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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 1990:2002+A1
December 2005
ICS 91.010.30
Supersedes ENV 19911:1994
Incorporating corrigenda December 2008
and April 2010
English version
Eurocodes structuraux – Eurocodes: Bases de calcul des structures  Eurocode: Grundlagen der Tragwerksplanung 
This European Standard was approved by CEN 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. Uptodate 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.
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© 2002 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 1990:2002
1Page  
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  
1.5.1  Common terms used in EN 1990 to EN 1999  14  
1.5.2  Special terms relating to design in general  15  
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  
4.1.1  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  
4.1.5  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  
5.1.1  Structural modelling  38  
5.1.2  Static actions  38  
5.1.3  Dynamic actions  38 2  
5.1.4  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  
6.3.1  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  
6.3.4  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 equilibrium 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  
A1.1  FIELD OF APPLICATION  51  
A1.2  COMBINATIONS OF ACTIONS  51  
A1.2.1  General  51  
A1.2.2  Values of ψ factors  51  
A1.3  ULTIMATE LIMIT STATES  52  
A1.3.1  Design values of actions in persistent and transient design situations  52  
A1.3.2  Design values of actions in the accidental and seismic design situations  56  
A1.4  SERVICEABILITY LIMIT STATES  57  
A1.4.1  Partial factors for actions  57  
A1.4.2  Serviceability criteria  57  
A1.4.3  Deformations and horizontal displacements  57  
A1.4.4  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 rules for road bridges  65  
A2.2.3  Combination rules for footbridges  66  
A2.2.4  Combination rules for railway bridges  66  
A2.2.5  Combinations of actions for accidental (non seismic) design situations  67  
A2.2.6  Values of ψ 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  
A2.4  SERVICEABILITY AND OTHER SPECIFIC LIMIT STATES  76  
A2.4.1  General  76  
A2.4.2  Serviceability criteria regarding deformation and vibration for road bridges  77 3  
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  
B1  SCOPE AND FIELD OF APPLICATION  86  
B2  SYMBOLS  86  
B3  RELIABILITY DIFFERENTIATION  87  
B3.1  Consequences classes  87  
B3.2  Differentiation by β 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  
C1  SCOPE AND FIELD OF APPLICATIONS  91  
C2  SYMBOLS  91  
C3  INTRODUCTION  92  
C4  OVERVIEW OF RELIABILITY METHODS  92  
C5  RELIABILITY INDEX β  93  
C6  TARGET VALUES OF RELIABILITY INDEX β  94  
C7  APPROACH FOR CALIBRATION OF DESIGN VALUES  95  
C8  RELIABILITY VERIFICATION FORMATS IN EUROCODES  97  
C9  PARTIAL FACTORS IN EN 1990  98  
C10  ψ_{0} FACTORS  99  
ANNEX D (INFORMATIVE) DESIGN ASSISTED BY TESTING  101  
D1  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 
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 19911:1994.
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 A1
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 BSI.
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.
5In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national 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 Representatives 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^{1} 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 Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products – CPD – and Council Directives 2004/17/EC and 2004/18/EC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).
The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts:
EN 1990  Eurocode:  Basis of Structural Design 
EN 1991  Eurocode 1:  Actions on structures 
EN 1992  Eurocode 2:  Design of concrete structures 
EN 1993  Eurocode 3:  Design of steel structures 
EN 1994  Eurocode 4:  Design of composite steel and concrete structures 
EN 1995  Eurocode 5:  Design of timber structures 
EN 1996  Eurocode 6:  Design of masonry structures 
EN 1997  Eurocode 7:  Geotechnical design 
EN 1998  Eurocode 8:  Design of structures for earthquake resistance 
EN 1999  Eurocode 9:  Design of aluminium structures 
Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.
^{1} Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89).
6The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes:
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents^{2} referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards.^{3} Therefore, technical aspects arising from the Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards and ETAGs 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 parts of works and structural construction products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.
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.
^{3} According to Art. 12 of the CPD the interpretative documents shall :
The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.
7There is a need for consistency between the harmonised technical specifications for construction products and the technical provisions for works^{4}. Furthermore, all the information accompanying the CE Marking of the construction products which use the Eurocodes 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 durability of structures. It is based on the limit state concept used in conjunction with a partial 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 :
EN 1990 is intended for use by :
EN 1990 may be used, when relevant, as a guidance document for the design of structures outside the scope of the Eurocodes EN 1991 to EN 1999, for :
^{4} see Art.3.3 and Art. 12 of the CPD, as well as 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.
8Numerical 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.
This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 1990 should have a National annex containing all Nationally Determined Parameters to be used for the design of buildings and civil engineering works to be constructed in the relevant country.
National choice is allowed in EN 1990 Annex Al through;
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) NOTE 1  Values of ψ factors 
A2.3.1(1)  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 γ_{P} 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 γ factors 
A2.3.1 Table A2.4(B) 
9 
A2.3.1 Table A2.4(C) 
Values of γ factors 
A2.3.2(1)  Design values in Table A2.5 for accidental designs 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(1) NOTE 1 (Table A2.6) NOTE 2 
Alternative γ 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 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(1) NOTE 2  Values of ψ_{1,infq} factors 
A2.2.6(1) NOTE 3  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(1)  Comfort criteria for footbridges 
Clauses specific for railway bridges
Clause  Item 

A2.2.4(1)  Combination rules for snow loading on railway bridges 
A2.2.4(4)  Maximum wind speed compatible with rail traffic 
A2.4.4.1(1) NOTE 3  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
10 
A2.4.4.2.2(3)P  Limiting values of the total deck twist for railway bridges 
A2.4.4.2.3(1)  Vertical deformation of ballasted and non ballasted railway bridges 
A2.4.4.2.3(2)  Limitations on the rotations of nonballasted 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 α_{i} and r_{i} 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 
NOTE For the design of special construction works (e.g. nuclear installations, dams, etc.), other provisions than those in EN 1990 to EN 1999 might be necessary.
NOTE Additional or amended provisions might be necessary where appropriate.
This European Standard incorporates by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only when incorporated in it by amendment or revision. For undated references the latest edition of the publication 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 normative clauses:
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 12 
EN 1997  Eurocode 7 : Geotechnical design 
EN 1998  Eurocode 8 : Design of structures for earthquake resistance 
EN 1999  Eurocode 9 : Design of aluminium structures 
NOTE There may be cases when the above assumptions need to be supplemented.
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.
NOTE For the purposes of this European Standard, the terms and definitions are derived from ISO 2394, ISO 3898, ISO 8930, ISO 8402.
everything that is constructed or results from construction operations
NOTE This definition accords with ISO 67071. The term covers both building and civil engineering works. It refers to the complete construction works comprising structural, nonstructural and geotechnical elements.
type of construction works designating its intended purpose, e.g. dwelling house, retaining wall, industrial building, road bridge
indication of the principal structural material, e.g. reinforced concrete construction, steel construction, timber construction, masonry construction, steel and concrete composite construction
manner in which the execution will be carried out, e.g. cast in place, prefabricated, cantilevered
material used in construction work, e.g. concrete, steel, timber, masonry
organised combination of connected parts designed to carry loads and provide adequate rigidity
14physically distinguishable part of a structure, e.g. a column, a beam, a slab, a foundation pile
arrangement of structural members
NOTE Forms of structure are, for example, frames, suspension bridges.
loadbearing members of a building or civil engineering works and the way in which these members function together
idealisation of the structural system used for the purposes of analysis, design and verification
all activities carried out for the physical completion of the work including procurement, the inspection and documentation thereof
NOTE The term covers work on site; it may also signify the fabrication of components off site and their subsequent erection on site.
quantitative formulations that describe for each limit state the conditions to be fulfilled
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 exceeded
design situation that is relevant during a period much shorter than the design working life 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.
15design situation that is relevant during a period of the same order as the design working life of the structure
NOTE Generally it refers to conditions of normal use.
design situation involving exceptional conditions of the structure or its exposure, including fire, explosion, impact or local failure
design of a structure to fulfil the required performance in case of fire
design situation involving exceptional conditions of the structure when subjected to a seismic event
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
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 deviation from intended dimensions
identification of the position, magnitude and direction of a free action
compatible load arrangements, sets of deformations and imperfections considered simultaneously with fixed variable actions and permanent actions for a particular verification
states beyond which the structure no longer fulfils the relevant design criteria
states associated with collapse or with other similar forms of structural failure
16NOTE They generally correspond to the maximum loadcarrying resistance of a structure or structural member.
states that correspond to conditions beyond which specified service requirements for a structure or structural member are no longer met
serviceability limit states where some consequences of actions exceeding the specified service requirements will remain when the actions are removed
serviceability limit states where no consequences of actions exceeding the specified service requirements will remain when the actions are removed
design criterion for a serviceability limit state
capacity of a member or component, or a crosssection of a member or component of a structure, to withstand actions without mechanical failure e.g. bending resistance, buckling resistance, tension resistance
mechanical property of a material indicating its ability to resist actions, usually given in units of stress
ability of a structure or a structural member to fulfil the specified requirements, including the design working life, for which it has been designed. Reliability is usually expressed in probabilistic terms
NOTE Reliability covers safety, serviceability and durability of a structure.
measures intended for the socioeconomic 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
17part of a specified set of variables representing physical quantities which characterise actions and environmental influences, geometrical quantities, and material properties including soil properties
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.
activities performed to preserve or to restore the function of a structure that fall outside the definition of maintenance
value fixed on nonstatistical bases, for instance on acquired experience or on physical conditions
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)
action that is likely to act throughout a given reference period and for which the variation 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
action for which the variation in magnitude with time is neither negligible nor monotonic
18action, 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 appropriate measures are taken.
NOTE 2 Impact, snow, wind and seismic actions may be variable or accidental actions, depending on the available information on statistical distributions.
action that arises due to earthquake ground motions
action transmitted to the structure by the ground, fill or groundwater
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
action that may have various spatial distributions over the structure
action that can be assumed to be statistically independent in time and space of any other action acting on the structure
action that does not cause significant acceleration of the structure or structural members
action that causes significant acceleration of the structure or structural members
dynamic action represented by an equivalent static action in a static model
principal representative value of an action
19NOTE 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 structure and the duration of the design situation.
chosen period of time that is used as a basis for assessing statistically variable actions, and possibly for accidental actions
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 ψ_{0} ≤ 1
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 ψ_{1} ≤ 1
NOTE For the frequent value of multicomponent traffic actions see load groups in EN 19912.
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 characteristic value by using a factor ψ_{2} ≤ 1
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 quasipermanent value.
value used for the verification of a limit state. A representative value may be the characteristic value (F_{k}) or an accompanying value (ψF_{k})
value obtained by multiplying the representative value by the partial factor γ_{f}
NOTE The product of the representative value multiplied by the partial factor γ_{F} = γ_{Sd} × γ_{f} may also be designated as the design value of the action (See 6.3.2).
20set of design values used for the verification of the structural reliability for a limit state under the simultaneous influence of different actions
value of a material or product property having a prescribed probability of not being attained 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 circumstances
value obtained by dividing the characteristic value by a partial factor γ_{m} or γ_{M} or, in special circumstances, by direct determination
value normally used as a characteristic value and established from an appropriate document such as a European Standard or Prestandard
value usually corresponding to the dimensions specified in the design. Where relevant, values of geometrical quantities may correspond to some prescribed fractiles of the statistical distribution
generally a nominal value. Where relevant, values of geometrical quantities may correspond to some prescribed fractile of the statistical distribution
NOTE The design value of a geometrical property is generally equal to the characteristic value. However, 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 imperfections on buckling. In such cases, the design value will normally be established as a value specified directly, for example in an appropriate European Standard or Prestandard. Alternatively, it can be established from a statistical basis, with a value corresponding to a more appropriate fractile (e.g. a rarer value) than applies to the characteristic value.
21NOTE 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.
procedure or algorithm for determination of action effects in every point of a structure
NOTE A structural analysis may have to be performed at three levels using different models : global analysis, member analysis, local analysis.
determination, in a structure, of a consistent set of either internal forces and moments, or stresses, that are in equilibrium with a particular defined set of actions on the structure, and depend on geometrical, structural and material properties
elastic structural analysis based on linear stress/strain or moment/curvature laws and performed on the initial geometry
linear elastic analysis in which the internal moments and forces are modified for structural design, consistently with the given external actions and without more explicit calculation of the rotation capacity
elastic structural analysis, using linear stress/strain laws, applied to the geometry of the deformed structure
structural analysis, performed on the initial geometry, that takes account of the nonlinear deformation properties of materials
NOTE First order nonlinear analysis is either elastic with appropriate assumptions, or elasticperfectly plastic (see 1.5.6.8 and 1.5.6.9), or elastoplastic (see 1.5.6.10) or rigidplastic (see 1.5.6.11).
structural analysis, performed on the geometry of the deformed structure, that takes account of the nonlinear deformation properties of materials
NOTE Second order nonlinear analysis is either elasticperfectly plastic or elastoplastic.
22structural analysis based on moment/curvature relationships consisting of a linear elastic part followed by a plastic part without hardening, performed on the initial geometry of the structure
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
structural analysis that uses stressstrain or moment/curvature relationships consisting of a linear elastic part followed by a plastic part with or without hardening
NOTE In general, it is performed on the initial structural geometry, but it may also be applied to the geometry of the displaced (or deformed) structure.
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 deformation and without hardening.
For the purposes 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_{d}  Design value of an accidental action 
A_{Ed}  Design value of seismic action A_{Ed} = γ_{I} A_{Ek} 
A_{Ek}  Characteristic value of seismic action 
C_{d}  Nominal value, or a function of certain design properties of materials 
E  Effect of actions 
E_{d}  Design value of effect of actions 
E_{d,dst}  Design value of effect of destabilising actions 
E_{d,stb}  Design value of effect of stabilising actions 
F  Action 
F_{d}  Design value of an action 
F_{k}  Characteristic value of an action 
F_{rep}  Representative value of an action 23 
F_{w}  Wind force (general symbol) 
F_{wk}  Characteristic value of the wind force 
Wind force compatible with road traffic  
Wind force compatible with railway traffic  
G  Permanent action 
G_{d}  Design value of a permanent action 
G_{d,inf}  Lower design value of a permanent action 
G_{d,sup}  Upper design value of a permanent action 
G_{k}  Characteristic value of a permanent action 
G_{k,j}  Characteristic value of permanent action j 
G_{k,j,sup}/G_{k,j,inf}  Upper/lower characteristic value of permanent action j 
G_{set}  Permanent action due to uneven settlements 
P  Relevant representative value of a prestressing action (see EN 1992 to EN 1996 and EN 1998 to EN 1999) 
P_{d}  Design value of a prestressing action 
P_{k}  Characteristic value of a prestressing action 
P_{m}  Mean value of a prestressing action 
Q  Variable action 
Q_{d}  Design value of a variable action 
Q_{k}  Characteristic value of a single variable action 
Q_{k,l}  Characteristic value of the leading variable action l 
Q_{k,i}  Characteristic value of the accompanying variable action i 
Q_{Sn}  Characteristic value of snow load 
R  Resistance 
R_{d}  Design value of the resistance 
R_{k}  Characteristic value of the resistance 
T  Thermal climatic action (general symbol) 
T_{k}  Characteristic value of the thermal climatic action 
X  Material property 
X_{d}  Design value of a material property 
X_{k}  Characteristic value of a material property 
Latin lower case letters
a_{d}  Design values of geometrical data 
a_{k}  Characteristic values of geometrical data 
a_{nom}  Nominal value of geometrical data 
d_{set}  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
Δa  Change made to nominal geometrical data for particular design purposes, e.g. assessment of effects of imperfections 
Δd_{set}  Uncertainty attached to the assessment of the settlement of a foundation or part of a foundation 
Greek lower case letters
γ  Partial factor (safety or serviceability) 
γ_{bt}  Maximum peak value of bridge deck acceleration for ballasted track 
γ_{df}  Maximum peak value of bridge deck acceleration for direct fastened track 
γ_{Gset}  Partial factor for permanent actions due to settlements, also accounting for model uncertainties 
γ_{f}  Partial factor for actions, which takes account of the possibility of unfavourable deviations of the action values from the representative values 
γ_{F}  Partial factor for actions, also accounting for model uncertainties and dimensional variations 
γ_{g}  Partial factor for permanent actions, which takes account of the possibility of unfavourable deviations of the action values from the representative values 
γ_{G}  Partial factor for permanent actions, also accounting for model uncertainties and dimensional variations 
γ_{G,j}  Partial factor for permanent action j 
γ_{G,j,sub}/γ_{G,j,inf}  Partial factor for permanent action j in calculating upper/lower design values 
γ_{I}  Importance factor (see EN 1998) 
γ_{m}  Partial factor for a material property 
γ_{M}  Partial factor for a material property, also accounting for model uncertainties and dimensional variations 
γ_{P}  Partial factor for prestressing actions (see EN 1992 to EN 1996 and EN 1998 to EN 1999) 
γ_{q}  Partial factor for variable actions, which takes account of the possibility of unfavourable deviations of the action values from the representative values 
γ_{Q}  Partial factor for variable actions, also accounting for model uncertainties and dimensional variations 
γ_{Q,i}  Partial factor for variable action i 
γ_{Rd}  Partial factor associated with the uncertainty of the resistance model 
γ_{Sd}  Partial factor associated with the uncertainty of the action and/or action effect model 
η  Conversion factor 
ξ  Reduction factor 
ψ_{0}  Factor for combination value of a variable action 
ψ_{1}  Factor for frequent value of a variable action 
ψ_{2}  Factor for quasipermanent value of a variable action 
NOTE See also 1.3, 2.1(7) and 2.4(1) P.
NOTE See also EN 199112
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 199117.
NOTE See 2.2(5) and Annex B
NOTE See also Annex B
NOTE Indicative categories are given in Table 2.1. The values given in Table 2.1 may also be used for determining timedependent performance (e.g. fatiguerelated calculations). See also Annex A.
Design working life category  Indicative design working life (years)  Examples 

1  10  Temporary structures^{(1)} 
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 reused should not be considered as temporary. 
NOTE The relevant EN 1992 to EN 1999 specify appropriate measures to reduce deterioration.
NOTE EN ISO 9001:2000 is an acceptable basis for quality management measures, where relevant.
NOTE In some cases, additional verifications may be needed, for example to ensure traffic safety.
NOTE Most time dependent effects are cumulative.
NOTE Information on specific design situations within each of these classes is given in EN 1991 to EN 1999.
NOTE The circumstances are those agreed for a particular project with the client and the relevant authority.
NOTE Different sets of partial factors are associated with the various ultimate limit states, see 6.4.1.
NOTE 1 In the context of serviceability, the term “appearance” is concerned with such criteria as high deflection and extensive cracking, rather than aesthetics.
NOTE 2 Usually the serviceability requirements are agreed for each individual project.
or that cause damage to finishes or nonstructural members ;
31NOTE Additional provisions related to serviceability criteria are given in the relevant EN 1992 to EN 1999.
NOTE 1 The relevant authority can give specific conditions for use.
NOTE 2 For a basis of probabilistic methods, see Annex C.
NOTE Indirect actions caused by imposed deformations can be either permanent or variable.
NOTE For some actions and some verifications, a more complex representation of the magnitudes of some actions may be necessary.
NOTE This coefficient of variation can be in the range of 0,05 to 0,10 depending on the type of structure.
NOTE For the settlement of foundations, see EN 1997.
NOTE The characteristic values of prestress, at a given time t, may be an upper value P_{k,sup}(t) and a lower value P_{k,inf}(t). For ultimate limit states, a mean value P_{m}(t) can be used. Detailed information is given in EN 1992 to EN 1996 and EN 1999.
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 timevarying part being exceeded for a reference period of one year. This is equivalent to a mean return period of 50 years for the timevarying part. However in some cases the character of the action and/or the selected design situation makes another fractile and/or return period more appropriate.
NOTE See also EN 199117.
NOTE See also EN 1998.
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.
NOTE 2 The infrequent value, represented as a product ψ_{1,infq}Q_{k}, may 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 19912) is based on a return period of one year.
NOTE 3 For the frequent value of multicomponent traffic actions see EN 19912.
NOTE For loads on building floors, the quasipermanent value is usually chosen so that the proportion of the time it is exceeded is 0,50 of the reference period. The quasipermanent 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 quasipermanent value is generally taken as zero.
NOTE For the consideration of material specific effects (for example, the consideration of mean stress influence or nonlinear effects), see EN 1992 to EN 1999.
NOTE Limits of use of these models are described in the various Parts of EN 1991.
35NOTE The EN 1992 to EN 1999 give the relevant measures.
NOTE See annex D and EN 1992 to EN 1999
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).
NOTE Suitable account may be taken where appropriate of the unfamiliarity of the application or materials/products used.
NOTE Particular methods for dealing with effects of deformations are given in EN 1991 to EN 1999.
NOTE For some equivalent dynamic amplification factors, the natural frequencies are determined.
NOTE Guidance for assessing these limits is given in Annex A and EN 1992 to EN 1999.
as well as the accompanying actions.
NOTE See also EN 199112.
NOTE See also EN 1991 to EN 1999.
NOTE Testing may be carried out, for example, in the following circumstances :
See Annex D.
in combination with partial and other factors as defined in this section and EN 1991 to EN 1999.
F_{d} = γ _{f} F_{rep} (6.1a)
with :
F_{rep} = ψF_{k} (6.1b)
where :
41F_{k}  is the characteristic value of the action. 
F_{rep}  is the relevant representative value of the action. 
γ_{f}  is a partial factor for the action which takes account of the possibility of unfavourable deviations of the action values from the representative values. 
ψ  is either 1,00 or ψ_{0}, ψ_{1} ψ_{2}. 
where :
a_{d}  is the design values of the geometrical data (see 6.3.4); 
γ_{sd}  is a partial factor taking account of uncertainties :

NOTE In a more general case the effects of actions depend on material properties.
with :
γ _{F,i} = γ_{Sd} × γ _{f,i} (6.2b)
NOTE When relevant, e.g. where geotechnical actions are involved, partial factors γ_{F,i} can be applied to the effects of individual actions or only one particular factor γ_{F} can be globally applied to the effect of the combination of actions with appropriate partial factors.
NOTE Except for rope, cable and membrane structures, most structures or structural elements are in categoiy a).
where :
X_{k}  is the characteristic value of the material or product (see 4.2(3)); 
η  is the mean value of the conversion factor taking into account

γ_{m}  is the partial factor for the material or product property to take account of:

NOTE The design value can be established by such means as :
a_{d} = a_{nom} (6.4)
43a_{d} = a_{nom} ± Δa (6.5)
Where :
Δa  takes account of :

NOTE 1 a_{d} can also represent geometrical imperfections where a_{nom} = 0 (i.e., Δa ≠ 0).
NOTE 2 Where relevant, EN 1991 to EN 1999 provide further provisions.
NOTE Tolerances are defined in the relevant standards on execution referred to in EN 1990 to EN 1999.
where :
γ_{Rd}  is a partial factor covering uncertainty in the resistance model, plus geometric deviations if these are not modelled explicitly (see 6.3.4(2)); 
X_{d,i}  is the design value of material property i. 
where :
γ _{M,i} = γ _{Rd} × γ _{m,i} (6.6b)
NOTE η_{i} may be incorporated in γ_{M,i,} see 6.3.3.(2).
44NOTE 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”.
NOTE In some cases, the design resistance can be expressed by applying directly γ_{M} partial factors to the individual resistances due to material properties.
NOTE For fatigue design, the combinations of actions are given in EN 1992 to EN 1995, EN 1998 and EN 1999.
NOTE See EN 1997.
NOTE See EN 1997.
E_{d,dst} ≤ E_{d,stb} (6.7)
where :
E_{d,dst}  is the design value of the effect of destabilising actions ; 
E_{d,stb}  is the design value of the effect of stabilising actions. 
E_{d} ≤ R_{d} (6.8)
where :
E_{d}  is the design value of the effect of actions such as internal force, moment or a vector representing several internal forces or moments ; 
R_{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.
NOTE This applies in particular to the verification of static equilibrium and analogous limit states, see 6.4.2(2).
NOTE For further guidance on this topic see the clauses on vectorial effects in EN 1992 to EN 1999.
NOTE For further guidance, see 5.1.2.4(P) and EN 1992 to EN 1999.
NOTE See also 6.4.3.2(4).
or, alternatively for STR and GEO limit states, the less favourable of the two following expressions:
Where :
“+”  implies “to be combined with” 
∑  implies “the combined effect of” 
ξ  is a reduction factor for unfavourable permanent actions G 
NOTE Further information for this choice is given in Annex A.
NOTE Guidance is given in the relevant Parts of EN 1991 to EN 1999.
For fire situations, apart from the temperature effect on the material properties, A_{d} should represent the design value of the indirect effects of thermal action due to fire.
E_{d} ≤ C_{d} (6.13)
where :
C_{d}  is the limiting design value of the relevant serviceability criterion. 
E_{d}  is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination. 
NOTE For other specific serviceability criteria such as crack width, stress or strain limitation, slip resistance, see EN 1991 to EN 1999.
NOTE It is assumed, in these expressions, that all partial factors are equal to 1. See Annex A and EN 1991 to EN 1999.
in which the combination of actions in brackets { } (called the characteristic combination), can be expressed as :
49NOTE The characteristic combination is normally used for irreversible limit states.
in which the combination of actions in brackets { }, (called the frequent combination), can be expressed as:
NOTE The frequent combination is normally used for reversible limit states.
in which the combination of actions in brackets { }, (called the quasipermanent combination), can be expressed as :
where the notation is as given in 1.6 and 6.4.3(1).
NOTE The quasipermanent combination is normally used for longterm effects and the appearance of the structure.
NOTE In some cases expressions (6.14) to (6.16) require modification. Detailed rules are given in the relevant Parts of EN 1991 to EN 1999.
(normative)
NOTE Guidance may be given in the National annex with regard to the use of Table 2.1 (design working life).
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 A1.2.1(2) and A1.2.1(3) are necessary for geographical reasons, these can be defined in the National annex.
NOTE Recommended values of ψ factors for the more common actions may be obtained from Table A1.1. For ψ factors during execution see EN 199116 Annex A 1.
51Action  ψ_{0}  ψ_{1}  ψ_{2} 

Imposed loads in buildings, category (see EN 199111)  
Category A : domestic, residential areas  0,7  0,5  0,3 
Category B : office areas  0,7  0,5  0,3 
Category C : congregation areas  0,7  0,7  0,6 
Category D : shopping areas  0,7  0,7  0,6 
Category E : storage areas  1,0  0,9  0,8 
Category F : traffic area,  
vehicle weight ≤ 30kN  0,7  0,7  0,6 
Category G : traffic area,  
30kN < vehicle weight ≤ 160kN  0,7  0,5  0,3 
Category H: roofs  0  0  0 
Snow loads on buildings (see EN 199113)*  
Finland, Iceland, Norway, Sweden  0,70  0,50  0,20 
Remainder of CEN Member States, for sites  0,70  0,50  0,20 
located at altitude H > 1000 m a.s.1.  
Remainder of CEN Member States, for sites  0,50  0,20  0 
located at altitude H ≤ 1000 m a.s.1.  
Wind loads on buildings (see EN 199114)  0,6  0,2  0 
Temperature (nonfire) in buildings (see EN 199115)  0,6  0,5  0 
NOTE The ψ values may be set by the National annex. * For countries not mentioned below, see relevant local conditions. 
NOTE The values in Tables A1.2 ((A) to (C)) can be altered e.g. for different reliability levels in the National annex (see Section 2 and Annex B).
NOTE In some cases, application of these tables is more complex, see EN 1997.
NOTE The use of approaches 1, 2 or 3 is chosen in the National annex.
Persistent and transient design situations  Permanent actions  Leading variable action (*)  Accompanying variable actions  
Unfavourable  Favourable  Main (if any)  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{Q,1} Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) Variable actions are those considered in Table A 1.1
NOTE 1 The γ values may be set by the National annex. The recommended set of values for γ are : γ_{G,j,sup} = 1,10 γ_{G,j,inf} = 0,90 γ_{Q,1} = 1,50 where unfavourable (0 where favourable) γ_{Q,i} = 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 A1.2(A) and A1.2(B), a combined verification, based on Table A1.2(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. γ_{G,j,sup} = 1,35 γ_{G,j,inf} = 1,15 γ_{Q,1} = 1,50 where unfavourable (0 where favourable) γ_{Q,i} = 1,50 where unfavourable (0 where favourable) provided that applying γ_{G,j,inf} = 1,00 both to the favourable part and to the unfavourable part of permanent actions does not give a more unfavourable effect. 
Persistent and transient design situations  Permanent actions  Leading variable action  Accompanying variable actions(*)  Persistent and transient design situations  Permanent actions  Leading variable action (*)  Accompanying variable actions (*)  
Unfavourable  Favourable  Main (if any)  Others  Unfavourable  Favourable  Action  Main  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{Q,1} Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  (Eq. 6.10a)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{Q,1}ψ_{0,1}Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(Eq. 6.10b)  ξγ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{Q,1} Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) 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 γ and ξ values may be set by the National annex. The follwing values for γ and ξ are recommended when using expression 6.10, or 6.10a and 6.10b. γ_{G,j,sup} = 1,35 γ_{G,j,inf} = 1,00 γ_{Q,1} = 1,50 where unfavourable (0 where favourable) γ_{Q,i} = 1,50 where unfavourable (0 where favourable) ξ = 0,85 (so that ξ γ_{G,j,sup} = 0,85 × 1,35 ≅ 1,15). See also EN 1991 to EN 1999 for γ values to be used for imposed deformations. NOTE 3 The characteristic values of all permanent actions from one source are multiplied by γ_{G,sup} if the total resulting action effect is unfavourable and γ_{G,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 γ_{G} and γ_{Q} may be subdivided into γ_{g} and γ_{q} and the model uncertainty factor γ_{sd}. A value of γ_{sd} in the range 1,05 to 1,15 can be used in most common cases and can be modified in the National annex. 
Persistent and transient design situation  Permanent actions  Leading variable action (*)  Accompanying variable actions (*)  
Unfavourable  Favourable  Main (if any)  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{Q,1} Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) Variable actions are those considered in Table A 1.1
NOTE The γ values may be set by the National annex. The recommended set of values for γ are : γ_{G,j,sup} = 1,00 γ_{G,j,inf} = 1,00 γ_{Q,1} = 1,30 where unfavourable (0 where favourable) γ_{Q,i} = 1,30 where unfavourable (0 where favourable) 
NOTE For the seismic design situation see also EN 1998.
Design situation  Permanent actions  Leading accidental or seismic action  Accompanying variable actions (**)  
Unfavourable  Favourable  Main (if any)  Others  
Accidental (*)(Eq. 6.11a/b)  G_{k,j,sup}  G_{k,j,inf}  A_{d}  ψ_{1,1} or ψ_{2,1}Q_{k,1} 
ψ_{2,i} Q_{k,i} 
Seismic (Eq. 6.12a/b)  G_{k,j,sup}  G_{k,j,inf}  A_{Ed} = γ_{1}A_{Ek}  ψ_{2,i} Q_{k,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 quasipermanent values. The choice will be in the National annex, depending on the accidental action under consideration. See also EN 199112. (**) Variable actions are those considered in Table A1.1. 
Combination  Permanent actions G_{d}  Variable actions Q_{d}  
Unfavourable  Favourable  Leading  Others  
Characteristic  G_{k,j,sup}  G_{k,j,inf}  Q_{k,1}  ψ_{0,i}Q_{k,i} 
Frequent  G_{k,j,sup}  G_{k,j,inf}  ψ_{1,1}Q_{k,1}  ψ_{2,i}Q_{k,i} 
Quasipermanent  G_{k,j,sup}  G_{k,j,inf}  ψ_{2,1}Q_{k,1}  ψ_{2,i}Q_{k,i} 
NOTE The serviceability criteria may be defined in the National annex.
Figure A1.1 – Definitions of vertical deflections
Key:
w_{c}  Precamber in the unloaded structural member 
w_{1}  Initial part of the deflection under permanent loads of the relevant combination of actions according to expressions (6.14a) to (6.16b) 
w_{2}  Longterm part of the deflection under permanent loads 
w_{3}  Additional part of the deflection due to the variable actions of the relevant combination of actions according to expressions (6.14a) to (6.16b) 
w_{tot}  Total deflection as sum of w_{1}, w_{2}, w_{3} 
w_{max}  Remaining total deflection taking into account the precamber 
NOTE Guidance on which expression (6.14a) to (6.16b) to use is given in 6.5.3 and EN 1992 to EN 1999.
Figure A1.2 – Definition of horizontal displacements
Key:
u  Overall horizontal displacement over the building height H 
u_{i}  Horizontal displacement over a storey height H_{i} 
Other aspects should be considered for each project and agreed with the client.
NOTE For further guidance, see EN 199111, EN 199114 and ISO 10137.
18) Modification to the Annexes
At the end of Annex A1 and before Annex B, add the following Annex A2:
(normative)
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) NOTE 1  Values of ψ factors 
A2.3.1(1)  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 γ_{p} 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 γ factors 
A2.3.1 Table A2.4(B) 

A2.3.1 Table A2.4 (C)  Values of γ factors 
A2.3.2(1)  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) NOTE 1 (Table A2.6) NOTE 2 
Alternative γ 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 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(1) NOTE 2  Values of ψ_{1,infq} factors 
A2.2.6(1) NOTE 3  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 
60  
A2.4.3.2(1)  Comfort criteria for footbridges 
Clauses specific for railway bridges
Clause  Item 

A2.2.4(1)  Combination rules for snow loading on railway bridges 
A2.2.4(4)  Maximum wind speed compatible with rail traffic 
A2.4.4.1(1) NOTE 3  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 
A2.4.4.2.2(3)P  Limiting values of the total deck twist for railway bridges 
A2.4.4.2.3(1)  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 α_{i} and r_{i} 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 
Text deleted
NOTE 1 Symbols, notations, Load Models and groups of loads are those used or defined in the relevant section of EN 19912.
NOTE 2 Symbols, notations and models of construction loads are those defined in EN 199116.
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 groundstructure interaction that may depend on movements or deformations of structural bearings.
Text deleted
62NOTE 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 199116.
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.
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.
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 199113, 14 and 16.
NOTE The individual project may specify limits on total settlement and differential settlement.
NOTE 1 Settlements 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 structure, or a part of it, becomes statically indeterminate). In addition, in the case of a concrete structure or a structure with concrete elements, there may be an interaction between the development of settlements and creep of concrete members.
NOTE Methods for the assessment of settlements are given in EN 1997
64NOTE The National Annex may refer to the infrequent combination of actions. The expression of this combination of actions is:
in which the combination of actions in brackets { } may be expressed as:
NOTE The combination rules for special vehicles (see EN 19912, Annex A, Informative) with normal traffic (covered by LM1 and LM2) and other variable actions may be referenced as appropriate in the National Annex or agreed for the individual project.
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.
NOTE For wind actions, see EN 199114.
NOTE Depending upon the local climatic conditions a different simultaneity rule for wind and thermal actions may be defined either in the National Annex or for the individual project.
NOTE Depending upon the local climatic conditions a different simultaneity rule for wind and thermal actions may be defined either in the National Annex or for the individual project.
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.
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 ψ factors for traffic actions being in accordance with Table A2.2, are recommended.
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.
NOTE The National Annex may give the limits of the maximum wind speed(s) compatible with rail traffic for determining . See also EN 199114.
66NOTE 1 For actions due to impact from traffic, see EN 199117.
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.
NOTE 1 For actions due to impact from traffic, see EN 199117.
NOTE 2 Actions for accidental design situations due to impact from rail traffic running on the bridge including derailment actions are specified in EN 19912, 6.7.1.
NOTE For ship impact, see EN199117. Additional requirements may be specified for the individual project.
NOTE 1 The ψ values may be set by the National Annex. Recommended values of ψ factors for the groups of traffic loads and the more common other actions are given in:
67Table 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.
Action  Symbol  ψ_{0}  ψ_{1}  ψ_{2}  
Traffic loads (see En 19912, Table 4.4)  grla (LMl+pedestrain or cycletract loads)^{1)}  TS  0,75  0,75  0 
UDL  0,40  0,40  0  
Pedestrian+cycletrack loads ^{2)}  0,40  0,40  0  
grlb (Single axle)  0  0,75  0  
gr2 (Horizontal forces)  0  0  0  
gr3 (Pedestrian loads)  0  0,40  0  
gr4 (LM4 – Crowd loading))  0  –  0  
gr5 (LM3 – Special vehicles))  0  –  0  
Wind forces  F_{Wk}  Persistent design situations  Execution 
0,6 0,8 
0,2  
0 0 

1,0      
Thermal actions  T_{k}  0,6^{3)}  0,6  0,5  
Snow loads  Q_{Sn,k} (during execution)  0,8      
Construction loads  Q_{c}  1,0    1,0  

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 ψ_{l,infq} The recommended values of ψ_{l,infq} are:
NOTE 3 The characteristic values of wind actions and snow loads during execution are defined in EN 199116. Where relevant, representative values of water forces (F_{wa}) may be defined in the National Annex or for the individual project.
Action  Symbol  ψ_{0}  ψ_{1}  ψ_{2} 
Traffic loads  grl  0,40  0,40  0 
Q_{fwk}  0  0  0  
gr2  0  0  0  
Wind forces  F_{Wk}  0,3  0,2  0 
Thermal actions  T_{k}  0,6^{1)}  0,6  0,5 
Snow loads  Q_{Sn,k} (during execution)  0,8    0 
Construction loads  Q_{c}  1,0    1,0 
1) The recommended ψ_{0} value for thermal actions may in most cases be reduced to 0 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.
68Action  ψ_{0}  ψ_{1}  ψ_{2}^{4)}  
Individual components of traffic actions^{5)}  LM71 SW/0 SW/2 Unloaded train HSLM 
0,80 0,80 0 1,00 1,00 
^{1)} ^{1)} 1,00 – 1,00 
0 0 0 – 0 

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 (multidirectional) leading action and not as groups of loads should use the same values of ψ 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 
0 0 0 0 0 

Main traffic actions (groups of loads)  gr11 (LM71 + SW/0)  Max. vertical 1 with max. longitudinal  0,80  0,80  0 
gr12(LM71 + SW/0)  Max. vertical 2 with max. transverse  
gr13 (Braking/traction)  Max. longitudinal  
gr14 (Centrifugal/nosing)  Max. lateral  
gr15 (Unloaded train)  Lateral stability with “unloaded train”  
gr16 (SW/2)  SW/2 with max. longitudinal  
gr17 (SW/2)  SW/2 with max. transverse  
gr21 (LM71 + SW/0)  Max. vertical 1 with max. longitudinal  0,80  0,70  0  
gr22 (LM71 +SW/0)  Max. vertical 2 with max transverse  
gr23 (Braking/traction)  Max. longitudinal  
gr24 (Centrifugal/nosing)  Max. lateral  
gr26 (SW/2)  SW/2 with max. longitudinal  
gr27 (SW2)  SW/2 with max. transverse  
gr31 (LM71 +SW/0)  Additional load cases  0,80  0,60  0  
Other operating actions  Aerodynamic effects  0,80  0,50  0  
General maintenance loading for non public footpaths  0,80  0,50  0  
Wind forces ^{2)}  F_{Wk}  0,75  0,50  0  
1,00  0  0 69 

Thermal actions ^{3)} 
T_{k}  0,60  0,60  0,50  
Snow loads  Q_{Sn,k} (during execution)  0,8    0  
Construction loads  Q_{c}  1,0    1,0  

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.
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.
NOTE Verification for fatigue excluded.
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).
NOTE The choice of approach 1, 2 or 3 is given in the National Annex.
NOTE For water actions and debris effects, see EN 199116. General and local scour depths may have to be assessed for the individual project. Requirements for taking account of forces due to ice pressure on bridge piers, etc., may be defined as appropriate in the National Annex or for the individual project.
NOTE In the cases where γ_{P} 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, inter alia, on:
See also EN199116 during execution.
Persistent and transient design situation  Permanent actions  Prestress  Leading variable action (*)  Accompanying variable actions (*)  
Unfavourable  Favourable  Main (if any)  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{P}P  γ_{Q,l} Q_{k,l}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) Variable actions are those considered in Tables A2.1 to A2.3.  
NOTE 1 The γ 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 γ are: γ_{G,sup} = 1,05 γ_{G,inf} = 0,95^{(1)} γ_{Q} = 1,35 for road and pedestrian traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,45 for rail traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,50 for all other variable actions for persistent design situations, where unfavourable (0 where favourable). γ_{P} = recommended values defined in the relevant design Eurocode. For transient design situations during which there is a risk of loss of static equilibrium, Q_{k,l} represents the dominant destabilising variable action and Q_{k,i} represents the relevant accompanying destabilising variable actions. During execution, if the construction process is adequately controlled, the recommended set of values for γ are: γ_{G,sup} = 1,05 γ_{G,inf} = 0,95^{(1)} γ_{Q} = 1,35 for construction loads where unfavourable (0 where favourable) γ_{Q} = 1,50 for all other variable actions, where unfavourable (0 where favourable) ^{(1)} 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:
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 auxiliary 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 γ values. The following values of γ are recommended: γ_{G,sup} = 1,35 γ_{G,inf} = 1,25 γ_{Q} = 1,35 for road and pedestrian traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,45 for rail traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,50 for all other variable actions for persistent design situations, where unfavourable (0 where favourable) γ_{Q} = 1,35 for all other variable actions, where unfavourable (0 where favourable) provided that applying γ_{G,inf} = 1,00 both to the favourable part and to the unfavourable part of permanent actions does not give a more unfavourable effect. 
Persistent and transient design situation  Permanent actions  Prestress  Leading variable action (*)  Accompanying variable actions (*)  Persistent and transient design situation  Permanent actions  Prestress  Leading variable action (*)  Accompanying variable actions (*)  
Unfavourable  Favourable  Main (if any)  Others  Unfavourable  Favourable  Main (if any)  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{P}P  γ_{Q,l}Q_{k,l}  γ_{Q,i}ψ_{0,i}Q_{k,i}  (Eq. 6.10a)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{P}P  γ_{Q,1}ψ_{0,1}Q_{k,1}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(Eq. 6.10b)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{P}P  γ_{Q,l}Q_{k,l}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) Variable actions are those considered in Tables A2.1 to A1.3. NOTE 1 The choice between 6.10, or 6.10a and 6.10b 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 γ and ξ values may be set by the National Annex. The following values for γ and ξ are recommended when using expressions 6.10, or 6.10a and 6.10b: γ_{G,sup} = 1.35^{1)} γ_{G,inf} = 1,00 γ_{Q} = 1,35 when Q represents unfavourable actions due to road or pedestrian traffic (0 when favourable) γ_{Q} = 1,45 when Q represents unfavourable actions due to rail traffic, for groups of loads 11 to 31 (except 16, 17, 26^{3)} and 27^{3)}), load models LM71, SW/0 and HSLM and real trains, when considered as individual leading traffi actions (0 when favourable) γ_{Q} = 1,20 when Q represents unfavourable actions due to rail trffic, for groups of loads 16 and 17 and SW/2 (0 when favourable) γ_{Q} = 1,50 for other traffic actions and other variable actions^{2)} ξ = 0,85 (so that ξγ_{G,sup} = 8,85 × 1,35 ≅ 1,15). γ_{Gset} = 1,20 in the case of a linear elastic analysis, and γ_{Gset} = 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 be taken into account. See also EN 1991 to EN 1999 for γ values to be used for imposed deformations. γ_{P} = recommended values defined in the Eurocode. ^{1)}This value covers: selfweight of structural elements, ballast, soil, ground water and free water, removable loads, etc. ^{2)}This value covers: variable horizontal earth pressure from soil, ground water, free water and ballast, traffic load surcharge earth pressure, traffic aerodynamic actions, wind thermal actions, etc. ^{3)} For rail traffic actions for groups of loads 26 and 27 γ_{Q} = 1,20 may be appliled to individual components of traffic actions associated with SW/2 and γ_{Q} = 1,45 may be applied to individual components of traffic actions associated with load models LM71, SW/0 and HSLM, etc. 73NOTE 3 The characteristic valules of all permanent actions from one source are multiplied by γ_{G,sup} if the total resulting action effect is unfavourable and γ_{G,inf} if the total resulting action effect is favourable. For example, all actions originating from the selfweight of the structure 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 valules for γ_{G} and γ_{Q} may be subdivided into γ_{g} and γ_{q} and the model uncertainity factor γ_{Sd}. A value of γ_{Sd} in the range 1,0–1,15 may be used in most common cases and may be modified in the National Annex. NOTE 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. 
Persistent and transient design situation  Permanent actions  Prestress  Leading variable action (*)  Accompanying variable actions (*)  
Unfavourable  Favourable  Main (if any)  Others  
(Eq. 6.10)  γ_{G,j,sup}G_{k,j,sup}  γ_{G,j,inf}G_{k,j,inf}  γ_{P}P  γ_{Q,l}Q_{k,l}  γ_{Q,i}ψ_{0,i}Q_{k,i}  
(*) Variable actions are those considered in Tables A2.1 to A2.3.  
NOTE 1 The γ values may be set by the National Annex. The recommended set of values for γ are: γ_{G,sup} = 1,00 γ_{G,inf} = 1,00 γ_{Gset} = 1,00 γ_{Q} = 1,15 for road and pedestrian traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,25 for rail traffic actions, where unfavourable (0 where favourable) γ_{Q} = 1,30 for all variable part of horizontal earth pressure form soil, ground water, free water and ballast, for traffic load surcharge horizontal earth pressure, where unfavourable (0 where favourable). γ_{Q} = 1,30 for all other variable actions where unfavourable (0 where favourable). γ_{Qset} = 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. γ_{P} = recommended values defined in the relevant design Eurocode. 
NOTE For the seismic design situation see also EN 1998.
75Design situation  Permanent actions  Prestress  Accidental or seismic action  Accompanying variable actions (**)  
Unfavourable  Favourable  Main (if any)  Others  
Accidental (*) (Eq. 6.11a/b) 
G_{k,j,sup}  G_{k,j,inf}  P  A_{d}  ψ_{l,l} Q_{k,l} or ψ_{2,l} Q_{k,l} 
ψ_{2,i} Q_{k,i} 
Seimsmic(***) (Eq. 6.12a/b) 
G_{k,j,sup}  G_{k,j,inf}  P  A_{Ed} = γ_{I} A_{Ek}  ψ_{2,i} Q_{k,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 quasipermanent values. The choice will be in the National Annex, depending on the accidental action under consideration. (**) 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 γ = 1,0 for all non seismic actions. 
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.
where:
Q_{c,k} is the characteristic value of construction loads as defined in EN 199116 (i.e. the characteristic value of the relevant combination of groups Q_{ca}, Q_{cc}, Q_{cd}, Q_{cc} and Q_{cf}).
NOTE 1 γ 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 γ factors being taken as 1,0.
76Combination 
Permanent actions G_{d}  Prestress  Variable actions Q_{d}  
Unfavourable  Favourable  Leading  Others  
Characteristic  G_{k,j,sup}  G_{k,j,inf}  P  Q_{k,l}  ψ_{0,i}Q_{k,i} 
Frequent  G_{k,j,sup}  G_{k,j,inf}  P  ψ_{1,l}Q_{k,l}  ψ_{2,i}Q_{k,i} 
Quasipermanent  G_{k,j,sup}  G_{k,j,inf}  P  ψ_{2,l}Q_{k,l}  ψ_{2,i}Q_{k,i} 
NOTE 2 The National Annex may also refer to the infrequent combination of actions.
NOTE Serviceability requirements and criteria may be defined as appropriate in the National Annex or for the individual project.
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.
NOTE 1 The verification of serviceability limit states concerning deformation and vibration needs to be considered only in exceptional cases for road bridges. The frequent combination of actions is recommended for the assessment of deformation.
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 199114. For vibrations due to traffic actions, comfort criteria may have to be considered. Fatigue may also have to be taken into account.
NOTE For vibrations due to wind actions, see EN 199114.
77NOTE The design situations may take into account the way the traffic will be authorised, regulated and controlled, depending on the individual project.
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.
NOTE The criteria may be defined as appropriate in the National Annex or for the individual project. The following accelerations (m/s^{2}) are the recommended maximum values for any part of the deck:
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.
NOTE 1 Excessive bridge deformations 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 Deformation 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 deformation 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).
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.
NOTE There are other implicit stiffness criteria in the limits of bridge natural frequency given in EN 19912, 6.4.4 and when determining dynamic factors for real trains in accordance with EN 19912, 6.4.6.4 and EN 19912 Annex C.
Vertical acceleration of the deck
NOTE Generally only characteristic rail traffic actions in accordance with EN19912, 6.4.6.1 need to be considered.
for all members supporting the track considering frequencies (including consideration of associated mode shapes) up to the greater of:
NOTE The values and the associated frequency limits may be defined in the National Annex. The recommended values are:
γ_{bt} = 3,5 m/s^{2}
γ_{df} = 5 m/s^{2}
Deck twist
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).
Figure A2.1 – Definition of deck twist
Speed range V (km/h)  Maximum twist t (mm/3m) 
V ≤ 120  t ≤ t_{1} 
120 < V ≤ 200  t ≤ t_{2} 
V > 200  t ≤ t_{3} 
NOTE The values for t may be defined in the National Annex.
The recommended values for the set of t are:
t_{1} = 4,5
t_{2} = 3,0
t_{3} = 1,5
Values for a track with a different gauge may be defined in the National Annex.
NOTE The value for t_{T} may be defined in the National Annex. The recommended value for t_{T} is 7,5 mm/3m.
Vertical deformation of the deck
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.
Figure A2.2 – Definition of angular rotations at the end of decks
81NOTE The requirements for non ballasted structures may be specified in the National Annex.
NOTE The additional limits of angular rotations may be defined in the National Annex or for the individual project.
Transverse deformation and vibration of the deck
NOTE The maximum differential transverse deflection may be specified in the National Annex or for the individual project.
Speed range V (km/h)  Maximum horizontal rotation (radian)  Maximum change of radius of curvature (m)  

Single deck  Multideck bridge  
V ≤ 120  α_{1}  r_{1}  r_{4} 
120 < V ≤ 200  α_{2}  r_{2}  r_{5} 
V > 200  α_{3}  r_{3}  r_{6} 
NOTE 1 The change of the radius of curvature may be determined using: NOTE 2 The transverse deformation includes the deformation of the bridge deck and the substructure (including piers, piles and foundations). 82NOTE 3 The values for the set of (α_{i} and r_{i} may be defined in the National Annex. The recommended values are: α_{1} = 0,0035; α_{2} = 0,0020; α_{3} = 0,0015; 
NOTE The value for f_{h0} may be defined in the National Annex. The recommended value is: f_{h0} = l,2 Hz.
Longitudinal displacement of the deck
NOTE Also see A2.4.4.2.3.
Comfort criteria
NOTE These levels of comfort and associated limiting values may be defined for the individual project. Recommended levels of comfort are given in Table A2.9.
Level of comfort  Vertical acceleration b_{v} (m/s^{2}) 
Very good  1,0 
Good  1,3 
Acceptable  2,0 
Deflection criteria for checking passenger comfort
Alternatively the vertical acceleration b_{v} may be determined by a dynamic vehicle/bridge interaction analysis (see A2.4.4.3.3).
83For bridges with two or more tracks only one track should be loaded.
Figure A2.3 – Maximum permissible vertical deflection δ for railway bridges with 3 or more successive simply supported spans corresponding to a permissible vertical acceleration of b_{v} = 1 m/s^{2} in a coach for speed V [km/h]
NOTE The requirements for passenger comfort for temporary bridges may be defined in the National Annex or for the individual project.
Requirements for a dynamic vehicle/bridge interaction analysis for checking passenger comfort
NOTE Any requirements for taking track roughness into account in the vehicle/bridge dynamic interaction analysis may be defined for the individual project.
(informative)
NOTE Reliability differentiation rules have been specified for particular aspects in the design Eurocodes, e.g. in EN 1992, EN 1993, EN 1996, EN 1997 and EN 1998.
NOTE Reliability classification can be represented by β indexes (see Annex C) which takes account of accepted or assumed statistical variability in action effects and resistances and model uncertainties.
NOTE Those quality management and control measures in design, detailing and execution which are given in B4 and B5 aim to eliminate failures due to gross errors, and ensure the resistances assumed in the design.
In this annex the following symbols apply.
K_{FI}  Factor applicable to actions for reliability differentiation 
β  Reliability index 
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, public 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) 
CC1  Low consequence for loss of human life, and economic, social or environmental consequences small or negligible  Agricultural buildings where people do not normally enter (e.g. storage buildings), greenhouses 
NOTE At the present time the requirements for reliability are related to the structural members of the construction works.
Reliability Class  Minimum values for β  

1 year reference period  50 years reference period  
RC3  5,2  4,3 
RC2  4,7  3,8 
RC1  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 β value greater than 3,8 for a 50 year reference period. Reliability classes for members of the structure above RC3 are not further considered in this Annex, since these structures each require individual consideration.
K_{FI} factor for actions  Reliability class  
RC1  RC2  RC3  
K_{FI}  0,9  1,0  1,1 
NOTE In particular, for class RC3, other measures as described in this Annex are normally preferred to using K_{FI} factors. K_{FI} should be applied only to unfavourable actions.
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 
Normal supervision  Checking by different persons than those originally responsible and in accordance with the procedure of the organisation. 
DSL1 Relating toRCl 
Normal supervision  Selfchecking: Checking perfonned by the person who has prepared the design 
NOTE The type of construction works, the materials used and the structural forms can affect this classification.
Inspection Levels  Characteristics  Requirements 

IL3 Relating to RC3 
Extended inspection  Third party inspection 
IL2 Relating to RC2 
Normal inspection  Inspection in accordance with the procedures of the organisation 
IL1 Relating to RC1 
Normal inspection  Self inspection 
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.
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.
(informative)
In this annex the following symbols apply.
Latin upper case letters
P_{f}  Failure probability 
Prob(.)  Probability 
P_{s}  survival probability 
Latin lower case letters
a  geometrical property 
g  performance function 
Greek upper case letters
Φ  cumulative distribution function of the standardised Normal distribution 
Greek lower case letters
α_{E}  FORM (First Order Reliability Method) sensitivity factor for effects of actions 
α_{R}  FORM (First Order Reliability Method) sensitivity factor for resistance 
β  reliability index 
θ  model uncertainty 
μ_{X}  mean value of X 91 
σ_{X}  standard deviation of X 
V_{X}  coefficient of variation of X 
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.
NOTE For most of the partial factors and the ψ factors proposed in the currently available Eurocodes this is the leading Principle.
NOTE 1 Full probabilistic methods (Level III) give in principle correct answers to the reliability problem as stated. Level III methods are seldom used in the calibration of design codes because of the frequent lack of statistical data.
NOTE 2 The level II methods make use of certain well defined approximations and lead to results which for most structural applications can be considered sufficiently accurate.
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.
NOTE An example of an equivalent method is design assisted by testing (see annex D).
Figure C1 – Overview of reliability methods
P_{f} = Φ(–β) (C.1)
where Φ is the cumulative distribution function of the standardised Normal distribution. The relation between Φ and β is given in Table C1.
P_{f}  10^{1}  10^{2}  10^{3}  10^{4}  10^{5}  10^{6}  10^{7} 
β  1,28  2,32  3,09  3,72  4,27  4,75  5,20 
P_{f} = Prob(g ≤ 0) (C.2a)
If R is the resistance and E the effect of actions, the performance function g is :
g = R – E (C.2b)
with R, E and g random variables.
where :
μ_{g}  is the mean value of g, and 
σ_{g}  is its standard deviation, 
so that:
μ_{g} – βσ_{g} = 0 (C.2d)
and
P_{f} = Prob(g ≤ 0) = Prob(g ≤ μ_{g} – βσ_{g}) (C.2e)
For other distributions of g, β is only a conventional measure of the reliability P_{s} = (l – P_{f}).
NOTE 1 For these evaluations of β
NOTE 2 When the main uncertainty comes from actions that have statistically independent maxima in each year, the values of β for a different reference period can be calculated using the following expression :
Φ(β_{n}) = [Φ(β_{1})]^{n} (C.3)
where :
β_{n}  is the reliability index for a reference period of n years, 
β_{1}  is the reliability index for one year. 
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 
^{1)} See Annex B ^{2)} Depends on degree of inspectability, reparability and damage tolerance. 
E_{d} < R_{d} (C.4)
where the subscript ‘d’ refers to design values. This is the practical way to ensure that the reliability index β is equal to or larger than the target value.
E_{d} and R_{d} can be expressed in partly symbolic form as :
E_{d} = E{F_{d1}, F_{d2}, … a_{d1}, a_{d2}, … θ_{d1}, θ_{d2}, …} (C.5a)
R_{d} = R{X_{d1}, X_{d2}, … a_{d1}, a_{d2}, … θ_{d1}, θ_{d2}, …} (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 ; 
θ  is a model uncertainty. 
For particular limit states (e.g. fatigue) a more general formulation may be necessary to express a limit state.
95Figure C2 – Design point and reliability index β according to the first order reliability method (FORM) for Normally distributed
P(E > E_{d}) = Φ(+α_{E}β) (C.6a)
P(R ≤ R_{d}) = Φ(α_{R}β) (C.6b)
where :
β is the target reliability index (see C6).
α_{E} and α_{R}, with α ≤ 1, are the values of the FORM sensitivity factors. The value of α is negative for unfavourable actions and action effects, and positive for resistances.
α_{E} and α_{R} may be taken as – 0,7 and 0,8, respectively, provided
0,16 < σ_{E}/σ_{R} < 7,6 (C.7)
where σ_{E} and σ_{R} are the standard deviations of the action effect and resistance, respectively, in expressions (C.6a) and (C.6b). This gives :
P(E > E_{d}) = Φ(0,7 β) (C.8a)
P(R ≤ R_{d}) = Φ(0,8 β) (C.8b)
96P(E > E_{d}) = Φ(0,4 × 0,7 × β) = Φ(0,28β) (C.9)
NOTE For β = 3,8 the values defined by expression (C.9) correspond approximately to the 0,90 fractile.
Distribution  Design values 

Normal  μ – αβσ 
Lognormal  μ exp(– αβV) for V = σ/μ < 0,2 
Gumbel 
NOTE In these expressions μ, σ and V are, 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 reference period as for β.
NOTE See also expression (C. 10). 97
Where an upper value for design resistance is used (see 6.3.3), the expression (6.3) takes the form :
X_{d} = η γ_{fM} X_{k,sup} (C.10)
where γ_{fM} is an appropriate factor greater than 1.
NOTE Expression (C.10) may be used for capacity design.
NOTE Non–linear resistance and actions models, and multivariable action or resistance models, are commonly encountered in Eurocodes. In such instances, the above relations become more complex.
Figure C3 – Relation between individual partial factors
Distribution  ψ_{o} = F_{accompanying} / F_{leading} 

General  
Approximation for very large N_{1}  
Normal (approximation)  
Gumbel (approximation)  
F_{s}(.) is the probability distribution function of the extreme value of the accompanying action in the reference period T; Φ(.) is the standard Normal distribution function; T is the reference period ; T_{1} is the greater of the basic periods for actions to be combined; N_{1} is the ratio T/T_{1}, approximated to the nearest integer; β is the reliability index ; V is the coefficient of variation of the accompanying action for the reference period. 
(informative)
In this annex, the following symbols apply.
Latin upper case letters
E(.)  Mean value of (.) 
V  Coefficient of variation [V = (standard deviation) / (mean value)] 
V_{x}  Coefficient of variation of X 
v_{δ}  Estimator for the coefficient of variation of the error term δ 
X  Array of j basic variables X_{1} ... X_{j} 
X_{k(n)}  Characteristic value, including statistical uncertainty for a sample of size n with any conversion factor excluded 
X_{m}  Array of mean values of the basic variables 
X_{n}  Array of nominal values of the basic variables 
Latin lower case letters
b  Correction factor 
b_{i}  Correction factor for test specimen i 
g_{rt}(X)  Resistance function (of the basic variables X) used as the design model 
k_{d,n}  Design fractile factor 
k_{n}  Characteristic fractile factor 
m_{X}  Mean of the n sample results 
n  Number of experiments or numerical test results 
r  Resistance value 
r_{d}  Design value of the resistance 
r_{e}  Experimental resistance value 
r_{ee}  Extreme (maximum or minimum) value of the experimental resistance [i.e. value of r_{e} that deviates most from the mean value r_{em}] 
r_{ei}  Experimental resistance for specimen i 
r_{em}  Mean value of the experimental resistance 
r_{k}  Characteristic value of the resistance 
r_{m}  Resistance value calculated using the mean values X_{m} of the basic variables 
r_{n}  Nominal value of the resistance 
r_{t}  Theoretical resistance determined from the resistance function g_{rt}(X) 101 
r_{ti}  Theoretical resistance determined using the measured parameters X for specimen i 
s  Estimated value of the standard deviation σ 
sΔ  Estimated value of σ_{Δ} 
s_{δ}  Estimated value of σ_{δ} 
Greek upper case letters
Φ  Cumulative distribution function of the standardised Normal distribution 
Δ  Logarithm of the error term δ [Δ_{i} = ln(δ_{i})] 
Estimated value for E(Δ) 
Greek lower case letters
α_{E}  FORM (First Order Reliability Method) sensitivity factor for effects of actions 
α_{R}  FORM (First Order Reliability Method) sensitivity factor for resistance 
β  Reliability index 
γ_{M}*  Corrected partial factor for resistances [γ_{M}* = r_{n}/r_{d} so γ_{M}* = k_{c} γ_{M}] 
δ  Error term 
δ_{i}  Observed error term for test specimen i obtained from a comparison of the experimental resistance r_{ei} and the mean value corrected theoretical resistance br_{ti} 
η_{d}  Design value of the possible conversion factor (so far as is not included in partial factor for resistance γ_{M}) 
η_{k}  Reduction factor applicable in the case of prior knowledge 
σ  Standard deviation 
σ_{Δ}^{2}  Variance of the term Δ 
NOTE Special techniques might be needed in order to evaluate type (c) test results.
Objectives and scope : The objective of the tests should be clearly stated, e.g. the required 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 effects) should be specified.
Prediction of test results : All properties and circumstances that can influence the prediction of test results should be taken into account, including :
The expected modes of failure and/or calculation models, together with the corresponding 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 accompanying pilot tests.
NOTE Attention needs to be given to the fact that a structural member can possess a number of fundamentally 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 :
The objective of the sampling procedure should be to obtain a statistically representative 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 :
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 account 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 representative 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 individual test specimen should be listed. Additionally a list should be made :
104Evaluation and reporting the test : For specific guidance, see D5 to D8. Any Standards on which the tests are based should be reported.
NOTE In general method a) is to be preferred provided the value of the partial factor is detennined from the normal design procedure (see (3) below).
then the calculation model should take such influences into account as appropriate.
NOTE Further information may be found in D6, D7 and D8.
NOTE At the level of interpretation of tests results, three main categories can be distinguished :
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.
106NOTE Adopting a lognormal 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 “V_{X} known” together with a conservative upper estimate of V_{X}, rather than to apply the rules given for the case “V_{X} unknown”. Moreover V_{X}, when unknown, should be assumed to be not smaller than 0,10.
where :
η_{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 k_{n} can be found from Table Dl.
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)).
V_{X} = s_{X} / m_{X} (D.3)
n  1  2  3  4  5  6  8  10  20  30  ∞ 
V_{X} known  2,31  2,01  1,89  1,83  1,80  1,77  1,74  1,72  1,68  1,67  1,64 
V_{X} 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 lognormal distribution expression (D.1) becomes :
where :
If V_{X} is known from prior knowledge,
If V_{X} is unknown from prior knowledge,
In this case, η_{d} should cover all uncertainties not covered by the tests.
n  1  2  3  4  5  6  8  10  20  30  ∞ 
V_{X} known  4,36  3,77  3,56  3,44  3,37  3,33  3,27  3,23  3,16  3,13  3,04 
V_{X} unknown        11,40  7,85  6,36  5,07  4,51  3,64  3,44  3,04 
NOTE 1 This table is based on the assumption that the design value corresponds to a product α_{R}β = 0,8×3,8 = 3,04 (see annex C) and that X is Normally distributed. This gives a probability of observing a lower value of about 0,1 %.
NOTE 2 With a lognormal distribution, expression (D.4) becomes :
X_{d} = η_{d} exp[m_{y} – k_{d,n}s_{y}]
These methods are presented as a number of discrete steps and some assumptions regarding the test population are made and explained ; these assumptions are to be considered to be no more than recommendations covering some of the commoner cases.
NOTE Adopting a lognormal distribution for a variable has the advantage that no negative values can occur.
Step 1 : Develop a design model
r_{t} = g_{rt}(X) (D.5)
Step 2 : Compare experimental and theoretical values
Figure Dl – r_{e} – r_{t} diagram
Step 3 : Estimate the mean value correction factor b
r = b r_{t}δ (D.6)
where :
b is the “Least Squares” bestfit to the slope, given by
Step 4 : Estimate the coefficient of variation of the errors
Δ_{i} = ln (δ _{i}) (D.10)
Step 5 : Analyse compatibility
NOTE The purpose is to improve the resistance function per subset by analysing each subset using the standard procedure. The disadvantage of splitting the test results into subsets is that the number of test results in each subset can become very small.
NOTE Attention is drawn to the fact that the frequency distribution for resistance can be better described by a bimodal or a multimodal function. Special approximation techniques can be used to transform these functions into a unimodal distribution.
Step 6 : Determine the coefficients of variation V_{Xi} of the basic variables
Step 7 : Determine the characteristic value r_{k} of the resistance
the mean value E(r) may be obtained from :
and the coefficient of variation V_{r} may be obtained from the product function :
with :
112the mean value E(r) may be obtained from :
and the coefficient of variation V_{rt} may be obtained from :
with :
where :
k_{n}  is the characteristic fractile factor from table Dl for the case V_{X} unknown ; 
k_{∞}  is the value of k_{n} for n → ∞ [k∞ = 1,64]; 
α_{rt}  is the weighting factor for Q_{rt} 
α_{δ}  is the weighting factor for Q_{δ} 
NOTE The value of V_{δ} is to be estimated from the test sample under consideration.
where :
k_{d,n}  is the design fractile factor from table D2 for the case “V_{X} unknown”; 
k_{d,∞}  is the value of k_{d,n} for n → ∞ [k_{d,∞} = 3,04]. 
NOTE The value of V_{δ} is to be estimated from the test sample under consideration.
r_{k} = η_{k} r_{e} (D.23)
where :
η_{k}  is a reduction factor applicable in the case of prior knowledge that may be obtained from : 
where :
V_{r}  is the maximum coefficient of variation observed in previous tests. 
r_{k} = η_{k} r_{em} (D.25)
where :
η_{k}  is a reduction factor applicable in the case of prior knowledge that may be obtained from: 
where :
V_{r}  is the maximum coefficient of variation observed in previous tests. 
provided that each extreme (maximum or minimum) value r_{ee} satisfies the condition:
Coefficient of variation V_{r} 
Reduction factor η_{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 
ISO 2394  General principles on reliability for structures 
ISO 2631:1997  Mechanical vibration and shock – Evaluation of human exposure to wholebody vibration 
ISO 3898  Basis for design of structures – Notations – General symbols 
ISO 67071  Building and civil engineering – Vocabulary – Part 1 : General terms 
ISO 8930  General principles on reliability for structures – List of equivalent 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 