(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "EN 1990: Eurocode - Basis of structural design"

l^-jsSi-. 



The European Union 

S^ EDICT OF GOVERNMENT "^1 

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. 



EN 1990 (2002) (English) : Eurocode - Basis of structural 
design [Authority: The European Union Per Regulation 
305/2011, Directive 98/34/EC, Directive 2004/18/EC] 




J,^!:''" 



BLANK PAGE 



^*-^^^ 





PROTECTED BY COPYRIGHT 



EUROPEAN STANDARD EN 1990:2002+A1 

NORME EUROPEENNE 

EUROPAlSCHE NORM December 2005 

ICS 91.010.30 Supersedes ENV 1991-1:1994 

Incorporating corrigenda December 2008 
and April 2010 

English version 

Eurocode - Basis of structural design 



Eurocodes structuraux - Eurocodes: Bases de calcul des Eurocode; Grundlagen der Tragwerksplanung 

structures 

This European Standard was approved by GEN on 29 November 2001. 

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. 

CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, 
Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom. 




EUROPEAN COMMITTEE FOR STANDARDIZATION 
COMITE EUROPEEN DE NORMALISATION 
EUROPAISCHES KOMITEE FUR NORMUNG 



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



© 2002 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 1990:2002 

worldwide for CEN national Members. 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Contents Page 

FOREWORD 5 

Background of the Eurocode programme 6 

Status AND FIELD OF APPLICATION OF EUROCODES 7 

National Standards IMPLEMENTING EuROCODES 7 

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

products 8 

Additional information specific TO EN 1990 8 

National annex for EN 1990 12 

SECTION 1 GENERAL 12 

1.1 Scope 12 

1.2 Normative references 12 

1.3 Assumptions 13 

1.4 Distinction BETWEEN Principles AND Application Rules 13 

1.5 Terms AND DEFINITIONS 14 

7.5.7 Common terms used in EN 1990 to EN 1999 14 

1.5.2 Special terms relating to design in general 75 

1.5.3 Terms relating to actions 18 

1.5.4 Terms relating to material and product properties 21 

1.5.5 Terms relating to geometrical data 21 

1.5.6 Terms relating to structural analysis 22 

1.6 Symbols 23 

SECTION 2 REQUIREMENTS 26 

2.1 Basic REQUIREMENTS 26 

2.2 Reliability MANAGEMENT 27 

2.3 Design WORKING LIFE 28 

2.4 Durability 28 

2.5 Quality MANAGEMENT 29 

SECTION 3 PRINCIPLES OF LIMIT STATES DESIGN 30 

3.1 General 30 

3.2 Design situations 30 

3.3 Ultimate LIMIT STATES 31 

3.4 Serviceability LIMIT states 31 

3.5 Limit STATE DESIGN 32 

SECTION 4 BASIC VARIABLES 33 

4.1 Actions AND ENVIRONMENTAL INFLUENCES 33 

^.7.7 Classification of actions 33 

4.1.2 Characteristic values of actions 33 

4.1.3 Other representative values of variable actions 35 

4.1.4 Representation of fatigue actions 35 

4 J, 5 Representation of dynamic actions 35 

4.1.6 Geotechnical actions 36 

4.1.7 Environmental influences 36 

4.2 Material AND PRODUCT PROPERTIES 36 

4.3 Geometrical DATA 37 

SECTION 5 STRUCTURAL ANALYSIS AND DESIGN ASSISTED BY TESTING 38 

5.1 Structural ANALYSIS 38 

5.7.7 Structural modelling 38 

5.1.2 Static actions 38 

5.1.3 Dynamic actions 38 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

5. L4 Fire design 39 

5.2 Design ASSISTED BY TESTING 40 

SECTION 6 VERIFICATION BY THE PARTIAL FACTOR METHOD 41 

6.1 General 41 

6.2 Limitations 41 

6.3 Design VALUES 41 

63 J Design values of actions 41 

6.3.2 Design values of the effects of actions 42 

6.3.3 Design values of material or product properties 43 

63.4 Design values of geometrical data 43 

6.3.5 Design resistance 44 

6.4 Ultimate LIMIT STATES 45 

6.4.1 General 45 

6.4.2 Verifications of static equiUbrium and resistance 46 

6.4.3 Combination of actions (fatigue verifications excluded) 46 

6.4.3.1 General 46 

6.4.3.2 Combinations of actions for persistent or transient design situations (fundamental combinations). ...47 

6.4.3.3 Combinations of actions for accidental design situations 48 

6.4.3.4 Combinations of actions for seismic design situations 48 

6.4.4 Partial factors for actions and combinations of actions 48 

6.4.5 Partial factors for materials and products 49 

6.5 Serviceability LIMIT STATES 49 

6.5.1 Verifications 49 

6.5.2 Serviceability criteria 49 

6.5.3 Combination of actions 49 

6.5.4 Partial factors for materials 50 

ANNEX Al (NORMATIVE) APPLICATION FOR BUILDINGS 51 

Al.l Field OF APPLICATION 51 

AL2 Combinations OF actions 51 

Al. 2.1 General 51 

Al.2.2 Values of \\f factors 51 

A1.3 Ultimate LIMIT STATES 52 

A 1.3.1 Design values of actions in persistent and transient design situations 52 

A 1.3. 2 Design values of actions in the accidental and seismic design situations 56 

A1.4 Serviceability LIMIT STATES 57 

A 1.4.1 Partial factors for actions 57 

Al.4.2 Serviceability criteria 57 

A 1.4. 3 Deformations and horizontal displacements 57 

Al.4.4 Vibrations 59 

ANNEX A2 (NORMATIVE) APPLICATION FOR BRIDGES 60 

National Annex for EN 1990 Annex A2 60 

A2.1 Field OF APPLICATION 62 

A2.2 Combinations OF ACTIONS 63 

A2.2.1 General 63 

A2.2.2 Combination rides for road bridges 65 

A2.2.3 Combination rides for footbridges 66 

A2.2.4 Combination rules for railway bridges 66 

A.2.2. 5 Combinations of actions for accidental (non seismic) design situations 67 

A2.2.6 Values of yj factors 67 

A2.3 Ultimate LIMIT STATES 70 

A2.3.1 Design values of actions in persistent and transient design situations 70 

A2. 3.2 Design values of actions in the accidental and seismic design situations 75 

A2.4SERVlCEABrLITY AND OTHER SPECIFIC LIMIT STATES 76 

A2.4.1 General 76 

A2.4.2 Seiyiceahility criteria regarding deformation and vibration for road bridges 77 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

A2. 4, 3 Verifications concerning vibration for footbridges due to pedestrian trafic 77 

A2.4.4 Verifications regarding deformations and vibrations for railway bridges 79 

ANNEX B (INFORMATIVE) MANAGEMENT OF STRUCTURAL RELIABILITY FOR 
CONSTRUCTION WORKS 86 

Bl Scope AND FIELD OF APPLICATION 86 

B2 Symbols 86 

B3 Reliability DIFFERENTIATION 87 

B3J Consequences classes 87 

B 3 .2 Differentiation by p values 87 

B3.3 Differentiation by measures relating to the partial factors 88 

B4 Design SUPERVISION DIFFERENTIATION 88 

B5 Inspection DURING EXECUTION 89 

B6 Partial FACTORS FOR RESISTANCE PROPERTIES 90 

ANNEX C (INFORMATIVE) BASIS FOR PARTIAL FACTOR DESIGN AND RELIABILITY 
ANALYSIS 91 

CI Scope AND Field OF Applications 91 

C2 Symbols 91 

C3 Introduction 92 

C4 Overview OF reliability METHODS 92 

C5 Reliability INDEX y9. 93 

C6 Target values OF reliability INDEX/? 94 

C7 Approach for calibration of design values 95 

C8 Reliability VERIFICATION formats IN EuROCODES 97 

C9 Partial factors IN EN 1990 98 

ClO ^factors 99 

ANNEX D (INFORMATIVE) DESIGN ASSISTED BY TESTING 101 

Dl Scope AND FIELD OF application 101 

D2 Symbols 101 

D3 Types OF tests 102 

D4 Planning OF tests 103 

D5 Derivation OF DESIGN values 105 

D6 General principles FOR statistical evaluations 106 

D7 Statistical DETERMINATION OF A SINGLE PROPERTY 106 

D7.1 General 106 

D7. 2 Assessment via the characteristic value 107 

D7.3 Direct assessment of the design value for ULS verifications 108 

D8 Statistical DETERMINATION OF RESISTANCE MODELS 109 

D8.1 General 109 

D8,2 Standard evaluation procedure (Method (a)) 109 

D8.2.1 General 109 

D8.2.2 Standard procedure 110 

D8.3 Standard evaluation procedure (Method (b)) 114 

D8.4 Use of additional prior knowledge 114 

BIBLIOGRAPHY 116 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Foreword 

This document (EN 1990:2002) 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 October 2002, and 
conflicting national standards shall be withdrawn at the latest by March 2010. 

This document supersedes ENV 1991-1:1994. 

CEN/TC 250 is responsible for all Structural Eurocodes. 

According to the CEN/CENELEC Internal Regulations, the national standards 
organizations of the following countries are bound to implement this European 
Standard: Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, 
Greece, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, 
Spain, Sweden, Switzerland and the United Kingdom. 



Foreword to amendment Al 

This European Standard (EN 1990:2002/A1:2005) has been prepared by Technical 
Committee CEN/TC 250 "Structural Eurocodes", the secretariat of which is held by 
BSL 

This Amendment to the EN 1990:2002 shall be given the status of a national standard, 
either by publication of an identical text or by endorsement, at the latest by June 2006, 
and conflicting national standards shall be withdrawn at the latest by June 2006. 

According to the CEN/CENELEC Internal Regulations, the national standards 
organizations of the following countries are bound to implement this European 
Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, 
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, 
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, 
Spain, Sweden, Switzerland and United Kingdom. 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(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 Ec^ national provisions ^ in force in the Member 
States and, ultimately, would replace them. 

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

In 1989, the Commission and the Member States of the EU and EFTA decided, on the 
basis of an agreement' between the Commission and CEN, to transfer the preparation 
and the publication of the Eurocodes to 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 Direcfives and/or Commission's De- 
cisions dealing with European standards {e.g. the Council Directive 89/106/EEC on 
construction products - CPD - and [aS> Council Directives 2004/1 7/EC and 2004/1 8/EC (Aca 
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 con- 
sisting of a number of Parts: 

EN 1990 Eurocode : 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 Mem- 
ber 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. 



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



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



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 Re- 
quirement N^^l - 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^ referred to in Article 12 of the CPD, 
although they are of a different nature from hannonised product standards^ 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 stan- 
dards [AC2) and ETAGs <acO 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 ES) parts of works and structural construction (a£3 products 
of both a traditional and an in-novative 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. 

The National annex 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. : 



2 . 

According to Art. 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the 
creation of the necessary links between the essential requirements and the mandates for harmonised ENs and ETAGs/ETAs. 
According to Art. 12 of the CPD the interpretative documents shall : 

a) 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 ; 

b) indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g. methods of calcula- 
tion and of proof, technical rules for project design, etc. ; 

c) 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. 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

- values and/or classes where alternatives are given in the Eurocode, 

- values to be used where a symbol only is given in the Eurocode, 

- country specific data (geographical, climatic, etc.), e.g. snow map, 

- the procedure to be used where alternative procedures are given in the Eurocode-. 
It may also contain 

- decisions on the application of informative annexes, 

- references to non-contradictory complementary information to assist the user to ap- 
ply the Eurocode. 

Links between Eurocodes and harmonised technical specifications 
(ENs and ETAs) for products 

There is a need for consistency between the harmonised technical specifications for 
construction products and the E) technical provisions <acD for works^ Furthermore, all 
the information accompanying the CE Marking of the construction products which |Aci)use 
the <a51 Euro- codes shall clearly mention which Nationally Determined Parameters have 
been taken into account. 

Additional information specific to EN 1990 

EN 1990 describes the Principles and requirements for safety, serviceability and dura- 
bility of structures. It is based on the limit state concept used in conjunction with a par- 
tial factor method. 

For the design of new structures, EN 1990 is intended to be used, for direct application, 
together with Eurocodes EN 1991 to 1999. 

EN 1990 also gives guidelines for the aspects of structural reliability relating to safety, 
serviceability and durability : 
- for design cases not covered by EN 1991 to EN 1999 (other actions, structures not 

treated, other materials) ; 
~ to serve as a reference document for other CEN TCs concerning structural matters. 

EN 1990 is intended for use by : 

- committees drafting standards for structural design and related product, testing and 
execution standards ; 

- clients (e.g. for the formulation of their specific requirements on reliability levels and 
durability) ; 

- designers and constructors ; 

- relevant authorities. 

EN 1990 may be used, when relevant, as a guidance document for the design of struc- 
tures outside the scope of the Eurocodes EN 1991 to EN 1999, for : 

- assessing other actions and their combinations ; 

- modelling material and structural behaviour ; 

- assessing numerical values of the reliability format. 



^ see Art.3.3 and Art.l2 of the CPD, as well as 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1. 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

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 of quality management applies. 
When EN 1990 is used as a base document by other CEN/TCs the same values need to 
be taken. 

National annex for EN 1990 

This standard gives alternative procedures, values and recommendations for classes 
with notes indicating where national choices may have to be made. Therefore the Na- 
tional Standard implementing EN 1990 should have a National annex containing all 
Nationally Determined Parameters to be used for the design of buildings and civil engi- 
neering works to be constructed in the relevant country. 

|Ac£> National choice is allowed in EN 1990 Annex Al through;^ 

- ALl(l) 

- A1.2.1(l) 

- Al.2.2 (Table Al.l) 

- A1.3.1(l) (Tables A1.2(A) to (C)) 

- A1.3.1(5) 

- Al.3.2 (Table A1.3) 

- Al. 4.2(2) 

E5) National choice is allowed in EN 1990 Annex A2 through: 

General clauses 



Clause 


Item 


A2.1 (1) NOTE 3 


Use of Table 2.1 : Design working life 


A2.2. 1(2) NOTE 1 


Combinations involving actions which are outside the scope of 
EN 1991 


A2.2.6(1)N0TE1 


Values of {i^ factors 


A2.3.1(l) 


Alteration of design values of actions for uhimate limit states 


A2.3.1(5) 


Choice of Approach 1, 2 or 3 


A2.3.1(7) 


Definition of forces due to ice pressure 


A2.3.1(8) 


Values of ;^ factors for prestressing actions where not specified 
in the relevant design Eurocodes 


A2.3.1 Table 
A2.4(A) NOTES 1 
and 2 


Values of 7 factors 


A2.3.1 Table 
A2.4(B) 


- NOTE 1 : choice between 6.10 and 6.10a/b 

- NOTE 2 : Values of y and ^factors 

- NOTE 4 : Values of ^d 



(M 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



[Ag) 







A2.3.1 Table 
A2.4(C) 


Values of ^factors 


A2.3.2(l) 


Design values in Table A2.5 for accidental designs situations, 
design values of accompanying variable actions and seismic 
design situations 


A2.3.2TableA2.5 
NOTE 


Design values of actions 


A2.4.1(l) 
NOTE 1 (Table 
A2.6) 
NOTE 2 


Alternative /values for traffic actions for the serviceability 

limit state 

Infrequent combination of actions 


A2.4.1(2) 


Serviceability requirements and criteria for the calculation of 
defonnations 



Clauses specific for road bridges 



Clause 


Item 


A2.2.2 (1) 


Reference to the infrequent combination of actions 


A2.2.2(3) 


Combination rules for special vehicles 


A2.2.2(4) 


Combination rules for snow loads and traffic loads 


A2.2.2(6) 


Combination rules for wind and thermal actions 


A2.2.6(l)NOTE2 


Values of y/unfy factors 


A2.2.6(l)NOTE3 


Values of water forces 



Clauses specific for footbridges 



Clause 


Item 


A2.2.3(2) 


Combination rules for wind and thermal actions 


A2.2.3(3) 


Combination rules for snow loads and traffic loads 


A2.2.3(4) 


Combination rules for footbridges protected from bad weather 


A2.4.3.2(l) 


Comfort criteria for footbridges 



Clauses specific for railway bridges 



Clause 


Item 


A2.2.4(l) 


Combination rules for snow loading on railway bridges 


A2.2.4(4) 


Maximum wind speed compatible with rail traffic 


A2.4.4.1(l)NOTE3 


Deformation and vibration requirements for temporary 
railway bridges 


A2.4.4.2.1(4)P 


Peak values of deck acceleration for railway bridges and 
associated frequency range 


A2.4.4.2.2~ Table 
A2.7 NOTE 


Limiting values of deck twist for railway bridges 



(M 



10 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005{E) 



f^ 



A2,4.4.2.2(3)P 


Limiting values of the total deck twist for railway bridges 


A2.4.4.2.3(l) 


Vertical deformation of ballasted and non ballasted railway 
bridges 


A2.4.4,2.3(2) 


Limitations on the rotations of non-ballasted bridge deck ends 
for railway bridges 


A2.4.4.2.3(3) 


Additional limits of angular rotations at the end of decks 


A2.4.4.2.4(2) - 
Table A2.8 NOTE 3 


Values of CA and n factors 


A2.4.4.2.4(3) 


Minimum lateral frequency for railway bridges 


A2.4.4.3.2(6) 


Requirements for passenger comfort for temporary bridges 



^ 



11 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Section 1 General 

1.1 Scope 

(1) EN 1990 establishes Principles and requirements for the safety, serviceability and 
durability of structures, describes the basis for their design and verification and gives 
guideUnes for related aspects of structural reliabihty. 

(2) EN 1990 is intended to be used in conjunction with EN 1991 to EN 1999 for the 
structural design of buildings and civil engineering works, including geotechnical as- 
pects, structural fire design, situations involving earthquakes, execution and temporary 
structures. 

NOTE For the design of special construction works {e.g, nuclear installations, dams, etc.), other provi- 
sions than those in EN 1990 to EN 1999 might be necessary. 

(3) EN 1990 is apphcable for the design of structures where other materials or other 
actions outside the scope of EN 1991 to EN 1999 are involved. 

(4) EN 1990 is applicable for the structural appraisal of existing construction, in devel- 
oping the design of repairs and alterations or in assessing changes of use. 

NOTE Additional or amended provisions might be necessary where appropriate. 

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 amend- 
ments to or revisions of any of these pubHcations apply to this European Standard only 
when incorporated in it by amendment or revision. For undated references the latest 
edition of the pubHcation referred to applies (including amendments). 

NOTE The Eurocodes were published as European Prestandards. The following European Standards which 
are published or in preparation are cited in nomiative clauses : 

EN 1991 Eurocode 1 : Actions on structures 

EN 1992 Eurocode 2 : Design of concrete struclxires 

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 



12 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

EN 1997 Eurocode 7 : Geotechnical design 

EN 1998 Eurocode 8 : Design of structures for earthquake resistance 

EN 1999 Eurocode 9 : Design of aluminium structures 

1.3 Assumptions 

(1) Design which employs the Principles and Application Rules is deemed to meet the 
requirements provided the assumptions given in EN 1990 to EN 1999 are satisfied (see 
Section 2). 

(2) The general assumptions of EN 1990 are : 

- the choice of the structural system and the design of the structure is made by appro- 
priately qualified and experienced personnel; 

- execution is carried out by personnel having the appropriate skill and experience; 

[Ac^ - adequate supervision and quality control is provided during design and during 
execution of the work, i.e., factories, plants, and on site; <acO 

- the construction materials and products are used as specified in EN 1990 or in 
EN 1991 to EN 1999 or in the relevant execution standards, or reference material or 
product specifications; 

- the structure will be adequately maintained; 

- the structure will be used in accordance with the design assumptions. 

NOTE There may be cases when the above assumptions need to be supplemented. 

1.4 Distinction between Principles and Application Rules 

(1) Depending on the character of the individual clauses, distinction is made in EN 1990 
between Principles and Application Rules. 

(2) The Principles comprise : 

- general statements and definitions for which there is no alternative, as well as ; 

- requirements and analytical models for which no alternative is permitted unless spe- 
cifically stated. 

(3) The Principles are identified by the letter P following the paragraph number. 

(4) The Application Rules are generally recognised rules which comply with the Princi- 
ples and satisfy their requirements. 

(5) It is peraiissible to use alternative design rules different from the Apphcation Rules 
given in EN 1990 for works, provided that it is shown that the alternative rules accord 
with the relevant Principles and are at least equivalent with regard to the structural 
safety, serviceability and durability which would be expected when using the Eurocodes. 



13 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

NOTE If an alternative design rule is substituted for an application rule, the resulting design cannot be 
claimed to be wholly in accordance with EN 1990 although the design will remain in accordance with the 
Principles of EN 1990. When EN 1990 is used in respect of a property listed in an Annex Z of a product 
standard or an ETAG, the use of an alternative design rule may not be acceptable for CE marking. 

(6) In EN 1990, the Application Rules are identified by a number in brackets e.g. as this 
clause. 

1.5 Terms and definitions 

NOTE For the purposes of this European Standard, the terms and definitions are derived from ISO 2394, 
ISO 3898, ISO 8930, ISO 8402. 

1.5.1 Common terms used in EN 1990 to EN 1999 

1.5.1.1 
construction works 

everything that is constructed or results from construction operations 

NOTE This definition accords with ISO 6707-1. The tenn covers both building and civil engineering works. 
It refers to the complete construction works comprising structural, non-structural and geotechnical elements. 

1.5.1.2 

type of building or civil engineering works 

type of construction works designating its intended purpose, e.g. dwelling house, retain- 
ing wall, industrial building, road bridge 

1.5.1.3 

type of construction 

indication of the principal structural material, e.g. reinforced concrete construction, 
steel construction, timber construction, masonry construction, steel and concrete com- 
posite construction 

1.5.1.4 

method of construction 

manner in which the execution will be carried out, e.g. cast in place, prefabricated, can- 
tilevered 

1.5.1.5 

construction material 

material used in construction work, e.g. concrete, steel, timber, masonry 

1.5.1.6 
structure 

organised combination of connected parts designed to carry loads and provide adequate 
rigidity 



14 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005{E) 

1.5.1.7 

structural member 

physically distinguishable part of a structure, e.g, a column, a beam, a slab, a foundation 
pile 

1.5.1.8 

form of structure 

arrangement of structural members 

NOTE Fonns of structure are, for example, frames, suspension bridges. 

1.5.1.9 
structural system 

load-bearing members of a building or civil engineering works and the way in which 
these members function together 

1.5.1.10 
structural model 

idealisation of the structural system used for the purposes of analysis, design and verifi- 
cation 

1.5.1.11 
execution 

all activities carried out for the physical completion of the work including procurement, 
the inspection and documentation thereof 

NOTE The tenn covers work on site; it may also signify the fabrication of components off site and their 
subsequent erection on site. 

1.5.2 Special terms relating to design in general 

1.5.2.1 
design criteria 

quantitative formulations that describe for each limit state the conditions to be fulfilled 

1.5.2.2 

design situations 

sets of physical conditions representing the real conditions occurring during a certain 
time interval for which the design will demonstrate that relevant limit states are not ex- 
ceeded 

1.5.2.3 

transient design situation 

design situation that is relevant during a period much shorter than the design working 
Hfe of the structure and which has a high probability of occurrence 

NOTE A transient design situation refers to temporary conditions of the structure, of use, or exposure, e.g. 
during construction or repair. 



15 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

1.5.2.4 

persistent design situation 

design situation that is relevant during a period of the same order as the design working 
hfe of the structure 

NOTE Generally it refers to conditions of nonnal use. 

L5.2.5 

accidental design situation 

design situation involving exceptional conditions of the structure or its exposure, in- 
cluding fire, explosion, impact or local failure 

1.5.2.6 
fire design 

design of a structure to fulfil the required performance in case of fire 

1.5.2.7 

seismic design situation 

design situation involving exceptional conditions of the structure when subjected to a 
seismic event 

1.5.2.8 

design working life 

assumed period for which a structure or part of it is to be used for its intended purpose 
with anticipated maintenance but without major repair being necessary 

1.5.2.9 
hazard 

for the purpose of EN 1990 to EN 1999, an unusual and severe event, e.g. an abnormal 
action or environmental influence, insufficient strength or resistance, or excessive de- 
viation from intended dimensions 

1.5.2.10 

load arrangement 

identification of the position, magnitude and direction of a free action 

1.5.2.11 
load case 

compatible load an'angements, sets of deformations and imperfections considered si- 
multaneously with fixed variable actions and permanent actions for a particular verifica- 
tion 

1.5.2.12 
limit states 

states beyond which the structure no longer fulfils the relevant design criteria 

1.5.2.13 

ultimate limit states 

states associated with collapse or with other similar forms of stmctural failure 



16 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

NOTE They generally correspond to the maximLim load-carrying resistance of a structure or structural 
member. 

1.5.2.14 

serviceability limit states 

states that correspond to conditions beyond which specified service requirements for a 
structure or structural member are no longer met 

1.5.2.14.1 

irreversible serviceability limit states 

serviceability limit states where some consequences of actions exceeding the specified 
sei-vice requirements will remain when the actions are removed 

1.5.2.14.2 

reversible serviceability limit states 

serviceability limit states where no consequences of actions exceeding the specified 
sei^vice requirements will remain when the actions are removed 

1.5.2.14.3 
serviceability criterion 

design criterion for a serviceability limit state 

1.5.2.15 
resistance 

capacity of a member or component, or a cross-section of a member or component of a 
structure, to withstand actions without mechanical failure e,g, bending resistance, buck- 
ling resistance, tension resistance 

1.5.2.16 
strength 

mechanical property of a material indicating its ability to resist actions, usually given in 
units of stress 

1.5.2.17 
reliability 

ability of a structure or a structural member to fulfil the specified requirements, includ- 
ing the design working life, for which it has been designed. Reliability is usually ex- 
pressed in probabilistic terms 

NOTE Reliability covers safety, serviceability and durability of a structure. 

1.5.2.18 

reliability differentiation 

measures intended for the socio-economic optimisation of the resources to be used to 
build construction works, taking into account all the expected consequences of failures 
and the cost of the construction works 



17 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

1.5.2.19 

basic variable 

part of a specified set of variables representing physical quantities which characterise 
actions and environmental influences, geometrical quantities, and material properties 
including soil properties 

1.5.2.20 
maintenance 

set of activities performed during the working life of the structure in order to enable it to 
fulfil the requirements for reliability 

NOTE Activities to restore the structure after an accidental or seismic event are normally outside the 
scope of maintenance. 

1.5.2.21 
repair 

activities performed to preserve or to restore the function of a structure that fall outside 
the definition of maintenance 

1.5.2.22 
nominal value 

value fixed on non-statistical bases, for instance on acquired experience or on physical 
conditions 

1.5.3 Terms relating to actions 

1.5.3.1 
action (F) 

a) Set of forces (loads) appHed to the structure (direct action); 

b) Set of imposed deformations or accelerations caused for example, by temperature 
changes, moisture variation, uneven settlement or earthquakes (indirect action). 

1.5.3.2 

effect of action (E) 

effect of actions (or action effect) on structural members, {e.g. internal force, moment, 
stress, strain) or on the whole structure {e.g. deflection, rotation) 

1.5.3.3 

permanent action (G) 

action that is likely to act throughout a given reference period and for which the varia- 
tion in magnitude with time is negligible, or for which the variation is always in the 
same direction (monotonic) until the action attains a certain limit value 

1.5.3.4 

variable action (0 

action for which the variation in magnitTide with time is neither negligible nor mono- 
tonic 



18 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

1.5.3.5 

accidental action (A) 

action, usually of short duration but of significant magnitude, that is unlikely to occur 
on a given structure during the design working life 

NOTE 1 An accidental action can be expected in many cases to cause severe consequences unless appropri- 
ate measures are taken. 

NOTE 2 Impact, snow, wind and seismic actions may be variable or accidental actions, depending on the 
available infomiation on statistical distributions. 

1.5.3.6 

seismic action (Ae) 

action that arises due to earthquake ground motions 

1.5.3.7 
geotechnical action 

action transmitted to the structure by the ground, fill or groundwater 

1.5.3.8 
fixed action 

action that has a fixed distribution and position over the structure or structural member 
such that the magnitude and direction of the action are determined unambiguously for 
the whole structure or structural member if this magnitude and direction are determined 
at one point on the structure or structural member 

1.5.3.9 

free action 

action that may have various spatial distributions over the structiire 

1.5.3.10 
single action 

action that can be assumed to be statistically independent in time and space of any other 
action acting on the structure 

1.5.3.11 

static action 

action that does not cause significant acceleration of the structure or structural members 

1.5.3.12 
dynamic action 

action that causes significant acceleration of the stmcture or structural members 

1.5.3.13 

quasi-static action 

dynamic action represented by an equivalent static action in a static model 

1.5.3.14 

characteristic value of an action (Fk) 

principal representative value of an action 



19 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



NOTE In so far as a characteristic value can be fixed on statistical bases, it is chosen so as to correspond to 
a prescribed probability of not being exceeded on the unfavourable side during a "reference period" taking 
into account the design working life of the staicture and the duration of the design situation. 

1.5.3.15 
reference period 

chosen period of time that is used as a basis for assessing statistically variable actions, 
and possibly for accidental actions 

1.5.3.16 

combination value of a variable action (^ gk) 

value chosen - in so far as it can be fixed on statistical bases - so that the probability that 
the effects caused by the combination will be exceeded is approximately the same as by 
the characteristic value of an individual action. It may be expressed as a determined part 
of the characteristic value by using a factor (//& < 1 

1.5.3.17 

frequent value of a variable action (yf^Qk) 

value determined - in so far as it can be fixed on statistical bases - so that either the total 
time, within the reference period, during which it is exceeded is only a small given part 
of the reference period, or the frequency of it being exceeded is limited to a given value. 
It may be expressed as a determined part of the characteristic value by using a factor 

?^i<l 

IAC2) NOTE For the frequent value of multi-component traffic actions see load groups in EN 1991-2. (ac^ 

1.5.3.18 

quasi-permanent value of a variable action (^Qk) 

value determined so that the total period of time for which it will be exceeded is a large 
fraction of the reference period. It may be expressed as a determined part of the charac- 
teristic value by using a factor i//2<l 

1.5.3.19 

accompanying value of a variable action (if^Qk) 

value of a variable action that accompanies the leading action in a combination 

NOTE The accompanying value of a variable action may be the combination value, the frequent value or 
the quasi-permanent value. 

1.5.3.20 

representative value of an action (Frep) 

value used for the verification of a limit state. A representative value may be the charac- 
teristic value (Fk) or an accompanying value (^k) 

1.5.3.21 

design value of an action (F^) 

value obtained by multiplying the representative value by the partial factor ^^ 

NOTE The product of the representative value multiphed by the partial factor yj7 = y^^ xy^- may also 
be designated as the design value of the action (See 6.3.2). 



20 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

1.5.3.22 

combination of actions 

set of design values used for the verification of the structural reliability for a limit state 
under the simultaneous influence of different actions 

1.5.4 Terms relating to material and product properties 

1.5.4.1 

characteristic value (^k or i?k) 

value of a material or product property having a prescribed probability of not being at- 
tained in a hypothetical unlimited test series. This value generally corresponds to a 
specified fractile of the assumed statistical distribution of the particular property of the 
material or product. A nominal value is used as the characteristic value in some circum- 
stances 

1.5.4.2 

design value of a material or product property (X^ or R^) 

value obtained by dividing the characteristic value by a partial factor }(^^ or %^, or, in 
special circumstances, by direct determination 

1.5.4.3 

nominal value of a material or product property (Xnom or i?nom) 
value normally used as a characteristic value and established from an appropriate docu- 
ment such as a European Standard or Prestandard 

1.5.5 Terms relating to geometrical data 

1.5.5.1 

characteristic value of a geometrical property (a^) 

value usually corresponding to the dimensions specified in the design. Where relevant, 
values of geometrical quantities may correspond to some prescribed fractiles of the sta- 
tistical distribution 

1.5.5.2 

design value of a geometrical property (a^) 

generally a nominal value. Where relevant, values of geometrical quantities may corre- 
spond to some prescribed fractile of the statistical distribution 

NOTE The design value of a geometrical property is generally equal to the characteristic value. How- 
ever, it may be treated differently in cases where the limit state under consideration is very sensitive to 
the value of the geometrical property, for example when considering the effect of geometrical imperfec- 
tions on buckhng. In such cases, the design value will normally be established as a value specified di- 
recdy, for example in an appropriate European Standard or Prestandard. Ahernatively, it can be estab- 
lished from a statistical basis, with a value corresponding to a more appropriate fractile (e.g. a rarer 
value) than appHes to the characteristic value. 



21 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

1.5.6 Terms relating to structural analysis 

NOTE The definitions contained in the clause may not necessarily relate to terms used in EN 1990, but 
are included here to ensure a harmonisation of terms relating to structural analysis for EN 1991 to 
EN 1999. 

1.5.6.1 

structural analysis 

procedure or algorithm for determination of action effects in every point of a structure 

NOTE A structural analysis may have to be perfonned at three levels using different models : global analysis, 
member analysis, local analysis. 

1.5.6.2 

global analysis 

determination, in a structure, of a consistent set of either intemal forces and moments, or 
stresses, that are in equiUbrium with a particular defined set of actions on the structure, and 
depend on geometrical, structural and material properties 

1.5.6.3 

first order linear-elastic analysis without redistribution 

elastic structural analysis based on linear stress/strain or moment/cui-vatTire laws and 
performed on the initial geometry 

1.5.6.4 

first order linear-elastic analysis with redistribution 

hnear elastic analysis in which the intemal moments and forces are modified for structural 
design, consistently with the given external actions and without more explicit calculation of 
the rotation capacity 

1.5.6.5 

second order linear-elastic analysis 

elastic structural analysis, using linear stress/strain laws, applied to the geometry of the 
deformed structure 

1.5.6.6 

first order non-linear analysis 

structural analysis, performed on the initial geometry, that takes account of the non-linear 
deformation properties of materials 

NOTE First order non-linear analysis is either elastic with appropriate assumptions, or elastic-perfectly plastic 
(see 1.5.6.8 and 1.5.6.9), or elasto-plastic (see 1.5.6.10) or rigid-plastic (see 1.5.6.1 1). 

1.5.6.7 

second order non-linear analysis 

structural analysis, perfomied on the geometry of the deformed structure, that takes account 
of the non-linear defoimation properties of materials 

NOTE Second order non-linear analysis is either elastic-perfectly plastic or elasto-plastic. 



22 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

1.5.6.8 

first order elaslic-perfectly plastic analysis 

structural analysis based on moment/cui'vature relationships consisting of a linear elastic 
part followed by a plastic part without hardening, perfomied on the initial geometry of the 
structure 

1.5.6.9 

second order elastic-perfectly plastic analysis 

structural analysis based on moment/curvature relationships consisting of a linear elastic 
part followed by a plastic part without hardening, performed on the geometry of the 
displaced (or deformed) structure 

1.5.6.10 
[Ag) elasto-plastic analysis (M 

structural analysis that uses stress-strain or moment/curvature relationships consisting of a 
linear elastic part followed by a plastic part with or without hardening 

NOTE In general, it is perfonned on the initial structural geometry, but it may also be applied to the geometiy 
of the displaced (or deformed) stmcture. 

1.5.6.11 

rigid plastic analysis 

analysis, performed on the initial geometry of the structure, that uses limit analysis 
theorems for direct assessment of the ultimate loading 

NOTE The moment/curvature law is assumed without elastic defonnation and without hardening. 

1.6 Symbols 

E5) For the puiposes of this European Standard, the following symbols apply. 

NOTE The notation used is based on ISO 3898:1987. 

Latin upper case letters 

A Accidental action 

A^ Design value of an accidental action 

Am Design value of seismic action A^^ - YjA^j^ 

A^k Characteristic value of seismic action 

Cd Nominal value, or a function of certain design properties of materials 

E Effect of actions 

£'d Design value of effect of actions 

£'d,dst Design value of effect of destabilising actions 

£'d,stb Design value of effect of stabilising actions 

F Action 

Fd Design value of an action 

Fk Characteristic value of an action 

Frep Representative value of an action (^ 



23 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

t^Fyv Wind force (general symbol) 

Fyyk Characteristic value of the wind force 

F"\ Wind force compatible with road traffic 

77*^ Wind force compatible with railway traffic 

G Permanent action 

Gd Design value of a permanent action 

Gd,inf Lower design value of a permanent action 

Gd,sup Upper design value of a permanent action 

Gk Characteristic value of a permanent action 

Gkj Characteristic value of permanent actiony 

Gkj,sup/ Upper/lower characteristic value of permanent actiony 

GkJ,inf 

G Permanent action due to uneven settlements 

set 

P Relevant representative value of a prestressing action (see EN 1992 

to EN 1996 and EN 1998 to EN 1999) 

Pd Design value of a prestressing action 

Pk Characteristic value of a prestressing action 

Pni Mean value of a prestressing action 

Q Variable action 

gd Design value of a variable action 

gk Characteristic value of a single variable action 

gk,i Characteristic value of the leading variable action 1 

gk,i Characteristic value of the accompanying variable action i 

Q^ Characteristic value of snow load 

R Resistance 

7?d Design value of the resistance 

i?k Characteristic value of the resistance 

T Thermal climatic action (general symbol) 

7), Characteristic value of the thermal climatic action 

X Material property 

Xd Design value of a material property 

Xk Characteristic value of a material property 



Latin lower case letters 

ad Design values of geometrical data 

ak Characteristic values of geometrical data 

a„om Nominal value of geometrical data 

d Difference in settlement of an individual foundation or part of a 

foundation compared to a reference level 

u Horizontal displacement of a structure or structural member 

w Vertical deflection of a structural member 



Greek upper case letters 

Aa Change made to nominal geometrical data for particular design 

purposes, e.g. assessment of effects of imperfections 

Ad^^^ Uncertainty attached to the assessment of the settlement of a 

foundation or part of a foundation (^ 

24 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



|Ac^ Greek lower case letters 



y Partial factor (safety or serviceability) 

y^_^^ Maximum peak value of bridge deck acceleration for ballasted track 

Y Maximum peak value of bridge deck acceleration for direct fastened 

track 
Y^.^^^ Partial factor for permanent actions due to settlements, also 

accounting for model uncertainties 
Yi Partial factor for actions, which takes account of the possibility of 

unfavourable deviations of the action values from the representative 

values 
^ Partial factor for actions, also accounting for model uncertainties and 

dimensional variations 
Yg Partial factor for pemianent actions, which takes account of the 

possibility of unfavourable deviations of the action values from the 

representative values 
Yq Partial factor for peiTnanent actions, also accounting for model 

uncertainties and dimensional variations 
^ j Partial factor for permanent actiony 

}(]js^p/ Partial factor for permanent action j in calculating upper/lower 

;^ J -^^f design values 

jl Importance factor (see EN 1 998) 

Y-n Partial factor for a material property 

Yj^ Partial factor for a material property, also accounting for model 

uncertainties and dimensional variations 
}f> Partial factor for prestressing actions (see EN 1992 to EN 1996 and 

EN 1998 to EN 1999) 
% Partial factor for variable actions, which takes account of the 

possibility of unfavourable deviations of the action values from the 

representative values 
Yq Partial factor for variable actions, also accounting for model 

uncertainties and dimensional variations 
Yq^{ Partial factor for variable action / 

Yu Partial factor associated with the uncertainty of the resistance model 

;^a Partial factor associated with the uncertainty of the action and/or 

action effect model 
;; Conversion factor 

^ Reduction factor 

^0 Factor for combination value of a variable action 

y/^ Factor for frequent value of a variable action 

y/2 Factor for quasi-permanent value of a variable action (^ 



25 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Section 2 Requirements 

2.1 Basic requirements 

(1)P A structure shall be designed and executed in such a way that it will, during its 
intended hfe, with appropriate degrees of reliability and in an economical way 

- sustain all actions and influences likely to occur during execution and use, and 

|Ac^ - meet the specified serviceabihty requirements for a structure or a structural element. 

NOTE See also 13, 2.1(7) and 2.4(1) P.(acT| 

(2)P A structure shall be designed to have adequate : 

- structural resistance, 

- serviceability, and 

- durability. 

(3)P In the case of fire, the structural resistance shall be adequate for the required period 
of time. 

NOTE See also EN 1991-1-2 

(4)P A structure shall be designed and executed in such a way that it will not be dam- 
aged by events such as : 

- explosion, 

- impact, and 

~ the consequences of human en'ors, 

to an extent disproportionate to the original cause. 

NOTE 1 The events to be taken into account are those agreed for an individual project with the client 
and the relevant authority. 

NOTE 2 Further information is given in EN 1991-1-7. 

(5)P Potential damage shall be avoided or limited by appropriate choice of one or more 
of the fohowing : 

- avoiding, ehminating or reducing the hazards to which the structxire can be sub- 
jected; 

- selecting a stmctural form which has low sensitivity to the hazards considered ; 

- selecting a structural form and design that can survive adequately the accidental re- 
moval of an individual member or a limited part of the structure, or the occurrence of 
acceptable localised damage ; 

- avoiding as far as possible stmctural systems that can collapse without warning ; 

- tying the structural members together. 

(6) The basic requirements should be met : 

- by die choice of suitable materials, 

- by appropriate design and detailing, and 

- by specifying control procedures for design, production, execution, and use 
relevant to the particular project. 



26 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(7) The provisions of Section 2 should be interpreted on the basis that due skill and care 
appropriate to the circumstances is exercised in the design, based on such knowledge 
and good practice as is generally available at the time that the design of the structure is 
carried out. 

2.2 Reliability management 

(1)P The reliability required for structures within the scope of EN 1990 shall be 
achieved: 

a) by design in accordance with EN 1990 to EN 1999 and 

b) by 

- appropriate execution and 

- quality management measures. 

NOTE See 2.2(5) and Annex B 

(2) Different levels of reliability may be adopted inter alia : 

- for structural resistance ; 

- for serviceability. 

(3) The choice of the levels of reliability for a particular structure should take account 
of the relevant factors, including : 

- the possible cause and /or mode of attaining a limit state ; 

- the possible consequences of failure in terms of risk to life, injury, potential eco- 
nomical losses ; 

- public aversion to failure ; 

- the expense and procedures necessary to reduce the risk of failure. 

(4) The levels of reliability that apply to a particular structure may be specified in one 
or both of the following ways : 

- by the classification of the structure as a whole ; 

- by the classification of its components. 

NOTE See also Annex B 

(5) The levels of reliability relating to structural resistance and serviceability can be 
achieved by suitable combinations of : 

a) preventative and protective measures (e.g. implementation of safety barriers, active 
and passive protective measures against fire, protection against risks of corrosion such 
as painting or cathodic protection) ; 

b) measures relating to design calculations : 

- representative values of actions ; 

- the choice of partial factors ; 

c) measures relating to quality management ; 



27 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

d) measures aimed to reduce errors in design and execution of the structure, and gross 
human errors ; 

e) other measures relating to the following other design matters : 

- the basic requirements ; 

- the degree of robustness (structural integrity) ; 

- durability, including the choice of the design working life ; 

- the extent and quality of preliminary investigations of soils and possible environ- 
mental influences ; 

- the accuracy of the mechanical models used ; 

- the detailing ; 

f) efficient execution, e,g. in accordance with execution standards referred to in 
EN 1991 to EN 1999. 

g) adequate inspection and maintenance according to procedures specified in the project 
documentation. 

(6) The measures to prevent potential causes of failure and/or reduce their consequences 
may, in appropriate circumstances, be interchanged to a limited extent provided that the 
required reliability levels are maintained. 

23 Design working life 

(1) The design working hfe should be specified. 

NOTE Indicative categories are given in Table 2.L The values given in Table 2.1 may also be used for 
determining time-dependent performance (e.g. fatigue-related calculations). See also Annex A. 

Table 2.1 - Indicative design working life 



Design working 
life category 


Indicative design 

working life 

(years) 


Examples 


1 


10 


Temporary structures ^^^ 


2 


10 to 25 


Replaceable structural parts, e.g. gantry girders, 
bearings 


3 


15 to 30 


Agricultural and similar structures 


4 


50 


Building structures and other common structures 


5 


100 


Monumental building structures, bridges, and other 
civil engineering structures 


(1) Structures or parts of structures that can be dismantled with a view to being re-used should 
not be considered as temporary. 



2,4 Durability 

(1)P The structure shall be designed such that deterioration over its design working life 
does not impair the performance of the structure below that intended, having due regard 
to its environment and the anticipated level of maintenance. 



28 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

(2) In order to achieve an adequately durable structure, the following should be taken 
into account : 

- the intended or foreseeable use of the stmcture ; 

- the required design criteria ; 

- the expected environmental conditions ; 

- the composition, properties and performance of the materials and products ; 

- the properties of the soil ; 

- the choice of the structural system ; 

- the shape of members and the structural detailing ; 

- the quality of workmanship, and the level of control ; 

- the particular protective measures ; 

- the intended maintenance during the design working life. 

NOTE The relevant EN 1992 to EN 1999 specify appropriate measures to reduce deterioration. 

(3)P The environmental conditions shall be identified at the design stage so that their 
significance can be assessed in relation to durability and adequate provisions can be 
made for protection of the materials used in the structure. 

(4) The degree of any deterioration may be estimated on the basis of calculations, ex- 
perimental investigation, experience from earlier constmctions, or a combination of 
these considerations. 

2.5 Quality management 

(1) In order to provide a structure that corresponds to the requirements and to the as- 
sumptions made in the design, appropriate quality management measures should be in 
place. These measures comprise : 

- definition of the reliability requirements, 

- organisational measures and 

- controls at the stages of design, execution, use and maintenance. 

NOTE EN ISO 9001:2000 is an acceptable basis for quality management measures, where relevant. 



29 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



Section 3 Principles of limit states design 

3-1 General 

(1)P A distinction shall be made between ultimate limit states and serviceability limit 
states. 

NOTE In some cases, additional verifications may be needed, for example to ensure traffic safety. 

(2) Verification of one of the two categories of limit states may be omitted provided that 
sufficient information is available to prove that it is satisfied by the other. 

(3)P Limit states shall be related to design situations, see 3.2. 

(4) Design situations should be classified as persistent, transient or accidental, see 3.2. 

(5) Verification of limit states that are concerned with time dependent effects (e.g. fatigue) 
should be related to the design working life of the construction, 

NOTE Most time dependent effects are cumulative. 

3.2 Design situations 

(1)P The relevant design situations shall be selected taking into account the circum- 
stances under which the structure is required to fulfil its function. 

(2)P Design situations shall be classified as follows : 

- persistent design situations, which refer to the conditions of normal use ; 

- transient design situations, which refer to temporary conditions applicable to the 
structure, e.g. during execution or repair ; 

- accidental design situations, which refer to exceptional conditions applicable to the 
structure or to its exposure, e.g. to fire, explosion, impact or the consequences of lo- 
calised failure ; 

- seismic design situations, which refer to conditions applicable to the structure when 
subjected to seismic events. 

NOTE Information on specific design situations within each of these classes is given in EN 1991 to 
EN 1999. 

(3)P The selected design situations shall be sufficiendy severe and varied so as to en- 
compass all conditions that can reasonably be foreseen to occur during the execution 
and use of the structure. 



30 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005{E) 

3,3 Ultimate limit states 

(1)P The limit states that concern : 

- the safety of people, and/or 

- the safety of the structure 

shall be classified as ultimate limit states. 

(2) In some circumstances, the limit states that concern the protection of the contents 
should be classified as ultimate limit states. 

NOTE The circumstances are those agreed for a particular project with the client and the relevant author- 
ity. 

(3) States prior to structural collapse, which, for simplicity, are considered in place of 
the collapse itself, may be treated as ultimate limit states. 

(4)P The following ultimate limit states shall be verified where they are relevant : 

- loss of equilibrium of the structure or any part of it, considered as a rigid body ; 

- failure by excessive deformation, transformation of the structure or any part of it into 
a mechanism, rupture, loss of stability of the structure or any part of it, including 
supports and foundations ; 

- failure caused by fatigue or other time-dependent effects. 

[AC2) NOTE Different sets of partial factors are associated with the various ultimate limit states, see 6.4.1. (MD 



3.4 Serviceability limit states 

(1)P The hmit states that concern : 

- the functioning of the structure or structural members under normal use ; 

- the comfort of people ; 

- the appearance of the construction works, 
shall be classified as serviceability hmit states. 

NOTE 1 In the context of serviceability, the term "appearance" is concerned with such criteria as high de- 
flection and extensive cracking, rather than aesthetics. 

NOTE 2 Usually the serviceability requirements are agreed for each individual project. 

(2)P A distinction shall be made between reversible and irreversible serviceability limit 
states. 

(3) The verification of serviceability limit states should be based on criteria concerning 

the following aspects : 

a) defoiTnations that affect 

- the appearance, 

- the comfort of users, or 

- the functioning of the stmcture (including the functioning of machines or ser- 
vices), 

or that cause damage to finishes or no n- structural members ; 



31 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

b) vibrations 

- that cause discomfort to people, or 

~ that Hmit the functional effectiveness of the structure ; 

c) damage that is likely to adversely affect 

- the appearance, 

- the durability, or 

- the functioning of the structure. 

NOTE Additional provisions related to serviceability criteria are given in the relevant EN 1992 to EN 1999. 

3*5 Limit state design 

(1)P Design for limit states shall be based on the use of structural and load models for 
relevant limit states. 

(2)P It shall be verified that no limit state is exceeded when relevant design values for 

- actions, 

~ material properties, or 

- product properties, and 

- geometrical data 

are used in these models. 

(3)P The verifications shall be carried out for all relevant design situations and load 
cases. 

(4) The requirements of 3.5(1)P should be achieved by the partial factor method, de- 
scribed in section 6, 

(5) As an alternative, a design directly based on probabilistic methods may be used. 

NOTE 1 The relevant authority can give specific conditions for use. 
NOTE 2 For a basis of probabilistic methods, see Annex C. 

(6)P The selected design situations shall be considered and critical load cases identified. 

(7) For a particular verification load cases should be selected, identifying compatible load 
arrangements, sets of deformations and imperfections that should be considered 
simultaneously with fixed variable actions and permanent actions. 

(8)P Possible deviations from the assumed directions or positions of actions shall be taken 
into account. 

(9) Staictural and load models can be either physical models or mathematical models. 



32 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Section 4 Basic variables 

4J Actions and environmental influences 

4.1.1 Classification of actions 

(1)P Actions shall be classified by their variation in time as follows : 

- permanent actions (G), e.g. self-weight of structures, fixed equipment and road sur- 
facing, and indirect actions caused by shrinkage and uneven settlements ; 

- variable actions (Q), e.g. imposed loads on building floors, beams and roofs, wind 
actions or snow loads ; 

- accidental actions (A), e.g. explosions, or impact from vehicles. 

NOTE Indirect actions caused by imposed defomiations can be either permanent or variable. 

(2) Certain actions, such as seismic actions and snow loads, may be considered as either 
accidental and/or variable actions, depending on the site location, see EN 1991 and 
EN 1998. 

(3) Actions caused by water may be considered as permanent and/or variable actions 
depending on the variation of their magnitude with time. 

(4)P Actions shall also be classified 

- by their origin, as direct or indirect, 

- by their spatial variation, as fixed or free, or 

- by their nature and/or the structural response, as static or dynamic. 

(5) An action should be described by a model, its magnitude being represented in the 
most common cases by one scalar which may have several representative values. 

NOTE For some actions and some verifications, a more complex representation of the magnitudes of 
some actions may be necessary. 

4.1.2 Characteristic values of actions 

(1)P The characteristic value Fk of an action is its main representative value and shall be 
specified : 

- as a mean value, an upper or lower value, or a nominal value (which does not refer to 
a known statistical distribution) (see EN 1991) ; 

- in the project documentation, provided that consistency is achieved with methods 
given in EN 1991. 

(2)P The characteristic value of a permanent action shall be assessed as follows : 

- if the variability of G can be considered as small, one single value Gk may be used ; 

- if the variability of G cannot be considered as small, two values shall be used : an 
upper value Gk,sup and a lower value Gkjnf. 



33 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(3) The variability of G may be neglected if G does not vary significantly during the 
design working life of the structure and its coefficient of variation is small. Gk should 
then be taken equal to the mean value. 

NOTE This coefficient of variation can be in the range of 0,05 to 0,10 depending on the type of structure. 

(4) In cases when the structure is very sensitive to variations in G (e.g. some types of 
prestressed concrete structures), two values should be used even if the coefficient of 
variation is small. Then Gk,inf is the 5% fractile and Gk,sup is the 95% fractile of the sta- 
tistical distribution for G, which may be assumed to be Gaussian. 

(5) The self-weight of the structure may be represented by a single characteristic value 
and be calculated on the basis of the nominal dimensions and mean unit masses, see EN 
1991-1-1. 

NOTE For the settlement of foundations, see EN 1997. 

(6) Prestressing (P) should be classified as a permanent action caused by either con- 
trolled forces and/or controlled deformations imposed on a structure. These types of 
prestress should be distinguished from each other as relevant (e.g. prestress by tendons, 
prestress by imposed deformation at supports). 

NOTE The characteristic values of prestress, at a given time t, may be an upper value /*k,sup(t) and a lower 
value Fk,inf(t)- Eor ultimate limit states, a mean value PJ^\) can be used. Detailed information is given in 
EN 1992 to EN 1996 and EN 1999. 

(7)P For variable actions, the characteristic value (gk) shall correspond to either : 

- an upper value with an intended probability of not being exceeded or a lower value 
with an intended probability of being achieved, during some specific reference pe- 
riod; 

- a nominal value, which may be specified in cases where a statistical distribution is 
not known. 

NOTE 1 Values are given in the various Parts of EN 1991. 

NOTE 2 The characteristic value of climatic actions is based upon the probability of 0,02 of its time- 
varying part being exceeded for a reference period of one year. This is equivalent to a mean return period 
of 50 years for the time-vaiying part. However in some cases the character of the action and/or the se- 
lected design situation makes another fractile and/or return period more appropriate. 

(8) For accidental actions the design value A^ should be specified for individual pro- 
jects. 

NOTE See also EN 1991-1-7. 

(9) For seismic actions the design value A^^ should be assessed from the characteristic 
value ^Ek or specified for individual projects. 

NOTE See also EN 1998. 

(10) For multi-component actions the characteristic action should be represented by 
groups of values each to be considered separately in design calculations. 



34 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



4.1.3 Other representative values of variable actions 

(1)P Other representative values of a variable action shall be as follows : 

(a) the combination value, represented as a product ^o gk, used for the verification of 
ultimate limit states and irreversible serviceability limit states (see section 6 and 
Annex C) ; 

(b) the frequent value, represented as a product y/\Q\^, used for the verification of ulti- 
mate limit states involving accidental actions and for verifications of reversible ser- 
viceability limit states ; 

NOTE 1 For buildings, for example, the frequent value is chosen so that the time it is exceeded is 0,01 of 
the reference period ; for road traffic loads on bridges, the frequent value is assessed on the basis of a 
return period of one week. 

Iac2)N0TE 2 The infrequent value, represented as a product \f/\^mfcQk^ iriay be used only for the verification of 
certain serviceability limit states specifically for concrete bridges The infrequent value which is defined 
only for road traffic loads (see EN 1991-2) is based on a return period of one year. 

NOTE 3 For the frequent value of multi-component traffic actions see EN 1991-2. <5SI 

(c) the quasi-permanent value, represented as a product y/iQ]^, used for the verification 
of ultimate limit states involving accidental actions and for the verification of reversi- 
ble serviceabiHty limit states. Quasi-permanent values are also used for the calculation 
of long-term effects. 

NOTE For loads on building floors, the quasi-permanent value is usually chosen so that the proportion 
of the time it is exceeded is 0,50 of the reference period. The quasi-permanent value can alternatively be 
determined as the value averaged over a chosen period of time. In the case of wind actions or road traffic 
loads, the quasi-permanent value is generally taken as zero. 

4.1.4 Representation of fatigue actions 

(1) The models for fatigue actions should be those that have been established in the 
relevant parts of EN 1991 from evaluation of structural responses to fluctuations of loads 
performed for common structures {e,g. for simple span and multi-span bridges, tall slender 
structures for wind). 

(2) For structures outside the field of application of models established in the relevant Parts 
of EN 1991, fatigue actions should be defined from the evaluation of measurements or 
equivalent studies of the expected action spectra. 

NOTE For the consideration of material specific effects (for example, the consideration of mean stress 
influence or non-linear effects), see EN 1992 to EN 1999. 

4.1.5 Representation of dynamic actions 

Ia5)(1) The load models defined by characteristic values, and fatigue load models, in EN 
1991 may include the effects of accelerations caused by the acfions either implicitly or 
explicitly by applying dynamic enhancement factors. (^£0 

NOTE Limits of use of these models are described in the various Parts of EN 1991. 

35 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



(2) When dynamic actions cause significant acceleration of the structure, dynamic 
analysis of the system should be used. See 5.1.3 (6). 

4.1.6 Geotechnical actions 

(1)P Geotechnical actions shall be assessed in accordance with EN 1997-1. 

4.1.7 Environmental influences 

(1)P The environmental influences that could affect the durability of the structure shall 
be considered in the choice of structural materials, their specification, the structural 
concept and detailed design. 

NOTE The EN 1992 to EN 1999 give the relevant measures. 

(2) The effects of environmental influences should be taken into account, and where 
possible, be described quantitatively. 

4.2 Material and product properties 

(1) Properties of materials (including soil and rock) or products should be represented 
by characteristic values (see 1.5.4.1). 

(2) When a limit state verification is sensitive to the variability of a material property, 
upper and lower characteristic values of the material property should be taken into ac- 
count. 

(3) Unless otherwise stated in EN 1991 to EN 1999 : 

- where a low value of material or product property is unfavourable, the characteristic 
value should be defined as the 5% fractile value; 

- where a high value of material or product property is unfavourable, the characteristic 
value should be defined as the 95% fractile value. 

(4)P Material property values shall be determined from standardised tests performed 
under specified conditions. A conversion factor shall be apphed where it is necessary to 
convert the test results into values which can be assumed to represent the behaviour of 
the material or product in the structure or the ground. 

NOTE See annex D and EN 1992 to EN 1999 

(5) Where insufficient statistical data are available to establish the characteristic values 
of a material or product property, nominal values may be taken as the characteristic val- 
ues, or design values of the property may be established directly. Where upper or lower 
design values of a material or product property are estabhshed directly (e,g. friction 
factors, damping ratios), they should be selected so that more adverse values would af- 
fect the probability of occurrence of the limit state under consideration to an extent 
similar to other design values. 



36 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



(6) Where an upper estimate of strength is required (e.g, for capacity design measures 
and for the tensile strength of concrete for the calculation of the effects of indirect ac- 
tions) a characteristic upper value of the strength should be taken into account. 

(7) The reductions of the material strength or product resistance to be considered result- 
ing from the effects of repeated actions are given in EN 1992 to EN 1999 and can lead 
to a reduction of the resistance over time due to fatigue. 

(8) The structural stiffness parameters (e.g. moduli of elasticity, creep coefficients) and 
thermal expansion coefficients should be represented by a mean value. Different values 
should be used to take into account the duration of the load. 

NOTE In some cases, a lower or higher value than the mean for the modulus of elasticity may have to be 
taken into account (e.g. in case of instability). 

(9) Values of material or product properties are given in EN 1992 to EN 1999 and in the 
relevant harmonised European technical specifications or other documents. If values are 
taken from product standards without guidance on interpretation being given in 
EN 1992 to EN 1999, the most adverse values should be used. 

(10)P Where a partial factor for materials or products is needed, a conseii/ative value 
shall be used, unless suitable statistical information exists to assess the reliability of the 
value chosen. 

NOTE Suitable account may be taken where appropriate of the unfamiliarity of the application or mate- 
rials/products used. 

4.3 Geometrical data 

(1)P Geometrical data shall be represented by their characteristic values, or (e.g. the 
case of imperfections) directly by their design values. 

(2) The dimensions specified in the design may be taken as characteristic values. 

(3) Where their statistical distribution is sufficiently known, values of geometrical quan- 
tities that correspond to a prescribed fractile of the statistical distribution may be used. 

(4) Imperfections that should be taken into account in the design of structural members 
are given in EN 1992 to EN 1999. 

(5)P Tolerances for connected parts that are made from different materials shall be mu- 
tually compatible. 



37 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Section 5 Structural analysis and design assisted by testing 

5.1 Structural analysis 

5.1.1 Structural modelling 

(1)P Calculations shall be carried out using appropriate structural models involving 
relevant variables. 

(2) The structural models selected should be those appropriate for predicting structural 
behaviour with an acceptable level of accuracy. The structural models should also be 
appropriate to the limit states considered. 

(3)P Structural models shall be based on established engineering theory and practice. If 
necessary, they shall be verified experimentally. 

5.1.2 Static actions 

(1)P The modelling for static actions shall be based on an appropriate choice of the 
force-deformation relationships of the members and their connections and between 
members and the ground, 

(2)P Boundary conditions applied to the model shall represent those intended in the 
structure. 

(3)P Effects of displacements and deformations shall be taken into account in the con- 
text of ultimate limit state verifications if they result in a significant increase of the ef- 
fect of actions. 

NOTE Particular methods for dealing with effects of deformations are given in EN 1991 to EN 1999. 

(4)P Indirect actions shall be introduced in the analysis as follows : 

- in linear elastic analysis, directly or as equivalent forces (using appropriate modular 
ratios where relevant) ; 

- in non-linear analysis, directly as imposed deformations. 

5.1.3 Dynamic actions 

(1)P The structural model to be used for determining the action effects shall be estab- 
lished taking account of all relevant structural members, their masses, strengths, stiff- 
nesses and damping characteristics, and all relevant non structural members with their 
properties. 

(2)P The boundary conditions applied to the model shall be representative of those in- 
tended in the stmcture. 



38 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

(3) When it is appropriate to consider dynamic actions as quasi-static, the dynamic parts 
may be considered either by including them in the static values or by applying equiva- 
lent dynamic amplification factors to the static actions. 

NOTE For some equivalent dynamic amplification factors, the natural frequencies are determined. 

(4) In the case of ground-structure interaction, the contribution of the soil may be mod- 
elled by appropriate equivalent springs and dash-pots. 

(5) Where relevant (e.g. for wind induced vibrations or seismic actions) the actions may 
be defined by a modal analysis based on linear material and geometric behaviour. For 
structures that have regular geometry, stiffness and mass distribution, provided that only 
the fundamental mode is relevant, an explicit modal analysis may be substituted by an 
analysis with equivalent static actions. 

(6) The dynamic actions may be also expressed, as appropriate, in terms of time histo- 
ries or in the frequency domain, and the structural response determined by appropriate 
methods. 

(7) Where dynamic actions cause vibrations of a magnitude or frequencies that could 
exceed serviceability requirements, a semceability limit state verification should be 
carried out. 

NOTE Guidance for assessing these limits is given in Annex A and EN 1992 to EN 1999. 

5.1.4 Fire design 

(l)P The structural fire design analysis shall be based on design fire scenarios (see EN 
1991-1-2), and shall consider models for the temperature evolution within the structure 
as well as models for the mechanical behaviour of the structure at elevated temperature. 

(2) The required performance of the structure exposed to fire should be verified by ei- 
ther global analysis, analysis of sub-assemblies or member analysis, as well as the use 
of tabular data or test results. 

(3) The behaviour of the structure exposed to fire should be assessed by taking into ac- 
count either : 

- nominal fire exposure, or 

- modelled fire exposure, 

as well as the accompanying actions. 

NOTE See also EN 1991-1-2. 

(4) The structural behaviour at elevated temperatures should be assessed in accordance 
with EN 1992 to EN 1996 and EN 1999, which give thermal and structural models for 
analysis. 



39 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



(5) Where relevant to the specific material and the method of assessment : 

- thermal models may be based on the assumption of a uniform or a non-uniform tem- 
perature within cross-sections and along members ; 

- structural models may be confined to an analysis of individual members or may ac- 
count for the interaction between members in fire exposure. 

(6) The models of mechanical behaviour of structural members at elevated temperatures 
should be non-linear. 

NOTE See also EN 1991 to EN 1999. 

5.2 Design assisted by testing 

(1) Design may be based on a combination of tests and calculations. 

NOTE Testing may be carried out, for example, in the following circmnstances : 

- if adequate calculation models are not available ; 

- if a large number of similar components are to be used ; 

- to confirm by control checks assumptions made in the design. 
See Annex D. 

(2)P Design assisted by test results shall achieve the level of reliability required for the 
relevant design situation. The statistical uncertainty due to a limited number of test re- 
sults shall be taken into account. 

(3) Partial factors (including those for model uncertainties) comparable to those used in 
EN 1991 to EN 1999 should be used. 



40 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Section 6 Verification by the partial factor method 

6.1 General 

(1)P When using the partial factor method, it shall be verified that, in all relevant design 
situations, no relevant limit state is exceeded when design values for actions or effects of 
actions and resistances are used in the design models. 

(2) For the selected design situations and the relevant limit states the individual actions for 
the critical load cases should be combined as detailed in this section. However actions that 
cannot occur simultaneously, for example due to physical reasons, should not be 
considered together in combination. 

(3) Design values should be obtained by using : 
the characteristic, or 

other representative values, 
in combination with partial and other factors as defined in this section and EN 1991 to 
EN 1999. 

(4) It can be appropriate to determine design values direcdy where conservative values 
should be chosen. 

(5)P Design values directly determined on statistical bases shall correspond to at least 
the same degree of reliability for the various limit states as imphed by the partial factors 
given in this standard. 

6.2 Limitations 

(1) The use of the Apphcation Rules given in EN 1990 is limited to ultimate and 
semceabihty limit state verifications of structures subject to static loading, including cases 
where the dynamic effects are assessed using equivalent quasi-static loads and dynamic 
amplification factors, including wind or traffic loads. For non-linear analysis and fatigue 
the specific rules given in various Parts of EN 1991 to EN 1999 should be apphed. 

6.3 Design values 

6.3.1 Design values of actions 

(1) The design value Fd of an action F can be expressed in general terms as : 
^d-Yf^rep (6.1a) 

with : 

Frep-y^k (6- lb) 

where : 



41 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

Fj^ is the characteristic value of the action. 

Frep is the relevant representative value of the action. 

Yf is a partial factor for the action which takes account of the possibility of unfa- 

vourable deviations of the action values from the representative values. 
y/ is either 1,00 or ^o, W\ <^^ ¥2- 

(2) For seismic actions the design value y^Ed should be determined taking account of the 
structural behaviour and other relevant criteria detailed in EN 1998. 

6.3.2 Design values of the effects of actions 

(1) For a specific load case the design values of the effects of actions {E^ can be expressed 
in general terms as : 

Ed-rsdE{rf,F,epy^a^} ^'^i (6.2) 

where : 

a^ is the design values of the geometrical data (see 6.3.4) ; 

^^ is a partial factor taking account of uncertainties : 

- in modelling the effects of actions ; 

- in some cases, in modelling the actions. 

NOTE In a more general case the effects of actions depend on material properties. 

(2) In most cases, the following simplification can be made : 
Ed^E[rF^rF,.^py.a^} i>\ (6.2a) 

with : 

YFj-^Ysd^rfj, (6.2b) 

NOTE When relevant, e.g. where geotechnical actions are involved, partial factors '}^^\ can be applied to 
the effects of individual actions or only one particular factor jf can be globally applied to the effect of the 
combination of actions with appropriate partial factors. 

(3)P Where a distinction has to be made between favourable and unfavourable effects of 
permanent actions, two different partial factors shall be used (x^jnf ^nd X},sup). 

(4) For non-linear analysis (i.e. when the relationship between actions and their effects is 
not linear), the following simplified rules may be considered in the case of a single 
predominant action : 

a) When the action effect increases more than the action, the partial factor j^ should be 
applied to the representative value of the action. 



42 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

b) When the action effect increases less than the action, the partial factor y^ should be 
applied to the action effect of the representative value of the action. 

NOTE Except for rope, cable and membrane structures, most structures or structural elements are in categoiy 
a). 

(5) In those cases where more refined methods are detailed in the relevant EN 1991 to 
EN 1999 (e.g. for prestressed structures), they should be used in preference to 6.3.2(4). 

6.3.3 Design values of material or product properties 

(1) The design value X^ of a material or product property can be expressed in general 
terms as : 

X, = 77^ (6.3) 

where : 

Xk is the characteristic value of the material or product property (see 4.2(3)) ; 

7] is the mean value of the conversion factor taking into account 

- volume and scale effects, 

- effects of moisture and temperature, and 

- any other relevant parameters ; 

Xn is the partial factor for the material or product property to take account of : 

- the possibility of an unfavourable deviation of a material or product property 
from its characteristic value ; 

- the random part of the conversion factor r/. 

(2) Alternatively, in appropriate cases, the conversion factor r/ may be : 

- implicitly taken into account within the characteristic value itself, or 

- by using ^fvi instead of Xn (see expression (6.6b)). 

NOTE The design value can be established by such means as : 

- empirical relationships with measured physical properties, or 

- with chemical composition, or 

- from previous experience, or 

- from values given in European Standards or other appropriate documents. 

6.3.4 Design values of geometrical data 

(1) Design values of geometrical data such as dimensions of members that are used to 
assess action effects and/or resistances may be represented by nominal values : 

Ctd = ^nom (6.4) 



43 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(2)P Where the effects of deviations in geometrical data (e.g, inaccuracy in the load 
appHcation or location of supports) are significant for the reUability of the structure (e.g, by 
second order effects) the design values of geometrical data shall be defined by : 

where : 

Aa takes account of : 

- the possibility of unfavourable deviations from the characteristic or nominal 
values ; 

- the cumulative effect of a simultaneous occurrence of several geometrical de- 
viations. 

NOTE 1 a^ can also represent geometrical imperfections where anom = (i.e., Aa ^0), 
NOTE 2 Where relevant, EN 1991 to EN 1999 provide further provisions. 

(3) Effects of other deviations should be covered by partial factors 

- on the action side (}f), and/or 

- resistance side (}^). 

NOTE Tolerances are defined in the relevant standards on execution referred to in EN 1990 to EN 1999. 
6.3.5 Design resistance 

(1) The design resistance i?d can be expressed in the following form : 

7?^^^7?{X^,-;^^}-^^ /7.-^;^j />1 (6.6) 

TRd YRcI [ YmJ J 

where : 

;^^d is a partial factor covering uncertainty in the resistance model, plus geometric 
deviations if these are not modelled exphcitly (see 6.3.4(2)); 

Xd,i is the design value of material property /. 

(2) The following simplification of expression (6.6) may be made : 
Rd=RWi^-^^d\'^^^ (6.6a) 

[ rM,i 

where : 

yM,i=rRdxrm,i (6-6b) 

NOTE 77i may be incorporated in %am see 6.3.3.(2). 



44 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 

(3) Alternatively to expression (6.6a), the design resistance may be obtained directly from 
the characteristic value of a material or product resistance, without explicit determination of 
design values for individual basic variables, using : 

Rd=^ (6.6c) 

7m 

NOTE This is applicable to products or members made of a single material (e.g. steel) and is also used in 
connection with Annex D "Design assisted by testing". 

(4) Alternatively to expressions (6.6a) and (6.6c), for structures or structural members that 
are analysed by non-linear methods, and comprise more than one material acting in 
association, or where ground properties are involved in the design resistance, the following 
expression for design resistance can be used : 

Rd = R\m^k,i;ni^kj(i>\) ^^;^^ (6.6d) 

NOTE In some cases, the design resistance can be expressed by applying directly %\ partial factors to the 
individual resistances due to material properties. 

6,4 Ultimate limit states 
6.4.1 General 

(1)P The following ultimate limit states shall be verified as relevant : 

a) EQU : Loss of static equilibrium of the structure or any part of it considered as a 
rigid body, where : 

|Ac^ - minor variations in the value or the spatial distribution of permanent actions from a 
single source are significant, and<Ac3 
- the strengths of construction materials or ground are generally not governing ; 

b) STR : Internal failure or excessive deformation of the structure or stmctural mem- 
bers, including footings, piles, basement walls, etc., where the strength of construc- 
tion materials of the structure governs ; 

c) GEO : Failure or excessive deformation of the ground where the strengths of soil or 
rock are significant in providing resistance ; 

d) FAT : Fatigue failure of the structure or structural members. 

|Ac^ NOTE For fatigue design, the combinations of actions are given in EN 1992 to EN 1995, EN 1998 and EN 
1999. 

e) UPL : loss of equilibrium of the stiTicture or the ground due to upHft by water 
pressure (buoyancy) or other vertical actions ; 

NOTE See EN 1997. 

f) HYD : hydraulic heave, internal erosion and piping in the ground caused by hydraulic 
gradients. 

NOTE SeeEN1997.<Aca 

(2)P The design values of actions shall be in accordance with Annex A. 

45 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



6.4.2 Verifications of static equilibrium and resistance 

(1)P When considering a limit state of static equilibrium of the structure (EQU), it shall be 
verified that : 

^d ,dst ^ ^d ,stb (6.7) 

where : 

fi'd ,dst is the design value of the effect of destabilising actions ; 

Ed ,stb is the design value of the effect of stabilising actions. 

(2) Where appropriate the expression for a limit state of static equilibrium may be 
supplemented by additional terms, including, for example, a coefficient of friction between 
rigid bodies. 

(3)P When considering a limit state of mpture or excessive deformation of a section, 
member or connection (STR and/or GEO), it shall be verified that : 

£d<i?d (6.8) 

where : 

E^ is the design value of the effect of actions such as intemal force, moment or a vector 
representing several intemal forces or moments ; 

7?d is the design value of the corresponding resistance. 
NOTE, 1 Details for the methods STR and GEO are given in Annex A. 

NOTE 2 Expression (6.8) does not cover all verification formats concerning buckling, i.e. failure that happens 
where second order effects cannot be limited by the structural response, or by an acceptable structural 
response. See EN 1992 to EN 1999. 

6.4.3 Combination of actions (fatigue verifications excluded) 

6.4.3.1 General 

(1)P For each critical load case, the design values of the effects of actions (E^) shall be 
determined by combining the values of actions that are considered to occur simultaneously. 

(2) Each combination of actions should include : 

- a leading variable action, or 

- an accidental action. 

(3) The combinations of actions should be in accordance with 6.4.3.2 to 6.4.3.4. 



46 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(4)P Where the results of a verification are very sensitive to variations of the magnitude of 
a permanent action from place to place in the structure, the unfavourable and the favourable 
parts of this action shall be considered as individual actions. 

NOTE This applies in particular to the verification of static equilibrium and analogous limit states, see 
6.4.2(2). 

(5) Where several effects of one action (e.g. bending moment and normal force due to self- 
weight) are not flilly correlated, the partial factor applied to any favourable component may 
be reduced. 

NOTE For further guidance on this topic see the clauses on vectorial effects in EN 1992 to EN 1999. 

(6) Imposed deformations should be taken into account where relevant. 
NOTE For further guidance, see 5.1.2.4(P) and EN 1992 to EN 1999. 

6.4,3.2 Combinations of actions for persistent or transient design situations (funda- 
mental combinations) 

(1) The general format of effects of actions should be : 

Ed ^ rsdE{rgjGkj ; TpP ; 7^,1^,1 ; TqjnjQkj} 7 ^ 1 ; ^' > 1 (6.9a) 

(2) The combination of effects of actions to be considered should be based on 

- the design value of the leading variable action, and 

- the design combination values of accompanying variable actions : 

NOTE See also 6.4.3.2(4). 

^d = ^[rGjGkj ; TpP ; rQ,iQk,i ; rQjWojQkj] y ^ 1 ; ^' > 1 (6.%) 

(3) The combination of actions in brackets { }, in (6.9b) may either be expressed as : 

z rc.;G,,"+YpP"+>Q,,a;'+" 2:rQ,^o,,a,i (6-io) 

j>\ i>i 

or, alternatively for STR and GEO limit states, the less favourable of the two following 
expressions: 

I rG,jGk,j"+"rpP"+"rQ,m,iQk,i'+''i^rQ,mjQk,i (6-ioa) 

7>1 />! 

I ^jrGjGkj"+"rpP''+"rQ,iQk,i'+" i^rgjnjQkj ^^.lob) 

7>1 i>l 

Where : 



"+ " implies "to be combined with" 

X implies "the combined effect of 

^ is a reduction factor for unfavourable permanent actions G 



47 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



NOTE Further infomiation for this choice is given in Annex A. 

(4) If the relationship between actions and their effects is not Hnear, expressions (6.9a) or 
(6.9b) should be applied directly, depending upon the relative increase of the effects of 
actions compared to the increase in the magnitude of actions (see also 6.3.2.(4)). 

6.4.3.3 Combinations of actions for accidental design situations 

(1) The general format of effects of actions should be : 

Ed = ^fej ; ^ M^ ; (¥u or w2,i)Qk,i ; v^ijQkj] 7 ^ i ; ^' > i (6.na) 

(2) The combination of actions in brackets { } can be expressed as : 

Z G,,"+"F'+'M;'+"(^i^l or?/.2,l)a."+"S?^2,iai (6.11b) 

J>[ i>l 

(3) The choice between y/\,\Qk,\ or i/f2,\Qk,] should be related to the relevant accidental 
design situation (impact, fire or survival after an accidental event or situation). 

NOTE Guidance is given in the relevant Parts of EN 1991 to EN 1999. 

(4) Combinations of actions for accidental design situations should either 

- involve an explicit accidental action^ (fire or impact), or 

- refer to a situation after an accidental event (^ ^ 0). 

ES> For fire situations, apart from the temperature effect on the material properties, A^ should 
represent the design value of the indirect effects of thermal action due to fire.^ 

6.4.3.4 Combinations of actions for seismic design situations 

(1) The general format of effects of actions should be : 

Ej = E{Gkj ■,P;AEd; W2,iQk,i\ 7 ^ 1 ; ' ^ 1 (6.12a) 

(2) The combination of actions in brackets { } can be expressed as : 

zG,.;'+"P"+"4;'+"z^2,ia.i (6.12b) 

j>\ i>i 

6.4.4 Partial factors for actions and combinations of actions 

(1) The values of the y and vj/ factors for actions should be obtained from EN 1991 and 
from Annex A. 



48 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



6.4.5 Partial factors for materials and products 

(1) The partial factors for properties of materials and products should be obtained from 
EN 1992 to EN 1999. 

6,5 Serviceability limit states 

6.5.1 Verifications 

(1)P It shall be verified that : 

£d<Cd (6,13) 

where : 

Cd is the limiting design value of the relevant serviceability criterion. 

E^ is the design value of the effects of actions specified in the serviceability 
criterion, detemiined on the basis of the relevant combination. 

6.5.2 Serviceability criteria 

(1) The deformations to be taken into account in relation to serviceability requirements 
should be as detailed in the relevant Annex A according to the type of construction 
works, or agreed with the client or the National authority. 

NOTE For other specific serviceability criteria such as crack width, stress or strain Hmitation, sHp 
resistance, see EN 1991 to EN 1999. 

6.5.3 Combination of actions 

(1) The combinations of actions to be taken into account in the relevant design 
situations should be appropriate for the serviceability requirements and perfonnance 
criteria being verified. 

(2) The combinations of actions for serviceability limit states are defined symbolically 
by the following expressions (see also 6.5.4) : 

NOTE It is assumed, in these expressions, that all partial factors are equal to 1. See Annex A and 
EN 1991 to EN 1999. 

a) Characteristic combination : 

E^ = E{Gkj ; P ; S/t,! ; ¥qAi] J^Ui>\ (6.14a) 

in which the combination of actions in brackets { } (called the characteristic combination), 
can be expressed as : 



49 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

z Gkj "+"P"+"ek,i "+" i?^o,iek,i (6-i4b) 

/>1 i>\ 

NOTE The characteristic combination is normally used for irreversible limit states. 

b) Frequent combination : 

Ed = E{Gkj ; P ; y/^^^Qj^^y ; y/ijQk,] 7 ^ 1 W' > 1 (6.15a) 

in which the combination of actions in brackets { }, (called the frequent combination), can 
be expressed as : 

z Gk^j "+"^"+>i,iSk,i "+" Z(^2,iek,i (6.15b) 

NOTE The frequent combination is normally used for reversible limit states. 

c) Quasi-permanent combination : 

E^ - E{Gkj ; P ; W2-,Qk,i\ 7 > 1 ; ^ > 1 (6.16a) 

in which the combination of actions in brackets { }, (called the quasi-permanent 
combination), can be expressed as : 

EG^^/'+'T"V'Z?/^2,iek,i (6.16b) 

where the notation is as given in 1.6 and 6.4.3(1). 

NOTE The quasi-pennanent combination is nonnally used for long-term effects and the appearance of 
the structure. 

(3) For the representative value of the prestressing action (i.e. Pk or Pm), reference 
should be made to the relevant design Eurocode for the type of prestress under 
consideration. 

(4)P Effects of actions due to imposed deformations shall be considered where relevant. 

NOTE In some cases expressions (6.14) to (6.16) require modification. Detailed rules are given in the 
relevant Parts of EN 1 99 1 to EN 1 999. 

6.5.4 Partial factors for materials 

(1) For serviceability limit states the partial factors y^ for the properties of materials 
should be taken as 1,0 except if differently specified in EN 1992 to EN 1999. 



50 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Annex Al 

(normative) 

Application for Buildings 

Al.l Field of application 

(1) This annex A I gives rules and methods for establishing combinations of actions for 
buildings. It also gives the recommended design values of permanent, variable and ac- 
cidental actions and ^factors to be used in the design of buildings. 

NOTE Guidance may be given in the National annex with regard to the use of Table 2.1 (design working 
life). 

A1.2 Combinations of actions 
AL2.1 General 

(1) Effects of actions that cannot exist simultaneously due to physical or functional 
reasons should not be considered together in combinations of actions. 

NOTE 1 Depending on its uses and the form and the location of a building, the combinations of actions 
may be based on not more than two variable actions. 

NOTE 2 Where modifications of AL2T(2) and A1.2.1(3) are necessary for geographical reasons, these 
can be defmed in the National annex. 



(2) The combinations of actions given in expressions 6.9a to 6.12b should be used when 
verifying ultimate limit states. 

(3) The combinations of actions given in expressions 6.14a to 6.16b should be used 
when verifying serviceability limit states. 

(4) Combinations of actions that include prestressing forces should be dealt with as 
detailed in EN 1992 to EN 1999. 

AL2.2 Values of ^factors 

(1) Values of {/i/^ factors should be specified. 

IAC2) NOTE Recommended values of y/ factors for the more common actions may be obtained from Table 
ALL For ^^ factors during execution see EN 1991-1-6 Annex A 1.(^51 



51 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



Table Al.l - Recommended values of {(^factors for buildings 



Action 


m 


m 


m 


Imposed loads in buildings, category (see 

EN 1991-1-1) 

Category A : domestic, residential areas 

Category B ; office areas 

Category C : congregation areas 

Category D ; shopping areas 

Category E : storage areas 

Category F : traffic area, 

vehicle weight < 30kN 
Category G ; traffic area, 

30kN < vehicle weight < 160kN 
Category H : roofs 


0,7 
0,7 
0,7 
0,7 
1,0 

0,7 

0,7 



0,5 
0,5 
0,7 
0,7 
0,9 

0,7 

0,5 



0,3 
0,3 
0,6 
0,6 
0,8 

0,6 

0,3 



Snow loads on buildings (see EN 1991-1-3)* 

Finland, Iceland, Norway, Sweden 

Remainder of CEN Member States, for sites 

located at altitude H > 1000 m a.s.l. 

Remainder of CEN Member States, for sites 

located at altitude H < 1000 m a.s.l. 


0,70 
0,70 

0,50 


0,50 
0,50 

0,20 


0,20 
0,20 




Wind loads on buildings (see EN 1991-1-4) 


0,6 


0,2 





Temperature (non-fire) in buildings (see EN 
1991-1-5) 


0,6 


0,5 





NOTE The ^i/ values may be set by the National annex. 

* For countries not mentioned below, see relevant local conditions. 



AU Ultimate limit states 

Al.3.1 Design values of actions in persistent and transient design situations 

(1) The design values of actions for ultimate limit states in the persistent and transient 
design situations (expressions 6.9a to 6.10b) should be in accordance with Tables 
A1.2(A)to(C). 

NOTE The values in Tables A 1.2 ((A) to (C)) can be altered e.g. for different reliability levels in the 
National annex (see Section 2 and Annex B). 

(2) In applying Tables A 1.2(A) to A 1.2(C) in cases when the limit state is very sensitive 
to variations in the magnitude of permanent actions, the upper and lower characteristic 
values of actions should be taken according to 4. 1 .2(2)P. 

(3) Static equihbrium (EQU, see 6.4.1) for building structures should be verified using 
the design values of actions in Table A1.2(A). 

(4) Design of structural members (STR, see 6.4.1) not involving geotechnical actions 
should be verified using the design values of actions from Table AL2(B). 

(5) Design of stmctural members (footings, piles, basement walls, etc.) (STR) involving 
geotechnical actions and the resistance of the ground (GEO, see 6.4.1) should be veri- 
fied using one of the following three approaches supplemented, for geotechnical actions 
and resistances, by EN 1997 : 



52 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

- Approach 1: Applying in separate calculations design values from Table A 1. 2(C) and 
Table AL2(B) to the geotechnical actions as well as the other actions on/from the 
structure. In common cases, the sizing of foundations is governed by Table A 1.2(C) 
and the structural resistance is governed by Table A1.2(B) ; 

NOTE In some cases, application of these tables is more complex, see EN 1997. 

- Approach 2 : Applying design values from Table Al .2(B) to the geotechnical actions 
as well as the other actions on/from the structure ; 

- Approach 3 : Applying design values from Table A 1.2(C) to the geotechnical actions 
and, simultaneously, applying partial factors from Table A 1.2(B) to the other actions 
on/from the structure, 

NOTE The use of approaches 1, 2 or 3 is chosen in the National annex. 

(6) Overall stability for building structures (e.g. the stability of a slope supporting a 
building) should be verified in accordance with EN 1997. 

E> (7) Hydraulic (HYD) and buoyancy (UPL) failure (e.g. in the bottom of an excavation 
for a building structure) should be verified in accordance with EN 1997.(^ 



53 



BS EN 1990:2002+A1:2005 
EN ig90:2002+A1:2005 (E) 



M) Table A1.2(A) - Design values of actions (EQU) (Set A) 



Persistent 

and 

transient 

design 

situations 


Permanent actions 


Leading 

variable 

action C^) 


Accompanying variable 
actions 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


(Eq.6.10) 


}tjj,sup^k,j,sup 


Jfj,j,infGk,j,inf 


Tqa Qk,i 




rQA¥o;rQK\ 


C^) Variable actions are those considered in Table A 1.1 

NOTE 1 The /values may be set by the National annex. The recommended set of values for y are : 

X},j,sup=l,10 
rG,j,inf-0,90 

Yqj = 1,50 where unfavourable (0 where favourable) 
Yq^, = 1,50 where unfavourable (0 where favourable) 

NOTE 2 In cases where the verification of static equilibrium also involves the resistance of structural 
members, as an alternative to two separate verifications based on Tables A 1.2(A) and A1.2(B), a 
combined verification, based on Table AL2(A), may be adopted, if allowed by the National annex, with 
the following set of recommended values. The recommended values may be altered by the National 
annex. 
Xj,j,sup - 1,35 

Yqj = 1,50 where unfavourable (0 where favourable) 

Yq;, = 1,50 where unfavourable (0 where favourable) 

provided that applying Xi.jjnf ^ ^fi^ both to the favourable part and to the unfavourable part of permanent 
acfions does not give a more unfavourable effect. 



<M 



54 



ES> Table AL2(B) - Design values of actions (STR/GEO) (Set B) 



Persistent 

and transient 

design 

situations 


Pemianent actions 


Leading 

variable 

action 


Accompanying 
variable actions (*) 




Persistent 

and transient 

design 

situations 


Pennanent actions 


Leading 
variable 
action (*) 


Accompanying 
variable actions (*) 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


Unfavourable 


Favourable 


Action 


Main 


Others 


(Eq. 6.10) 


}tr,j,SUp^k,j,SUp 


X3j,ini^ko,inf 


7qjQk\ 




7Q,i?^o.ek,i 


(Eq. 6.10a) 


}ti,j,sup^k,j,sup 


}frjj,inf^k,j,inf 




YQAnAQkA 


rQ^Wo,QK. 


(Eq. 6.10b) 


9}tiJ,sup^kJ,sup 


i't}J,inf^k,j,inf 


TqaQki 




YqsWo.Qu 


(*) Variable actions are those considered in Table A 1.1 

NOTE 1 The choice between 6.10, or 6.10a and 6.10b will be in the National annex. In case of 6.10a and 6.10b, the National annex may in addition modify 6.10a to include 
permanent actions only. 

NOTE 2 The ;rand Rvalues may be set by the National annex. The following values for y and ^are recommended when using expressions 6. 10, or 6. 10a and 6. 10b. 

/Uj.sup ~ 1 5 -5 J 
rG,j,inf=l,00 

Yq^] = 1,50 where unfavourable (0 where favourable) 

Yq-, = 1,50 where unfavourable (0 where favourable) 

^- 0,85 (so that ^7go,sup = 0,85 x 1,35 = 1,15). 

See also EN 1991 to EN 1999 for y values to be used for imposed deformations. 

NOTE 3 The characteristic values of all permanent actions from one source are multiplied by ;ti,siip if the total resulting action effect is unfavourable and X3,inf if the total resulting 
action effect is favourable. For example, all actions originating from the self weight of the structure may be considered as coming from one source; this also applies if different 
materials are involved. 

NOTE 4 For particular verifications, the values for Yq and Yq may be subdivided into y^ and Yq and the model uncertainty factor Ysd- A value of Ysd in the range 1,05 to 1,15 can be 
used in most common cases and can be modified in the National annex. 



moo 

■ ■ to 

roio 



<M ic 



en lo 



en 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



ES) Table A1.2(C) - Design values of actions (STR/GEQ) (Set C) 



Persistent 

and 

transient 

design 

situation 


Permanent actions 


Leading 
variable 
action C^) 


Accompanying variable 
actions (*) 


Unfavourable 


Favourable 


Main (if any) 


Others 


(Eq.6.10) 


/uj,sup^k,j,sup 


yGl'mfG]^,j,mf 


7q,i Gk,i 




rQ,i?^0,iGk,i 


(*) Variable actions are those considered in Table Al.l 

NOTE The ^/values may be set by the National annex. The recommended set of values for ;Kare : 

rGj,sup= 1,00 

rG,j.nr= 1,00 

Yqj = 1,30 where unfavourable (0 where favourable) 

Yq-^ =1,30 where unfavourable (0 where favourable) 



Al.3.2 Design values of actions in tiie accidental and seismic design situations 

(1) The partial factors for actions for the ultimate limit states in the accidental and seis- 
mic design situations (expressions 6T la to 6.12b) should be 1,0. ^values are given in 
Table ALL 

NOTE For the seismic design situation see also EN 1998. 



{ac3 



(a5) 



Table A1.3 - Design values of actions for use in accidental and seismic 

combinations of actions 



Design 
situation 


Pemianent actions 


Leading 

accidental 

or seismic 

action 


Accompanying 
variable actions ('^'^) 


Unfavourable 


Favourable 


Main (if any) 


Others 


Accidental C^) 
(Eq.6.11a/b) 


^k,j,sup 


GkJJnf 


^d 




^2,i ek,i 


Seismic 
(Eq. 6.12a/b) 


^k,j,sup 


GkJ,inf 


AEd = MEk 


^2,i 0k,i 


(*) In the case of accidental design situations, the main variable action may be taken with its frequent or, 
as in seismic combinations of actions, its quasi-permanent values. The choice will be in the National 
annex, depending on the accidental action under consideration. See also EN 1991-1-2. 

C^*) Variable actions are those considered in Table ALL 



(M 



56 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



A 1.4 Serviceability limit states 

Al.4.1 Partial factors for actions 

(1) For serviceability limit states the partial factors for actions should be taken as 1,0 
except if differently specified in EN 1991 to EN 1999. 

Table A1.4 - Design values of actions for use in the combination of actions 



ES) 



Combination 


Permanent actions G^ 


Variable actions Qd 1 


Unfavourable 


Favourable 


Leading 


Others 


Characteristic 

Frequent 

Quasi-permanent 


^k,j,sup 
^kj,sup 
^k,j,sup 


G^k,j,mf 
G'kJ,inf 


¥2,\Qk\ 


^O.gk,! 

^2,iek,i 



<M 



Al.4.2 Serviceability criteria 



(1) Serviceability limit states in buildings should take into account criteria related, for 
example, to floor stiffness, differential floor levels, storey sway or/and building sway 
and roof stiffness. Stiffness criteria may be expressed in terms of limits for vertical de- 
flections and for vibrations. Sway criteria may be expressed in terms of limits for hori- 
zontal displacements. 

(2) The serviceability criteria should be specified for each project and agreed with the 
client. 

NOTE The serviceability criteria may be defined in the National annex. 

(3)P The serviceability criteria for deformations and vibrations shall be defined : 

- depending on the intended use ; 

- in relation to the serviceability requirements in accordance with 3.4 ; 

- independently of the materials used for supporting structural member. 

Al.4.3 Deformations and horizontal displacements 

(1) Vertical and horizontal deformations should be calculated in accordance with 
EN 1992 to EN 1999, by using the appropriate combinafions of actions according to 
expressions (6.14a) to (6.16b) taking into account the serviceability requirements given 
in 3.4(1). Special attention should be given to the distinction between reversible and 
irreversible limit states. 

(2) Vertical deflections are represented schematically in Figure. Al.l. 



57 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 




Figure Al,l - Definitions of vertical deflections 



Key: 



Wc Precamber in the unloaded structural member 

W] Initial part of the deflection under permanent loads of the relevant combination of 

actions according to expressions (6.14a) to (6.16b) 

W2 Long-term part of the deflection under permanent loads 

W3 Additional part of the deflection due to the variable actions of the relevant combi- 

nation of actions according to expressions (6.14a) to (6.16b) 

wtot Total deflection as sum of wi ,W2,W3 

vi^max Remaining total deflection taking into account the precamber 



(3) If the functioning or damage of the structiire or to finishes, or to non-structural 
members (e.g. partition walls, claddings) is being considered, the verification for deflec- 
tion should take account of those effects of permanent and variable actions that occur 
after the execution of the member or finish concerned. 

NOTE Guidance on which expression (6.14a) to (6.16b) to use is given in 6.5.3 and EN 1992 to 
EN 1999. 

(4) If the appearance of the structure is being considered, the quasi-permanent combina- 
tion (expression 6.16b) should be used. 

(5) If the comfort of the user, or the functioning of machinery are being considered, the 
verification should take account of the effects of the relevant variable actions. 

(6) Long term defoiTnations due to shrinkage, relaxation or creep should be considered 
where relevant, and calculated by using the effects of the permanent actions and quasi- 
permanent values of the variable actions. 

(7) Horizontal displacements are represented schematically in Figure A 1,2. 



58 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 




Figure AL2 - Definition of horizontal displacements 



Key: 



u 



Overall horizontal displacement over the building height H 
Horizontal displacement over a storey height Hi 



Al.4.4 Vibrations 

(1) To achieve satisfactory vibration behaviour of buildings and their structural 
members under serviceability conditions, the following aspects, amongst others, 
should be considered : 

a) the comfort of the user; 

b) the functioning of the structure or its structural members {e.g. cracks in 
partitions, damage to cladding, sensitivity of building contents to vibrations). 

Other aspects should be considered for each project and agreed with the client. 

(2) For the serviceability limit state of a structure or a structural member not to be 
exceeded when subjected to vibrations, the natural frequency of vibrations of the 
structure or structural member should be kept above appropriate values which 
depend upon the function of the building and the source of the vibration, and agreed 
with the client and/or the relevant authority, 

(3) If the natural frequency of vibrations of the structure is lower than the 
appropriate value, a more refined analysis of the dynamic response of the structure, 
including the consideration of damping, should be perfoiTued, 

NOTE For further guidance, see EN 1991-Fl, EN 1991-1-4 and ISO 10137. 

(4) Possible sources of vibration that should be considered include walking, 
synchronised movements of people, machinery, ground borne vibrations from traffic, 
and wind actions. These, and other sources, should be specified for each project and 
agreed with the client. 



59 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



|aS)18) Modification to the Annexes 

At the end of Annex A 1 and before Annex B, add the following Annex /\2;(ac^ 



E) 



Annex A2 

(normative) 
Application for bridges 



National Annex for EN 1990 Annex A2 

National choice is allowed in EN 1990 Annex A2 through the following clauses: 
General clauses 



Clause 


Item 


A2.1 (1) NOTE 3 


Use of Table 2.1: Design working life 


A2.2. 1(2) NOTE 1 


Combinations involving actions which are outside the scope of EN 1991 


A2.2.6(1)N0TE1 


Values of ^factors 


A2.3.1(l) 


Alteration of design values of actions for ultimate limit states 


A2.3.1(5) 


Choice of Approach 1, 2 or 3 


A2.3.1(7) 


Definition of forces due to ice pressure 


A2.3.1(8) 


Values of y^ factors for prestressing actions where not specified in the 
relevant design Eurocodes 


A2.3J TableA2.4(A) 
NOTES 1 and 2 


Values of ^factors 


A2.3.1 Table A2.4(B) 


- NOTE 1 : choice between 6.10 and 6.10a/b 

- NOTE 2: Values of y and ^factors 

- NOTE 4: Values of ^^ 


A2.3.1 Table A2.4(C) 


Values of /factors 


A2.3.2(l) 


Design values in Table A2.5 for accidental design situations, design values 
of accompanying variable actions and seismic design situations 


A2.3.2 Table A2,5 
NOTE 


Design values of actions 


A2.4.1(l) 

NOTE 1 (Table A2.6) 

NOTE 2 


Alternative /values for traffic actions for the serviceability limit state 
Infrequent combination of acfions 


A2.4.1(2) 


Serviceability requirements and criteria for the calculation of deformations 



Clauses specific for road bridges 



Clause 


Item 


A2.2.2 (1) 


Reference to the infrequent combination of actions 


A2.2.2(3) 


Combination rules for special vehicles 


A2.2.2(4) 


Combination rules for snow loads and traffic loads 


A2.2.2(6) 


Combination rules for wind and thermal actions 


A2.2.6(l) NOTE 2 


Values of y/^MQ factors 


A2.2.6(l)NOTE3 


Values of water forces 



Clauses specific for footbridges 



Clause 


Item 


A2.2.3(2) 


Combination rules for wind and thermal actions 


A2,23(3) 


Combination rules for snow loads and traffic loads 


A2.2.3(4) 


Combination rules for footbridges protected from bad weather 



m 



60 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



E) 



A2.4.3.2(l) 


Comfort criteria for footbridi^es 


Clauses specific for railway bridges 


Clause 


Item 


A2.2.4(l) 


Combination rules for snow loading on railway bridges 


A2.2.4(4) 


Maximum wind speed compatible with rail traffic 


A2.4.4.1(l)NOTE3 


Deformation and vibration requirements for temporary railway bridges 


A2.4.4.2.1(4)P 


Peak values of deck acceleration for railway bridges and associated 
frequency range 


A2.4.4.2.2 - Table 
A2.7NOTE 


Limiting values of deck twist for railway bridges 


A2.4.4.2.2(3)P 


Limiting values of the total deck twist for railway bridges 


A2.4.4.2.3(l) 


Vertical deformation of ballasted and non ballasted railway bridges 


A2.4.4.2.3(2) 


Limitations on the rotations of non ballasted bridge deck ends for railway 
bridges 


A2.4.4.2.3(3) 


Additional limits of angular rotations at the end of decks 


A2.4.4.2.4(2)- Table 
A2.8NOTE3 


Values of Oi and n factors 


A2.4.4.2.4(3) 


Minimum lateral frequency for railway bridges 


A2.4.4.3.2(6) 


Requirements for passenger comfort for temporary bridges 



(B 



61 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

A2.1 Field of application 

ES) Text deleted ^M 

(1) This Annex A2 to EN 1990 gives rules and methods for establishing combinations of 
actions for serviceability and ultimate limit state verifications (except fatigue verifications) 
with the recommended design values of permanent, variable and accidental actions and y/ 
factors to be used in the design of road bridges, footbridges and railway bridges. It also 
applies to actions during execution. Methods and rules for verifications relating to some 
material-independent serviceability limit states are also given. 

NOTE 1 Symbols, notations, Load Models and groups of loads are those used or defined in the relevant section 
of EN 1991-2. 

NOTE 2 Symbols, notations and models of construction loads are those defined in EN 1991-1-6. 

NOTE 3 Guidance may be given in the National Annex with regard to the use of Table 2.1 (design working 
life). 

NOTE 4 Most of the combination rules defined in clauses A2.2.2 to A2.2.5 are simplifications intended to avoid 
needlessly complicated calculations. They may be changed in the National Annex or for the individual project as 
described in A2.2.1 to A2.2.5. 

NOTE 5 This Annex A2 to EN 1990 does not include rules for the determination of actions on structural 
bearings (forces and moments) and associated movements of bearings or give rules for the analysis of bridges 
involving ground-structure interaction that may depend on movements or deformations of structural bearings. 

(2) The iTjles given in this Annex A2 to EN 1990 may not be sufficient for: 

— bridges that are not covered by EN 1991-2 (for example bridges under an airport 
runway, mechanically-moveable bridges, roofed bridges, bridges cariying water, etc.), 

— bridges carrying both road and rail traffic, and 

— other civil engineering stmctures caiTying traffic loads (for example backfill behind a 
retaining wall). <g| 

E) Text deleted ^M 



62 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



A2.2 Combinations of actions 
A2.2.1 General 

(1) Effects of actions that camiot occur simultaneously due to physical or functional reasons 
need not be considered together in combinations of actions. 

(2) Combinations involving actions which are outside the scope of EN 1991 (e.g. due to 
mining subsidence, particular wind effects, water, floating debris, flooding, mud slides, 
avalanches, fire and ice pressure) should be defined in accordance with EN 1990, 1.1(3). 

NOTE 1 Combinations involving actions that are outside the scope of EN 1991 may be defined either in the 
National Annex or for the individual project. 

NOTE 2 For seismic actions, see EN 1998. 

NOTE 3 For water actions exerted by currents and debris effects, see also EN 1991-1-6. 

(3) The combinations of actions given in expressions 6.9a to 6.12b should be used when 
verifying ultimate limit states. 

NOTE Expressions 6.9a to 6.12b are not for the verification of the limit states due to fatigue. For fatigue 
verifications, see EN 1991 to EN 1999. 

(4) The combinations of actions given in expressions 6.14a to 6.16b should be used when 
verifying serviceability Hmit states. Additional rules are given in A2.4 for verifications 
regarding deformations and vibrations. 

(5) Where relevant, variable traffic actions should be taken into account simultaneously with 
each other in accordance with the relevant sections of EN 1991-2. 

(6)P During execution the relevant design situations shall be taken into account. 

(7)P The relevant design situations shall be taken into account where a bridge is brought into 
use in stages. r^ 



63 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

(8) Where relevant, particular construction loads should be taken into account simultaneously 

in the appropriate combinations of actions. 

NOTE Where construction loads cannot occur simultaneously due to the implementation of control measures 
they need not be taken into account in the relevant combinations of actions. 

(9)P For any combination of variable traffic actions with other variable actions specified in 
other parts of EN 1991, any group of loads, as defined in EN 1991-2, shall be taken into 
account as one variable action. 

(10) Snow loads and wind actions need not be considered simultaneously with loads arising 
from construction activity Q^^ (i.e. loads due to working personnel). 

NOTE For an individual project it may be necessary to agree the requirements for snow loads and wind actions 
to be taken into account simultaneously with other construction loads (e.g. actions due to heavy equipment or 
cranes) during some transient design situations. See also EN 1991-1-3, 1-4 and 1-6. 

(11) Where relevant, thermal and water actions should be considered simultaneously with 
construction loads. Where relevant the various parameters governing water actions and 
components of thermal actions should be taken into account when identifying appropriate 
combinations with construction loads. 

(12) The inclusion of prestressing actions in combinations of actions should be in accordance 
with A2.3.1(8) and EN 1992 to EN 1999. 

(13) Effects of uneven settlements should be taken into account if they are considered 
significant compared to the effects from direct actions. 

NOTE The individual project may specify limits on total settlement and differential settlement. 

(14) Where the structure is very sensitive to uneven settlements, uncertainty in the assessment 
of these settlements should be taken into account. 

(15) Uneven settlements on the structure due to soil subsidence should be classified as a 
permanent action, G^eh and included in combinations of actions for ultimate and serviceability 
limit state verifications of the structure. Gset should be represented by a set of values 
corresponding to differences (compared to a reference level) of settlements between 
individual foundations or parts of foundations, dsetj {i is the number of the individual 
foundation or part of foundation). 

NOTE 1 Setdements are mainly caused by permanent loads and backfill. Variable actions may have to be taken 
into account for some individual projects. 

NOTE 2 Settlements vary monotonically (in the same direction) with time and need to be taken into account 
from the time they give rise to effects in the structure (i.e. after the stmcture, or a part of it, becomes statically 
indetemiinate). In addition, in the case of a concrete structure or a structure with concrete elements, there may be 
an interaction between the development of setdements and creep of concrete members. 

(16) The differences of settlements of individual foundations or parts of foundations, dsetj, 
should be taken into account as best-estimate predicted values in accordance with EN 1 997 with 
due regard for the construction process of the structure. 

NOTE Methods for the assessment of settlements are given in EN 1997 



64 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

(17) In the absence of control measures, the permanent action representing settlements should 

be determined as follows: 

the best-estimate predicted values dseu are assigned to all individual foundations or parts of 

foundations, 
- two individual foundations or parts of an individual foundation, selected in order to obtain 

the most unfavourable effect, are subject to a settlement dsetj ± ^dsetj, where Adsetj takes 

account of uncertainties attached to the assessment of settlements. 



A2.2.2 Combination rules for road bridges 

(1) The infrequent values of variable actions may be used for certain serviceability limit states 
of concrete bridges. 

NOTE The National Annex may refer to the infrequent combination of actions. The expression of this 
combination of actions is: 

E, = e{g,- ; P ; ^, -,„,,a,, ; r,,fi,„} ./ > 1 ; / > 1 (A2.1a) 

in which the combination of actions in brackets { } may be expressed as: 

(2) Load Model 2 (or associated group of loads grlb) and the concentrated load g/wA: (see 
5.3.2.2 in EN 1991-2) on footways need not be combined with any other variable non traffic 
action. 

(3) Neither snow loads nor wind actions need be combined with: 

- braking and acceleration forces or the centrifugal forces or the associated group of loads 

- loads on footways and cycle tracks or with the associated group of loads gr3, 

- crowd loading (Load Model 4) or the associated group of loads gr4. 

NOTE The combination rules for special vehicles (see EN 1991-2, Annex A, Infonnative) with normal traffic 
(covered by LMl and LM2) and other variable actions may be referenced as appropriate in the National Annex 
or agreed for the individual project. 

(4) Snow loads need not be combined with Load Models 1 and 2 or with the associated groups 
of loads grla and grlb unless otherwise specified for particular geographical areas. 

NOTE Geographical areas where snow loads may have to be combined with groups of loads grla and grlb in 
combinations of actions may be specified in the National Annex. 

(5) No wind action greater than the smaller of F^y and ^o^^n should be combined with Load 
Model 1 or with the associated group of loads grla. 

NOTE For wind actions, see EN 199 1-1 -4. 

(6) Wind actions and thermal actions need not be taken into account simultaneously unless 
otherwise specified for local climatic conditions. 

NOTE Depending upon the local climatic conditions a different simultaneity rule for wind and themial actions 
may be defined either in the National Annex or for the individual project. ^ 



65 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

A2.2.3 Combination rules for footbridges 

(1) The concentrated load Qf^k need not be combined with any other variable actions that are 
not due to traffic. 

(2) Wind actions and thermal actions need not be taken into account simultaneously unless 
otherwise specified for local climatic conditions. 

NOTE Depending upon the local climatic conditions a different simultaneity rule for wind and themial actions 
may be defined either in the National Annex or for the individual project. 

(3) Snow loads need not be combined with groups of loads grl and gr2 for footbridges unless 
otherwise specified for particular geographical areas and certain types of footbridges. 

NOTE Geographical areas, and certain types of footbridges, where snow loads may have to be combined with 
groups of loads grl and gr2 in combinations of actions may be specified in the National Annex. 

(4) For footbridges on which pedestrian and cycle traffic is fully protected from all types of 
bad weather, specific combinations of actions should be defined. 

NOTE Such combinations of actions may be given as appropriate in the National Annex or agreed for the 
individual project. Combinations of actions similar to those for buildings (see Annex Al), the imposed loads 
being replaced by the relevant group of loads and the ^/factors for traffic actions being in accordance with Table 
A2.2, are recommended. 

A2.2.4 Combination rules for railway bridges 

(1) Snow loads need not be taken into account in any combination for persistent design situations 
nor for any transient design situation after the completion of the bridge unless otherwise specified 
for particular geographical areas and certain types of railway bridges. 

NOTE Geographical areas, and certain types of railway bridges, where snow loads may have to be taken into 
account in combinations of actions are to be specified in the National Annex. 

(2) The combinations of actions to be taken into account when traffic actions and wind actions 
act simultaneously should include: 

vertical rail traffic actions including dynamic factor, horizontal rail traffic actions and 
wind forces with each action being considered as the leading action of the combination of 
actions one at a time; 
ES) - vertical rail traffic actions excluding dynamic factor and lateral rail traffic actions from 
the "unloaded train" defined in EN 1991-2 (6.3.4 and 6.5) with wind forces for checking 
stability."(Ac3 

(3) Wind action need not be combined with: 

- groups of loads gr 13 or gr 23; 

- groups of loads gr 16, gr 17, gr 26, gr 27 and Load Model SW/2 (see EN 1991-2, 6.3.3). 

(4) No wind action greater than the smaller of F^* and y/^Fiyj. should be combined with traffic 
actions. 



NOTE The National Annex may give the limits of the maximum wind speed(s) compatible with rail traffic for 



detemiining t^y . See also EN 1991-1-4. 



66 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



(5) Actions due to aerodynamic effects of rail traffic (see EN 1991-2, 6.6) and wind actions 
should be combined together. Each action should be considered individually as a leading variable 
action. 

(6) If a structural member is not directly exposed to wind, the action q-± due to aerodynamic 
effects should be determined for train speeds enhanced by the speed of the wind. 

(7) Where groups of loads are not used for rail traffic loading, rail traffic loading should be 
considered as a single multi-directional variable action with individual components of rail 
traffic actions to be taken as the maximum unfavourable and minimum favourable values as 
appropriate. 

A2.2.5 Combinations of actions for accidental (non seismic) design situations 

(1) Where an action for an accidental design situation needs to be taken into account, no other 
accidental action or wind action or snow load need be taken into account in the same 
combination. 

(2) For an accidental design situation concerning impact from traffic (road or rail traffic) 
under the bridge, the loads due to the traffic on the bridge should be taken into account in the 
combinations as accompanying actions with their frequent value. 

(Ag) NOTE 1 For actions due to impact from traffic, see EN 1991-1-7. (acD 

NOTE 2 Additional combinations of actions for other accidental design situations (e.g. combination of road or 
rail traffic actions with avalanche, flood or scour effects) may be agreed for the individual project. 

NOTE 3 Also see 1) in Table A2.1. 

(3) For railway bridges, for an accidental design situation concerning actions caused by a 
derailed train on the bridge, rail traffic actions on the other tracks should be taken into account 
as accompanying actions in the combinations with their combination value. 

E5) NOTE 1 For actions due to impact from traffic, see EN 1991-1-7. {ac^ 

NOTE 2 Actions for accidental design situations due to impact from rail traffic running on the bridge including 
derailment actions are specified in EN1991-2, 6.7.1. 

(4) Accidental design situations involving ship collisions against bridges should be identified. 
NOTE For ship impact, see EN 1991 -1-7. Additional requirements may be specified for the individual project. 

A2.2.6 Values of ^^factors 

(1) Values of ^^ factors should be specified. 

NOTE 1 The ^values may be set by the National Annex. Recommended values of ^factors for the groups of 
traffic loads and the more common other actions are given in: 

Table A2. 1 for road bridges, 

Table A2.2 for footbridges, and 

Table A2.3 for railway bridges, both for groups of loads and individual components of traffic actions. 



67 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



E> 



Table A2.1 - Recommended values of ^factors for road bridges 



Action 


Symbol 


V/o 


¥^ 


Wi 


Traffic loads 
(see EN 1991-2, 
Table 4.4) 


grla 

(LMl+pedestrian or 
cycle-track loads) ^) 


TS 


0,75 


0,75 





UDL 


0,40 


0,40 





Pedestrian+cycle-track loads "^ 


0,40 


0,40 





grlb (Single axle) 





0,75 





gr2 (Horizontal forces) 











gr3 (Pedestrian loads) 





|Aci}0,40^ 





gr4 (LM4 - Crowd loading)) 





|AC^ -<ACD 





gr5 (LM3 - Special vehicles)) 





(AC£> -<Acn 





Wind forces 


Pwk 

Persistent design situations 
Execution 


0,6 
0,8 


0,2 






Fw 


1,0 


- 


- 


Thermal actions 


n 


0,6^^ 


0,6 


0,5 


Snow loads 


Qsn k (during execution) 


0,8 


- 


- 


Construction loads 


a 


1,0 


- 


1,0 


1) The recommended values of ij/q, y/\ and y/j for grla and grlb are given for road traffic corresponding to 
adjusting factors Oqi, a,^,, Cfq, and pg equal to 1. Those relating to UDL correspond to common traffic 

scenarios, in which a rare accumulation of lorries can occur. Other values may be envisaged for other classes of 
routes, or of expected traffic, related to the choice of the corresponding a factors. For example, a value of y/i 
other than zero may be envisaged for the UDL system of LMl only, for bridges supporting severe continuous 
traffic. See also EN 1998. 

2) The combination value of the pedestrian and cycle-track load, mentioned in Table 4.4a of EN 1991-2, is a 
"reduced" value. y/Q and y/\ factors are applicable to this value. 

3) The recommended ^/q value for thermal actions may in most cases be reduced to for ultimate limit states 
EQU, STR and GEO. See also the design Eurocodes. 



NOTE 2 When the National Annex refers to the infrequent combination of actions for some serviceability limit 
states of concrete bridges, the National Annex may define the values of y/imfq- The recommended values of y/}j,r(q are 

- 0,80 for grla (LMI), grlb (LM2), gr3 (pedestrian loads), gr4 (LM4, crowd loading) and r(themial actions); 

- 0,60 for F(i7, in persistent design situations; 

- 1 ,00 in other cases (i.e. the characteristic value is used as the infrequent value). 

NOTE 3 Tire characteristic values of wind actions and snow loads during execution are defined in EN 199LL6. 
Where relevant, representative values of water forces (F^J may be defined in the National Annex or for the 
individual project. 



Table A2.2 - Recommended values of ^factors for footbridges 



Action 


Symbol 


^0 


m 


^2 


Traffic loads 


grl 


0,40 


0,40 





Qm 











gr2 











Wind forces 


Fwk 


0,3 


0,2 





Themial actions 


T, 


0,6'^ 


0,6 


0,5 


Snow loads 


Qsn.k (during execution) 


0,8 


- 





Construction loads 


a 


1,0 


- 


1,0 


1) The recommended y/o value for themial actions may in most cases be reduced to for ultimate limit states 
EQU, STR and GEO. See also the design Eurocodes. 



NOTE 4 For footbridges, the infrequent value of variable actions is not relevant. 



(M 



68 



BS EN 19gO:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



Table A2.3 - Recommended values of ^factors for railway bridges 



Actions 


m 


W^ 


^/^ 


Individual 
components 
of traffic 
actions^- 


LM71 
SW/0 
SW/2 

Unloaded train 
HSLM 


0,80 
0,80 


1,00 
LOO 


1) 
1) 

1,00 
1,00 









Traction and braking 

Centrifugal forces 

Interaction forces due to deformation under vertical 

traffic loads 


Individual components of 
traffic actions in design 
situations where the traffic 
loads are considered as a 
single (multi-directional) 
leading action and not as 
groups of loads should use 
the same values of ^factors 
as those adopted for the 
associated vertical loads 


Nosing forces 

Non public footpaths loads 

Real trains 

Horizontal earth pressure due to traffic load 

surcharge 

Aerodynamic effects 


1,00 
0,80 
1,00 
0,80 
0,80 


0,80 
0,50 

1,00 

1) 

0,50 









Main traffic 

actions 

(groups of loads) 


grll(LM71+SW/0) 

grl2(LM71 + SW/0) 

grl3 (Braking/traction) 
grl4 (Centrifugal/nosing) 
grl5 (Unloaded train) 

gr 16 (SW/2) 

gr 17 (SW/2) 

gr21 (LM71 + SW/0) 

gr22(LM71 + SW/0) 

gr23 (Braking/traction) 
gr24 (Centrifugal/nosing) 
gr26 (SW/2) 

gr27 (SW2) 

gr31 (LM71 + SW/0) 


Max. vertical 1 with max. 
longitudinal 


0,80 


0,80 





Max. vertical 2 with max. 
transverse 


Max. longitudinal 


Max. lateral 


Lateral stability with 
"unloaded train" 


SW/2 with max. 
longitudinal 


SW/2 with max. 
transverse 


Max. vertical 1 with max. 
longitudinal 


0,80 


0,70 





Max. vertical 2 with max 
transverse 


Max. longitudinal 


Max. lateral 


SW/2 with max. 
longitudinal 


SW/2 with max. 
transverse 


Additional load cases 


0,80 


0,60 





Other operating 
actions 


Aerodynamic effects 


0,80 


0,50 





General maintenance loading for non public footpaths 


0,80 


0,50 





Wind forces ^^ 


^Wk 


0,75 


0,50 







1,00 








Table continued on next page 









^ 



69 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 



Table continued from previous page 








Themial 
actions ^^ 


T, 


0,60 


0,60 


0,50 


Snow loads 


Osn k (during execution) 


0,8 


- 





Construction loads 


ft 


1,0 


- 


1,0 


1) 0,8 if 1 track only is loaded 

0,7 if 2 tracks are simultaneously loaded 

0,6 if 3 or more tracks are simultaneously loaded. 

2) When wind forces act simultaneously with traffic actions, the wind force xj/q Fwk should be taken as 
no greater than Ff (see EN 1991-1-4). See A2.2.4(4). 

3) See EN 1991-1-5. 

4) If deformation is being considered for Persistent and Transient design situations, y/i should be 
taken equal to 1,00 for rail traffic actions. For seismic design situations, see Table A2.5. 

5) Minimum coexistent favourable vertical load with individual components of rail traffic actions 
(e.g. centrifugal, traction or braking) is 0,5LM71, etc. 



NOTE 5 For specific design situations (e.g. calculation of bridge camber for aesthetics and drainage 
consideration, calculation of clearance, etc.) the requirements for the combinations of actions to be used may be 
defined for the individual project. 

NOTE 6 For railway bridges, the infrequent value of variable actions is not relevant. 

[Ac^ (2) For railway bridges, a unique Rvalue should be applied to one group of loads as defined 
in EN 1991-2, and taken as equal to the Rvalue apphcable to the leading component of the 
group. <Ac3 

(3) For railway bridges, where groups of loads are used the groups of loads defined in 
EN 1991-2, 6.8.2, Table 6.1 1 should be used. 

(4) Where relevant, combinations of individual traffic actions (including individual 
components) should be taken into account for railway bridges. Individual traffic actions may 
also have to be taken into account, for example for the design of bearings, for the assessment of 
maximum lateral and minimum vertical traffic loading, bearing restraints, maximum overtiming 
effects on abutments (especially for continuous bridges), etc., see Table A2.3.(^ 

NOTE Individual traffic actions may also have to be taken into account, for example for the design of bearings, for 
the assessment of maximum lateral and minimum vertical traffic loading, bearing restraints, maximum overturning 
effects on abutments (especially for continuous bridges), etc., see Table A2.3. 

A2.3 Ultimate limit states 

NOTE Verification for fatigue excluded. 

A2.3.1 Design values of actions in persistent and transient design situations 

(1) The design values of actions for ultimate limit states in the persistent and transient design 
situations (expressions 6.9a to 6.10b) should be in accordance with Tables A2.4(A) to (C). 

NOTE The values in Tables A2.4(A) to (C) may be changed in the National Annex (e.g. for different reliability 
levels see Section 2 and Annex B). 

(2) In applying Tables A2.4(A) to A2.4(C) in cases when the limit state is very sensitive to 
variations in the magnitude of permanent actions, the upper and lower characteristic values of 
these actions should be taken according to 4. 1 .2(2)P. ^^ 



70 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

(3) Static equilibrium (EQU, see 6.4.1 and 6.4.2(2)) for bridges should be verified using the 
design values of actions in Table A2.4(A). 

(4) Design of structural members (STR, see 6.4.1) not involving geotechnical actions should 
be verified using the design values of actions in Table A2.4(B). 

(5) Design of structural members (footings, piles, piers, side walls, wing walls, flank walls 
and front walls of abutments, ballast retention walls, etc.) (STR) involving geotechnical 
actions and the resistance of the ground (GEO, see 6.4.1) should be verified using one only of 
the following three approaches supplemented, for geotechnical actions and resistances, by EN 
1997: 

- Approach 1: Applying in separate calculations design values from Table A2.4(C) and 
Table A2.4(B) to the geotechnical actions as well as the actions on/from the structure; 

- Approach 2: Applying design values of actions from Table A2.4(B) to the geotechnical 
actions as well as the actions on/from the structure; 

- Approach 3: Applying design values of actions from Table A2.4(C) to the geotechnical 
actions and, simultaneously, applying design values of actions from Table A2.4(B) to the 
actions on/from the stmcture. 

NOTE The choice of approach 1, 2 or 3 is given in the National Annex. 

(6) Site Stability (e.g. the stability of a slope supporting a bridge pier) should be verified in 
accordance with EN 1997. 

E§) (7) Hydraulic (HYD) and buoyancy (UPL) failure (e.g. in the bottom of an excavation for a 
bridge foundation), if relevant, should be verified in accordance with EN 1997. (^ 

NOTE For water actions and debris effects, see EN 1991-1-6. General and local scour depths may have to be 
assessed for the individual project. Requirements for taking account offerees due to ice pressure on bridge piers, etc., 
may be defined as appropriate in the National Annex or for the individual project. 

(8) The }f> values to be used for prestressing actions should be specified for the relevant 
representative values of these actions in accordance with EN 1990 to EN 1999. 

NOTE In the cases where }f> values are not provided in the relevant design Eurocodes, these values may be defined 
as appropriate in the National Annex or for the individual project. They depend, intej^ alia, on: 

the type of prestress (see the Note in 4. 1 .2(6)) 

the classification of prestress as a direct or an indirect action (see 1 .5.3.1) 

the type of stmctural analysis (see 1.5.6) 

the unfavourable or favourable character of the prestressing action and the leading or accompanying character of 

prestressing in the combination. 
See also EN 1991-1-6 during execution. 



71 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



lEz) Table A2.4(A) - Design values of actions (EQU) (Set A) 



Persistent and 
transient 
design 
situation 



Pemianent actions 



Unfavourable 



Favourable 



Prestress 



Leading 

variable 
action C^) 



Accompanying variable 
actions C^) 



Main 
(if any) 



Others 



(Eq. 6.10) 



Jtj,j,sup^k,j,sup 



?t}J,inf^kJ,inf 



7pP 



rQ,i Qk 



7Q,m^Qk,i 



(*) Variable actions are those considered in Tables A2.1 to A2.3. 



NOTE 1 The /values for the persistent and transient design situations may be set by the National Annex. 
For persistent design situations^ the recommended set of values for }^are: 

}f^ = 1,35 for road and pedestrian traffic actions, where unfavourable (0 where favourable) 

Yq^ 1,45 for rail traffic actions, where unfavourable (0 where favourable) 

Yq = 1,50 for all other variable actions for persistent design situations, where unfavourable (0 where favourable). 

Y> = recommended values defined in the relevant design Eurocode. 

For transient design situations during which there is a risk of loss of static equilibrium, Q\,] represents the dominant 
destabilising variable action and 2k a represents the relevant accompanying destabilising variable actions. 

During execution, if the construction process is adequately controlled, the recommended set of values for /are: 
rG.sup==l,05 

Yq = 1,35 for construction loads where unfavourable (0 where favourable) 

Yq = 1,50 for all other variable actions, where unfavourable (0 where favourable) 

^'- Where a counterweight is used, the variability of its characteristics may be taken into account, for example, by 
one or both of the following recommended rules: 

- applying a partial factor Yg inf ~ ^^^ where the self-weight is not well defined (e.g. containers); 

- by considering a variation of its project-defined position specified proportionately to the dimensions of the 
bridge, where the magnitude of the counterweight is well defined. For steel bridges during launching, the 
variation of the counterweight position is often taken equal to ± 1 m. 

NOTE 2 For the verification of uplift of bearings of continuous bridges or in cases where the verification of static 
equilibrium also involves the resistance of structural elements (for example where the loss of static equilibrium is 
prevented by stabilising systems or devices, e.g. anchors, stays or auxihary columns), as an alternative to two 
separate verifications based on Tables A2.4(A) and A2.4(B), a combined verification, based on Table A2.4(A), may 
be adopted. The National Annex may set the /values. The following values of /are recommended: 

/Gj,f=l,25 

Yq= 1,35 for road and pedestrian traffic actions, where unfavourable (0 where favourable) 

Yq= 1,45 for rail traffic actions, where unfavourable (0 where favourable) 

Yq = 1,50 for all other variable actions for persistent design situations, where unfavourable (0 where favourable) 

Yq ^ 1,35 for all other variable actions, where unfavourable (0 where favourable) 

provided that applying Ycmf^ 1,00 both to the favourable part and to the unfavourable part of permanent actions 

does not give a more unfavourable effect. 



(Aca 



72 



tm Table A2.4(B) - Design values of actions (STR/GEO) (Set B) 



Persistent 

and 

transient 

design 

situation 


Pemianent actions 


Pre stress 


Leading 
variable 
action (*) 


Accompanying 
variable actions (*) 




Persistent 
and transient 
design 
situation 


Pemianent actions 


Prestress 


Leading 
variable 
action (*) 


Accompanying 
variable actions (*) 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


(Eq.6.10) 


}tl.j,sup^k,j,siip 


YcjM^KjM 


}tp 


TqaQk^ 




YQ;mK^QKi 


(Eq. 6.10a) 


?tl,i\sup^k,j,sup 


?6,j,inl'^kj,inr 


}^P 




YQA^AQkJ 


Yq^mQu 


(Eq. 6.10b) 


b"?&,j,sup^k.j,sup 


?ti,i,inL^k.j,inr 


Y^P 


rQ.,\QK\ 




Yq,\ ^o,i2k,, 


(*) Variab 


e actions are those considered in Tables A2.1 to A2.3. 


NOTE 1 The choice between 6.10, or 6.10a and 6T0b will be in the National Annex. In the case of 6.10a and 6.10b, the National Annex may in addition modify 6.10a to include permanent actions 
only. 

NOTE 2 The /and <^ values may be set by the National Annex. The following values for /and *f are recommended when using expressions 6.10, or 6.10a and 6.10b: 

rG,mt-=i,oo 

Yq= 1,35 when Q represents unfavourable actions due to road or pedestrian traffic (0 when favourable) 

Yq = 1,45 when Q represents unfavourable actions due to rail traffic, for groups of loads 11 to 31 (except 16, 17, 26''^ and 27^^), load models LM71, SW/0 and HSLM and real trains, when 

considered as individual leading traffic actions (0 when favourable) 

Yq= \,20 when Q represents unfavourable actions due to rail traffic, for groups of loads 16 and 17 and SW/2 (0 when favourable) 

;t^ = 1,50 for other traffic actions and other variable actions ^^ 

^= 0,85 (so that ^7g,sup = 0,85 x 1,35 = 1,15). 

Yc^^t = 1,20 in the case of a linear elastic analysis, and Yc^^t = 1,35 in the case of a non linear analysis, for design situations where actions due to uneven settlements may have unfavourable effects. 

For design situations where actions due to uneven settlements may have favourable effects, these actions are not to be taken into account. 

See also EN 1991 to EN 1999 for /values to be used for imposed deformations. 

Y> = recommended values defined in the relevant design Eurocode. 

'^This value covers: self- weight of structural and non structural elements, ballast, soil, ground water and free water, removable loads, etc. 

^^This value covers: variable horizontal earth pressure from soil, ground water, free water and ballast, traffic load surcharge earth pressure, traffic aerodynamic actions, wind and thermal actions, etc. 
^¥or rail traffic actions for groups of loads 26 and 27 Yo = U^O may be applied to individual components of traffic actions associated with SW/2 and Yq = U45 may be applied to individual 
components of traffic actions associated with load models LM71, SW/0 and HSLM, etc. 


Table continued on next page 



<AC3 



mro 
zc/> 

o-^ 

§p 

roro 

+ 2 

>o 

<to 
rr + 

oil 
o-. 
oiro 

5g 



•>4 



-g 

^ 



mD3 
zc/) 

^ z 



ro 



iO 



Table continued from previous page 



lo to 

+ o 
>o 

<ji ro 
m o 



NOTE 3 The characteristic values of all pemianent actions from one source are multiplied by Xt,sup if the total resulting action effect is unfavourable and Xjjnf if the total resulting action effect is 
favourable. For example, all actions originating from the self-weight of the staicture may be considered as coming from one source; this also applies if different materials are involved. See however 
A2.3.1(2). 

NOTE 4 For particular verifications, the values for Xi and jf^ may be subdivided into ^ and % and the model uncertainty factor }^d- A value of ;^d in the range 1,0-1,15 may be used in most common 
cases and may be modified in the National Annex. 

N OTE 5 Where actions due to water are not covered by EN 1997 (e.g. flowing water), the combinations of actions to be used may be specified for the individual project. 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



\Ei} Table A2.4(C) - Design values of actions (STR/GEO) (Set C) 



Persistent and 
transient 
design 
situation 


Permanent actions 


Prestress 


Leading 

variable 

action C^) 


Accompanying variable 
actions {^) 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


(Eq.6.10) 


7Gj,sup^kj,sup 


^GjJnfG'kj.inf 


TpP 


n)A QkA 




7Q^W0,lQKi 


C^) Variable actions are those considered in Tables A2.1 to A2.3 


NOTE The /values may be set by the National Annex. The recoiraiiended set of values for /are: 
7g,sup=U00 

feet =1,00 

Xj = 1,15 for road and pedestrian traffic actions where unfavourable (0 where favourable) 

^ = 1,25 for rail traffic actions where unfavourable (0 where favourable) 

7q = 1,30 for the variable part of horizontal earth pressure from soil, ground water, free water and ballast, 

for traffic load surcharge horizontal earth pressure, where unfavourable (0 where favourable) 

^ = 1,30 for all other variable actions where unfavourable (0 where favourable) 

^set = 1,00 in the case of linear elastic or non linear analysis, for design situations where actions due to 

uneven settlements may have unfavourable effects. For design situations where actions due to uneven 

settlements may have favourable effects, these actions are not to be taken into account. 

]^ ^ recommended values defined in the relevant design Eurocode. 



|Ai) A2.3.2 Design values of actions in the accidental and seismic design situations 

(1) The partial factors for actions for the ultimate limit states in the accidental and 
seismic design situations (expressions 6.11a to 6.12b) are given in Table A2.5. ?^values 
are given in Tables A2.1 to A2.3. 



NOTE For the seismic design situation see also EN 1998. 



<B 



75 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Table A2.5 - Design values of actions for use in accidental and seismic 

combinations of actions 



IM) 



Design 
situation 


Permanent actions 


Prestress 


Accidental 

or seismic 

action 


Accompanying 
variable actions {^^) 


Unfavourable 


Favourable 


Main 
(if any) 


Others 


Accidental(*) 
(Eq.6.11a/b) 


^k,j,sup 


Gk,j,mf 


P 


A, 


or 


W2a Gk,i 


SeismicC^*"^') 
(Eq.6.12a/b) 


^kj,siip 


GkJ,inf 


P 


A Ed - Yl^Ek 


¥2,i 0k,i 


(*) In the case of accidental design situations, the main variable action may be taken with its frequent or, 
as in seismic combinations of actions, its quasi-permanent values. The choice will be in the National 
Annex, depending on the accidental action under consideration. 

C^*) Variable actions are those considered in Tables A2.1 to A2.3. 

(***) The National Annex or the individual project may specify particular seismic design situations. For 
railway bridges only one track need be loaded and load model SW/2 may be neglected. 

NOTE The design values in this Table A2.5 may be changed in the National Annex. The recommended 
values are y= 1 ,0 for all non seismic actions. 



E) (2) Where, in special cases, one or several variable actions need to be considered 
simultaneously with the accidental action, their representative values should be defined. 

NOTE As an example, in the case of bridges built by the cantilevered method, some construction loads 
may be considered as simultaneous with the action corresponding to the accidental fall of a prefabricated 
unit. The relevant representative values may be defined for the individual project. 

(3) For execution phases during which there is a risk of loss of static equilibrium, the 
combination of actions should be as follows: 



Z^.,.,p"+"ZG,,i„f"+"^"+"4,"+'y2a, 

where: 



(A2.2) 



Q^i^ is the characteristic value of construction loads as defined in EN 1991-1-6 (i.e. 
the characteristic value of the relevant combination of groups gca, 2cb, 2cc, 2cd, 
gee and gef). 

A2.4 Serviceability and other specific limit states 

A2.4.1 General 

(1) For serviceability limit states the design values of actions should be taken from 
Table A2.6 except if differently specified in ENT991 to EN1999. 

NOTE 1 7 factors for traffic and other actions for the serviceability limit state may be defined in the 
National Annex. The recommended design values are given in Table A2.6, with all ^^factors being taken 
as 1,0. /— - 



76 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

Table A2.6 - Design values of actions for use in the combination of actions 



E© 



Combination 


Permanent actions G^ 


Prestress 


Variable actions Q^\ \ 


Unfavourable 


Favourable 


Leading 


Others 


Characteristic 

Frequent 

Quasi-permanent 


^k,j,sup 
^k,j,sup 

<^k,j,si.p 


<J^k.j,inf 
^k,j,inf 
^k,i,iiif 


P 
P 
P 


Gk,i 

^Kiekj 


¥2,Qk:^ 

¥2,Qk.i 



E) NOTE 2 The National Annex may also refer to the infrequent combination of actions. 

(2) The serviceability criteria should be defined in relation to the serviceability 
requirements in accordance with 3.4 and EN 1992 to EN 1999. Deformations should be 
calculated in accordance with EN 1991 to EN 1999 by using the appropriate 
combinations of actions according to expressions (6.14a) to (6.16b) (see Table A2.6) 
taking into account the serviceability requirements and the distinction between 
reversible and irreversible limit states. 

NOTE Serviceability requirements and criteria may be defined as appropriate in the National Annex or 
for the individual project. 

A2.4.2 Serviceability criteria regarding deformation and vibration for road bridges 

(1) Where relevant, requirements and criteria should be defined for road bridges 
concerning: 

- uplift of the bridge deck at supports, 
damage to struclTiral bearings. 

NOTE Uplift at the end of a deck can jeopardise traffic safety and damage structural and non structural 
elements. Uplift may be avoided by using a higher safety level than usually accepted for serviceability 
limit states. 

(2) Serviceability limit states during execution should be defined in accordance with EN 
1990 to EN 1999 

(3) Requirements and criteria should be defined for road bridges concerning 
deformations and vibrations, where relevant. 

NOTE 1 The verification of serviceability limit states concerning defonnation and vibration needs to be 
considered only in exceptional cases for road bridges. The frequent combination of actions is 
recommended for the assessment of defonnation. 

NOTE 2 Vibrations of road bridges may have various origins, in particular traffic actions and wind 
actions. For vibrations due to wind actions, see EN 1991-1-4. For vibrations due to traffic actions, 
comfort criteria may have to be considered. Fatigue may also have to be taken into account. 

A2.4.3 Verifications concerning vibration for footbridges due to pedestrian traffic 

NOTE For vibrations due to wind actions, see EN 1 99 1 - 1 -4. 



<M 



77 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

E) 

A2.4.3.1 Design situations and associated traffic assumptions 

(1) The design situations (see 3.2) should be selected depending on the pedestrian traffic 
to be admitted on the individual footbridge during its design working life. 

NOTE The design situations may take into account the way the traffic will be authorised, regulated and 
controlled, depending on the individual project. 

(2) Depending on the deck area or the part of the deck area under consideration, the 
presence of a group of about 8 to 15 persons walking normally should be taken into 
account for design situations considered as persistent design situations. 

(3) Depending on the deck area or the part of the deck area under consideration, other 
traffic categories, associated with design situations which may be persistent, transient or 
accidental, should be specified when relevant, including: 

- the presence of streams of pedestrians (significantly more than 15 persons), 

- occasional festive or choreographic events. 

NOTE 1 These traffic categories and the relevant design situations may have to be agreed for the 
individual project, not only for bridges in highly populated urban areas, but also in the vicinity of railway 
and bus stations, schools, or any other places where crowds may congregate, or any important building 
with public admittance. 

NOTE 2 The definition of design situations corresponding to occasional festive or choreographic events 
depends on the expected degree of control of them by a responsible owner or authority. No verification 
rule is provided in the present clause and special studies may need to be considered. Some information on 
the relevant design criteria may be found in the appropriate literature. 

A2.4.3.2 Pedestrian comfort criteria (for serviceability) 

(1) The comfort criteria should be defined in tenns of maximum acceptable acceleration 
of any part of the deck. 

NOTE The criteria may be defined as appropriate in the National Annex or for the individual project. 

The following accelerations (ni/s^) are the recommended maximum values for any part of the deck; 

i) 0,7 for verfical vibrations, 

ii) 0,2 for horizontal vibradons due to nonnal use, 

iii) 0,4 for exceptional crowd conditions. 

(2) A verification of the comfort criteria should be performed if the fundamental 
frequency of the deck is less than: 

5 Hz for vertical vibrations, 

- 2,5 Hz for horizontal (lateral) and torsional vibrations. 

NOTE The data used in the calculations, and therefore the results, are subject to very high uncertainties. 
When the comfort criteria are not satisfied with a significant margin, it may be necessary to make provision 
in the design for the possible installation of dampers in the structure after its completion. In such cases the 
designer should consider and identify any requirements for commissioning tests. 



78 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

E) 

A2.4.4 Verifications regarding deformations and vibrations for railway bridges 

A2.4.4.1 General 

(1) This clause A2.4.4 gives the Hmits of defomiation and vibration to be taken into 
account for the design of new railway bridges. 

NOTE 1 Excessive bridge defonnations can endanger traffic by creating unacceptable changes in vertical 
and horizontal track geometry, excessive rail stresses and vibrations in bridge structures. Excessive 
vibrations can lead to ballast instability and unacceptable reduction in wheel rail contact forces. Excessive 
deformations can also affect the loads imposed on the track/bridge system, and create conditions which 
cause passenger discomfort. 

NOTE 2 Defonnation and vibration limits are either explicit or implicit in the bridge stiffness criteria 
given in A2.4.4.1(2)P. 

NOTE 3 The National Annex may specify limits of defonnation and vibration to be taken into account for 
the design of temporary railway bridges. The National Annex may give special requirements for temporary 
bridges depending upon the conditions in which they are used (e.g. special requirements for skew bridges). 

(2)P Checks on bridge deformations shall be performed for traffic safety purposes for 
the following items: 

- vertical accelerations of the deck (to avoid ballast instability and unacceptable 
reduction in wheel rail contact forces - see A2.4.4.2.1), 

- vertical deflection of the deck throughout each span (to ensure acceptable vertical 
track radii and generally robust structures - see A2.4.4.2.3(3)), 

~ unrestrained uplift at the bearings (to avoid premature bearing failure), 

- vertical deflection of the end of the deck beyond bearings (to avoid destabilising the 
track, limit uplift forces on rail fastening systems and limit additional rail stresses - 
see A2A4.2.3(1) and EN1991-2, 6.5.4.5.2), 

- twist of the deck measured along the centre line of each track on the approaches to a 
bridge and across a bridge (to minimise the risk of train derailment - see A2.4.4.2.2), 

NOTE A2.4.4.2.2 contains a mix of traffic safety and passenger comfort criteria that satisfy both traffic 
safety and passenger comfort requirements. 

- rotation of the ends of each deck about a transverse axis or the relative total rotation 
between adjacent deck ends (to limit additional rail stresses (see EN 1991-2, 6.5.4), 
limit uplift forces on rail fastening systems and limit angular discontinuity at 
expansion devices and switch blades - see A2. 4. 4. 2. 3(2)), 

- longitudinal displacement of the end of the upper surface of the deck due to 
longitudinal displacement and rotation of the deck end (to limit additional rail 
stresses and minimise disturbance to track ballast and adjacent track formation - see 
EN 1991-2, 6.5.4.5.2), 

- horizontal transverse deflection (to ensure acceptable horizontal track radii - see 
A2.4.4.2.4, Table A2.8), 

~ horizontal rotation of a deck about a vertical axis at ends of a deck (to ensure 
acceptable horizontal track geometry and passenger comfort - see A2.4.4.2.4, Table 
A2.8), 

- limits on the first natural frequency of lateral vibration of the span to avoid the 
occurrence of resonance between the lateral motion of vehicles on their suspension 
and the bridge - see A2.4.4.2.4(3). ^ 



79 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

NOTE There are other implicit stiffness criteria in the limits of bridge natural frequency given in EN 
1991-2, 6.4.4 and when determining dynamic factors for real trains in accordance with EN 1991-2, 
6.4.6.4 and EN1991-2 Annex C. 

(3) Checks on bridge deformations should be performed for passenger comfort, i.e. 
vertical deflection of the deck to limit coach body acceleration in accordance with 
A2.4.4.3. 

(4) The limits given in A2.4.4.2 and A2.4.4.3 take into account the mitigating effects of 
track maintenance (for example to overcome the effects of the settlement of 
foundations, creep, etc.). 

A2.4.4.2 Criteria for traffic safety 

A2. 4.4. 2.1 Vertical acceleration of the deck 

(1)P To ensure traffic safety, where a dynamic analysis is necessary, the verification of 
maximum peak deck acceleration due to rail traffic actions shall be regarded as a traffic 
safety requirement checked at the serviceability limit state for the prevention of track 
instability. 

(2) The requirements for determining whether a dynamic analysis is necessary are given in 
EN 1991-2, 6.4.4. 

(3)P Where a dynamic analysis is necessary, it shall comply with the requirements given in 
EN 1991-2, 6.4.6. 

NOTE Generally only characteristic rail traffic actions in accordance with EN1991-2, 64.6.1 need to be 
considered. 

(4)P The maximum peak values of bridge deck acceleration calculated along each track 

shall not exceed the following design values: 

i) %( for ballasted track; 

ii) y^f for direct fastened tracks with track and structural elements designed for high 

speed traffic 
for all members supporting the track considering frequencies (including consideration of 
associated mode shapes) up to the greater of: 
i) 30 Hz; 

ii) 1,5 times the frequency of the fundamental mode of vibration of the member being 

considered; 
iii) the frequency of the third mode of vibration of the member. 

NOTE The values and the associated frequency limits may be defined in the National Annex. The 
recommended values are: 

%, = 3,5 m/s" 
Yjf= 5 nVs^ 

A2.4.4.2.2 Deck twist 

(1)P The twist of the bridge deck shall be calculated taking into account the characteristic 
values of Load Model 71 as well as SW/0 or SW/2 as appropriate multiplied by 0m\d a 
and Load Model HSLM including centrifugal effects, all in accordance with EN 199 1-2, 6. 



80 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

Twist shall be checked on the approach to the bridge, across the bridge and for the 

departure from the bridge (see A2.4.4.1(2)P). 

(2) The maximum twist / [mm/3m] of a track gauge s [m] of 1,435 m measured over a 
length of 3 m (Figure A2.1) should not exceed the values given in Table A2.7: 




Figure A2.1 - Definition of deck twist 
Table A2.7 - Limiting values of deck twist 



speed range K(km/h) 


Maximum twist / (mra/3m) 


F<120 


/<?, 


120 < F<200 


t<t2 


F>200 


t<h 



NOTE The values for / may be defined in the National Annex. 

The recommended values for the set of/ are: 

h = 4,5 

^2 = 3,0 

^3=1,5 

Values for a track with a different gauge may be defined in the National Annex. 

(3) P The total track twist due to any twist which may be present in the track when the 
bridge is not subject to rail traffic actions (for example in a transition curve), plus the 
track twist due to the total deformation of the bridge resulting from rail traffic actions, 
shall not exceed tj. 

NOTE The value for tj may be defined in the National Annex. The recommended value for tj is 7,5 
mm/3m. 

A2.4.4.2.3 Vertical deformation of the deck 



(1) For all structure configurations loaded with the classified characteristic vertical 
loading in accordance with EN 1991-2, 6.3.2 (and where required classified SW/0 and 
SW/2 in accordance with EN 1991-2, 6.3.3) the maximum total vertical deflection 
measured along any track due to rail traffic actions should not exceed L/600. 

NOTE Additional requirements for limiting vertical deformation for ballasted and non ballasted bridges 
may be specified as appropriate in the National Annex or for the individual project. 



=^^ 



^:^^ 




9a 
Figure A2.2 - Deflnition of angular rotations at tlie end of decks 



m 



81 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

e 

(2) Limitations on the rotations of ballasted bridge deck ends are implicit in EN 1991-2, 
6.5.4. 

NOTE The requirements for non ballasted structures may be specified in the National Annex. 

(3) Additional limits of angular rotations at the end of decks in the vicinity of expansion 
devices, switches and crossings, etc., should be specified. 

NOTE The additional limits of angular rotations may be defined in the National Annex or for the 
individual project. 

(4) Limitations on the vertical displacement of bridge deck ends beyond bearings are 
given in EN1991-2, 6.5.4.5.2. 

A2.4.4.2.4 Transverse deformation and vibration of the deck 

(1)P Transverse deformation and vibration of the deck shall be checked for characteristic 
combinations of Load Model 71 and SW/0 as appropriate multipUed by the dynamic factor 
<?>and a (or real train with the relevant dynamic factor if appropriate), wind loads, nosing 
force, centrifugal forces in accordance with EN 1991 -2, 6 and the effect of a transverse 
temperature differential across the bridge. 

(2) The transverse deflection 4^ at the top of the deck should be limited to ensure: 

a horizontal angle of rotation of the end of a deck about a vertical axis not greater 

than the values given in Table A2.8, or 

the change of radius of the track across a deck is not greater than the values in Table 

A2.8, or 
- at the end of a deck the differential transverse deflection between the deck and 

adjacent track formation or between adjacent decks does not exceed the specified 

value. 

NOTE The maximum differential transverse deflection may be specified in the National Annex or for the 
individual project. 

Table A2.8 - Maximum horizontal rotation and maximum change of radius of 

curvature 



Speed range V (km/h) 


Maximum 

horizontal 

rotation 

(radian) 


Maximum change of radius of 
curvature (m) 






Single deck 


Multi-deck bridge 


F<120 


ax 


r\ 


^4 


120<F<200 


ai 


ri 


rs 


F>200 


a^ 


Tl 


^6 


NOTE 1 The change of the radius of curvature may be determined using: 

r=—r (A2.7) 

NOTE 2 The transverse deformation includes the defonnation of the bridge deck and the substructure 
(including piers, piles and foundations). 



<Aa 



82 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



E> 



NOTE 3 The values for the set of a^ and n may be defined in the National Annex. The recommended 

values are: 

a^ = 0,0035; ai = 0,0020; a^ - 0,0015; 

r, = 1700; r2 = 6000; r3= 14000; 

r4 = 3500; r5 = 9500; r6= 17500 



(3) The first natural frequency of lateral vibration of a span should not be less than/ho- 

NOTE The value for/ho may be defmed in the National Annex. The recommended value is: 
Ao=l,2Hz. 



A2.4.4.2.5 Longitudinal displacement of the deck 

(1) Limitations on the longitudinal displacement of the ends of decks are given in 
EN1991-2, 6.5.4.5.2. 

NOTE Also see A2.4.4.2.3. 

A2.4.4.3 Limiting values for the maximum vertical deflection for passenger 
comfort 

A2.4.4.3.1 Comfort criteria 

(1) Passenger comfort depends on the vertical acceleration h^ inside the coach during travel 
on the approach to, passage over and departure from the bridge. 

(2) The levels of comfort and associated limiting values for the vertical acceleration 
should be specified. 

NOTE These levels of comfort and associated limiting values may be defmed for the individual project. 
Recommended levels of comfort are given in Table A2.9. 

Table A2.9 - Recommended levels of comfort 



Level of comfort 


Vertical acceleration b^ (m/s^) 


Very good 


1,0 


Good 


1,3 


Acceptable 


2,0 



A2.4.4.3.2 Deflection criteria for checking passenger comfort 

(1) To limit vertical vehicle acceleration to the values given in A2.4.4.3.1(2) values are 
given in this clause for the maximum permissible vertical deflection cJ along the centre line 
of the track of railway bridges as a function ofi 
the span length L [m], 

- the train speed V [km/h], 

- the number of spans and 

- the configuration of the bridge (simply supported beam, continuous beam). 
AlteiTiatively the vertical acceleration by may be determined by a dynamic vehicle/bridge 
interaction analysis (see A2.4.4.3 .3). ^ 



83 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

E) 

(2) The vertical deflections ^should be determined with Load Model 71 multiplied by the 
factor and with the value of a=\, in accordance with EN1991-2, Section 6. 

For bridges with two or more tracks only one track should be loaded. 

(3) For exceptional structures, e.g. continuous beams with widely varying span lengths 
or spans with wide variations in stiffness, a specific dynamic calculation should be 
carried out. 



3.000 



2.500 



2.000 



^ 



1.500 



1.000 



500 




10 20 30 40 50 60 70 80 90 100 110 120 

Mm] 
The factors listed in A2.4.4.3.2.(5) should not be applied to the limit of L/5= 600. 

Figure A2.3 - Maximum permissible vertical deflection ^for railway bridges with 3 

or more successive simply supported spans corresponding to a permissible vertical 

acceleration ofby = l m/s^ in a coach for speed V [km/h] 

(4) The limiting values of L/^ given in Figure A2.3 are given for by = 1,0 m/s^ which 
may be taken as providing a "very good" level of comfort. 

For other levels of comfort and associated maximum permissible vertical accelerations 
b\ the values of L/^ given in Figure A2.3 may be divided by b\ [m/s^]. 



(5) The values of L/S given in Figure A2.3 are given for a succession of simply 
supported beams with three or more spans. 

For a bridge comprising of either a single span or a succession of two simply supported 
beams or two continuous spans the values of L/5 given in Figure A2.3 should be 
multiplied by 0,7. 

For continuous beams with three or more spans the values of L/^ given in Figure A2.3 
should be multiplied by 0,9. 

(6) The values of i/^ given in Figure A2.3 are valid for span lengths up to 120 m. For 
longer spans a special analysis is necessary. 

NOTE The requirements for passenger comfort for temporary bridges may be defined in the National 
Annex or for the individual project. r^ 



84 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

E) 

A2.4.4.3.3 Requirements for a dynamic vehicle/bridge interaction analysis for checking 

passenger comfort 

(1) Where a vehicle/bridge dynamic interaction analysis is required the analysis should 

take account of the following behaviours: 

iv) a series of vehicle speeds up to the maximum speed specified, 

v) characteristic loading of the real trains specified for the individual project in 

accordance with EN1991-2, 6.4.6.1.1, 
vi) dynamic mass interaction between vehicles in the real train and the structure, 
vii) the damping and stiffness characteristics of the vehicle suspension, 
viii) a sufficient number of vehicles to produce the maximum load effects in the 

longest span, 
ix) a sufficient number of spans in a structure with multiple spans to develop any 

resonance effects in the vehicle suspension. 

NOTE Any requirements for taking track roughness into account in the vehicle/bridge dynamic 
interaction analysis may be defined for the individual project. 



85 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



Annex B 

(informative) 

Management of Structural Reliability for Construction Works 



Bl Scope and field of application 

(1) This annex provides additional guidance to 2.2 (Reliability management) and to 
appropriate clauses in EN 1991 to EN 1999. 

NOTE Reliability differentiation rules have been specified for particular aspects in the design Euro- 
codes, e.g. in EN 1992, EN 1993, EN 1996, EN 1997 and EN 1998. 

(2) The approach given in this Annex recommends the following procedures for the 
management of structural reliability for construction works (with regard to ULSs, ex- 
cluding fatigue) : 

a) In relation to 2.2(5)b, classes are introduced and are based on the assumed 
consequences of failure and the exposure of the construction works to hazard. A 
procedure for allowing moderate differentiation in the partial factors for actions and 
resistances corresponding to the classes is given in B3. 

NOTE Reliability classification can be represented by p indexes (see Annex C) which takes account of 
accepted or assumed statistical variability in action effects and resistances and model uncertainties. 

b) In relation to 2.2(5)c and 2,2(5)d, a procedure for allowing differentiation between 
various types of constmction works in the requirements for quality levels of the design and 
execution process are given in B4 and B5. 

NOTE Those quality management and control measures in design, detailing and execution which are given in 
B4 and B5 aim to ehminate failures due to gross errors, and ensure the resistances assumed in the design. 

(3) The procedure has been formulated in such a way so as to produce a framework to al- 
low different rehability levels to be used, if desired. 

B2 Symbols 

In this annex the following symbols apply. 

ATfi Factor applicable to actions for reliability differentiation 

p Reliability index 



86 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005{E) 

B3 Reliability differentiation 
B3.1 Consequences classes 

(1) For the purpose of reliability differentiation, consequences classes (CC) may be 
established by considering the consequences of failure or malfunction of the stmcture 
as given in Table Bl. 

Table Bl - Definition of consequences classes 



Consequences 
Class 


Description 


Examples of buildings and civil 
engineering works 


CC3 


High consequence for loss of human life, 
or economic, social or environmental 
consequences very great 


Grandstands, pubHc buildings where 
consequences of failure are high (e.g. a 
concert hall) 


CC2 


Medium consequence for loss of human 
life, economic, social or environmental 
consequences considerable 


Residential and office buildings, public 
buildings where consequences of failure 
are medium (e.g. an office building) 


CCl 


Low consequence for loss of human life, 
and econoixiic, social or environmental 
consequences small or negligible 


Agricultural buildings where people do 
not normally enter (e.g. storage 
buildings), greenhouses 



(2) The criterion for classification of consequences is the importance, in terms of 
consequences of failure, of the structure or structural member concerned. See B3.3 

(3) Depending on the structural form and decisions made during design, particular 
members of the structure may be designated in the same, higher or lower consequences 
class than for the entire structure. 

NOTE At the present time the requirements for reliability are related to the structural members of the 
construction works. 

B3.2 Differentiation by yff values 

(1) The reliability classes (RC) may be defined by the ^rehabihty index concept. 

(2) Three rehability classes RCl, RC2 and RC3 may be associated with the tliree 
consequences classes CCl, CC2 and CC3. 

(3) Table B2 gives recommended minimum values for the reliability index associated with 
rehability classes (see also annex C). 



87 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 

Table B2 - Recommended minimum values for reliability index yff (ultimate limit 

states) 



Reliability Class 


Minimum values for fi 


1 year reference period 


50 years reference period 


RC3 


5,2 


4,3 


RC2 


4,7 


3,8 


RCl 


4,2 


3,3 



NOTE A design using EN 1990 with the partial factors given in annex Al and EN 1991 to EN 1999 is 
considered generally to lead to a structure with a P value greater than 3,8 for a 50 year reference period. 
Rehability classes for members of the structure above RC3 are not further considered in this Annex, since 
these structures each require individual consideration. 

B3.3 Differentiation by measures relating to tiie partial factors 

(1) One way of achieving reliability differentiation is by distinguishing classes of ;^^ 
factors to be used in fundamental combinations for persistent design situations. For ex- 
ample, for the same design supervision and execution inspection levels, a multiplication 
factor J^Fi, see Table B3, may be applied to the partial factors. 

Table B3 - Kn factor for actions 



Kr^i factor for actions 


Reliability class 


RCl 


RC2 


RC3 


^FI 


0,9 


1,0 


1,1 



NOTE In particular, for class RC3, other measures as described in this Annex are nonrially preferred to 
using Ky\ factors. Ky\ should be applied only to unfavourable actions. 

(2) Reliability differentiation may also be applied through the partial factors on resistance 
'^, However, this is not normally used. An exception is in relation to fatigue verification 
(see EN 1993). See also B6. 

(3) Accompanying measures, for example the level of quality control for the design and 
execution of the structure, may be associated to the classes of ;f . In this Annex, a three 
level system for control during design and execution has been adopted. Design supervision 
levels and inspection levels associated with the reliability classes are suggested. 

(4) There can be cases {e.g. lighting poles, masts, etc.) where, for reasons of economy, the 
structure might be in RCl, but be subjected to higher corresponding design supervision and 
inspection levels. 

B4 Design supervision differentiation 

(1) Design supervision differentiation consists of various organisational quality control 
measures which can be used together. For example, the definition of design supervision 



88 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

level (B4(2)) may be used together with other measures such as classification of designers 
and checking authorities (B4(3)). 

(2) Three possible design supervision levels (DSL) are shown in Table B4. The design 
supei'vision levels may be linked to the reliability class selected or chosen according to the 
importance of the structure and in accordance with National requirements or the design 
brief, and implemented through appropriate quality management measures. See 2.5. 

Table B4 - Design supervision levels (DSL) 



Design Supervision 
Levels 


Characteristics 


Minimum recommended requirements for 

checking of calculations, drawings and 

specifications 


DSL3 
relating to RC3 


Extended supervision 


Third party checking : 

Checking performed by an organisation different from 

that which has prepared the design 


DSL2 
relating to RC2 


Nonnal supervision 


Checking by different persons than those originally 
responsible and in accordance with the procedure of the 
organisation. 


DSLl 

Relating to RCl 


Normal supervision 


Self-checking: 

Checking performed by the person who has prepared 

the design 



(3) Design supervision differentiation may also include a classification of designers 
and/or design inspectors (checkers, controlling authorities, etc.), depending on their 
competence and experience, their internal organisation, for the relevant type of con- 
struction works being designed. 

NOTE The type of construction works, the materials used and the structural forms can affect this classi- 
fication. 

(4) Alternatively, design supervision differentiation can consist of a more refined detailed 
assessment of the nature and magnitude of actions to be resisted by the structure, or of a 
system of design load management to actively or passively control (restrict) these actions. 

B5 Inspection during execution 

(1) Three inspection levels (IL) may be introduced as shown in Table B5. The inspection 
levels may be linked to the quality management classes selected and implemented through 
appropriate quality management measures. See 2.5. Further guidance is available in 
relevant execution standards referenced by EN 1992 to EN 1996 and EN 1999. 

Table B5 - Inspection levels (IL) 



Inspection Levels 


Characteristics 


Requirements 


1L3 
Relating to RC3 


Extended inspection 


Third party inspection 


1L2 

Relating to RC2 


Normal inspection 


Inspection in accordance with the 
procedures of the organisation 


ILl 

Relating to RCl 


Nonnal inspection 


Self inspection 



89 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

NOTE Inspection levels define the subjects to be covered by inspection of products and execution of 
works including the scope of inspection. The rules will thus vary from one structural material to another, 
and are to be given in the relevant execution standards. 

B6 Partial factors for resistance properties 

(1) A partial factor for a material or product property or a member resistance may be 
reduced if an inspection class higher than that required according to Table B5 and/or more 
severe requirements are used. 

NOTE For verifying efficiency by testing see section 5 and Annex D. 

NOTE Rules for various materials may be given or referenced in EN 1992 to EN 1999. 

NOTE Such a reduction, which allows for example for model uncertainties and dimensional variation, is 
not a reliability differentiation measure : it is only a compensating measure in order to keep the reliability 
level dependent on the efficiency of the control measures. 



90 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Annex C 

(informative) 
Basis for Partial Factor Design and Reliability Analysis 

CI Scope and Field of Applications 

(1) This annex provides infonnation and theoretical background to the partial factor 
method described in Section 6 and annex A. This Annex also provides the background 
to annex D, and is relevant to the contents of annex B. 

(2) This annex also provides information on 

- the structural reliability methods ; 

- the application of the reliability-based method to detennine by calibration design 
values and/or partial factors in the design expressions ; 

- the design verification formats in the Eurocodes. 
C2 Symbols 

In this annex the following symbols apply. 

Latin upper case letters 

Pf Failure probability 

Prob(.) Probability 

Ps survival probability 

Latin lower case letters 

a geometrical property 

g performance function 

Greek upper case letters 

cumulative distribution function of the standardised Normal distribution 

Greek lower case letters 

a^ FORM (First Order Reliability Method) sensitivity factor for effects of 

actions 
a\i FORM (First Order Reliabihty Method) sensitivity factor for resistance 

/? reliability index 

9 model uncertainty 

fix mean value of X 



91 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

Ox standard deviation of X 

Vx coefficient of variation of X 

C3 Introduction 

(1) In the partial factor method the basic variables (i.e. actions, resistances and geomet- 
rical properties) through the use of partial factors and ^factors are given design values, 
and a verification made to ensure that no relevant limit state has been exceeded. See C7. 

NOTE Section 6 describes the design values for actions and the effects of actions, and design values of 
material and product properties and geometrical data. 

(2) In principle numerical values for partial factors and y/ factors can be detennined in 
either of two ways : 

a) On the basis of calibration to a long experience of building tradition. 

NOTE For most of the partial factors and the i/f factors proposed in the currently available Eurocodes 
this is the leading Principle. 

b) On the basis of statistical evaluation of experimental data and field observations. 
(This should be carried out within the framework of a probabilistic reliability the- 
ory.) 

(3) When using method 2b), either on its own or in combination with method 2a), ulti- 
mate limit states partial factors for different materials and actions should be calibrated 
such that the reliabiUty levels for representative structures are as close as possible to the 
target reliability index. See C6. 

C4 Overview of reliability methods 

(1) Figure CI presents a diagrammatic overview of the various methods available for 
calibration of partial factor (limit states) design equations and the relation between 
them. 

(2) The probabilistic calibration procedures for partial factors can be subdivided into 
two main classes : 

- full probabilistic methods (Level III), and 

- first order reliability methods (FORM) (Level II). 

NOTE 1 Full probabilistic methods (Level III) give in principle correct answers to the rehability problem 
as stated. Level 111 methods are seldom used in the calibration of design codes because of the frequent 
lack of statistical data. 

NOTE 2 The level 11 methods make use of certain well defined approximations and lead to results which 
for most structural applications can be considered sufficiently accurate. 

(3) In both the Level II and Level III methods the measure of reliability should be iden- 
tified with the survival probability Ps ^ (1 - Pi), where Pf is the failure probability for 
the considered failure mode and within an appropriate reference period. If the calculated 



92 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

failure probability is larger than a pre-set target value Po, then the structure should be 
considered to be unsafe. 

NOTE The 'probability of failure' and its corresponding reliability index (see C5) are only notional 
values that do not necessarily represent the actual failure rates but are used as operational values for code 
calibration purposes and comparison of reliability levels of structures. 

(4) The Eurocodes have been primarily based on method a (see Figure CI). Method c or 
equivalent methods have been used for further development of the Eurocodes. 

NOTE An example of an equivalent method is design assisted by testmg (see annex D). 



Deterministic methods 



Historical methods 
Empirical methods 



Calibration 



Method a 



Probabihstic methods 



FORM 
(Level II) 


^ 


Full probabihstic 
(Level ni) 



Calibration 



Semi-probabilistic 
methods 
(Level I) 



Method c 



Partial factor 
design 



Calibration 



Method b 



Figure CI - Overview of reliability methods 

C5 Reliability index P 

(1) In the Level II procedures, an alternative measure of reliability is conventionally 

defined by the reliability index y5 which is related to Pfhy : 

Pf-^{-P) (C.l) 

where cPis the cumulative distribution function of the standardised Normal distribution. 
The relation between cPand y5is given in Table CI. 







Table < 


Zi - Relation between >!?ancl P\ 


r 




Pi 


10' 


10-^ 


10-^ 


10-^ 


10-^ 


10"*^ 


10-^ 


p 


1,28 


2,32 


3,09 


3,72 


4,27 


4,75 


5,20 



(2) The probability of failure P^ can be expressed through a performance function g 
such that a structure is considered to survive if g > and to fail if g < : 



93 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

Pi- = ?voh(g < 0) (C.2a) 

If 7? is the resistance and £ the effect of actions, the performance function g is : 

g = R-E (C.2b) 

with R, E and g random variables. 

(3) If g is Normally distributed, y^is taken as : 

fi^^ (C.2c) 

where : 

jjg is the mean value of g, and 
(jg is its standard deviation, 

so that : 

fi^-pa^^O (C.2d) 

and 

Pf = Prob(g < 0) - Prob(g <^g- J3ag) (C.2e) 

For other distributions of g, y9is only a conventional measure of the reliability 

C6 Target values of reliability index J3 

(1) Target values for the reliability index y9 for various design situations, and for refer- 
ence periods of 1 year and 50 years, are indicated in Table C2. The values of y^in Table 
C2 con'espond to levels of safety for reliability class RC2 (see Annex B) structural 
members. 

NOTE 1 For these evaluations of/? 

- Lognormal or Weibul] distributions have usually been used for material and structural resistance pa- 
rameters and model uncertainties ; 

- Normal distributions have usually been used for self-w^eight ; 

- For simplicity, when considering non-fatigue verifications, Normal distributions have been used for 
variable actions. Extreme value distributions w^ould be more appropriate. 

NOTE 2 When the main uncertainty comes from actions that have statistically independent maxima in 
each year, the values of fl for a different reference period can be calculated using the following expres- 
sion : 

$(y9„) = [0(/?|)]" (C.3) 

where : 

Pn is the reliability index for a reference period of n years, 
pi is the rehability index for one year. 



94 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Table C2 - Target reliability index fiior Class RC2 structural members '• 



Limit state 


Target reliability index 


1 year 


50 years 


Ultimate 


4,7 


3,8 


Fatigue 




1,5 to 3,8 2^ 


Serviceability (irreversible) 


2,9 


1,5 


'^ See Annex B 

'^^ Depends on degree of inspectability, reparability and damage tolerance. 



(2) The actual frequency of failure is significantly dependent upon human error, which 
are not considered in partial factor design (See Annex B). Thus (3 does not necessarily 
provide an indication of the actual frequency of structural failure. 

C7 Approach for calibration of design values 

(1) In the design value method of rehability verification (see Figure CI), design values 
need to be defined for all the basic variables. A design is considered to be sufficient if 
the limit states are not reached when the design values are introduced into the analysis 
models. In symbohc notation this is expressed as : 



£d<^d 



(C.4) 



where the subscript 'J' refers to design values. This is the practical way to ensure that 
the reliability index /? is equal to or larger than the target value. 

Ed and Rd can be expressed in partly symbolic form as : 

Ed ^ E {Fdu Fdi, ... <^di, ^d2, •.. Od\, Odi , ..•} (C.5a) 

Rd ^ R {Xdi,Xd2, •.. ad\, adi, ... 9d\, Odi, .••} (C.5b) 

where : 

E is the action effect ; 

R is the resistance ; 

F is an action ; 

X is a material property ; 

a is a geometrical property ; 

is a model uncertainty. 

For particular limit states {e,g, fatigue) a more general formulation may be necessary to 
express a limit state. 



95 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 




(S) failure boundary g = R-E = 
P design point 

Figure C2 - Design point and reliability index J3 
according to the first order reliability method (FORM) for Normally distributed 

uncorrelated variables 

(2) Design values should be based on the values of the basic variables at the FORM 
design point, which can be defined as the point on the failure surface (g = 0) closest to 
the average point in the space of normalised variables (as diagrammatically indicated in 
Figure C2). 

(3) The design values of action effects E^ and resistances Rd should be defined such that 
the probability of having a more unfavourable value is as follows : 



P(R<Rd)=0(-aK/J) 



(C.6a) 
(C.6b) 



where : 

J3is the target rehability index (see C6). 

aE and Or, with |<^ < 1, are the values of the FORM sensitivity factors. The value of 
a is negative for unfavourable actions and action effects, and positive for resis- 
tances. 



6fe and aR may be taken as - 0,7 and 0,8, respectively, provided 
0,16 < c7E/crR<7,6 



(C.7) 



where ofe and <7r are the standard deviations of the action effect and resistance, respec- 
tively, in expressions (C.6a) and (C.6b). This gives : 



P{R<Ra)=^-0,S/3) 



(CM) 
(C.8b) 



96 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(4) Where condition (C.7) is not satisfied 6^= ± 1,0 should be used for the variable with 
the larger standard deviation, and a= ± 0,4 for the variable with the smaller standard 
deviation. 

(5) When the action model contains several basic variables, expression (C.8a) should be 
used for the leading variable only. For the accompanying actions the design values may 
be defined by : 

PiE> £d) ^ (P i-OAxOJxj3) = i'OaSjS) (C.9) 

NOTE For yff = 3,8 the values defined by expression (C.9) correspond approximately to the 0,90 fractile. 

(6) The expressions provided in Table C3 should be used for deriving the design values 
of variables with the given probability distribution. 

Table C3 - Design values for various distribution functions 



Distribution 


Design values 


Normal 


ju-aj3(7 


Lognormal 


juQxp{-aj3V) for V=a/ju<OJ 


Gumbel 


a 

. 0,577 TT 
where u = [i — ; a^ — j= 

a tJV6 



NOTE In these expressions //, (J and Fare, respectively, the mean value, the standard deviation and the 
coefficient of variation of a given variable. For variable actions, these should be based on the same refer- 
ence period as for yS 

(7) One method of obtaining the relevant partial factor is to divide the design value of a 
variable action by its representative or characteristic value. 

C8 Reliability verification formats in Eurocodes 

(1) In EN 1990 to EN 1999, the design values of the basic variables, Xd and Fa, are usu- 
ally not introduced directly into the partial factor design equations. They are introduced 
in terms of their representative values Xrep and i^rep, which may be : 

- characteristic values, i.e. values with a prescribed or intended probability of being 
exceeded, e.g. for actions, material properties and geometrical properties (see 
1.5.3.14, 1.5.4.1 and 1.5.5.1, respectively) ; 

- nominal values, which are treated as characteristic values for material properties (see 
1.5.4.3) and as design values for geometrical properties (see 1.5.5.2). 

(2) The representative values Xrep and Frep, should be divided and/or multipHed, respec- 
tively, by the appropriate partial factors to obtain the design values X^ and F^. 

NOTE See also expression (CIO). 



97 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

(3) Design values of actions F, material properties X and geometrical properties a are 
given in expressions (6.1), (6.3) and (6.4), respectively. 

Where an upper value for design resistance is used (see 6.3.3), the expression (6.3) 
takes the form : 

X^= T/^fTvI^Mup (C.IO) 

where y{y\ is an appropriate factor greater than 1 . 
NOTE Expression (CIO) may be used for capacity design. 

(4) Design values for model uncertainties may be incorporated into the design expres- 
sions through the partial factors ^d and ;^d applied on the total model, such that : 

Ed = rsdE{rgjGkr^rFP;rgiQkb^^^^^ (cii) 

Rd-R{n^k/rrn-^^d-]/rRd (c.i2) 

(5) The coefficient ^which takes account of reductions in the design values of variable 
actions, is applied as y/o , y/i or y/2 to simultaneously occurring, accompanying variable 
actions. 

(6) The following simplifications may be made to expression (C.ll) and (C.12), when 
required. 

a) On the loading side (for a single action or where linearity of action effects exists) : 

E6 = E{)^,Frcp,ua6} (C.13) 

b) On the resistance side the general format is given in expressions (6.6), and further 
simphfications may be given in the relevant material Eurocode. The simplifications 
should only be made if the level of reliability is not reduced. 

NOTE Non-linear resistance and actions models, and multi-variable action or resistance models, are 
commonly encountered in Eurocodes. In such instances, the above relations become more complex, 

C9 Partial factors in EN 1990 

(1) The different partial factors available in EN 1990 are defined in 1.6. 

(2) The relation between individual partial factors in Eurocodes is schematically shown 
Figure C3. 



98 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Uncertainty in representative values 
of actions 



Model uncertainty in actions and 
action effects 



Model uncertainty in structural resistance 



Uncertainty in material properties 




Figure C3 - Relation between individual partial factors 

CIO ^0 factors 

(1) Table C4 gives expressions for obtaining the ^o factors (see Section 6) in the case of 
two variable actions, 

(2) The expressions in Table C4 have been derived by using the following assumptions 
and conditions : 

- the two actions to be combined are independent of each other ; 

- the basic period (T] or T2) for each action is constant ; T\ is the greater basic period ; 

- the action values within respective basic periods are constant ; 

- the intensities of an action within basic periods are uncorrelated ; 

- the two actions belong to ergodic processes. 

(3) The distribution functions in Table C4 refer to the maxima within the reference pe- 
riod T. These distribution functions are total functions which consider the probability 
that an action value is zero during certain periods. 



99 



BS EN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 



Table C4 - Expressions for y/o for the case of two variable actions 



Distribution 



(^0= F: 



accompany: 



{no/F\ 



leading 



General 



)(0,4;5') 



..^TV, 



F7>(0,7y5) 



TVi 



with J3' =-0~^ {^(-0,7 /3)/N^] 



Approximation for very large Ni 



/7Hexp[-A^lO(-0,4/?')]} 



Fi'i^iOJ/3)] 
with j3'=-^~^{^{-0J/3)/Ni] 



Normal (approximation) 



l + (0,28y5-0,71nA^jK 



l + 0,7y^)>^ 



Gumbel (approximation) 



1 - Q,78)>^[0,58 + ln(-lnO(0,28yg)) + lniVi] 



1 - 0,78/>^[0,58 + ln(- \n^(0 J J3))] 



Fs(.) is the probability distribution function of the extreme value of the accompanying ac- 
tion in the reference period T ; 
<I>(.) is the standard Normal distribution function ; 
ris the reference period ; 

T\ is the greater of the basic periods for actions to be combined ; 
N\ is the ratio T/Ti, approximated to the nearest integer ; 
/?is the rehability index ; 
V\s the coefficient of variation of the accompanying action for the reference period. 



100 



BS EN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



Annex D 

(infomiative) 
Design assisted by testing 

Dl Scope and field of application 

(1) This annex provides guidance on 3.4, 4.2 and 5.2. 

(2) This annex is not intended to replace acceptance rules given in harmonised European 
product specifications, other product specifications or execution standards. 

D2 Symbols 

In this annex, the following symbols apply. 

Latin upper case letters 

E{,) Mean value of (.) 

V Coefficient of variation [ V = (standard deviation) / (mean value)] 

Vx Coefficient of variation of X 

F5 Estimator for the coefficient of variation of the error term S 

X Array of 7 basic variables X\ ... X-^ 

A'k(n) Characteristic value, including statistical uncertainty for a sample of size n 

with any conversion factor excluded 

Xyn Array of mean values of the basic variables 

Xa Array of nominal values of the basic variables 

Latin lower case letters 

b Correction factor 

bi Con'ection factor for test specimen / 

grt iK) Resistance function (of the basic variables X) used as the design model 

^d,ii Design fractile factor 

kr, Characteristic fractile factor 

mx Mean of the n sample results 

n Number of experiments or numerical test results 

r Resistance value 

Td Design value of the resistance 

Te Experimental resistance value 

Tee Extreme (maximum or minimum) value of the experimental resistance [i.e. 

value of 7"e that deviates most from the mean value re^] 

Te/ Experimental resistance for specimen / 

rem Mean value of the experimental resistance 

Tk Characteristic value of the resistance 

Tm Resistance value calculated using the mean values X^-^ of the basic variables 

7"n Nominal value of the resistance 

Tt Theoretical resistance determined from the resistance function g^^iX) 



101 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 

Fa Theoretical resistance detennined using the measured parameters X for 

specimen / 
s Estimated value of the standard deviation a 

sa Estimated value of Oa 

56 Estimated value of (T5 

Greek upper case letters 

Cumulative distribution function of the standardised Normal distribution 

A Logarithm of the error term 5 [A/ = ln(^ )] 

A Estimated value for £'(A) 

Greek lower case letters 

as FORM (First Order Reliability Method) sensitivity factor for effects of 

actions 
Or form (First Order Reliability Method) sensitivity factor for resistance 

/] Reliability index 

^^' Corrected partial factor for resistances [jiA^ = rjr^ so %a^ = kc ]U] 

S Error term 

Si Observed error term for test specimen / obtained from a comparison of the 

experimental resistance r^i and the mean value corrected theoretical 

resistance br^i 

7]^ Design value of the possible conversion factor (so far as is not included in 

partial factor for resistance ]iA) 
rjY^ Reduction factor applicable in the case of prior knowledge 

(J Standard deviation [a ^ V variance ] 

Ga Variance of the term A 

D3 Types of tests 

(1) A distinction needs to be made between the following types of tests : 

a) tests to establish directly the ultimate resistance or serviceability properties of struc- 
tures or structural members for given loading conditions. Such tests can be performed, 
for example, for fatigue loads or impact loads ; 

b) tests to obtain specific material properties using specified testing procedures ; for 
instance, ground testing in situ or in the laboratory, or the testing of new materials ; 

c) tests to reduce uncertainties in parameters in load or load effect models; for instance, 
by wind tunnel testing, or in tests to identify actions from waves or currents ; 

d) tests to reduce uncertainties in parameters used in resistance models ; for instance, by 
testing structural members or assemblies of structural members (e.g. roof or floor struc- 
tures) ; 



102 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

e) control tests to check the identity or quality of delivered products or the consistency 
of production characteristics ; for instance, testing of cables for bridges, or concrete 
cube testing ; 

f) tests carried out during execution in order to obtain information needed for part of the 
execution ; for instance, testing of pile resistance, testing of cable forces during execu- 
tion ; 

g) control tests to check the behaviour of an actual structure or of structural members 
after completion, e,g, to find the elastic deflection, vibrational frequencies or damping ; 

(2) For test types (a), (b), (c), (d), the design values to be used should wherever practicable 
be derived from the test results by applying accepted statistical techniques. See D5 to D8. 

NOTE Special techniques might be needed in order to evaluate type (c) test results. 

(3) Test types (e), (f), (g) may be considered as acceptance tests where no test results are 
available at the time of design. Design values should be conservative estimates which are 
expected to be able to meet the acceptance criteria (tests (e), (f), (g)) at a later stage. 

D4 Planning of tests 

(1) Prior to the carrying out of tests, a test plan should be agreed with the testing organi- 
sation. This plan should contain the objectives of the test and all specifications neces- 
sary for the selection or production of the test specimens, the execution of the tests and 
the test evaluation. The test plan should cover : 

- objectives and scope, 

- prediction of test results, 

- specification of test specimens and sampling, 

- loading specificafions, 

- testing arrangement, 

- measurements, 

- evaluation and reporting of the tests. 

Objectives and scope : The objective of the tests should be clearly stated, e.g. the re- 
quired properties, the influence of certain design parameters varied during the test and 
the range of validity. Limitations of the test and required conversions {e.g. scaling ef- 
fects) should be specified. 

Prediction of test results : All properties and circumstances that can influence the pre- 
diction of test results should be taken into account, including : 

- geometrical parameters and their variability, 

- geometrical imperfections, 

- material properties, 

- parameters influenced by fabrication and execution procedures, 

- scale effects of environmental conditions taking into account, if relevant, any se- 
quencing. 



103 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

The expected modes of failure and/or calculation models, together with the correspond- 
ing variables should be described. If there is a significant doubt about which failure 
modes might be critical, then the test plan should be developed on the basis of accom- 
panying pilot tests. 

NOTE Attention needs to be given to the fact that a structural member can possess a number of funda- 
mentally different failure modes. 

Specification of test specimen and sampling : Test specimens should be specified, or 
obtained by sampling, in such a way as to represent the conditions of the real structure. 

Factors to be taken into account include : 
~ dimensions and tolerances, 

- material and fabrication of prototypes, 
~ number of test specimens, 

- sampling procedures, 

- restraints. 

The objective of the sampling procedure should be to obtain a statistically representa- 
tive sample. 

Attention should be drawn to any difference between the test specimens and the product 
population that could influence the test results. 

Loading specifications : The loading and environmental conditions to be specified for 
the test should include : 

- loading points, 
~ loading history, 

- restraints, 

- temperatures, 

- relative humidity, 

- loading by deformation or force control, etc. 

Load sequencing should be selected to represent the anticipated use of the structural 
member, under both normal and severe conditions of use. Interactions between the 
structural response and the apparatus used to apply the load should be taken into ac- 
count where relevant. 

Where structural behaviour depends upon the effects of one or more actions that will 
not be varied systematically, then those effects should be specified by their representa- 
tive values. 

Testing arrangement : The test equipment should be relevant for the type of tests and 
the expected range of measurements. Special attention should be given to measures to 
obtain sufficient strength and stiffness of the loading and supporting rigs, and clearance 
for deflections, etc. 

Measurements : Prior to the testing, all relevant properties to be measured for each indi- 
vidual test specimen should be listed. Additionally a list should be made : 



104 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

a) of measurement-locations, 

b) of procedures for recording results, including if relevant : 

- time histories of displacements, 

- velocities, 

- accelerations, 

- strains, 

- forces and pressures, 

- required frequency, 

- accuracy of measurements, and 

- appropriate measuring devices. 

Evaluation and reporting the test : For specific guidance, see D5 to D8. Any Standards 
on which the tests are based should be reported. 

D5 Derivation of design values 

(1) The derivation from tests of the design values for a material property, a model 
parameter or a resistance should be carried out in one of the following ways : 

a) by assessing a characteristic value, which is then divided by a partial factor and 
possibly multiplied if necessary by an exphcit conversion factor (see D7.2 and D8.2) ; 

b) by direct determination of the design value, implicitly or explicitly accounting for the 
conversion of results and the total reliability required (see D7.3 and D8.3). 

NOTE In general method a) is to be preferred provided the value of the partial factor is detemiined from the 
normal design procedure (see (3) below). 

(2) The derivation of a characteristic value from tests (Method (a)) should take into account 

a) the scatter of test data ; 

b) statistical uncertainty associated with the number of tests ; 

c) prior statistical knowledge. 

(3) The partial factor to be applied to a characteristic value should be taken from the 
appropriate Eurocode provided there is sufficient similarity between the tests and the usual 
field of appHcation of the partial factor as used in numerical verifications. 

(4) If the response of the structure or structural member or the resistance of the material 
depends on influences not sufficiently covered by the tests such as : 

- time and duration effects, 

- scale and size effects, 

- different environmental, loading and boundary conditions, 

- resistance effects, 

then the calculation model should take such influences into account as appropriate. 

(5) In special cases where the method given in D5(l)b) is used, the following should be 
taken into account when deteraiining design values : 



105 



BS EN 1990:2002+A1:2005 
EN 1 990:2002+ A1:2005(E) 

- the relevant limit states ; 

- the required level of reliability ; 

- compatibility with the assumptions relevant to the actions side in expression (C.8a) ; 

- where appropriate, the required design working life ; 

- prior Imowledge from similar cases. 

NOTE Further infonnation may be found in D6, D7 and D8. 

D6 General principles for statistical evaluations 

(1) When evaluating test results, the behaviour of test specimens and failure modes 
should be compared with theoretical predictions. When significant deviations from a 
prediction occur, an explanation should be sought : this might involve additional test- 
ing, perhaps under different conditions, or modification of the theoretical model. 

(2) The evaluation of test results should be based on statistical methods, with the use of 
available (statistical) information about the type of distribution to be used and its asso- 
ciated parameters. The methods given in this Annex may be used only when the follow- 
ing conditions are satisfied : 

- the statistical data (including prior information) are taken from identified populations 
which are sufficiently homogeneous ; and 

- a sufficient number of obsei'vations is available. 

NOTE At the level of interpretation of tests results, three main categories can be distinguished : 

- where one test only (or very few tests) is (are) performed, no classical statistical interpretation is pos- 
sible. Only the use of extensive prior infonnation associated with hypotheses about the relative de- 
grees of importance of this infonxiation and of the test results, make it possible to present an interpre- 
tation as statistical (Bayesian procedures, see ISO 12491) ; 

- if a larger series of tests is performed to evaluate a parameter, a classical statistical interpretation 
might be possible. The commoner cases are treated, as examples, in D7. This interpretation will still 
need to use some prior information about the parameter ; however, this will normally be less than 
above. 

~ when a series of tests is carried out in order to calibrate a model (as a function) and one or more as- 
sociated parameters, a classical statistical interpretation is possible. 

(3) The result of a test evaluation should be considered vahd only for the specifications 
and load characteristics considered in the tests. If the results are to be extrapolated to 
cover other design parameters and loading, additional information from previous tests 
or from theoretical bases should be used. 

D7 Statistical determination of a single property 

D7.1 General 

(1) This clause gives working expressions for deriving design values from test types (a) 
and (b) of D3(3) for a single property (for example, a strength) when using evaluation 
methods (a) and (b) of D5(l). 

NOTE The expressions presented here, which use Bayesian procedures with "vague" prior distributions, 
lead to almost the same results as classical statistics with confidence levels equal to 0,75. 



106 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 



(2) The single property Jf may represent 

a) a resistance of a product, 

b) a property contributing to the resistance of a product. 

(3) In case a) the procedure D7.2 and D7.3 can be applied directly to determine charac- 
teristic or design or partial factor values. 

(4) In case b) it should be considered that the design value of the resistance should also 
include : 

the effects of other properties, 

the model uncertainty, 

other effects (scaling, volume, etc.) 

(5) The tables and expressions in D7.2 and D7.3 are based on the following assump- 
tions: 

- all variables follow either a Normal or a log-normal distribution ; 

- there is no prior knowledge about the value of the mean ; 

- for the case "Fx unknown", there is no prior knowledge about the coefficient of 
variation ; 

- for the case "Kx known", there is full knowledge of the coefficient of variation. 

NOTE Adopting a log-normal distribution for certain variables has the advantage that no negative values 
can occur as for example for geometrical and resistance variables. 

In practice, it is often preferable to use the case "Kx known" together with a conserva- 
tive upper estimate of Fx, rather than to apply the rules given for the case "Fx un- 
known". Moreover Vx , when unknown, should be assumed to be not smaller than 0,10. 

D7,2 Assessment via the characteristic value 

(1) The design value of a property X should be found by using : 
X^-V.^^^-^mxO-knVx) (D.l) 

where : 

7]d is the design value of the conversion factor. 

NOTE The assessment of the relevant conversion factor is strongly dependent on the type of test and the 
type of material. 

The value of kn can be found from Table D 1 . 

(2) When using table Dl, one of two cases should be considered as follows. 

- The row "Kx known" should be used if the coefficient of variation, Vx, or a realistic 
upper bound of it, is known from prior knowledge. 



107 



BSEN1990:2002+A1:2005 
EN 1990:2002+A1:2005 (E) 

NOTE Prior knowledge might come from the evaluation of previous tests in comparable situations. What 
is 'comparable' needs to be determined by engineering judgement (see D7.1(3)). 

- The row " Vx unknown" should be used if the coefficient of variation Vx is not known 
from prior knowledge and so needs to be estimated from the sample as : 



2 



1 



n-1 



2 (xi - mx / 



(D.2) 
(D.3) 



(3) The partial factor /^^ should be selected according to the field of application of the 
test results. 

Table Dl : Values of An for the 5% characteristic value 



n 


1 


2 


3 


4 


5 


6 


8 


10 


20 


30 


oo 


Vx blown 


2,31 


2,01 


1,89 


1,83 


1,80 


1,77 


1,74 


1,72 


1,68 


1,67 


1,64 


Vx 
unknown 


- 


- 


3,37 


2,63 


2,33 


2,18 


2,00 


1,92 


1,76 


1,73 


1,64 



NOTE 1 This table is based on the Normal distribution. 

NOTE 2 With a log-noimal distribution expression (D.l) becomes : 

where : 

m =~Xln(x,-) 
n 

If Vx is known from prior knowledge, s = ^j\n(Vx +1) -Vx 



If Fx is unknown from prior knowledge, Sy = J Z(lnx^- - my) 



D7.3 Direct assessment of the design value for ULS verifications 

(1) The design value Xd for X should be found by using : 

In this case, r/^ should cover all uncertainties not covered by the tests. 

(2) kd,n should be obtained from table D2. 

Table D2 - Values ofk^^n for the ULS design value. 



(D.4) 



n 


1 


2 


3 


4 


5 


6 


8 


10 


20 


30 


OO 


Vx known 


4,36 


3,77 


3,56 


3,44 


3,37 


3,33 


3,27 


3,23 


3,16 


3,13 


3,04 


Vx 
unknown 


- 


- 


- 


11,40 


7,85 


6,36 


5,07 


4,51 


3,64 


3,44 


3,04 



108 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

NOTE 1 This table is based on the assumption that the design value corresponds to a product a^ = 
0,8x3,8 = 3,04 (see annex C) and that Z is Nonnally distributed. This gives a probability of observing a 
lower value of about 0,1 %. 

NOTE 2 With a log-normal distribution, expression (D.4) becomes : 

D8 Statistical determination of resistance models 
D8.1 General 

(1) This clause is mainly intended to define procedures (methods) for calibrating resis- 
tance models and for deriving design values from tests type d) (see D3(l)). Use will be 
made of available prior information (knowledge or assumptions). 

(2) Based on the observation of actual behaviour in tests and on theoretical considerations, 
a "design model" should be developed, leading to the derivation of a resistance function. 
The validity of this model should be then checked by means of a statistical interpretation 
of all available test data. If necessary the design model is then adjusted until sufficient 
correlation is achieved between the theoretical values and the test data. 

(3) Deviation in the predictions obtained by using the design model should also be 
detemiined from the tests. This deviation will need to be combined with the deviations of 
the other variables in the resistance function in order to obtain an overall indication of 
deviation. These other variables include : 

- deviation in material strength and stiffness ; 

- deviation in geometrical properties. 

(4) The characteristic resistance should be detemiined by taking account of the deviations 
of all the variables. 

(5) In D5(l) two different methods are distinguished. These methods are given in D8.2 
and D8.3 respectively. Additionally, some possible simplifications are given in D8.4. 

These methods are presented as a number of discrete steps and some assumptions re- 
garding the test population are made and explained ; these assumptions are to be con- 
sidered to be no more than recommendations covering some of the commoner cases. 

D8.2 Standard evaluation procedure (Method (a)) 
D8.2.1 General 

(1) For the standard evaluation procedure the following assumptions are made : 

a) the resistance function is a function of a number of independent variables X ; 

b) a sufficient number of test results is available ; 

c) all relevant geometrical and material properties are measured ; 

d) there is no coiTelation (statistical dependence) between the variables in the resistance 
fiinction ; 

e) all variables follow either a Normal or a log-normal distribution. 



109 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

NOTE Adopting a log-normal distribution for a variable has the advantage that no negative values can 
occur. 

(2) The standard procedure for method D5(l)a) comprises the seven steps given m 
D8.2.2.1toD8.2.2.7. 



D8.2.2 Standard procedure 

D8.2.2.1 Step 1 : Develop a design model 

(1) Develop a design model for the theoretical resistance n of the member or structural 
detail considered, represented by the resistance function : 



rt=gA^) 



(D.5) 



(2) The resistance function should cover all relevant basic variables X that affect the resis- 
tance at the relevant limit state. 

(3) All basic parameters should be measured for each test specimen / (assumption (c) in 
D8.2.1) and should be available for use in the evaluation. 

D8.2.2.2 Step 2 : Compare experimental and theoretical values 

(1) Substitute the actual measured properties into the resistance function so as to obtain 
theoretical values ra to form the basis of a comparison with the experimental values r^i 
from the tests. 

(2) The points representing pairs of corresponding values ( rn, r^i ) should be plotted on a 
diagram, as indicated in figure Dl. 



i 

* 


y 


. • . X 


Te = brt 




► 



Figure Dl - re - rt diagram 

(3) If the resistance function is exact and complete, then all of the points will lie on the 
line d - KJA , In practice the points will show some scatter, but the causes of any system- 
atic deviation from that line should be investigated to check whether this indicates errors 
in the test procedures or in the resistance function. 



110 



BSEN 1990:2002+A1:2005 
EN19gO:2002+A1:2005(E) 

D8.2.2.3 Step 3 : Estimate the mean value correction factor b 

(1) Represent the probabiUstic model of the resistance r in the format : 

r=bnS (D.6) 

where : 

b is the "Least Squares" best-fit to the slope, given hy h = — ^ (D.7) 

(2) The mean value of the theoretical resistance function, calculated using the mean values 
Xm of the basic variables, can be obtained from : 

r..-br,{xJS=bgn{xJS (D.8) 

D8. 2.2.4 Step 4 : Estimate the coefficient of variation of the en'ors 

(1) The en-or term Si for each experimental value r^i should be determined from expression 
(D.9) : 

Si=^ (D.9) 

(2) From the values of S, an estimated value for F5 should be determined by defining : 
A/=ln(^,) (D.IO) 

(3) The estimated value A for E(A) should be obtained from : 

^-™Z4 (Dii) 

n tr 



(4) The estimated value ^a^ for (Ja^ should be obtained from 

si 



^- ^ H^i-Af (D.12) 



(5) The expression : 

Vs^^l^xlp(si)-l (D.13) 

may be used as the coefficient of variation V^ of the ^ error terms. 

D8.2.2.5 Step 5 : Analyse compatibility 

(1) The compatibility of the test population with the assumptions made in the resistance 
function should be analysed. 

(2) If the scatter of the (r^i , rti) values is too high to give economical design resistance 
functions, this scatter may be reduced in one of the following ways : 



111 



BSEN 1990:2002+A1:2005 
EN 1990:2002+A1:2005(E) 

a) by correcting the design model to take into account parameters which had previously 
been ignored ; 

b) by modifying h and F5 by dividing the total test population into appropriate sub-sets 
for which the influence of such additional parameters may be considered to be con- 
stant. 

(3) To determine which parameters have most influence on the scatter, the test results may 
be split into subsets with respect to these parameters. 

NOTE The purpose is to improve the resistance function per sub-set by analysing each subset using the 
standard procedure. The disadvantage of splitting the test results into sub-sets is that the number of test 
resuhs in each sub-set can become very small. 

(4) When determining the fractile factors k^^ (see step 7), the k^^ value for the sub-sets may 
be determined on the basis of the total number of the tests in the original series. 

NOTE Attention is drawn to the fact that the frequency distribution for resistance can be better described 
by a bi-modal or a multi-modal function. Special approximation techniques can be used to transform 
these functions into a uni-modal distribution. 

D8.2.2.6 Step 6 : Determine the coefficients of variation Vxi of the basic variables 

(1) If it can be shown that the test population is fully representative of the variation in re- 
ality, then the coefficients of variation Vxi of the basic variables in the resistance function 
may be determined from the test data. However, since this is not generally the case, the 
coefficients of variation Fxi will normally need to be determined on the basis of some 
prior knowledge. 

D8.2,2.7 Step 7 : Determine the characteristic value }\ of the resistance 

(1) If the resistance function for j basic variables is a product function of the form : 

r = bn5-h{X^xX2..,X■^}^ 

the mean value E{r) may be obtained from : 

E{r) = b {E{Xx)xE{X2) ... E{X-) ] = bgr,{X^) (D.14a) 

and the coefficient of variation Vx may be obtained from the product function : 

-1 (D.14b) 



v^={vl + \) 



/: = i 



(2) Alternatively, for small values of Vf and Vxi the following approximation for V^ 
may be used : 

Vr-Vl+V^t (D.15a) 

with : 



112 



BSEN1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



r2 _ xp T/2 



V,,= Wxi (D-15b) 

/ = 1 

(3) If the resistance function is a more complex function of tlie form : 

r^bnS = bgrt{Xu...,Xi)S 

the mean value E(r) may be obtained from : 

E(r) = bgAE(X:), ..., E(X-))=bgA]L) (D.16a) 



and the coefficient of variation V^i may be obtained from : 



,■ r-,^ a2 



yl ^ VAR[g,t{X)\ __^ 1 ^ i dgrt 

grtiX„) gliXj i = l 



^dXi'^'j 



(D.16b) 



(4) If the number of tests is limited (say n < 100) allowance should be made in the distri- 
bution of A for statistical uncertainties. The distribution should be considered as a central 
t-distribution with the parameters A , Va and n. 

(5) In this case the characteristic resistance n should be obtained from : 

rk ^bgn (Xrr,) exp(- k^ On Qn- K O^Qi-0,5 Q^) (D. 1 7) 



with 


^ <^\a{rt) 




Qrt - 


= Vln(F,?+l) 


Qs- 


" <^\xi{5) 


-Vl^H+l) 


e- 


O-ln(r) - 


Vln(F,2+l) 


ttrt- 


Q 




ag-- 


Q 





(D.18a) 
(D.18b) 
(D.18c) 
(D.19a) 

(D.19b) 
where : 

^n is the characteristic fractile factor from table Dl for the case Fx unknown ; 

koo is the value of A:n for n^oo \_k^ = 1,64]; 

On is the weighting factor for Qn 

as is the weighting factor for Q^ 

NOTE The value of V^ is to be estimated from the test sample under consideration. 

(6) If a large number of tests (n > 100) is available, the characteristic resistance rk may 
be obtained from : 



113 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

rk = 6 grt (Z.) exp(- k^ Q - 0,5 g') (D.20) 

D8.3 Standard evaluation procedure (Method (b)) 

(1) In this case the procedure is the same as in D8.2, excepted that step 7 is adapted by 
replacing the characteristic fractile factor kr^ by the design fractile factor A:d,n equal to the 
product aRp assessed at 0,8 x 3,8 = 3,04 as commonly accepted (see Annex C) to obtain 
the design value r^ of the resistance. 

(2) For the case of a hmited number of tests the design value r^ should be obtained from : 

n = bgrt (Xm) exp(-ytd,oo On Qrt " ^d,n <% 05 "0,5 g^ ) (D.2 1) 

where : 

kd,n is the design fractile factor from table D2 for the case "Vx unknown" ; 
A:d,oo is the value of itd,n for n^oo [k^^ = 3,04]. 

NOTE The value of V^ is to be estimated from the test sample under consideration. 

(2) For the case of a large number of tests the design value rd may be obtained from : 

Td = bgn (Xn.) exp(- /cd,co Q - 0,5 Q" ) (D.22) 

D8.4 Use of additional prior knowledge 

(1) If the validity of the resistance function rt and an upper bound (conservative estimate) 
for the coefficient of variation V^ are already known from a significant number of previous 
tests, the following simplified procedure may be adopted when further tests are carried out. 

(2) If only one further test is canied out, the characteristic value rk may be determined 
from the result r^ of this test by applying : 

rk=/7kre (D.23) 

where : 

% is a reduction factor applicable in the case of prior knowledge that may be ob- 
tained from : 

7^ = 0,9 exp(-2,3 1 Vj - 0,5 Vj^ ) (D.24) 

where : 

Vj is the maximum coefficient of variation observed in previous tests. 

(3) If two or three further tests are carried out, the characteristic value rk may be deter- 
mined from the mean value rem of the test results by applying : 



114 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 



(D.25) 



where : 



T/k is a reduction factor applicable in the case of prior knowledge that may be ob- 
tained from : 



;^ = exp(-2,0Fr-0,5K/) 
where : 



(D.26) 



Kr is the maximum coefficient of variation observed in previous tests. 

provided that each extreme (maximum or minimum) value Tcc satisfies the condition : 



r -r <0 lOr 



em 



(D.27) 



(4) The values of the coefficient of variation Vr given in table D3 may be assumed for the 
types of failure to be specified {e.g. in the relevant design Eurocode), leading to the listed 
values of //k according to expressions (D.24) and (D.26). 

Table D3 - Reduction factor 7]\^ 



Coefficient of 
variation F",- 


Reduction factor //k 


For 1 test 


For 2 or 3 tests 


0,05 


0,80 


0,90 


0,11 


0,70 


0,80 


0,17 


0,60 


0,70 



115 



BSEN 1990:2002+A1:2005 
EN1990:2002+A1:2005(E) 

Bibliography 

ISO 2394 General principles on reliability for structures 

ISO 263 1 : 1997 Mechanical vibration and shock - Evaluation of human expo- 

sure to whole-body vibration 

ISO 3898 Basis for design of structures - Notations - General symbols 

ISO 6707-1 Building and civil engineering - Vocabulary - Part 1 : General 

terms 

ISO 8930 General principles on reliability for structures - List of equiva- 

lent terms 

EN ISO 9001 :2000 Quality management systems - Requirements (ISO 9001 :2000) 

ISO 10137 Basis for design of structures - Serviceability of buildings 

against vibrations 

ISO 8402 Quality management and quality assurance - Vocabulary 



116 



blank