PREAMBLE (NOT PART OF THE STANDARD)
In order to promote public education and public safety, equal justice for all,
a better informed citizenry, the rule of law, world trade and world peace,
this legal document is hereby made available on a noncommercial basis, as it
is the right of all humans to know and speak the laws that govern them.
END OF PREAMBLE (NOT PART OF THE STANDARD)
EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 199911:2007+A1
June 2009
ICS 91.010.30; 91.080.10
Supersedes ENV 199911:1998
English Version
Eurocode 9: Design of aluminium structures  Part 11: General structural rules
Eurocode 9: Calcul des structures en aluminium  Partie 11: 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. Uptodate 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.
Management Centre: rue de Stassart, 36 B1050 Brussels
© 2007 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 199911:2007: 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 199911 
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 
Groundstructure 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 crosssections 
53 


6.1.5 
Local buckling resistance 
58 


6.1.6 
HAZ softening adjacent to welds 
59 

6.2 
Resistance of crosssections 
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 builtup 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 builtup members 
85 

6.5 
Unstiffened plates under inplane loading 
85 


6.5.1 
General 
85 


6.5.2 
Resistance under uniform compression 
86 


6.5.3 
Resistance under inplane 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 inplane loading 
89 


6.6.1 
General 
89 


6.6.2 
Stiffened plates under uniform compression 
90 


6.6.3 
Stiffened plates under inplane moment 
92 


6.6.4 
Longitudinal stress gradient on multistiffened plates 
92 


6.6.5 
Multistiffened 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 inplane 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 slipresistant 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 
Heataffected 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 Tstub in tension 
140 

B.1 
General rules for evaluation of resistance 
140 

B.2 
Individual boltrow, boltgroups and groups of boltrows 
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 nonheat treatable alloys 
149 

C.3 
Cast products 
150 


C.3.1 
General 
150 


C.3.2 
Heat treatable casting alloys EN AC42100, EN AC42200, EN AC43000 and EN AC43300 
150 


C.3.3 
Nonheat treatable casting alloys EN AC44200 and EN AC51300 
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 nonmetallic 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 ε_{u} 
165 
Annex F [informative]  Behaviour of crosssections beyond the elastic limit 
166 


F.1 
General 
166 


F.2 
Definition of crosssection limit states 
166 


F.3 
Classification of crosssections 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 torsionalflexural 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 crosssections symmetrical about the minor or major axis 
174 


I.1.3 
Beams with uniform crosssections symmetrical about major axis, centrally symmetric and doubly symmetric crosssections 
179 


I.1.4 
Cantilevers with uniform crosssections symmetrical about the minor axis 
180 

I.2 
Slenderness for lateral torsional buckling 
182 

I.3 
Elastic critical axial force for torsional and torsionalflexural buckling 
184 

I.4 
Slenderness for torsional and torsionalflexural buckling 
185 
Annex J [informative]  Properties of cross sections 
190 

J.1 
Torsion constant I_{t} 
190 

J.2 
Position of shear centre S 
190 

J.3 
Warping constant I_{w} 
190 

J.4 
Cross section constants for open thinwalled 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 
Inplane 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 
Builtin 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 
6
Foreword
This European Standard (EN 199911:2007) 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 199911: 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 agreement^{1} 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:
  as a means to prove compliance of building and civil engineering works with the essential requirements of Council Directive 89/106/EEC, particularly Essential Requirement N°1  Mechanical resistance and stability  and Essential Requirement N°2  Safety in case of fire;
  as a basis for specifying contracts for construction works and related engineering services;
  as a framework for drawing up harmonised technical specifications for construction products (ENs and ETAs)
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents^{2} referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standard^{3}. 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. :
  values for partial factors and/or classes where alternatives are given in the Eurocode,
  values to be used where a symbol only is given in the Eurocode,
  geographical and climatic data specific to the Member State, e.g. snow map,
  the procedure to be used where alternative procedures are given in the Eurocode,
  references to noncontradictory complementary information to assist the user to apply the Eurocode.
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 works^{4}. Furthermore, all the information accompanying the CE Marking of the
^{2}According 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.
^{3}According to Art. 12 of the CPD the interpretative documents should :
 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 ;
 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. ;
 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 199911
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 199911 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 19991 2 to EN 19991 5.
The four other parts EN 199912 to EN 199915 are each addressing specific aluminium components, limit states or type of structures.
EN 199911 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 199911 is intended for use by
  committees drafting design related product, testing and execution standards,
  owners of construction works (e.g. for the formulation of their specific requirements)
  designers and constructors
  relevant authorities
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 199911
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 199911 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 199911 through clauses:
  1.1.2(1)
  2.1.2(3)
  2.3.1(1)
  3.2.1(1)
  3.2.2(1)
  3.2.2(2)
  3.2.3.1(1)
  3.3.2.1(3)
  3.3.2.2(1)
  5.2.1(3)
  5.3.2(3)
  5.3.4(3)
  6.1.3(1)
  6.2.1(5)
  7.1(4)
  7.2.1(1)
  7.2.2(1)
  7.2.3(1)
  8.1.1(2)
  8.9(3)
  A(6) (Table A.1)
  C.3.4.1(2)
  C.3.4.1(3)
  C.3.4.1(4)
  K.1(1)
  K.3(1)
10
1 General
1.1 Scope
1.1.1 Scope of EN 1999
 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.
 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.
 EN 1999 is intended to be used in conjunction with:
  EN 1990 “Basis of structural design”
  EN 1991 “Actions on structures”
  European Standards for construction products relevant for aluminium structures
  prEN 10901: Execution of steel structures and aluminium structures – Part 1: Requirements for conformity assessment of structural components
  EN 10903: Execution of steel structures and aluminium structures – Part 3: Technical requirements for aluminium structures
 EN 1999 is subdivided in five parts:
EN 199911 Design of Aluminium Structures: General structural rules.
EN 199912 Design of Aluminium Structures: Structural fire design.
EN 199913 Design of Aluminium Structures: Structures susceptible to fatigue.
EN 199914 Design of Aluminium Structures: Coldformed structural sheeting.
EN 199915 Design of Aluminium Structures: Shell structures.
1.1.2 Scope of EN 199911
 EN 199911 gives basic design rules for structures made of wrought aluminium alloys and limited guidance for cast alloys (see section 3 and Annex C).
NOTE Minimum material thickness may be defined in the National Annex. The following limits are recommended – if not otherwise explicitly stated in this standard:
 – components with material thickness not less than 0,6 mm;
 – welded components with material thickness not less than 1,5 mm;
 – connections with:
 ∘ steel bolts and pins with diameter not less than 5 mm;
 ∘ aluminium bolls and pins with diameter not less than 8 mm;
 ∘ rivets and thread forming screws with diameter not less than 4.2 mm
 The following subjects are dealt with in EN 199911:
Section 1: General
Section 2: Basis of design
Section 3: Materials
footnote deleted
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 Tstub 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 flexuraltorsional 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 
 Sections 1 to 2 provide additional clauses to those given in EN 1990 “Basis of structural design”.
 Section 3 deals with material properties of products made of structural aluminium alloys.
 Section 4 gives general rules for durability.
 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.
 Section 6 gives detailed rules for the design of cross sections and members.
 Section 7 gives rules for serviceability.
 Section 8 gives detail rules for connections subject to static loading: bolted, riveted, welded and adhesive bonded connections.
1.2 Normative references
 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 10901: Execution of steel structures and aluminium structures – Part 1: Requirements for conformity assessment of structural components
EN 10903: Execution of steel structures and aluminium structures – Part 3: Technical requirements for aluminium structures
1.2.2 References on structural design
footnote deleted
EN 1990 
Basis of structural design 12 
EN 1991 
Actions on structures – All parts 
Text deleted
EN 199912 
Design of aluminium structures  Part 12: Structural fire design 
EN 199913 
Design of aluminium structures  Part 13: Structures susceptible to fatigue 
EN 199914 
Design of aluminium structures  Part 14: Coldformed structural sheeting 
EN 199915 
Design of aluminium structures  Part 15: Shell structures 
1.2.3 References on aluminium alloys
Text deleted
1.2.3.1 Technical delivery conditions
EN 4851 
Aluminium and aluminium alloys  Sheet, strip and plate  Part 1: Technical conditions for inspection and delivery 
EN 5861 
Aluminium and aluminium alloys  Forgings  Part 1: Technical conditions for inspection and delivery 
EN 7541 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 1: Technical conditions for inspection and delivery 
EN 7551 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles  Part 1: Technical conditions for inspection and delivery 
Text deleted
EN 28839 
Fasteners  Mechanical properties of fasteners  Bolts, screws, studs and nuts made from nonferrous metals 
EN ISO 8981 
Mechanical properties of fasteners made of carbon steel and alloy steel  Part 1: Bolts, screws and studs 
EN ISO 35061 
Mechanical properties of corrosionresistant stainlesssteel fasteners  Part 1: Bolts, screws and studs 
1.2.3.2 Dimensions and mechanical properties
EN 4852 
Aluminium and aluminium alloys  Sheet, strip and plate  Part 2: Mechanical properties 
EN 4853 
Aluminium and aluminium alloys  Sheet, strip and plate  Part 3: Tolerances on shape and dimensions for hotrolled products 
EN 4854 
Aluminium and aluminium alloys  Sheet, strip and plate  Part 4: Tolerances on shape and dimensions for coldrolled products 13 
EN 5082 
Roofing products from metal sheet  Specifications for self supporting products of steel, aluminium or stainless steel  Part 2: Aluminium 
EN 5862 
Aluminium and aluminium alloys  Forgings  Part 2: Mechanical properties and additional property requirements 
EN 5863 
Aluminium and aluminium alloys  Forgings  Part 3: Tolerances on dimension and form 
EN 7542 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 2: Mechanical properties 
EN 7543 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 3: Round bars, tolerances on dimension and form 
EN 7544 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 4: Square bars, tolerances on dimension and form 
EN 7545 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 5: Rectangular bars, tolerances on dimension and form 
EN 7546 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 6: Hexagonal bars, tolerances on dimension and form 
EN 7547 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 7: Seamless tubes, tolerances on dimension and form 
EN 7548 
Aluminium and aluminium alloys  Cold drawn rod/bar and tube  Part 8: Porthole tubes, tolerances on dimension and form 
EN 7552:2008 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles  Part 2: Mechanical properties 
EN 7553 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 3: Round bars, tolerances on dimension and form 
EN 7554 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 4: Square bars, tolerances on dimension and form 
EN 7555 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 5: Rectangular bars, tolerances on dimension and form 
EN 7556 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 6: Hexagonal bars, tolerances on dimension and form 
EN 7557 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 7: Seamless tubes, tolerances on dimension and form 
EN 7558 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 8: Porthole tubes, tolerances on dimension and form 
EN 7559 
Aluminium and aluminium alloys  Extruded rod/bar, tube and profiles Part 9: Profiles, tolerances on dimension and form 
Text deleted
1.2.3.3 Aluminium alloy castings
EN 15591 
Founding  Technical conditions of delivery  Part 1: General 
EN 15594 
Founding  Technical conditions of delivery  Part 4: Additional requirements for aluminium alloy castings 14 
EN 13711 
Founding  Liquid penetrant inspection  Part I: Sand, gravity die and low pressure die castings 
EN 12681 
Founding  Radiographic examination 
EN 5711 
Non destructive testing  Penetrant testing  Part 1: General principles 
EN 130681 
Nondestructive testing  Radioscopic testing  Part 1: Quantitative measurement of imaging properties 
EN 130682 
Nondestructive testing  Radioscopic testing  Part 2: Check of long term stability of imaging devices 
EN 130683 
Nondestructive testing  Radioscopic testing  Part 3: General principles of radioscopic testing of metallic materials by X and gamma rays 
EN 444 
Nondestructive testing  General principles for radiographic examination of metallic materials by X and gammarays 
Text deleted
EN 1706 
Aluminium and aluminium alloys  Castings  Chemical composition and mechanical properties 
1.2.4 References on welding
Text deleted
EN 10114:2000 
Welding – Recommendations for welding of metallic materials – Part 4: Arc welding of aluminium and aluminium alloys 
Text deleted
1.2.5 Other references
Text deleted
ISO 8930 
General principles on reliability for structures  List of equivalent terms 
ISO 110031 
Adhesives  Determination of shear behaviour of structural adhesives  Part l: Torsion test method using buttbonded hollow cylinders 
ISO 110032 
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. 15 
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. 
1.3 Assumptions
 In addition to the general assumptions of EN 1990 the following assumptions apply:
 – execution complies with EN 10903
1.4 Distinction between principles and application rules
 The rules in EN 1990 1.4 apply.
1.5 Terms and definitions
 The definitions in EN 1990 1.5 apply.
 The following terms are used in EN 199911 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 momentresisting frames and triangulated frames; it covers both plane frames and threedimensional frames
1.5.2
subframe
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:
  semicontinuous, in which the structural properties of the members and connections need explicit consideration in the global analysis
  continuous, in which only the structural properties of the members need be considered in the global analysis
  simple, in which the joints are not required to resist moments
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 crosssection 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
 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 199911. Symbols may have various meanings.
Section 1 General
x  x 
axis along a member 
y  y 
axis of a crosssection 
z  z 
axis of a crosssection 
u  u 
major principal axis (where this does not coincide with the yy axis) 
v  v 
minor principal axis (where this does not coincide with the zz axis) 
Section 2 Basis of design
P_{k} 
nominal value of the effect of prestressing imposed during erection 
G_{k} 
nominal value of the effect of permanent actions 
X_{k} 
characteristic values of material property 
X_{n} 
nominal values of material property 
R_{d} 
design value of resistance 
R_{k} 
characteristic value of resistance 
γ_{M} 
general partial factor 
γ_{Mi} 
particular partial factor 
γ_{Mf} 
partial factor for fatigue 
η 
conversion factor 
a_{d} 
design value of geometrical data 
Section 3 Materials
f_{o} 
characteristic value of 0,2 % proof strength 
f_{u} 
characteristic value of ultimate tensile strength 
f_{oc} 
characteristic value of 0,2 % proof strength of cast material 
f_{uc} 
characteristic value of ultimate tensile strength of cast material 
A_{50} 
elongation value measured with a constant reference length of 50 mm, see EN 10 002 
, elongation value measured with a reference length , see EN 10 002 
A_{0} 
original crosssection area of test specimen 
f_{o,haz} 
0,2 % proof strength in heat affected zone, HAZ 
f_{u,haz} 
ultimate tensile strength in heat affected zone, HAZ 
ρ_{o,haz} 
= f_{o,haz} / f_{o} , ratio between 0,2 % proof strength in HAZ and in parent material 
ρ_{u,haz} 
= f_{u,haz} / f_{u} , ratio between ultimate strength in HAZ and in parent material 
BC 
buckling class 17 
n_{p} 
exponent in RambergOsgood 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
α_{cr} 
factor by which the design loads would have to be increased to cause elastic instability in a global mode 
F_{Ed} 
design loading on the structure 
F_{cr} 
elastic critical buckling load for global instability mode based on initial elastic stiffness 
H_{Ed} 
design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal loads 
V_{Ed} 
total design vertical load on the structure on the bottom of the storey 
δ_{H,Ed} 
horizontal displacement at the top of the storey, relative to the bottom of the storey 
h 
storey height, height of the structure 

non dimensional slenderness 
N_{Ed} 
design value of the axial force 
ϕ 
global initial sway imperfection 
ϕ_{0} 
basic value for global initial sway imperfection 
α_{h} 
reduction factor for height h applicable to columns 
α_{m} 
reduction factor for the number of columns in a row 
m 
number of columns in a row 
e_{0} 
maximum amplitude of a member imperfection 
L 
member length 
e_{0,d} 
design value of maximum amplitude of an imperfection 
M_{Rk} 
characteristic moment resistance of the critical cross section 
N_{Rk} 
characteristic resistance to normal force of the critical cross section 
q 
equivalent force per unit length 
δ_{q} 
inplane deflection of a bracing system 
q_{d} 
equivalent design force per unit length 
M_{Ed} 
design bending moment 
k 
factor for e_{o,d} 
Section 6 Ultimate limit states for members
γ_{M1} 
partial factor for resistance of crosssections whatever the class is 
γ_{M1} 
partial factor for resistance of members to instability assessed by member checks 
γ_{M2} 
partial factor for resistance of crosssections in tension to fracture 
b 
width of cross section part 
t 
thickness of a crosssection part 
β 
widthtothickness ratio b/t 
η 
coefficient to allow for stress gradient or reinforcement of cross section part 
Ψ 
stress ratio 
σ_{cr} 
elastic critical stress for a reinforced cross section part 
σ_{cr0} 
elastic critical stress for an unreinforced cross section part 
R 
radius of curvature to the midthickness of material 18 
D 
diameter to midthickness of tube material 
β_{1}, β_{2}, β_{3} 
limits for slenderness parameter 
ε 
, coefficient 
z_{1} 
distance from neutral axis to most severely stressed fibre 
z_{2} 
distance from neutral axis to fibre under consideration 
C_{1}, C_{2} 
Constants 
ρ_{c} 
reduction factor for local buckling 
b_{haz} 
extent of HAZ 
T_{1} 
interpass temperature 
α_{2} 
factor for b_{haz} 
6.2 Resistance of cross sections
σ_{x,Ed} 
design value of the local longitudinal stress 
σ_{y,Ed} 
design value of the local transverse stress 
τ_{Ed} 
design value of the local shear stress 
N_{Ed} 
design normal force 
M_{y,Ed} 
design bending moment, yy axis 
M_{z,Ed} 
design bending moment, zz axis 
N_{Rd} 
design values of the resistance to normal forces 
M_{y,Rd} 
design values of the resistance to bending moments, yy axis 
M_{z,Rd} 
design values of the resistance to bending moments, zz 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 zigzag line progressively across the member or part of the member 
d 
diameter of hole 
A_{g} 
area of gross crosssection 
A_{net} 
net area of crosssection 
A_{eff} 
effective area of crosssection 
N_{t,Rd} 
design values of the resistance to tension force 
N_{o,Rd} 
design value of resistance to general yielding of a member in tensions 
N_{u,Rd} 
design value of resistance to axial force of the net crosssection at holes for fasteners 
N_{c,Rd} 
design resistance to normal forces of the crosssection for uniform compression 
M_{Rd} 
design resistance for bending about one principal axis of a crosssection 
M_{u,Rd} 
design resistance for bending of the net crosssection at holes 
M_{o,Rd} 
design resistance for bending to general yielding 
α 
shape factor 
W_{el} 
elastic modulus of the gross section (see 6.2.5.2) 
W_{net} 
elastic modulus of the net section allowing for holes and HAZ softening, if welded 
W_{pl} 
plastic modulus of gross section 
W_{eff} 
effective elastic section modulus, obtained using a reduced thickness t_{eff} for the class 4 parts 
W_{el,haz} 
effective elastic modulus of the gross section, obtained using a reduced thickness ρ_{o,haz}t for the HAZ material 19 
W_{pl,haz} 
effective plastic modulus of the gross section, obtained using a reduced thickness ρ_{o,haz}t for the HAZ material 
W_{eff,haz} 
effective elastic section modulus, obtained using a reduced thickness ρ_{c}t for the class 4 parts or a reduced thickness ρ_{o,haz}t for the HAZ material, whichever is the smaller 
α_{3,u} 
shape factor for class 3 cross section without welds 
α_{3,w} 
shape factor for class 3 cross section with welds 
V_{Ed} 
design shear force 
V_{Rd} 
design shear resistance 
A_{v} 
shear area 
η_{v} 
factor for shear area 
h_{w} 
depth of a web between flanges 
t_{w} 
web thickness 
A_{e} 
the section area of an unwelded section, and the effective section area obtained by taking a reduced thickness ρ_{o,haz}t for the HAZ material of a welded section 
T_{Ed} 
design value of torsional moment 
T_{Rd} 
design St. Venant torsion moment resistance 
W_{T,pl} 
plastic torsion modulus 
T_{t,Ed} 
design value of internal St. Venant torsional moment 
T_{w,Ed} 
design value of internal warping torsional moment 
τ_{t,Ed} 
design shear stresses due to St. Venant torsion 
τ_{w,Ed} 
design shear stresses due to warping torsion 
σ_{w,Ed} 
design direct stresses due to the bimoment B_{Ed} 
B_{Ed} 
bimoment 
V_{T,Rd} 
reduced design shear resistance making allowance for the presence of torsional moment 
f_{o,V} 
reduced design value of strength making allowance for the presence of shear force 
M_{v,Rd} 
reduced design value of the resistance to bending moment making allowance for the presence of shear force 
6.3 Buckling resistance
N_{Rd} 
resistance of axial compression force 
M_{y,Rd} 
bending moment resistance about yy axis 
M_{z,Rd} 
bending moment resistance about zz axis 
η_{0}, γ_{0}, ξ_{0}, Ψ 
exponents in interaction formulae 
ɷ_{0} 
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 
N_{b,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 

limit of the horizontal plateau of the buckling curves 
N_{cr} 
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 crosssection 

relative slenderness 

relative slenderness for torsional or torsionalflexural buckling 20 
N_{cr} 
elastic torsionalflexural buckling force 
k 
buckling length factor 
M_{b,Rd} 
design buckling resistance moment 
χ_{LT} 
reduction factor for lateraltorsional buckling 
ϕ_{LT} 
value to determine the reduction factor χ_{LT} 
α_{LT} 
imperfection factor 

non dimensional slenderness for lateral torsional buckling 
M_{cr} 
elastic critical moment for lateraltorsional buckling 

plateau length of the lateral torsional buckling curve 
η_{c}, γ_{c}, ξ_{c}, Ψ_{c} 
exponents in interaction formulae 
ɷ_{x}, ɷ_{x,LT} 
factors for section with localized weld 

relative slenderness parameters for section with localized weld 
x_{s} 
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 builtup compression members
L_{ch} 
buckling length of chord 
h_{0} 
distance of centrelines of chords of a builtup column 
a 
distance between restraints of chords 
α 
angle between axes of chord and lacings 
i_{min} 
minimum radius of gyration of single angles 
A_{ch} 
area of one chord of a builtup column 
N_{ch,Ed} 
design chord force in the middle of a builtup member 

design value of the maximum moment in the middle of the builtup member 
I_{eff} 
effective second moment of area of the builtup member 
S_{V} 
shear stiffness of builtup member from the lacings or battened panel 
n 
number of planes of lacings 
A_{d} 
area of one diagonal of a builtup column 
d 
length of a diagonal of a builtup column 
A_{v} 
area of one post (or transverse element) of a builtup column 
I_{ch} 
plane second moment of area of a chord 
I_{bl} 
plane second moment of area of a batten 
μ 
efficiency factor 
i_{y}, i_{z} 
radius of gyration (yy axis and zz axis) 
6.5 Unstiffened plates under inplane loading
v_{1} 
reduction factor for shear buckling 
k_{τ} 
buckling coefficient for shear buckling 
6.6 Stiffened plates under inplane loading
c 
elastic support from plate 
l_{w} 
half wavelength in elastic buckling 
χ 
reduction factor for flexural buckling of subunit 
I_{eff} 
second moment of area off effective cross section of plating for inplane bending 
y_{st} 
distance from centre of plating to centre of outermost stiffener 
B_{x} 
bending stiffness of orthotropic plate in section x = constant 21 
B_{y} 
bending stiffness of orthotropic plate in section y = constant 
H 
torsional stiffness of orthotropic plate 
I_{L} 
second moment of area of one stiffener and adjacent plating in the longitudinal direction 
I_{xT} 
torsional constant of one stiffener and adjacent plating in the longitudinal direction 
a 
half distance between stiffeners 
t_{1}, t_{2} 
thickness of layers in orthotropic plate 
s 
developed width of stiffeners and adjacent plate 
τ_{cr,g} 
shear buckling stress for orthotropic plate 
ϕ, η_{h} 
factors 
6.7 Plate girders
b_{f} 
Flange width 
h_{w} 
web depth = clear distance between inside flanges 
b_{w} 
depth of straight portion of a web 
t_{w} 
web thickness 
t_{f} 
flange thickness 
I_{st} 
second moment of area of gross crosssection of stiffener and adjacent effective parts of the web plate 
b_{1}, b_{2} 
distances from stiffener to inside flanges (welds) 
a_{c} 
half wave length for elastic buckling of stiffener 
ρ_{v} 
factor for shear buckling resistance 
η 
factor for shear buckling resistance in plastic range 
λ_{w} 
slenderness parameter for shear buckling 
V_{w,Rd} 
shear resistance contribution from the web 
V_{f,Rd} 
shear resistance contribution from the flanges 
k_{τ,st} 
contribution from the longitudinal stiffeners to the buckling coefficient k_{τ} 
k_{τ1} 
buckling coefficient for subpanel 
c 
factor in expression for V_{f,Rd} 
M_{f,Rd} 
design moment resistance of a cross section considering the flanges only 
A_{f1}, A_{f2} 
cross section area of top and bottom flange 
F_{Ed} 
design transverse force 
F_{Rd} 
design resistance to transverse force 
L_{eff} 
effective length for resistance to transverse force 
l_{y} 
effective loaded length for resistance to transverse force 
χ_{F} 
reduction factor for local buckling due to transverse force 
s_{s} 
length stiff bearing under transverse force 
λ_{F} 
slenderness parameter for local buckling due to transverse force 
k_{F} 
buckling factor for transverse force 
γ_{s} 
relative second moment of area of the stiffener closest to the loaded flange 
I_{s1} 
second moment of area of the stiffener closest to the loaded flange 
m_{1}, m_{2} 
parameters in formulae for effective loaded length 
l_{e} 
parameter in formulae for effective loaded length 
M_{N,Rd} 
reduced moment resistance due to presence of axial force 
A_{w} 
cross section area of web 
A_{fc} 
crosssection area of compression flange 
k 
factor for flange induced buckling 22 
r 
radius of curvature 
h_{f} 
distance between centres of flanges 
6.8 members with corrugated webs
b_{1}, b_{2} 
flange widths 
t_{1}, t_{2} 
flange thicknesses 
ρ_{z} 
reduction factor due to transverse moments in the flanges 
M_{z} 
transverse bending moment in the flanges 
ρ_{c,g} 
reduction factor for global buckling 
λ_{c,g} 
slenderness parameter for global buckling 
τ_{cr,g} 
shear buckling stress for global buckling 
ρ_{c,1} 
reduction factor for local buckling 
λ_{c,1} 
slenderness parameter for local buckling 
τ_{cr,1} 
shear buckling stress for local buckling 
a_{0}, a_{1}, a_{2}, a_{3}, a_{max} widths of corrugations 
Section 7 Serviceability limit state
I_{ser} 
effective section moment of area for serviceability limit state 
I_{eff} 
section moment of area for the effective crosssection at the ultimate limit state 
σ_{gr} 
maximum compressive bending stress at the serviceability limit state based on the gross cross section 
Section 8 Design of connections
γ_{M3} → γ_{M7} partial safety factors 
γ_{Mw} 
partial safety factor for resistance of welded connection 
γ_{Mp} 
partial safety factor for resistance of pin connection 
γ_{Ma} 
partial safety factor for resistance of adhesive bonded connection 
γ_{Mser} 
partial safety factor for serviceability limit state 
Text deleted 
e_{1} → e_{4}, 
edge distances 
p, p_{1}, p_{2} 
spacing between bolt holes 
d 
diameter of fastener 
d_{0} 
hole diameter 
V_{eff,1,Rd} 
design block tearing resistance for concentric loading 
V_{eff,2,Rd} 
design block tearing resistance for eccentric loading 
A_{nt} 
net area subject to tension 
A_{nv} 
net area subject to shear 
A_{1} 
area of part of angle outside the bolt hole 
β_{2}, β_{3} 
reduction factors for connections in angles 23 
F_{v,Ed} 
design shear force per bolt for the ultimate limit state 
F_{v,Ed,ser} 
design shear force per bolt for the serviceability limit state 
F_{v,Rd} 
design shear resistance per bolt 
F_{b,Rd} 
design bearing resistance per bolt 
F_{s,Rd,ser} 
design slip resistance per bolt at the serviceability limit state 
F_{s,Rd} 
design slip resistance per bolt at the ultimate limit state 
F_{t,Ed} 
design tensile force per bolt for the ultimate limit state 
F_{t,Rd} 
design tension resistance per bolt 
N_{net,Rd} 
design resistance of section at bolt holes 
B_{t,Rd} 
design tension resistance of a boltplate assembly 
f_{ub} 
characteristic ultimate strength of bolt material 
f_{ur} 
characteristic ultimate strength of rivet material 
A_{0} 
cross section area of the hole 
A 
gross cross section of a bolt 
A_{s} 
tensile stress area of a bolt 
k_{2} 
factor for tension resistance of a bolt 
d_{m} 
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; 
t_{p} 
thickness of the plate under the bolt head or the nut; 
F_{p,C} 
preloading force 
μ 
slip factor 
n 
number of friction interfaces 
β_{Lf} 
reduction factor for long joint 
L_{j} 
distance between the centres of the end fasteners in a long joint 
β_{p} 
reduction factor for fasteners passing through packings 
a, b 
plate thickness in a pin connection 
c 
gap between plates in a pin connection 
f_{w} 
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 
γ_{Mw} 
partial safety factor for welded joints 
L_{w} 
total length of longitudinal fillet weld 
L_{w,eff} 
effective length of longitudinal fillet weld 
a 
effective throat thickness 
σ_{haz} 
design normal stress in HAZ, perpendicular to the weld axis 
τ_{haz} 
design shear stress in HAZ 
f_{v,haz} 
characteristic shear strength in HAZ 
Annex A Execution classes
Annex B Equivalent Tstub in tension
F_{u,Rd} 
tension resistance of a Tstub flange 
B_{u} 
tension resistance of a boltplate assembly 
B_{0} 
conventional bolt strength at elastic limit 24 
A_{s} 
stress area of bolt 
I_{eff} 
effective length 
e_{min} 
minimum edge distance 
m 
distance from weld toe to centre of bolt 
Annex C Materials selection
σ_{eq,Ed} 
equivalent design stress for castings 
σ_{x,Ed} 
design stress in xaxis direction for castings 
σ_{y,Ed} 
design stress in yaxis direction for castings 
τ_{xy,Ed} 
design shear stress for castings 
σ_{Rd} 
design resistance for castings 
γ_{Mo,c} , γ_{Mu,c} 
partial factors for yields strength and ultimate strength castings respectively 
γ_{M2,co} , γ_{M2,cu} 
partial factors for yields strength and ultimate strength for bearing resistance of bolts, rivets in castings 
γ_{Mp,co} , γ_{Mp,cu} 
partial factors for yields strength and ultimate strength for bearing resistance of pins in castings 
Annex E Analytical model for stressstrain relationship
The symbols are defined in the Annex
Annex F Behavior of crosssections beyond elastic limit
α_{0} 
geometrical shape factor 
α_{5} , α_{10} 
generalized shape factors corresponding to ultimate curvature values χ_{u} = 5χ_{e1} and χ_{u} = 10χ_{e1} 
α_{M ,red} 
correction factor for welded class 1 cross section 
Annex G Rotation capacity
χ_{u} 
ultimate bending curvature 
χ_{e1} 
elastic bending curvature (= χ_{0.2}) 
ξ 
ductility factor 
M_{o} 
elastic bending moment corresponding to the attainment of the proof stress f_{o} 
m, k 
numerical parameters 
R 
rotation capacity 
θ_{p}, θ_{el} 
and θ_{u}, plastic rotation, elastic rotation and maximum plastic rotation corresponding to ultimate curvature χ_{u} 
Annex H Plastic hinge method for continuous beams
η 
parameter depending on geometrical shape factor and conventional available ductility of the material 
α_{ξ} 
shape factor α_{5} or α_{10} 
a, b, c 
coefficients in expression for η 
Annex I Lateral torsional buckling of beams and torsional or flexuraltorsional buckling of compression members
I_{t} 
torsion constant 
I_{w} 
warping constant 
I_{z} 
second moment of area of minor axis 
k_{z} 
end condition corresponding to restraints against lateral movement 
k_{w} 
end condition corresponding to rotation about the longitudinal axis 
k_{y} 
end condition corresponding to restraints against movement in plane of loading 25 
K_{wt} 
nondimensional torsion parameter 
ϛ_{g} 
relative nondimensional coordinate of the point of load application 
ϛ_{j} 
relative nondimensional cross section monosymmetry parameter 
μ_{cr} 
relative nondimensional critical moment 
z_{a} 
coordinate of the point of load application related to centroid 
z_{s} 
coordinate of the shear centre related to centroid 
z_{g} 
coordinate of the point of load application related to shear centre 
z_{j} 
monosymmetry constant 
c 
depth of a lip 
ψ_{f} 
monosymmetry factor 
h_{f} 
distance between centrelines of flanges 
h_{s} 
distance between shear centre of upper flange and shear centre of bottom flange 
I_{fc} 
second moment of area of the compression flange about the minor axis of the section 
I_{ft} 
second moment of area of the tension flange about the minor axis of the section 
C_{1}, C_{2}, C_{3}, C_{1,1}, C_{12} coefficients in formulae for relative nondimensional critical moment 
N_{cr,y}, N_{cr,z} , N_{cr,T} elastic flexural buckling load (yy and zz axes) and torsional buckling load 
i_{s} 
polar radius of gyration 
α_{yw}, α_{zw} 
coefficients in equation for torsional and torsionalflexural buckling 
k, λ_{t} 
coefficients in formula for relative slenderness parameter 
λ_{0}, s, X 
coefficients to calculate λ_{t} 
Annex J Properties of cross sections
β, δ, γ 
fillet or bulb factors 
b_{sh} 
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
b_{eff} 
effective width for shear lag 
β_{S} 
effective width factor for shear lag 
K 
notional widthtolength ratio for flange 
A_{st} 
area of all longitudinal stiffeners within half the flange width 
a_{st,1} 
relative area of stiffeners = area of stiffeners divided by centre to centre distance of stiffeners 
s_{e} 
loaded length in section between flange and web 
b_{0} 
width of outstand or half width of internal crosssection part 
L_{e} 
points of zero bending moment 
Annex L Classification of joints
F 
load, generalized force force 
F_{u} 
ultimate load, ultimate generalized force 
v 
generalized deformation 
v_{u} 
deformation corresponding to ultimate generalized force 
Annex M Adhesive bonded connection
f_{v,adh} 
characteristic shear strength values of adhesives 
τ 
average shear stress in the adhesive layer 
γ_{Ma} 
material factor for adhesive bonded joint 
26
1.7 Conventions for member axes
 In general the convention for member axes is:
xx 
 along the member 
yy 
 axis of the crosssection 
zz 
 axis of the crosssection 
 For aluminium members, the conventions used for crosssection axes are:
  generally:
yy 
 crosssection axis parallel to the flanges 
zz 
 crosssection axis perpendicular to the flanges 
  for angle sections:
yy 
 axis parallel to the smaller leg 
zz 
 axis perpendicular to the smaller leg 
  where necessary:
uu 
 major principal axis (where this does not coincide with the yy axis) 
vv 
 minor principal axis (where this does not coincide with the zz axis) 
 The symbols used for dimensions and axes of aluminium sections are indicated in Figure 1.1.
 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 yy and zz for symmetrical sections and by the uu and vv axis for unsymmetrical section such as angles.
1.8 Specification for execution of the work
 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 nonnormative tolerances in EN 10903 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 10903 contains a checklist for information to be provided.
27
Figure 1.1  Definition of axes for various crosssections
28
2 Basis of design
2.1 Requirements
2.1.1 Basic requirements
 P The design of aluminium structures shall be in accordance with the general rules given in EN 1990.
 P The supplementary provisions for aluminium structures given in this section shall also be applied.
 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.
 The rules for resistances, serviceability and durability given in the various parts of EN 1999 should be applied.
2.1.2 Reliability management
 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, EN 10903 .
 Aluminium structures and components are classified in execution classes, see Annex A of this standard.
 The execution should be carried out in accordance with prEN 10901 and EN 10903. The information, which EN 10903 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 199911 to suit the reliability level required.
2.1.3 Design working life, durability and robustness
 Depending on the type of action affecting durability and the design working life (see EN 1990) aluminium structures should as applicable be
  designed for corrosion (see Section 4)
  designed for sufficient fatigue life (see EN 19991 3)
  designed for wearing
  designed for accidental actions (see EN 199117)
  inspected and maintained.
NOTE 1 Recommendarions for the design for corrosion are given in Annex C and Annex D
NOTE 2 Requirements for fatigue, see EN 199913
2.2 Principles of limit state design
 The resistances of cross sections and members specified in this EN 199911 for the ultimate limit states as defined in EN 1990 are based on simplified design models of recognised experimental evidence.
 The resistances specified in this EN 199911 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
 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.
 The actions to be considered in the erection stage should be obtained from EN 199116.
 Where the effects of predicted absolute and differential settlements need be considered best estimates of imposed deformations should be used.
 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 P_{k} as permanent action and grouped with other permanent actions G_{k} to a single action (G_{k} + P_{k}).
 Fatigue loading not defined in EN 1991 should be determined according to EN 199913.
2.3.2 Material and product properties
 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
 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
 Geometrical data for cross sections and systems may be taken from product standards or drawings for the execution according to EN 10903 and treated as nominal values.
 Design values of geometrical imperfections specified in this standard comprise
  the effects of geometrical imperfections of members as governed by geometrical tolerances in product standards or the execution standard.
  the effects of structural imperfections from fabrication and erection, residual stresses, variations of the yield strength and heataffected zones.
2.4.3 Design resistances
 For aluminium structures equation (6.6c) or equation (6.6d) of EN 1990 applies:
where:
R_{k} 
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 
γ_{M} 
is the global partial factor for the particular resistance 
NOTE For the definition of η_{1} , η_{i} , X _{k1} , X _{ki} a_{d} see EN 1990.
30
2.4.4 Verification of static equilibrium (EQU)
 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
 The resistances R_{K} in this standard have been determined using Annex D of EN 1990.
 In recommending classes of constant partial factors γ_{Mi} the characteristic values R_{k} were obtained from
R_{k} = R_{d} · γ_{Mi} (2.2)
where:
R_{d} 
are design values according to Annex D of EN 1990 
γ_{Mi} 
are recommended partial factors. 
NOTE 1 The numerical values of the recommended partial factors γ_{Mi} have been determined such that R_{k} represents approximately the 5 %fractile for an infinite number of tests.
NOTE 2 For characteristic values of fatigue strength and partial factors γ_{Mf} for fatigue see EN 199913.
 Where resistances R_{k} for prefabricated products are determined by tests, the procedure referred in (2) should be followed.
31
3 Materials
3.1 General
 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.
 Other material properties arc given in the ENs listed in 1.2.1.
3.2 Structural aluminium
3.2.1 Range of materials
 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 AW3004 
EN AWAlMn 1Mg 1 
SH, ST, PL 
A 
EN AW3005 
EN AWAlMn 1Mg0,5 
SH, ST, PL 
A 
EN AW3103 
EN AWAl Mn 1 
SH, ST, PL, ET, EP, ER/B 
A 
EN AW5005 / 5005A 
EN AWAlMg1(B) / (C) 
SH, ST, PL 
A 
EN AW5049 
EN AWAlMg2Mn0,8 
SH, ST, PL 
A 
EN AW5052 
EN AWAl Mg2,5 
SH, ST, PL, ET^{2)}, EP^{2)}, ER/B, DT 
A 
EN AW5083 
EN AWAl Mg4,5Mn0,7 
SH, ST, PL, ET^{2)}, EP^{2)}, ER/B, DT, FO 
A^{1)} 
EN AW5454 
EN AWAl Mg3Mn 
SH, ST, PL, ET^{2)}, EP^{2)}, ER/B 
A 
EN AW5754 
EN AWAl Mg3 
SH, ST, PL, ET^{2)}, EP^{2)}, ER/B, DT, FO 
A 
EN AW6060 
EN AWAl MgSi 
ET,EP,ER/B,DT 
B 
EN AW6061 
EN AWAl MglSiCu 
SH, ST,PL,ET,EP,ER/B,DT 
B 
EN AW6063 
EN AWAl Mg0,7Si 
ET, EP, ER/B,DT 
B 
EN AW6005A 
EN AWAl SiMg(A) 
ET, EP, ER/B 
B 
EN AW6082 
EN AWAl SilMgMn 
SH, ST, PL, ET, EP, ER/B, DT, FO 
B 
EN AW6106 
EN AWAlMgSiMn 
EP 
B 
EN AW7020 
EN AWAl Zn4,5Mg1 
SH, ST, PL, ET, EP, ER/B, DT 
C 
EN AW8011A 
EN AWAlFeSi 
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 thickwalled 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 rating^{1)} 
Numerical 
Chemical symbols 
EN AC42100 
EN ACAl Si7Mg0,3 
B 
EN AC42200 
EN ACAl Si7Mg0,6 
B 
EN AC43000 
EN ACAl Si10Mg(a) 
B 
EN AC43300 
EN ACAlSi9Mg 
B 
EN AC44200 
EN ACAl Si 12(a) 
B 
EN AC51300 
EN ACAl 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
 Characteristic values of the 0,2% proof strength f_{o} and the ultimate tensile strength f_{u} 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 15921 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.
 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 (f_{o}, f_{u}, f_{o,haz} and f_{u,haz}) may be reduced according to
X_{kT} = [1  k_{100}(T  80) / 20] X_{k} (3.1)
where:
X_{k} 
is the characteristic value of a strength property of a material 
X_{kT} 
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 
k_{100} = 0,1 
for strain hardening alloys (3xxxalloys, 5xxxalloys and EN AW 8011 A) 
k_{100} = 0,2 
for precipitation hardening material (6xxxalloys and EN AW7020) 
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.
 Characteristic values for the heat affected zone (0,2% proof strength f_{o,haz} and ultimate tensile strength f_{u,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 RambergOsgood expression for plastic resistance.
33
Table 3.2a  Characteristic values of 0,2% proof strength f_{o}, ultimate tensile strength f_{u} (unwelded and for HAZ), min elongation A, reduction factors ρ_{o,haz} and ρ_{u,haz} in HAZ, buckling class and exponent n_{p} for wrought aluminium alloys  Sheet, strip and plate
Alloy ENAW 
Temper ^{1)} 
Thickness mm ^{1)} 
f_{o} ^{1)} 
f_{u} 
A_{50} ^{1)} ^{6)}
% 
f_{o,haz} ^{2)} 
f_{u,haz} ^{2)} 
HAZfactor^{2)} 
BC 4) 
n_{p} 1),5) 
N/mm^{2} 
N/mm^{2} 
ρ_{o,haz}^{1)} 
ρ_{u,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 f_{o} , A and n_{p}.). 2) The HAZvalues 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 ρfactors. For higher thickness  unless other data are available  the HAZ values and ρfactors 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 , not A_{50}. 4) BC = buckling class, see 6.1.4.4, 6.1.5 and 6.3.1. 5) nvalue in RambergOsgood expression for plastic analysis. It applies only in connection with the listed f_{o}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 4852.

34
Table 3.2b  Characteristic values of 0,2% proof strength f_{o} and ultimate tensile strength f_{u} (unwelded and for HAZ), min elongation A, reduction factors ρ_{o,haz} and ρ_{u,haz} in HAZ, buckling class and exponent n_{p} for wrought aluminium alloys  Extruded profiles, extruded tube, extruded rod/bar and drawn tube
Alloy ENAW 
Product form 
Temper 
Thickness t mm 1) 3) 
f_{o} ^{1)} 
f_{u} ^{1)} 
A ^{5) 2)} 
f_{o,haz} ^{4)} 
f_{u,haz} ^{4)} 
HAZfactor^{4)} 
BC 6) 
n_{p} 7) 
N/mm^{2} 
% 
N/mm^{2} 
ρ_{o,haz} 
ρ_{u,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 
t ≤ 25 
85 
200 
16 
85 
200 
1 
1 
B 
5 
5754 
ET, EP,ER/B 
O/H 111 F/H 112 
t ≤ 25 
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 
t ≤ 5 
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 
t ≤ 15 
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 
t ≤ 15 
120 
180 
12 
60 
100 
0,50 
0,56 
A 
12 
EP,ET,ER/B 
T66 
t ≤ 3 
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 
t ≤ 25 
110 
180 
15 
95 
150 
0,86 
0,83 
B 
8 
DT 
t ≤ 20 
110 
205 
16 
0,73 
B 
8 
EP,ET,ER/B 
T6 
t ≤ 25 
240 
260 
8 
115 
175 
0,48 
0,67 
A 
55 
DT 
t ≤ 20 
240 
290 
10 
0,60 
A 
23 
6063 
EP,ET,ER/B 
T5 
t ≤ 3 
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 
t ≤ 25 
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 
t ≤ 10 
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 
t ≤ 5 
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 < t ≤ 10 
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 35 
6082 
EP, ET, ER/B 
T4 
t ≤ 25 
110 
205 
14 
100 
160 
0,91 
0,78 
B 
8 
EP 
T5 
t ≤ 5 
230 
270 
8 
125 
185 
0,54 
0,69 
B 
28 
EP ET 
T6 
t ≤ 5 
250 
290 
8 
125 
185 
0,50 
0,64 
A 
32 
5 < t ≤ 15 
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 
t ≤ 15 
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 R_{p0,2} and R_{m} values can be taken as f_{o} and f_{u}. If using such higher values the corresponding HAZfactors ρ have to be calculated acc. to expression (6.13) and (6.14) with the same values for f_{o,haz} and f_{u,haz}. 2): Where minimum elongation values are given in bold, higher minimum values may be given for some forms or thicknesses. 3): According to EN 7552:2008 : following rule applies: “if a profile crosssection 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 crosssection.” 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 HAZvalues are valid for MIG welding and thickness up to 15mm. For TIG welding strain hardening alloys (3xxx and 5xxx) 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 ρfactors. For higher thickness  unless other data are available  the HAZ values and ρfactors 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) 6) BC = buckling class, see 6.1.4.4, 6.1.5 and 6.3.1. 7) nvalue in RambergOsgood expression for plastic analysis. It applies only in connection with the listed f_{o}value (= minimum standardized value). Text deleted 
Table 3.2c  Characteristic values of 0,2% proof strength f_{o}, ultimate tensile strength f_{u} (unwelded and for HAZ), minimum elongation A and buckling class for wrought aluminium alloys  Forgings
Alloy ENAW 
Temper 
Thickness up to mm 
Direction 
f_{o} 
f_{u} 
f_{o,haz} ^{1)} 
f_{u,haz} ^{1)} 
A ^{3)} % 
Buckling class 
N/mm^{2} 
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) ρ_{o,haz}; ρ_{u,haz} to be calculated according to expression (6.13) and (6.14) 2) For thicknesses over 15 mm (MIGwelding) or 6 mm (TIGwelding) see table 3.2.b footnote 4). 3) 
36
3.2.3 Material properties for cast aluminium alloys
3.2.3.1 General
 EN 199911 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
 The characteristic values of the 0,2% proof strength f_{o} and the ultimate tensile strength f_{u} 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 A_{50} 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)
Table 3.3  Characteristic values of 0,2% proof strength f_{o} and ultimate tensile strength f_{u} for cast aluminium alloys – Gravity casting
Alloy 
Casting process 
Temper 
f_{o} (f_{oc}) N/mm^{2} 
f_{u} (f_{uc}) N/mm^{2} 
A_{50} ^{1)} % 
EN AC42100 
Permanent mould 
T6 
147 
203 
2,0 
Permanent mould 
T64 
126 
175 
4 
EN AC42200 
Permanent mould 
T6 
168 
224 
1,5 
Permanent mould 
T64 
147 
203 
3 
EN AC43000 
Permanent mould 
F 
63 
126 
1,25 
EN AC43300 
Permanent mould 
T6 
147 
203 
2,0 
Sand cast 
T6 
133 
161 
1,0 
Permanent mould 
T64 
126 
175 
3 
EN AC44200 
Permanent mould 
F 
56 
119 
3 
Sand cast 
F 
49 
105 
2,5 
EN AC51300 
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
 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.
 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
 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/mm^{2}; 
 shear modulus 
G = 27 000 N/mm^{2}; 
 Poisson’s ratio 
v = 0,3; 
 coefficient of linear thermal expansion 
α = 23 × 10^{6} per °C; 
 unit mass 
ρ = 2 700 kg/m^{3}. 
 For material properties in structures subject to elevated temperatures associated with fire see EN 199912.
37
3.3 Connecting devices
3.3.1 General
 Connecting devices should be suitable for their specific use.
 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
 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.
 The minimum values of the 0,2% proof strength f_{o} and the ultimate strength f_{u} to be adopted as characteristic values in calculations, are given in Table 3.4.
 Aluminium bolts and rivets should be used only for connections of category A (bearing type, see Table 8.4).
NOTE 1 Presently no ENstandard, 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 ENstandard, 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.
 Selftapping and selfdrilling screws and blind rivets may be used for thinwalled structures. Rules are given in EN 199914.
38
Table 3.4  Minimum values of 0,2 % proof strength f_{o} and ultimate strength f_{u} for bolts and solid rivets
Material 
Type of fastener 
Alloy Numerical designation: EN AW. 
Alloy Chemical designation: EN AW 
Temper or grade 
Diameter 
f_{o} ^{7)} N/mm^{2} 
f_{u} ^{7)} N/mm^{2} 
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) text deleted 2) see 3.3.2.1 (3) text deleted 3) Material designation according to EN 28839 4) No grade designation in EN 28839 5) Grade according to EN ISO 8981 6) Designation and grade according to EN ISO 35061 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 0,2proof 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
 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
 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
 The minimum guaranteed values of the 0,2% proof strength f_{o} and the ultimate strength f_{u} to be adopted as characteristic values in calculations, are given in Table 3.4.
3.3.4 Welding consumables
 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.
 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, 4047A^{1)} 
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 

AlSi castings 
AlMg castings 
3xxx series alloys 
5xxx series alloys except 5083 
5083 
6xxxseries alloys 
7020 
7020 
NR^{2)} 
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 4^{4)} 
6xxxseries 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 
NR^{2)} 
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 
NR^{2)} 
Type 5 Type 5 Type 5 
Type 5 Type 5 Type 5 
Type 5^{3)}
Type 5 



3xxx series alloys 
Type 4 Type 4 Type 4 
Type 5 Type 5 Type 5 
Type 3 Type 3 Type 3 




AlMg castings 
NR^{2)} 
Type 5 Type 5 Type 5 





AlSi 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 ENAW 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 AlSi filler metal, or viceversa is not recommended because sufficient Mg_{2}Si precipitate is formed at the fusion boundaries to embrittle the weld. Where unavoidable see prEN 10114. ^{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 ENAW 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
 The basic requirements for durability are given in EN 1990.
NOTE For aluminium in contact with other material, recommendations are given in Annex D.
 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 loadbearing 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.
 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.
 The requirements and means for execution of protective treatment undertaken offsite and onsite are given in EN 10903 .
 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
 Analysis should be based upon calculation models of the structure that are appropriate for the limit state under consideration.
 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
 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 semicontinuous joints) they should be taken into account.
 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:
  simple, in which the joint may be assumed not to transmit bending moments;
  continuous, in which the stiffness and/or the resistance of the joint allow full continuity of the members to be assumed in the analysis;
  semicontinuous, in which the behaviour of the joint needs to be taken into account in the analysis
NOTE Recommendations for the various types of joints are given in Annex L.
5.1.3 Groundstructure interaction
 Account should be taken of the deformation characteristics of the supports where significant.
NOTE EN 1997 gives guidance for calculation of soilstructure interaction.
5.2 Global analysis
5.2.1 Effects of deformed geometry of the structure
 The internal forces and moments may generally be determined using either:
  firstorder analysis, using the initial geometry of the structure or
  secondorder analysis, taking into account the influence of the deformation of the structure.
 P The effects of the deformed geometry (secondorder effects) shall be considered if they increase the action effects significantly or modify significantly the structural behaviour.
 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:
where:
α_{cr} 
is the factor by which the design loading would have to be increased to cause elastic instability in a global mode 43 
F_{Ed} 
is the design loading on the structure 
F_{cr} 
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 α_{cr} for neglecting the influence of second order effects.
 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.
 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
 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.
 The verification of the stability of frames or their parts should be carried out considering imperfections and second order effects.
 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:
 both totally by the global analysis,
 partially by the global analysis and partially through individual stability checks of members according to 6.3,
 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.
 Second order effects may be calculated by using an analysis appropriate to the structure (including stepbystep 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.
 In accordance with 5.2.2(3) a) and b) the stability of individual members should be checked according to the following:
 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.
 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).
 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
 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 in accordance with the essential tolerances given in EN 10903 are considered in the resistance formulae, the buckling curves and the γ_{M}values in EN 1999.
 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.
 The following imperfections should be taken into account:
 global imperfections for frames and bracing systems
 local imperfections for individual members
5.3.2 Imperfections for global analysis of frames
 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.
 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.
 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:
 global initial sway imperfections, see Figure 5.1(d):
ϕ = ϕ_{0}α_{h}α_{m} (5.2)
where:
ϕ_{0} 
is the basic value: ϕ_{0} = 1 / 200 
α_{h} 
is the reduction factor for height h applicable to columns: 

h 
is the height of the structure in meters 
α_{m} 
is the reduction factor for the number of columns in a row: 
m 
is the number of columns in a row including only those columns which carry a vertical load N_{Ed} 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
 relative initial local bow imperfections of members for flexural buckling
e_{0} / L (5.3)
where L is the member length
NOTE The values e_{0}/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 e_{0} / L
Buckling class acc. to Table 3.2 
elastic analysis 
plastic analysis 
e_{0}/L 
e_{0}/L 
A 
1/300 
1/250 
B 
1/200 
1/150 
 For building frames sway imperfections may be disregarded where
H_{Ed} ≥ 0,15 V_{Ed} (5.4)
where:
H_{Ed} is the design value of the horizontal force
V_{Ed} is design value of the vertical force.
 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
 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:
  at least one moment resistant joint at one member end
where:
N_{Ed} is the design value of the compression force
is the inplane 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.
 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
 These initial sway imperfections should apply in all relevant horizontal directions, but need only be considered in one direction at a time.
 Where, in multistorey beamandcolumn building frames, equivalent forces are used they should be applied at each floor and roof level.
 The possible torsional effects on a structure caused by antisymmetric sways at the two opposite faces, should also be considered, see Figure 5.4.
Figure 5.4  Translational and torsional effects (plan view)
 As an alternative to (3) and (6) the shape of the elastic critical buckling mode η_{cr} 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:
where:
48
and 
m 
denotes the crosssection where reaches its maximum in the case of uniform normal force and uniform crosssection; 

α 
is the imperfection factor for the relevant buckling curve, see Table 6.6; 

is the relative slenderness of the structure; 


is the limit given in Table 6.6; 

χ 
is the reduction factor for the relevant buckling curve, see 6.3.1.2; 

N_{cr,m} = α_{cr}N_{Ed,m} is the value of axial force in crosssection m when the elastic critical buckling was reached; 

α_{cr} 
is the minimum force amplifier for the axial force configuration N_{Ed} in members to reach the elastic critical buckling; 

M_{Rk,m} is the characteristic moment resistance of the crosssection m according to (6.25) 6.2.5.1; 

N_{Rk,m} is the characteristic normal force resistance of the crosssection m according to (6.22) 6.2.4; 
is the bending moment due to η_{cr} at the crosssection m; 


is the second derivative of η_{cr} (x) 
NOTE 1 For calculating the amplifier α_{cr} the members of the structure may be considered to be loaded by axial forces N_{Ed} only that result from the first order elastic analysis of the structure for the design loads.
NOTE 2 The ration may be replaced by
where:
η_{cr}_{max} 
is the maximum value of the amplitude of the buckling. mode of the structure (arbitrary value may be taken); 
η^{II}_{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 η_{cr} with maximum amplitude η_{cr}_{max} ; 

is the bending moment in crosssection m calculated as given for η^{II}_{max}. 
The bending moments in the structure due to η_{init} (x) with allowing for second order effects may be then calculated from:
NOTE 3 Formula (5.6) is based on the requirement that the imperfection η_{init} having the shape of the elastic buckling mode η_{cr}, should have the same maximum curvature as the equivalent uniform member.
5.3.3 Imperfection for analysis of bracing systems
 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:
e_{0} = α_{m}L/500 (5.9)
49
where:
L is the span of the member and
in which m is the number of members to be restrained.
 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:
where:
δ_{q} is the inplane deflection of the bracing system due to q_{0} plus any external loads calculated from first order analysis.
NOTE 1 δ_{q} may be taken as 0 if second order theory is used.
NOTE 2 As δ_{q} in (5.11) depends on q_{0}, it results in an iterative procedure.
 Where the bracing system is required to stabilise the compression flange of a beam of constant height, the force N_{Ed} in Figure 5.5 may be obtained from:
N_{Ed} = M_{Ed} / h (5.12)
where:
M_{Ed} 
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.
 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 α_{m}N_{Ed} / 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.
 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 5.6  Bracing forces at splices in compression members
51
5.3.4 Member imperfections
 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.
 Where the stability of members is accounted for by second order analysis according to 5.2.2(5)a) for compression members imperfections e_{0} according to 5.3.2(3)b) or 5.3.2(5) or (6) should be considered.
 For a second order analysis taking account of lateral torsional buckling of a member in bending the imperfections may be adopted as ke_{0}, where e_{0} 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
 The internal forces and moments may be determined using either
 elastic global analysis
 plastic global analysis.
NOTE For finite element model (FEM) analysis see EN 199315.
 Elastic global analysis may be used in all cases.
 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
 Elastic global analysis is based on the assumption that the stressstrain behaviour of the material is linear, whatever the stress level is.
NOTE For the choice of a semicontinuous joint model see 5.1.2.
 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.
 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
 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.
 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
 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
 Resistance calculations for members are made using characteristic value of strength as follows:
f_{o} is the characteristic value of the strength for bending and overall yielding in tension and compression
f_{u} is the characteristic value of the strength for the local capacity of a net section in tension or compression
 The characteristic value of the 0,2% proof strength f_{o} and the ultimate tensile strength f_{u} for wrought aluminium alloys are given in 3.2.2.
6.1.3 Partial safety factors
 The partial factors γ_{M} 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 crosssections whatever the class is: 
γ_{M1} 
resistance of members to instability assessed by member checks: 
resistance of crosssections in tension to fracture: 
γ_{M2} 
resistance of joints: 
See Section 8 
NOTE 1 Partial factors γ_{Mi} may be defined in the National Annex. The following numerical values are recommended:
γ_{M1} = 1,10
γ_{M2} = 1,25
NOTE 2 For other recommended numerical values see EN 1999 Part 12 to Part 15. For structures not covered by EN 1999 Part 12 to Part 15 the National Annex may give information.
6.1.4 Classification of crosssections
6.1.4.1 Basis
 The role of crosssection classification is to identify the extent to which the resistance and rotation capacity of crosssections is limited by its local buckling resistance.
NOTE See also Annex F.
6.1.4.2 Classification
 Four classes of crosssections are defined, as follows:
 In Class 4 crosssections 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.
 The classification of a crosssection depends on the width to thickness ratio of the parts subject to compression.
 Compression parts include every part of a crosssection that is either totally or partially in compression under the load combination considered.
 The various compression parts in a crosssection (such as web or a flange) can, in general, be in different classes. A crosssection is classified according to the highest (least favourable) class of its compression parts.
 The following basic types of thinwalled part are identified in the classification process:
 flat outstand parts;
 flat internal parts;
 curved internal parts.
These parts can be unreinforced, or reinforced by longitudinal stiffening ribs or edge lips or bulbs (see Figure 6.1).
Figure 6.1  Types of crosssection parts
6.1.4.3 Slenderness parameters
 The susceptibility of an unreinforced flat part to local buckling is defined by the parameter β, which has the following values:
 flat internal parts with no stress gradient or
flat outstands with no stress gradient or peak compression at toe β = b/t (6.1)
 internal parts with a stress gradient that results in a neutral axis at the centre β = 0,40 b/t (6.2)
 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 crosssection part 54 
t 
is the thickness of a crosssection 
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.
 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 subparts 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 subpart 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
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 Values of β are found as follows:
 Mode l, uniform compression, standard reinforcement:
When the reinforcement is a singlesided rib or lip of thickness equal to the part thickness t,
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.
 Mode 1, uniform compression, nonstandard 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 midplane of the plate part is equal to that of the nonstandard reinforcement about the same plane. An alternative method is given in 6.6.
 Mode 1, uniform compression, complex reinforcement:
For unusual shapes of reinforcement not amenable to the analysis described above,
σ_{cr} 
is the elastic critical stress for the reinforced part assuming simply supported edges 
σ_{cr0} 
is the elastic critical stress for the unreinforced part assuming simply supported edges. 
 Mode 1, stress gradient:
The value of β is found from the expression (6.8), where σ_{cr} and σ_{cr0} now relate to the stress at the more heavily compressed edge of the part.
 Mode 2:
The value of β is found separately for each subpart in accordance with 6.1.4.3(1)
 The susceptibility of a uniformly compressed shallow curved unreinforced internal part to local buckling is defined by β, where:
R 
is radius of curvature to the midthickness of material 
b 
is developed width of the part at midthickness 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.
 The susceptibility of a thinwalled round tube to local buckling, whether in uniform compression or in bending is defined by β, where:
56
D = diameter to midthickness of tube material.
Figure 6.4  Values of η for reinforced cross section parts
6.1.4.4 Classification of crosssection parts
 The classification of parts of crosssections is linked to the values of the slenderness parameter as β follows:
Parts in beams 
Parts in struts 
β ≤ β_{1} 
: class 1 
β ≤ β_{2} 
: class 1 or 2 
β_{1} < β ≤ β_{2} 
: class 2 
β_{2} < β ≤ β_{3} 
: class 3 
β_{2} < β ≤ β_{3} 
: class 3 
β_{3} < β 
: class 4 
β_{3} < β 
: class 4 

57
 Values of β_{1}, β_{2} and β_{3} are given in Table 6.2.
Table 6.2  Slenderness parameters β_{1} / ε , β_{2} / ε and β_{3} / ε
Material classification according to Table 3.2 
Internal part 
Outstand part 
β_{1} / ε 
β_{2} / ε 
β_{3} / ε 
β_{1} / ε 
β_{2} / ε 
β_{3} / 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 

 In the Table 6.2, a crosssection part is considered with welds if it contains welding at an edge or at any point within its width. However, a crosssections 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 crosssection part with welds the classification is independent of the extent of the HAZ.
 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 may be used. In this expression, z_{1} is the distance from the elastic neutral axis of the effective section to the most severely stressed fibres, and z_{2} is the distance from the elastic neutral axis of the effective section to the part under consideration. z_{1} and z_{2} should be evaluated on the effective section by means of an iterative procedure (minimum two steps).
6.1.5 Local buckling resistance
 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 ρ_{c} to factor down the thickness. ρ_{c} 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.
 The factor ρ_{c} 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 C_{1} and C_{2} in Table 6.3. The relationships between ρ_{c} and β / ε are summarised in Figure 6.5.
ρ_{c} = 1,0 if β ≤ β_{3} (6.11)
Table 6.3  Constants C_{1} and C_{2} in expressions for ρ_{c}
Material classification according to Table 3.2 
Internal part 
Outstand part 
C_{1} 
C_{2} 
C_{1} 
C_{2} 
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 
 For flat outstand parts in unsymmetrical crosssections (Figure 6.1), ρ_{c} is given by the above expressions for flat outstand in symmetrical sections, but not more than 120/(β / ε)^{2}.
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 For reinforced crosssection parts: Consider all possible modes of buckling, and take the lower value of ρ_{c}. In the case of mode 1 buckling the factor ρ_{c} 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.
 For the determination of ρ_{c} 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 ρ_{c} and β / ε for outstands, internal parts and round tubes
6.1.6 HAZ softening adjacent to welds
6.1.6.1 General
 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.
 Exceptions to this rule, where there is no weakening adjacent to welds, occur in alloys in the Ocondition; or if the material is in the F condition and design strength is based on Ocondition properties.
 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
 The characteristic value of the 0,2 % proof strengths f_{o,haz} and the ultimate strength f_{a,haz} in the heat affected zone are listed in Table 3.2. Table 3.2 also gives the reduction factors
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 wellknown alloys by interpolation.
Figure 6.6  The extent of heataffected zones (HAZ)
 The values of f_{o,haz} and f_{u,haz} 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:
  6xxx series alloys 3 days
  7xxx series alloys 30 days.
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 f_{o,haz} and f_{u,haz}, in the HAZ (Table 3.2) as for the parent metal, or by reducing the assumed crosssectional area over which the stresses acts with the factors ρ_{o,haz} and ρ_{u,haz} (Table 3.2). Thus the characteristic resistance of a simple rectangular section affected by HAZ softening can be expressed as A f_{u,haz} = (ρ_{u,haz} A) f_{u} if the design is dominated by ultimate strength or as A f_{o,haz} = (ρ_{o,haz} A) f_{o} if the design is dominated by the 0,2% proof strength.
6.1.6.3 Extent of HAZ
 The HAZ is assumed to extend a distance b_{haz} in any direction from a weld, measured as follows (see Figure 6.6).
 transversely from the centre line of an inline butt weld;
 transversely from the point of intersection of the welded surfaces at fillet welds;
 transversely from the point of intersection of the welded surfaces at butt welds used in corner, tee or cruciform joints;
 in any radial direction from the end of a weld.
 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 b_{haz}, as shown in Figure 6.6.
60
 For a MIG weld laid on unheated material, and with interpass cooling to 60°C or less when multipass welds are laid, values of b_{haz} are as follows:
0 < t ≤ 6 mm: 
b_{haz} = 20 mm 
6 < t ≤ 12 mm: 
b_{haz} = 30 mm 
12 < t ≤ 25 mm: 
b_{haz} = 35 mm 
t > 25 mm: 
b_{haz} = 40 mm 
 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.
 The above figures apply to inline butt welds (two valid heat paths) or to fillet welds at Tjunctions (three valid heat paths) in 6xxx and 7xxx series alloys, and in 3xxx and 5xxx series alloys in the workhardened condition.
 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 inline butt or fillet welds in 6xxx, 7xxx and workhardened 3xxx and 5xxx series alloys, have a value of b_{haz} given by:
0 < t ≤ 6 mm: 
b_{haz} = 30 mm 
 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 3b_{haz}. In these circumstances assume that the entire width of the outstand is subject to the factor ρ_{o,haz}.
 Other factors that affect the value of b_{haz} are as follows:
 Influence of temperatures above 60°C
When multipass welds are being laid down, there could be a buildup of temperature between passes. This results in an increase in the extent of the HAZ. If the interpass temperature T_{1}(°C) is between 60°C and 120°C, it is conservative for 6xxx, 7xxx and workhardened 3xxx and 5xxx series alloys to multiply b_{haz} by a factor α_{2} as follows:
 6xxx alloys and workhardened 3xxx and 5xxx series alloys: 
α_{2} = 1 + (T_{1} − 60)/120; 
 7xxx alloys: 
α_{2} = 1 + 1,5(T_{1} − 60)/120. 
If a less conservative value of α_{2} 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.
 Variations in thickness
If the crosssection 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.
 Variations in numbers of heat paths
If the junctions between crosssection parts are fillet welded, but have different numbers of heat paths (n) from the three designated at (5) above, multiply the value of b_{haz} by 3/n.
6.2 Resistance of crosssections
6.2.1 General
 P The design value of an action effect in each crosssection 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.
 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.
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NOTE For the effect of shear lag. see Annex K
 The design values of resistance depend on the classification of the crosssection.
 Verification according to elastic resistance may be carried out for all crosssectional classes provided the effective crosssectional properties are used for the verification of class 4 crosssections.
 For the resistance the following yield criterion for a critical point of the crosssection may be used unless other interaction formulae apply, see 6.2.7 to 6.2.10.
where:
σ_{x,Ed} 
is the design value of the local longitudinal stress at the point of consideration 
σ_{z,Ed} 
is the design value of the local transverse stress at the point of consideration 
τ_{Ed} 
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 crosssection
 The properties of the gross crosssection (A_{g}) 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
 The net area of a crosssection (A_{net}) should be taken as the gross area less appropriate deductions for holes, other openings and heat affected zones.
 For calculating net section properties, the deduction for a single fastener hole should be the text deleted crosssectional area of the hole in the plane of its axis. For countersunk holes, appropriate allowance should be made for the countersunk portion.
 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 crosssection 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.
 Where the fastener holes are staggered, the total area to be deducted for fastener holes should be the greater of (see Figure 6.7):
 the deduction for nonstaggered holes given in (3)
 a deduction taken as ∑td − ∑tb_{s} where b_{s} is the lesser of
s^{2} /(4p) or 0,65s (6.16)
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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 centres 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 6.8  Angles with holes in both legs
 In an angle or other member with holes in more than one plane, the spacing p should be measured along the centre of thickness of the material (see Figure 6.8).
6.2.2.3 Shear lag effects
 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
 P The design value of the tensile force N_{Ed} shall satisfy:
NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected.
 The design tension resistance of the crosssection N_{t,Rd} should be taken as the lesser of N_{o,Rd} and N_{u,Rd} where:
a) general yielding along the member: 
N_{o,Rd} = A_{g}f_{o} / γ_{M1} 
(6.18) 
b) local failure at a section with holes: 
N_{u,Rd} = 0,9A_{net} f_{u} / γ_{M2} 
(6.19a) 
c) local failure at a section with HAZ: 
N_{u,Rd} = A_{eff} f_{u} / γ_{M2} 
(6.19b) 
where:
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A_{g} is either the gross section or a reduced crosssection to allow for HAZ softening due to longitudinal welds. In the latter case A_{g} is found by taking a reduced area equal to ρ_{o,haz} times the area of the HAZ, see 6.1.6.2
A_{net} 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 ρ_{u,haz}t.
A_{eff} is the effective area based on the reduced thickness of ρ_{u,haz}t.
 For angles connected through one leg see 8.5.2.3 . Similar consideration should also be given to other types of sections connected through outstands such as Tsections and channels.
(4) For staggered holes, see 6.2.2.2.
6.2.4 Compression
 P The design value of the axial compression force N_{Ed} shall satisfy:
NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected.
 The design resistance for uniform compression N_{c,Rd} should be taken as the lesser of N_{u,Rd} and N_{c,Rd} where :
a) in sections with unfilled holes 
N_{u,Rd} = A_{net} f_{u} / γ_{M2} 
(6.21) 
b) other sections 
N_{c,Rd} = A_{eff} f_{o} / γ_{M1} 
(6.22) 
in which:
A_{net} 
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. 
A_{eff} 
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
 P The design value of the bending moment M _{Ed} at each cross section shall satisfy
NOTE Eccentricity due to the shift of centroidal axis of asymmetric welded sections may be neglected.
 The design resistance for bending about one principal axis of a cross section M _{Rd} is determined as the lesser of M_{u,Rd} and M_{o,Rd} where:
M_{u,Rd} = W_{net} f_{u} / γ_{M2} in a net section and (6.24)
M_{o,Rd} = αW_{el} f_{o} / γ_{M1} at each crosssection (6.25)
where:
α is the shape factor, see Table 6.4
W_{el} is the elastic modulus of the gross section (see 6.2.5.2)
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W_{net} 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 ρ_{u,haz}t.
Table 6.4  Values of shape factor α
Crosssection class 
Without welds 
With longitudinal welds 
1 
W_{pl} / W_{el} *) 
W_{pl, haz} / W_{el} *) 
2 
W_{pl} / W_{el} 
W_{pl,haz} / W_{el} 
3 
α_{3},u 
α_{3},w 
4 
W_{eff} / W_{el} 
W_{eff,haz} / W_{el} 
*) 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 α_{3,u} , α_{3,w} are defined as:
W_{pl} 
plastic modulus of gross section 
W_{eff} 
effective elastic section modulus, obtained using a reduced thickness t_{eff} for the class 4 parts (see 6.2.5.2) 
W_{el,haz} 
effective elastic modulus of the gross section, obtained using a reduced thickness ρ_{o,haz}t for the HAZ material (see 6.2.5.2) 
W_{pl,haz} 
effective plastic modulus of the gross section, obtained using a reduced thickness ρ_{o,haz}t for the HAZ material (see 6.2.5.2) 
W_{eff,haz} 
effective elastic section modulus, obtained using a reduced thickness ρ_{c}t for the class 4 parts or a reduced thickness ρ_{o,haz}t for the HAZ material, whichever is the smaller (see 6.2.5.2) 
α_{3,u} = 1 or may alternatively be taken as:
α_{3}, w = W_{el,haz} / W_{el} or may alternatively be taken as:
where:
 β is the slenderness parameter for the most critical part in the section
 β_{2} and β_{3} are the limiting values for that same part according to Table 6.2
The critical part is determined by the lowest value of β_{2} / β
 Refer to 6.2.8 for combination of bending moment and shear force.
 In addition, the resistance of the member to lateraltorsional buckling should also be verified, see 6.3.2.
6.2.5.2 Design cross section
 The terminology used in this section is as follows:
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 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.
 effective section includes the allowance for HAZ softening and local buckling, but with no reduction for holes. See Figure 6.9.
 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:
 Class 4 part free of HAZ effects. A value t_{eff} = ρ_{c}t is taken for the compressed portion of the crosssection part, where ρ_{c} is found as in 6.1.5. Application of an effective section can result in an iteration procedure. See 6.7.
 Class 1, 2 or 3 parts subject to HAZ effects. A value ρ_{o,haz}t is taken in the softened portions of the crosssection part, where ρ_{o,haz} and the extent of the softening are as given in 6 1.6.2 and 6.1.6.3.
 Class 4 part with HAZ effects. The allowance is taken as the lesser of that corresponding to the reduced thickness t_{eff} and that corresponding to the reduced thickness in the softened part, ρ_{o,haz}t and as t_{eff} in the rest of the compressed portion of the crosssection part. See Figure 6.9.
 In the case of reinforced crosssection parts (see 6.1.4.3(2)), ρ_{c} should be applied to the area of the reinforcement as well as to the basic plate thickness.
 For a welded part in a Class 3 or 4 section a more favourable assumed thickness may be taken as follows:
6.2.6 Shear
 P The design value of the shear force V_{Ed} at each crosssection shall satisfy:
where:
V_{Rd} is the design shear resistance of the crosssection.
 For nonslender sections, h_{w} / t_{w} < 39ε , see 6.5.5(2)
66
where A_{v} is the shear area, taken as:
 For sections containing shear webs
where:
h_{w} 
is the depth of the web between flanges. 
b_{haz} 
is the total depth of HAZ material occurring between the clear depth of the web between flanges. For sections with no welds, ρ_{o,haz} = 1. If the HAZ extends the entire depth of the web panel b_{haz} = h_{w} − ∑ d 
t_{w} 
is the web thickness 
d 
is the diameter of holes along the shear plane 
n 
is the number of webs. 
 For a solid bar and a round tube
A_{v} = η_{v}A_{e} (6.31)
where:
η_{v} 
= 0,8 for a solid bar 
η_{v} 
= 0,6 for a round tube 
A_{e} 
is the full section area of an unwelded section, and the effective section area obtained by taking a reduced thickness ρ_{o,haz}t for the HAZ material of a welded section. 
 For slender webs and stiffened webs, see 6.7.4  6.7.6.
 Where a shear force is combined with a torsional moment, the shear resistance V_{Rd} should be reduced as specified in 6.2.7(9).
6.2.7 Torsion
6.2.7.1 Torsion without warping
 P For members subjected to torsion for which distortional deformations and warping torsion may be disregarded the design value of the torsional moment T_{Ed} at each crosssection shall satisfy:
where:
is the design St. Venants torsion moment resistance of the crosssection in which W_{T,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 crosssections are given in Annex J
 For the calculation of the resistance T_{Rd} of hollow sections with slender cross section parts the design shear strength of the individual parts of the crosssection should be taken into account according to 6.7.4 or 6.7.5.
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6.2.7.2 Torsion with warping
 For members subjected to torsion for which distortional deformations may be disregarded but not warping torsion the total torsional moment at any crosssection should be considered as the sum of two internal effects:
T_{Ed} = T_{t,Ed} + T_{w,Ed} (6.33)
where:
T_{t,Ed} 
is the internal St. Venants torsion moment; 
T_{w,Ed} 
is the internal warping torsion moment. 
 The values of T_{t,Ed} and T_{w,Ed} at any crosssection may be determined from T_{Ed} 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 T_{Rd} can be given in this case
 The following stresses due to torsion should be taken into account:
 – the shear stresses τ_{t,Ed} due to St. Venant torsion moment T_{t,Ed}
 – the direct stresses σ_{w,Ed} due to the bimoment B_{Ed} and shear stresses τ_{w,Ed} due to warping torsion moment T_{w,Ed}.
NOTE Cross section constants are given in Annex J.
 For elastic resistance the yield criterion in 6.2.1(5) may be applied.
 For determining the moment resistance of a crosssection due to bending and torsion only, torsion effects B_{Ed} should be derived from elastic analysis, see (3).
 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
 P For combined shear force and torsional moment the shear force resistance accounting for torsional effects shall be reduced from V_{Rd} to V_{T,Rd} and the design shear force shall satisfy:
in which V_{T,Rd} may be derived as follows:
6.2.8 Bending and shear
 Where a shear force is present allowance should be made for its effect on the moment resistance.
 If the shear force V_{Ed} is less than half the shear resistance V_{Rd} its effect on the moment resistance may be neglected except where shear buckling reduces the section resistance, see 6.7.6.
 Otherwise the reduced moment resistance should be taken as the design resistance of the crosssection, calculated using a reduced strength
f_{o,V} = f_{o} (1 − (2V_{Ed} / V_{Rd} − 1)^{2}) (6.38)
where V_{Rd} is obtained from 6.2.6.
 In the case of an equalflanged Isection classified as class 1 or 2 in bending, the resulting value of the reduced moment resistance M_{v,Rd} is:
where h is the total depth of the section and h_{w} is the web depth between inside flanges.
 In the case of an equalflanged Isection classified as class 3 in bending, the resulting value of M_{v,Rd} is given by expression (6.39) but with the denominator 4 in the second term replaced by 6:
 For sections classified as class 4 in bending or affected by HAZ softening, see 6.2.5.
 Where torsion is present V_{Rd} in expression (6.38) is replaced by V_{T,Rd} , see 6.2.7, but f_{o, V} = f_{o} for V_{Ed} ≤ 0,5V_{T,Rd}
 For the interaction of bending, shear force and transverse loads see 6.7.6.
6.2.9 Bending and axial force
6.2.9.1 Open crosssections
 For doubly symmetric crosssections (except solid sections, see 6.2.9.2) the following two criterions should be satisfied:
where:
η_{0} = 1,0 or may alternatively be taken as but 1 ≤ η_{0} ≤ 2 (6.42a)
69
γ_{0} = 1,0 or may alternatively be taken as but 1 ≤ γ_{0} ≤ 1,56 (6.42b)
ξ_{0} = 1,0 or may alternatively be taken as but 1 ≤ ξ_{0} ≤ 1,56 (6.42c)
N_{Ed} is the design values of the axial compression or tension force
M_{y,Ed} and M_{z,Ed} are the bending moments about the yy and zz axis
N_{Rd} = A_{eff} f_{o} / γ_{M1}, see 6.2.4
M_{y,Rd} = α_{y}W_{y,el} f_{o} / γ_{M1}
M_{z,Rd} = α_{z}W_{z,el} f_{o} / γ_{M1}
α_{y}, α_{z} 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.
ω_{0} = 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).
 Criterion (6.41) may also be used for monosymmetrical crosssections with (but 1 ≤ η_{0} ≤ 2,0) and γ_{0} = ξ_{0} = 1, where α_{y} = max (α_{y1}, α_{y2}), see Figure 6.10, if the axial force and the bending moment give stresses with the same sign in the larger flange and α_{y} = min (α_{y1}, α_{y2}) 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 monosymmetrical class 1 or 2 crosssection
6.2.9.2 Hollow sections and solid crosssections
 Hollow sections and solid crosssections should satisfy the following criterion:
where ψ = 1,3 for hollow sections and ψ = 2 for solid crosssections. Alternatively ψ may be taken as α_{y}α_{z} but 1 ≤ ψ ≤ 1,3 for hollow sections and 1 ≤ ψ ≤ 2 for solid crosssections.
6.2.9.3 Members containing localized welds
 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 ρ_{u,haz} f_{u} / γ_{M2} of the reduced strength material.
ω_{o} = (ρ_{u,haz} f_{u} / γ_{M2}) / (f_{o} / γ_{M1}) (6.44)
NOTE This includes HAZ effects due to the welding of temporary attachments.
 If the softening extends longitudinally a distance greater than the least width of the member the limiting stress should be taken as the strength ρ_{o,haz} f_{o} for overall yielding of the reduced strength material, thus
ω_{o} = ρ_{o,haz} (6.45)
70
6.2.10 Bending, shear and axial force
 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.
 Provided that the design value of the shear force V_{Ed} does not exceed 50% of the shear resistance V_{Rd} 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.
 Where V_{Ed} exceeds 50% of V_{Rd} the design resistance of the crosssection to combinations of moment and axial force should be reduced using a reduced yield strength
(1 – ρ) f_{o} (6.46)
for the shear area where:
ρ = (2V_{Ed}/ V_{Rd} – 1)^{2} (6.47)
and V_{Rd} 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
 This clause concerns the design of webs subjected to localised forces caused by concentrated loads or reactions applied to a beam. For unstiffened and longitudinally stiffened web this subject is covered in 6.7.5.
 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 outofplane 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
 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
 P A compression member shall be verified against both flexural and torsional or torsionalflexural buckling as follows:
where:
N_{Ed} 
is the design value of the compression force 
N_{b,Rd} 
design buckling resistance of the compression member 
 The design buckling resistance of a compression member N_{b,Rd} should be taken as:
71
N_{b,Rd} = Kχ A_{eff} f_{o} / γ_{M1} (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 torsionalflexural buckling. In case of transversally welded member K = ω_{x} according to 6.3.3.3. k = 1 if there are no welds. 
A_{eff} 
is the effective area allowing for local buckling for class 4 crosssection. For torsional and torsionalflexural buckling see Table 6.7. 
A_{eff} = A for class 1, 2 or 3 crosssection 
6.3.1.2 Buckling curves
 For axial compression in members the value of χ for the appropriate value of should be determined from the relevant buckling curve according to:
where:
α 
is an imperfection factor 

is the limit of the horizontal plateau 
N_{cr} 
is the elastic critical force for the relevant buckling mode based on the gross crosssectional properties 
NOTE In a member with a local weld the slenderness parameter according to 6.3.3.3 (3)should be used for the section with the weld
 The imperfection factor α and limit of horizontal plateau corresponding to appropriate buckling curve should be obtained from Table 6.6 for flexural buckling and Table 6.7 for torsional or torsionalflexural buckling.
 Values of the reduction factor χ for the appropriate relative slenderness may be obtained from Figure 6.11 for flexural buckling and Figure 6.12 for torsional or torsionalflexural buckling.
 For slenderness or for the buckling effects may be ignored and only crosssectional 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 
with A_{1} = A − A_{haz} (1 − ρ_{o,haz}) in which A_{haz} = area of HAZ 
k = 1 if ≤ 0,2
if > 0,2 
Table 6.6  Values of α and for flexural buckling
Material buckling class according to Table 3.2 
α 

Class A 
0,20 
0,10 
Class b 
0,32 
0,00 
72
Figure 6.11  Reduction factor χ for flexural buckling
Table 6.7  Values of α, and A_{eff} for torsional and torsionalflexural buckling
Crosssection 
α 

A_{eff} 
General^{1)}
Composed entirely of radiating outstands ^{2)} 
0,35
0,20 
0,4
0,6 
A_{eff} ^{1)}
A ^{2)} 
 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 A_{eff} determined allowing for either of both local buckling and HAZ material.
 For sections such as angles, tees and cruciforms, composed entirely of radiating outstands, local and torsional buckling are closely related. When determining A_{eff} allowance should be made, where appropriate, for the presence of HAZ material but no reduction should be made for local buckling i,e. ρ_{c} = 1.

Figure 6.12  Reduction factor χ for torsional and torsionalflexural buckling
6.3.1.3 Slenderness for flexural buckling
 The relative slenderness is given by:
where:
L_{cr} 
is the buckling length in the buckling plane considered 73 
i 
is the radius of gyration about the relevant axis, determined using the properties of gross crosssection. 
 The buckling length L_{cr}. 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 
6.3.1.4 Slenderness for torsional and torsionalflexural buckling
 For members with open crosssections account should be taken of the possibility that the resistance of the member to either torsional or torsionalflexural buckling could be less than its resistance to flexural buckling
NOTE The possibility of torsional and torsionalflexural buckling may be ignored for the following:
 hollow sections
 doubly symmetrical Isections
 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
 The relative slenderness for torsional and torsionalflexural buckling should be taken as:
where:
A_{eff} 
is the crosssection area according to Table 6.7 
N_{cr} 
is the elastic critical load for torsional buckling, allowing for interaction with flexural buckling if necessary (torsionalflexural buckling) 
NOTE Values of N_{cr} and are given in Annex I.
6.3.1.5 Eccentrically connected single  bay struts
 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:
 single angle connected through one leg only;
 back to back angles connected to one side of a gusset plate;
 single channel connected by its web only;
 single tee connected by its flange only.
74
 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 N_{b,Rd} should be taken as 40% of the value for centroidal loading.
 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
 The following resistances should normally be checked:
 bending (see 6.2.5), including, where appropriate, allowance for coincident shear (see 6.2.8);
 shear (see 6.2.6 and 6.2.8);
 web bearing (see 6.7.5);
 lateral torsional buckling (see 6.3.2.1).
 Due account should be taken of the class of crosssection (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).
 For members required to resist bending combined with axial load reference is made to 6.3.3.
 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:
 bending takes place about the minor principal axis and at the same time the load application is not over the shear centre;
 the member is fully restrained against lateral movement throughout its length;
 the relative slenderness (see 6.3.2.3) between points of effective lateral restraint is less than 0,4.
 P A laterally unrestrained member subject to major axis bending shall be verified against lateraltorsional buckling as follows:
where:
M_{Ed} 
is the design value of the bending moment 
M_{b,Rd} 
is the design buckling resistance moment. 
 The design buckling resistance moment of laterally unrestrained member should be taken as:
M_{b,Rd} = χ_{LT} αW_{el,y} f_{o} / γ_{M1} (6.55)
where:
W_{el,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 α ≤ W_{pl,y}/W_{el,y}. 
χ_{LT} 
is the reduction factor for lateral torsional buckling (see 6.3.2.2). 
6.3.2.2 Reduction factor for lateral torsional buckling
 The reduction factor for lateral torsional buckling χ_{LT} for the appropriate relative slenderness should be determined from:
75
where

α_{LT} 
is an imperfection factor 

is the relative slenderness 

is the limit of the horizontal plateau 
M_{cr} 
is the elastic critical moment for lateraltorsional buckling. 
 The value of α_{LT} and should be taken as:
α_{LT} = 0,10 and = 0,6 for class 1 and 2 crosssections
α_{LT} = 0,20 and = 0,4 for the class 3 and 4 crosssections.
 Values of the reduction factor χ_{LT} for the appropriate relative slenderness may be obtained from Figure 6.13
 For slenderness or for M _{Ed} the buckling effects may be ignored and only crosssectional check apply.
Figure 6.13  Reduction factor for lateraltorsional buckling
6.3.2.3 Slenderness
 The relative slenderness parameter should be determined from
where:
α 
is taken from Table 6.4 subject to the limitation α ≤ W_{pl,y} / W_{el,y}. 
M_{cr} 
is the elastic critical moment for lateraltorsional buckling. 
 M_{cr} 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 M_{cr} for certain sections and boundary conditions are given in Annex I.1 and approximate values of for certain Isections and channels are given in Annex 1.2.
76
6.3.2.4 Effective Lateral Restraints
 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
 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:
 – members that are not susceptible to torsional deformations, e.g. circular hollow sections or sections restrained from torsion (flexural buckling only);
 – members that are susceptible to torsional deformations, e.g. members with open crosssections not restrained from torsion (lateraltorsional buckling or flexural buckling).
 Two checks are in general needed for members that are susceptible to torsional deformations:
 – flexural buckling;
 – lateraltorsional buckling.
 For calculation of the resistance N_{Rd}, M_{y,Rd} and M_{z,Rd} due account of the presence of HAZsoftening from longitudinal welds should be taken. (See 6.2.4 and 6.2.5). The presence of localized HAZsoftening 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.
 All quantities in the interaction criterion should be taken as positive.
NOTE 1 Classification of crosssections 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 crosssection 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 crosssection. 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 crosssection.
NOTE 3 Section check is included in the check of flexural and lateraltorsional buckling if the methods in 6.3.3.1 and 6.3.3.5 are used.
6.3.3.1 Flexural buckling
 For a member with open doubly symmetric crosssection (solid sections, see (2)), one of the following criterions should be satisfied:
  For major axis (yaxis) bending:
  For minor axis (zaxis) bending:
where:
η_{c} = 0,8 or may alternatively be taken as η_{c} = η_{0} χ_{z} but η_{c} ≥ 0,8 (6.61a)
77
ξ_{yc} = 0,8 or may alternatively be taken as ξ_{yc} = ξ_{0} χ_{y} but ξ_{yc} ≥ 0,8 (6.61b)
ξ_{zc} = 0,8 or may alternatively be taken as ξ_{zc} = ξ_{0} χ_{z} but ξ_{zc} ≥ 0,8 (6.61 c)
η_{0} and ξ_{0} are according to 6.2.9.1
ω_{x} = ω_{0} = 1 for beamcolumns without localized welds and with equal end moments. Otherwise, see 6.3.3.3, 6.3.3.4 and 6.3.3.5 , respectively.
 For solid crosssections criterion (6.60) may be used with the exponents taken as 0,8 or
η_{c} = 2χ but η_{c} ≥ 0,8 (6.61d)
ξ_{c} = l,56 χ but ξ_{c} ≥ 0,8 (6.61e)
 Hollow crosssections and tubes should satisfy the following criterion:
where ψ_{c} = 0,8 or may alternatively be taken as l,3 χ_{y} or l,3 χ_{z} depending on direction of buckling, but ψ_{c} ≥ 0,8. χ_{min} = min(χ_{y},χ_{z})
 For other open monosymmetrical cross sections, bending about either axis, expression (6.59) may be used with ξ_{yc}, M_{y,Ed}, M_{y,Rd} and χ_{y} replaced by ξ_{zc}, M _{z,Ed}, M_{z,Rd} and χ_{z}
 The notations in the criterions (6.59) to (6.62) are:
N_{Ed} is the design value of the axial compressive force
M_{y,Ed}, M_{z,Ed} are the design values of bending moment about the y and zaxis. The moments are calculated according to first order theory
N_{Rd} = A f_{o} / γ_{M1} or A_{eff} f_{o}/ γ_{M1} for class 4 crosssections. For members with longitudinal welds but without localized welds N_{Rd} = k A f_{o} / γ_{M1} or k A_{eff} f_{o} / γ_{M1}, see 6.3.1.
χ_{y} and χ_{z} are the reduction factor for buckling in the zx plane and the yx plane, respectively
M _{y,Rd} = α_{y} W_{y} f_{o} / γ_{M1} bending moment capacity about the yaxis
M _{z,Rd} = α_{z} W_{z} f_{o} / γ_{M1} bending moment capacity about the zaxis
α_{y}, α_{z} are the shape factors, but α_{y} and a_{z} should not be taken larger than 1,25. See 6.2.5 and 6.2.9.1(1)
6.3.3.2 Lateraltorsional buckling
 Members with open crosssection symmetrical about major axis, centrally symmetric or doubly symmetric crosssection, the following criterion should satisfy:
where:
N_{Ed} 
design value of axial compression force 
M_{y,Ed} 
is bending moment about the yaxis. In the case of beamcolumns with hinged ends and in the case of members in nonsway frames, M_{y,Ed} is moment of the first order. For members in frames free to sway, M_{y,Ed} is bending moment according to second order theory. 
M_{z,Ed} 
bending moment about the zaxis. M_{z,Ed} is bending moment according to first order theory 
N_{Rd} = Af_{o} / γ_{M1} or A_{eff} f_{o} / γ_{M1} for class crosssections. For members with longitudinal welds but without localized welds N_{Rd} = KAf_{o} / γ_{M1} or KA_{eff} f_{o} / γ_{M1}, see 6.3.1. 78 
χ_{z} 
is the reduction factor for buckling when one or both flanges deflects laterally (buckling in the xy plane or lateraltorsional buckling) based on (6.68a) in section with localized weld 
M_{y,Rd} = α_{y} W_{y,el} f_{o} / γ_{M1} = bending moment capacity for yaxis bending 
M_{z,Rd} = α_{z} W_{z,el} f_{o} / γ_{M1} = bending moment capacity for zaxis bending 
α_{y}, α_{z} 
are the shape factors but α_{y} and α_{z} should not be taken larger than l ,25. See 6.2.5 and 6.2.9.1(1) 
χ_{LT} 
is the reduction factor for lateraltorsional buckling 
η_{c} = 0,8 or alternatively η_{0} χ_{z} but η_{c} ≥ 0,8 
γ_{c} = γ_{0} 
ξ_{zc} = 0,8 or alternatively ξ_{0} χ_{z} but ξ_{zc} ≥ 0,8 
where η_{0}, γ_{0} and ξ_{0} are defined according to the expression in 6.2.9.1. 
ω_{x}, ω_{0} and ω_{xLT} = HAZsoftening factors, see 6.3.3.3 or factors for design section, see 6.3.3.5. 
 The criterion for flexural buckling, see 6.3.3.1, should also be satisfied.
6.3.3.3 Members containing localized welds
 The value of ω_{x}, ω_{0} and ω_{xLT} 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 ω_{x}, ω_{0} and ω_{xLT} in the expressions in 6.3.3.1 and 6.3.3.2 are:
Where ρ_{u,haz} is the reduction factor for the heat affected material according to 6.1.6.2.
 However, if HAZ softening occurs close to the ends of the bay, or close to points of contra flexure only, ω_{x} and ω_{xLT} may be increased in considering flexural and lateraltorsional 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.
where:
χ = χ_{y} or χ_{z} depending on buckling direction 
χ_{LT} 
is the reduction factor for lateraltorsional buckling of the beamcolumn in bending only 
x_{s} 
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. 
l_{c} 
is the buckling length. 
 Calculation of χ (χ_{y} or χ_{z}) and χ_{LT} the section with the localized weld should be based on the ultimate strength of the heat affected material for the relative slenderness parameters
79
 If the length of the softening region is larger than the least width (e.g. flange width) of the section, then the factor ρ_{u,haz} for local failure in the expressions for ω_{x} , ω_{xLT} , should be replaced by the factor ρ_{o,haz} for overall yielding.
 If the localized softening region covers a part of the crosssection (e.g. one flange) then the whole crosssection is supposed to be softened.
6.3.3.4 Members containing localized reduction of crosssection
 Members containing localized reduction of crosssection, e.g. bolt holes or flange cutouts, should be checked according to 6.3.3.3 by replacing ρ_{u,haz} in ω_{x} and ω_{xLT} with A_{net} / A_{g} where A_{net} is net section area, with reduction of holes and A_{g} gross section area.
6.3.3.5 Unequal end moments and/or transverse loads
 For members subjected to combined axial force and unequal end moments and/or transverse loads, different sections along the beamcolumn should be checked. The actual bending moment in the studied section is used in the interaction expressions. ω_{x} and ω_{xLT} should be:
where x_{s} 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.
 For end moments M_{Ed,1} > M_{Ed,2} only, the distance x_{s} can be calculated from
Figure 6.14  Buckling length l_{c} and definition of x_{s} (= x_{A} or x_{B})
6.4 Uniform builtup members
6.4.1 General
 Uniform builtup compression members with hinged ends that are laterally supported should be designed with the following model, see Figure 6.15.
80
 The member may be considered as a column with a bow imperfection e_{0} = L / 500
 The elastic deformations of lacings or battenings, see Figure 6.15, may be considered by continuous (smeared) shear stiffness S_{v} of the column.
NOTE For other end conditions appropriate modifications may be performed.
 The model of a uniform builtup compression member applies if:
 the lacings or battenings consist of equal modules with parallel chords;
 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.
 The design procedure is applicable to builtup members with lacings in two directions, see Figure 6.16.
 The chords may be solid members or may themselves be laced or battened in the perpendicular plane.
Figure 6.15  Uniform builtup columns with lacings and battenings
Figure 6.16  Lacings on four sides and buckling length L_{ch} of chords
 Checks should be performed for chords using the design chord forces N_{ch,Ed} from compression forces N_{Ed} and moments M_{Ed} at mid span of the builtup member.81
 For a member with two identical chords the design force N_{ch,Ed} should be determined from:
where:
N_{cr} = π^{2} EI_{eff} / L^{2} is the critical force of the effective builtup member 
N_{Ed} 
is the design value of the compression force to the builtup member 
M_{Ed} 
is the design value of the maximum moment in the middle of the builtup member considering second order effects 

is the design value of the maximum moment in the middle of the builtup member without second order effects 
h_{0} 
is the distance between the centroids of chords 
A_{ch} 
is the crosssectional area of one chord 
I_{eff} 
is the effective second moment of area of the builtup member, see 6.4.2 and 6.4.3 
S_{v} 
is the shear stiffness of the lacings or battened panel, see 6.4.2 and 6.4.3 
 The checks for the lacings of laced builtup members or for the frame moments and shear forces of the battened panels of battened builtup members should be performed for the end panel taking account of the shear force in the builtup member:
6.4.2 Laced compression members
6.4.2.1 Resistance of components of laced compression members
 The chords and diagonal lacings subject to compression should be designed for buckling.
NOTE Secondary moments may be neglected.
 P For chords the buckling verification shall be performed as follows:
where:
N_{ch,Ed} is the design compression force in the chord at midlength of the builtup member according to 6.4.1(6)
N_{b,Rd} is the design value of the buckling resistance of the chord taking the buckling length L_{ch} from Figure 6.16.
 The shear stiffness S_{y} of the lacings should be taken from Figure 6.17.
 The effective second order moment of area of laced builtup members may be taken from (6.77) with μ = 0. Then :
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Figure 6.17  Shear stiffness of lacings of builtup members
6.4.2.2 Constructional details
 Single lacing system in opposite faces of the builtup 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.
 If the single lacing systems on opposite faces of a builtup 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.
 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 builtup member with two parallel laced planes
6.4.3 Battened compression members
6.4.3.1 Resistance of components of battened compression members
 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 midspan as indicated in Figure 6.19.
NOTE For simplicity the maximum chord forces N_{ch,Ed} may he combined with the maximum shear force V_{Ed}.
83
Figure 6.19  Moments and forces in an end panel of a battened builtup members
 The shear stiffness S_{v} should be taken as follows:
 The effective second moment of area of battened builtup members may be taken as:
where:
I_{ch} 
is in plane second moment of area of one chord 
I_{b} 
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 
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6.4.3.2 Constructional details
 Battens should be provided at each end of a member.
 Where parallel planes of battens are provided, the battens in each plane should be arranged opposite each other.
 Battens should also be provided at intermediate points where loads are applied or lateral restraint is supplied.
6.4.4 Closely spaced builtup members
 Builtup 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 (S_{v} = ∞), if the conditions in Table 6.10 are met.
Figure 6.20  Closely spaced builtup members
Table 6.10  Maximum spacing for interconnection in closely spaced builtup or star battened angle members
Type of builtup member 
Maximum spacing between interconnection *) 
Members according to Figure 6.20 in contact or connected through packing by bolts or Welds 
15i_{min} 
Members according to Figure 6.21 in contact or connected by pair of battens and by bolts of welds 
70i_{min} 
*) centretocentre distance of interconnections
i_{min} is the minimum radius of gyration of one chord or one angle

 The shear forces to be transmitted by the battens should be determined from 6.4.3.1(1).
 In the case of unequalleg angles, see Figure 6.21, buckling about the yy axis may be verified with:
i_{y} ≅ 0,87i_{0} (6.78)
where i_{0} is the radius of gyration of the builtup member about the 00 axis.
Figure 6.21  Starbattened angle members
6.5 Unstiffened plates under inplane loading
6.5.1 General
 In certain types of structure unstiffened 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
6.5.2 Resistance under uniform compression
 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.
 The susceptibility of the unstiffened plate to buckling is defined by the parameter β, where β = b/t. The classification of the crosssection 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
β ≤ β_{2} 
class 1 or 2 
β_{2} ≤ β ≤ β_{3} 
class 3 
β_{3} < β 
class 4 
where values of β_{2} and β_{3} are given in Table 6.2.
 P The design value of the compression force N_{Ed} shall satisfy
where N_{Rd} is the lesser of
N_{o,Rd} = A_{eff} f _{o} / γ_{M1} 
(overall yielding and local buckling) and 
(6.80) 
N _{u,Rd} = A_{net} f _{u} / γ _{M2} 
(local failure) 
(6.81) 
where:
A_{eff} 
is the effective area of the crosssection taking account of local buckling for class 4 crosssections and HAZ softening of longitudinal welds 
A_{net} 
is the area of the least favourable crosssection taking account of unfilled holes and HAZ softening of transverse or longitudinal welds if necessary 
 A_{eff} for class 4 crosssection is obtained by taking a reduced thickness to allow for buckling as well as for HAZ softening, but with the presence of holes ignored. A_{eff} is generally based on the least favourable crosssection, taking a thickness equal to the lesser of ρ_{c}t and ρ_{o,haz}t in HAZ regions, and ρ_{c}t elsewhere. In this check HAZ softening due to welds at the loaded edges may be ignored.
86
The factor ρ_{c} is found from the more favourable of the following treatments:
 Calculate ρ_{c} 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.
 Take ρ_{c} = χ, where χ is the column buckling reduction factor from 6.3.1. In calculating χ take a slenderness parameter equal to 3,5 a/t, which corresponds to simple support at the loaded edges. For restrained loaded edges a lower value of can be used at the discretion of the designer.
6.5.3 Resistance under inplane moment
 If a pure inplane 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 crosssection is carried out in the same way as described in section 6.5.2.
 P The design value of the bending moment M_{Ed} shall satisfy
where the design bending moment resistance M_{Rd} is the lesser of M_{o,Rd} and M_{u,Rd} according to (3) and (4).
 The design bending moment resistance M_{o,Rd} for overall yielding and local buckling is as follows:
Class 1 and 2 crosssections
M_{o,Rd} = W _{p1} f _{o} / γ _{M1} (6.83)
Class 3 crosssections
Class 4 crosssections
M_{o,Rd} = W _{eff} f _{o} / γ _{M1} (6.85)
where
W _{pl} and W_{el} are the plastic and elastic moduli for the gross crosssection or a reduced crosssection to allow for HAZ softening from longitudinal welds, but with the presence of holes ignored 
W _{eff} is the elastic modulus for the effective crosssection 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 
β_{2} and β_{3} are the class 2 and class 3 limiting values of β for that part 
text deleted 
 The design bending moment resistance M_{u,Rd} for local failure at sections with holes or transverse welds is:
M_{u,Rd} = W_{net} f _{u} / γ_{M2} (6.86)
where
W_{net} is the section modulus allowing for holes and taking a reduced thickness ρ_{u,haz}t in any region affected by HAZ softening. See 6.2.5.1 (2).
87
6.5.4 Resistance under transverse or longitudinal stress gradient
 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.
 If the applied compression or inplane 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 crosssections at any crosssection should not be less than the action arising at that section under factored loading. For class 4 crosssections the yielding check should be performed at every crosssection, 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
 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.
 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 nonslender as follows:
β ≤ 39ε 
nonslender plate 
β > 39ε 
slender plate 
where:
 The design value of the shear force V_{Ed} at each crosssection should satisfy
V_{Ed} ≤ V_{Rd} (6.87)
where V_{Rd} is the design shear resistance of the crosssection based on the least favourable crosssection as follows.
 nonslender plate (β ≤ 39ε):
where A_{net} is the net effective area allowing for holes, and taking a reduced thickness ρ_{o,haz}t 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 crosssection. In allowing for holes, the presence of small holes may be ignored if their total crosssectional area is less than 20% of the total crosssectional area bt.
 slender plate (β > 39ε):
Values of V_{Rd} for both yielding and buckling should be checked. For the yielding check use a) above for nonslender plates. For the buckling check:
where:
but not more than and v_{1} ≤ 1,0
k_{τ} = 5,34 + 4,00(b/a)^{2} if a /b ≥ 1
88
k_{τ} = 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
 A plate subjected to combined axial force and inplane 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 (N_{Ed}) and the moment (M_{Ed}) act separately.
 If the plate is class 4, each individual resistance, N_{c,Rd} and M_{o,Rd} should be based on the specific type of action considered.
 If the combined action is axial force and inplane moment, the following condition should be satisfied:
 If the combined action includes the effect of a coincident shear force, V_{Ed}, then V_{Ed} may be ignored if it does not exceed 0,5V_{Rd} (see 6.5.8). If V_{Ed} > V_{Rd} the following condition should be satisfied:
6.6 Stiffened plates under inplane loading
6.6.1 General
 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.
 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 “subcritical”, i.e. it can deform with the plating in an overall buckling mode.
 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 unstiffened plates (see 6.7.6). The treatments are valid also if the crosssection contains parts that are classified as slender.
89
Figure 6.23  Stiffened plates and types of stiffeners
 If the structure consists of flat plating with 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 inplane direct stress .
6.6.2 Stiffened plates under uniform compression
 P General
The crosssection 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 N_{Ed} shall satisfy
where N_{Rd} is the lesser of N_{u,Rd} and N_{c,Rd} according to (2) and (3).
 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 N_{u,Rd} should be based on the net section area A_{net} for the least favourable crosssection, taking account of text deleted HAZ softening if necessary, and also any unfilled holes.
N _{u,Rd} = A_{net} f _{u} / γ_{M2} (6.92)
90
 Column check
The plating is regarded as an assemblage of identical column subunits, each containing one centrally located stiffener or corrugation and with a width equal to the pitch 2a . The design axial resistance N_{c,Rd} is then taken as:
N_{c,Rd} = A_{eff} χ f _{o} / γ_{M 1} (6.93)
where:
χ 
is the reduction factor for flexural buckling 
A_{eff} 
is the effective area of the crosssection 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 A_{eff}. Also unfilled holes may be ignored. 
The reduction factor χ should be obtained from the appropriate column curve relevant to column buckling of the subunit as a simple strut out of the plane of the plating.
 The relative slenderness parameter in calculating χ is
where
N_{cr} = the elastic orthotropic buckling load based on the gross crosssection
 For a plate with open stiffeners:
where c is the elastic support from the plate according to expressions (6.97), (6.98) or (6.99) and I_{y} is the second moment of area of all stiffeners and plating within the width b with respect to yaxes in Figure 6.23f.
 For a crosssection part with one central or eccentric stiffener (Figure 6.23(f)):
where t is the thickness of the plate, b is the overall width of the plate and b_{1} and b_{2} are the width of plate parts on both sides of the stiffener.
 For a crosssection part with two symmetrical stiffeners located a distance b_{1} from the longitudinal supports (Figure 6.23(g)):
 For a multistiffened plate with open stiffeners (Figure 6.23(c), (b) (h) and (i)) with small torsional stiffness
 For a multistiffened plate with closed or partly closed stiffeners (Figure 6.23 (e) and (j))
N_{cr} is the elastic orthotropic buckling load. See 6.6.6.
91
 The halfwavelength in elastic buckling, used if the applied action varies in the direction of the stiffener or corrugations (see 6.6.4(3)) is
6.6.3 Stiffened plates under inplane moment
 General
Two checks should be performed, a yielding check (see 6.6.3(3)) and a column check (see 6.6.3(4)).
 Section classification and local buckling
The crosssection 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, it should generally be assumed 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.
 Yielding check
The entire crosssection of the plating should be treated as a beam under inplane bending (see 6.2.5). The design moment resistance M_{Rd} should be based on the least favourable crosssection, taking account of local buckling and HAZ softening if necessary, and also any holes.
 Column check
The plating is regarded as an assemblage of column subunits in the same general way as for axial compression (see 6.6.2(3)), the design moment resistance M_{o,Rd} being taken as follows
where:
χ 
is the reduction factor for flexural buckling of subunit 
I_{eff} 
is the second moment of area of the effective crosssection of the plating for inplane bending 
y_{st} 
is the distance from centre of plating to centre of outermost stiffener 
The reduction factor χ should be determined in the same way as for uniform compression (see 6.6.2(3)).
6.6.4 Longitudinal stress gradient on multistiffened plates
 General
Cases where the applied action N_{Ed} or M_{Ed} on a multistiffened plate varies in the direction of the stiffeners or corrugations are described in 6.6.4(2) and 6.6.4(3).
 Yielding check
The design resistance at any crosssection should be not less than the design action effect arising at that section.
92
 Column check
For the column check it is sufficient to compare the design resistance with the design action effect arising at a distance 0,4l_{w} from the more heavily loaded end of a panel, where l_{w} is the half wavelength in elastic buckling according to 6.6.2(10).
6.6.5 Multistiffened plating in shear
 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:
 effectively connected to the transverse framing at either end;
 continuous at any transverse stiffener position.
 Yielding check: The design shear force resistance V_{Rd} is taken as the same as that for a flat unstiffened plate of the same overall aspect (L × b) text deleted in accordance with 6.5.5(2).
 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):
B_{y} = Et^{3} /10,9 for a flat plate with stiffeners, otherwise see 6.6.6(1)
B_{x} = EI_{y} / b where I_{y} is the second moment of area of stiffeners and plating within the width b about a centroidal axis parallel to the plane of the plating
h_{w} 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 V_{o,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
 For an orthotropic plate under uniform compression the procedure in 6.6.2 may be used. The elastic orthotropic buckling load N_{cr} for a simply supported orthotropic plate is given by
Expressions for B_{x}, B_{y} and H for different crosssections are given in Table 6.1 1 where the expressions (6.104) to (6.110) are given below. (Indexes x and y indicates rigidity in section x = constant and y = constant, respectively).
Table 6.11, Case No. 2:
where
93
Table 6.11, Case No. 5:
where:
94
Figure 6.24  Crosssection notations of closed stiffener
 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:
k_{τ} = 3,25 − 0,567ϕ + 1,92ϕ^{2} + (1,95 + 0,1ϕ + 2,75ϕ^{2}) η_{h} (6.112)
B_{x} , B_{y} 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(t_{1} + t_{2}) 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 = b∑t.
6.7 Plate girders
6.7.1 General
 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.
 Webs buckle in shear at relatively low applied loads, but considerable amount of postbuckled strength can be mobilized due to tension field action. Plate girders are sometimes constructed with transverse web reinforcement in the form of corrugations or closelyspaced transverse stiffeners.
 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.
 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 inplane bending
 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 crosssectional area of the web. The web depth between flanges is h_{w} and the distance between the weld toes of the flanges is b_{w}.
 P For the yielding check, the design value of the moment, M_{Ed} at each crosssection shall satisfy
M_{Ed} ≤ M_{o,Rd} (6.115)
where M_{o,Rd}, for any class crosssection, is the design moment resistance of the crosssection that would apply if the section were designated class 3. Thus,
M_{o,Rd} = W_{net} f_{o} / γ_{M1} (6.116)
where W_{net} is the elastic modulus allowing for holes and taking a reduced thickness ρ_{o,haz}t in regions adjacent to the flanges which might be affected by HAZ softening (see 6.1.6.2).
 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
 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, M_{o,Rd} for that bay, where:
M_{o,Rd} = W _{eff} f _{o} / γ_{M1} (6.117)
W_{eff} 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 ρ_{o,haz}t and ρ_{c}t in HAZ regions, and ρ_{c}t elsewhere, see 6.2.5.
 The thickness is reduced in any class 4 part that is wholly or partly in compression (b_{c} in Figure 6.25). The stress ratio Ψ used in 6.1.4.3 and corresponding width b_{c} 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 G_{1}.
 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 crosssection defined at the end of the previous step.
Figure 6.25  Plate girder in bending
6.7.3 Resistance of girders with longitudinal web stiffeners
 Plate buckling due to longitudinal compressive stresses may be taken into account by the use of an effective crosssection applicable to class 4 crosssections.
 The effective crosssection properties should be based on the effective areas of the compression parts and their locations within the effective crosssection.
 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.
 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).
 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.
 The relative slenderness parameter in calculating χ is
where
97
A_{st,eff} is the effective area of the column from the first step, see Figure 6.26c. N_{cr} is the elastic buckling load given by the following expression:
where:
I_{st} 
is second moment of area of the gross crosssection of the stiffener and adjacent part of web (see (7)) about an axis through its centroid and parallel to the plane of the web 
b_{1} and b_{2} are distances from longitudinal edges to the stiffener (b_{1} + b_{2} = b_{w}). 
a_{c} 
is the half wave length for elastic buckling of stiffener 
 For calculation of I_{st} the column consists of the actual stiffener together with an effective width 15t_{w} of the web plate on both sides of the stiffener. See Figure 6.26(d1) and (d2).
 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
6.7.4 Resistance to shear
 This section gives rules for plate buckling effects from shear force where the following criteria are met:
 panels are rectangular and flanges are parallel within an angle not greater than 10°;
 stiffeners if any are provided in the longitudinal and /or transverse direction;
 open holes or cut outs are small and limited to diameters d that satisfies d / h_{w} ≤ 0,05 where h_{w} is the width of the plate;
 members are uniform.
98
 P A plate girder in shear shall be verified against buckling as follows:
where:
V_{Ed} 
is the design value of the shear force 
V_{Rd} 
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
 This section gives rules for plate buckling effects from shear force where stiffeners are provided at supports only.
 Plates with should be checked for resistance to shear buckling.
NOTE For η see Table 6.13, for h_{w} and t_{w} see Figure 6.27.
 For webs with transverse stiffeners at supports only, the design resistance V_{Rd} for shear should be taken as
in which ρ_{v} is a factor for shear buckling obtained from Table 6.13 or Figure 6.28.
Table 6.13  Factor ρ_{v} for shear buckling
Ranges of λ_{w} 
Rigid end post 
Nonrigid end post 
λ_{w} ≤ 0,83/η 0,83/η < λ_{w} < 0,937 0,937 ≤ λ_{w} 
η 0,83/λ_{w} 2/3(1,66 + λ_{w}) 
η 0,83/λ_{w} 0,83/λ_{w} 
η = 0,7 + 0,35 f_{uw} / f_{ow} but not more than 1,2 where than 1,2 where f_{ow} is the strength for overall yielding and f_{uw} is the ultimate strength of the web material 
Figure 6.27  Endstiffeners
Figure 6.27 shows various end supports for girders:
 no end post, see 6.7.5, type c);
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 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;
 nonrigid end posts, see 6.7.8.2;
 bolted connection, see 6.7.8.2, to be classified as nonrigid in resistance calculation.
Figure 6.28  Factor ρ_{v} for shear buckling
 The slenderness parameter λ_{w} in Table 6.13 and Figure 6.28 is
6.7.4.2 Plate girders with intermediate web stiffeners
 This section gives rules for plate buckling effects from shear force where web stiffeners are provided in the longitudinal and/or transverse direction
 Plates with 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 h_{w} and t_{w} see Figure 6.29 and for k_{τ} see (6)
 For beams with transverse and longitudinal stiffeners the design resistance for shear buckling V_{Rd} is the sum of the contribution V_{w,Rd} of the web and V_{f,Rd} of the flanges.
V_{Rd} = V_{w,Rd} + V_{f,Rd} (6.124)
in which V_{w,Rd} includes partial tension field action in the web according to (4) and V_{f,Rd} is an increase of the tension field caused by local bending resistance of the flanges according to (10).
 The contribution from the web to the design resistance for shear should be taken as:
where ρ_{v} is the factor for shear buckling obtained from Table 6.13 or Figure 6.28.
 The slenderness parameter λ_{w} is
100
in which k_{τ} 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.
 The second moment of area of the longitudinal stiffeners should be reduced to 1/3 of its value when calculating k_{τ}. Formulae for k_{τ} taking this into account are given in (7) and (8).
 For plates with rigid transverse stiffeners and without longitudinal stiffeners or more than two longitudinal stiffeners, the shear buckling coefficient k_{τ} in (5) is:
k_{τ} = 5,34 + 4,00(b_{w}/a)^{2} + k_{τst} if a/b_{w} ≥ 1 (6.127)
k_{τ} = 4,00 + 5,34(b_{w}/a)^{2} + k_{τst} if a/b_{w} < 1 (6.128)
where:
a is the distance between transverse stiffeners. See Figure 6.29.
I_{st} is the second moment of area of the longitudinal stiffener with regard to the zaxis. See Figure 6.29(b). For webs with two or more equal stiffeners, not necessarily equally spaced, I_{st} is the second moment of area of all individual stiffeners.
 The expression (6.129) also applies to plates with one or two longitudinal stiffeners, if the aspect ratio a/b_{w} ≥ 3. For plates with one or two longitudinal stiffeners and an aspect ratio a/b_{w} < 3 the shear buckling coefficient should be taken from:
 For webs with longitudinal stiffeners the relative slenderness parameter λ_{w} should be taken not less than
where k_{τ1} and b_{w1} refers to the subpanel with the largest slenderness parameter λ_{w} of all subpanels within the webpanel under consideration. To calculate k_{τ1} the expression in 6.7.4.2(7) may be used with k_{τst} = 0.
 If the flange resistance is not completely utilized in withstanding the bending moment (M_{Ed} < M_{f,Rd}, curve (1) in Figure 6.32) the shear resistance contribution V_{f,Rd} from the flanges may be included in the shear buckling resistance as follows:
in which b_{f} and t_{f} are taken for the flange leading to the lowest resistance,
b_{f} being taken as not larger than 15t_{f} on each side of the web
M_{f,Rd} is the design moment resistance of the cross section considering of the effective flanges only
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Figure 6.29  Web with transverse and longitudinal stiffeners
 If an axial force N_{Ed} is present, the value of M_{f,Rd} should be reduced by a factor
where A_{f1} and A_{f2} are the areas of the top and bottom flanges.
 If M_{Ed} ≥ M_{f,Rd} then V_{f,Rd} = 0. For further interaction, see 6.7.6.
6.7.5 Resistance to transverse loads
6.7.5.1 Basis
 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.
 A load can be applied as follows:
 Load applied through one flange and resisted by shear forces in the web. See Figure 6.30(a).
 Load applied to one flange and transferred through the web to the other flange, see Figure 6.30(b)
 Load applied through one flange close to an unstiffened end, see Figure 6.30(c).
 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.
 P The resistance of the web to transverse forces applied through a flange shall be verified as follows:
where:
F_{Ed} is the design transverse force;
F_{Rd} is the design resistance to transverse forces, see 6.7.5.2;
 The interaction of the transverse force, bending moment and axial force should be verified using 6.7.6.2.
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6.7.5.2 Design resistance
 For unstiffened or stiffened webs the design resistance F_{Rd} to local buckling under transverse loads should be taken as
F_{Rd} = L_{eff} t_{w} f_{ow} / γ_{M1} (6.134)
where:
f_{ow} is the characteristic value of strength of the web material.
L_{eff} is the effective length for resistance to transverse loads, which should be determined from
L_{eff} = χ_{F}l_{y} (6.135)
where:
l_{y} is the effective loaded length, see 6.7.5.5, appropriate to the length of stiff bearings s_{s}, see 6.7.5.3
χ_{F} 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
 The length of stiff bearing, s_{s}, 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, s_{s} should not be taken as larger than b_{w}.
 If several concentrated loads are closely spaced (s_{s} 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 centretocentre distance between the outer loads.
Figure 6.31  Length of stiff bearing
6.7.5.4 Reduction factor χ_{F} for resistance
 The reduction factor χ_{F} for resistance should be obtained from:
but not more than 1,0 (6.136)
where:
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l_{y} is effective loaded length obtained from 6.7.5.5.
 For webs without longitudinal stiffeners the factor k_{F} should be obtained from Figure 6.30
 For webs with longitudinal stiffeners k_{F} should be taken as
Where:
b_{1} is the depth of the loaded subpanel taken as the clear distance between the loaded flange and the stiffener
where I_{s1} is the second moment of area (about zz 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 ≤ b_{1} / h_{w} ≤ 0,3 and loading according to type (a) in Figure 6.30.
6.7.5.5 Effective loaded length
 The effective loaded length l_{y} should be calculated using the two dimensionless parameters m_{1} and m_{2} obtained from
where b_{f} is the flange width, see Figure 6.31. For box girders, b_{f} in expression (6.141) is limited to 15t_{f} on each side of the web.
 For cases (a) and (b) in Figure 6.30, l_{y} should be obtained using:
 For case (c) in Figure 6.30, l_{y} should be obtained as the smaller of the values obtained from the equations (6.143), (6.144) and (6.145). However, s_{s} 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.
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6.7.6 Interaction
6.7.6.1 Interaction between shear force, bending moment and axial force
 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).
 If M_{Ed} > M_{f,Rd} the following two expressions (corresponding to curve (2) and (3) in Figure 6.32) should be satisfied:
M_{Ed} ≤ M_{o,Rd}
where:
M_{o,Rd} 
is the design bending moment resistance according to 6.7.2 (4). 
M_{f,Rd} 
is the design bending moment resistance of the flanges only (= min(A_{fl} · h_{f}f_{o}/γ_{Ml}, A_{f2} · h_{f}f_{o}/γ_{M1}). 
M_{pl,Rd} 
is the plastic design bending moment resistance 
 If an axial force N_{Ed} is also applied, then M_{pl,Rd} should be replaced by the reduced plastic moment resistance M_{N,Rd} given by
where A_{f1}, A_{f2} are the areas of the flanges.
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
 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
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where:
M_{o, Rd} 
is the design bending moment resistance according to 6.7.2 (4). 
N_{c,Rd} 
is the design axial force resistance, see 6.3.1.1. 
 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
 To prevent the possibility of the compression flange buckling in the plane of the web, the ratio b_{w}/t_{w} of the web should satisfy the following expression
where:
A_{w} 
is the cross section area of the web 
A_{fc} 
is the cross section area of the compression flange 
f_{of} 
is the 0,2% proof strength of the flange material 
The value of the factor k should be taken as follows:
 plastic rotation utilized 
k = 0,3 
 plastic moment resistance utilized 
k = 0,4 
 elastic moment of resistance utilized 
k = 0,55 
 If the girder is curved in elevation, with the compression flange on the concave face, the ratio b_{w} / t_{w} for the web should satisfy the following criterion:
in which r is the radius of curvature of the compression flange.
 If the girder is provided with transverse web stiffeners, the limiting value of b_{w} / t_{w} may be increased by the factor 1 + (b_{w} / a)^{2}.
6.7.8 Web stiffeners
6.7.8.1 Rigid end post
 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.
 A rigid end post may comprise of one stiffener at the girder end and one doublesided transverse stiffener that together form the flanges of a short beam of length h_{f} , 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.
 The doublesided transverse stiffener may act as a bearing stiffener resisting the reaction at the girder support (see 6.2.11).
 The stiffener at the girder end should have a crosssectional area of at least where e is the centre to centre distance between the stiffeners and e > 0,1h_{f}, see Figure 6.27(b).
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 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 endpost section about the centreline of the web (I_{ep}) should satisfy:
where:
t_{f} is the maximum value of flange thickness along the girder
R_{Ed} is the reaction at the end of the girder under design loading
W_{Ed} is the total design loading on the adjacent span.
6.7.8.2 Nonrigid end post and bolted connection
 A nonrigid end post may be a single doublesided 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).
 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 nonrigid end post provided that the distance between bolts is p < 40t_{w}.
6.7.8.3 Intermediate transverse stiffeners
 Intermediate stiffeners that act as rigid supports of interior panels of the web should be checked for strength and stiffness.
 Other intermediate transverse stiffeners may be considered flexible, their stiffness being considered in the calculation of k_{τ} in 6.7.4.2.
 Intermediate transverse stiffeners acting as rigid supports for web panels should have a minimum second moment of area I_{st}:
The strength of intermediate rigid stiffeners should be checked for an axial force equal to V_{Ed} − ρ_{v}b_{w}t_{w}f_{v} / γ_{M1} where ρ_{v} 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 0,5h_{w} from the edge of the panel with the largest shear force.
6.7.8.4 Longitudinal stiffeners
 Longitudinal stiffeners may be either rigid or flexible. In both cases their stiffness should be taken into account when determining the relative slenderness λ_{w} in 6.7.4.2(5).
 If the value of λ_{w} is governed by the subpanel then the stiffener may be considered as rigid.
 The strength should be checked for direct stresses if the stiffeners are taken into account for resisting direct stress.
6.7.8.5 Welds
 The web to flange welds may be designed for the nominal shear flow V_{Ed} / h_{w} if V_{Ed} does not exceed ρ_{v}h_{w}t_{w}f_{o}/(). For larger values the weld between flanges and webs should be designed for the shear flow ηt_{w}f_{o}/() unless the state of stress is investigated in detail.
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6.8 Members with corrugated webs
 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
 The bending moment resistance may be derived from:
where f_{o,r} = ρ_{z}f_{o} includes the reduction due to transverse moments in the flanges
M_{z} is the transverse bending moment in the flange
χ_{LT} is the reduction factor for lateral torsional buckling according to 6.3.2.
NOTE The transverse moment M_{z} may result from the shear flow introduction in the flanges as indicated in Figure 6.33(d).
Figure 6.33  Corrugated web
6.8.2 Shear force resistance
 The shear force resistance V _{Rd} may be taken as
where ρ_{c} is the smallest of the reduction factors for local buckling ρ_{c,l}, reduction factor for global buckling ρ_{c,g} and HAZ softening factor ρ_{o,haz}:
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 The reduction factor ρ_{c,l} for local buckling may be calculated from:
where the relative slenderness λ_{c,l} for trapezoidal corrugated webs may be taken as
with a_{max} as the greatest width of the corrugated web plate panels, a_{0}, a_{1} or a_{2}, see Figure 6.33.
 The reduction factor ρ_{c,g} for global buckling should be taken as
where the relative slenderness λ_{c,g} may be taken as
where the value τ_{cr,g} may be taken from:
where:
2a is length of corrugation, see Figure 6.33
a_{0}, a_{1} and a_{2} are widths of folded web panels, see Figure 6.33
I_{x} 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.
 The reduction factor ρ_{o,haz} in HAZ is given in 6.1.6.
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7 Serviceability Limit States
7.1 General
 P An aluminium structure shall be designed and constructed such that all relevant serviceability criteria are satisfied.
 The basic requirements for serviceability limit states are given in 3.4 of EN 1990.
 Any serviceability limit state and the associated loading and analysis model should be specified for a project.
 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
 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
 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
 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
 The calculation of elastic deflection should generally be based on the properties of the gross crosssection 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.
 For class 4 sections the following effective second moment of area I_{ser}, constant along the beam may be used
where:
I_{gr} 
is the second moment of area of the gross crosssection 
I_{eff} 
is the second moment of area of the effective crosssection at the ultimate limit state, with allowance for local buckling, see 6.2.5.2 
σ_{gr} 
is the maximum compressive bending stress at the serviceability limit state, based on the gross crosssection (positive in the formula). 
 Deflections should be calculated making also due allowance for the rotational stiffness of any semirigid joints, and the possible recurrence of local plastic deformation at the serviceability limit state.
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8 Design of joints
8.1 Basis of design
8.1.1 Introduction
 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.
 The partial safety factors γ_{M} for joints should be applied to the characteristic resistance for the various types of joints.
NOTE Numerical values for γ_{M} may be defined in the National Annex. Recommended values are given in Table 8.1
Table 8.1  Recommended partial factors γ_{M} for joints
Resistance of members and crosssection 
γ_{M1} and γ_{M2} see 6.1.3 
Resistance of bold connections 
γ_{M2} = 1,25 
Resistance of rivet connections 
Resistance of plates in bearing 
Resistance of pin connections 
γ_{Mp} = 1,25 
Resistance of welded connections 
γ_{Mw} = 1,25 
Slip resistance, see 8.5.9.3  for serviceability limit states  for ultimate limit states 
γ_{Ms,ser} = 1,1 γ_{Ms,ult} = 1,25 
Resistance of adhesive bonded connections 
γ_{Ma} ≥ 3,0 
Resistance of pins at serviceability limit state 
γ_{Mp,ser} = 1,0 
 Joints subject to fatigue should also satisfy the rules given in EN 199913.
8.1.2 Applied forces and moments
 The forces and moments applied to joints at the ultimate limit state should be determined by global analysis conforming to 5.
 These applied forces and moments should include:
  second order effects;
  the effects of imperfections (see 5.3);
  the effects of connection flexibility
NOTE For the effect of connection flexibility, see Annex L.
8.1.3 Resistance of joints
 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
 Linearelastic analysis should generally be used in the design of the joint. Alternatively nonlinear analysis of the joint may be employed provided that it takes account of the load deformation characteristics of all the components of the joint.
 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
 Joints may be designed by distributing the internal forces and moments in whatever rational way is best, provided that:
 the assumed internal forces and moments are in equilibrium with the applied forces and moments;
 each part in the joint is capable of resisting the forces or stresses assumed in the analysis;
 the deformations implied by this distribution are within the deformation capacity of the fasteners or welds and of the connected parts, and
 the deformations assumed in any design model based on yield lines are based on rigid body rotations (and inplane deformations) which are physically possible.
 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.
 Residual stresses and stresses due to tightening of fasteners and due to ordinary accuracy of fitup need not usually be allowed for.
8.1.5 Fabrication and execution
 Ease of fabrication and execution should be considered in the design of all joints and splices.
 Attention should be paid to:
  the clearances necessary for safe execution;
  the clearances needed for tightening fasteners;
  the need for access for welding;
  the requirements of welding procedures, and
  the effects of angular and length tolerances on fitup.
 Attention should also be paid to the requirements for:
  subsequent inspection;
  surface treatment, and
  maintenance.
Requirements to execution of aluminium structures are given in EN 10903
8.2 Intersections for bolted, riveted and welded joints
 Members meeting at a joint should usually be arranged with their centroidal axes intersecting at a point.
 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
 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.
 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 slipresistant connection (category B or C as appropriate, see 8.5.3), fitted bolts or welding should be used.
 For wind and/or stability bracings, bolts in bearing type connections (category A in 8.5.3) may be used.
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
 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.
 In case of minimum end distances, minimum edge distances and minimum spacings no minus tolerances are allowed.
 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.
 Minimum and maximum spacing, end and edge distances are given in Table 8.2.
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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 
Maximum^{1) 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 e_{1} 
1,2d_{0} ^{6)} 
2,0d_{0} 
4t + 40 mm 
The larger of 12t or 150 mm 
Edge distance e_{2} 
1,2d_{0} ^{6)} 
1,5d_{0} 
4t + 40 mm 
The larger of 12t or 150 mm 
End distance e_{3} for slotted holes ^{4)} 
Slotted holes are not recommended. Slotted holes of category A see 8.5.1(5) – (10) 
Edge distance e_{4} for slotted holes ^{4)} 
Slotted holes are not recommended. Slotted holes of category A see 8.5.1(5) – (10) 
Compression members (see Figure 8.2): Spacing p_{1} 
2,2d_{0} 
2,5d_{0} 
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 p_{1}, p_{1,0}, p_{1,i} 
2,2d_{0} 
2,5d_{0} 
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)} 
2,4d_{0} 
3,0d_{0} 
The smaller of 14t or 200 mm 
The smaller of 14t or 200 mm 
 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.
 The local buckling resistance of the plate in compression between the fasteners should be calculated according to 6.3 Text deleted by using 0,6 p_{1} as buckling length. Local buckling between the fasteners need not to be checked if p_{1}/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. Text deleted
 t is the thickness of the thinner outer connected part.
 Slotted holes are not recommended, slotted holes of category A see 8.5.1 (5)
 For staggered rows of fasteners a minimum line spacing p_{2} = 1,2d_{0} may be used, if the minimum distance between any two fasteners in a staggered row is p_{1} = 2,4d_{0}, see Figure 8.2
 The minimum values of e_{1} and e_{2} should be specified with no minus deviation but only plus deviations.

114
Figure 8.1  Symbols for spacing of fasteners
Figure 8.2  Staggered spacing – compression
Figure 8.3  Spacing in tension member
Figure 8.4  Slotted holes
 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.
 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.
 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.
 The distance e_{3} 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 e_{4} 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.
 The distance p_{3} between the edges of two adjacent holes in the direction of the load and the distance p_{4} between the edges of two adjacent holes perpendicular to the direction of the load should be greater than 2(d + 1 mm).
 Bolts in slotted holes according to category A should be verified according to Table 8.5, see 8.5.5.
 For oversized holes the rules in (8), (9) and (10) apply.
 Oversized holes in bolted connections of Category A may be used if the following conditions are met:
 – a possible greater setting of the structure or of the component can be accepted;
 – no reversal loads are acting;
 – oversized bolts holes are used on one side of a joint, where they should be applied in the component to be connected or in the connecting devices (cover plates, gussets);
 – the rules for geometrical tolerances for oversized holes given in EN 10903 are applied;
 – for bolts with diameter d ≤ 10 mm the design resistance of the bolt group based on bearing is less than the design resistance of the bolt group based on shear. See also 8.5.5 (7).
115
8.5.2 Deductions for fastener holes
8.5.2.1 General
 For detailed rules for the design of members with holes see 6.3.4.
8.5.2.2 Design for block tearing resistance
 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.
 For a symmetric bolt group subject to concentric loading the design block tearing resistance, V_{eff,1,Rd} is given by:
V_{eff,1,Rd} = f_{u} A_{nt} / γ_{M2} + (1 / √3)f_{o} A_{nv} / γ_{M1} (8.1)
where:
A_{nt} is net area subjected to tension;
A_{nv} is net area subjected to shear.
 For a bolt group subject to eccentric loading the design block shear tearing resistance V_{eff,2,Rd} is given by:
V_{eff,2,Rd} = 0,5 f_{u} A_{nt} / γ_{M2} + (1 / √3)f_{o} A_{nv} / γ_{M1} (8.2)
Figure 8.5  Block tearing
8.5.2.3 Angles and angles with bulbs
 In the case of unsymmetrical or unsymmetrically connected members under tension and compression 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.
 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:
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Figure 8.6  Connection of angles
where:
β_{2} and β_{3} are reduction factors dependent on the pitch p_{1} as given in Table 8.3 for intermediate values p_{1} the values of β may be determined by linear interpolation.
A_{net} is the net area of the angle. For an unequalleg angle connected by its smaller leg, A_{net} should be taken as equal to the net section area of an equivalent equalleg angle of leg size equal to that of the smaller leg.
Text deleted
Table 8.3  Reduction factors β_{2} and β_{3}
Pitch p1 
≤ 2,5 d_{0} 
≥ 5,0 d_{0} 
β_{2} for 2 bolts 
0,4 
0,7 
β_{3} for 3 bolts or more 
0,5 
0,7 
8.5.3 Categories of bolted connections
8.5.3.1 Shear connections
 The design of a bolted connection loaded in shear should conform to one of the following categories, see Table 8.4.
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Table 8.4  Categories of bolted connections
Shear connections 
Category 
Criteria 
Remarks 
A; bearing type 
F_{v,Ed} ≤ F_{v,Rd} F_{v,Ed} ≤ F_{b,Rd} ΣF_{v,Ed} ≤ N_{net,Rd} 
No preloading required. All grades from 4.6 to 10.9 N_{net,Rd} = 0,9A_{net}f_{u} / γ_{M2} 
B; slip resistant at serviceability 
F_{v,Ed,ser} ≤ F_{s,Rd,ser} F_{v,Ed} ≤ F_{v,Rd} F_{v,Ed} ≤ F_{b,Rd} ΣF_{v,Ed} ≤ N_{net,Rd} ΣF_{v,Ed,ser} ≤ N_{net,Rd,ser} 
Preloaded high strength bolts. No slip at the serviceability limit state. N_{net,Rd} = 0,9A_{net}f_{u} / γM_{2} N_{net,Rd,ser} = A_{net}f_{o} / γM_{1} 
C; slip resistant at ultimate 
F_{v,Ed} ≤ F_{s,Rd} F_{v,Ed} ≤ F_{b,Rd} ΣF_{v,Ed} ≤ N_{net,Rd} ΣF_{v,Ed} ≤ N_{net,Rd,ser } 
Preloaded high strength bolts. No slip at the ultimate limit state. N_{net,Rd} = 0,9A_{net}f_{u}/M_{2} N_{net,Rd,ser} = A_{net}f_{o}/M_{1} 
Tension connections 
Category 
Criterion 
Remarks 
D; nonpreloaded 
F_{t,Ed} ≤ F_{t,Rd} F_{t,Ed} ≤ B_{p,Rd} 
Bolt class from 4.6 to 10.9. 
E; preloaded 
F_{t,Ed} ≤ F_{t,Rd} F_{t,Ed} ≤ B_{p,Rd} 
Preloaded 8.8 or 10.9 bolts. 
Key: 
F_{v,Ed} 
design shear force per bolt for the ultimate limit state 
F_{v,Ed,ser} 
design shear force per bolt for the serviceability limit state 
F_{v,Rd} 
design shear resistance per bolt 
F_{b,Rd} 
design bearing resistance per bolt 
F_{s,Rd,ser} 
design slip resistance per bolt at the serviceability limit state 
F_{s,Rd} 
design slip resistance per bolt at the ultimate limit state 
F_{t,Ed} 
design tensile force per bolt for the ultimate limit state 
F_{t,Rd} 
design tension resistance per bolt 
A_{net} 
net area, see 6.2.2.2 (tension members only) 
B_{p,Rd} 
design resistance for punching resistance, see Table 8.5. 

 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.
Text deleted
 Category B: Slipresistant at serviceability limit state
In this category preloaded high strength bolts with controlled tightening in conformity with EN 10903 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.
Text deleted
 Category C: Slip resistant at ultimate limit state
118
In this category preloaded high strength bolts with controlled tightening in conformity with EN 10903 should be used. Slip should not occur at the ultimate limit state. Text deleted
 In addition, at the ultimate limit state the design plastic resistance of the net section at bolt holes N_{net,Rd} should be taken as:
N_{net,Rd} = 0,9A_{net}f_{u} / γ_{M2} (8.6)
8.5.3.2 Tension connections
 The design of a bolted connection loaded in tension should conform with one of the following categories, see Table 8.4.
 Category D: Connections with nonpreloaded 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.
 Category E: Connections with preloaded high strength bolts
In this category preloaded high strength bolts with controlled tightening in conformity with EN 10903 should be used. Such preloading improves fatigue resistance. However, the extent of the improvement depends on detailing and tolerances.
 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 EB or EC).
8.5.4 Distribution of forces between fasteners
 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:
  category C slipresistant connections;
  other shear connections where the design shear resistance F_{v,Rd} of a fastener is less than the design bearing resistance F_{b,Rd}.
 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).
 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)
8.5.5 Design resistances of bolts
 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 EN 10903 . For aluminium bolts the additional requirements of C.4.1 should be followed.
 P At the ultimate limit state the design shear force F_{v,Ed} on a bolt shall not exceed the lesser of:
  the design shear resistance F_{v,Rd};
  the design bearing resistance F_{b,Rd} of that bolt with the minimum bearing capacity of the connection, both as given in Table 8.5.
 P At the ultimate limit state the design tensile force F_{t,Ed}, inclusive of any force due to prying action, shall not exceed the design tension resistance B_{t,Rd} of the boltplate assembly.
 Bolts subject to both shear force and tensile force should in addition be verified as given in Table 8.5.
 P The design tension resistance of the boltplate assembly B_{t,Rd} shall be taken as the smaller of the design tension resistance F_{t,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, B_{p,Rd} obtained from Table 8.5.
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Table 8.5  Design resistance for bolts and rivets
Failure mode 
Bolts 
Rivets 
Shear resistance per shear plane: 
  where the shear plane passes through the threaded portion of the bolt (A is the tensile stress area of the bolt A_{S}):
  for steel bolts with classes 4.6, 5.6 and 8.8: α_{v} = 0,6
  for steel bolts with classes 4.8, 5.8, 6.8 and 10.9, stainless steel bolts and aluminium bolts: α_{v} = 0,5

f_{ur} = characteristic ultimate strength of the rivet material
A_{0} = 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): α_{v} = 0,6 f_{ub} = characteristic ultimate strength of the bolt material 
Bearing resistance 1) 2) 3) 4) 5) 6) 
where α_{b} is the smallest of α_{d} or 1,0; but ≤ 0,66 for slotted holes in the direction of the load transfer: (8.12)
  for end bolts: for inner bolts (8.13 and 8.14)
perpendicular to the direction of the load transfer:
  for edge bolts: k_{1} is the smallest of
  for inner bolts: k_{1} is the smallest of
f_{u} is the characteristic ultimate strength of the material of the connected parts
f_{ub} is the characteristic ultimate strengths of the bolt material
d is the bolt diameter
d_{0} is the hole diameter
e1, e2, p1, p2 see Figure 8.1 ^{5)} 
Tension resistance 
where
 k_{2} = 0,9 for steel bolts,
 k_{2} = 0,50 for aluminium bolts and
 k_{2} = 0,63 for countersunk steel bolts,

For solid rivets with head dimensions according to Annex C, Figure C.1 or greater on both sides. 
Punching shear resistance 
B_{p,Rd} = 0,6 π d_{m} t_{p} f_{u} / γ_{M2} (8.19) where: d_{m} 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; t_{p} is the thickness of the plate under the bolt head or the nut; f_{u} characteristic ultimate strength of the member material. 
Combined shear and tension 
121 
 The bearing resistance F_{b,Rd} for bolts
  in oversized holes according to EN 10903 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.
 For countersunk bolts:
  the bearing resistance F_{b,Rd} should be based on a plate thickness t equal to the thickness of the connected plate minus half the depth of the countersinking,
 In addition to bearing resistance, the net section resistance needs to be checked
 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.
 Aluminium bolts should not be used in connections with slotted holes.
 For slotted holes replace d_{0} by (d + 1 mm), e_{1} by (e_{3} + d/2), e_{2} by (e_{4} + d/2), p_{1} by (p_{3} + d) and p_{2} by (p_{4} + d) where p_{3}, p_{4}, e_{3} and e_{4} are found in Figure 8.4.

 The design resistances for tension and for shear through the threaded portion given in Table 8.5 are restricted to bolts with rolled threads. For bolts with cut threads, the relevant values from Table 8.5 should be reduced by multiplying them by a factor of 0,85.
 (7) The values for design shear resistance F_{v,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 10903. For oversized holes and slotted holes F_{v, RD} is reduced by a factor of 0,7.
8.5.6 Design resistance of rivets
 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
 P At the ultimate limit state the design shear force F_{v,Ed} on a rivet shall not exceed the lesser of:
  the design shear resistance F_{v, Rd}
  the design bearing resistance F_{b,Rd}
 both as given in Table 8.5.
 Tension in aluminium rivets should be limited to exceptional cases (see Table 8.5).
 P At the ultimate limit state the design tension force F_{t,Ed} on a rivet shall not exceed the design ultimate tension resistance F_{t, Rd} as given in Table 8.5.
 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.
Text deleted
 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
 Single rivets should not be used in single lap joints.
8.5.7 Countersunk bolts and rivets
 Connections with countersunk bolts or rivets made from steel should be designed to transfer forces in shear and bearing.
 P At the ultimate limit state the design shear force F_{v,Ed} on a countersunk bolt or rivet made from steel shall not exceed the lesser of:
  0,7 times the design shear resistance F_{v, Rd} as given in Table 8.5 and
  the design bearing resistance F_{b,Rd}, which should be calculated as specified in 8.5.5 or 8.5.6 respectively, with half the depth of the countersink deducted from the thickness t of the relevant part jointed.
 Tension in a countersunk bolt made from steel should be designed to transfer tension force F_{t,Ed}. It should be limited to exceptional cases (see Table 8.5).
 P At the ultimate limit state the design tension force F_{t,Ed} on a countersunk bolt made from steel shall not exceed the design ultimate tension resistance F_{t,Rd} as given in Table 8.5.
 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.
 The angle and depth of countersinking should conform with EN 10903 .
Text deleted
 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.
 Single countersunk bolts or rivets should not be used in single lap joints.
8.5.8 Hollow rivets and rivets with mandrel
 For the design strength of hollow rivets and rivets with mandrel, see EN 199914.
8.5.9 High strength bolts in slipresistant connections
8.5.9.1 General
 Slip resistant connections should only be used if the proof strength of the material of the connected parts is higher than 200 N/mm^{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
 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, F_{v,Ed} on a high strength bolt shall not exceed the lesser of:
  the design shear resistance F_{v,Rd}
  the design bearing resistance F_{b,Rd}
  the tensile text deleted resistance of the member in the net section and in the gross cross section.
8.5.9.3 Slip resistance / Shear resistance
123
 The design slip resistance of a preloaded highstrength bolt should be taken as:
where:
F_{p,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. 
 For bolts in standard nominal clearance holes, the partial safety factor for slip resistance γ_{Ms} should be taken as γ_{Ms,ult} for the ultimate limit state and γ_{Ms,ser} for the serviceability limit state where γ_{Ms,ult} and γ_{Ms,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.
 Slotted or oversized holes are not covered by these clauses
8.5.9.4 Preloading
 For high strength bolts grades 8.8 or 10.9 with controlled tightening, the preloading force F_{p,C} to be used in the design calculations, should be taken as:
F_{p,C} = 0,7 f_{ub} AS (8.22)
8.5.9.5 Slip factor
 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 R_{a} 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.
 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 EN 10903 .
8.5.9.6 Combined tension and shear
 If a slipresistant connection is subjected to an applied tensile force F_{t} in addition to the shear force F_{v} tending to produce slip, the slip resistance per bolt should be taken as follows:
Category B: Slipresistant at serviceability limit state
Category C: Slipresistant at ultimate limit state
124
8.5.10 Prying forces
 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)
 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
 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
 Where the distance L_{j} 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 F_{v,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 β_{Lf}, given by:
125
but 0,75 ≤ β_{Lf} ≤ 1,0.
Figure 8.10  Long joints
 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
 A single rivet or one row of rivets should not be used in single lap joints.
 The bearing resistance F_{b,Rd} determined in accordance with 8.5.5 should be limited to:
F_{b,Rd} ≤ f_{u} d t / γM2 (8.26)
Figure 8.11  Single lap joint with one row of bolts
 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
 Where bolts or rivets transmitting load in shear and bearing pass through packings of total thickness t_{p} greater than onethird of the nominal diameter d, the design shear resistance F_{v,Rd} calculated as specified in 8.5.5 or 8.5.6 as appropriate, should be reduced by multiplying it by a reduction factor β_{p} given by:
 (2 For double shear connections with packings on both sides of the splice, t_{p} should be taken as the thickness of the thicker packing.
 Any additional fasteners required due to the application of the reduction factor β_{p} may optionally be placed in an extension of the packing.
8.5.14 Pin connections
8.5.14.1 General
 Pin connections where rotation is required should be designed according to 8.5.14.2  8.5.14.3.
 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.
126
8.5.14.2 Pin holes and pin plates
 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
 P At the ultimate limit state the design force F_{Ed} in the plate shall not exceed the design resistance given in Table 8.7.
 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.
8.5.14.3 Design of pins
 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.
 The bending moments in a pin should be calculated as indicated in Figure 8.13.
 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.
 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:
σ_{h,Ed} ≤ f_{h,Rd} (8.28a)
where:
f_{h,Rd} = 2,5 f_{o/}γ_{M6,ser}
where:
d is the diameter of the pin
127
d_{0} 
is the diameter of the pin hole 
F_{Ed,ser} 
is the design value of the force to be transferred in bearing under the characteristic load combination for serviceability limit state 
E_{p}, E_{pl} 
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 
F_{v,Rd} = 0,6 A f_{up}/γ_{Mp} ≥F_{v,Ed}
F_{v,Rd, ser} = 0,6 A f_{op}/γ_{M6,ser} ≥F_{v,Ed,ser} 
Bearing of the plate and the pin
If the pin is intended to be replaceable this requirement should also be satisfied 
F_{b,Rd} = 1,5 t d f_{o,min}/γ_{M1} ≥F_{b,Ed}
F_{b,Rd} = 0,6 t d f_{0}/γ_{M6,ser} ≥F_{b,Ed,ser} 
Bending of the pin
If the pin is intended to be replaceable this requirement should also be satisfied 
M_{Rd} = 1,6 W_{el}f_{op}/γ_{M1} ≥M_{Rd}
M_{Rd} = 0,8 W_{el} f_{op}/γ_{M6,ser} ≥M_{Ed,ser} 
Combined shear and bending of the pin 
(M_{Ed}/M_{Rd})^{2} + (F_{v,Rd})^{2} ≤ l,0 
d 
is the diameter of the pin 
f_{o,min} 
is the lower of the design strengths of the pin and the connected part 
f_{up} 
is the ultimate tensile strength of the pin 
f_{op} 
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
128
8.6 Welded connections
8.6.1 General
 In the design of welded joints consideration should be given both to the strength of the welds and to the strength of the HAZ.
 The design guidance given here applies to:
 – the welding process MIG and TIG for material thicknesses according to Table 3.2a and Table 3.2b; text deleted
 – quality level according to EN 10903
 – combinations of parent and filler metal as given in 3.3.4;
 – structures loaded with predominantly static loads.
 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.
 If for secondary or non loadbearing members a lower quality level has been specified lower design strength values should be used.
8.6.2 Heataffected zone (HAZ)
 For the following classes of alloys a heataffected zone should be taken into account (see also 6.1.6 ):
  heattreatable alloys in temper T4 and above (6xxx and 7xxx series);
  nonheattreatable alloys in any workhardened condition (3xxx, 5xxx and 8xxx series).
 The severity and extent (dimensions) of HAZ softening given in 6.1.6 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 heatinput should be applied.
 The characteristic strengths f_{u,haz} for the material in the HAZ are given in Table 3.2. The characteristic shear strength in the HAZ is defined as: f_{v,haz} = f_{v,haz} /
8.6.3 Design of welded connections
 For the design of welded connections the following should be verified:
  the design of the welds, see 8.6.3.2 and 8.6.3.3;
  the design strength of the HAZ adjacent to a weld, see 8.6.3.4;
  the design of connections with combined welds, see 8.6.3.5.
 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
 For the characteristic strength of weld metal (f_{w}) 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.
 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 f_{w}
Characteristic strength 
Filler metal 
Alloy 
3103 
5052 
5083 
5454 
6060 
6005A 
6061 
6082 
7020 
f_{w} [N/mm^{2}] 
5356 
 
170 
240 
220 
160 
180 
190 
210 
260 

4043A 
95 
 
 
 
150 
160 
170 
190 
210 
 For alloys EN AW5754 and EN AW5049 the values of alloy 5454 can be used;
 for EN AW6063, EN AW3005 and EN AW5005 the values of alloy 6060 can be used;
 for EN AW6106 the values of alloy 6005A can be used;
 for EN AW3004 the values of alloy 6082 can be used;
 for EN AW8011 A a value of 100 N/mm^{2} for filler metal Type 4 and Type 5 can be used.
 If filler metals 5056,5356A, 5556A/5556B, 5183/5183A are used then the values for 5356 have to be applied.
 If filler metals 4047A or 3103 are used then the values of 4043A have to be applied.
 For combinations of different alloys the lowest characteristic strength of the weld metal has to be used.

 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
 Full penetration butt welds should be applied for primary loadbearing members.
 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.
 Reinforcement or undercut of the weld within the limits as specified should be neglected for the design.
 The effective length should be taken as equal to the total weld length if runon and runoff plates are used. Otherwise the total length should be reduced by twice the thickness t.
8.6.3.2.2 Partial Penetration Butt Welds
 Partial penetration butt welds should only be used for secondary and non loadbearing members.
 For partial penetration butt welds an effective throat section t_{e} should be applied (see Figure 8.21).
8.6.3.2.3 Design Formulae for Butt Welds
 For the design stresses the following applies:
  normal stress, tension or compression, perpendicular to the weld axis, see Figure 8.14:
  shear stress, see Figure 8.15:
  combined normal and shear stresses:
130
where:
f_{w} 
characteristic strength weld metal according to Table 8.8; 
σ_{⊥Ed} 
normal stress, perpendicular to the weld axis; 
τ_{Ed} 
shear stress, parallel to the weld axis; 
γ_{Mw} 
partial safety factor for welded joints, see 8.1.1. 
 Residual stresses and stresses not participating in the transfer of load need not be included when checking the resistance of a weld. Text deleted
Figure 8.14  Butt weld subject to normal stresses
Figure 8.15  Butt weld subject to shear stresses
8.6.3.3 Design of fillet welds
 For the design of fillet welds the throat section should be taken as the governing section.
 The throat section should be determined by the effective weld length and the effective throat thickness of the weld.
 The effective length should be taken as the total length of the weld if:
  the length of the weld is at least 8 times the throat thickness;
  the length of the weld does not exceed 100 times the throat thickness with a nonuniform stress distribution;
  the stress distribution along the length of the weld is constant for instance in case of lap joints as shown in Figure 8.16a.
 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:
L_{w,eff} = (1,2  0,2 L_{w}/100 a)L_{w} with L_{w} ≥ 100 a (8.32)
131
where:
L_{w,eff} 
=effective length of longitudinal fillet welds 
L_{w} 
=total length longitudinal fillet welds 
a 
=effective throat thickness, see Figure 8.17. 
NOTE With nonuniform 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 zippereffect.
Figure 8.16  Stress Distributions in Joints with Fillet Welds
 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).
 If the qualification specimens show a consistent, positive root penetration, for design purposes the following may be assumed:
 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. 
 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 τ_{∥}, acting on the throat section of a fillet weld.
 The design resistance of a fillet weld should fulfil:
where:
f_{w} 
is the characteristic strength of weld metal according to Table 8.8; 
γ_{Mw} 
is the partial safety factor for welded joints, see 8.1.1. 
 For two frequently occurring cases the following design formulas, derived from formula (8.33), should be applied:
  Double fillet welded joint, loaded perpendicularly to the weld axis (see Figure 8.19). The throat thickness a should satisfy the following formula:
where:
normal stress in the connected member; (8.35)
F_{Ed} 
design load in the connected member; 
f_{w} 
characteristic strength of weld metal according to Table 8.8; 
t 
thickness of the connected member, see Figure 8.19; 
b 
width of the connected member. 
Figure 8.19  Double fillet welded joint loaded perpendicularly to the weld axis
  Double fillet welded joint, loaded parallel to the weld axis (see Figure 8.20). For the throat thickness a should be applied:
133
where:
shear stress in the connected member; (8.37)
F_{Ed} 
load in the connected member; 
f_{w} 
characteristic strength of weld metal according to Table 8.8; 
t 
thickness of the connected member, see Figure 8.20; 
h 
height of the connected member, see Figure 8.20. 
Figure 8.20  Double fillet welded joint loaded parallel to the weld axis
8.6.3.4 Design resistance in HAZ
 The design of a HAZ adjacent to a weld should be taken as follows:
 Tensile force perpendicular to the failure plane (see Figure 8.21):
where:
σ_{haz,Ed} 
design normal stress perpendicular to the weld axis; 
Text deleted 
f_{u,haz} 
characteristic strength HAZ, see 8.6.2; 
γ_{Mw} 
partial safety factor for welded joints, see 8.1.1. 
 Shear force in failure plane:
where:
τ_{haz,Ed} 
shear stress parallel to the weld axis; 
f_{v,haz} 
characteristic shear strength HAZ, see 8.6.2; 
γ_{Mw} 
partial safety factor for welded joints, see 8.1.1;. 
 Combined shear and tension:
  HAZ butt welds:
at the toe of the weld (full cross section) for full penetration welds and effective throat section te for partial penetration welds (8.42)
  HAZ fillet welds:
at the fusion boundary and at the toe of the weld (full cross section) (8.43)
Symbols see 8.6.3.4a) and b).
Figure 8.21  Failure planes in HAZ adjacent to a weld
 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
 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. 
 Applying one of the above methods the design of connections with combined welds is reduced to the design of the constituent welds.
 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
 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.
 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.
 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
 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.
 In general the degree of collaboration may be evaluated through a consideration of the loaddisplacement curves of the particular connection with individual kind of joining, or also by adequate tests of the complete hybrid connection.
 In particular normal bolts with hole clearance should not collaborate with welding.
 Preloaded highstrength bolts in connections designed as slipresistant 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 γ_{M} value.
8.8 Adhesive bonded connections
NOTE Recommendations for adhesive bonded connections are given in Annex M.
8.9 Other joining methods
 Rules for the design of mechanical fasteners are given in EN 199914
 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:
 – to demonstrate the suitability of the method for structural application;
 – to derive the design resistance of the method used.
 Examples of other joining methods are:
 – welding methods like for instance friction stir welding and laser welding;
 – mechanical fastening methods like screws in screw grooves and selfpiercing rivets.
NOTE The National Annex may give provisions for other joining methods.
136
Annex A – Reliability differentiation
[informative]
A.1 Introduction
 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)
 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.
 This annex is a guide for the application of the various parts of EN 1999 and for drafting the execution specification required by EN 10903.
A.2 Design provisions for reliability differentiation  Design supervision levels
 The guidance in EN 1990, Annex B for reliability differentiation provides:
 – rules for design supervision and checking of structural documentation, expressed by Design Supervision Levels;
 – rules for determination of design actions and combination of actions, expressed by the partial factors for actions.
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
 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.
 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 199913.
 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.
 It is a condition that the execution of structures and structural components is undertaken according to EN 10903 following the rules for the various execution classes given in EN 10903.
A.4 Governing factors for choice of execution class
 The execution class should be selected based on the following three conditions:
 the consequences of a structural failure, either human, economical or environmental;
 the type of loading, i.e. whether the structure is subject to predominantly static loading or a significant fatigue loading;
137
 the technology and procedures to be used for the work connected with the requirements for the quality level of the component.
 For considerations of the conditions under (a.) by use of consequence classes, see A. 1.
 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 199913 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 10903 requires that the execution class is defined in the execution specification.
NOTE 2 EN 10903 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
 The recommended procedure for determination of the execution class is the following:
 Determination of consequence class, expressed in terms of predictable consequences of a failure or collapse of a component, see EN 1990;
 determination of service category and production category, see Table A.1 and A.2;
 determination of execution class from the results of the operations a) and b) in accordance with the recommended matrix in Table A.3.
138
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
 Utilization grades are used to determine requirements to the amount of inspection and to the acceptance criteria for welds, see EN 10903.
 The utilization grade U for structures and components subject to predominantly static loading is defined by
where:
E_{k} 
is the characteristic action effect; 
R_{k} 
is the characteristic resistance. 
For combined actions U is given by the interaction formulae.
 The utilization grade for structures and components subject to fatigue loads is defined in EN 199913.
139
Annex B  Equivalent Tstub in tension
[normative]
B.1 General rules for evaluation of resistance
 In bolted connections an equivalent Tstub may be used to model the resistance of the basic components of several structural systems (for instance beamtocolumn joints), rather then as a stand alone connection as indicated in Figure 8.8.
 The possible modes of failure of the flange of an equivalent Tstub may be assumed to be similar to those expected to occur in the basic component that it represents, see Figure B.1.
 The total effective length ∑l_{eff} of an equivalent Tstub 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 Tstub is a notional length and does not necessarily correspond to the physical length of the basic joint component that it represents.
Figure B.1  Tstub as basic component of other structural systems
 In cases where prying forces may develop, see 8.5.10 of EN 199911, the tension resistance of a Tstub flange F_{u,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 beamtocolumn joints or beam splices it may be assumed that prying forces will develop):
  Mode 1: Flange failure by developing four hardening plastic hinges, two of which are at the webtoflange connection (w) and two at the bolt location (b):
In the formula, (M_{u,1})_{w} should be evaluated according to (B.5) with ρ_{u,haz} < 1, while (M_{u,1})_{b} with ρ_{u,haz} = 1 and considering the net area.
  Mode 2a: Flange failure by developing two hardening plastic hinges with bolt forces at the elastic limit:
140
Figure B.2  Failure modes of equivalent Tstub
  Mode 2b: Bolt failure with yielding of the flange at the elastic limit:
  Mode 3: Bolt failure:
F_{u,Rd} = ∑ B_{u} (B.4)
with
n = e_{min} but n ≤ 1,25m
where:
ε_{u} 
is the ultimate strain of the flange material; 
B_{u} 
is the tension resistance B_{t,Rd} of boltplate assembly given in 8.5.5; 141 
where:
A_{s} 
is the stress area of bolt; 
ΣB_{u} 
is the total value of B_{u} for all the bolts in the Tstub; 
l_{eff,1} 
is the value of l_{eff} for mode 1; 
l_{eff,2} 
is the value of l_{eff} for mode 2; 
e_{min} 
and m are as indicated in Figure B.3; 
NOTE In absence of more precise data, for ε_{u} use the minimum guarantied value A_{50} given in Section 3.
Figure B.3  Dimensions of an equivalent Tstub.
 In case where prying forces may not develop (failure mode 3), the tension resistance of a Tstub flange F_{u,Rd} should be taken as the smallest value, determined as follows:
 Methods for determination effective lengths l_{eff} for the individual boltrows and the boltgroup, for modeling basic components of a joint as equivalent Tstub flanges, are given in:
  Table B.1 for a Tstub with unstiffened flanges;
  Table B.2 for Tstub with stiffened flanges;
where the dimension e_{min} 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
Boltrow location 
Boltrow considered individually 
Boltrow considered as part of a group of boltrows 
Circular patterns l_{eff,cp} 
Noncircular patterns l_{eff,np} 
Circular patterns l_{eff,cp} 
Noncircular patterns l_{eff,cp} 
Inner boltrow 
2πm 
4m + 1,25e 
2p 
P 
End boltrow 
The smaller of: 2πm πm + 2e_{1} 
The smaller of: 4m + l,25e 2m + 0,625e + e_{1} 
The smaller of: πm + p 2e_{1} + p 
The smaller of: 2m + 0,625e + 0,5p e_{1} + 0,5_{p} 
Mode 1: 
l_{eff, 1} = l_{eff,nc} but l_{eff, l} ≤ l_{eff,cp} 
Σl_{eff,1} = Σl_{leff,nc} but Σl_{eff,1} ≤ Σl_{eff,cp} 
Mode 2: 
l_{eff, 1} = l_{eff,nc} 
Σl_{eff,l} = Σl_{eff,nc} 
NOTE See figures 8.1 to 8.4. 
Table B.2  Effective length for stiffened flanges
Boltrow location 
Boltrow considered individually 
Boltrow considered as part of a group of boltrows 
Circular patterns l_{eff,cp} 
Noncircular patterns l_{eff,cp} 
Circular patterns l_{eff,cp} 
Noncircular patterns l_{eff,cp} 
Boltrow adjacent to a stiffener 
2πm 
αm 
πm + p 
0,5p + αm − (2m + 0,625e) 
Other inner boltrow 
2πm 
4m + 1,25e 
2p 
P 
Other end boltrow 
The smaller of: 2πm
πm + 2e_{1}

The smaller of: 4m + l,25e
2m + 0,625e + e_{1}

The smaller of: πm + p 2e_{1} + p 
The smaller of: 2m + 0,625e + 0,5p 
End bolt row adjacent to a stiffener 
The smaller of 2πm
πm + 2e_{1}

e_{1} + αm − (2m + 0,625e) 
not relevant 
not relevant 
Mode 1: 
l_{eff, 1} = l_{eff,nc} but l_{eff, l} ≤ l_{eff,cp} 
Σl_{eff,1} = Σl_{leff,nc} but Σl_{eff,1} ≤ Σl_{eff,cp} 
Mode 2: 
l_{eff, 1} = l_{eff,nc} 
Σl_{eff,l} = Σl_{eff,nc} 
143
Figure B.4  Values of factor α for the effective length for stiffened flanges
B.2 Individual boltrow, boltgroups and groups of boltrows
Although in an actual Tstub flange the forces at each boltrow are generally equal, if an equivalent Tstub flange is used to model a basic component in a joint, allowance should be made for the forces are generally different at each boltrow.
When modeling a basic joint component by equivalent Tstub flanges, if necessary more than one equivalent Tstub may be used, with the boltrows divided into separate boltgroups corresponding to each equivalent Tstub flange (see Figure B.1).
 The following conditions should be satisfied:
 the force at each boltrow should not exceed the resistance determined considering only that individual boltrow;
 the total force on each group of bolt row, comprising two or more adjacent boltrow within the same boltgroup, should not exceed the resistance of that group of boltrow.
 Accordingly, when obtaining the tension resistance of the basic component represented by an equivalent Tstub flange, the following parameters should generally be determined:
 the maximum resistance of an individual boltrow, determined considering only that boltrow, see Figure B.5(a);
 the contribution of each boltrow to the maximum resistance of two or more adjacent boltrow within a boltgroup, determined considering only those boltrows, see Figure B.5(b).
 In the case of an individual boltrow Σl_{eff} should be taken as equal to the effective length l_{eff} given in Table B.1 and Table B.2 for that boltrow as an individual boltrow.
 In the case of a group of boltrows Σl_{eff} should be taken as equal to the effective length l_{eff} given in Table B.1 and Table B.2 for each relevant boltrow as part of a bolt group.
144
Figure B.5  Equivalent Tstub for individual boltrows and groups of boltrows.
145
Annex C  Materials selection
[informative]
C.1 General
 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 nonheat treatable alloys.
 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.
 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
 Within the 6xxx series alloys, the alloys EN AW6082, EN AW6061, EN AW6005A, EN AW6106, EN AW6063 and EN AW6060 are suitable for structural applications. These alloys have durability rating B. Within the 7xxx series alloys, the alloy EN AW7020 is suitable for general structural applications and has durability rating C.
C.2.1.1 Alloys EN AW6082 and EN AW6061
 EN AW6082 is one of the most widely used heat treatable alloy and often the principal structural alloy for welded and nonwelded 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 AW6061 is also a widely used heat treatable alloy for welded and nonwelded applications available in solid and hollow extrusions and tube. Both alloys are used normally in the fully heattreated condition EN AW6082T6 and EN AW6061T6.
 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 heataffected 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. AW6082 is a common alloy for extrusions, plate and sheet from stock. The alloy may be riveted using alloys EN AW6082, EN AW5754 or EN AW5019 in O or harder tempers, filler metals for welding are specified in prEN 1011 4.
C.2.1.2 Alloys EN AW6005A
 EN AW6005A 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 AW6082 or EN AW6061. This is particularly true for thinwalled hollow shapes. Like EN AW6082 and EN AW6061, 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 10114.
 The corrosion resistance of welded and unwelded components is similar or better than EN AW6082. The machining properties are similar to those of EN AW6082.
146
Table C.1  Comparison of general characteristics and other properties for structural alloys
Alloy ENDesignation 
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 AW3004 

 
 
 
 

III/IV 
A 
I 
I 
EN AW3005 

 
 
 
 

III/IV 
A 
I 
I 
EN AW3103 






III/IV 
A 
I 
II 
EN AW5005 






III/IV 
A 
I 
I 
EN AW5049 

 
 
 
 

II/III 
A 
I 
I/II 
EN AW5052 


x) 
x) 



A 
I 
I/II 
EN AW5083 


x) 
x) 


I/II 
A 
I 
I/II 
EN AW5454 


x) 
x) 
 

II/III 
A 
I 
I/II 
EN AW5754 


x) 
x) 


II/III 
A 
I 
I/II 
EN AW6060 
 





II/III 
B 
I 
I 
EN AW6061 
 





II/III 
B 
I 
II/III 
EN AW6063 
 





II/III 
B 
I 
I/II 
EN AW6005A 
 



 

II 
B 
I 
II/III 
EN AW6106 
 
 
 

 

II/III 
B 
I 
I/II 
EN AW6082 






I/II 
B 
I 
II/III 
EN AW7020 






I 
C 
I 
II/III 
EN AW8011A 

 
 
 
 
 
III/IV 
B 
II 
III/IV 
Key: 

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 
Weldability 
Designation 
Sand 
Chill or permanent mould 
EN AC42100 

⚫ 
II 
II/III 
B 
IV 
II 
EN AC42200 

⚫ 
II 
II 
B 
IV 
II 
EN AC43300 
⚫ 
⚫ 
I 
II 
B 
V 
II 
EN AC43000 

⚫ 
I/II 
IV 
B 
V 
II 
EN AC44200 
⚫ 
⚫ 
I 
IV 
B 
V 
II 
EN AC51300 
⚫ 
⚫ 
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 AW6060, EN AW6063 and EN AW 6106
 EN AW6060, EN AW6063 and EN AW6106 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 10114.
C.2.1.4 Alloys EN AW7020
 EN AW7020 alloys are recommended for structural applications for welded and nonwelded 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 AW7020 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 heattreated 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 nonheat treatable alloys
 Within the 5xxx series alloys, the alloys EN AW5049, EN AW5052 EN AW5454 and EN AW5754 and EN AW5083 are recommended for structural applications all have durability rating A. Other nonheat treatable alloys considered for less stressed structural applications are EN AW 3004, EN AW3005, EN AW 3103 and EN AW5005 again with durability rating A.
C.2.2.1 EN AW 5049, EN AW5052, EN AW5454 and EN AW5754
 EN AW5049; EN AW5052, EN AW5454 and EN AW5754 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 10114 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.
 The alloys can be easily machined in the harder tempers. EN AW5754 is the strongest 5xxx series alloy offering practical immunity to intergranular corrosion and stress corrosion.
C.2.2.2 EN AW5083
 EN AW5083 is the strongest nonheat 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.
 EN AW5083 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 AW5754 should be selected instead.
 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.
 EN AW5083 is fitted to be welded with the MIG and the TIG processes applying filler metals specified in prEN 10114. 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 thickwalled simple solid profiles and seamless hollow profiles with one hollow space (tubes).
 EN AW 5083 has good machining properties in all tempers.
C.2.2.3 EN AW3004, EN AW3005, EN AW3103 and EN AW 5005
 EN AW3004, EN AW3005, EN AW3103 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 AW8011A
 EN AW8011A belongs to the AlFeSi group and has a long tradition used preferably as material for packaging. Due to its advantages in fabrication EN AW8011A finds more and more application in building industry especially for facades.
149
C.3 Cast products
C.3.1 General
 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.
 Six foundry alloys are recommended for structural applications, four heat treatable alloys EN AC42100, EN AC42200, EN AC43000 and EN AC43300 plus two nonheat treatable alloys, EN AC44200 and EN AC51300. 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 AC42100, EN AC42200, EN AC43000 and EN AC43300
 EN AC42100, EN AC42200, EN AC43000 and EN AC43300 are all alloys in the AlSiMg 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 AC42200T6 but with a lower ductility than EN AC42100.
 EN AC43300 exhibits the best foundry castability with fair resistance to corrosion, good machinability and weldability. Foundry castability of alloys EN AC42100 and EN AC42200 is good, with good resistance to corrosion and machinability.
C.3.3 Nonheat treatable casting alloys EN AC44200 and EN AC51300
 EN AC44200 and EN AC51300 alloys are suitable for sand and chill or permanent mould castings but not recommended for pressure die castings. Alloy EN AC44200 possesses excellent foundry castability, but EN AC51300 has fair castability and is only suitable for more simple shapes. EN AC51300 has the highest strength, has excellent resistance to corrosion and is machinable. The EN AC51300 alloy may be decoratively anodised.
C.3.4 Special design rules for castings
C.3.4.1 General design provisions
 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.
 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
with the design strength σ_{Rd}, where σ_{Rd} is the lesser of f_{oc}/γ_{Mo,c} and f_{uc}/γ_{Mu,c}
NOTE Partial factors γ_{Mo,c} and γ_{Mu,c} may he defined in the National Annex. The following numerical values are recommended for buildings:
γ_{Mo,c} = 1,1 and γ_{Mu,c} = 2,0
 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:
F_{b,Rd} = k_{1}α_{b} f_{uc}dt/γ_{M2,cu} (C.2)
F_{b,Rd} = k_{1}α_{b}f_{oc}dt/γ_{M2,co} (C.3)
NOTE Partial factors γ_{M2,cu} and γ_{M2,co} may be defined in the National Annex. The following numerical values are recommended for buildings:
γ_{M2,cu} = γ_{Mu,c} = 2,0 and γ_{M2,co} = γ_{Mo,c} = 1,1
150
 The design bearing resistance for the plate material of pin connections F_{b,Rd} should be taken as the lesser value from the following two expressions, based on Table 8.7:
F_{b,Rd} = 1,5 f_{uc}dt/γ_{Mp,cu} (C.4)
F_{b,Rd} = 1,5 f_{oc}dt/γ_{Mp,co} (C.5)
NOTE Partial factors γ_{Mp,co} and γ_{Mp,cu} may be defined in the National Annex. The following numerical values are recommended for buildings:
γ_{Mp,co} = γ_{Mp} = 1,25 and γ_{Mp,cu} = γ_{Mu,c} = 2,0
 The specification for the cast part should include the following information:
 areas with tension stresses and utilization of the design resistance of more than 70 % (areas H);
 areas with tension stresses and utilization of the design resistance between 70 and 30 % (areas M);
 areas with compressive stresses and utilization of the design resistance between 100 and 30 % (areas M);
 areas with utilization of the design resistance of less than 30 % (areas N);
 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;
 all tests to be performed and any test conditions deviating from EN 1706, qualification procedures and qualification requirements;
 the required minimum values for strength and elongation.
C.3.4.2 Quality requirements, testing and quality documentation
 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 Aselongation 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.
 The following requirements apply to limitation of internal defects:
 Cracks in the cast parts are not allowed.
 For porosity the limiting values are:
  Hareas: 4 %
  Mareas: 6 %
  Nareas: 8 %
The diameter of pores should be less than 2 mm.
 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 13711 in combination with EN 571 for the penetrant testing and prEN 13068 (radiology) EN 12681 (radiography) in combination with EN 444 for carrying out the radiation test.
 Test procedures and delivery details regarding the test and the quality requirements of EN 15591 and EN 15594 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.
 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
 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
 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.
 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.
 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)
152
Annex D – Corrosion and surface protection
[informative]
D.1 Corrosion of aluminium under various exposure conditions
 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.
 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.
 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.
 In coastal and marine environments the surface will roughen and acquire a grey, stonelike, appearance, and protection of some alloys is necessary. Where aluminium is immersed in water special precautions may be necessary.
 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 5xxxalloys are affected by long exposure to high ambient temperatures, particularly if in marine environment.
 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.
 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 semiproducts, 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 123731
D.2 Durability ratings of aluminium alloys
 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.
 For advice on the durability rating of aluminium alloys see Annex C.
 Table D.1 gives recommendation for corrosion protection for the three classes of durability ratings.
153
D.3 Corrosion protection
D.3.1 General
 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.
 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.
 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 123731.
 Passivation is a shortterm protection or for mild conditions.
D.3.2 Overall corrosion protection of structural aluminium
 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 EN 10903. For the protection of sheet used in roofing and siding see EN 5082 .
 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.
 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.
 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.
 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 
Nonindustrial 
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 EN 5082. 
 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
 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 EN 10903. For the protection of metal to metal contacts including joints for sheet used in roofing and siding see EN 5082 .
 Where prepainted 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 preprotected components.
D.3.4 Aluminium surfaces in contact with nonmetallic materials
D.3.4.1 Contact with concrete, masonry or plaster
 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 heavyduty 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.
 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
 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.
 Where the concrete contains chlorides (e.g. as additives or due to the use of seadredged aggregate), at least two coats of plasticised coaltar pitch should be applied in accordance with the manufacturer’s instructions and the finished assembly should be overpainted 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
 In an industrial, damp or marine environment the timber should be primed and painted.
 Some wood preservatives may be harmful to aluminium. The following preservatives are generally accepted as safe for use with aluminium without special precautions:
 Creosote; zinc napthanates and zinccarboxylates; formulations containing nonionic organic biocides, e.g. propiconazole, carbendazim also solvent born preservatives.
 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:
 Copper naphtenate; fixated CC, CCA and CCBpreservatives, formulations containing boron compounds or quaterny ammonium compounds.
 The following preservatives should not be used in association with aluminium:
 non fixing inorganic formulations containing watersoluble copper or zinccompounds, also formulations containing acid and alkaline ingredients (pH < 5 and pH> 8).
 Oak, chestnut and western red cedar, unless well seasoned, are likely to be harmful to aluminium, particularly where these are through fastenings.
D.3.4.4 Contact with soils
 The surface of the metal should be protected with at least two coats of bituminous paint, hot bitumen, or plasticised coal tar pitch. Additional wrappingtapes may be used to prevent mechanical damage to the coating.
D.3.4.5 Immersion in water
 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 corrosionresisting steel or fastened by welding. Tables D.1 and D.2 give the protection requirements for fresh water and sea water immersion.
 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
 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
 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 metaltometal 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 
Zinccoated steel 
0 
(2) 
(1) (2) 
1(2) 
(1) (2) 
(1) (2) 
1(2) 
l 2 
1 2 
Zinccoated 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 
Zinccoated 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 
Zinccoated 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 EN 5082 NOTE 4 For stainless steels see also EN 199314.
Legend:
M = metal, B = bolt, R = rivet,
Treatments applied to the contact areas of structural members
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, pretreated and receive one priming coat, see EN 10903 , or sealing compound, extending beyond the contact area. The surfaces should be brought together while priming coat is still wet. Where assembling prepainted 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 nonabsorbent, nonconducting 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 EN 10903 ;), care being taken to seal all crevices. (2) Where zinccoated 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 zinccoated steel parts, the surrounding zinccoated 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 zinccoated structural parts as a whole may be necessary

159
Annex E  Analytical models for stress strain relationship
[informative]
E.1 Scope
 This Annex provides the models for the idealization of the stressstrain relationship of aluminium alloys. These models are conceived in order to account for the actual elastichardening behaviour of such materials.
 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
 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:
  Piecewise models
  Continuous models
 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
 These models are based on the assumption that material σε 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.
 According to this assumption, the characterization of the stressstrain relationship may generally be performed using either:
  bilinear model with and without hardening (Figure E.1)
  threelinear model with and without hardening (Figure E.2)
E.2.1.1 Bilinear model
 If a bilinear model with hardening is used (Figure E.1a), the following relationships may be assumed:
σ = Eε for 0 ≤ ε ≤ ε_{p} (E.1)
σ = f_{p} + E_{1} (ε − ε_{p}) for ε_{p} < ε ≤ ε_{max} (E.2)
where:
f_{p} 
= 
conventional elastic limit of proportionality 
ε_{p} 
= 
strain corresponding to the stress f_{p} 
ε_{max} 
= 
strain corresponding to the stress f_{max} 
E 
= 
elastic modulus 
E_{1} 
= 
hardening modulus 
 In case the “ElasticPerfectly plastic” model is assumed (Figure E.1b), the material remains perfectly elastic until the elastic limit stress f_{p}. Plastic deformations without hardening (E_{1} = 0) should be considered up to ε_{max}.
 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):
f_{p} 
= 
nominal value of f_{o} (see Section 3) 
f_{max} 
= 
nominal value of f_{u} (see Figure E.1a and Section 3) or f_{p} (see Figure E.1b) 
ε_{max} 
= 
0,5 ε_{u} 
ε_{u} 
= 
nominal value of ultimate strain (see E.3) 
ε_{p} 
= 
f_{o}/E 
E_{1} 
= 
(f_{u} − f_{o})/(0,5 ε_{u} − ε_{p}) 
160
E.2.1.2 Threelinear model
 If threelinear model with hardening is used (Figure E.2a), the following relationships may be assumed:
σ = Eε for 0≤ ε ≤ ε_{p} (E.3)
σ = f_{p} + E_{1} (ε  ε_{p}) for ε_{p} < ε ≤ ε_{e} (E.4)
σ = f_{e} + E_{2} (ε  ε_{e}) for ε_{p} < ε ≤ ε_{max} (E.5)
where:
f_{p} 
= 
conventional elastic limit of proportionality (see E.2.1.2(3)) 
f_{e} 
= 
conventional limit of elasticity (see E.2.1.2(3)) 
ε_{p} 
= 
strain corresponding to the stress f_{p} 
ε_{e} 
= 
strain corresponding to the stress f_{e} 
ε_{max} 
= 
strain corresponding to the stress f_{max} 
E 
= 
elastic modulus 
E_{1} 
= 
first hardening modulus 
E_{2} 
= 
second hardening modulus 
 In case the “Perfectly plastic” model is assumed (Figure E.2b), plastic deformations without hardening (E_{2} = 0) should be considered for strain ranges from ε_{e} to ε_{max}.
Figure E.1  Bilinear models
Figure E.2  Threelinear models
 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):
f_{p} 
= 
f_{0,01}

f_{e} 
= 
nominal value of f_{o} (see Section 3) 
f_{max} 
= 
nominal value of f_{u} (see Figure E.2a and Section 3) of f_{e} (See Figure E.2b) 
ε_{u} 
= 
nominal value of ultimate strain (see E.3) 
ε_{max} 
= 
0,5 ε_{u} 
ε_{p} 
= 
f_{0,01}/E 
E_{1} 
= 
(f_{e} − f_{p}/(ε_{e} − ε^{p}) 
E_{2} 
= 
(f_{max} − f_{e})/(ε_{max} − ε_{e}) in Figure E.2a) 
161
E.2.2 Continuous models
 These models are based on the assumption that the material σε law is described by means of a continuous relationship representing the elastic, inelastic and plastic, with or without hardening, region respectively.
 According to this assumption, the characterization of the stressstrain relationship may generally be performed using either:
  Continuous models in the form σ = σ(ε)
  Continuous models in the form ε = ε(σ)
E.2.2.1 Continuous models in the form σ = σ(ε)
 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):
  Region 1 elastic behavior
  Region 2 inelastic behavior
  Region 3 strainhardening behavior
 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 stressstrain relationship may be expressed as follows (Figures E.3b):
σ = Eε (E.6)
where:
f_{e} 
= 
conventional limit of elasticity 
f_{max} 
= 
tensile strength at the top point of σ  ε curve 
ε_{e} 
= 
strain corresponding to the stress f_{e} 
ε_{max} 
= 
strain corresponding to the stress f_{max} 
E 
= 
elastic modulus 
 In the absence of more accurate evaluation of the above parameters the following values may be assumed:
f_{e} 
= 
nominal value of f_{o} (see Section 3) 
f_{max} 
= 
nominal value of f_{u} (see Section 3) 
ε_{max} 
= 
0,5 ε_{u} 
ε_{u} 
= 
nominal value of ultimate strain (see E.3) 162 
E 
= 
nominal value of elastic modulus (see Section 3) 
Figure E.3  Continuous models in the form σ = σ(ε)
E.2.2.2 Continuous models in the form ε = ε (σ)
 For materials of roundhouse type, as aluminium alloys, the RambergOsgood 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):
where:
f_{e} 
= 
conventional limit of elasticity 
ε_{o,e} 
= 
residual strain corresponding to the stress f_{e} 
n 
= 
exponent characterizing the degree of hardening of the curve 
 In order to evaluate the n exponent, the choice of a second reference stress f_{x}, in addition to the conventional limit of elasticity f_{e}, is required. Assuming (Figure E.4b):
f_{x} 
= 
second reference stress 
ε_{o,x} 
= 
residual strain corresponding to the stress f_{x} 
The exponent n is expressed by:
 As conventional limit of elasticity , the proof stress f_{o} evaluated by means of 0,2% offset method may be assumed, i.e.:
f_{e} = f_{o}
ε_{o,e} = 0,002
and the model equation become:
163
Figure E.4  Continuous models in the form ε = ε(σ)
 The choice of the second reference point (f_{x}  ε_{o,x}) should be based on the strain range corresponding to the phenomenon under investigation. The following limit cases may be considered:
 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:
f_{x} = f_{0,1}
ε_{o,x} = 0,001
and, therefore,
 if the analysis concerns the range of plastic deformations, the tensile stress at the top point of the σε curve may be assumed as the second reference point (see Figure E.4d), giving:
f_{x} = f_{max}
ε_{o,x}  ε_{o,max} = residual strain corresponding to the stress f_{max}
and, therefore,
 Based on extensive tests, the following values may be assumed instead of the ones given in E.2.2.2(4):
164
where:
 elastic range (f_{x} = f_{p}, ε_{p} = 0,000001)
where the proportional limit f_{p} only depends on the value of the f_{o} yield stress:
f_{p} = f_{0,2} / 2 if f_{0,2} ≤ 160 N/mm^{2} (E.17)
 plastic range (f_{x} = f_{u})
E.3 Approximate evaluation of ε_{u}
According to experimental data the values of ε_{u} 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:
ε_{u} = 0,08 if f_{o} ≥ 400 N/mm^{2} (E.20)
NOTE This formulation can be used to quantify the stressstrain model beyond the elastic limit for plastic analysis purposes but it is not relevant for material ductility judgement.
165
Annex F  Behaviour of crosssections beyond the elastic limit
[informative]
F.1 General
 This Annex provides the specifications for estimating the postelastic behaviour of crosssections according to the mechanical properties of the material and the geometrical features of the section.
 The actual behaviour of crosssections 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.
 The choice of the generalized forcedisplacement relationship for the crosssections should be consistent with the assumptions for the material law and with the geometrical features of the section itself (see F.3).
 The reliability of the assumptions on behaviour of crosssections can be checked on the basis of tests.
F.2 Definition of crosssection limit states
 The behaviour of crosssections 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.
 Referring to the global behaviour of a crosssection, regardless of the internal action considered (axial load, bending moment or shear), the following limit states can be defined:
  elastic buckling limit state;
  elastic limit state;
  plastic limit state;
  collapse limit state.
 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.
 Elastic limit state is related to the strength corresponding to the attainment of the conventional elastic limit f_{o} of material in the most stressed parts of the section.
 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 f_{o}, without considering the effect of hardening.
 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 forcedisplacement curve is generally increasing, the collapse strength refers to a given limit of the generalized displacement (see F.5).
F.3 Classification of crosssections according to limit states
 Crosssections 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, crosssections can be divided as follows (see Figure F. 1):
  ductile sections (Class 1);
  compact sections (Class 2);
  semicompact sections (Class 3);
  slender sections (Class 4).
166
Figure F.1  Classification of crosssections
 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.
 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.
 Semicompact 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.
 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 crosssection 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
 The loadbearing resistance of crosssections under axial compression may be evaluated with reference to the above mentioned limit states, by means of the following practical rules.
 The value of axial load for a given limit state can be expressed by the generalized formula:
N_{Ed} = α_{N,j} A f _{d} (F.1)
where:
f_{d} = f_{o} / γ_{M1} 
the design value of 0,2% proof strength, see 6.1.2 
A 
the net cross sectional area 
α_{N,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 
N_{u} 
Collapse 
Class 1 
α_{N,1} = f_{1} / f_{d} 
N_{pl} 
Plastic 
Class 2 
α_{N,1} = 1 
N_{el} 
Elastic 
Class 3 
α_{N,1} = 1 
N_{red} 
Elastic buckling 
Class 4 
α_{N,4} = A_{eff} / A 
where A_{eff} is the effective cross sectional area, evaluated accounting for local buckling phenomena (see 6.2.4).
f_{t} = f_{u} / γ_{M2} the design value of ultimate strength, see 6.1.2
 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.
 If welded sections are involved, a reduced value A_{rec} 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
 The loadbearing resistance of crosssections under bending moment can be evaluated with reference to the above mentioned limit states, by means of the following rules.
 The value of bending moment for a given limit state can be expressed by the generalized formula:
M_{Rd} = α_{M,j} W_{el}f_{d} (F.2)
where:
f_{d} = f_{o}/γ_{M1} 
the design value of 0,2 % proof strength, see 6.1.2 
W_{el} 
the elastic section modulus 
α_{M,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 
M_{u} 
Collapse 
Class 1 
(depending on the alloy  see Annex (G) 
M_{pl} 
Plastic 
Class 2 
α_{M,2} = α_{0} = W_{pl}/W_{el} 
M_{el} 
Elastic 
Class 3 
α_{M,3} = 1 
M_{red} 
Elastic buckling 
Class 4 
α_{M,4} = W_{eff}/W_{el}(see 6.2.5) 
where:
n = n_{p} is the exponent of RambergOsgood law representing the material behaviour in plastic range (see Annex E) 
α_{5} and α_{10}, are the section generalized shape factors corresponding respectively to ultimate curvature168 
values χ_{u} = 5χ_{el} and 10_{χel,χel} being the elastic limit curvature (See Annex G) 
α_{0} 
the geometrical shape factor 
W_{pl} 
is the section plastic modulus 
W_{eff} 
is the effective section resistance modulus evaluated accounting for local buckling phenomena (see 6.2.5). 
 If welded sections are involved, reduced values W_{eff,haz} and W_{pl,haz} of section resistance and plastic modulus should be used, evaluated by accounting for HAZ (See 6.2.5).
 The evaluation of the correction factor α_{M,j} for a welded section of class 1 may be done by means of the following formula:
where:
Ψ = α_{M,1} / α_{M,2} being the correction factors for unwelded sections of class 1 and 2, respectively.
169
Annex G  Rotation capacity
[informative]
 The provisions given in this Annex G apply to class 1 crosssections 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
 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 M_{u} should be referred to a conventional ultimate bending curvature given by:
χ_{u} = ξχ_{el} (G.1)
where
ξ is a ductility factor depending on the type of alloy and χ_{el} conventionally assumed equal to the elastic bending curvature χ_{0,2}, which corresponds to the attainment of the proof stress f_{o} in the most stressed fibres.
 From the ductility point of view the common alloys can be subdivided into two groups (see also Annex H):
  brittle alloys, having 4 % ≤ ε_{u} ≤ 8 %, for which it can be assumed ξ = 5;
  ductile alloys, having ε_{u} ≥ 8 %, for which it can be assumed ξ = 10.
 The evaluation of elastic and postelastic behaviour of the crosssection may be done through the momentcurvature relationship, written in the RambergOsgood form:
where:
  M_{o.2} and χ_{0,2} are the conventional elastic limit values corresponding to the attainment of the proof stress f_{o}
  m and k are numerical parameters which for sections in pure bending are given by:
  α_{5} and α_{10} being the generalized shape factors corresponding to curvature values equal to 5 and 10 times the elastic curvature, respectively.
 The stable part of the rotation capacity R is defined as the ratio between the plastic rotation at the collapse limit state θ_{p} = θ_{u}  θ_{el} to the limit elastic rotation θ_{el} (Figure G.I):
where
Θ_{u} is the maximum plastic rotation corresponding to the ultimate curvature χ_{u}.
170
Figure G.1  Definition of rotation capacity
 The rotation capacity R may be calculated through the approximate formula:
with m and k: defined before.
The value of α_{M,j} is given in Table F.2 for the different behavioural classes.
 If the material exponent n is known (see Annex H), an approximate evaluation of α_{5} and α_{10} can be done through the formulas:
α_{0} = W_{pl}/W being the geometrical shape factor.
In the absence of more refined evaluations, the value n = n_{p} should be assumed (Annex H).
171
Annex H  Plastic hinge method for continuous beams
[informative]
 The provisions given in this Annex H apply to crosssections of class 1 in structures where collapse is defined by a number of crosssections that are reaching an ultimate strain. The provisions may be used also for structures with crosssections 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
 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).
 Plastic hinge method should not be used for members with transverse welds on the tension side of the member at the plastic hinge location.
 Adjacent to plastic hinge locations, any fastener holes in tension flange should satisfy
A_{f,net} 0,9 f_{u} / γ_{M2} ≥ A_{f} f_{o} / γ_{M1} (H.1)
for a distance each way along the member from the plastic hinge location of not less than the greater of:
  2h_{w}, where h_{w} is the clear depth of the web at the plastic hinge location
  the distance to the adjacent point at which the moment in the member has fallen to 0,8 times the moment resistance at the point concerned.
A_{f} is the area of the tension flange and A_{f,net} is the net area in the section with fastener holes.
 These rules arc not applicable to beams where the cross section vary along their length.
 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).
 With regard to ductility, two groups of alloys are defined, depending on whether the conventional curvature limits 5χ_{e} and 10χ_{e} are reached or not (see also Annex G):
  Brittle alloys (for which 4 % ≤ ε_{u} ≤ 8 %),
if the ultimate tensile deformation is sufficient to develop a conventional ultimate bending curvature χ_{u} equal at least to 5χ_{e};
  Ductile alloys (for which ε_{u} > 8 %),
if the ultimate tensile deformation is sufficient to develop a conventional ultimate bending curvature χ_{u} equal or higher than 10χ_{e}.
 Assuming an elastic (orrigid) 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:
M_{u} = α_{0}ηf_{o}W_{el} (H.2)
where:
η 
is the previously defined correction factor; 
W_{el} 
is the section elastic modulus. 
 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
M_{u} = α_{ξ}ηf_{o}W_{el} (H.3)
where, in addition to η and W_{el} 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 α_{5} and α_{10} refer to Annex F and G):
 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:
where n_{p} is the alloy RambergOsgood 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 H.4 are provided in Table H.1. Values of the correction coefficient η are shown in Figure H.1.
 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
Table H.1  Values of coefficients a, b and c.
Coefficients of the law: 
α_{0} = l,4 – 1,5 
α_{0} = 1,1 – 1,2 
Brittle alloys (χ_{u} = 5χ_{e}) 
Ductile alloys (χ_{u} = 10χ_{e}) 
Brittle alloys (χ_{u} = 10χ_{e}) 
Ductile alloys (χ_{u} = 10χ_{e}) 
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 torsionalflexural buckling of compressed members
[informative]
I.1 Elastic critical moment and slenderness
I.1.1 Basis
 The elastic critical moment for lateraltorsional buckling of a beam of uniform symmetrical crosssection with equal flanges, under standard conditions of restraint at each end and subject to uniform moment in plane going through the shear centre is given by:
where:
I_{t} 
is the torsion constant 
I_{w} 
is the warping constant 
I_{z} 
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 
 The standard conditions of restraint at each end are:
  restrained against lateral movement, free to rotate on plan (k_{z} = 1);
  restrained against rotation about the longitudinal axis, free to warp (k_{w}  1);
  restrained against movement in plane of loading, free to rotate in this plane (k_{y} = 1).
I.1.2 General formula for beams with uniform crosssections symmetrical about the minor or major axis
 In the case of a beam of uniform crosssection which is symmetrical about the minor axis, for bending about the major axis the elastic critical moment for lateraltorsional buckling is given by the general formula:
where relative nondimensional critical moment μ_{cr} is
nondimensional torsion parameter is
relative nondimensional coordinate of the point of load application related to shearcentre
relative nondimensional crosssection monosymmetry parameter
174
where:
C_{1}, C_{2} and C_{3} are factors depending mainly on the loading and end restraint conditions (See Table I.1 and I.2)
k_{z} and k_{w} are buckling length factors
z_{g} = z_{a}  z_{s}
z_{a} 
is the coordinate of the point of load application related to centroid (see Figure I.1) 
z_{s} 
is the coordinate of the shear centre related to centroid 
z_{g} 
is the coordinate of the point of load application related to shear centre . 
NOTE 1 See I.1.2 (7) and (8) for sign conventions and I.1.4 (2) for approximations for z_{j}.
NOTE 2 z_{j} = 0 (y_{j} = 0) for cross sections with yaxis (zaxis) being axis of symmetry.
NOTE 3 The following approximation for z_{j} can be used:
where:
c 
is the depth of a lip 
h_{f} 
is the distance between centrelines of the flanges. 
I_{fc} 
is the second moment of area of the compression flange about the minor axis of the section 
I_{ft} 
is the second moment of area of the tension flange about the minor axis of the section 
h_{s} 
is the distance between the shear centre of the upper flange and shear centre of the bottom flange (S_{u} and S_{b} in Figure I.1). 
For an Isection with unequal flanges without lips and as an approximation also with lips:
 The buckling length factors k_{z} (for lateral bending boundary conditions) and k_{w} (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).
 The factor k_{z} refers to end rotation on plan. It is analogous to the ratio L_{cr}/L for a compression member.
 The factor k_{w} refers to end warping. Unless special provision for warping fixity of both beam ends (k_{w} = 0,5) is made, k_{w} should be taken as 1,0.
175
Figure I.1  Notation and sign convention for beams under gravity loads (F_{z}) or for cantilevers under uplift loads ( F_{z})
 Values of C_{1}, C_{2} and C_{3} 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 k_{z} and in Table I.2 also corresponding to various values of k_{w}.
 For cases with k_{z} = 1,0 the value of C_{1} for any ratio of end moment loading as indicated in Table I.1, is given approximately by:
C_{1} = (0.310 + 0.428Ψ + 0.262Ψ^{2})^{0.5} (I.6)
 The sign convention for determining z and z_{j}, see Figure I.1, is:
 – coordinate z is positive for the compression flange. When determining z_{j} from formula in I.1.2(1), positive coordinate z goes upwards for beams under gravity loads or for cantilevers under uplift loads, and goes downwards for beams under uplift loads or cantilevers under gravity loads
 – sign of z_{j} is the same as the sign of crosssection monosymmetry factor Ψ_{f} in I.1.4(1). Take the cross section located at the Mside in the case of moment loading, Table I.1, and the crosssection located in the middle of the beam span in the case of transverse loading, Table I.2.
 The sign convention for determining z_{g} is:
 – for gravity loads z_{g} is positive for loads applied above the shear centre
 – in the general case z_{g} is positive for loads acting towards the shear centre from their point of application.
176
Table I.1  Values of factors C_{1} and C_{3} corresponding to various end moment ratios Ψ, values of buckling length factor k_{z} and crosssection parameters Ψ_{f} and k_{wt}.
End moment loading of the simply supported beam with buckling length factors k_{y} = 1 for major axis bending and k_{w} = 1 for torsion
Loading and support conditions.
Crosssection monosymmetry factor Ψ_{f} 
Bending moment diagram.
End moment ratio Ψ. 
k_{z}^{2)} 
Values of factors 
C_{l}^{1)} 
C_{3} 
C_{1,0} 
C_{1,1} 




M side 
ΨM side 


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 

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 

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 

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 

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 

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 

1,0 
2,331 
2,591 
1,85 
1,000 
1,31,2Ψ_{f} 
0,70 
0,7L 
3,078 
3,399 
2,70 
1,450 
11,2Ψ_{f} 
1,15 
0,7R 
1,711 
1,897 
1,45 
0,780 
0,9  0,75Ψ_{f} 
0,53 
0,5 
2,230 
2,579 
2,00 
0,950 
0,75  Ψ_{f} 
0,85 

1,0 
2,547 
2,852 
2,00 
1,000 
0,55  Ψ_{f} 
1,45 
0,7L 
2,592 
2,770 
2,00 
0,850 
0,23  0,9Ψ_{f} 
1,55 
0,7R 
1,829 
2,027 
1,55 
0,700 
0,68  Ψ_{f} 
1,07 
0,5 
2,352 
2,606 
2,00 
0,850 
0,35  Ψ_{f} 
1,45 

1,0 
2,555 
2,733 
2,00 
Ψ_{f} 
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 
0,1250,7Ψ_{f} 
0,1250,7Ψ_{f} 
1,88 
1) C_{1} = C_{1,0} + (C_{1,1} C_{1,0})κ_{wt} ≤ C_{1,1} , (C_{1} = C_{1,0} for κ_{wt} = 0, C_{1} = C_{1,1} for κ_{wt} ≥ 1) 2) 0,7 L = left end fixed, 0,7R = right end fixed 
177
Table I.2  Values of factors C_{1}, C_{2} and C_{3} corresponding to various transverse loading cases, values of buckling length factors k_{y}, k_{z}, k_{w} , crosssection monosymmetry factor Ψ_{f} and torsion parameter κ_{wt}.
Loading and support conditions 
Buckling length factors 
Values of factors 
k_{y} 
k_{Z} 
k_{w} 
C^{1}^{1)} 
C^{2} 
C^{3} 
C_{1,0} 
C_{1,1} 







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 

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 

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 

Ψ_{f} = 1 
0,5 ≤ Ψ_{f} ≤ 0,5 
Ψ_{f} = 1 
Ψ_{f} = 1 
0,5 ≤ Ψ_{f} ≤ 0,5 
Ψ_{f} = 1 

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 

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) C_{1} = C_{1,0} + (C_{1,1}  C_{1,0})κ_{wt} ≤ C_{1,1} , (C_{1} = C_{1,0} for κ_{wt} = 0, C_{1} = C_{1,1} for κ_{wt} ≥ 1). 2) Parameter Ψ_{f} refers to the middle of the span. 3) Values of critical moments M_{cr} refer to the cross section, where M_{max} is located 
178
I.1.3 Beams with uniform crosssections symmetrical about major axis, centrally symmetric and doubly symmetric crosssections
 For beams with uniform crosssections symmetrical about major axis, centrally symmetric and doubly symmetric crosssections loaded perpendicular to the major axis in the plane going through the shear centre, Figure I.2, z_{j} = 0, thus
 For endmoment loading C_{2} = 0 and for transverse loads applied at the shear centre z_{g} = 0. For these cases:
 If also κ_{wt} = 0: µ_{cr} = C_{1}/k_{z}
Figure I.2  Beams with uniform crosssections symmetrical about major axis, centrally symmetric and doubly symmetric crosssections
 For beams supported on both ends (k_{y} = 1, k_{z} = 1, 0,5 ≤ k_{w} ≤ 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 C_{1} may be used in the above two formulas given in I.1.3 (2) and (3) to obtain approximate value of critical moment:
where
M_{max} is maximum design bending moment,
M_{o,25}, M_{o,75} are design bending moments at the quarter points and
M_{o,5} is design bending moment at the midpoint of the beam or beam segment with length equal to the distance between adjacent crosssections which are laterally restrained.
 Factor C_{1} defined by (I.9) may be used also in formula (I.7), but only in combination with relevant value of factor C_{2} valid for given loading and boundary conditions. This means that for the six cases in Table I.2 with boundary condition k_{y} = 1, k_{z} = 1, 0,5 ≤ k_{w} ≤ 1, as defined above, the value C = 0,5 may be used together with (I.9) in (I.7) as an approximation.
 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 inplane moment distribution (formula (I.9) for C_{1} 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 crosssections symmetrical about the minor axis
 In the case of a cantilever of uniform crosssection, which is symmetrical about the minor axis, for bending about the major axis the elastic critical moment for lateraltorsional buckling is given by the formula (I.2), where relative nondimensional critical moment µ_{cr} is given in Table I.3 and I.4. In table I.3 and I.4 nonlinear interpolation should be used.
 The sign convention for determining z_{j} and z_{g} is given in I.1,2(7) and (8).
Table I.3  Relative nondimensional critical moment µ_{cr} for cantilever (k_{y} = k_{z} = k_{w} = 2) loaded by concentrated end load F.
Loading and support conditions 



4 
2 
1 
0 
1 
2 
4 

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 z_{j} = 0, z_{g} = 0 and κ_{wt0} ≤ 8: µ_{cr} = 1,27 + 1,14 κ_{wt0} + 0,017. b) For z_{j} = 0, 4 ≤ ζ_{g} ≤ 4 and κ_{wt} ≤ 4, µ_{cr} may be calculated also from formulae (I.7) and (I.8), where the following approximate values of the factors C_{1}, C_{2} should be used for the cantilever under tip load F: C_{1} = 2,56 + 4,675 κ_{wt}  2,62 + 0,5, if κ_{wt} ≤ 2 C_{1} = 5,55 if κ_{wt} > 2 C_{2} = 1,255 + 1,566κ_{wt}  0,931 + 0,245  0,024, if ζ_{g} ≥ 0 C_{2} = 0,192 + 0,585 κ_{wt}  0,054  (0,032 +0,102 κ_{wt} 0,013) ζ_{g} ,if ζ_{g} <0 
180
Table I.4  Relative nondimensional critical moment µ_{cr} for cantilever (k_{y} = k_{z} = k_{w} = 2) loaded by uniformly distributed load q
Loading and support conditions 



4 
2 
1 
0 
1 
2 
4 

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 z_{j} = 0, z_{g} = 0 and κ_{wt0} ≤ 8: µ_{cr} = 2,04 + 2,68 κ_{wt0} + 0,021. b) For z_{j} = 0, −4 ≤ ζ_{g} ≤ 4 and κ_{wt} ≤ 4, µ_{cr} may be calculated also from formulae (I.7) and (I.8), where the following approximate values of the factors C_{1}, C_{2} should be used for the cantilever under uniform load q: C_{1} = 4,11 + 11.2 κ_{wt} − 5,65 + 0,975 , if κ_{wt} ≤ 2 C_{1} = 12 if κ_{wt} > 2 C_{2} = 1,661 + 1,068 κ_{wt} − 0,609 + 0,153 − 0,014 , if ζ_{g} ≥ 0 C_{2} = 0,535 + 0,426 κ_{wt} − 0,029 − (0,061 + 0,074 κ_{wt} − 0,0085 ) ζ_{g} ,if ζ_{g} < 0 
181
I.2 Slenderness for lateral torsional buckling
 The general relative slenderness parameter _{LT} for lateraltorsional buckling is given by:
where:
α is the shape factor taken from Table 6,4.
 Alternatively, for I sections and channels covered by Table I.5, the value of _{LT} may be obtained from:
where:
L_{cr,z} is the buckling length for lateral torsional buckling
i_{z} is the minor axis radius of gyration of the gross section
h is the overall section depth
t_{2} is the flange thickness (t_{2} = 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.
 If the flange reinforcement to an Isection or channel is not of the precise form shown in Table I.5 (simple lips), it is still permissible to obtain _{LT} using the above expression, providing X and Y are taken as for an equivalent simple lip having the same internal depth c, while i_{z} is calculated for the section with its actual reinforcement.
 Normally L_{cr,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 zaxis, 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 crosssections 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 endpost can be allowed for by further increasing L_{cr,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 L_{cr,z} taking into account all type of cantilever restraints and destabilizing effect of transverse loads is not known.
182
Table I.5  Lateraltorsional buckling of beams, coefficients X and Y

1,5 ≤ h / b ≤ 4,5 1 ≤ t_{2} / t_{1} ≤ 2 
X = 0,90 − 0,03h / b + 0,04t_{2} / t_{1}


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 

1,5 ≤ h / b ≤ 4,5 1 ≤ t_{2} / t_{1} ≤ 2 
X = 0,95 − 0,03h / b + 0,06t_{2} / t_{1}


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 torsionalflexural buckling
 The elastic critical axial force N_{cr} for torsional and torsionalflexural buckling of a member of uniform crosssection, under various conditions at its ends and subject to uniform axial force in the gravity centre is given by:
where:
I_{t}, I_{w}, I_{z}, k_{y}, k_{z}, k_{w} and G see I.1,1.
L is the length of the member between points that have lateral restraint.
y_{s} and z_{s} are the coordinates of the shear centre related to centroid
α_{yw} (k_{y}, k_{w}) and α_{zw} (k_{z}, k_{w}) 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 α_{yw} or α_{zw} for combinations of bending and torsion boundary conditions
Bending boundary condition k _{y} or k _{z} 
Torsion boundary condition, k_{w} 
1,0 
0,7 
0,7 
0,5 
2,0 
2,0 
1,0 
1,0 
2,0 
1,0 
1 
0,817 
0,817 
0,780 
a) 
a) 
a) 
a) 
a) 
0,7 
0,817 
1 
a) 
0,766 
a) 
a) 
a) 
a) 
a) 
0,7 
0,817 
a) 
1 
0,766 
a) 
a) 
a) 
a) 
a) 
0,5 
0,780 
0,766 
0,766 
1 
a) 
a) 
a) 
a) 
a) 
2,0 
a) 
a) 
a) 
a) 
1 
a) 
a) 
a) 
a) 
2,0 
a) 
a) 
a) 
a) 
a) 
1 
a) 
a) 
a) 
1,0 
a) 
a) 
a) 
a) 
a) 
a) 
1 
a) 
a) 
1,0 
a) 
a) 
a) 
a) 
a) 
a) 
a) 
1 
a) 
2,0 
a) 
a) 
a) 
a) 
a) 
a) 
a) 
a) 
1 
a) conservatively, use α_{yw} = 1 and α_{zw} = 1 
184
Table I.7  Torsion boundary conditions in Table I.6
Symbol in Table I.6 
Deformation of member end 
Torsion boundary condition 


Rotation restrained, warping free 


Rotation restrained, warping restrained 


Rotation free, warping free 


Rotation free, warping restrained 
 For crosssections symmetrical about the zaxis y_{s} = 0 and the solution to equation (I.13) is:
N_{cr,1} = N_{cr,y} (flexural buckling) (I.18)
 For doubly symmetrical cross sections y_{s} = 0 and z_{s} = 0 and the solution to equation (I.13) is:
N_{cr,1} = N_{cr,y}, N_{cr,2} = N_{cr,z} (flexural buckling) and N_{cr,3} = N_{cr,T} (torsional buckling)
 Slenderness based on approximate formulae for certain cross sections are given in I.4(2).
I.4 Slenderness for torsional and torsionalflexural buckling
 The general expression for relative slenderness parameter _{T} for torsional and torsionalflexural buckling is:
where
A_{eff} is the effective area for torsional or torsionalflexural buckling, see 6.3.1.2, Table 6.7
N_{cr} is the elastic critical load for torsional buckling, allowing for interaction with flexural buckling if necessary (torsionalflexural buckling). See I.3.
 Alternatively, for sections as given in Table I.8
where k is read from Figure 1,3 or given by the expression:
in which X > 0 and s are found in Table I.8.
185
λ_{t} is found as follows:
 for angles, tees, cruciforms λ_{t} = λ_{0} (I.23)
 for channels, tophats
Table I.8 contains expressions for λ_{0} and Y and also for s and X (needed in expression (I.22) and for Figure I.3).
In expression (I.24) the quantity λ_{y} should be taken as the effective slenderness for column buckling about axis yy (as defined in Table I.8, Cases 15 to 18).
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

ρ ≤ 5 See Note 3 for ρ 
λ_{0} = 5b / t − 0,6ρ^{1,5}(b / t)^{0,5} s = λ_{u} / λ_{0} X = 0,6 

ρ ≤ 5 1 ≤ δ ≤ 2,5 See Note 3 for ρ 
λ_{0} = 5b / t − 0,6ρ^{1,5}(b / t)^{0,5} − −(δ – 1)[2(δ − 1)^{2} − 1,5ρ] s = λ_{u} / λ_{0} X = 0,6 

b / t = 20 r_{i} / t = 2 δ = 3 β ≈ 4 See Note 3 for r_{i} 
λ_{0} = 66 s = λ_{u} / λ_{0} X = 0,61 (Equal legs) 

ρ ≤ 5 0,5 ≤ b / h ≤ 1 See Note 3 for ρ 


ρ ≤ 5 0,5 ≤ b / h ≤ 1 1 ≤ δ ≤ 2,5 See Note 3 for ρ 


h / t = 20 b / t = 15 r_{i} / t = 2 δ = 3, β ≈ 4 See Note 3 for r_{i} 
λ_{0} = 57 s = 1,4λ_{u} / λ_{0} X = 0,6 (Unequal lags, equal bulbs) 

ρ ≤ 3,5 See Note 3 for ρ 
λ_{0} = 5,1b / t − ρ^{1,5}(b / t)^{0,5} X = 1 187 

ρ ≤ 5 0,5 ≤ h / b ≤ 2 See Note 3 for ρ 
s = λ_{z} / λ_{0} X = 1,1 – 0,3h / b 

ρ ≤ 5 0,5 ≤ h / b ≤ 2 1 ≤ δ ≤ 2,5 See Note 3 for ρ 
s = λ_{z} / λ_{0} X = 1,1 – 0,3h / b 

Shape of angles as Case 3. 
λ_{0} = 70 s = λ_{z} / λ_{0} X = 0,83 

Shape of angles as Case 6. 
λ_{0} = 60 s = λ_{z} / λ_{0} X = 0,76 

Shape of angles as Case 6. 
λ_{0} = 63 s = λ_{z} / λ_{0} X = 0,89 

ρ ≤ 3,5 0,5 ≤ h / b ≤ 2 See Note 3 for ρ 
λ_{0} = (1,4 + 1,5b / h + 1,1h / b)h / t − ρ^{1,5}(h / t)^{0,5} s = λ_{z} / λ_{0} X = 1,3 − 0,8h / b + 0,2(h / b)^{2} 

h / t = 25 b / h = 1,2 r_{i} / t = 0,5 See Note 3 for r_{i} 
λ_{0} = 65 s = λ_{z} / λ_{0} X = 0,78 188 

1 ≤ h / b ≤ 3 1 ≤ t_{2} / t_{1} ≤ 2 
λ_{0} = (b / t_{2})(7 + 1,5(h / b)t_{2} / t_{1}) s = λ_{y} / λ_{t} X = 0,38h / b − 0,04(h / b)^{2} Y = 0,14 − 0,02h / b − 0,02t_{2} / t_{1} 

1 ≤ h / b ≤ 3 c / b ≤ 0,4 
λ_{0} = (b / t)(7 + 1,5h / b + 5c / b) s = λ_{y} / λ_{t} X = 0,38h / b − 0,04(h / b)^{2} − 0,25c / b


1 ≤ h / b ≤ 3 c / b ≤ 0,4 
λ_{0} = (b / t)(7 + 1,5h / b + 5c / b) s = λ_{y} / λ_{t} X = 0,38h / b − 0,04(h / b)^{2}


h / t = 32 b / h = 0,5 r_{i} / t = 2 See Note 3 for r_{i} 
λ_{0} = 126 s = λ_{y} / λ_{t} X = 0,59 Y = 0,104 
1) The sections are generally of uniform thickness t, except Cases 14 and 15 2) λ_{u}, λ_{y} or λ_{z} 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:
4) The values given for λ_{0}, X and Y are only valid within the limits shown. In the case of backtoback 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 I_{t}
 For an open thinwalled section composed solely of flat plate parts, each of uniform thickness, and reinforced with fillets and/or bulbs, the value of the torsion constant I_{t} is given by
I_{t} = ∑b_{sh}t^{3} / 3 − 0,105∑t^{4} + ∑(β + δ γ)^{4}t^{4} (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 crosssection parts
β, δ and γ are fillet or bulb factors, see Figure J.I, Case 3 to 11
b_{sh} = width of flat crosssection parts, measured to the edge of the shaded area in Figure J.1 in the case of a flat crosssection part abutting a fillet or bulb.
 For Case 1 and 2 in Figure J.1, with different thickness t_{1} and t_{2}
I_{t} = ∑bt^{3} / 3 − 0,105∑ t^{4} + ∑ α D^{4} (J.1a)
in which α and δ are fillet factors and D is diameter of inscribed circle, see Figure J.1.
 For a simple rectangular crosssection with any b/t ratio ≥ 1
 For closed cross sections I_{t} is found in J.6.
J.2 Position of shear centre S
 Figure J.2 gives the position of the shear centre for a number of crosssections. See J.4 and J.5 for open thinwalled cross sections and J.6 for monosymmetrical closed cross sections.
J.3 Warping constant I_{w}
 Values of the warping constant I_{w} for certain types of crosssection may be found as follows:
 for sections composed entirely of radiating outstands e.g. angles, tees, cruciforms, I_{w} may conservatively be taken as zero or
I_{w} = ∑ b^{3}t^{3} / 36 (J.3)
where b is the width and t is thickness of outstand crosssection parts, see Lsection and Tsection in Figure J.2.
 For simple rectangular crosssection with any b/t ratio ≥ 1
 for the specific types of section illustrated in Figure J.2 values of I_{w} may be calculated using the expression given there.
 formulae for section constants, including shear centre position and warping constant I_{w} , 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
191
Figure J.1  Torsion constant factors for certain fillets and bulbs (continued)
192
Figure J.2  Shearcentre position S and warping constant I_{w} for certain thinwalled sections
193
J.4 Cross section constants for open thinwalled cross sections
Figure J.3  Cross section nodes
 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, coordinates and (effective) thickness.
Nodes and parts j = 0..n i = 1..n
Area of cross section parts
Cross section area
First moment of area with respect to yaxis and coordinate for gravity centre
Second moment of area with respect to original yaxis and new yaxis through gravity centre
First moment of area with respect to zaxis and gravity centre
Second moment of area with respect to original zaxis and new zaxis through gravity centre
Product moment of area with respect of original y and zaxis and new axes through gravity centre
Principal axis
Sectorial coordinates
ω_{0} = 0 ω_{0i} = y_{i−1} · z_{i} − y_{i} · z_{i−1} ω_{i} = ω_{i−1} + ω_{0i} (J.15)
Mean of sectorial coordinate
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Sectorial constants
Shear centre
Warping constant
I_{w} = I_{ωω} + z_{sc} · I_{yω} − y_{sc} · I_{zω} (J.21)
Torsion constant
Sectorial coordinate with respect to shear centre
ω_{sj} = ω_{j} − ω_{mean} + z_{sc} ·(y_{j} − y_{gc}) − y_{sc} · (z_{j} − z_{gc}) (J.23)
Maximum sectorial coordinate and warping modulus
Distance between shear centre and gravity centre
y_{s} = y_{sc} − y_{gc} z_{s} = z_{sc} − z_{gc} (J.25)
Polar moment of area with respect to shear centre
Nonsymmetry factors z_{j} and y_{j} according to Annex I
where the coordinates for the centre of the cross section parts with respect to shear centre are
NOTE Z_{j} = 0 (y_{j} = 0) for cross sections with yaxis (zaxis) being axis of symmetry, see Figure J.3.
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J.5 Cross section constants for open cross section with branches
Figure J.4  Nodes and parts in a cross section with branches
 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 centre of cross section with closed part
Figure J.5  Cross section with closed part
 For a symmetric or nonsymmetric cross section with a closed part, Figure J.5, the torsion constant is given by
where
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Annex K  Shear lag effects in member design
[informative]
K.1 General
 Shear lag in flanges may be neglected provided that b_{0} < L_{e} /50 where the flange width b_{0} is taken as the outstand or half the width of an internal cross section part and L_{e} 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. b_{0} < L_{e} / 25 is recommended for support regions, cantilevers and region with concentrated load. For sagging bending regions b_{0} < L_{e} / 15 is recommended.
 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.
 Stresses under elastic conditions from the introduction of inplane 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
 The effective width b_{eff} for shear lag under elastic condition should be determined from:
b_{eff} = β_{s} b_{0} (K.1)
where the effective factor β_{s} is given in Table K.1.
NOTE This effective width may be relevant for serviceability limit states.
 Provided adjacent internal spans do not differ more than 50% and cantilever span is not larger than half the adjacent span the effective length L_{e} may be determined from Figure K.1. In other cases L_{e} should be taken as distance between adjacent points of zero bending moment.
Figure K.1  Effective length L_{e} for continuous beam and distribution of effective width
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Figure K.2  Definitions of notations for shear lag
Table K.1  Effective width factor β_{s}
K 
Location for verification 
β_{s} 
K ≤ 0,02 

β_{s} = 1,0 
0,02 < K ≤ 0,70 
sagging bending 

hogging bending 

K > 0,70 
sagging bending 

hogging bending 

All K 
end support 
β_{S,0} = (0,55 + 0,025 / K)β_{s,1} but β_{s,0} ≤ β_{s,1} 
All K 
cantilever 
β_{s} = β_{s,2} at support and at the end 
k = α_{0}b_{0} / L_{e} with in which A_{st} is the area of all longitudinal stiffeners within the width b_{0} and other symbols as defined in Figure K.1 and Figure K.2. 
K.2.2 Stress distribution for shear lag
 The distribution of longitudinal stresses across the plate due to shear lag should be obtained from Figure K.3.
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Figure K.3  Distribution of longitudinal stresses across the plate due to shear lag
K.2.3 Inplane load effects
 The elastic stress distribution in a stiffened or unstiffened plate due to the local introduction of inplane forces (see Figure K.4) should be determined from:
where a_{st,1} is the grosssectional area of the smeared stiffeners per unit length, i.e. the area of the stiffener divided by the centretocentre distance.
Figure K.4  Inplane load introduction
NOTE The stress distribution may be relevant for the fatigue verification.
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K.3 Shear lag at ultimate limit states
 At ultimate limit states shear lag effects may be determined using one of the following methods:
 elastic shear lag effects as defined for serviceability and fatigue limit states;
 interaction of shear lag effects with geometric effects of plate buckling;
 elasticplastic 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 elasticplastic shear lag effects allowing for limited plastic strains.
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Annex L  Classification of joints
[informative]
L.1 General
 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 beamtocolumn 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”
 Structural properties (of a joint): Its resistance to internal forces and moments in the connected members, its rotational stiffness and its rotation capacity.
 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.
 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):
  fully restoring connections;
  partially restoring connection.
 With respect to the single behavioural property of the connected member, connections may be classified according to (Figures L.2.b)d)):
  rigidity;
  strength;
  ductility.
 The types of connection should conform with the member design assumptions and the method of global analysis.
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L.2 Fully restoring connections
 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 forcedisplacement curve of the connection lies above those of the connected members.
 The existence of the connection may be ignored in the structural analysis.
L.3 Partially restoring connections
 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 forcedisplacement curve may in some part fall below the one of the connected member.
 The existence of such connections must be considered in the structural analysis.
Figure L.2.a)  d)  Classification of connections
L.4 Classification according to rigidity
 With respect to rigidity, joints should be classified as (Figure L.2.b):
  rigidity restoring (rigid) joints (Rl);
  rigidity nonrestoring joints (semirigid) joints (R2),
depending on whether the initial stiffness of the jointed member is restored or not, regardless of strength and ductility.
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L.5 Classification according to strength
 With respect to strength, connections can be classified as (Figure L.2.c):
  strength restoring (full strength) connections;
  strength nonrestoring connections (partial strength) connections,
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
 With respect to ductility, connections can be classified as (Figure L.2.d):
  ductility restoring (ductile) connections;
  ductility nonrestoring (semiductile or brittle) connections,
depending on whether the ductility of the connection is higher or lower than that of the connected member, regardless of strength and rigidity.
 Ductile connections have a ductility equal or higher than that of the connected member; elongation or rotation limitations may be ignored in structural analysis.
 Semiductile 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.
 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
 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
 With respect to the momentcurvature relationship, the connection types adopted in frame structures can be divided into:
  nominally pinned connections;
  builtin connections.
 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).
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Figure L.3  Main connection types
L.8.2 Nominally pinned connections
 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.
 Nominally pinned connections should be capable of transmitting the forces calculated in design and should be capable of accepting the resulting rotations.
 The rotation capacity of a nominally pinned connection should be sufficient to enable all the necessary plastic hinges to develop under the design loads.
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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 
Semirigid connections (full or partial strength, ductile or nonductile with or without restoring of member elastic strength)
Partial strength connections (rigid or semirigid, ductile or nonductile) without restoring of member elastic strength 
Fully restoring connections
Rigid connections (full or partial strength, ductile or nonductile) with restoring of member elastic strength
Partial strength connections (rigid, ductile or nonductile) with restoring of member elastic strength 
PLASTIC
(rigidplastic elasticplastic inelasticplastic) 
Partial strength connections (rigid or semirigid ductile or nonductile) without restoring of member elastic strength 
Fully restoring connections
Partial strength, ductile connections (rigid or semirigid) with restoring of member elastic strength
Full strength connections 
HARDENING (rigidhardening elastichardening genetically inelastic) 
Partially restoring connections 
Fully restoring connections 
L.8.3 Builtin connections
 Builtin 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):
  rigid connections;
  semirigid connections;
  full strength connections;
  partial strength connections.
 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.
 The deformations of rigid connections should be such that they do not reduce the resistance of the structure by more than 5%.
 Semirigid connections should provide a predictable degree of interaction between members, based on the design momentrotation characteristics of the joints.
 Rigid and semirigid connections should be capable of transmitting the forces and moments calculated in design.
 The rigidity of fullstrength and partialstrength connections should be such that, under the design loads, the rotations at the necessary plastic hinges do not exceed their rotation capacities.
 The rotation capacity of a partialstrength 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.
 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.
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Annex M  Adhesive bonded connections
[informative]
M.1 General
 Structural joints in aluminium may be made by bonding with adhesive.
 Bonding needs an expert technique and should be used with great care.
 The design guidance in this Annex M should only be used under the condition that:
 – the joint design is such that only shear forces have to be transmitted (see M.3.1);
 – appropriate adhesives are applied (see M.3.2);
 – the surface preparation procedures before bonding do meet the specifications as required by the application (see M.3.2(3)).
 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.
 Adhesive jointing can be suitably applied for instance for plate/stiffener combinations and other secondary stressed conditions.
 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
 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 collarassemblies.
 On receipt of the adhesive, its freshness can be checked before curing by the following methods:
  chemical analysis;
  thermal analysis;
  measurements of the viscosity and of the dry extract in conformity with existing ENs, prENs and ISO Standards related to adhesives.
 The strength of an adhesive joint depends on the following factors:
 the specific strength of the adhesive itself, that can be measured by standardised tests (see ISO 110032);
 the alloy, and especially its proof stress if the yield stress of the metal is exceeded before the adhesive fails;
 the surface pretreatment: 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;
 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 pretreatments);
 the configuration of the joint and the related stress distribution, i.e. the ratio of the maximum shear stress τ_{max} to the mean one (τ_{max}/τ_{mean}) and the ratio of the maximum peel stress σ_{max} to the mean shear one (σ_{max}/τ_{mean}), 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.
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 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/pretreatment/adhesive, and the ageing or environment (see M.3 and 2.5).
 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
 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.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
 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.
 Pretreatments 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 EN 10903 .
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 For the characteristic shear strength of adhesives f_{v,adh} for structural applications the values of Table M.1 may be used.
Table M.1  Characteristic shear strength values of adhesives
Adhesive types 
f_{v,adh} N/mm^{2} 
l  component, heat cured, modified epoxide 2 components, cold cured, modified epoxide 2 components, cold cured, modified acrylic 
35 25 20 
 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
 The design shear stress should be taken as
where:
τ 
nominal shear stress in the adhesive layer; 
f_{v,adh} 
characteristic shear strength value of adhesive, see M.3.2; 
γ_{Ma} 
partial safety factor for adhesive bonded joints, see 8,1.1. 
NOTE The high value of γ_{Ma} in 8,1.1 has to be used since:
 – the design of the joint is based on ultimate shear strength of the adhesive;
 – the scatter in adhesive strength can be considerable;
 – the experience with adhesive bonded joints is small;
 – the strength decreases due to ageing.
M.4 Tests
 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.
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Bibliography
EN 15921 
Aluminium and aluminium alloys  HF seam welded tubes  Part 1: Technical conditions for inspection and delivery 
EN 15922 
Aluminium and aluminium alloys  HF seam welded tubes  Part 2:  Mechanical properties 
EN 15923 
Aluminium and aluminium alloys  HF seam welded tubes  Part 3:  Tolerance on dimensions and shape of circular tubes 
EN 15924 
Aluminium and aluminium alloys  HF seam welded tubes  Part 4:  Tolerance on dimensions and form for square, rectangular and shaped tubes 
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