DRAFT FOR DEVELOPMENT
Eurocode 1: Basis of design and actions on structures Part 1: Basis of design (together with United Kingdom National Application Document)
ICS 91.040
DD ENV 1991-1:1996
DD ENV 1991-1:1996
Committees responsible for this Draft for Development The preparation of this National Application Document for use in the UK with ENV 1991-1:1996 was entrusted by Technical Committee B/525, Building and civil engineering structures, to Subcommittee B/525/1, Actions (loadings) and basis of design, upon which the f ollowing bodies were represented: British Constructional Steelwork Association British Iron and Steel Producers’ Association British Masonry Society Concrete Society Department of the Environment (Building Research Establishment) Department of the Environment (Property and Buildings Directorate) Highways Agency Institution of Structural Engineers National House Building Council Royal Institute of British Architects Steel Construction Institute
This Draft for Development, having been prepared under the direction of the Sector Board for Building and Civil Engineering, was published under the authority of the Standards Board and comes into effect on 15 September 1996 © BSI 04-2000
The following BSI reference relates to the work on this Draft for Development: Committee reference B/525/1
ISBN 0 580 25895 5
Amendments issued since publication Amd. No.
Date
Comments
DD ENV 1991-1:1996
Committees responsible for this Draft for Development The preparation of this National Application Document for use in the UK with ENV 1991-1:1996 was entrusted by Technical Committee B/525, Building and civil engineering structures, to Subcommittee B/525/1, Actions (loadings) and basis of design, upon which the f ollowing bodies were represented: British Constructional Steelwork Association British Iron and Steel Producers’ Association British Masonry Society Concrete Society Department of the Environment (Building Research Establishment) Department of the Environment (Property and Buildings Directorate) Highways Agency Institution of Structural Engineers National House Building Council Royal Institute of British Architects Steel Construction Institute
This Draft for Development, having been prepared under the direction of the Sector Board for Building and Civil Engineering, was published under the authority of the Standards Board and comes into effect on 15 September 1996 © BSI 04-2000
The following BSI reference relates to the work on this Draft for Development: Committee reference B/525/1
ISBN 0 580 25895 5
Amendments issued since publication Amd. No.
Date
Comments
DD ENV 1991-1:1996
Contents Committees responsible National foreword Text of National Application Document Foreword Text of ENV 1991-1
© BSI 04-2000
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DD ENV 1991-1:1996
National foreword This publication has been prepared by Subcommittee B/525/1. It comprises the English language version of ENV 1991-1:1994 Eurocode 1: Basis of design and actions on structures Part 1: Basis of design , as published by the European Committee for Standardization (CEN), together with the corresponding National Application Document (NAD). The NAD has been prepared for use in the design of buildings and civil engineering works to be constructed in the United Kingdom. ENV 1991-1 results from a programme of work sponsored by the European Commission to make available a common set of rules for the structural and geotechnical design of buildings and civil engineering works. The full range of codes covers the basis of design and actions, the design of structures in concrete, steel, composite construction, aluminium alloy, timber and masonry and also geotechnical and seismic design. An ENV, or European Prestandard, is made available for provisional application, but does not have the status of a European Standard. The aim is to use the experience gained to modify the ENV so that it can be adopted as a European Standard. The values of certain parameters in the ENV Eurocodes may be set by CEN Members so as to meet requirements in national regulations. The numerical values of these parameters in the ENV are indicated as “boxed” or by [ ]. During the ENV period, reference should be made to the supporting documents listed in the National Application Documents (NADs). Generally, the purpose of the NADs in DD ENV Eurocodes is to provide essential information, particularly in relation to safety, to enable the corresponding ENVs to be used for the design of buildings and civil engineering works to be constructed in the UK. The requirements of the NADs take precedence in the UK over the corresponding provisions in the ENVs. However, the purpose of the NAD to Eurocode 1: Part 1 is somewhat different, as discussed in the text below. There is no equivalent British design code to DD ENV 1991-1. Unlike other design codes for various structural materials which contain detailed recommendations for design, ENV 1991-1 contains only general structural criteria which are material independent. However, the “Basis of design” sections of ENV 1992 to ENV 1996 contain material common to ENV 1991-1; these Eurocodes (ENV 1992 to ENV 1996) with their UK NADs contain sufficient information to enable designs to be effected without recourse to ENV 1991-1. ENV 1997-1 Geotechnical design does require recourse to ENV 1991-1, but only for the definition of some terms and symbols, and not for quantitative values. This situation will change when the ENV Eurocode Prestandards are converted into full EN Eurocode Standards. Material currently in ENV 1992 to ENV 1997 which is also covered by ENV 1991- 1 will then be removed and the corresponding relevant provisions of ENV 1991-1 will apply. One implication is that the same partial factors for loads and the same load combination factors will apply to all structural materials, which is not currently the case. Numerical values of coefficients in the UK NADs to ENV 1992 to ENV 1997 have been calibrated to give an acceptable degree of conformity to current British Standards. By contrast, the coefficients given in the UK NAD to ENV 1991-1 are not always in accordance with current British Standards, nor with the UK NADs to ENV 1992 to ENV 1997, although this is not expected to result in other than minor differences in most circumstances. The differences between the loading codes referred to in DD ENV 1991-1 and those referred to in DD ENV 1992 to DD ENV 1997 may result in more significant differences. Where differences remain, the “Basis of design” sections of ENV 1992 to ENV 1997 (as modified by the applicable UK NAD) should take precedence over DD ENV 1991-1 during the ENV trial application stage.
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This NAD also provides clarification to certain clauses which were considered ambiguous; these clarifications are not intended to change the original intention of the drafters of ENV 1991-1. The main reasons for publishing the UK NAD to Eurocode 1: Part 1 a re as follows. a) For essentially informative purposes, to enable s tructural designers in the UK to familiarize themselves with the contents of ENV 1991-1, which, as referred to above, has no existing equivalent British Standard. b) Following from a), to enable UK comments on ENV Eurocode 1: Part 1 to be obtained during its ENV period, so that these can be considered during the conversion to an EN. c) To provide information in cases where the “Basis of design” sections of DD ENV 1992 to DD ENV 1997 require amplification, for example under unusual circumstances not adequately covered by those Eurocodes. d) To provide definitions for certain terms and symbols used in DD ENV 1997-1. e) To enable comparative designs to be performed which compare the approach of ENV 1991-1 with those of DD ENV Eurocodes predating ENV 1991-1.
Compliance with DD ENV 1991-1:1996 does not of itself confer immunity from legal obligations. For consideration of the conversion of ENV 1991-1 into a full European Standard, it is important to get as much feedback as possible from practising engineers. Such feedback is therefore strongly encouraged, and users of this document are invited to comment on its technical content, ease of use and any ambiguities or anomalies. These comments will be taken into account when preparing the UK national response to CEN on the question of whether the ENV can be converted into an EN. Comments should be made in writing to the Secretary of Subcommittee B/525/1, BSI, 389 Chiswick High Road, London W4 4AL, quoting this document, the reference to the relevant clause and, if possible, a proposed revision.
Summary of pages This document comprises a front cover, an inside front cover, pages i to x, the ENV title page, pages 2 to 52 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. © BSI 04-2000
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DD ENV 1991-1:1996
National Application Document for use in the UK with ENV 1991-1:1994
© BSI 04-2000
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DD ENV 1991-1:1996
Contents of National Application Document Introduction 1 Scope 2 Informative references 3 Partial load factors, combination factors and other values 4 Loading codes 5 Reference standards 6 Additional recommendations Table 1 Table and equation substitutions Table 2.1 Notional classification of design working life List of references
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DD ENV 1991-1:1996
Introduction
4 Loading codes
This National Application Document (NAD) has been prepared by Subcommittee B/525/1. It has been developed from:
Where punished, the UK national implementation of the appropriate Part of Eurocode 1 (e.g. DD ENV 1991-2-3) should be used for applications within the scope specified. Where such DD ENVs are not available, the appropriate equivalent standards listed in the NADs to DD ENV 1992 to DD ENV 1997 should be adopted.
a) a textual examination of ENV 1991-1; b) a comparison with the material independent sections of the following DD ENV Eurocodes. DD ENV 1992-1-1:1992
5 Reference standards
DD ENV 1993-1-1:1992 DD ENV 1994-1-1:1994 DD ENV 1995-1-1:1995
Standard referred to in ENV 1991-1
Equivalent standard to be used in the UK
DD ENV 1996-1-1:1995
ISO 2631
ISO 2631
DD ENV 1997-1:1995
ISO 8930:1987
ISO 8930:1987
ISO 6707-1:1989
ISO 6707-1:1989
ISO 3898:1987
ISO 3898:1987
ENV Eurocode Prestandard
Equivalent DD ENV (see also clause 4 above)
1 Scope This National Application Document is issued to enable the use of ENV 1991-1 in the circumstances discussed in the national foreword, for conditions pertinent to the UK.
2 Informative references
6 Additional recommendations 6.1 Sub-clause 1.5 Definitions
This National Application Document refers to other publications that provide information or guidance. Editions of these publications current at the time of issue of this standard are listed on page ix, but reference should be made to the latest editions.
a) 1.5.4.3 A new definition should be added:
3 Partial load factors, combination factors and other values
b) 1.5.5.2 A new note should be added:
The tables and equations of ENV 1991-1:1994 listed below should be replaced with tables and equations in this NAD, as is shown in Table 1. In all other cases, the “boxed” values (see item 25 of the foreword to ENV 1991-1:1994) should be used.
Table 1 Table and equation substitutions ENV 1991-1
This NAD
Table 2.1: Design working life classification
Table 1: Notional classification of design working life
Equation 9.10a and 9.10b: special combination rules for ultimate limit state
Equation 9.10a and 9.10b should not be used, pending calibration work
© BSI 04-2000
“nominal value of a material property: a characteristic value established from an appropriate document such as a European Standard or Prestandard.” “NOTE The design value of a geometrical property is generally equal to the characteristic value. However, it may differ 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 on a statistical basis, with a value corresponding to a more extreme fractile (i.e. a rarer value) than applies to the characteristic value.”
6.2 Clause 8. Design by testing a) 8.1 A new paragraph should be added “(5) This section includes for fatigue within its scope.”. b) 8.3 The final paragraph of (2) should be replaced with: “The field of application of the partial factor used in method a) should be similar to the tests under consideration.”.
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6.3 Clause 9. Verification by the partial factor method a) 9.3.2 A new note should be added to (2) as follows: *Sd for the NOTE Information on appropriate values of analysis of bridges is given in BS 5400-1.”.
b) (3)b) The phrase: “the partial factor is applied” should be replaced by the phrase: “the partial factor *F is applied.”.
d) 9.4.3 The second sentence of (2)P should be replaced by the following: NOTE Examples of where this may apply are as follows. i) When considering Case A of Table 2 for the static equilibrium of balanced cantilevers. ii) When considering Case B of Table 2 for the bending strength needed within a span of a multispan beam which has adjacent span lengths that differ greatly.”
6.4 Annex A to Annex D (informative)
c) 9.4.2 In (3)a) equations (9.10a) and (9.10b) should not be used, pending calibration work.
Annex A to Annex D need further development work before they can be considered adequately validated for design purposes.
In (6) a note should be added at the end of the paragraph:
6.5 Table 2.1
“NOTE For example, in the design of a section subject to both bending moment and axial force due to a single action, the axial force may be reduced by 20 % if it is a favourable action effect.”.
Table 2.1 should be replaced by the one listed below.
Table 2.1 Notional classification of design working life Class
Notional design working life (years)
Examples
1
1–5
2
25
Replaceable structural parts, e.g. gantry girders, bearings
3
50
Buildings and other common structures, other than those listed below
4
100
Monumental buildings, and other special or important structures
5
120
Bridges
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Temporary structures
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List of references (see clause 2) Informative reference BSI standards publication BRITISH STANDARDS INSTITUTION, London
BS 5400, Steel, concrete and composite bridges. BS 5400-1:1988, General statement.
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EUROPEAN PRESTANDARD
ENV 1991-1
PRÉNORME EUROPÉENNE September 1994
EUROPÄISCHE VORNORM
ICS 91.040.00
Descriptors: Buildings, civil engineering, structures, building codes, design, safety, reliability, mechanical strength, verification
English version
Eurocode 1 Basis of design and actions on structures Part 1: Basis of design
Eurocode 1 Bases du calcul et actions sur les structures Partie 1: Bases du calcul
Eurocode 1 Grundlagen der Tragwerksplanung und Einwirkungen auf Tragwerke Teil 1: Grundlagen der Tragwerksplanung
This European Prestandard (ENV) was approved by CEN on 1993-05-28 as a prospective standard for provisional application. The period of validity of this ENV is limited initially to three years. After two years the members of CEN will be requested to submit their comments, particularly on the question of whether the ENV can be converted into a European Standard (EN). CEN members are required to announce the existence of this ENV in the same way as for an EN and to make the ENV available promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the ENV) until the final decision about the possible conversion of the ENV into an EN is reached. CEN members are the national standards bodies of Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.
CEN European Committee for Standardization Comité Européen de Normalisation ür Normung Europäisches Komitee f
Central Secretariat: rue de Stassart 36, B-1050 Brussels © 1994 Copyright reserved to CEN members Ref. No. ENV 1991-1:1994 E
ENV 1991-1:1994
Foreword Objectives of the Eurocodes (1) The Structural Eurocodes comprise a group of standards for the structural and geotechnical design of buildings and civil engineering works. (2) They cover execution and control only to the extent that is necessary to indicate the quality of the construction products, and the standard of the workmanship, needed to comply with the assumptions of the design rules. (3) Until the necessary set of harmonized technical specifications for products and for methods of testing their performance are available, some of the Structural Eurocodes cover some of these aspects in informative annexes.
(8) Separate subcommittees have been formed by CEN/TC 250 for the various Eurocodes listed above. (9) This Part of ENV 1991 is intended to develop for a broader field of application the rules already published in sections 1 and 2 of Parts 1.1 of ENVs 1992, 1993 and 1994. It is being published as European Prestandard ENV 1991-1. (10) This prestandard is intended for experimental application and for the submission of comments. (11) After approximately two years CEN members will be invited to submit formal comments to be taken into account in determining future actions. (12) Meanwhile feedback and comments on this prestandard should be sent to the secretariat of CEN/TC 250 at the following address:
Background to the Eurocode Programme
BSI
(4) The Commission of the European Communities (CEC) initiated the work of establishing a set of harmonized technical rules for the design of building and civil engineering works which would initially serve as an alternative to the different rules in force in the various member states and would ultimately replace them. These technical rules became known as the Structural Eurocodes.
British Standards House
(5) In 1990, after consulting their respective member states, the CEC transferred the work of further development, issue and updating of the Structural Eurocodes to CEN, and the EFTA secretariat agreed to support the CEN work. (6) CEN Technical Committee CEN/TC 250 is responsible for all Structural Eurocodes.
Eurocode Programme (7) Work is in hand on the following Structural Eurocodes, each generally consisting of a number of parts:
389 Chiswick High Road London W4 England or to your national standards organization.
Purpose of this Part of Eurocode 1 Technical objectives (13) This Part of Eurocode 1 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. Regarding modifications of the proposed method, see (24) of the foreword. (14) For the design of new structures, this Part is intended to be used, for direct application, together with: the other Parts of ENV 1991; the design Eurocodes (ENVs 1992 to 1999).
EN 1991, Eurocode 1: Basis of design and actions on structures.
NOTE The above mentioned European Prestandards are either published or in preparation.
EN 1992, Eurocode 2: Design of concrete structures.
(15) This Part also gives guidelines for the aspects of structural reliability relating to safety, serviceability and durability:
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.
for design cases not covered by ENVs 1991 to 1999 (other actions, structures not treated, other materials); to serve as a reference document for other CEN TC’s concerned with structural aspects. (16) It is intended that the material-independent clauses in section 2 of the design Eurocodes will be superseded by this Part of ENV 1991 at a future stage (EN stage).
EN 1999, Eurocode 9: Design of aluminium alloy structures.
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ENV 1991-1:1994
Intended users (17) This prestandard is intended for the consideration of more categories of users, than are the other Eurocodes. The categories include: code drafting committees; clients (e.g. for the formulation of their specific requirements on reliability level and durability); designers and contractors, as for other Eurocodes;
The National Application Documents are intended to authorize experimental use of the Eurocodes as prestandards for design during the ENV period, with due consideration for the current regulations and codes relevant in individual countries, and to facilitate these uses. The NADs may also introduce modifications of the partial factor method in this prestandard. Establishing the NAD is the responsibility of the national competent authorities.
In particular each NAD may specify whether the public authorities. annexes can be used fully or partly in connection with the main text and what are then the specific Intended uses conditions for their application, e.g. the application (18) This prestandard is intended for the design of of 3.4(3), and of 8.3(1) together with Annex A. structures within the scope of the Eurocodes. (25) In particular, for this prestandard attention (19) As a guidance document, for the design of should be paid to: structures outside the scope of the Eurocodes, this confirming or amending the numerical values prestandard may be used when relevant for: identified as “boxed” or by [ ]; it is recommended assessing other actions and their that modifications are introduced only where combinations; considered to be necessary; however, for those modelling material and structural behaviour; countries in which reliability differentiation assessing numerical values of the reliability measures are already codified there is no format. objection to numerical amendments intended to supplement this Eurocode by such operational (20) Numerical values for safety factors and other measures; safety elements are given as indications. Together with the material-dependent indicative values given in the design Eurocodes, they provide an acceptable degree of reliability, assuming that an appropriate level of workmanship and of quality assurance is achieved. Therefore, if this Part is used as a reference document by other CEN/TCs the same indicative values should be taken.
Division into main text and annexes (21) Because of the various categories of use mentioned above, this Part is divided into a main text and a series of annexes. This division also takes into account the development expected during the ENV period. (22) The main text includes most of the principal and operational rules necessary for direct application for designs in the field covered by ENV 1991, and ENVs 1992 to 1999. The principal provisions for bridges are also included. (23) The annexes are informative only. Other background information and items for further development during the ENV period may be published separately in a CEN report.
National Application Documents (NADs)
considering the variety of intended users and uses of this prestandard [see (17) above], with regard to the existing national professional organizations and the respective responsibilities of each category of user.
Intended future developments of this Part (26) The objective of this Part is to ensure the consistency of design rules for a wide set of construction works made of various materials. It should be understood that this is a long-term objective which will be reached progressively. At the present stage the objective is limited to: ensuring the consistency between the Eurocodes already published or in preparation, without contradicting them; covering the structures treated in the same Eurocodes in less detail for those for which Parts of Eurocodes are in preparation, e.g. for bridges, silos, etc. Therefore it should be understood that by publication of the present version of this Part it is not intended to inhibit the work of development and improvement of the reliability format.
(24) It is intended that, during the ENV period, this prestandard is used for design purposes, in conjunction with the particular National Application Document valid in the country where the designed structures are to be located.
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ENV 1991-1:1994
In parallel with the publication of new Parts of Eurocodes during the ENV period, it is envisaged that some developments may be made to some items, e.g:
Page
more precise definition of differentiated reliability levels; numerical revision, probabilistic justification of numerical values of partial factors and possibly supplementing this method with a probabilistic approach;
4
Actions and environmental influences
4.1
Principal classifications
20
4.2
Characteristic values of actions
20
4.3
Other representative values of variable and accidental actions
21
4.4
Environmental influences
22
5
Material Properties
6
Geometrical data
more precise consideration of various types of 7 limit state equations, soil-structure interaction, non-linear analysis, dynamic actions and the 7.1 associated analysis and reliability verification 7.2 format; 7.3 assessment and re-design of existing structures. 7.4
Contents Foreword
Modelling for structural analysis and resistance General
25
Modelling in the case of static actions
25
Modelling in the case of dynamic actions
25
Modelling for fire actions
25
8
Design assisted by testing
Page
8.1
General
26
2
8.2
Types of tests
26
8.3
Derivation of design values
26
9
Verification by the partial factor method
9.1
Introduction
28
9.2
Limitations and simplifications
28
1
General
1.1
Scope
7
1.2
Normative references
7
1.3
Assumptions
8
1.4
Distinction between principles and application rules
8
9.3
Design values
28
1.5
Definitions
8
9.3.1
Design values of actions
28
1.5.1
Common terms used in the Structural Eurocodes (ENVs 1991-1999)
9.3.2
Design values of the effects of actions
29
8
9.3.3
Design values of material properties
29
Special terms relating to design in general
9.3.4
Design values of geometric data
29
9
9.3.5
Design resistance
30
1.5.2 1.5.3
Terms relating to actions
10
9.4
Ultimate limit states
30
1.5.4
Terms relating to material properties
12
9.4.1
1.5.5
Terms relating to geometric data
12
Verification of static equilibrium and strength
30
1.6
Symbols
13
9.4.2
Combination of actions
31
2
Requirements
9.4.3
Partial factors
32
2.1
Fundamental requirements
15
9.4.4
? factors
34
2.2
Reliability differentiation
15
9.4.5
2.3
Design situations
16
Simplified verification for building structures
34
2.4
Design working life
16
9.4.6
Partial safety factors for materials
34
2.5
Durability
16
9.5
Serviceability limit states
34
2.6
Quality assurance
17
9.5.1
Verifications of serviceability
34
3
Limit states
9.5.2
Combination of actions
35
3.1
General
18
9.5.3
Partial factors
35
3.2
Ultimate limit states
18
9.5.4
? factors
35
3.3
Serviceability limit states
18
9.5.5
3.4
Limit state design
18
Simplified verification for building structures
35
Partial factors for materials
36
4
9.5.6
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Page Annex A (informative) Partial factor design
37
Annex B (informative) Fatigue
43
Annex C (informative) Serviceability limit state: verification of structures susceptible to vibrations
44
Annex D (informative) Design assisted by testing
46
Figure A.1 Overview of reliability methods
38
Figure A.2 Design point definition according to first order reliability methods (FORM)
40
Table 2.1 Design working life classification
16
Table 9.1 Design values of actions for use in the combination of actions
31
Table 9.2 Partial factors: ultimate limit states for buildings
33
? factors for buildings Table 9.3
34
Table 9.4 Design values of actions for use in the combination of actions
35
Table A.1 Relation between " and P 1
38
Table A.2 Indicative values for the target reliability index ".
39
Table A.3 Design values for various distribution functions
40
Table A.4 Expression for ?o
42
kn for the 5 % Table D.1 Values of characteristic value
49
kn for the ULS Table D.2 Values of design value, if is dominating X (P {X < X } = 0,1 %) d
50
kn for the ULS Table D.3 Values of X design value, if is non-dominating (P {X < X } = 10 %) d
50
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ENV 1991-1:1994
Section 1. General 1.1 Scope (1) This Part 1 of ENV 1991 establishes the principles and requirements for safety and serviceability of structures, describes the basis for design and verification and gives guidelines for related aspects of structural reliability. (2)P Part 1 of ENV 1991 provides the basis and general principles for the structural design of buildings and civil engineering works including geotechnical aspects and shall be used in conjunction with the other parts of ENV 1991 and ENVs 1992 to 1999. Part 1 relates to all circumstances in which a structure is required to give adequate performance, including fire and seismic events. (3) Part 1 of ENV 1991 may also be used as a basis for the design of structures not covered in ENVs 1992 to 1999 and where other materials or other actions outside the scope of ENV 1991 are involved. (4)P Part 1 of ENV 1991 is also applicable to structural design for the execution stage and structural design for temporary structures, provided that appropriate adjustments outside the scope of ENV 1991 are made. (5) Part 1 of ENV 1991 also gives some simplified methods of verification which are applicable to buildings and other common construction works. (6) Design procedures and data relevant to the design of bridges and other construction works which are not completely covered in this Part may be obtained from other Parts of Eurocode 1 and other relevant Eurocodes. (7) Part 1 of ENV 1991 is not directly intended for the structural appraisal of existing construction in developing the design of repairs and alterations or assessing changes of use but may be so used where applicable. (8) Part 1 of ENV 1991 does not completely cover the design of special construction works which require unusual reliability considerations, such as nuclear structures, for which specific design procedures should be used. (9) Part 1 of ENV 1991 does not completely cover the design of structures where deformations modify direct actions.
1.2 Normative references This European Prestandard incorporates by dated or undated reference, provisions from other standards. These normative references are cited at the appropriate places in the text and publications listed hereafter. ISO 2631, Evaluation of human exposure to whole-body vibration. ISO 8930:1987, General principles on reliability for structures List of equivalent terms. ISO 6707-1:1989, Building /civil engineering Vocabulary Part 1: General terms. ISO 3898:1987, Basis of design for structures Notations General symbols. NOTE The following European Prestandard which are published or in preparation are cited at the appropriate places in the text and publications listed hereafter. ENV 1991-1, Eurocode 1: Basis of design and actions on structures Part 1: Basis of design . ENV 1991-2-1, Eurocode 1: Basis of design and actions on structures Part 2.1: Densities, self-weight and imposed loads . ENV 1991-2-2, Eurocode 1: Basis of design and actions on structures Part 2.2: Actions on structures exposed to fire . ENV 1991-2-3, Eurocode 1: Basis of design and actions on structures Part 2.3: Snow loads . ENV 1991-2-4, Eurocode 1: Basis of design and actions on structures Part 2.4: Wind loads . ENV 1991-2-5, Eurocode 1: Basis of design and actions on structures Part 2.5: Thermal actions . ENV 1991-2-6, Eurocode 1: Basis of design and actions on structures Loads and deformations imposed during execution . ENV 1991-2-7, Eurocode 1: Basis of design and actions on structures Part 2.7: Accidental actions . ENV 1991-3, Eurocode 1: Basis of design and actions on structures Part 3: Traffic loads on bridges . ENV 1991-4, Eurocode 1: Basis of design and actions on structures Part 4: Actions in silos and tanks . ENV 1991-5, Eurocode 1: Basis of design and actions on structures Part 5: Actions induced by cranes and machinery . ENV 1992, Eurocode 2: Design of concrete structures. ENV 1993, Eurocode 3: Design of steel structures. ENV 1994, Eurocode 4: Design of composite steel and concrete structures. ENV 1995, Eurocode 5: Design of timber structures. ENV 1996, Eurocode 6: Design of masonry structures. ENV 1997, Eurocode 7: Geotechnical design. ENV 1998, Eurocode 8: Earthquake resistant design of structures. ENV 1999, Eurocode 9: Design of aluminium alloy structures.
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1.3 Assumptions The following assumptions apply: The choice of the structural system and the design of a structure is made by appropriately qualified and experienced personnel. Execution is carried out by personnel having the appropriate skill and experience. Adequate supervision and quality control is provided during execution of the work, i.e. in design offices, factories, plants, and on site. The construction materials and products are used as specified in this Eurocode or in ENVs 1992 to 1999 or in the relevant supporting material or product specifications. The structure will be adequately maintained. The structure will be used in accordance with the design assumptions. Design procedures are valid only when the requirements for the materials, execution and workmanship given in ENVs 1992 to 1996 and 1999 are also complied with.
1.4 Distinction between principles and application rules (1)P Depending on the character of the individual clauses, distinction is made in this Part 1 of ENV 1991 between principles and application rules. (2)P The principles comprise: general statements and definitions for which there is no alternative; requirements and analytical models for which no alternative is permitted unless specifically stated. (3) The principles are identified by the letter P following the paragraph number. (4)P The application rules are generally recognized rules which follow the principles and satisfy their requirements. It is permissible to use alternative rules to the application rules given in this Eurocode, provided that it is shown that the alternative rules accord with the relevant principles and have at least the same reliability. (5) In this Part of ENV 1991 the application rules have only a paragraph number, e.g. as this paragraph.
1.5 Definitions For the purposes of this prestandard, the following definitions apply. NOTE
Most definitions are reproduced from ISO 8930:1987.
1.5.1 Common terms used in the Structural Eurocodes (ENVs 1991 to 1999) 1.5.1.1 construction works everything that is constructed or results from construction operations NOTE This definition accords with ISO 6707-1. The term covers both building and civil engineering works. It refers to the complete construction worlds comprising structural, non-structural and geotechnical elements.
1.5.1.2 type of building or civil engineering works type of construction works designating its intended purpose, e.g. dwelling house, retaining wall, industrial building, road bridge
1.5.1.3 type of construction indication of principal structural material, e.g. reinforced concrete construction, steel construction, timber construction, masonry construction, composite steel and concrete construction
1.5.1.4 method of construction manner in which the execution will be carried out, e.g. cast in place, prefabricated, cantilevered
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1.5.1.5 construction material material used in construction work, e.g. concrete, steel, timber, masonry
1.5.1.6 structure organized combination of connected parts designed to provide some measure of rigidity NOTE ISO 6707-1 gives the same definition but adds “or a construction works having such an arrangement”. In the Structural Eurocodes this addition is not used in order to facilitate unambiguous translation.
1.5.1.7 form of structure the arrangement of structural elements, such as beam, column, arch, foundation piles NOTE
Forms of structure are, for example, frames, suspension bridges.
1.5.1.8 structural system the load-bearing elements of a building or civil engineering works and the way in which these elements function together
1.5.1.9 structural model the idealization of the structural system used for the purposes of analysis and design
1.5.1.10 execution the activity of creating a building or civil engineering works NOTE
The term covers work on site; it may also signify the fabrication of components off site and their subsequent erection on site.
1.5.2 Special terms relating to design in general 1.5.2.1 design criteria the quantitative formulations which describe for each limit state the conditions to be fulfilled
1.5.2.2 design situations those sets of physical conditions representing a certain time interval for which the design will demonstrate that relevant limit states are not exceeded
1.5.2.3 transient design situation design situation which is relevant during a period much shorter than the design working life of the structure and which has a high probability of occurrence NOTE
It refers to temporary conditions of the structure, of use, or exposure, e.g. during construction or repair.
1.5.2.4 persistent design situation design situation which is relevant during a period of the same order as the design working lif e of the structure NOTE
Generally it refers to conditions of normal use.
1.5.2.5 accidental design situation design situation involving exceptional conditions of the structure or its exposure, e.g. fire, explosion, impact or local failure
1.5.2.6 design working life the assumed period for which a structure is to be used for its intended purpose with anticipated maintenance but without substantial repair being necessary
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1.5.2.7 hazard exceptionally unusual and severe event, e.g. an abnormal action or environmental influence, insufficient strength or resistance, or excessive deviation from intended dimensions
1.5.2.8 load arrangement identification of the position, magnitude and direction of a free action
1.5.2.9 load case compatible load arrangements, sets of deformations and imperfections considered simultaneously with fixed variable actions and permanent actions for a particular verification
1.5.2.10 limit states states beyond which the structure no longer satisfies the design performance requirements
1.5.2.11 ultimate limit states states associated with collapse, or with other similar forms of structural failure NOTE
They generally correspond to the maximum load-carrying resistance of a structure or structural part.
1.5.2.12 serviceability limit states States which correspond to conditions beyond which specified service requirements for a structure or structural element are no longer met.
1.5.2.12.1 irreversible serviceability limit states limit states which will remain permanently exceeded when the responsible actions are removed
1.5.2.12.2 reversible serviceability limit states limit states which will not be exceeded when the responsible actions are removed
1.5.2.13 resistance mechanical property of a component, a cross-section, or a number of a structure, e.g. bending resistance, buckling resistance
1.5.2.14 maintenance the total set of activities performed during the working life of the structure to preserve its function
1.5.2.15 strength mechanical property of a material, usually given in units of stress
1.5.2.16 reliability reliability covers safety, serviceability and durability of a structure
1.5.3 Terms relating to actions 1.5.3.1 action a) Force (load) applied to the structure (direct action) b) An imposed or constrained deformation or an imposed acceleration caused for example, by temperature changes, moisture variation, uneven settlement or earthquakes (indirect a ction).
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1.5.3.2 action effect the effect of actions on structural members, e.g. internal force, moment, stress, strain
1.5.3.3 permanent action (G) action which is likely to act throughout a given design situation and for which the variation in magnitude with time is negligible in relation to the mean value, or for which the variation is always in the same direction (monotonic) until the action attains a certain limit value
1.5.3.4 variable action (Q) action which is unlikely to act throughout a given design situation or for which the variation in magnitude with time is neither negligible in relation to the mean value nor monotonic
1.5.3.5 accidental action (A) action, usually of short duration, which is unlikely to occur with a significant magnitude over the period of time under consideration during the design working life NOTE
An accidental action can be expected in many cases to cause severe consequences unless special measures are taken.
1.5.3.6 seismic action (AE) action which arises due to earthquake ground motions
1.5.3.7 fixed action action which has a fixed distribution over the structure such that the magnitude and direction of the action are determined unambiguously for the whole structure if this magnitude and direction are determined at one point on the structure
1.5.3.8 free action action which may have any spatial distribution over the structure within given limits
1.5.3.9 single action action that can be assumed to be statistically independent in time and space of any other action acting on the structure
1.5.3.10 static action action which does not cause significant acceleration of the structure or structural members
1.5.3.11 dynamic action action which causes significant acceleration of the structure or structural members
1.5.3.12 quasi-static action dynamic action that can be described by static models in which the dynamic effects are included
1.5.3.13 representative value of an action value used for the verification of a limit state
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1.5.3.14 characteristic value of an action the principal representative value of an action. In so far as this 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
1.5.3.15 reference period See 1.5.3.14.
1.5.3.16 combination values values associated with the use of combinations of actions (see 1.5.3.20) to take account of a reduced probability of simultaneous occurrence of the most unfavourable values of several independent actions
1.5.3.17 frequent value of a variable action the value determined such that: the total time, within a chosen period of time, during which it is exceeded for a specified part, or the frequency with which it is exceeded, is limited to a given value.
1.5.3.18 quasi-permanent value of a variable action the value determined such that the total time, within a chosen period of time, during which it is exceeded is a considerable part of the chosen period of time
1.5.3.19 design value of an action F d the value obtained by multiplying the representative value by the partial safety factor *F
1.5.3.20 combination of actions set of design values used for the verification of the structural reliability for a limit state under the simultaneous influence of different actions
1.5.4 Terms relating to material properties 1.5.4.1 characteristic value X k the value of a material property having a prescribed probability of not being a ttained 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. A nominal value is used as the characteristic value in some circumstances
1.5.4.2 design value of a material property X d value obtained by dividing the characteristic value by a partial factor *M or, in special circumstances, by direct determination
1.5.5 Terms relating to geometrical data 1.5.5.1 characteristic value of a geometrical property ak the value usually corresponding to the dimensions specified in the design. Where relevant, values of geometrical quantities may correspond to some prescribed fractile of the statistical distribution
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1.5.5.2 design value of a geometrical property ad generally a nominal value. Where relevant, values of geometrical quantities may correspond to some prescribed fractile of the statistical distribution
1.6 Symbols For the purposes of this prestandard, the following symbols apply. NOTE
The notation notation used used is based based on ISO 3898:19 3898:1987 87
Latin upper case letters A Ad
Accidental action Design value of an accidental action
AEd
Design value of seismic action
AEk
Characteristic seismic action
Ak
Characteristic value of an accidental action
C d
Nominal value, or a function of certain design properties of materials
E E d
Effect of an action Design value of effects of actions
E d,dst d,dst
Design effect of destabilizing actions
E d,stb
Design effect of stabilizing actions
F F d
Action Design value of an action
F k
Characteristic value of an action
F rep rep
Representative value of an action
G Gd
Permanent action Design value of a permanent action
Gd,inf
Lower design value of a permanent action
Gid
Characteristic value of permanent action j
Gd,sup
Upper design value of a permanent action
Gind
Indirect permanent action
Gk
Characteristic value of a permanent action
Gk,inf
Lower characteristic value of a permanent action
Gk,sup
Upper characteristic value of a permanent action
P P d
Prestressing action Design value of a prestressing action
P k
Characteristic value of a prestressing action
Q Qd
Variable action Design value of a variable action
Qind
Indirect variable action
Qk
Characteristic value of a single variable action
Qk1
Characteristic value of the dominant variable action
Qid
Characteristic value of the non-dominant variable action i
R Rd
Resistance Design value of the resistance
Rk
Characteristic resistance
X X d
Material property Design value of a material property
X k
Characteristic value of a material property
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Latin lower case letters ad Design value of geometrical data ak
Characteristic dimension
anom
Nominal value of geometrical data
Greek upper case letters %a Change made to nominal geometrical data for particular design purposes, e.g. assessment of effects of imperfections Greek lower case letters Partial factor (safety or serviceability) *
*A *F *G *GA *GAj *G,inf *Gj *G,sup *I *m *M *P *PA *Q *Qi *rd *R *Rd *Sd ) K ?0 ?1 ?2
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Partial factor for accidental actions Partial factor for actions, also accounting for model uncertainties and dimensional variations Partial factor for permanent actions As *G but for accidental design situations As *Gj but for accidental design situations Partial factor for permanent actions in calculating lower design values Partial factor for permanent action j Partial factor for permanent actions in calculating upper design values Importance factor Partial factor for a material property Partial factor for a material property, also accounting for model uncertainties and dimensional variations Partial factor for prestressing actions As *p but for accidental design situations Partial factor for variable actions Partial factor for variable action i Partial factor associated with the uncertainty of the resistance model and the dimensional variations Partial factor for the resistance, including uncertainties in material properties, model uncertainties and dimensional variations Partial factor associated with the uncertainty of the resistance model Partial factor associated with the uncertainty of the action and/or action eff ect model Conversion factor Reduction factor Coefficient for combination value of a variable action Coefficient for frequent value of a variable action Coefficient for quasi-permanent value of a variable action
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Section 2. Requirements 2.1 Fundamental requirements (1)P A structure shall be designed and executed in such a way that it will, during its intended life with appropriate degrees of reliability and in an economic way: remain fit for the use for which it is required; and sustain all actions and influences likely to occur during execution and use. (2) Design according to 2.1(1) implies that due regard is given to structural safety and serviceability, including durability, in both cases. (3)P A structure shall also be designed and executed in such a way that it will not be damaged by events like fire, explosion, impact or consequences of human errors, to an extent disproportionate to the original cause. (4)P The potential damage shall be avoided or limited by appropriate choice of one or more of the following: avoiding, eliminating or reducing the hazards which the structure may sustain; selecting a structural form which has low sensitivity to the hazards considered; selecting a structural form and design that can survive adequately the accidental removal of an individual element or a limited part of the structure, or the occurrence of acceptable localized damage; avoiding as far as possible structural systems which may collapse without warning; tying the structure together. (5)P The above requirements shall be met by the choice of suitable materials, by appropriate design and detailing, and by specifying control procedures for design, production, execution and use relevant to the particular project.
2.2 Reliability differentiation (1)P The reliability required for the majority of structures shall be obtained by design and execution according to ENVs 1991-1999, and appropriate quality assurance measures. (2) A different level of reliability may be generally adopted: for structural safety; for serviceability; (3) A different level of reliability may depend on: the cause and mode of failure; the possible consequences of failure in terms of risk to life, injury, potential economic losses and the level of social inconvenience; the expense and procedures necessary to reduce the risk of failure; different degrees of reliability required at national, regional or local level. (4) Differentiation of the required levels of reliability in relation to structural safety and serviceability may be obtained by the classification of whole structures or by the classification of structural components. (5) The required reliability relating to structural safety or serviceability may be achieved by suitable combinations of the following measures: a) Measures relating to design: serviceability requirements; representative values of actions; the choice of partial factors or appropriate quantities in design calculations; consideration of durability; consideration of the degree of robustness (structural integrity); the amount and quality of preliminary investigations of soils and possible environmental influences; the accuracy of the mechanical models used; the stringency of the detailing rules.
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b) Measures relating to quality assurance to reduce the risk of hazards in: gross human errors; design; execution. (6) Within individual reliability levels, the procedures to reduce risks ass ociated with various potential causes of failure may, in certain circumstances, be interchanged to a limited extent. An increase of effort within one type of measure may be considered to compensate for a reduction of effort within another type.
2.3 Design situations (1)P The circumstances in which the structure may be required to fulfil its function shall be considered and the relevant design situations selected. The selected design situations shall be sufficiently severe and so varied as to encompass all conditions which can reasonably be foreseen to occur during the execution and use of the structure. (2)P Design situations are classified as follows: persistent situations, which refer to the conditions of normal use; transient situations, which refer to temporary conditions applicable to the structure, e.g. during execution or repair; accidental situations, which refer to exceptional conditions applicable to the structure or to its exposure, e.g. to fire, explosion, impact; seismic situations, which refer to exceptional conditions applicable to the structure when subjected to seismic events. (3) Information for specific situations for each class is given in other Parts of ENV 1991 and in ENVs 1992 to 1999.
2.4 Design working life (1)P The design working life is the assumed period for which a structure is to be used for its intended purpose with anticipated maintenance but without major repair being necessary. (2) An indication of the required design working life is given in Table 2.1.
Table 2.1 Design working life classification Class
Required Design working life (years)
Example
1
[1–5]
Temporary structures
2
[25]
Replaceable structural parts, e.g. gantry girders, bearings
3
[50]
Building structures and other common structures
4
[100]
Monumental building structures, bridges, and other civil engineering structures
2.5 Durability (1) It is an assumption in design that the durability of a structure or part of it in its environment is such that it remains fit for use during the design working life given appropriate maintenance. (2) The structure should be designed in such a way that deterioration should not impair the durability and performance of the structure having due regard to the anticipated level of maintenance. (3)P The following interrelated factors shall be considered to ensure an adequately durable structure: the intended and possible future use of the structure; the required performance criteria; the expected environmental influences; the composition, properties and performance of the materials; the choice of the structural system; the shape of members and the structural detailing;
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the quality of workmanship, and level of control; the particular protective measures; the maintenance during the intended life. (4) The relevant ENVs 1992-1999 specify the appropriate measures. (5)P The environmental conditions shall be appraised at the design stage to assess their significance in relation to durability and to enable adequate provisions to be made for protection of the materials and products. (6) The degree of deterioration may be estimated on the basis of calculations, experimental investigation, experience from earlier constructions, or a combination of these considerations.
2.6 Quality assurance (1) It is assumed that appropriate quality assurance measures are taken in order to provide a structure which corresponds to the requirements and to the assumptions made in the design. These measures comprise definition of the reliability requirements, organizational measures and controls at the stages of design, execution, use and maintenance.
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Section 3. Limit states 3.1 General (1)P Limit states are states beyond which the structure no longer satisfies the design performance requirements. (2) In general, a distinction is made between ultimate limit states and serviceability limit states. NOTE Verification of one of the two limit states may be omitted if sufficient information is available to prove that the requirements of one limit state are met by the other.
(3) Limit states may relate to persistent, transient or accidental design situations.
3.2 Ultimate limit states (1)P Ultimate limit states are those associated with collapse or with other similar forms of structural failure. (2) States prior to structural collapse, which, for simplicity, are considered in place of the collapse itself are also treated as ultimate limit states. (3)P Ultimate limit states concern: the safety of the structure and its contents; the safety of people. (4) Ultimate limit states which may require consideration include: loss of equilibrium of the structure or any part of it, considered as a rigid body; failure by excessive deformation, transformation of the structure or any part of it into a mechanism, rupture, loss of stability of the structure or any part of it, including supports and foundations; failure caused by fatigue or other time-dependent effects.
3.3 Serviceability limit states (1)P Serviceability limit states correspond to conditions beyond which specified service requirements for a structure or structural element are no longer met. (2)P The serviceability requirements concern: the functioning of the construction works or parts of them; the comfort of people; the appearance. (3)P A distinction shall be made, if relevant, between reversible and irreversible serviceability limit states. (4) Unless specified otherwise, the serviceability requirements should be determined in contracts and/or in the design. (5) Serviceability limit states which may require consideration include: deformations and displacements which affect the appearance or effective use of the structure (including the functioning of machines or services) or cause damage to finishes or non-structural elements; vibrations which cause discomfort to people, damage to the structure or to the materials it supports, or which limit its functional effectiveness;. damage (including cracking) which is likely to affect appearance, durability or the function of the structure adversely; observable damage caused by fatigue and other time-dependent effects.
3.4 Limit state design (1)P Limit state design shall be carried out by: setting up structural and load models for relevant ultimate and s erviceability limit states to be considered in the various design situations and load cases; verifying that the limit states are not exceeded when design values for actions, material properties and geometrical data are used in the models.
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(2) Design values are generally obtained by using the characteristic or representative values (as defined in sections 4 to 6 and specified in ENVs 1991-1999) in combination with partial and other factors as defined in section 9 and ENV 1991 to 1999. (3) In exceptional cases, it may be appropriate to determine design values directly. The values should be chosen cautiously and should correspond to at least the same degree of reliability for the various limit states as implied in the partial factors in this code (see also section 8). NOTE 1 Partial factor design is discussed in Annex A. NOTE 2 Principles and application rules for verification are given in section 9.
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Section 4. Actions and environmental influences 4.1 Principal classifications (1)P An action (F ) is: a direct action, i.e. force (load) applied to the structure; or an indirect action, i.e. an imposed or constrained deformation or an imposed acceleration caused, for example, by temperature changes, moisture variation, uneven settlement or earthquakes. (2)P Actions are classified: a) by their variation in time: permanent actions (G), e.g. self-weight of structures, fixed equipment and road surfacings; variable actions (Q), e.g. imposed loads, wind loads or snow loads; accidental actions (A), e.g. explosions, or impact from vehicles. b) by their spatial variation: fixed actions, e.g. self-weight; free actions, e.g. movable imposed loads, wind loads, snow loads. c) by their nature and/or the structural response: static actions, which do not cause significant acceleration of the structure or structural member; dynamic actions, which cause significant acceleration of the structure or structural member. (3) In many cases, dynamic effects of actions may be calculated from quasi-static actions by increasing the magnitude of the static actions or by the introduction of an equivalent static action (see 7.3). (4) Some actions, for example seismic actions and snow loads, can be considered as either accidental and/or variable actions, depending on the site location (see other Parts of ENV 1991). (5) Prestressing (P ) is a permanent action. Detailed information is given in ENVs 1992, 1993, and 1994. (6) Indirect actions are either permanent Gind, (e.g. settlement of support), or variable Qind, (e.g. temperature effect), and should be treated accordingly. (7) An action is described by a model, its magnitude being represented in the most common cases by one scalar which may take on several representative values. For some actions (multi-component actions) and some verifications (e.g. for static equilibrium) the magnitude is represented by several values. For fatigue verifications and dynamic analysis a more complex representation of the magnitudes of some actions may be necessary.
4.2 Characteristic values of actions (1)P The characteristic value of an action is its main representative value. (2)P Characteristic values of actions F k shall be specified: in the relevant parts of ENV 1991, as a mean value, an upper or lower value, or a nominal value (which does not refer to a known statistical distribution); in the design, provided that the provisions, specified in ENV 1991 are observed. NOTE
The provisions may be specified by the relevant competent authority.
(3)P The characteristic value of a permanent action shall be determined as follows: G is small, one single value Gk may be used; if the variability of G is not small, two values have to be used; an upper value Gk,sup and a lower if the variability of value Gk,inf . G can be assumed to be small if G does not vary significantly during the (4) In most cases the variability of design working life of the structure and its coefficient of variation is not greater than [0,1]. However in such cases when the structure is very sensitive to variations in G (e.g. some types of prestressed concrete structures), two values have to be used even if the coefficient of variation is small.
(5) The following may be assumed in most cases: Gk is the mean value; Gidnf is the [0,05] fractile, and Gksup is the [0,95] fractile of the statistical; distribution for G which may be assumed to be Gaussian.
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(6) The self-weight of the structure can, in most cases, be represented by a single characteristic value and be calculated on the basis of the nominal dimensions and mean unit masses. The values are given in ENV 1991-2. (7)P For variable actions the characteristic value (Qk) corresponds to either: an upper value with an intended probability of not being exceeded or a lower value with an intended probability of not falling below, during some reference period; a nominal value which may be specified in cases where a statistical distribution is not known. Values are given in ENVs 1991-2 and 1991-3. (8) The following may be assumed for the time-varying part for most cases of characteristic values of variable actions: the intended probability is [0,98]; the reference period is [one] year. However in some cases the character of the action makes another reference period more appropriate. In addition, design values for other variables within the action model may have to be chosen, which may influence the probability of being exceeded for the resulting total action. (9) Actions caused by water should normally be based on water levels and include a geometrical parameter to allow for fluctuation of water level. Tides, currents and waves should be taken into account where relevant. (10) For accidental actions the representative value is generally a characteristic value Ak corresponding to a specified value. Ak for explosion and for some impacts are given in ENV 1991-2-7. (11) Values of
(12) For accidental actions arising from fire, information is given in ENV 1991-2-2. AEd for seismic actions are given in ENV 1998-1. (13) Values of
(14) For accidental actions on bridges arising from the traffic, characteristic values to be used as design values are given in ENV 1991-3. (15) For multi-component actions [see 4.1(7)] the characteristic action is represented by groups of values, to be considered alternatively in design calculations.
4.3 Other representative values of variable and accidental actions (1)P In the most common cases the other representative values of a variable action are: the combination value generally represented as a product: ?0 Qk; the frequent value generally represented as a product: ?1Qk; the quasi-permanent value generally represented as a product: ?2Qk. (2)P Combination values are associated with the use of combinations of actions, to take account of a reduced probability of simultaneous occurrence of the most unfavourable values of several independent actions. NOTE
For methods for determining ?0 see Annex A
(3)P The frequent value is determined such that: the total time, within a chosen period of time, during which it is exceeded f or a specified part, or the frequency with which it is exceeded, is limited to a given value. (4) The part of the chosen period of time or the frequency, mentioned in 4.3(3) should be chosen with due regard to the type of construction works considered and the purpose of the calculations. Unless other values are specified the part may be chosen to be 0,05 or the frequency to be 300 per year for ordinary buildings. (5)P The quasi-permanent value is so determined that the total time, within a chosen period of time, during which it is exceeded is a considerable part of the chosen period of time. (6) The part of the chosen period of time, mentioned in 4.3(5), may be chosen to be 0,5. The quasi-permanent value may also be determined as the value averaged over the chosen period of time.
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(7)P These representative values and the characteristic value are used to define the design values of the actions and the combinations of actions as explained in section 9. The combination values are used for the verification of ultimate limit states and irreversible serviceability limit states. The frequent values and quasi-permanent values are used for the verification of ultimate limit states involving accidental actions and for the verification of reversible serviceability limit states. The quasi-permanent values are also used for the calculation of long term effects of serviceability limit states. More detailed rules concerning the use of representative values are given, for example, in ENVs 1992 to 1999. (8) For some structures or some actions other representative values or other types of description of actions may be required, e.g. the fatigue load and the number of cycles when fatigue is considered. NOTE Further information concerning the specification and combination of actions is given in Annex A and other parts of ENV 1991.
4.4 Environmental influences The environmental influences which may affect the durability of the structure shall be considered in the choice of structural materials, their specification, the structural concept and detailed design. The ENVs 1992 to 1999 specify the relevant measures.
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Section 5. Material properties (1)P Properties of materials (including soil and rock) or products are represented by characteristic values which correspond to the value of the property having a prescribed probability of not being attained in a hypothetical unlimited test series. They generally correspond for a particular property to a specified fractile of the assumed statistical distribution of the property of the material in the structure. (2) Unless otherwise stated in ENVs 1992 to 1999, the characteristic values should be defined as the 5 % fractile for strength parameters and as the mean value for stiffness parameters. NOTE
For operational rules, see Annex D; for fatigue, information is given in Annex B
(3)P Material property values shall normally be determined from standardized tests performed under specified conditions. A conversion factor shall be applied where it is necessary to convert the test results into values which can be ass umed to represent the behaviour of the material in the structure or the ground (see also ENVs 1992 to 1999). (4) A material strength may have two characteristic values, an upper and a lower. In most cases only the lower value will need to be considered. In some cases, different values may be adopted depending on the type of problem considered. Where an upper estimate of strength is required (e.g. for the tensile strength of concrete for the calculation of the effects of indirect actions) a nominal upper value of the strength should normally be taken into account. (5) Where there is a lack of information on the statistical distribution of the property a nominal value may be used; where the limit state equation is not significantly sensitive to its variability a mean value may be considered as the characteristic value. (6) Values of material properties are given in ENVs 1992 to 1999.
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Section 6. Geometrical data (1)P Geometrical data are represented by their characteristic values, or in the case of imperfections directly by their design values. (2) The characteristic values usually correspond to dimensions specified in the design. (3) Where relevant, values of geometrical quantities may correspond to some prescribed fractile of the statistical distribution. (4)P Tolerances for connected parts which are made from different materials shall be mutually compatible. Imperfections which have to be taken into account in the design of structural members are given in ENVs 1992 to 1999.
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Section 7. Modelling for structural analysis and resistance 7.1 General (1)P Calculations shall be performed using appropriate design models involving relevant variables. The models shall be appropriate for predicting the structural behaviour and the limit states considered. (2) Design models should normally be ba sed on established engineering theory and practice, verified experimentally if necessary. NOTE
Further information is given in Annex C and Annex D.
7.2 Modelling in the case of static actions (1) The modelling for static actions should normally be based on an appropriate choice of the force deformation relationships of the members and their connections. (2) Effects of displacements and deformations should be considered in the context of ultimate limit state verifications (including static equilibrium) if they result in an increase of the effects of actions by more than 10 %. (3) In general the structural analysis models for serviceability limit states and fatigue may be linear.
7.3 Modelling in the case of dynamic actions (1) When dynamic actions may be considered as quasi-static, the dynamic parts are considered either by including them in the static values or by applying equivalent dynamic amplification factors to the static actions. For some equivalent dynamic amplification factors, the natural frequencies have to be determined. (2) In some cases (e.g. for cross wind vibrations or seismic actions) the actions may be defined by provisions for a modal analysis based on a linear material and geometric behaviour. For regular structures, where only the fundamental mode is relevant, an explicit modal analysis may be substituted by an analysis with equivalent static actions, depending on mode shape, natural frequency and damping. (3) In some cases the dynamic actions may be expressed in terms of time histories or in the frequency domain, for which the structural response may be determined by appropriate methods. NOTE When dynamic actions may cause vibrations that may infringe serviceability limit states guidance for assessing these limit states is given in Annex C, together with the models of some actions.
7.4 Modelling for fire actions (1)P The structural analysis for fire design shall be performed using appropriate models for the fire situation, involving thermal and mechanical actions, and for the structural behaviour at elevated temperatures. The analysis may be assisted by testing. (2) For fire design situations, see ENV 1991-2 which covers thermal actions in terms of: nominal (standard) fire exposures; and parametric fire exposure; and specific rules for mechanical actions. (3) The structural behaviour at elevated temperatures, should be assessed in accordance with ENVs 1992 to 1996 and ENV 1999, which give thermal and structural models for analysis. Where relevant to the specific material and the method of assessment: thermal models may be based on the assumption of a uniform temperature within cross-sections or may result in thermal gradients within cross-sections and along members; structural models may be confined to an analysis of members or may account for the interaction between members in fire exposure. The b ehaviour of materials or sections at elevated temperatures may be modelled as linear-elastic, rigid-plastic or non-linear. (4) Where tabulated data are given in ENVs 1992 to 1996 and ENV 1999, these data are mainly obtained from test results or numerical simulation based only on the action as described by the s tandard fire exposure.
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Section 8. Design assisted by testing 8.1 General (1)P Where calculation rules or material properties given in ENVs 1991 to 1999 are not sufficient or where economy may result from tests on prototypes, part of the design procedure may be performed on the basis of tests. NOTE Some of the clauses in this section may also be helpful in cases where the performance of an existing structure is to be investigated.
(2)P Tests shall be set up and evaluated in such a way that the structure has the same level of reliability with respect to all possible limit states and design situations as achieved by design based on calculation procedures specified in ENVs 1991 to 1999, including this Part of ENV 1991. (3) Sampling of test specimens and conditions during testing should be representative. (4) Where ENVs 1991 to 1999 include implicit safety provisions related to comparable situations, these provisions shall be taken into account in as sessing the test results and may give rise to corrections. An example is the effect of tensile strength in the bending resistance of concrete beams, which is normally neglected during design.
8.2 Types of tests (1) The following test types are distinguished: a) tests to establish directly the ultimate resistance or serviceability properties of structural parts e.g. fire tests; b) tests to obtain specific material properties, e.g. ground testing in situ or in the laboratory, testing of new materials; c) tests to reduce uncertainties in parameters in load or resistance models, e.g. wind tunnel testing, testing of full size prototypes, testing of scale models; d) control tests to check the quality of the delivered products or the consistency of the production characteristics, e.g. concrete cube testing; e) tests during execution in order to take account of actual conditions experienced e.g. post-tensioning, soil conditions; f) control tests to check the behaviour of the actual structure or structural elements after completion, e.g. proof loading for the ultimate or serviceability limit states. (2) For test types a), b) and c), the test results may be available at the time of design; in those cases the design values can be derived from the tests. For test types d), e) and f) the test results may not be available at the time of design; in these cases the design values correspond to that part of the production that is expected to meet the acceptance criteria at a la ter stage.
8.3 Derivation of design values (1)P The derivation of the design values for a material property, a model parameter or a resistance value from tests can be performed in either of the following two ways: a) by assessing a characteristic value, which is divided by a partial factor and possibly multiplied by an explicit conversion factor; b) by direct determination of the design value, implicitly or explicitly accounting for the conversion aspects and the total reliability required. (2) In general method a) should be used. The derivation of a characteristic value from tests should be performed taking account of: 1) the scatter of test data; 2) statistical uncertainty resulting from a limited number of tests; 3) implicit or explicit conversion factors resulting from influences not sufficiently covered by the tests such as: i) time and duration effects, not taken care of in the tests; ii) scale, volumes and length effects; iii) deviating environmental, loading and b oundary conditions;
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iv) the way that safety factors as partial factors or additive elements are applied to get design values (see 9.3). The partial factor used in method a) should be chosen in such a way that there is sufficient similarity between the tests under consideration and the usual application field of the partial factor used in numerical verifications. (see also 3.4). (3) When for special cases method b) is used, the determination of the design values should be carried out by considering: the relevant limit states; the required level of reliability; the statistical and model uncertainties; the compatibility with the assumptions for the action side; the classification of design working life of the relevant structure according to Section 2; prior knowledge from similar cases or calculations. (4) Further information may be found in ENVs 1992 to 1999. NOTE
see also Annex A and Annex D.
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Section 9. Verification by the partial factor method 9.1 General (1)P In ENVs 1992 to 1999 the reliability according to the limit state concept is achieved by application of the partial factor method. In the partial factor method, it is verified that, in all relevant design situations, the limit states are not exceeded when design values for actions, material properties and geometrical data are used in the design models. (2)P In particular, it shall be verified that: a) the effects of design actions do not exceed the design resistance of the structure at the ultimate limit state; and b) the effects of design actions do not exceed the performance criteria for the serviceability limit state. Other verifications may also need to be considered for particular structures e.g. fatigue. Details are presented in the relevant parts of ENV 1991 and in ENVs 1992 to 1999. NOTE
see also Annex A and Annex B.
(3)P The selected design situations shall be considered and critical load cases identified. For each critical load case, the design values of the effects of actions in combination shall be determined. load case identifies compatible load arrangements, sets of deformations and imperfections which (4) A should be considered simultaneously for a particular verification.
(5) Rules for the combination of independent actions in design situations are given in this section. Actions which cannot occur simultaneously, for example, due to physical reasons, should not be considered together in combination. (6) A load arrangement identifies the position, magnitude and direction of a free action. Rules for different arrangements within a single action are given in ENVs 1991-2, 1991-3 and 1991-4. (7) Possible deviations from the assumed directions or positions of actions should be considered. (8) The design values used for different limit states may be different and are specified in this section.
9.2 Limitations and simplifications (1) Application rules in ENV 1991-1 are limited to ultimate and serviceability limit states for structures subject to static loading. This includes cases where the dynamic effects are assessed using equivalent quasi-static loads and dynamic amplification factors, e.g. wind. Modifications for non-linear analysis and fatigue are given in other parts of ENV 1991 and in ENVs 1992 to 1999. (2) Simplified verification based on the limit state concept may be used: by considering only limit states and load combinations which from experience or special criteria are known to be potentially critical for the design; by using the simplified verification for ultimate limit states and/or serviceability limit states as specified for buildings in 9.4.5 and 9.5.5; by specifying particular detailing rules and/or provisions to meet the safety and serviceability requirements without calculation. NOTE For those cases where ENVs 1991 to 1999 do not give adequate rules for the verification, for instance for new materials, special structures, unusual limit states, guidance is given in Annex A. For those cases where the Eurocodes give adequate rules, Annex A can be considered as background information.
9.3 Design values 9.3.1 Design values of actions (1)P The design value F d of an action is expressed in general terms as: F d = *F F rep
(9.1)
where:
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*F
is the partial factor for the action considered taking account of:
F rep
the possibility of unfavourable deviations of the actions; the possibility of inaccurate modelling of the actions; uncertainties in the assessment of effects of actions. is the representative value of the action.
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(2) Depending on the type of verification and combination procedures, design values for particular actions are expressed as follows:
*GGk or Gk Qd = *QQk, *Q?0Qk, ?1Qk, ?2Qk or Qk Ad = *A Ak or Ad P = *P P d k or P k =
Gd
=
AEd
(9.2)
AEd
(3)P Where distinction has to be made between favourable and unfavourable effects of permanent actions, two different partial factors shall be used. (4) For seismic actions the design value may depend on the structural behaviour characteristics (see ENV 1998).
9.3.2 Design values of the effects of actions (1) The effects of actions (E ) are responses (for example internal forces and moments, stresses, strains and displacements) of the structure to the actions. For a specific load case the design value of the effect of actions (E d) is determined from the design values of the actions, geometrical data and material properties when relevant: (F E d = E d1, F d2, ... ad1, ad2, ... X d1, X d2, ...)
(9.3)
where: F d1, ..., ad1, ... and X d1, ... are chosen according to 9.3.1, 9.3.3 and 9.3.4 respectively.
(2) In some cases, in particular for non-linear analysis, the effect of the uncertainties in the models used in the calculations should be considered explicitly. This may lead to the application of a coefficient of model uncertainty, *Sd applied either to the actions or to the action effects, whichever is the more conservative. The factor *Sd may refer to uncertainties in the action model and/or the action effect model. (3) For non-linear analysis, i.e. when the effect is not proportional to the action, the following simplified rules may be considered in the case of a single predominant action. a) When the effect increases more than the action, the partial factor is applied to the representative value of the action. b) When the effect increases less than the action, the partial factor is applied to the action effect of the representative value of the action. In other cases more refined methods are necessary which are defined in the relevant Eurocodes (e.g. for prestressed structures).
9.3.3 Design values of material properties (1)P The design value X d of a material or product property is generally defined as: X d = )X k / *M or X d = X k / *M
(9.4)
where:
*M is the partial factor for the material or product property, given in ENVs 1992 to 1999, which covers:
)
unfavourable deviations from the characteristic values; inaccuracies in the conversion factors; and uncertainties in the geometric properties and the resistance model. is the conversion factor taking into account the effect of the duration of the load, volume and scale effects, effects of moisture and temperature and so on.
In some cases the conversion is implicitly taken into account by the characteristic value itself, as indicated by the definition of ), or by *M.
9.3.4 Design values of geometrical data (1)P Design values of geometrical data are generally represented by the nominal values: ad = anom
(9.5)
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Where necessary ENVs 1992 to 1999 may give further specifications. (2)P In some cases when deviations in the geometrical data have a significant effect on the reliability of a structure, the geometrical design values are defined by: ad = anom + %a
(9.6)
where %a takes account of the possibility of unfavourable deviations from the characteristic values.
%a is only introduced where the influence of deviations is critical, e.g. imperfections in buckling analysis. Values of %a are given in ENVs 1992 to 1999. 9.3.5 Design resistance (1)P Design values for the material properties, geometrical data and effects of actions, when relevant, shall be used to determine the design resistance Rd from: Rd = R(ad1, ad2, ... X d1, X d2, ...)
(9.7)
where ad1, ... is defined in 9.3.4 and X d1, ... in 9.3.3. (2) Operational verification formulae, based on the principle of expression (9.7), may have one of the following forms: Rd = R { X k/*M, anom }
(9.7a)
Rd = R { X k, anom }/*R
(9.7b)
Rd = R { X k/*m, anom }/*rd
(9.7c)
where: *R is a partial factor for the resistance; *m is a material factor; *rd covers uncertainties in the resistance model and in the geometrical properties. NOTE
For further information, see Annex A
(3) The design resistance may also be obtained directly from the characteristic value of a product resistance, without explicit determination of design values for individual basic variables, from: Rd = Rk/*R
(9.7d)
This is applicable for steel members, piles, etc. and is often used in connection with design by testing.
9.4 Ultimate limit states 9.4.1 Verifications of static equilibrium and strength (1)P When considering a limit state of static equilibrium or of gross displacement of the structure as a rigid body, it shall be verified that: E d ,dst k E d ,stb
(9.8)
where: E d ,dst
is the design value of the effect of destabilizing actions;
E d ,stb
is the design value of the effect of stabilizing actions.
In some cases it may be necessary to replace expression (9.8) by an interaction formula. (2)P When considering a limit state of rupture or excessive deformation of a section, member or connection, it shall be verified that: E d k Rd
(9.9)
where: E d Rd
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is the design value of the effect of actions such as internal force, moment or a vector representing several internal forces or moments; is the corresponding design resistance, associating all structural properties with the respective design values.
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In some cases it may be necessary to replace expression (9.9) by an interaction formula. The required load cases are identified as described in 9.1.
9.4.2 Combination of actions (1)P For each critical load case, the design values of the effects of actions (E d) should be determined by combining the values of actions which occur simultaneously, as follows: a) Persistent and transient situations: Design values of the dominant variable actions and the combination design values of other actions. b) Accidental situations: Design values of permanent actions together with the frequent value of the dominant variable action and the quasi-permanent values of other variable actions and the design value of one accidental action. c) Seismic situations: Characteristic values of the permanent actions together with the quasipermanent values of the other variable actions and the design value of the s eismic actions. (2) When the dominant action is not obvious, each variable action should be considered in turn as the dominant action. (3) The above combination process is represented in Table 9.1.
Table 9.1 Design values of actions for use in the combination of actions Design situation
Permanent actions Gd
Single variable actions Qd Dominant
Others
Accidental actions or seismic actions Ad
Persistent and transient
*GGk (*PP k)
*Q1Qk1
*Qi?OiQid
Accidental
Gk (*PA P *GA k)
?11Qk1
?2iQid
Ak or Ad *A
Seismic
Gk
?2iQid
AEd *A
Symbolically the combinations may be represented as follows a) persistent and transient design situations for ultimate limit states verification other than those relating to fatigue (9.10) NOTE
This combination rule is an amalgamation of two separate load combinations:
(9.10a)
(9.10b) [K] is a reduction factor for *Gj within the range 0.85 and 1. From the expressions (9.10a) and (9.10b) the more favourable may be applied instead of expression (9.10) under conditions defined by the relevant National Application Document.
b) Combinations for accidental design situations (9.11) c) Combination for the seismic design situation (9.12) where: “+”
implies “to be combined with”; implies “the combined effect of”;
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Gkj P k Qk1 Qid Ad AEd
*Gj *GAj *PA *P *Qi
*i ?
is the characteristic value of permanent actions; is the characteristic value of a prestressing action; is the characteristic value of the variable action i; is the characteristic value of the variable actions; is the design value of the accidental action; is the design value of seismic action; is the partial factor for permanent action j; is the same as *Gj, but for accidental design situations; is the same as *P, but for accidental actions; is the partial factor for prestressing actions; is the partial factor for variable action i; is the importance factor (see ENV 1998); are combination coefficients (see 4.3).
(4) Combinations for accidental design situations either involve an explicit accidental action A (e.g. fire or impact) or refer to a situation after an accidental event (A = 0). For fire situations, apart from the temperature effect on the material properties, Ad refers to the design value of the indirect thermal action. (5) Expressions (9.10) to (9.11) may refer to either actions or action effects; for non-linear analysis, see 9.3.2(3). (6) Where components of a vectorial force are partially correlated, the factors to any favourable component may be reduced by [20 %]. (7) Imposed deformations should be considered where relevant. (8) In some cases expressions (9.10) to (9.12) need modification; detailed rules are given in the relevant parts of ENVs 1991 to 1999.
9.4.3 Partial factors (1)P In the relevant load cases, those permanent actions that increase the effect of the variable actions (i.e. produce unfavourable effects) shall be represented by their upper design values, those that decrease the effect of the variable actions (i.e. produce favourable effects) by their lower design values. (2)P Where the results of a verification may be very sensitive to variations of the magnitude of a permanent action from place to place in the structure, the unfavourable and the favourable parts of this action shall be considered as individual actions. This applies in particular to the verification of static equilibrium. (3) For building structures, the partial factors for ultimate limit states in the persistent, transient and accidental design situations are given in Table 9.2. The values have been based on theoretical considerations, experience and back calculations on existing designs. NOTE
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These values may be used for the design of silos covered in ENV-1991-4.
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Table 9.2 Partial factors: ultimate limit states for buildings Casea
Action
Case A Loss of static equilibrium; strength of structural material or ground insignificant (see 9.4.1)
Permanent actions: self weight of structural and non-structural components, permanent actions caused by ground, ground-water and free water
Symbol
Situations P/T
A
unfavourable
*Gsupd
[1,10]b
[1,00]
favourable
d *Ginf
[0,90]b
[1,00]
unfavourable
*Q
[1,50]
[1,00]
Accidental actions
*A
Variable actions
Case Be Failure of structure or structural elements, including those of the footing, piles, basement walls etc., governed by strength of structural material (see 9.4.1)
Case Ce Failure in the ground
[1,00]
Permanent actionsf (see above) unfavourable
*Gsupd
[1,35]c
[1,00]
favourable
d *Ginf
[1,00]c
[1,00]
unfavourable
*Q
[1,50]
[1,00]
Accidental actions
*A
Variable actions [1,00]
Permanent actions (see above) unfavourable
*Gsupd
[1,00]
[1,00]
favourable
d *Ginf
[1,00]
[1,00]
unfavourable
*Q
[1,30]
[1,00]
Accidental actions
*A
Variable actions
P: Persistent situation
T: Transient situation
[1,00] A: Accidental situation
a
The design should be verified for each case A, B and C separately as relevant. this verification the characteristic value of the unfavourable part of the permanent action is multiplied by the factor [1,1] and the favourable part by the factor [0,9]. More refined rules are given in ENV 1993 and ENV 1994. c In the verification the characteristic values of all permanent actions from one source are multiplied by [1,35] if the total resulting action effect is unfavourable and by [1,0] if the total resulting action effect is favourable. d In cases when the limit state is very sensitive to variations of permanent actions, the upper and lower characteristic values of these actions should be taken according to 4.2(3). e For cases B and C the design ground properties may be different, see ENV 1997-1-1 f Instead of using *G (1,35) and *Q (1,50) for lateral earth pressure actions the design ground properties may be introduced in accordance with ENV 1997 and a model factor *Sd is applied. b In
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9.4.4 ? factors (1) ? factors for buildings are given in Table 9.3. For other applications see relevant parts of ENV 1991.
Table 9.3 ? factors for buildings ?0
Action
?1
?2
Imposed loads in buildingsa category A: domestic, residential
[0,7]
[0,5]
[0,3]
category B: offices
[0,7]
[0,5]
[0,3]
category C: congregation areas
[0,7]
[0,7]
[0,6]
category D: shopping
[0,7]
[0,7]
[0,6]
category E: storage
[1,0]
[0,9]
[0,8]
category F: vehicle weight k 30 kN
[0,7]
[0,7]
[0,6]
category G: 30 kN < vehicle weight k 160 kN
[0,7]
[0,5]
[0,3]
category H: roofs
[0]
[0]
[0]
Snow loads on buildings
[0,6]b
[0,2]b
[0]b
Wind loads on buildings
[0,6]b
[0,5]b
[0]b
Temperature (non-fire) in buildingsc
[0,6]b
[0,5]b
[0]b
Traffic loads in buildings
a For combination of imposed loads in multistorey buildings, see ENV b Modification for different geographical regions may be required. c
1991-2-1.
See ENV 1991-2-5.
9.4.5 Simplified verification for building structures (1) The process for the persistent and transient situations described in 9.4.2 may be simplified by considering the most unfavourable for the following combinations: a) Design situations with only one variable action Qk1 (9.13) b) Design situations with two or more variable actions Qk ,i (9.14) In this case the effect of actions should also be verified for the dominant variable actions using expression (9.13). (2) The *G values are given in Table 9.2.
9.4.6 Partial safety factors for materials Partial safety factors for properties of materials and products are given in ENVs 1992 to 1999.
9.5 Serviceability limit states 9.5.1 Verifications of serviceability (1)P It shall be verified that: E d k C d
(9.15)
where: C d E d
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is a nominal value or a function of certain design properties of materials related to the design effects of actions considered; and is the design value of the action effect (e.g. displacement, acceleration), determined on the basis of one of the combinations defined in 9.5.2.
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NOTE Guidance for C d may be found in ENV 1992 to 1999.
9.5.2 Combination of actions (1) The combination of actions to be considered for serviceability limit states depends on the nature of the effect of actions being checked, e.g. irreversible, reversible or long term. Three combinations designated by the representative value of the dominant action are given in Table 9.4.
Table 9.4 Design values of actions for use in the combination of actions Combination
Permanent actions Gd
Variable actions Qd Dominant
Others
Characteristic (rare)
Gk
(P k)
Qk1
?0iQki
Frequent
Gk
(P k)
?11Qk1
?2iQki
Quasi-permanent
Gk
(P k)
?21Qk1
?2iQki
NOTE For serviceability limit states, the partial factors (serviceability) *G and *Q are taken as 1,0 except where specified otherwise.
(2) Three combinations of actions for serviceability limit states are defined symbolically by the following expressions: a) Characteristic (rare) combination (9.16) b) Frequent combination (9.17) c) Quasi-permanent combination (9.18) where the notation is as given in 1.6 and 9.4.2. (3) Loads due to imposed deformations should be considered where relevant. (4) In some cases expressions (9.16) to (9.18) may require a modification; detailed rules are given in the relevant Parts of ENVs 1991 to 1999.
9.5.3 Partial factors The partial factors for serviceability limit states are equal to [1,0] except where specified otherwise, e.g. in ENVs 1992 to 1999.
9.5.4 ? factors
? factors are given in Table 9.3. Values of 9.5.5 Simplified verification for building structures (1) For building structures the characteristic (rare) combination may be simplified to the following expressions, which may also be used as a substitute for the frequent combination. a) Design situations with only one variable action, Qk1 (9.19)
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b) Design situations with two or more variable actions, Qk1 (9.20) In this case the effect of actions should also be verified for the dominant variable action using expression (9.19). (2) Where simplified prescriptive rules are given for serviceability limit states, detailed calculations using combinations of actions are not required.
9.5.6 Partial factors for materials Partial factors for the properties of materials and products are given in ENVs 1992 to 1999.
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Annex A (informative) Partial factor design A.1 General (1) This annex gives information and theoretical background concerning the partial factor method as described in section 9. This annex is also an introduction to Annex D. The information in these annexes may be used if the verification rules of ENVs 1991-1999 are not considered adequate for the case considered. (2) In the partial factor method it is verified that all relevant limit states are not exceeded, given design values for actions, resistances and geometrical data. The design values are the products or quotients of the characteristic values and the appropriate partial factors and ? values, as indicated in 9.3 to 9.5. In general, partial factors are intended to take account of: unfavourable deviations from the representative values; inaccuracies in the action models and structural models; inaccuracies in the conversion factors. (3) The value of the partial factors should depend on the degree of uncertainty in the actions, resistances, geometrical quantities and models, and on the type of construction works and the type of limit state. (4) In principle there are two ways to determine numerical values for partial factors: a) on the basis of calibration to a long and successful history of building tradition; for most of the factors proposed in the currently available Eurocodes this is the leading principle; b) on the basis of the statistical evaluation of experimental data and field observations; this should be done within the framework of a probabilistic reliability theory. (5) In practice, the two methods described in A.1(4) can also be used in combination. In particular, a mere statistical (probabilistic) approach usually fails from a lack of sufficient data. Some reference to traditional design methods should always be made. Where there has been a long and successful building tradition, it is of great value to obtain a rational understanding of that success. Understanding may justify the reduction of some factors for specified conditions, which in their turn may lead to economy. From this point of view, the statistical methods should be considered as giving added value to the more traditional approach.
A.2 Overview of reliability methods (1) Figure A.1 presents an overview of the various methods for reliability verification and the interactions between them. The probabilistic verification procedures can be subdivided into two main classes: exact methods and first order reliability methods (FORM), sometimes referred to as level III and level II methods respectively. In both methods the measures of reliability are f ailure probabilities P 1 for the failure modes under consideration and for some appropriate reference period. These values are calculated and compared with some preset target value P 0. If the failure probability is larger than the target, the structure is considered to be unsafe.
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Figure A.1 Overview of reliability methods (2) In the level II procedures one generally works with an a lternative measure of safety, the so-called reliability index ", which is related to P 1 by: P 1 = 9(-")
(A.1)
where 9 is the distribution function of the normal distribution. Although fully equivalent to the failure probability itself, the use of the reliability index emphasizes the formal and notional nature of the reliability analysis. The relationship between " and P 1 is presented in Table A.1.
Table A.1 Relation between " and P 1 P 1
10–1
10–2
10–3
10–4
10–5
10–6
10–7
"
1,3
2,3
3,1
3,7
4,2
4,7
5,2
(3) According to Figure A.1, the safety elements of the partial factor method (level I) can be obtained in three ways: a) from calibration to historical and empirical design methods; b) from calibration to probabilistic methods; c) as a simplification of FORM via the (calibrated) design value method as described in A.3. The present generation of Eurocodes has been primarily based on method a), with amendments based on c) or equivalent methods, mainly in the field of design assisted by testing. (4) Indicative target values for " in various design situations are given in Table A.2. Values are given for the design working life (see Table 2.1 of ENV 1999-1) and for one year. Values for one year might be relevant for transient design situations and temporary structures where human safety is of great importance. (5) The values in Table A.2 are intended as “appropriate for most cases”. For reasons related to the type and consequences of failure and economy of building, it may be appropriate to use higher or lower values (see 2.2). A class difference in reliability level is usually associated with differences in " values in the order of 0,5 to 1,0. A difference of reliability level may be desired for a total building, some specific components or some specific hazards. NOTE 1 A given reliability level may lead to different partial factors for various material properties and loads, depending on their variability and influence, see A.3 and A.4. This should not be confused with reliability differentiation. NOTE 2 Choosing a different target reliability index is not the only possible measure for reliability differentiation; other measures are related to the accuracy of calculation, the degree of quality assurance and the stringency of detailing rules.
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(6) The values in Table A.2 should be considered as reasonable minimum requirements, following from calibration calculations to design codes in various countries. In these calibrations lognormal or Weibull distributions for resistance parameters and model uncertainties were usually used. Normal distributions were usually taken for self weight and extreme value distributions for variable loads. It should be noted, however, that these calibrations showed a wide scatter, depending on the code at hand, the type of structural component, and the quantification of the various uncertainties. (7) The value of 3.8 for the ultimate limit state target reliability index is in particular, accepted for many applications mainly relating to resistance. This, however, does not mean that standard design according to the Eurocodes automatically would lead to "-values equal or close to this target. In fact, up to now, the present generation of Eurocodes have not been wholly evaluated in this way. Such an evaluation is not very straightforward as serviceability, durability, round off effects or multimodal distribution effects may disturb the picture in many cases. Additionally design rules in codes may also include implicit safety differentiations depending on the type of failure, especially ductile or brittle behaviour. (8) Finally, it should be stressed that a "-value and the corresponding failure probability are formal or notional numbers, intended primarily as a tool for developing consistent design rules, rather than giving a description of the structural failure frequency.
Table A.2 Indicative values for the target reliability index " Target reliability index (design working life)
Limit state
Target reliability index (one year)
Ultimate
3,8
4,7
Fatigue
1,5 to 3,8a
Serviceability (irreversible)
1,5
3,0
a Depends
on degree of inspectability, reparability and damage tolerance.
A.3 Reliability verification using design values (1) In the design value method (method Ib in Figure A.1), design values are defined for all variables that should be considered as uncertain (basic variables). The design is considered to be sufficient if the limit states are not reached when design values are used in the models. In symbolic notation (see section 9): E d < Rd
(A.2)
E {F d = E d1, F d2, ... ad1, ad2, ... Fd1, Fd2, ...} Rd = R {f d1, f d2, ... ad1, ad2, ... Fd1, Fd2, ...}
where E R F f a
F
is the action effect; is the resistance; is action; is material property; is geometrical property; model uncertainty.
Note that expression (A.2) is partly symbolic and that sometimes a more general formulation is necessary. (2) The set of design values for the design point corresponds to the point on the failure surface having the highest probability of occurrence (see Figure A.2). In this way the design value method is related to the probabilistic level II method [see A.2(1)]. (3) The design value of action effects E d and the resistances Rd are defined such that the probability of having a more unfavourable value is as follows: P (E > E d) = 9 (+ µ E") = 9 (– 0,7")
(A.3a)
P µ (R < Rd) = 9 (– R") = 9 (– 0,8")
(A.3b)
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where:
! is the FORM weight factor (– 1 k ! k + 1); " is the target value for the reliability index (see Table A.2). For a load ! is negative; for a resistance parameter ! is positive. (4) The essence of the method is the setting of the !E and !R values to – 0,7 and + 0,8 respectively. The validity range for these values is limited for the case " = 3,8 (accepting a maximum deviation of 0.5) to the ratios: 0,16 < BE/BR < 7,6
B. Outside this range it is recommended to use ! = ± 1.0 for the variable having the largest value of (5) When the load or resistance model contains several basic variables (other loads, conversion factors, more materials) expressions (A.3a) and (A.3b) only hold for the dominating variables. For non-dominating variables: P {E > E d} = 9 (– 0,4 × 0,7 × ") = 9 (– 0,28 ")
(A.4a)
P {R < Rd} = 9 (– 0,4 × 0,8 × ") = 9 (– 0,32 ")
(A.4b)
For " = 3,8 these values correspond approximately to the 0,90 and 0,10 f ractiles respectively. (6) Table A.3 gives expressions for calculating the design values for given ! and ".
Table A.3 Design values for various distribution functions Distribution
Design values
Remarks
Normal
4 – !"B
4 is the mean, B is the standard deviation
Lognormal
4 exp(– !"V )
for V = B/4 < 0,2
Gumbel
!")} u – a–1 In {– In9(–
0,577 u = 4 – /a, a = ;/(BÆ6)
Figure A.2 Design point definition according to first order reliability methods (FORM) A.4 Reliability verification formats in Eurocodes (1) In ENVs 1991 to 1999 design values X d and F d are not introduced directly. Basic variables are first F introduced by their representative values X and k k, which can be defined as: values with a prescribed or intended probability of being exceeded, e.g. loads and material properties; nominal values, e.g. geometrical properties;
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values calibrated to reach the aimed reliability, e.g. coefficients and model factors. Additionally there is a set of partial safety factors and load combination factors. (2) The design values for actions F , material properties X and geometrical properties follow from: F ?F Fk or F (? can be ?0, ?1 or ?2) d = *f d = *f k
(A.5)
X d = X k/*m
(A.6)
ad = anom ± %a
(A.7)
The index k denotes characteristic values. (3) The design values for model uncertainties normally enter the equations by partial fa ctors *Sd and *Rd on the total model. It follows that: E ? F {*f F d = *sd E k, *f k, anom ± %a ...}
(A.8)
Rd = R {X k/*m, anom
(A.9)
±
%a ...}/*Rd
In this model:
*f takes account of: the possibility of unfavourable deviations of the action values from the representative values.
*m takes account of: the possibility of unfavourable deviations of the material properties from the characteristic values; the systematic part of the conversion factor [ if relevant, see also 8.3(1)]; uncertainties of the conversion factor.
%a takes account of: the possibility of unfavourable deviations of the geometrical data from the characteristic (specified) values governed by the tolerance specifications; the importance of variations; the cumulative effect of a simultaneous occurrence of several geometrical deviations.
*Rd takes account of: the uncertainties of the resistance model if these uncertainties are not covered by the model itself.
*Sd takes account of the uncertainties: in the action model; in the action effect model.
? takes account of reductions in design values for loads, in particular: the combination value ?0*FF k is determined in such a way that the probability of combined action effect values being exceeded is approximately the same a s when a single variable action only is present. Within the context of a design value approach (A.3), operational formulae are presented in Table A.4 for the case of two fluctuating loads. The frequent value of a variable action ?1F k corresponds to the value which is exceeded either 5 % of the time or 300 times per year; the highest value should be chosen. The quasi-permanent value ?2F k corresponds to the time average or to the value with a probability of being exceeded of 50 %. (4) The procedure described by expressions (A.8) and (A.9) is theoretically perfect but cumbersome from a practical point of view. Therefore the following simplifications are made. a) On the loading side (for a single loading): E {*FF d = E k, anom}
(A.10)
Providing E is proportional to F , a, and a model uncertainty F, i.e. , E FaF ù
the value of *F may follow from [see expression (A.8) and (A.10)]: F *FF kanom = *f k(anom + %a)*Sd
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*F = *f *Sd (1 + %a/anom)
(A.11)
In addition, *F is highly standardized. For instance *F = 1,5 for all variable loads. Therefore, the characteristic value is recommended to be adjusted when necessary. b) On the resistance side (depending on the particular Eurocode): Rd = R {X k/*M, anom}
(ENVs 1992 and 1995)
(A.12)
Rd = R {X k, anom}/*R
(ENV 1993)
(A.13)
Rd = R {X k/*m, anom}/*rd
(ENV 1994)
(A.14)
Providing R is proportional to the strength X , the model uncertainty F and the geometrical property a, i.e. R ! FaX. the following simple relations apply:
*M = *m*Rd/{1 + %a/anom} *R = *m*Rd/{1 + %a/anom} *rd = *Rd/{1 + %a/anom}
(ENVs 1992 and 1995)
(A.15)
(ENV 1993)
(A.16)
(ENV 1994)
(A.17)
For non-linear models, or in the case of multi-variable load or resistance models, commonly encountered in Eurocodes, these relations become more complicated.
Table A.4 Expression for ?0 Distribution
?o = F non dom/F dom
General
Normal (approximation) Gumbel
F s()
is the probability distribution function of the extreme value of the non dominating load in the design period T ;
9()
is the standard normal distribution function;
N is the T /T 1; T
is the design period;
T 1
is the period of an independent load variation of the slower varying load;
"
is the reliability index;
V is the coefficient of variation for the non dominating load. NOTE For intermittent loads, the parameter T 1 is equal to the duration of the load and F s ( ) represents the unconditional distribution function of the load intensity; so F s( ) is not the conditional distribution function given that the load is active.
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A.5 Closure It is clear from A.1 to A.4 that the same level of formal reliability can be obtained in many different ways. Some partial factors may be put equal to 1,0 and the required safety margin may be included in another factor. High characteristic values and low safety factors may be taken or vice versa. The various safety elements form a set of “communicating vessels”. For every individual design situation, however, there is the possibility of calibrating the specific coefficients in order to obtain the required reliability level. In the currently available set of Eurocodes, the characteristic values for loads and strength parameters and the geometrical properties are generally taken in accordance with A.2 to A.4. ENV 1991-1 gives values for the partial load factors and the material-related design codes give values for the partial resistance factors. This is mainly done in a global way, partly based on probabilistic considerations, partly on a historical or empirical motivation. Furthermore, the choice of the representative values and the corresponding values for partial factors was done taking into account the needs for and aspects of an easy and economic application of the verification procedure in practical design. This has led to the following requests. For common structures the design values for actions or action effects should be independent of the design values of the resistance.
*F values. There should be only a small set of Only one constant *M value should be given for each material property. Further simplifications concerning the safety and serviceability verification as well as in structural analysis should be possible, i.e. avoiding the need to consider too many load arrangements, load cases, and load combinations in the relevant design situations.
Annex B (informative) Fatigue B.1 The fatigue phenomenon (1) Fatigue is a local material deterioration caused by repeated variations of stresses or strains. (2) Low cycle fatigue and high cycle fatigue may be distinguished.
low cycle fatigue is associated with non-linear material and geometric behaviour, e.g. alternating plastic strains in plastic zones. Criteria to exclude low cycle fatigue are given in ENVs 1992 to 1999.
high cycle fatigue is mainly governed by elastic behaviour. Therefore the analysis model can be elastic. (3) Criteria for determining whether fatigue assessment is needed are given in ENVs 1992 to 1999.
B.2 Fatigue resistance (1) Except for cases where the fatigue strength of members is determined in specific tests with a load-time history close to the actual loading to which they are subjected, the fatigue behaviour of structural members is generally studied for code purposes by simplified tests. In these tests the members are subjected to constant amplitude load variations, until excessive deformations or fractures due to cracking occur. (2) The fatigue strength of a given detail is then defined by a %BR – N R relationship, which approximately represents the 95 % fractile of survival; where %BR is the stress range and N R the number of cycles up to failure. This relationship may be modelled by a standardized linear, bilinear or trilinear line in double logarithmic scale. (3) For a range of details, a system of such equidistant %BR – N R curves may be established to allow for classification.
B.3 Determination of fatigue action effects compatible with the fatigue resistance (1) Fatigue actions are specified in the other Parts of ENV 1991. (2) When stress-time histories representative of the fatigue action on a given detail are available, any stress-time history may be evaluated using the reservoir counting method or rainflow counting method. These methods enable stress ranges and the numbers of cycles to be determined, together with the associated mean stresses when these are relevant. (3) The stress ranges and the number of cycles may be ordered in stress-range frequency distributions or stress-range spectra. (4) The stress-range frequency distributions or stress range spectra may be transformed to fatigue-damage-equivalent constant amplitude stress-range spectra using Miner’s rule. © BSI 04-2000
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B.4 Fatigue verification (1) The safety verification for fatigue may be carried out by: a damage calculation, where the damage caused by the fatigue actions is related to an ultimate damage representing the limit state; a fatigue life verification, where, for a representative level of stress range, a damage equivalent number of load cycles caused by the fatigue action is related to an ultimate number of cycles representing the limit state; a stress range verification, where, for a representative number of stress cycles, the magnitude of the damage-equivalent stress range, caused by the fatigue action is related to an ultimate stress-range resistance representing the limit state. (2) Further information is given in ENVs 1992 to 1999.
B.5 Safety concept (1) In general the design of a structure susceptible to fatigue should be such that it is damage-tolerant. To be damage-tolerant the structure should be capable of sustaining all loads with sufficient reliability until cracks can be detected by regular inspections and appropriate remedial measures can be undertaken before structural failure occurs. (2) For structures that can be verified to be damage-tolerant, the safety factor *M on the fatigue resistance side may be taken as 1,00. (3) For structures for which the damage-tolerance cannot be verified, the safety factors have to be chosen such that they take account of the uncertainties in defining the fatigue a ctions, the fatigue action effects, and the fatigue resistances, and also the possible decrease of resistances by corrosion or other time-dependent phenomena, having due regard for the consequences of a failure without pre-warning. (4) Further information on design against fatigue is given in ENVs 1992 to 1999.
Annex C (informative) Serviceability limit state: verification of structures susceptible to vibrations C.1 General C.1.1 Objective (1) This annex gives guidance for serviceability limit state verifications of structures susceptible to vibrations. (2) It deals with the treatment of the action side, the determination of the structural response and the limits to be considered for the structural response to ensure that vibrations are not disturbing or harmful. (3) Dynamic effects relating to ultimate limit states or fatigue are treated in the other Parts of ENV 1991 and therefore are not considered in this annex.
C.1.2 Sources of vibrations (1) Vibrations may be induced by the following: a) people, e.g. on: pedestrian bridges; floors where people walk; floors for sport or dance activities; floors with fixed seating and spectator galleries. b) machines, e.g. on: machine foundations and s upports; bell towers; ground with transmitted vibrations. c) wind, e.g. on: buildings; towers;
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chimneys and masts; guyed masts; pylons; bridges; cantilevered roofs. d) traffic, e.g. on: rail or road bridges; buildings, such as in exhibition halls or car parks. e) earthquakes.
C.1.3 Modelling of actions and structures (1) For serviceability limit states the modelling of these actions and of the structure depends on how the serviceability limits are formulated. (2) These limits may refer to; human comfort; limits for the proper functioning of machines or other installations; maximum deflection limits to avoid damages or pounding. (3) In order to verify that these limits are not exceeded the actions may be modelled in terms of force-time histories, for which the structural responses may then be determined as time histories of deflections or accelerations by using appropriate integration methods. (4) Where the structural response may significantly influence the force-time histories to be applied (e.g. when vehicles are excited to self vibrations by the vibrations of the structure or when synchronising effects of moving masses occur) these interactions have to be considered either in modelling a combined load-structure vibration system or by appropriate modifications of the force-time histories.
C.2 Force-time histories C.2.1 General (1) The force-time histories used in the dynamic analysis should sufficiently represent the relevant loading situations for which the serviceability limits are to be verified. (2) The force-time histories may model: human induced vibrations, e.g. the walking or running of a single person or a number of persons, or dancing or motions in stadia or concert halls; machine induced vibrations, e.g. by force vectors due to mass eccentricities and frequencies, that may be variable with time; wind induced vibrations; traffic loads, e.g. fork-lift trucks, cars or heavy vehicles; crane operations; other dynamic actions such as wave loads or earthquake actions.
C.3 Modelling of structures C.3.1 General (1) The dynamic analysis model to be used for determining the action effects from force-time histories shall be established such that all relevant structural elements, their masses and stiffness and damping ratios are realistically considered. (2) In the case when dynamic actions are caused by the motion of masses (e.g. by persons, machinery etc.) these masses should be included in the analysis (e.g. when determining the eigen frequencies). (3) For other variable actions to be combined with the self weight of the structure the quasi-static values should be used, unless other specifications are given in the identification of the serviceability limit states. (4) Where there is significant ground-structure interaction, the contribution of the soil may be modelled by appropriate equivalent springs and dampers. (5) In general the behaviour of the structure should be taken as linear, unless other specifications are given in defining the limit states.
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(6) Damping ratios should be evaluated by using suitable experimental procedures, approved theoretical methods and values derived from collections of reliable measurements of homogenous structural classes.
C.4 Evaluation of the structural responses C.4.1 General (1) The evaluation of structural responses depends on the limits that are specified for them. (2) Limits may be expressed in terms of: a) r.m.s (root-mean-square) values determined for a certain exposure time (C.1) where: aeff
the effective or r.m.s value or the response e.g. the effective acceleration
T ai
is the exposure time; is the response value (e.g. acceleration) for each time step %ti;
t
is time; is the time step.
%ti
b) extreme values during a certain exposure time T for narrow banded stochastic responses only (C.2) where: n amax
is the natural frequency of the structure is the expected maximum value of the response, e.g. the maximum acceleration
(3) The structural responses aeff or amax should be compared with the specified limits.
C.4.2 Limiting values for vibrations C.4.2.1 Human comfort (1) Where conditions for human comfort are specified, these conditions should be given in terms of an acceptance criteria according to ISO 2631. (2) The acceptance criteria should include the relevant acceleration ( aeff ) – frequency (f s) line for the selected exposure time and direction of vibration.
C.4.2.2 Functioning of machines (1) Limits for the movements of the machines should be specified in terms of maximum deflections and frequency (maximum deflection-frequency lines).
C.4.2.3 Other limits (1) Limits not covered by acceleration-frequency lines or deflection-frequency lines may be: the attainment of a maximum stress ( e.g. to avoid permanent deformations); the attainment of a maximum stress range (e.g. to avoid a limited fatigue life or accumulative deflections); the attainment of a maximum deformation (e.g. to avoid bumping and for continuous operations). These limits should be given in the design specifications.
Annex D (informative) Design assisted by testing D.1 Scope and objectives (1) This annex is intended to give guidance for the planning and evaluation of experiments to be carried out in connection with structural design as indicated in Section 8, when the number of tests is sufficient for a statistical interpretation of their results.
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(2) Testing may be carried out in the following circumstances: if material properties or load parameters are not sufficiently known; if adequate calculation models are not available; if a large number of similar components will be used; if the real behaviour is of special interest; to define control checks assumed in design. (3) The following types of tests are distinguished: a) tests to establish directly the ultimate resistance or serviceability properties of structural parts, e.g. fire tests; b) tests to obtain specific material properties, e.g. ground investigations or testing of new materials; c) tests to reduce uncertainties in load or resistance models, e.g. wind tunnel testing, testing of full-size prototypes, testing of scale models; d) control tests to check the quality of the delivered products or the consistency of the production characteristics, e.g. concrete cube testing; e) tests during execution in order to take account of actual conditions experienced e.g. post-tensioning, soil conditions; f) control tests to check the behaviour of the actual structure or structural elements after completion, e.g. proof loading for the ultimate or serviceability limit states. (4) The results may be used for a specific structure or may serve as a basis for the design of a wide range of structures, including the development of rules in structural codes. (5) Further information on design assisted by testing may be found in ENVs 1992 to 1999.
D.2 Planning Prior to the execution of tests, a test plan should be agreed with the testing organization. This plan should contain the objective of the test and all specifications necessary for the selection or production of the test specimens, the execution of the tests and the test evaluation. In particular, the test plan should deal with the following items. a) Scope The information required from 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 should be specified. b) Expected behaviour It is essential to present a description of all properties and circumstances which may influence the behaviour at the limit state under consideration, e.g. geometrical parameters and their tolerances, material properties, parameters influenced by fabrication and erection procedures, scale effects and environmental conditions. Modes of failure and/or calculation models with the corresponding variables should be described. When the prediction of the critical failure modes to be expected in the tests is extremely doubtful, the test plan should be developed on the basis of accompanying pilot tests. c) Specification of test specimen Properties of the test specimen should be specified; in particular dimensions, material and fabrication of prototypes, number of test specimens, sampling procedures, restraints. Normally a representative sample in the statistical sense should be aimed for. d) Loading specifications Based on item b) loading and environmental conditions in the test should be specified, in particular, loading points, loading paths in time and space, temperatures, loading by deformation or force control, etc. Loading paths should be selected such that they are representative for the anticipated scope of application of the structural member. Account should be taken of possible unfavourable paths and/or of those paths which are considered in calculations in comparable cases. Interactions with structural response should be considered where relevant.
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Where structural properties are conditioned by one or several effects of actions which are not varied systematically, then these effects should be specified at least by their design values. Where they are independent of the other parameters of the loading path, design values related to estimated values of lead combination may be adopted. e) Testing arrangements Special attention should be given to measures to ensure sufficient strength and stiffness of the loading and supporting rigs, and clearance for deflections, etc. f) Measurements A list should be made of all relevant properties of each individual test specimen to be determined prior to the execution of the tests. Similarly a list should be made of observation points and methods for observation and recording, e.g. time histories of displacements, velocities, accelerations, strains, forces and pressures, required frequency and accuracy of measurements and measuring devices. Depending on the type of test it could be recommended to have some measurements available during the test. g) Evaluation and reporting of the test For specific guidance, see ENVs 1992 to 1999.
D.3 Evaluation of test results D.3.1 General (1) All test results should be evaluated critically. The general behaviour and failure modes should be compared with the expected ones. When large deviations from the expectation occurs, an explanation should be sought, involving additional tests if necessary. (2) Where relevant, the evaluation of test results should be on the basis of statistical methods. In principle the tests should lead to a statistical distribution for the preselected unknown variables, including the statistical uncertainties. Based on this distribution, design values, characteristic values and partial safety factors to be used in partial coefficient design may be derived. If possible, only the characteristic value may be derived while the partial factor is taken from normal design procedure (3) If the response (or the strength) of the material depends on the load duration or history, the volume or scale, the environmental conditions, or other non-structural effects, then the calculation model should take these items into account by use of appropriate factors (conversion) and scaling rules. Further guidance may be found in ENVs 1991 to 1999. In particular where codes include implicit safety provisions related to comparable situations, these provisions should also be applied when testing and may give rise to additional safety elements in the formulae. An example is the effect of tensile strength in concrete test specimens, which in many cases is neglected during design. (4) The result of a test evaluation is valid for the specifications and load characteristics considered. Extrapolation to cover other design parameters and loadings requires additional information, e.g. from previous tests or theoretical considerations.
D.3.2 Statistical evaluation of resistance/material tests D.3.2.1 General (1) This clause is intended to give the operational formulae for deriving design values from the test types a) and b) for resistance and material testing [see D.1(3)], where the characteristic value is determined from a standardized or established distribution of the material properties. Use will be made of Bayesian procedures with vague prior distributions. NOTE
This leads to almost the same result as classical statistics with confidence levels equal to 0.75.
(2) In 8.3 two different methods are distinguished. In method a) a characteristic value is derived first and then divided by the relevant partial factor. In method b) a direct determination of the design value is made. These methods are discussed in D.3.2.2 and D.3.2.3 respectively. (3) The tables and formulae in D.3.2.2 and D.3.2.3 are based on: the normal distribution; a complete lack of prior knowledge for the mean; a complete lack of prior knowledge for the coefficient of variation in the case “V x unknown” or, on the other hand, full knowledge for the coefficient of variation in the case “Vx known”.
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In practice there may be prior knowledge that the distribution type is of a more favourable nature (for instance the lognormal distribution) and there might be partial prior knowledge, both about the mean and about the standard deviation. This prior knowledge may be based on previous experience with similar cases and will in general lead to more favourable design values. Further guidance is, however, outside the scope of this annex.
D.3.2.2 Method a) Assessment via the characteristic value n numerical test results is available. The design value of a variable X Assume that a sample of is obtained from:
(D.1) where:
*M )d
is the partial factor for the design; is the design value of the conversion factor;
X k(n) is the characteristic value including statistical uncertainty; mx
is the mean of the sample results
V x
X is the coefficient of variation of ;
kn
is the coefficient following from Table D.1.
The assessment of the conversion factor is strongly dependent on the type of test and the type of material. No further guidance is given here. The partial factor should be selected from the field of application under consideration in the test. kn follows from Table D.1. Table D.1 is based on the 5 % characteristic value and on the normal The value of distribution. Two cases are considered as follows.
i) The coefficient of variation V x is known from pre-knowledge; pre-knowledge might be found from the evaluation of previous tests in comparable situations. What is comparable is determined by engineering judgement. In that case the row “V x known” should be used. The coefficient of variation V x is not known from pre-knowledge, but must be estimated from the sample: (D.2) V x = sx/mx
(D.3)
In this case the row “V x unknown” should be used.
Table D.1 Values of kn for the 5 % characteristic value n
1
2
3
4
5
6
8
10
20
30
Z
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
D.3.2.3 Method b) Direct assessment of the design value In method b) the design value for X follows from: (D.4) The meaning of all variables is the same in D.3.2.2, however, )d should now cover all uncertainties not covered by the tests. The value of kn should now follow from Table D.2 or Table D.3. If is the dominating variable in the resistance model, kn may follow from Table D.2. The table is based on X the assumption that the design value corresponds to ¶ = 3,8 and ! = 0,8 (see Annex A) and that X is normally distributed. This gives a value with about 0 ,1 % probability of observing a lower value.
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If both a design value and a characteristic value are determined, a partial factor can be found from *M = X k/X d. X If is a non-dominating variable, then ! = 0,4 × 0,8 (see Annex A) and Table D.3 should be used. The probability of observing a lower value is about 10 %.
Table D.2 Values of is dominating (P {X < X kn for the ULS design value, if X d} = 0,1 %) n
1
2
3
4
5
6
8
10
20
30
Z
V x known
4,36
3,77
3,56
3,44
3,37
3,33
3,27
3,23
3,16
3,13
3,08
V x unknown
11,40 7,85
6,36
5,07
4,51
3,64
3,44
3,08
Table D.3 Values of is non-dominating (P {X < X kn for the ULS design value, if X d} = 10 %) n
1
2
3
4
5
6
8
10
20
30
Z
V x known
1,81
1,57
1,48
1,43
1,40
1,38
1,36
1,34
1,31
1,30
1,28
V x unknown
3,77
2,18
1,83
1,68
1,56
1,51
1,45
1,36
1,33
1,28
D.3.3 Evaluation of tests for determining model factors (1) In some cases a tentative calculation model is available, but the accuracy of the model is not known or the uncertainty is too large for some fields of application. In those circumstances tests can be carried out to find the statistical characteristics and design values of the model factors test type c as described in D.1(3). This type of testing is often performed in the process of codification of design formulae. It is assumed that the available model, although incomplete, predicts adequately the basic tendencies. In principle the calculation model can range from simple semi-empirical formulae to advanced finite element models. (2) For resistance testing account should be taken of the fact that a structural member may possess a number of fundamentally different failure modes. For example; a girder may fail by bending at midspan or shear at the supports. It is possible that the average strength region is governed by different modes than the low strength region. As the low strength region (e.g. mean value minus two to three standard deviations) is most important in reliability analysis, the modelling of the member should focus on the corresponding mode. (3) Assume that the calculation model available is as follows: R = D Rt (X , W )
(D.5)
where: X W Rt
is the vector of random variables; is the set of measurable deterministic variables; is the theoretical model;
R D
is the measurable result of the experiment; is the unknown coefficient, to be determined by the experiment.
n experiments (i = 1 ... n) is carried out, where: (4) Assume a series of W the values of have been taken equal to wi; X the values of have been measured as xi; R have been measured as r the values of i.
(5) It is recommended that the observed experimental results r i are plotted against the calculated values Rt (x i wi) according to the model and versus each of the observed basic variables. This plotting procedure is intended to check whether the calculation models adequately account for the respective variables. (6) If more than one failure mode is observed in the test results, it is recommended that the tests in a number of series are repeated. In every series all modes but one should be excluded. (7) From the test results the following set of observations for the unknown coefficient D may by derived: di = r i / Rt {x i, wi}
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(D.6)
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(8) It will be assumed that D has a normal distribution. It should be noted that the normal distribution may be replaced by a lognormal distribution, provided that this can be justified from experience with similar tests in the past. D is the same as in D.3.2. For cases where the deterministic (9) The further statistical evaluation of specifications W are varied and/or the random basic variables X are measured indirectly or not at all, specialist literature should be consulted.
D.3.4 Design value for quality control tests (1) Control tests, as defined as test type d in D.1(3), are intended to check the quality of the delivered products or the consistency of the production characteristics. (2) It will be assumed that the product under consideration is produced in batches. A batch is tentatively defined as a set of units, produced by one producer, in a relatively short period, with no obvious changes in production circumstances. (3) For discrete products the definition of a unit is generally self-evident. For continuously produced materials, a unit may be defined as one test specimen, e.g. a concrete test cube. In practice, batches correspond to, for example: a single production of concrete from the same materials and plant; structural steel from one melt processed according to the same conditions; foundation piles for a specific site. (4) Quality control may be performed on every unit (total control) or on samples (batch control). Typically, testing all units requires a non-destructive testing technique. In general a non-destructive testing technique is not able to predict the strength with the same precision as a destructive testing technique. Therefore some kind of measurement error has to be included. In theory there is always a measurement error present, but this can often be ignored. (5) If sampling is used, a random sample is usually taken. In a random sample each unit of the batch has the same probability of being sampled. (6) If quality control is performed on the basis of pre-defined selection rules, the control may lead to three possible outcomes: the batch or unit is rejected: d < 0; the batch or unit is critical: d = 0; the batch or unit is fully acceptable: d > 0. Where d is a function of the test result of a single unit or of the combined test result of the units in a sample. A common formulation for an acceptance rule is given by: mx > X c + 2 n sx
(D.7)
where: mx
is the sample mean;
sx
is the sample standard deviation;
X c
is a fixed value, for instance the required characteristic value;
2 n
is a number, normally depending on n.
From which d = mx – X 2 n sx – c The number of tests n and the parameters 2 n and X c should be determined in such a way that an economical and efficient test is obtained. (7) In practice two requirements are often defined which should be met simultaneously. In those cases the batch is accepted only if for example d1 > 0 and d2 > 0. The second requirement is often related to the lowest observation, and could be of the type: x min > X c
(D.8)
(8) The design value corresponding to given quality control criteria should be calculated on the basis of: the operations characteristic of the control rules; this is the probability of some given batch being accepted;
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the production characteristic; this is the information about the batch-to-batch variation in the uncontrolled supply. General formulae are out of the scope of this annex. (9) Consider by way of example the case that x has a normal distribution, a known standard deviation, that there is no prior knowledge about the mean and that a single criterion [as in expression (D.7)] is present. The design or characteristic value based on the critical batch (having d = 0) is then given by: X kn)Bx k or X d = X c + (2 n –
(D.9)
kn follows from Table D.1, Table D.2 and Table D.3, where “V The value of x known” must be assumed. It should be noted that in most quality control tests there is s ubstantial information on the mean, which leads to more favourable values. This is as also stated in D.3.4(8) and is outside the scope of this annex.
(10) Finally for total or unit-by-unit testing, it is reasonable to expect s ome substantial error, as this is normally carried out by a non-destructive testing procedure. It is assumed here that an error e is present with mean zero and standard deviation Be. It is further assumed that the mean and standard deviation of , either of the batch or the total supply, are known: x (D.10) The result for this case is also conservatively based on the “critical unit” and not on the “arbitrary accepted kn follows from Table D.1, Table D.2, and Table D.3, where “V unit”. The value of known” may be assumed. x
D.3.5 Proof Loading (1) Proof loading is a test on the actual structure, i.e. test type f in D.1(3). Special care should be taken that the structure is not unnecessarily damaged during the test. This requires a continuous monitoring of the load and the response. (2) A distinction is made between: an acceptance test and a strength test. (3) The acceptance test is intended to confirm that the overall structural performance complies with design intentions. The load is raised to values between the characteristic value and the design value for the ultimate limit state. Requirements may be set for the deformations, the degree of non-linearity and the residual deformations after removal of the test loading. (4) The strength test is intended to s how that the structure or the structural element has at least the strength that is assumed in the design. If an assessment for the test element only is required, it is sufficient to raise the load to the design load for the ultimate limit state. Obviously, as already stated in D.3.5(1) care should be taken not to damage the structure unnecessarily. (5) If the strength test is intended to prove that other but similar elements also have the required strength, a higher load is required. A minimum requirement in this respect would be to correct the design load for the presence of better material properties in the tested element, compared to the design values. This means that the material properties of the tested element have to be measured. (6) If the relationship between the resistance and the material property is linear, the design strength Rd corresponding to a successful test with test load F t is: Rd = F t X d / X t
(D.11)
X t is the strength of material in the test.
From the requirement Rd U F d, the minimum test load can be calculated. (7) If it is not possible to measure the material properties, the design value for the resistance can conservatively be found from: Rd = F kn V t (1 – R)
(D.12)
Here V R is the known coefficient of variation f or the resistance of the element population under consideration and kn follows from Table D.2. The case with V x unknown is outside the scope of this annex. (8) It is also possible to use a combination of expressions (D.11) and (D.12), e.g. if only a part of the relevant V random variables can be measured. If is not know by pre-knowledge, a more sophisticated analysis is required. This is outside the scope of this annex.
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