ÖNORM
EN 1999-1-1 Edition: 2010-08-15
Eurocode 9: Design of aluminium structures Part 1-1: General structural rules (consolidated version) Eurocode 9: Bemessung und Konstruktion von Aluminiumtragwerken ― Teil 1-1: Allgemeine Bemessungsregeln (konsolidierte Fassung)
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Eurocode 9: Calcul des structures en aluminium ― Partie 1-1: Règles générales (version consolidée)
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ICS Identical (IDT) with
91.010.30; 91.080.10 EN 1999-1-1:2007-05 + A1:2009-07
Supersedes
ÖNORM ENV 1999-1-1:1998-11 (PRESTANDARD) and ÖNORM ENV 1999-1-1:2000-06 (PRESTANDARD)
responsible
Committee 013 Steel-, composite- and aluminium-structures
ÖNORM EN 1999-1-1:2010
National Foreword The present EN 1999-1-1 has been prepared by the Technical Committee CEN/TC 250 “Structural Eurocodes”, Sub-committee SC9 “Aluminium structures”. Parameters (NDPs) for which, according to CEN Internal Regulation, a national decision is taken should be published as National Annex. NOTE: This is also recommended by Guidance Paper L1) of the European Commission. In Austria, the National Annex is being prepared by the competent Technical Committee 013 „ Steel-, composite- and aluminium-structures“ and published as ÖNORM B 1999-1-1. ÖNORM EN 1999-1-1 and ÖNORM B 1999-1-1 are to be applied jointly. This ÖNORM EN 1999-1-1 shall be applied jointly with the other standards of the ÖNORM EN 199x series. For further Information concerning this document see www.eurocode.at. Possible printing errors in this ÖNORM are announced by an “Errata Sheet”. This document is available at the internet platform www.eurocode.at
National Foreword to EN 1999-1-1:2007/A1:2009-07 The present ÖNORM EN has been reissued without prior public enquiry and represents a consolidated national new edition of EN 1999-1-1:2007-05, including Amendment EN 1999-1-1:2007/A1:2009-07.
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The preceding European amendment EN 1999-1-1:2007/A1:2009-07 as well as amendment EN 1999-1-1:2007/A1:2009-07 have been considered and incorporated in this version of ÖNORM EN 1999-1-1. The start and finish of text introduced or altered by amendment is indicated in the text by tags !".
1
) Guidance Paper L, concerning the Construction Product Directive – 89/106/EEC, “Application and Use of Eurocodes”, European Commission, Enterprise Directorate – General
2
EN 1999-1-1
EUROPEAN STANDARD
May 2007
NORME EUROPÉENNE
+ A1
EUROPÄISCHE NORM
July 2009
ICS 91.010.30; 91.080.10
Supersedes for ENV 1999-1-1:1998
English version
Eurocode 9: Design of aluminium structures Part 1-1:General structural rules Eurocode 9: Calcul des structures en aluminium Partie 1-1: Règles générales
Eurocode 9: Bemessung und Konstruktion von Aluminiumtragwerken - Teil 1-1: Allgemeine Bemessungsregeln
This European Standard was approved by CEN on 18. September 2006. This amendment A1 modifies the European Standard EN 1999-1-1:2007; it was approved by CEN on 12 March 2009. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the 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 Management Centre has the same status as the official versions.
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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.
EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2009 CEN
All rights of exploitation in any form and by any means reserved worldwide for CEN national Members..
Ref. Nr. EN 1999-1-1:2007 + A1:2009 E
EN 1999-1-1: 2007 (E) + A1:2009 (E)
Content
Page
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Foreword ……………. ................................................................................................................................ 7 !Foreword of the Amendment 1 ............................................................................................................. 7 1 General ……………. .............................................................................................................. 11 1.1 Scope ........................................................................................................................................ 11 1.1.1 Scope of EN 1999 .................................................................................................................... 11 1.1.2 Scope of EN 1999-1-1 ............................................................................................................. 11 1.2 Normative references................................................................................................................ 12 1.2.1 General references ................................................................................................................... 12 1.2.2 References on structural design ............................................................................................... 12 1.2.3 References on aluminium alloys .............................................................................................. 12 1.2.4 References on welding ............................................................................................................. 14 1.2.5 Other references ....................................................................................................................... 14 1.3 Assumptions ............................................................................................................................. 15 1.4 Distinction between principles and application rules ............................................................... 15 1.5 Terms and definitions ............................................................................................................... 15 1.6 Symbols .................................................................................................................................... 15 1.7 Conventions for member axes .................................................................................................. 25 1.8 Specification for execution of the work ................................................................................... 26 2 Basis of design……………. .................................................................................................... 28 2.1 Requirements ............................................................................................................................ 28 2.1.1 Basic requirements................................................................................................................... 28 Reliability management ........................................................................................................... 28 2.1.2 2.1.3 Design working life, durability and robustness ....................................................................... 28 2.2 Principles of limit state design.................................................................................................. 28 2.3 Basic variables .......................................................................................................................... 28 2.3.1 Actions and environmental influences ..................................................................................... 28 2.3.2 Material and product properties ............................................................................................... 29 2.4 Verification by the partial factor method ................................................................................. 29 2.4.1 Design value of material properties ......................................................................................... 29 2.4.2 Design value of geometrical data............................................................................................. 29 2.4.3 Design resistances .................................................................................................................... 29 2.4.4 Verification of static equilibrium (EQU) ................................................................................. 29 2.5 Design assisted by testing ......................................................................................................... 29 3 Material……………. .............................................................................................................. 30 3.1 General ..................................................................................................................................... 30 3.2 Structural aluminium ................................................................................................................ 30 3.2.1 Range of materials ................................................................................................................... 30 3.2.2 Material properties for wrought aluminium alloys .................................................................. 31 3.2.3 Material properties for cast aluminium alloys ......................................................................... 35 3.2.4 Dimensions, mass and tolerances ............................................................................................ 36 3.2.5 Design values of material constants......................................................................................... 36 3.3 Connecting devices ................................................................................................................... 36 3.3.1 General..................................................................................................................................... 36 3.3.2 Bolts, nuts and washers............................................................................................................ 37 3.3.3 Rivets ....................................................................................................................................... 38 3.3.4 Welding consumables .............................................................................................................. 38 3.3.5 Adhesives................................................................................................................................. 38 4 Durability……………. ........................................................................................................... 40 5 Structural analysis ……………. ............................................................................................ 40 5.1 Structural modelling for analysis.............................................................................................. 40 5.1.1 Structural modelling and basic assumptions ............................................................................ 40 5.1.2 Joint modelling ........................................................................................................................ 40 5.1.3 Ground-structure interaction .................................................................................................... 40 5.2 Global analysis ......................................................................................................................... 40 5.2.1 Effects of deformed geometry of the structure ........................................................................ 40 5.2.2 Structural stability of frames ................................................................................................... 41 2
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EN 1999-1-1: 2007 (E) + A1:2009 (E)
5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.4 5.4.1 5.4.2 5.4.3 6 6.1 6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 6.1.6 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.2.7 6.2.8 6.2.9 6.2.10 6.2.11 6.3 6.3.1 6.3.2 6.3.3 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.5.5 6.5.6 6.6 6.6.1 6.6.2 6.6.3 6.6.4 6.6.5 6.6.6 6.7 6.7.1 6.7.2 6.7.3 6.7.4 6.7.5
Imperfections............................................................................................................................. 42 Basis ......................................................................................................................................... 42 Imperfections for global analysis of frames ............................................................................. 42 Imperfection for analysis of bracing systems ........................................................................... 46 Member imperfections ............................................................................................................. 48 Methods of analysis................................................................................................................... 49 General ..................................................................................................................................... 49 Elastic global analysis .............................................................................................................. 49 Plastic global analysis .............................................................................................................. 49 Ultimate limit states for members ……………. .................................................................... 49 Basis .......................................................................................................................................... 49 General ..................................................................................................................................... 49 Characteristic value of strength ................................................................................................ 49 Partial safety factors ................................................................................................................. 50 Classification of cross-sections ................................................................................................ 50 Local buckling resistance ......................................................................................................... 55 HAZ softening adjacent to welds ............................................................................................. 56 Resistance of cross-sections ...................................................................................................... 58 General ..................................................................................................................................... 58 Section properties ..................................................................................................................... 59 Tension ..................................................................................................................................... 60 Compression ............................................................................................................................. 61 Bending moment ...................................................................................................................... 61 Shear ......................................................................................................................................... 63 Torsion...................................................................................................................................... 64 Bending and shear .................................................................................................................... 65 Bending and axial force ............................................................................................................ 66 Bending, shear and axial force ................................................................................................. 67 Web bearing ............................................................................................................................. 67 Buckling resistance of members ............................................................................................... 68 Members in compression.......................................................................................................... 68 Members in bending ................................................................................................................. 72 Members in bending and axial compression ............................................................................ 74 Uniformed built-up members ....................................................................................................77 General ..................................................................................................................................... 77 Laced compression members .................................................................................................... 77 Battened compression members ............................................................................................... 80 Closely spaced built-up members ............................................................................................. 82 Un-stiffened plates under in-plane loading ............................................................................... 83 General ..................................................................................................................................... 83 Resistance under uniform compression .................................................................................... 83 Resistance under in-plane moment ........................................................................................... 84 Resistance under transverse or longitudinal stress gradient ..................................................... 85 Resistance under shear ............................................................................................................. 85 Resistance under combined action ........................................................................................... 86 Stiffened plates under in-plane loading ..................................................................................... 86 General ..................................................................................................................................... 86 Stiffened plates under uniform compression ............................................................................ 87 Stiffened plates under in-plane moment ................................................................................... 89 Longitudinal stress gradient on multi-stiffened plates ............................................................. 89 Multi-stiffened plating in shear ................................................................................................ 89 Buckling load for orthotropic plates ......................................................................................... 90 Plate girders ............................................................................................................................... 92 General ..................................................................................................................................... 92 Resistance of girders under in-plane bending........................................................................... 93 Resistance of girders with longitudinal web stiffeners ............................................................. 94 Resistance to shear ................................................................................................................... 95 Resistance to transverse loads .................................................................................................. 99 3
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EN 1999-1-1: 2007 (E) + A1:2009 (E)
6.7.6 6.7.7 6.7.8 6.8 6.8.1 6.8.2 7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 8 8.1 8.1.1 8.1.2 8.1.3 8.1.4 8.1.5 8.2 8.3 8.4 8.5 8.5.1 8.5.2 8.5.3 8.5.4 8.5.5 8.5.6 8.5.7 8.5.8 8.5.9 8.5.10 8.5.11 8.5.12 8.5.13 8.5.14 8.6 8.6.1 8.6.2 8.6.3 8.7 8.8 8.9
Interaction .............................................................................................................................. 102 Flange induced buckling ........................................................................................................ 103 Web stiffeners ........................................................................................................................ 104 Members with corrugated webs .............................................................................................. 105 Bending moment resistance ................................................................................................... 105 Shear force resistance ............................................................................................................ 106 Serviceability Limit States ……………. ............................................................................. 107 General ................................................................................................................................... 107 Serviceability limit states for buildings .................................................................................. 107 Vertical deflections ................................................................................................................ 107 Horizontal deflections ............................................................................................................ 107 Dynamic effects ..................................................................................................................... 107 Calculation of elastic deflection ............................................................................................ 107 Design of joints ……………. ................................................................................................ 108 Basis of design ........................................................................................................................ 108 Introduction ........................................................................................................................... 108 Applied forces and moments ................................................................................................. 108 Resistance of joints ................................................................................................................ 109 Design assumptions ............................................................................................................... 109 Fabrication and execution ...................................................................................................... 109 Intersections for bolted, riveted and welded joints ................................................................. 109 Joints loaded in shear subject to impact, vibration and/or load reversal ................................ 109 Classification of joints ............................................................................................................ 110 Connections made with bolts, rivets and pins ........................................................................ 110 Positioning of holes for bolts and rivets ................................................................................ 110 Deductions for fastener holes ................................................................................................ 113 Categories of bolted connections ........................................................................................... 114 Distribution of forces between fasteners ............................................................................... 116 Design resistances of bolts..................................................................................................... 117 Design resistance of rivets ..................................................................................................... 119 Countersunk bolts and rivets ................................................................................................. 119 Hollow rivets and rivets with mandrel ................................................................................... 120 High strength bolts in slip-resistant connections ................................................................... 120 Prying forces .......................................................................................................................... 121 Long joints ............................................................................................................................. 122 Single lap joints with fasteners in one row ............................................................................ 122 Fasteners through packings.................................................................................................... 123 Pin connections ...................................................................................................................... 123 Welded connections................................................................................................................ 125 General................................................................................................................................... 125 Heat-affected zone (HAZ) ..................................................................................................... 126 Design of welded connections ............................................................................................... 126 Hybrid connections ................................................................................................................. 133 Adhesive bonded connections ................................................................................................ 133 Other joining methods ............................................................................................................ 133
!Annex A (informative) Reliability differentiation .............................................................................. 134 A.1 A.2 A.3 A.4 A.5 A.6
Introduction ............................................................................................................................ 134 Design provisions for reliability differentiation - Design supervision levels ......................... 134 Execution provisions for reliability differentiation – Execution classes ................................ 134 Governing factors for choice of execution class..................................................................... 134 Determination of execution class ........................................................................................... 135 Utilization grades.................................................................................................................... 135
Annex B (normative) Equivalent T-stub in tension .................................................................................. 136 B.1
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General rules for evaluation of resistance .............................................................................. 136
EN 1999-1-1: 2007 (E) + A1:2009 (E)
B.2
Individual bolt-row, bolt-groups and groups of bolt-rows ...................................................... 140
Annex C (informative) Materials selection ................................................................................................. 142 C.1 C.2 C.2.1 C.2.2 C.3 C.3.1 C.3.2 C.3.3 C.3.4 C.4 C.4.1 C.4.2
General .................................................................................................................................... 142 Wrought products .................................................................................................................... 142 Wrought heat treatable alloys ................................................................................................. 142 Wrought non-heat treatable alloys.......................................................................................... 144 Cast products ........................................................................................................................... 145 General ................................................................................................................................... 145 Heat treatable casting alloys EN AC-42100, EN AC-42200, EN AC-43000 and EN AC-43300 ......................................................................................................................... 145 Non-heat treatable casting alloys EN AC-44200 and EN AC-51300..................................... 145 Special design rules for castings............................................................................................. 146 Connecting devices ................................................................................................................. 147 Aluminium bolts ..................................................................................................................... 147 Aluminium rivets .................................................................................................................... 147
Annex D (informative) Corrosion and surface protection ........................................................................ 148 D.1 D.2 D.3 D.3.1 D.3.2 D.3.3 D.3.4
Corrosion of aluminium under various exposure conditions .................................................. 148 Durability ratings of aluminium alloys ................................................................................... 148 Corrosion protection................................................................................................................ 149 General ................................................................................................................................... 149 Overall corrosion protection of structural aluminium ............................................................ 149 Aluminium in contact with aluminium and other metals ....................................................... 150 Aluminium surfaces in contact with non-metallic materials .................................................. 150
Annex E (informative) Analytical models for stress strain relationship ................................................. 154
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E.1 E.2 E.2.1 E.2.2 E.3
Scope ....................................................................................................................................... 154 Analytical models.................................................................................................................... 154 Piecewise linear models ......................................................................................................... 154 Continuous models ................................................................................................................. 156 Approximate evaluation of εu .................................................................................................. 159
Annex F (informative) Behaviour of cross-sections beyond the elastic limit........................................... 160 F.1 F.2 F.3 F.4 F.5
General .................................................................................................................................... 160 Definition of cross-section limit states .................................................................................... 160 Classification of cross-sections according to limit states ........................................................ 160 Evaluation of ultimate axial load ............................................................................................ 161 Evaluation of ultimate bending moment ................................................................................. 162
Annex G (informative) Rotation capacity .................................................................................................. 164 Annex H (informative) Plastic hinge method for continuous beams ....................................................... 166 Annex I (informative) Lateral torsional buckling of beams and torsional or torsional-flexural buckling of compressed members ........................................................................................ 168 I.1 Elastic critical moment and slenderness.................................................................................. 168 I.1.1 Basis ........................................................................................................................................... 168 I.1.2 General formula for beams with uniform cross-sections symmetrical about the minor or major axis ................................................................................................................................... 168 I.1.3 Beams with uniform cross-sections symmetrical about major axis, centrally symmetric and doubly symmetric cross-sections ................................................................................................ 173 I.1.4 Cantilevers with uniform cross-sections symmetrical about the minor axis .............................. 173 I.2 Slenderness for lateral torsional buckling ............................................................................... 176 I.3 Elastic critical axial force for torsional and torsional-flexural buckling ................................. 178 I.4 Slenderness for torsional and torsional-flexural buckling ....................................................... 179 Annex J (informative) Properties of cross sections.................................................................................... 184 5
EN 1999-1-1: 2007 (E) + A1:2009 (E)
J.1 J.2 J.3 J.4 J.5 J.6
Torsion constant It .................................................................................................................. 184 Position of shear centre S ....................................................................................................... 184 Warping constant Iw................................................................................................................ 184 Cross section constants for open thin-walled cross sections .................................................. 188 Cross section constants for open cross section with branches ................................................ 190 Torsion constant and shear !centre" of cross section with closed part .......................... 190
Annex K (informative) Shear lag effects in member design .................................................................... 191 K.1 K.2 K.2.1 K.2.2 K.2.3 K.3
General ................................................................................................................................... 191 Effective width for elastic shear lag ....................................................................................... 191 Effective width factor for shear lag ........................................................................................ 191 Stress distribution for shear lag ............................................................................................. 192 In-plane load effects .............................................................................................................. 193 Shear lag at ultimate limit states ............................................................................................. 194
Annex L (informative) Classification of joints .......................................................................................... 195 L.1 L.2 L.3 L.4 L.5 L.6 L.7 L.8 L.8.1 L.8.2 L.8.3
General ................................................................................................................................... 195 Fully restoring connections .................................................................................................... 196 Partially restoring connections ............................................................................................... 196 Classification according to rigidity......................................................................................... 197 Classification according to strength ....................................................................................... 197 Classification according to ductility ....................................................................................... 197 General design requirements for connections ........................................................................ 197 Requirements for framing connections................................................................................... 197 General................................................................................................................................... 197 Nominally pinned connections .............................................................................................. 198 Built-in connections ............................................................................................................... 199
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Annex M (informative) Adhesive bonded connections ............................................................................. 200 M.1 M.2 M.3 M.3.1 M.3.2 M.3.3 M.4
General ................................................................................................................................... 200 Adhesives ............................................................................................................................... 200 Design of adhesive bonded joints ........................................................................................... 201 General................................................................................................................................... 201 Characteristic strength of adhesives ...................................................................................... 202 Design shear stress ................................................................................................................. 202 Tests........................................................................................................................................ 202
Bibliography ................................................................................................................................................ 203
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EN 1999-1-1: 2007 (E) + A1:2009 (E)
Foreword This European Standard (EN 1999-1-1:2007) has been prepared by Technical Committee CEN/TC 250 «Structural Eurocodes», the secretariat of which is held by BSI. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by August 2007, and conflicting national standards shall be withdrawn at the latest by March 2010. This European Standard supersedes ENV 1999-1-1:1998. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom.
!Foreword of the Amendment A1 This document (EN 1991-1-1:2005/A1:2009) has been prepared by Technical Committee CEN/TC 250 “Structural Eurocodes”, the secretariat of which is held by BSI. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by July 2010, and conflicting national standards shall be withdrawn at the latest by January 2010.
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Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights. 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, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom."
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EN 1999-1-1: 2007 (E) + A1:2009 (E)
Background of the Eurocode programme In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications. Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works, which in a first stage would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them. For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980s. In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement1) between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products – CPD – and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).
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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
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)
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).
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