distribution of internal forces and moments in the structure, nor on its overall deformation.
  3. The deformations of rigid connections should be such that they do not reduce the resistance of the structure by more than 5%.
  4. Semi-rigid connections should provide a predictable degree of interaction between members, based on the design moment-rotation characteristics of the joints.
  5. Rigid and semi-rigid connections should be capable of transmitting the forces and moments calculated in design.
  6. The rigidity of full-strength and partial-strength connections should be such that, under the design loads, the rotations at the necessary plastic hinges do not exceed their rotation capacities.
  7. The rotation capacity of a partial-strength connection which occurs at a plastic hinge location should be not less than that needed to enable all the necessary plastic hinges to develop under the design loads.
  8. The rotation capacity of a connection may be demonstrated by experimental evidence. Experimental demonstration is not required if using details which experience has proved have adequate properties in relation with the structural scheme.
205

Annex M - Adhesive bonded connections

[informative]

M.1 General

  1. Structural joints in aluminium may be made by bonding with adhesive.
  2. Bonding needs an expert technique and should be used with great care.
  3. The design guidance in this Annex M should only be used under the condition that:
  4. The use of adhesive for main structural joints should not be contemplated unless considerable testing has established its validity, including environmental testing and fatigue testing if relevant.
  5. Adhesive jointing can be suitably applied for instance for plate/stiffener combinations and other secondary stressed conditions.
  6. Loads should be carried over as large an area as possible. Increasing the width of joints usually increases the strength pro rata. Increasing the length is beneficial only for short overlaps. Longer overlaps result in more severe stress concentrations in particular at the ends of the laps.

M.2 Adhesives

  1. The recommended families of adhesives for the assembly of aluminium structures are: single and two part modified epoxies, modified acrylics, one or two part polyurethane; anaerobic adhesives can also be used in the case of pin- and collar-assemblies.
  2. On receipt of the adhesive, its freshness can be checked before curing by the following methods:
  3. The strength of an adhesive joint depends on the following factors:
    1. the specific strength of the adhesive itself, that can be measured by standardised tests (see ISO 11003-2);
    2. the alloy, and especially its proof stress if the yield stress of the metal is exceeded before the adhesive fails;
    3. the surface pre-treatment: chemical conversion and anodising generally give better long term results than degreasing and mechanical abrasion; the use of primers is possible provided that one makes sure that the primer, the alloy and the adhesive are compatible by using bonding tests;
    4. the environment and the ageing: the presence of water or damp atmosphere or aggressive environment can drastically lower the long term performance of the joint (especially in the case of poor surface pre-treatments);
    5. the configuration of the joint and the related stress distribution, i.e. the ratio of the maximum shear stress τmax to the mean one (τmax/τmean) and the ratio of the maximum peel stress σmax to the mean shear one (σmax/τmean), both maxima occurring at the end of the joint; the stress concentrations should be reduced as much as possible; they depend on the stiffness of the assembly (thickness and Young’s modulus of the adherent) and on the overlap length of the joint.
    206
  4. Knowledge of the specific strength of the adhesive is not sufficient to evaluate the strength of the joint, one must evaluate it by laboratory tests taking into account the whole assembly, i.e. the combinations of alloy/pre-treatment/adhesive, and the ageing or environment (see M.3 and 2.5).
  5. The strength obtained on specimens at the laboratory should be used as guidelines; one must check the joint performances in real conditions: the use of prototypes is recommended (see M.3).

M.3 Design of adhesive bonded joints

M.3.1 General

  1. In adhesive bonded joints, it should be aimed to transfer the loads by shear stresses; tensile stresses – in particular peeling or other forces tending to open the joint – should be avoided or should be transmitted by complementary structural means. Furthermore uniform distribution of stresses and sufficient deformation capacity to enable a ductile type of failure of the component are to be strived for.

    Sufficient deformation capacity is arrived at in case the design strength of the joint is greater than the yield strength of the connected member.

    Figure M.1 – Example of snap joints: tensile forces transmitted transverse to extrusion direction by snapping parts, but no shear transfer in longitudinal direction

    Figure M.1 – Example of snap joints: tensile forces transmitted transverse to extrusion direction by snapping parts, but no shear transfer in longitudinal direction

    Figure M.2 – Example of bonded extruded members: bonding allows transmitting tensile forces transverse by shear stresses and shear forces parallel to extrusion direction

    Figure M.2 – Example of bonded extruded members: bonding allows transmitting tensile forces transverse by shear stresses and shear forces parallel to extrusion direction

M.3.2 Characteristic strength of adhesives

  1. As far as the mechanical properties are concerned high strength adhesives should be used for structural applications (see Table M.1). However, also the toughness should be sufficient to overcome stress/strain concentrations and to enable a ductile type of failure.
  2. Pre-treatments of the surfaces to be bonded have to be chosen such that the bonded joint meets the design requirements during service life of the structure. See Image EN 1090-3 Image. 207
  3. For the characteristic shear strength of adhesives fv,adh for structural applications the values of Table M.1 may be used.
    Table M.1 - Characteristic shear strength values of adhesives
    Adhesive types fv,adh N/mm2
    l - component, heat cured, modified epoxide
    2- components, cold cured, modified epoxide
    2- components, cold cured, modified acrylic
    35
    25
    20
  4. The adhesive types as mentioned in Table M.1 may be used in structural applications under the conditions as given earlier in M.3.1 and M.3.2 respectively. The values given in Table M.1 are based on results of extensive research. However, it is allowed to use higher shear strength values than the ones given in Table M.1, see M.4.

M.3.3 Design shear stress

  1. The design shear stress should be taken as

    Image

    where:

    τ nominal shear stress in the adhesive layer;
    fv,adh characteristic shear strength value of adhesive, see M.3.2;
    Image γMa partial safety factor for adhesive bonded joints, see 8,1.1. Image

    NOTE The high value of γMa in 8,1.1 has to be used since:

M.4 Tests

  1. Higher characteristic shear strength values of adhesives than given in Table M.1 may be used if appropriate shear tests are carried out, see also ISO 11003.
208

Bibliography

EN 1592-1 Aluminium and aluminium alloys - HF seam welded tubes - Part 1: Technical conditions for inspection and delivery
EN 1592-2 Aluminium and aluminium alloys - HF seam welded tubes - Part 2: - Mechanical properties
EN 1592-3 Aluminium and aluminium alloys - HF seam welded tubes - Part 3: - Tolerance on dimensions and shape of circular tubes
EN 1592-4 Aluminium and aluminium alloys - HF seam welded tubes - Part 4: - Tolerance on dimensions and form for square, rectangular and shaped tubes
209