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DRAFT FOR DEVELOPMENT DD ENV 1992-1-2:1996

Eurocode 2: Design of concrete structures —

Part 1.2 General rules — Structural fire design —

(together with United Kingdom National Application Document)

ICS 91.040; 91.080.40

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DD ENV 1992-1-2:1996

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 on15 July 1996

© BSI 03-2000

The following BSI references relate to the work on this Draft for Development:Committee reference B/525/2

ISBN 0 580 25809 2

Committees responsible for this Draft for Development

The preparation of this Draft for Development was entrusted by Technical Committee B/525, Building and civil engineering structures, to Subcommittee B/525/2, Structural use of concrete, upon which the following bodies were represented:

Association of Consulting EngineersBritish Cement AssociationBritish Precast Concrete Federation Ltd.Department of the Environment (Property and Buildings Directorate)Department of Transport (Highways Agency)Federation of Civil Engineering ContractorsInstitution of Civil EngineersInstitution of Structural EngineersSteel Reinforcement Commission

Amendments issued since publication

Amd. No. Date Comments

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Contents

PageCommittees responsible Inside front coverNational foreword iiForeword 2Text of National Application Document vText of ENV 1992-1-2 7

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National foreword

This Draft for Development was prepared by Subcommittee B/525/2 and is the English language version of ENV 1992-1-2:1995 Eurocode 2: Design of concrete structures — Part 1.2: General rules — Structural fire design, as published by the European Committee for Standardization (CEN). This Draft for Development also includes the United Kingdom (UK) National Application Document (NAD) to be used with the ENV in the design of buildings to be constructed in the UK.ENV 1992-1-2 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 building and civil engineering works.This publication should not be regarded as a British Standard.An ENV 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 publication of this ENV and its National Application Document should be considered to supersede any reference to a British Standard in previous DD ENV Eurocodes concerning the subject covered by these documents.The values for certain parameters in the ENV Eurocodes may be set by individual CEN Members so as to meet the requirements of national regulations. These parameters are designated by|_|in the ENV.During the ENV period of validity, reference should be made to the supporting documents listed in the National Application Document (NAD).The purpose of the NAD is to provide essential information, particularly in relation to safety, to enable the ENV to be used for buildings constructed in the UK and the NAD takes precedence over corresponding provisions in the ENV.The Building Regulations 1991, Approved Document A 1992, draws attention to the potential use of ENV Eurocodes as an alternative approach to Building Regulation compliance. ENV 1992-1-2 is considered to offer such an alternative approach, when used in conjunction with its NAD.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 to an EN.Comments should be sent in writing to the Secretary of Subcommittee B/525/2, BSI, 389 Chiswick High Road, London W4 4AL, quoting the document reference, the relevant clause and, where possible, a proposed revision, by 31 October 1996.

Summary of pagesThis document comprises a front cover, an inside front cover, pages i to x, the ENV title page, pages 2 to 63 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.

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© BSI 03-2000 iii

National Application Document for use in the UK with ENV 1992-1-2:1995

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Contents of National Application Document

PageIntroduction v1 Scope v2 Partial factors, combination factors and other values v3 Tabulated data v4 Reference standards x5 Additional recommendations xTable 1 — Values to be used in referenced clauses instead of boxed values vTable N4.1 — Minimum dimensions and axis distances for reinforced concrete columns; rectangular and circular section vTable N4.2 — Minimum wall thickness of non load-bearing walls (partitions) viTable N4.3 — Minimum dimensions and axis distances for load-bearing reinforced concrete walls viTable N4.4 — Minimum dimensions and axis distances for reinforced and prestressed concrete tensile members viTable N4.5 — Minimum dimensions and axis distances for simply supported beams made with reinforced and prestressed concrete viiTable N4.6 — Minimum dimensions and axis distances for continuous beams made with reinforced and prestressed concrete viiTable N4.7 — Reinforced and prestressed concrete continuous I beams: increased beam width and web thickness for conditions according to Table N4.6 viiiTable N4.8 — Minimum dimensions and axis distances for reinforced and prestressed concrete simply supported one-way and two-way slabs viiiTable N4.9 — Minimum dimensions and axis distances for reinforced and prestressed concrete flat slabs viiiTable N4.10 — Minimum dimensions and axis distance for two-way spanning, simply supported ribbed slabs in reinforced or prestressed concrete ixTable N4.11 — Minimum dimensions and axis distances for two-way spanning ribbed slabs in reinforced or prestressed concrete with at least one restrained edge ixTable 2 — Reference in EC2-1.2 to other codes and standards x

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IntroductionThis National Application Document (NAD) has been prepared by Subcommittee B/525/2. It has been developed from the following.

a) A textual examination of ENV 1992-1-2.b) A parametric calibration against BS 8110, supporting standards and test data.c) Trial calculations.

1 ScopeThis NAD provides information to enable ENV 1992-1-2 (hereafter referred to as EC2-1.2) to be used for the design of buildings to be constructed in the UK. It is assumed that it will be used in conjunction with DD ENV 1992-1-1, the NAD of which refers to BSI publications for values of actions. Since publication of ENV 1992-1-1 (hereafter referred to as EC2-1.1), ENVs for actions (Parts of Eurocode 1) have been published. Where appropriate this NAD refers to them. It should be borne in mind that designs should be consistent in their use of UK and CEN standards for all parameters.

2 Partial factors, combination factors and other valuesa) The values for combination coefficients (Ó) should be those given in Table 1 of the NAD for EC2-1.1.b) The values for partial factors for normal temperature design should be those given in EC2-1.1 except where modified by the NAD for that code.The values for partial factors for fire design should be those given in EC2-1.2. For thermal and mechanical actions reference should be made to ENV 1991-2-2 (hereafter referred to as EC1-2.2) and its NAD.c) Other values should be those given in EC2-1.1, except where modified by the NAD for that code, and in EC2-1.2 except for those given in Table 1 of this NAD.

Table 1 — Values to be used in referenced clauses instead of boxed values

3 Tabulated dataTables 4.1 to 4.11 of EC2-1.2:1995 are replaced with Table N4.1 to Table N4.11 respectively as given below. All the tables in 4.2 of EC2-1.2:1995 have been reproduced, regardless of whether changes have been made, to avoid unnecessary cross referencing. Changes in values from those given in EC2-1.2 are shown in bold. These changes largely reflect the current values in BS 8110.

Table N4.1 — Minimum dimensions and axis distances for reinforced concrete columns; rectangular and circular section

Reference in EC2-1.2 Definition UK values

4.2.3 (4) Limit to fire resistance for distribution bars along sides of columns 120 min.

4.2.7.4 (2) Minimum top reinforcement over span in column strip 10 %

Standard fire resistance

Minimum dimensionsmm

Column width bmin/axis distance a

Column exposed on more than one side Exposed on one side

Èfi = 0.2 Èfi = 0.5 Èfi = 0.7 Èfi = 0.7

1 2 3 4 5

R 30R 60R 90R 120R 180R 240

150/10a

150/10a

180/10a

200/40240/50300/50

150/10a

180/10a

210/10a

250/40320/50400/50

150/10a

200/10a

240/35280/40360/50450/50

100/10a

120/10a

140/10a

160/45200/60300/60

a Normally the cover required by ENV 1992-1-1 will control.

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Table N4.2 — Minimum wall thickness of non load-bearing walls (partitions)

Table N4.3 — Minimum dimensions and axis distances for load-bearing reinforced concrete walls

Table N4.4 — Minimum dimensions and axis distances for reinforced and prestressed

concrete tensile members

Standard fire resistanceMinimum wall thickness

mm

1 2

EI 30EI 60EI 90EI 120EI 180EI 240

6080

100120150175

Standard fire resistance

Minimum dimensionsmm

Wall thickness/axis distance for

Èf = 0.35 Èf = 0.7

Wall exposed on one side

Wall exposed on two sides

Wall exposed on one side

Wall exposed on two sides

1 2 3 4 5

REI 30REI 60REI 90REI 120REI 180REI 240

100/10a

110/10a

120/20a

150/25180/35230/45

120/10a

120/10a

140/10a

160/25200/35250/45

120/10a

130/10a

140/25160/35210/45270/55

120/10a

140/10a

170/25220/35250/45300/55

a Normally the cover required by ENV 1992-1-1 will control.

Standard fire resistance

Minimum dimensionsmm

Possible combinations of member width bmin/axis distance a

1 2 3

R 30R 60R 90R 120R 180R 240

80/25120/40150/55200/65240/80280/90

200/10a

300/25400/45500/45600/60700/70

NOTE For prestressed members the increase of axis distance according to 4.2.2(4) should be noted.a Normally the cover required by ENV 1992-1-1 will control.

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Table N4.5 — Minimum dimensions and axis distances for simply supported beams made with reinforced and prestressed concrete

Table N4.6 — Minimum dimensions and axis distances for continuous beams made with reinforced and prestressed concrete

Standard fire resistance

Minimum dimensionsmm

Possible combinations of a and bmin where a is the average axis distance and bmin is the width of beam Web thickness bw

1 2 3 4 5 6

R 30 bmin 80 120 160 200 80a 25 15a 10a 10a

R 60 bmin 120 160 200 300 100a 40 35 30 25

R 90 bmin 150 200 250 400 100a 55 45 40 35

R 120 bmin 200 240 300 500 120a 65 55 50 45

R 180 bmin 240 300 400 600 140a 80 70 65 60

R 240 bmin 280 350 500 500 160a 90 80 75 70

asd = a + 10 mm(see note 2.)NOTE 1 For prestressed beams the increase of axis distance according to 4.2.2(4) of this Part 1-2 should be noted.NOTE 2 asd is the axis distance to the side of beam for the corner bars (tendon or wire) of beams with only one layer of reinforcement. For values of bmin greater than that given in column 4 no increase of a is required.a Normally the cover required by ENV 1992-1-1 will control.

Standard fire resistance

Minimum dimensions

mmPossible combinations of a and bmin where a is the average

axis distance and bmin is the width of beam Web thickness bw

1 2 3 4 5

R 30 bmin 80 160 200 80a 12a 12a 12a

R 60 bmin 120 200 300 100a 25 12a 12a

R 90 bmin150 250 400 100a 35 25 25

R 120 bmin 180 300 450 120a 55 45 35

R 180 bmin 225 350 550 140a 70 60 50

R 240 bmin 275 450 650 160a 80 70 60

asd = a + 10 mm(see note 2.)NOTE 1 For prestressed beams the increase of axis distance according to 4.2.2(4) should be noted.NOTE 2 asd is the axis distance to the side of beam for the corner bars (tendon or wire) of beams with only one layer of reinforcement. For values of bmin greater than that given in column 3 no increase of a is required.a Normally the cover required by ENV 1992-1-1 will control.

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Table N4.7 — Reinforced and prestressed concrete continuous I beams: increased beam width and web

thickness for conditions according to Table N4.6

Table N4.8 — Minimum dimensions and axis distances for reinforced and prestressed concrete simply supported one-way and two-way slabs

Table N4.9 — Minimum dimensions and axis distances for reinforced and prestressed concrete flat slabs

Standard fire resistance

Minimum beam width bmin and web thickness bw

mm

1 2

R 120 220R 180 380R 240 480

Standard fire resistanceMinimum dimensions

mm

Slab thickness hs

mm

Average axis-distance aOne way Two way:

ly/lx u 1.5 1.5 u ly/lx u 2

1 2 3 4 5

REI 30 60 10a 10a 10a

REI 60 80 20 10a 15a

REI 90 100 30 15a 20REI 120 120 40 20 25REI 180 150 55 30 40REI 240 175 65 40 50NOTE 1 lx and ly are the spans of a two-way slab (two directions at right angles) where ly is the longer spanNOTE 2 The minimum cover of any bar should not be less than half of required average axis distance, am’ defined in 4.2.2.NOTE 3 For prestressed slabs the increase of axis distance according to 4.2.2(4) should be noted.NOTE 4 The axis distance, a, in columns 4 and 5 for two way slabs relate to slabs supported at all four edges. Otherwise, they should be treated as one-way spanning slab.a Normally the cover required by ENV 1992-1-1 will control.

Standard fire resistance

Minimum dimensions

mm

Slab thickness hs Axis-distance a

1 2 3

REI 30 75 10a

REI 60 95 15a

REI 90 110 25

REI 120 125 35

REI 180 150 45

REI 240 170 50a Normally the cover required by ENV 1992-1-1 will control.

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Table N4.10 — Minimum dimensions and axis distance for two-way spanning, simply supported ribbed slabs in reinforced or prestressed concrete

Table N4.11 — Minimum dimensions and axis distances for two way spanning ribbed slabs in reinforced or prestressed concrete with at least one restrained edge

Standard fire resistance

Minimum dimensions

mm

Possible combinations of width of ribs bmin and axis distance a

Slab thickness hs and axis distance a, in span

1 2 3 4 5

REI 30 bmin W 80 hs 80a 15a a 10a

REI 60 bmin 100 120 W 200 hs 80a 35 25 15a a 10a

REI 90 bmin 120 160 W 250 hs 100a 45 40 30 a 15a

REI 120 bmin 140 190 W 300 hs 120a 60 55 40 a 20

REI 180 bmin 170 260 W 410 hs 150a 75 75 60 a 30

REI 240 bmin 200 350 W 500 hs 175a 90 75 70 a 40

asd = a + 10 mmNOTE 1 For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4)NOTE 2 asd denotes the distance measured between the axis of the reinforcement and the lateral surface of the rib exposed to fire.a Normally the cover required by ENV 1992-1-1 will control.

Standard fire resistance

Minimum dimensions

mm

Possible combinations of width of ribs bmin and axis distance a

Slab thickness hs and axis distance a, in span

1 2 3 4 5

REI 30 bmin W 80 hs 80a 10a a 10a

REI 60 bmin 100 120 W 200 hs 80a 25 15a 10a a 10a

REI 90 bmin 120 160 W 250 hs 100a 35 25 15a a 15a

REI 120 bmin 140 190 W 300 hs 120a 45 40 30 a 20

REI 180 bmin 175 300 W 400 hs 150a 60 50 40 a 30

REI 240 bmin 200 400 W 500 hs 175a 70 60 50 a 40

asd = a + 10 mmNOTE 1 For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).NOTE 2 asd denotes the distance measured between the axis of the reinforcement and the lateral surface of the rib exposed to fire.a Normally the cover required by ENV 1992-1-1 will control.

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4 Reference standardsSupporting standards including materials specifications and standards for construction are listed inTable 2 of this NAD.

Table 2 — Reference in EC2 Part 1.2 to other codes and standards

5 Additional recommendations5.1 Chapter 4. Structural fire design

a) Clause 4.2.2(4)Current British practice assumes a less conservative increase in axis distance, a, from that given in this clause. The second sentence onwards of this clause may be replaced with the following:If no special check according to (4) is made in prestressed tensile members and beams the required axis distance, a, should be increased by:

10 mm for prestressing bars, corresponding to Ûcr = 400 °C;

15 mm for prestressing wires and strands, corresponding to Ûcr = 350 °C.

If no special check according to (4) is made in prestressed simply supported slabs (including simply supported ribbed slabs) the required axis distance, a, may be increased by 5 mm for prestressing bars, wires and strands.If no special check according to (4) is made in prestressed continuous slabs (including continuous ribbed slabs) the required axis distance, a, should be increased by:

5 mm for prestressing bars;10 mm for prestressing wires and strands.

b) Clause 4.2.2(14)Current British practice assumes a less conservative increase in axis distance, a, from that given in this clause. The value of %ap in equation (4.6) may be assumed as follows:

c) Clause 4.2.7.1(4) — additionThe effective thickness, he, of hollow concrete slabs should be obtained by considering the total solid part of the cross-section area as follows:

he = h1. M0.7 (4.12A)

where

Reference in EC2-1.2 Document referred to Subject area Status

Various ENV 1992-1-1 Design of concrete structures. General rules and rules for buildings

Published 1991

Various ENV 1991-2-1 Thermal and mechanical actions Published 1995

1.1(1)P 2.4.3(4) ENV 1991-2-2 Design for accidental situation of fire exposure Published 1995

1.3(1) ISO 834 Standards for fire tests Published 1975

1.4.12 ENV 1991-1 Fundamental combination of actions Published 1994

4.2.4.2(2) ENV 1992-1-6 Minimum thickness of plain concrete walls Published 1994

%ap = 5 mm for prestressing bars;= 15 mm for prestressing wires and strands.

h1 is the total thickness of concrete slab (See Figure 4.7 of EC2-1.2);M is the proportion of concrete cross section area to the total cross section area of

concrete slab including voids.

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EUROPEAN PRESTANDARD

PRÉNORME EUROPÉENNE

EUROPÄISCHE VORNORM

ENV 1992-1-2:1995

November 1995

ICS 91.040.00; 91.080.40

Descriptors: Buildings, concrete structure, design, computation, fire resistance

English version

Eurocode 2: Design of concrete structures — Part 1-2: General rules — Structural fire design

Eurocode 2: Calcul des structures en béton — Partie 1-2: Règles générales — Calcul du comportement au feu

Eurocode 2: Planung von Stahlbeton- und Spannbetontragwerken — Teil 1-2: Allgemeine Regeln — Tragwerksbemessung für den Brandfall

This European Prestandard (ENV) was approved by CEN on 1994-01-14 as aprospective standard for provisional application. The period of validity of thisENV is limited initially to three years. After two years the members of CENwill be requested to submit their comments, particularly on the questionwhether the ENV can be converted into an European Standard (EN).CEN members are required to announce the existence of this ENV in the sameway as for an EN and to make the ENV available promptly at national level inan appropriate form. It is permissible to keep conflicting national standards inforce (in parallel to the ENV) until the final decision about the possibleconversion 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 andUnited Kingdom.

CEN

European Committee for StandardizationComité Européen de NormalisationEuropäisches Komitee für Normung

Central Secretariat: rue de Stassart 36, B-1050 Brussels

© 1995 All rights of reproduction and communication in any form and by any means reserved in all countries to CEN and its members

Ref. No. ENV 1992-1-2:1995 E

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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 the methods of testing their performance are available, some of the Structural Eurocodes cover some of these aspects in informative Annexes.Background of the Eurocode program(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”.(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/TC250 is responsible for all Structural Eurocodes.Eurocode program(7) Work is in hand on the following Structural Eurocodes, each generally consisting of a number of parts:

EN 1991, Eurocode 1: Basis of design and actions on structures.EN 1992, Eurocode 2: Design of concrete structures.EN 1993, Eurocode 3: Design of steel structures.EN 1994, Eurocode 4: Design of composite steel and concrete structures.EN 1995, Eurocode 5: Design of timber structures.EN 1996, Eurocode 6: Design of masonry structures.EN 1997, Eurocode 7: Geotechnical design.EN 1998, Eurocode 8: Design provisions for earthquake resistance of structures.EN 1999, Eurocode 9: Design of aluminium alloy structures.

(8) Separate subcommittees have been formed by CEN/TC250 for the various Eurocodes listed above.(9) This Part 1-2 of Eurocode 2 is being published as a European Prestandard (ENV) with an initial life of three years.(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/TC250/SC2 at the following address:

Deutsches Institut für Normung e.V. (DIN)Burggrafenstrasse 6D-10787 BerlinPhone:(+49) 30 2601 2501Fax:(+49) 30 2601 1231

or to your national standards organisationNational Application Documents (NAD’S)(13) In view of the responsibilities of authorities in member countries for safety, health and other matters covered by the essential requirements of the Construction Products Directive (CPD), certain safety elements in this ENV have been assigned indicative values which are identified by|_|(“boxed values”). The authorities in each member country are expected to assign definitive values to these safety elements.(14) Some of the supporting European or International Standards may not be available by the time this Prestandard is issued. It is therefore anticipated that a National Application Document (NAD) giving definitive values for safety elements, referencing compatible supporting standards and providing national guidance on the application of this Prestandard, will be issued by each member country or its Standards Organisation.(15) It is intended that this Prestandard is used in conjunction with the NAD valid in the country where the building or civil engineering works is located.Matters specific to this prestandard(16) The scope of Eurocode 2 is defined in 1.1.1 of ENV 1992-1-1 and the scope of this Part of Eurocode 2 is defined in 1.1. Additional Parts of Eurocode 2 which are planned are indicated in 1.1.3 of ENV 1992-1-1; these will cover additional technologies or applications, and will complement and supplement this Part.

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(17) In using this Prestandard in practice, particular regard should be paid to the underlying assumptions and conditions given in 1.3 of ENV 1992-1-1.(18) The provisions of this Prestandard are based substantially on recent CEB and FIP documents.(19) This Part 1-2 of Eurocode 2 complements ENV 1992-1-1 for the particular aspects of structural fire design of concrete structures. The provisions in this Part 1-2 have to be considered additionally to those in other Parts of ENV 1992.(20) The framework and structure of this Part 1-2 do not correspond to ENV 1992-1-1.(21) This Part 1-2 contains five sections and four informative Annexes. These Annexes have been introduced by moving some of the more detailed Application Rules, which are needed in particular cases, out of the main part of the text to aid its clarity.(22) Required functions and levels of performance are generally specified by the National Authorities — mostly in terms of standard fire resistance rating. Where fire safety engineering for assessing passive and active measures is accepted, requirements by authorities will be less prescriptive and may allow for alternative strategies.

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Contents

PageForeword 21 General 71.1 Scope 71.2 Distinction between principles

and application rules 71.3 Normative References 71.4 Definitions 71.5 Symbols 101.6 Units 102 Basic principles 112.1 Performance requirements 112.2 Actions 112.3 Design values of material properties 112.4 Verification methods 122.4.1 General 122.4.2 Global structural analysis 122.4.3 Analysis of parts of the structure 122.4.4 Member analysis 132.4.5 Testing 133 Material properties 143.1 General 143.2 Concrete 143.3 Steel 144 Structural fire design 174.1 General 174.2 Tabulated data 174.2.1 Scope 174.2.2 General design rules 184.2.3 Columns 204.2.4 Walls 214.2.5 Tensile members 224.2.6 Beams 234.2.7 Slabs 274.3 Simplified calculation method 314.3.1 General 314.3.2 Temperature profiles 324.3.3 Reduced cross section 324.4 General calculation methods 354.4.1 General 354.4.2 Thermal response 354.4.3 Mechanical response 354.4.4 Validation of general calculation method 364.5 Shear and torsion 36

Page4.6 Anchorage 365 Protective layers 37Annex A (informative) Additional information on material properties 38Annex B (informative) Temperature profiles and reduced cross section 54Annex C (informative) Simplified method of calculation for beams and slabs 58Annex D (informative) A procedure for assessing the structural response of reinforced concrete elements under fire 59Figure 2.1 — Variation of ½fi as a function of ß = Qk1/Gk for different values of Ó1,1 13Figure 3.1 — Coefficient kc(G) allowing for decrease of compressive strength (fck) of silicious concrete at elevated temperature 15Figure 3.2 — Coefficient ks(G) allowing for decrease of characteristic strength (fyk) of reinforcing steels at elevated temperature 16Figure 3.3 — Coefficient kp(G) allowing for decrease of characteristic strength (fpk) of prestressing steels at elevated temperature 16Figure 4.1 — Sections through structural members, showing nominal axis distance a, and nominal concrete cover c to reinforcement 19Figure 4.2 — Dimensions used to calculate average axis distance am 19Figure 4.3 — Exposure of built-in columns 21Figure 4.4 — Definition of dimensions for different types of beam section 23Figure 4.5 — I-shaped beam with increasing web width bw satisfying the requirements of an imaginary cross-section 24Figure 4.6 — Envelope of resisting bending moments over supports in fire conditions 25Figure 4.7 — Concrete slab with floor finishes 27Figure 4.8 — Slab systems for which minimum reinforcement areas according to 4.2.7.3 (3) should be provided 29Figure 4.9 — Reductions of strength and cross-sections found by means of equivalent walls (wall1 and wall2) exposed to fire on both sides 33Figure 4.10 — Divisions of a wall, exposed on both sides, into zones for use in calculation of strength reduction and az values 34

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PageFigure A.1 — Coefficient kct(G) allowing for decrease of tensile strength, (fctk) of concrete at elevated temperature 38Figure A.2 — Model for compression stress-strain relationships of siliceous and calcareous concrete at elevated temperatures 39Figure A.3 — Parameters for stress-strain relationships of concrete at elevated temperatures, according to Figure A.2 and Table A.1 40Figure A.4 — Stress-strain relationships of siliceous concrete under uniaxial compression at elevated temperatures 41Figure A.5 — Model for stress-strain relationships of reinforcing and prestressing steels at elevated temperatures (notations for prestressing steels “p” instead of “s”) 42Figure A.6 — Stress-strain relationships of hot-rolled reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.3 45Figure A.7 — Parameters for stress-strain relationships of hot-rolled reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.3 45Figure A.8 — Stress-strain relationships for cold-worked reinforcing steels at elevated temperatures, according toFigure A.5 and Table A.4 46Figure A.9 — Parameters for stress-strain relationships of cold-worked reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.4 47Figure A.10 — Stress-strain relationships for quenched and tempered prestressing steels (bars) at elevated temperatures, according to Figure A.5 and Table A.5 47Figure A.11 — Parameters for stress-strain relationships of quenched and tempered prestressing steels (bars) at elevated temperatures, according to Figure A.5; and Table A.5 48Figure A.12 — Stress-strain relationships for cold-worked prestressing steels (wires and strands) at elevated temperatures, according to Figure A.5 and Table A.6 48Figure A.13 — Parameters for stress-strain relationships of cold-worked prestressing steels (wires and strands) at elevated temperatures, according to Figure A.5 and Table A.6 49

PageFigure A.14 — Thermal elongation of concrete 50Figure A.15 — Specific heat of concrete 51Figure A.16 — Thermal conductivity of concrete 51Figure A.17 — Thermal elongation of steel 53Figure A.18 — Relationship between Öc,fi and h (or b) for risk of explosive spalling for normal weight concrete members 54Figure B.1 — Temperature profiles for beams 55Figure B.2 — Temperature profiles for slabs 56Figure B.3 — Reduction in cross section and concrete strength assuming a standard fire 57Figure C.1 — Positioning the free bending moment diagram MSd,fi to establish equilibrium 59Figure D.1 — Temperature profiles in concrete elements. Gm is the average temperature along a horizontal section y-y 60Figure D.2 — Layers of thermo-elements assumed free to move axially 60Figure D.3 — Hypothetical and equalising forces 61Figure D.4 — Final internal self-equilibrating stresses 62Figure D.5 — Equivalent temperature values Geff for typical reinforced concrete sections exposed to a standard fire 63Table 4.1 — Minimum dimensions and axis distances for reinforced concrete columns; rectangular and circular section 21Table 4.2 — Minimum wall thickness of non load-bearing walls (partitions) 22Table 4.3 — Minimum dimensions and axis distances for load-bearing reinforced concrete walls 22Table 4.4 — Minimum dimensions and axis distances for reinforced and prestressed concrete tensile members 23Table 4.5 — Minimum dimensions and axis distances for simply supported beams made with reinforced and prestressed concrete 26Table 4.6 — Minimum dimensions and axis distances for continuous beams made with reinforced and prestressed concrete 26Table 4.7 — Reinforced and prestressed concrete continuous I-beams; increased beam width and web thickness for conditions according to 4.2.6.3 (6) 27Table 4.8 — Minimum dimensions and axis distances for reinforced and prestressed concrete simply supported one-way and two-way slabs 28

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PageTable 4.9 — Minimum dimensions and axis distances for reinforced and prestressed concrete flat slabs 29Table 4.10 — Minimum dimensions and axis distance for two-way spanning, simply supported ribbed slabs in reinforced or prestressed concrete 30Table 4.11 — Minimum dimensions and axis distances for two-way spanning ribbed slabs in reinforced or prestressed concrete with at least one restrained edge 31Table A.1 — Values for the main parameters of the stress-strain relationships in compression of siliceous and calcareous concrete at elevated temperatures (range I in Figure A.2) 39Table A.2 — Recommended values for ºc1(G) and ºcu(G) and admissible range of ºc1(G) 41Table A.3 — Values for the parameters of the stress-strain relationship of hot rolled reinforcing steel 43Table A.4 — Values for the parameters of the stress-strain relationship of cold worked reinforcing steel 43Table A.5 — Values for the parameters of the stress-strain relationship of quenched and tempered prestressing steel 44Table A.6 — Values for the parameters of the stress-strain relationship of cold worked prestressing steel 44

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1 General

1.1 Scope(1)P ENV 1992-1-2 deals with the design of concrete structures for the accidental situation of fire exposure and shall be used in conjunction with ENV 1992-1-1 and ENV 1991-2-2. It provides additions to and identifies differences from the design of structures at normal temperatures.(2)P Part 1-2 applies only to passive methods of fire protection. Active methods are not included.(3)P Part 1-2 applies to structures which for reasons of general fire safety, are required to fulfil the following criteria when exposed to fire:

— avoid premature collapse of the structure (load-bearing function)— limit fire spread (flames, hot gases, excessive heat) beyond designated areas (separation function)

(4)P Part 1-2 gives Principles and Application Rules (see 1.2 in ENV 1992-1-1) in respect to the design of structures to fulfil the criteria given in (3)P (e.g. in terms of required standard fire resistance).(5)P Part 1-2 applies to those structures or parts of structures which are within the scope of Part 1-1, 1-3 to 1-6. However, it does not cover:

— structures with prestressing by external tendons— shell structures.

(6) For structures using unbonded tendons reference should be made to 4.1(6) and 4.2.2(6).

1.2 Distinction between principles and application rules(1) Depending on the character of the individual clauses, distinction is made in this Part between principles and application rules.(2) The principles comprise:

— general statements and definitions for which there is no alternative, as well as— requirements and analytical models for which no alternative is permitted unless specifically stated.

(3) The principles are identified by the letter P following the paragraph number.(4) The application rules are generally recognized rules which follow the principles and satisfy their requirements.(5) It is permissible to use alternative rules different from the application rules given in this Eurocode, provided it is shown that the alternative rules accord with the relevant principles and have at least the same reliability.(6) In this Part the application rules are identified by a number in brackets eg. as this clause.

1.3 Normative references(1) European standards for fire tests are under preparation. In National Application Documents reference may be made to national or International Standards. For structural members ISO 834 is generally used.

1.4 Definitions1.4.1 critical temperature of reinforcement

the temperature at which failure is expected to occur in reinforcement at a given load level

1.4.2 design fire

a specified fire development assumed for design purposes

1.4.3 effects of actions E (as described in ENV 1992-1-1, 2.2.2.5)

the effects of actions (E) are responses (for example internal forces and moments, stresses, strains) of the structure to the actions

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1.4.4 fire compartment

a space within a building extending over one or several floors which is enclosed by separating members such, that fire spread beyond the compartment is prevented during the relevant fire exposure

1.4.5 fire resistance

the ability of a structure or part of it to fulfil its required functions (load-bearing and/or separating function) for a specified fire exposure, for a specified period of time

1.4.6 global structural analysis (for fire)

the analysis of the entire structure, when either the entire structure or only parts of it are exposed to fire. Indirect fire actions are considered throughout the structure

1.4.7 indirect fire actions

thermal expansions or thermal deformations causing forces and moments

1.4.8 integrity criterion “E”

a criterion by which the ability of a separating member to prevent passage of flames and hot gases is assessed

1.4.9 load-bearing criterion “R”

a criterion by which the ability of a structure or a member to sustain specified actions during the relevant fire, is assessed

1.4.10 load-bearing function

the ability of a structure or member to sustain specified actions during the relevant fire

1.4.11 member analysis (for fire)

the thermal and mechanical analysis of a structural member exposed to fire in which the member is considered as isolated with appropriate support and boundary conditions. Indirect fire actions are not considered, apart from those resulting from thermal gradients

1.4.12 normal temperature design

ultimate limit state design for ambient temperatures according to ENV 1992-1-1 for the fundamental combination of actions (see ENV 1991-1)

1.4.13 protected members

members for which measures are taken to reduce the temperature rise in the member due to fire

1.4.14 separating function

the ability of a separating member to prevent fire spread by passage of flames or hot gases (integrity) or ignition beyond the exposed surface (thermal insulation) during the relevant fire

1.4.15 separating members

structural and non-structural members (walls or floors) forming the enclosure of a fire compartment

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1.4.16 standard fire resistance

the ability of a structure or part of it (usually only members) to fulfil required functions (load-bearing function and/or separating function) for exposure to heating according to the standard temperature-time curve, for a stated period of time

1.4.17 structural members

the load-bearing members of a structure including bracings

1.4.18 sub-assembly analysis (for fire)

the structural analysis of parts of the structure exposed to fire in which the respective part of the structure is considered as isolated with appropriate support and boundary conditions. Indirect fire actions within the sub-assembly are considered, but time-dependent interaction with other parts of the structure is not consideredNOTE 1 Where the effects of indirect fire actions within the sub-assembly are negligible, sub-assembly analysis is equivalent to member analysis.NOTE 2 Where the effects of indirect fire actions between sub-assemblies are negligible, sub-assembly analysis is equivalent to global structural analysis.

1.4.19 support and boundary conditions

description of restraints at supports and boundaries for structural modelling

1.4.20 temperature analysis

the procedure to determine the temperature development in members on the basis of thermal actions and the thermal material properties of the members and of the protective layers, where relevant

1.4.21 temperature-time curves

gas temperatures in the environment of member surfaces as a function of time. They may be either— Nominal: Conventional curves, adopted for classification or verification of fire resistance, e.g. the standard temperature-time curve.— Parametric: Determined on the basis of fire models and the specific physical parameters defining the conditions in the fire compartment.

1.4.22 thermal actions

actions on the structure described by the net heat flux to the members

1.4.23 thermal insulation criterion “I”

a criterion by which the ability of a separating member to prevent excessive transmission of heat is assessed

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1.5 SymbolsThe following symbols supplement those given in ENV 1992-1-1:

1.6 Units(1) Temperature G in degrees Celsius (°C)

Temperature difference in kelvins (K)Specific heat c in joule per kilogramme per kelvin (J/kgK)Coefficient of thermal conductivity Æ in watts per metre per kelvin (W/mK)

Ed,fi design effect of actions in the fire situationEd design effect of actions for normal temperature designRd,fi design load bearing capacity (resistance) in the fire situation Rd,fi(t) at a given time t.R 30 or R 60,... a member meeting the load-bearing criterion for 30, or 60... minutes in standard fire exposureE 30 or E 60,... a member meeting the integrity criterion for 30, or 60... minutes in standard fire exposureI 30 or I 60,... a member meeting the thermal insulation criterion for 30, or 60... minutes in standard fire exposureXk characteristic value of a strength or deformation property for normal temperature designXd,fi design strength or deformation property in the fire situationa axis distance of the steel from the nearest exposed surfacec specific heat (characteristic value) [J/kgK]fck(G) characteristic value of compressive strength of concrete at temperature G for a specified strainfpk(G) characteristic value of strength of prestressing steel at temperature G for a specified strainfsk(G) characteristic strength of reinforcing steel at temperature G for a specified straink(G) = Xk,(G)/Xk reduction factor to describe a strength or deformation property at temperature Gt time of fire exposure (min)YM,fi partial safety factor for a material in fire design½fi = Ed,fi/Ed ratio of design effect of actions in the fire situation to that in normal designºs,fi strain of the reinforcing or prestressing steel at temperature G.Æ thermal conductivity (characteristic value) [W/mK]Èfi = Ed,fi/Rd,fi(0) ratio of design effect of actions in the fire situation to the design resistance of the structural element at time t = 0Öc,fi compressive stress of concrete in fire situationÖs,fi steel stress in fire situationG temperature [°C]Gcr critical temperature [°C]

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2 Basic principles

2.1 Performance requirements(1)P Where structures are required to have mechanical resistance under fire conditions, they shall be designed and constructed in such a way that they maintain their load bearing function during the relevant fire exposure — Criterion “R”.(2)P Where compartmentation is required, the members forming the compartment, including joints, shall be designed and constructed in such a way that they maintain their separating function during the relevant fire exposure, i.e.

— no integrity failure due to cracks, holes or other openings, which are large enough to cause fire penetration by hot gases or flame — Criterion “E”— no insulation failure due to temperatures of the non-exposed surface exceeding ignition temperatures — Criterion “I”.

(3) Criterion “I” may be assumed to be met where the average temperature rise over the whole of the non-exposed surface during the standard fire exposure does not exceed 140K and the maximum temperature rise of that surface does not exceed 180K.(4)P Members shall comply with criteria R, E and I as follows:

separating only: E and Iloadbearing only: Rseparating and loadbearing: R, E and I

(5) When using general calculation methods (see 4.4) the deformation criteria should be used where separating members or protective measures are affected by the deformation of the load bearing structure. Reference should be made to the relevant product specifications.

2.2 Actions(1)P Thermal and mechanical actions shall be obtained from ENV 1991-2-2.(2) Where rules given in this Part 1-2 are only valid for the standard fire exposure, this is identified in the relevant clauses.

2.3 Design values of material properties(1)P Design values of thermal and mechanical properties (Xd,fi) are defined as follows:

— thermal properties for thermal analysisif an increase of the property is favourable for safety

if an increase of the property is unfavourable for safety

— strength and deformation properties for structural analysis

whereXk(G) is the characteristic value of a material property in fire design, generally dependent on the material temperatureXk is the characteristic value of a strength or deformation property (e.g. fck and fyk) for normal temperature design to ENV 1992-1-1k(G) = Xk(G)/Xk is the reduction factor for a strength or deformation property dependent on the material temperature — see 3.2 and 3.3YM,fi is the partial safety factor for material property in fire design

(2) For thermal and mechanical properties of concrete and steel reinforcement the partial safety factor for fire design should be taken as

Xd,fi = Xk(G)/YM,fi (2.1)

Xd,fi = Xk(G) YM,fi (2.2)

Xd,fi = k(G) Xk/YM,fi (2.3)

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YM,fi =|1,0|

2.4 Verification methods2.4.1 General

(1)P The fire resistance of a concrete structure may be determined by any of the methods given in 2.4.2 to 2.4.5.(2) Tabulated data given in 4.2 are based on the standard temperature-time curve. The simplified and general calculation methods may also be used with parametrical temperature-time relationship, see ENV 1991-2-2.

2.4.2 Global structural analysis

(1)P For the global structural analysis, it shall be verified that

whereEd,fi(t) is the design effect of actions in the fire situation, determined from the general rule given in ENV 1991-2-2, including indirect fire actionsRd,fi(t) is the corresponding design resistance at elevated temperatures

t is the relevant duration of fire exposure(2)P The structural model adopted for design to this ENV 1992-1-2 shall reflect the expected performance of the structure in fire exposure.(3) The global structural analysis should take into account the relevant failure mode in fire exposure, the temperature-dependent material properties including stiffness, and effects of thermal expansions and deformations (indirect fire actions).(4) General calculation methods given in 4.4 are suitable for global structural analysis. They are based on models which determine the temperature development within the structure and the mechanical behaviour of the structure.

2.4.3 Analysis of parts of the structure

(1) As an alternative to the global structural analysis of the entire structure for various fire situations, a structural analysis of parts of the structure (sub-assemblies) may be performed, where the sub-assemblies are exposed to fire and analyzed in accordance with 2.4.2(2) Sub-assemblies should be specified on the basis of the potential thermal expansions and deformations such, that their interaction with other parts of the structure can be approximated by time-independent support and boundary conditions during fire exposure.(3) Effects of (permanent and variable) actions at supports and boundaries may be assumed to correspond to those in ENV 1992-1-1.(4) As an approximation to performing a global structural analysis for t = 0, effects of (permanent and variable) actions at supports and boundaries may be obtained from the normal temperature design by using

where

Values of Ó1,i are given in ENV 1991-1. Equation (2.6) is graphically represented presented in Figure 2.1.(5) As a simplification ½fi =|0,6|may be used, except for load category E as given in ENV 1991-2-1 (areas susceptible to accumulation of goods, including access areas) for which a value of|0,7|should be used.

Ed,fi(t) u Rd,fi(t) (2.4)

Ed,fi = ½fi.Ed (2.5)

Ed is the design effect of actions from ultimate limit state design to ENV 1992-1-1 using the fundamental combination½fi is a reduction factor, depending on ß = Qk1/Gk, which is the ratio between the main variable and permanent actions applied to the structure, see ENV 1991-2-2:½fi = ([1,0] + Ó1,1,ß)/(YG + YQ.ß) (2.6)

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(6) Simplified and general methods given in 4.3 and 4.4 respectively are suitable for analysis of parts of the structure.

2.4.4 Member analysis

(1) The support and boundary conditions of members corresponding to those in ENV 1992-1-1 may be used. Where different conditions apply, they are identified in the relevant clauses.(2) 2.4.3 (4) also applies to member analysis.(3) The effects of thermal expansion need not, in general, be taken into account for member analysis.(4) For verifying standard fire resistance requirements, member analysis is sufficient.(5) Tabulated data, simplified or general methods given in 4.2, 4.3 and 4.4 respectively are suitable for verifying members under fire conditions.The tabulated data method consists of simple checks of dimensions of cross-sections and of axis distances of the reinforcement. In some cases simple checks of the load level and additional detailing rules are also required. When the actual steel stress and temperature are known more accurately, the values in the tables may be modified.

2.4.5 Testing

(1) As an alternative to the use of calculation methods, fire design may be based on the results of tests.(2) Combinations of testing and calculations may also be used.

Figure 2.1 — Variation of ½fi as a function of ß = Qk1/Gk for different values of Ó1,1

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3 Material properties

3.1 General(1)P In fire conditions the temperature dependent properties shall be taken into account.(2) The material properties at 20 °C should be assessed according to ENV 1992-1-1.(3) Values for the reduction of the characteristic compressive strength of concrete, and of the characteristic strength of reinforcing and prestressing steels are given in this section. They may be used with the simplified calculation methods. These values may also be used for the evaluation of the critical temperature of reinforcement when adapting tabulated data for critical temperatures other than 500 °C (see 4.2.2).(4) Additional information on thermo-mechanical properties for general calculation methods is given in Informative Annex A. Reference may also be made to appropriate documents.(5) The material models given in 3.2 and 3.3 below should only be applied for heating rates similar to those appearing under standard fire exposure until the time of the maximum temperature.(6) Alternative formulations of material laws (e.g. for parametric fires) may be applied, provided solutions are within the range of appropriate experimental evidence.(7) The standard fire conditions are defined between 20 °C and 1 200 °C, the properties are also defined between the same limits.The values at the higher temperatures shown dashed in Figure 3.1, Figure 3.2 and Figure 3.3 are given as indication only.

3.2 Concrete(1) The reduction of the characteristic compressive strength of concrete as a function of the temperature G is allowed for by the coefficient kc(G) for which:

(2) In the absence of more accurate information the following kc(G) values, applicable to concretes with siliceous aggregates, should be used (see Figure 3.1).They may be considered as conservative values for other types of concrete.

3.3 Steel(1) The reduction of the characteristic strength of a reinforcing steel as a function of the temperature G is allowed for by the coefficient ks(G) for which:

(2) The reduction of the characteristic strength of a prestressing steel as a function of the temperature G is allowed for by the coefficient kp(G) for which:

(3) Where ks(G) and kp(G) are taken from documented data they should be derived from tests performed under constant stress and variable temperature (transient tests).(4)In the absence of more accurate information the following ks(G) values should be used for reinforcement (see Figure 3.2).

fck(G) = kc(G) fck(20 °C) (3.1)

kc(G) = 1,0 for 20 °C u G u 100 °Ckc(G) = (1 600 – G)/1 500 for 100 °C u G u 400 °Ckc(G) = (900 – G)/625 for 400 °C u G u 900 °Ckc(G) = 0 for 900 °C u G u 1 200 °C

fsk(G) = ks(G)fyk(20 °C) (3.2)

fpk(G) = kp(G)fpk(20 °C) (3.3)

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For tension reinforcement in beams and slabs where ºs,fi W 2 %, the strength reduction may be used as given below (see Figure 3.2, Curve 1). This corresponds to the values given in the tables in 4.2.

For compression reinforcement in columns and compressive zones of beams and slabs the strength reduction at 0,2 % proof strain should be used as given below (see Figure 3.2, Curve 2). This also applies for tension reinforcement where ºs,fi < 2 % when using the simplified or general calculation methods.

(5) In the absence of more accurate information the following kp(G) values should be used for prestressing steel (see Figure 3.3).For prestressing steel bars:

For prestressing steel wires and strands:

ks(G) = 1,0 for 20 °C u G u 350 °Cks(G) = (6 650 – 9G)/3 500 for 350 °C u G u 700 °Cks(G) = (1 200 – G)/5 000 for 700 °C u G u 1 200 °C

ks(G) = 1,0 for 20 °C u G u 100 °Cks(G) = (1 100 – G)/1 000 for 100 °C u G u 400 °Cks(G) = (8 300 – 12 G)/5 000 for 400 °C u G u 650 °Cks(G) = (1 200 – G)/5 500 for 650 °C u G u 1 200 °C

kp(G) = 1,0 for 20 °C u G u 100 °Ckp(G) = (1 600 – G)/1 500 for 100 °C u G u 250 °Ckp(G) = (700 – G)/500 for 250 °C u G u 650 °Ckp(G) = (1 000 – G)/3 500 for 650 °C u G u 1 000 °Ckp(G) = 0 for 1 000 °C u G u 1 200 °C

kp(G) = 1,0 for 20 °C u G u 100 °Ckp(G) = (850 – G)/750 for 100 °C u G u 250 °Ckp(G) = (650 – G)/500 for 250 °C u G u 600 °Ckp(G) = (1 000 – G)/4 000 for 600 °C u G u 1 000 °Ckp(G) = 0 for 1 000 °C u G u 1 200 °C

Figure 3.1 — Coefficient kc(G) allowing for decrease of compressive strength (fck) of silicious concrete at elevated temperature

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Figure 3.2 — Coefficient ks(G) allowing for decrease of characteristic strength (fyk) of reinforcing steels at elevated temperature

Figure 3.3 — Coefficient kp(G) allowing for decrease of characteristic strength (fpk) of prestressing steels at elevated temperature

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4 Structural fire design

4.1 General(1)P This section deals with the following design procedures as indicated in 2.4.1

— detailing according to recognized design solutions (tabulated data), see 4.2— simplified calculation methods for specific types of members, see 4.3— general calculation methods for simulating the behaviour of structural members, sub-assemblies or the entire structure, see 4.4.

(2)P Where necessary, explosive spalling shall be avoided by appropriate measures.(3) In the absence of more accurate data, the risk of explosive spalling can be assessed on the safe side by using Figure A.18. For more accurate assessments, moisture content, type of aggregate, tightness of concrete and heating rate should be considered.(4) As a rule a check of explosive spalling is not required for members designed to exposure class 1 of Table 4.1 of ENV 1992-1-1.(5) Where local experience indicates increased susceptibility of lightweight concrete to explosive spalling relevant documents should be used to determine member size.(6) For prestressed members with unbonded tendons the danger of progressive collapse should be considered which may occur with excessive steel elongation due to heating (see appropriate documents). Special precautions should be taken to protect the anchorages.

4.2 Tabulated data4.2.1 Scope

(1) In absence of more precise methods for structural fire design (i.e. general calculation method, simplified calculation method), reference should be made to the tabulated data given in this section.The following rules refer to member analysis according to 2.4.4. The tables apply for the standard fire exposure as defined in 1.3 above.(2) The tables have been developed on an empirical basis confirmed by experience and theoretical evaluation of tests.Therefore, this data is derived from approximate conservative assumptions for the more common structural elements. More specific tabulated data can be found in the product standards for some particular types of concrete products.(3) The values given in the tables apply to normal weight concrete-made with siliceous aggregates (see ENV 1992-1-1, 3.1.2.1).If calcareous aggregates are used in beams and slabs either the minimum dimension of the cross-section or the minimum value of the axis distance, a, of reinforcement may be reduced by|10 %|.For lightweight aggregate concrete with an oven dry density of up to|1 200|kg/m3 the reduction may be |20 %|, except for non-load bearing walls (see 4.2.4.1). For densities between|1 200|kg/m3 and |2 000|kg/m3 linear interpolation is permitted [see also 4.1(5)].(4) The tabulated data takes into account requirements to prevent explosive spalling for all exposure classes in Table 4.1 of ENV 1992-1-1 [see 4.1 (2)P to (4)] and no further check is required.(5) Unless stated otherwise when using tabulated data no further checks are required concerning shear and torsion capacity (4.5) and anchorage details (4.6).(6) When using tabulated data, protective layers may be taken into account (see Section 5).

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4.2.2 General design rules

(1) Requirements for separating function (Criterion E and I, see 1.3) may be considered satisfied where the minimum thickness of walls or slabs accords with Table 4.2.(2) For loadbearing function (Criterion R), the minimum requirements concerning section sizes and heat protection (axis distance) of steel have been set up in the tables so that

where:Ed,fi is the design effect of actions in the fire situation.

Rd,fi is the design load-bearing capacity (resistance) in the fire situation.

(3) In order to ensure the necessary steel protection (covers, axis distance) in tensile zones of simple supported members, the Table 4.4, Table 4.5 and Table 4.8, Column 3 (one way), are based on a critical steel temperature of Gcr = 500 °C. Gcr is the critical temperature of reinforcement at which yielding becomes imminent under the actual steel stress Ös,fi. This assumption corresponds approximately to Ed,fi = 0,7Ed and Ys = 1,15 [see Equation (4.2)] where Ed denotes the design effect of actions according to ENV 1992-1-1.(4) For prestressing tendons the critical temperature for bars is assumed to be 400 °C and for strands and wires to be 350 °C. If no special check according to (5) is made in prestressed tensile members, beams and slabs the required axis distance, a, should be increased by

10 mm for prestressing bars, corresponding to Gcr = 400 °C

15 mm for prestressing wires and strands, corresponding to Gcr = 350 °C.

(5) For tensile and simply supported bending members, except for those with unbonded tendons, modification of the required axis distance a, given in the Table 4.4, Table 4.5 and Table 4.8, Column 3, for critical temperatures of reinforcement other than 500 °C may be carried out as follows:

a) evaluate the steel stress Ös,fi for the actions in a fire situation (Ed,fi) using Equation (4.2).

where:

b) evaluate the critical temperature of reinforcement Gcr, corresponding to the reduction factor ks(G) = Ös,fi/fyk(20 °C) using Figure 3.2 (Curve 1) for reinforcement or kp(G) = Öp,fi/fpk(20 °C) using Figure 3.3 for prestressing steel.c) adjust the minimum axis distance given in the Tables, for the new critical temperature, Gcr, using the approximate Equation (4.3) where %a is the change in axis distance in millimetres:

(6) The above approximation is valid for 350 °C < Gcr < 700 °C. For prestressing steel, Equation (4.2) may be applied analogously.For unbonded tendons critical temperatures greater than 350 °C should only be used where more accurate methods are used to determine the effects of deflections.(7) For tensile members or beams where the design requires Gcr to be below 400 °C the cross sectional dimensions should be increased by increasing the minimum width of the tensile member or beam according to Equation (4.4).

Ed,fi/Rd,fi u 1,0 (4.1)

(4.2)

Ys is the partial safety factor for reinforcing steel;Ys = 1,15 (see 2.3.3.2 of ENV 1992-1-1)

As,req is the area of reinforcement required for ultimate limit state according to ENV 1992-1-1As,prov is the area of reinforcement providedEd,fi/Ed may be assessed using 2.4.3 (4) and (5).

%a = 0,1 (500 – Gcr) (mm) (4.3)

bmod W bmin + 0,8 (400 – Gcr) (mm) (4.4)

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where bmin is the minimum dimension b given in the Tables, related to the required standard fire resistance.An alternative to increasing the width according to Equation (4.4) may be to adjust the axis distance of the reinforcement in order to obtain the temperature required for the actual stress. This requires using a more accurate method such as that given in Annex B.(8) Values given in the Tables provide minimum dimensions for fire resistance in addition to the detailing rules required by ENV 1992-1-1. Some values of the axis distance of the steel, used in the Tables are less than that required by ENV 1992-1-1 and should be considered for interpolation only.(9) Linear interpolation between the values given in the Tables is allowed.(10) In situations for which the Tables do not apply, reference should be made to appropriate documents.(11) Symbols used in the tables are defined in Figure 4.1.

(12) The nominal values of axis distance a to a steel bar, wire or tendon, should not be less than the minimum values given in the Tables below.(13) When reinforcement is arranged in several layers similar to Figure 4.2, and where it consists of either reinforcing or prestressing steel with the same characteristic strength fyk and fpk respectively, the average axis distance am should not be less than the axis distance a given in the Tables. The average axis distance may be determined by Equation (4.5).

where:Asi is the cross sectional area of steel bar (tendon, wire) “i”

ai is the axis distance of steel bar (tendon, wire) “i” from the nearest exposed surface.

When reinforcement consists of steels with different characteristic strength Asi should be replaced by Asi fyki (or Asi fpki) in Equation (4.5).

Figure 4.1 — Sections through structural members, showing nominal axis distance a, and nominal concrete cover c to reinforcement

(4.5)

Figure 4.2 — Dimensions used to calculate average axis distance am

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(14) Where reinforcing and prestressing steel is used simultaneously (e.g. in a partially prestressed member), the axis distances of the prestressing steel should be introduced in Equation (4.5) as a nominal value given by:

where:

(15) The minimum axis distance for any individual bar should not be less than that required for R 30 and not less than half the average axis distance [see Equation (4.5)].(16) In tensile members, beams and slabs with concrete covers c W|50|mm to the main longitudinal reinforcement, surface reinforcement should be provided in order to prevent the fall off of the concrete unless it can be justified, generally by tests, that falling off does not occur within the period of fire resistance. Where necessary, for the cover to surface reinforcement reference should be made to ENV 1992-1-1, 4.1.3.3 (6) and (7).

4.2.3 Columns

(1) Fire resistance of reinforced concrete columns may be satisfied by the use of Table 4.1 and the following rules.(2) In Table 4.1 a load level in the fire situation Èfi has been introduced accounting for load combinations and the design column resistance to compression and, possibly, bending, including second order effects. The effective length lo, is assumed to be equal to the actual column length lcol (notation as in ENV 1992-1-1, 4.3.5).Èfi may be taken as|0,7|in all cases. However, a more accurate value may be obtained using Equation (4.7):

where:½fi = Ed,fi/Ed [see 2.4.3 (4)];

Rd,fi(0) denotes the design resistance calculated according to ENV 1992-1-1 with lo = lcol, YM = 1 and t = 0

(3) For concrete made with calcareous or lightweight aggregate, no reduction of the minimum column width b [see 4.2.1 (3)] given in Table 4.1 is permitted.(4) In columns where As W|0,02|Ac, distribution of the bars along the sides of the cross-section is required for a fire resistance higher than|90|minutes. However, this rule does not apply to lapping zones.(5) The dimension b in Table 4.1 for columns exposed to fire on one side only (Column 5), applies to columns which lie flush with wall of the same standard fire resistance or to protruding columns if that part of the cross-section embedded in the wall is able to carry the whole load. Any opening in the wall should not be nearer to the column than the minimum dimension b given in Table 4.1, Column 5 for the standard fire resistance required (see Figure 4.3). Otherwise it should be treated as a column exposed to fire on more than one side.

ai,nom = ai – %ap (4.6)

ai is the actual axis distance of the tendon considered%ap is an allowance for the different critical temperatures of reinforcing and prestressing steel.%ap may be assumed as follows:%ap = 10 mm for prestressing bars

= 15 mm for prestressing wires and strands

Èfi = Ed,fi/Rd,fi(0) = ½fi Ed/Rd,fi(0) (4.7)

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(6) Where the actual width or diameter b of column is at least 1,2 times the minimum value bmin given in Table 4.1 the axis distance a may be reduced to a value not less than the nominal cover required by ENV 1992-1-1. Linear interpolation of the axis distance may be used for values b/bmin between 1 and 1,2. For such situation 4.2.3 (4) does not apply.

Table 4.1 — Minimum dimensions and axis distances for reinforced concrete columns; rectangular and circular section

4.2.4 Walls

4.2.4.1 Non load-bearing walls (partitions)

(1) Where the fire resistance of a partition is only required to meet the thermal insulation criterion I and integrity criterion E, the minimum wall thickness should not be less than that given in Table 4.2 below. Requirements of axis distance may be disregarded.(2) If calcareous or lightweight aggregates are used the minimum wall thickness given in Table 4.2 may be reduced by|10 %|.(3) To avoid excessive thermal deformation and subsequent failure of integrity between wall and slab, the ratio of clear height of wall lw to wall thickness t should not exceed|40|.

NOTE t × b is the load bearing part of the cross section

Figure 4.3 — Exposure of built-in columns

Standard fire resistance

Minimum dimensions (mm)

Column width bmin/axis distance a

Column exposed on more than one side Exposed on one side

Èfi = 0,2 Èfi = 0,5 Èfi = 0,7 Èfi = 0,7

1 2 3 4 5

R 30 |150/10|a |150/10|a |150/10|a |100/10|a

R 60 |150/10|a |180/10|a |200/10|a |120/10|a

R 90 |180/10|a |210/10|a |240/35| |140/10|a

R 120 |200/40| |250/40| |280/40| |160/45|

R 180 |240/50| |320/50| |360/50| |200/60|

R 240 |300/50| |400/50| |450/50| |300/60|a Normally the cover required by ENV 1992-1-1 will control.

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Table 4.2 — Minimum wall thickness of nonload-bearing walls (partitions)

4.2.4.2 Load-bearing solid walls

(1) Adequate fire resistance of load-bearing reinforced concrete walls may be assumed if the data given in Table 4.3 and the following rules are applied.(2) For plain concrete walls (see ENV 1992-1-6) the minimum wall thickness values given in Table 4.3 may be used.(3) 4.2.3 (2), (3) and (6) also apply for load-bearing solid walls.

Table 4.3 — Minimum dimensions and axis distances for load-bearing reinforced concrete walls

4.2.5 Tensile members

(1) Fire resistance of reinforced or prestressed concrete tensile members may be assumed adequate if the data given in Table 4.4 and the following rules are applied.(2) Where excessive elongation of a tensile member affects the load bearing capacity of the structure it may be necessary to reduce the steel temperature in the tensile member to 400 °C. In such situations the axis distances in Table 4.4 should be increased by 10 mm. For the assessment of the reduced elongation reference is made to appropriate documents.(3) The cross-section of tensile members should not be less than 2bmin

2, where bmin is the minimum member width given in Table 4.4.

Standard fire resistance Minimum wall thickness (mm)

1 2

EI 30 |60|

EI 60 |80|

EI 90 |100|

EI 120 |120|

EI 180 |150|

EI 240 |175|

Standard fire resistance

Minimum dimensions (mm)

Wall thickness/axis distance for

Èf = 0,35 Èf = 0,7

wall exposed on one side

wall exposed on two sides

wall exposed on one side

wall exposed on two sides

1 2 3 4 5

REI 30 |100/10|a |120/10|a |120/10|a |120/10|a

REI 60 |110/10|a |120/10|a |130/10|a |140/10|a

REI 90 |120/20|a |140/10|a |140/25| |170/25|

REI 120 |150/25| |160/25| |160/35| |220/35|

REI 180 |180/45| |200/45| |210/55| |300/55|

REI 240 |230/60| |250/60| |270/70| |360/70|a Normally the cover required by ENV 1992-1-1 will control.

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Table 4.4 — Minimum dimensions and axis distances for reinforced and prestressed concrete tensile members

4.2.6 Beams

4.2.6.1 General

(1) Adequate fire resistance of reinforced and prestressed concrete beams may be assumed if the data given in Table 4.5 to Table 4.7 together with the following rules are used.(2) The Tables apply to beams which can be exposed to fire on three sides, i.e. the upper side is insulated by slabs or other elements which continue their insulating function during the whole fire resistance period. For beams, exposed to fire on all sides, 4.2.6.4 applies.(3) Values in the Tables are valid for the cross-sections shown in Figure 4.4. Rules (5) to (8) ensure adequate cross-sectional dimensions to protect the reinforcement.

(4) For beams with varying width [Figure 4.4 (b)] the minimum value b relates to the centroid of the tensile reinforcement.(5) The effective height deff of the bottom flange of I-shaped beams with varying webs [Figure 4.4 (c)] should not be less than:

where bmin is the minimum value of beam width according to Table 4.5This rule does not apply if an imaginary cross section [(a) in Figure 4.5] which fulfils the minimum requirements with regard to fire resistance and which includes the whole reinforcement can be drawn inside the actual cross section.

Standard fire resistance

Minimum dimensions (mm)

Possible combinations of member width bmin/axis distance a

1 2 3

R 30 |80/25| |200/10|a

R 60 |120/40| |300/25|

R 90 |150/55| |400/45|

R 120 |200/65| |500/45|

R 180 |240/80| |600/60|

R 240 |280/90| |700/70|For prestressed members the increase of axis distance according to 4.2.2(4) should be noted.

a Normally the cover required by ENV 1992-1-1 will control.

Figure 4.4 — Definition of dimensions for different types of beam section

deff = d1 + 0,5 d2 W bmin (4.8)

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(6) Where the actual width of the bottom flange b exceeds the limit 1,4 bw, [bw denotes the actual width of web, see Figure 4.4 (c)], the axis distance to the reinforcing or prestressing steel should be increased to:

where:deff is given by Equation (4.8)

bmin is the minimum beam width given in Table 4.5.

(7) For flanges with b > 3,5 bw [see (6) above for definitions] 4.2.6.4 applies.(8) Holes through the webs of beams do not affect the fire resistance provided that the remaining cross-sectional area of the member in the tensile zone is not less than Ac = 2b2

min where bmin is given by Table 4.5 below.(9) Higher temperature concentrations occur at the bottom corners of beams. For this reason the axis distance asd to the side of beam for corner bar (tendon or wire) in the bottom of beams with only one layer of reinforcement, should be increased by|10| mm for widths of beam up to that given in Column 4 ofTable 4.5 for simply supported beams, and Column 3 of Table 4.6 for continuous beams, for the relevant standard fire resistance.

4.2.6.2 Simply supported beams

(1) Table 4.5 provides minimum values of axis distance to the soffit and sides of simply supported beams together with minimum values of the width of beam, for standard fire resistances of R 30 to R 240.

4.2.6.3 Continuous beams

(1) Table 4.6 provides minimum values of axis distance to the soffit and sides of continuous beams together with minimum values of the width of beam, for standard fire resistance of R 30 to R 240.(2) Table 4.6 and the following rules apply for beams where the moment redistribution according to ENV-1992-1-1, 2.5.3.4.2 does not exceed|15 %|. In the absence of a more rigorous calculation and where the redistribution exceeds|15 %|, or the detailing rules of this Part 1-2 are not followed, each span of a continuous beam should be assessed using Table 4.5 for simple supported beams.

Figure 4.5 — I-shaped beam with increasing web width bw satisfying the requirements of an imaginary cross-section

(4.9)

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(3) The area of top reinforcement over each intermediate support for standard fire resistance of|R90|and above, for up to a distance of|0,3|/eff (as defined in ENV 1992-1-1, 2.5.2.2.2) from the centre line of support should not be less than (see Figure 4.6):

where:x is the distance from the section considered to the centre line of the support (x u 0,3/eff)

As,req(0) is the area of top reinforcement required over the support, according to ENV 1992-1-1

As,req(x) is the minimum area of top reinforcement required in the section considered but not less than As(x) required by ENV 1992-1-1.

Where leff varies in the adjacent spans it should be taken as the greater value.

As,req(x) = As,req(0) × (1 – 2,5x/leff) (4.10)

Explanation:(1) Diagram of bending moments for the actions in a fire situation at t = 0(2) Envelope line of acting bending moments to be resisted by tensile reinforcement according to ENV 1992-1-1(3) Diagram of bending moments in fire conditions(4) Envelope line of resisting bending moments according to Equation (4.10)

Figure 4.6 — Envelope of resisting bending moments over supports in fire conditions

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Table 4.5 — Minimum dimensions and axis distances for simply supported beams made with reinforced and prestressed concrete

Table 4.6 — Minimum dimensions and axis distances for continuous beams made with reinforced and prestressed concrete

(4) Table 4.6 applies to continuous beams using unbonded tendons only, where additional bonded top reinforcement over intermediate supports is provided to ensure static equilibrium under fire conditions.

Standard fire resistance

Minimum dimensions (mm)

Possible combinations of a and bmin where a is the average axis distance and bmin is the width of beam

Web thicknessbw

1 2 3 4 5 6

R 30 bmin = |80| |120| |160| |200| |80|a = |25| |15|a |10|a |10|a

R 60 bmin = |120| |160| |200| |300| |100|a = |40| |35| |30| |25|

R 90 bmin = |150| |200| |250| |400| |100|a = |55| |45| |40| |35|

R 120 bmin = |200| |240| |300| |500| |120|a = |65| |55| |50| |45|

R 180 bmin = |240| |300| |400| |600| |140|a = |80| |70| |65| |60|

R 240 bmin = |280| |350| |500| |500| |160|a = |90| |80| |75| |70|

asd = a + 10 mm (see note below)

For prestressed beams the increase of axis distance according to 4.2.2(4) should be noted.asd is the axis distance to the side of beam for the corner bars (tendon or wire) of beams with only one layer of reinforcement. For values of bmin greater than that given in Column 4 no increase of a is required.a Normally the cover required by ENV 1992-1-1 will control.

Standard fire resistance

Minimum dimensions (mm)

Possible combinations of a and bmin where a is the average axis distance and bmin is the width of beam Web thickness bw

1 2 3 4 5

R 30 bmin = |80| |160| |200| |80|a = |12|a |12|a |12|a

R 60 bmin = |120| |200| |300| |100|a = |25| |12|a |12|a

R 90 bmin = |150| |250| |400| |100|a = |35| |25| |25|

R 120 bmin = |220| |300| |500| |120|a = |45| |35| |35|

R 180 bmin = |380| |400| |600| |140|a = |60| |60| |50|

R 240 bmin = |480| |500| |700| |160|a = |70| |70| |60|

asd = a + 10 mm (see note below)

For prestressed beams the increase of axis distance according to 4.2.2(4) should be noted.asd is the axis distance to the side of beam for the corner bars (tendon or wire) of beams with only one layer of reinforcement. For values of bmin greater than that given in Column 3 no increase of a is required.a Normally the cover required by ENV 1992-1-1 will control.

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(5) The web thickness of I-shaped continuous beams bw [see Figure 4.4 (c)] should not be less than the minimum value bmin in Table 4.6, Columns 2 to 4, for a distance of 2h from an intermediate support unless it can be shown that explosive spalling will not occur using Figure A.18.(6) In order to prevent a concrete compression or shear failure of a continuous beam at the first intermediate support, the beam width and web thickness should be increased for standard fire resistances |R 120 – R 240|in accordance with Table 4.7, if both the following conditions exist:

a) no bending resistance is provided at the end support, either by the joint or beam (for the purposes of this clause ENV 1992-1-1, 5.4.2.1.2 (1) does provide moment resistance when incorporated in a joint which can transfer moment), andb) Vsd > 2/3 VRd2 at the first intermediate support, where VRd2 is the design shear resistance of the compression struts according to ENV 1992-1-1, 4.3.2.

Table 4.7 — Reinforced and prestressed concrete continuous I-beams; increased beam width and web

thickness for conditions according to 4.2.6.3 (6)

4.2.6.4 Beams exposed on all sides

(1) Table 4.5, Table 4.6 and Table 4.7 apply: however— the height of the beam should not be less than the minimum width required for the respective fire resistance period,— the cross-sectional area of the beam should not be less than

Where bmin is given by Table 4.5 to Table 4.7.

4.2.7 Slabs

4.2.7.1 General

(1) Fire resistance of reinforced and prestressed concrete slabs may be considered adequate if the values in Table 4.8 and together with the following rules are applied.(2) The minimum slab thickness hs given in Table 4.8 ensures adequate separating function (Criterion E and I). Floor-finishes will contribute to the separating function in proportion to their thickness (see Figure 4.7). If loadbearing function (Criterion R) is required only the necessary slab thickness assumed for design to ENV 1992-1-1 may be taken.

(3) The rules given in 4.2.7.2 and 4.2.7.3 also apply for the flanges of T- or TT-shaped beams.

Standard fire resistance

Minimum beam width bmin (mm) and web thickness bw (mm)

1 2

R 120 |220|R 180 |380|R 240 |480|

Ac = 2b2min (4.11)

Explanation:

(1) Concrete slab

(2) Flooring (non-combustible)

(3) Sound insulation (possibly combustible)

h1 + h2 = hs as given in Table 4.8Figure 4.7 — Concrete slab with floor finishes

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4.2.7.2 Simply supported slabs

(1) Table 4.8 provides minimum values of axis distance to the soffit of simply supported slabs for standard fire resistances of R 30 to R 240.(2) In two-way spanning slabs, a denotes the axis distance of the reinforcement in the lower layer. Table 4.8 — Minimum dimensions and axis distances for reinforced and prestressed concrete simply supported

one-way and two-way slabs

4.2.7.3 Continuous slabs

(1) The values given in Table 4.8 (Columns 2 and 4) also apply to one-way or two-way continuous slabs.(2) The rules in 4.2.6.3 (2) and (3) for continuous beams also apply to continuous slabs. If these rules are not followed each span of a continuous slab should be assessed as a simply supported slab using Table 4.8 (Columns 2, 3, 4 or 5 respectively).(3) A minimum negative reinforcement As W|0,005|Ac over intermediate support should be provided if the following conditions apply:

a) normal ductility steel is used (see ENV 1992-1-1, 3.2.4.2)b) in two-span continuous slabs, no restraint to bending at end supports is provided by design provisions according to ENV 1992-1-1 and/or by adequate detailing [see, for example, ENV 1992-1-1, 5.4.3.2.2 (2)].c) no possibility is given to redistribute load-effects transverse to the span direction, such, for example, intermediate walls or other supports in span direction, not taken into account in the design (see Figure 4.8).

Standard fire resistance

Minimum dimensions (mm)

slab thickness hs (mm)

axis-distance a

one way two way:

ly/lx u 1,5 1,5 < ly/lx u 2

1 2 3 4 5

REI 30 |60| |10|a |10|a |10|a

REI 60 |80| |20| |10|a |15|a

REI 90 |100| |30| |15|a |20|

REI 120 |120| |40| |20| |25|

REI 180 |150| |55| |30| |40|

REI 240 |175| |65| |40| |50|lx and ly are the spans of a two-way slab (two directions at right angles) where ly is the longer span.For prestressed slabs the increase of axis distance according to 4.2.2(4) should be noted.The axis distance a in Column 4 and 5 for two way slabs relate to slabs supported at all four edges. Otherwise, they should be treated as one-way spanning slab.a Normally the cover required by ENV 1992-1-1 will control.

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4.2.7.4 Flat slabs

(1) The following rules apply to flat slabs where the moment redistribution according to ENV 1992-1-1, 2.5.3.5.4 does not exceed|15 %|. Otherwise axis distances should be taken as for one-way slab (Column 3 in Table 4.8) and the minimum thickness from Table 4.9.(2) For fire ratings of|REI 90|and above, at least|20 %|of the total top reinforcement in each direction over intermediate supports, required by ENV 1992-1-1, should be continuous over the full span. This reinforcement should be placed in the column strip.(3) Minimum slab-thicknesses should not be reduced (e.g. by taking floor finishes into account).(4) The axis distance a denotes the axis distance of the reinforcement in the lower layer.

Table 4.9 — Minimum dimensions and axis distances for reinforced and prestressed

concrete flat slabs

4.2.7.5 Ribbed slabs

(1) For the assessment of the fire resistance of one-way reinforced and prestressed ribbed slabs, 4.2.6.2, 4.2.6.3 and 4.2.7.3, Table 4.8, Columns 2 and 5, apply.(2) For two-way reinforced and prestressed ribbed slabs, adequate fire resistance may be assumed if the values in Table 4.10 and Table 4.11, together with the following rules, are applied.

Explanation:

(a) Span direction of slab

(b) Large extent of system without cross walls

(c) No rotational restraint provided

Figure 4.8 — Slab systems for which minimum reinforcement areas according to 4.2.7.3 (3) should be provided

Standard fire resistance

Minimum dimensions (mm)

slab-thickness hs axis-distance a

1 2 3

REI 30 |150| |10|a

REI 60 |200| |15|a

REI 90 |200| |25|

REI 120 |200| |35|

REI 180 |200| |45|

REI 240 |200| |50|a Normally the cover required by ENV 1992-1-1 will control.

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(3) The values in Table 4.10 and Table 4.11 are valid for ribbed slabs subjected to uniformly distributed loading.(4) For ribbed slabs with reinforcement placed in several layers, 4.2.6.1 (4) applies.(5) In continuous ribbed slabs, the top reinforcement should be placed in the upper half of the flange.(6) Table 4.10 is valid for simply supported, two-way spanning ribbed slabs. It is also valid for two-way spanning ribbed slabs with at least one restrained edge and standard fire resistances lower than REI 180 where the detailing of the upper reinforcement does not meet the requirements in 4.2.6.3 (3).Table 4.11 is valid for two-way spanning ribbed slabs with at least one restrained edge. For the detailing of the upper reinforcement, 4.2.6.3 (3) applies for all standard fire resistances.

Table 4.10 — Minimum dimensions and axis distance for two-way spanning, simply supported ribbed slabs in reinforced or prestressed

concrete

Standard Fire Resistance

Minimum dimensions (mm)

Possible combinations of width of ribs bmin and axis distance a

slab thickness hs and axis distance a in span

1 2 3 4 5

REI 30 bmin = |W 80| hs = |80|a = |15|a a = |10|a

REI 60 bmin = |100| |120| |W 200| hs = |80|a = |35| |25| |15|a a = |10|a

REI 90 bmin = |120| |160| |W 250| hs = |100|a = |45| |40| |30| a = |15|a

REI 120 bmin = |160| |190| |W 300| hs = |120|a = |60| |55| |40| a = |20|

REI 180 bmin = |W 220| |260| |W 410| hs = |150|a = |75| |70| |60| a = |30|

REI 240 bmin = |280| |W 500| hs = |175|a = |90| |70| a = |40|

asd = a +|10|For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).asd denotes the distance measured between the axis of the reinforcement lateral surface of the rib exposed to fire.

a Normally the cover required by ENV 1992-1-1 will control.

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Table 4.11 — Minimum dimensions and axis distances for two-way spanning ribbed slabs in reinforced or prestressed concrete with at least one restrained edge

4.3 Simplified calculation method4.3.1 General

(1)P The simplified calculation method described below determines the ultimate load bearing capacity of a heated cross section.(2)P The method is applicable to structures subjected to a standard fire exposure until the time of maximum gas-temperature.(3)P The procedure is also applicable for the calculation of the ultimate resistance at a specified time for any other fire exposure, if the temperature profiles corresponding to that exposure are known or calculated, and correct data for material properties corresponding to it are used. However, this Part 1-2 only provides temperature profiles and material data for the standard fire exposure up to the time of maximum gas temperature.(4) The procedure is to first determine the temperature profile of the cross section, reduce the concrete cross section, the strength and the short term modulus of elasticity of concrete and reinforcement and then calculate the ultimate load bearing capacity of the construction with the reduced cross section in accordance with the rules of ENV 1992-1-1, and to compare the capacity with the relevant combination of actions, see 2.4.2.(5) Structural members should be detailed so that spalling, anchorage failure and lack of rotational capacity will have a lower probability of occurrence than failure caused by bending moments, shear or axial loads.(6) The reduction factor µ given in ENV 1992-1-1, 4.2.1.3.3 (11) and (12) is assumed to be|1,0|in fire design. Thus the design compressive strength of concrete in fire design is

Standard Fire Resistance

Minimum dimensions (mm)

possible combinations of width of ribs bmin and axis distance a

slab thickness hs and axis distance a in span

1 2 3 4 5

REI 30 bmin = |W 80| hs = |80|a = |10|a a = |10|a

REI 60 bmin = |100| |120| |W 200| hs = |80|a = |25| |15|a |10|a a = |10|a

REI 90 bmin = |120| |160| |W 250| hs = |100|a = |35| |25| |15|a a = |15|a

REI 120 bmin = |160| |190| |W 300| hs = |120|a = |45| |40| |30| a = |20|

REI 180 bmin = |310| |600| hs = |150|a = |60| |50| a = |30|

REI 240 bmin = |450| |700| hs = |175|a = |70| |60| a = |40|

asd = a +|10|For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).asd denotes the distance measured between the axis of the reinforcement lateral surface of the rib exposed to fire.a Normally the cover required by ENV 1992-1-1 will control.

fcd(G) = kc(G) fck(20 °C). (4.12)

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4.3.2 Temperature profiles

(1) Temperatures in a concrete structure exposed to a fire may be determined from tests or by calculation. The temperature profiles given in Annex B may be used where more accurate information is not available.(2) The temperature profiles given in Annex B are acceptable for determining the temperatures in cross-sections with silicious aggregate and exposed to a standard fire up to the time of maximum gas temperature. The profiles are conservative for most other aggregates, but not in general for other than the standard fire exposure.

4.3.3 Reduced cross section

(1) It is assumed that the isotherms in the compression zone of a rectangular cross section are parallel with the sides.(2) The fire damaged cross-section is represented by a reduced cross-section by ignoring a damaged zone of thickness az at the fire exposed surfaces, as shown in Figure 4.9.(3) For a rectangular shape exposed to fire on one face only the width is assumed to be w, see Figure 4.9 c) and the flange of Figure 4.9 f). Where two opposite faces are exposed to fire the width is assumed to be 2w [see Figure 4.9 a), Figure 4.9 b), Figure 4.9 d), Figure 4.9 e) and the web of Figure 4.9 f)]. For any rectangular part of a member an equivalent wall of thickness 2w is considered for which the thickness az is calculated. For example the slab in Figure 4.9 c) is related to the equivalent wall in Figure 4.9 d), and the flange of Figure 4.9 f) is also related to the equivalent wall in Figure 4.9 d), but the web of Figure 4.9 f) is related to the equivalent wall of Figure 4.9 a).(4) For the bottom and ends of rectangular members exposed to fire, where the width is less than the height, the value of az is assumed to be the same as that calculated for the sides [see Figure 4.9 b), Figure 4.9 e) and Figure 4.9 f)].(5) The compressive strength and the modulus of elasticity of the reduced concrete cross section are assumed to be constant and equal to that calculated for the point M. M corresponds to any point in the middle plane of the equivalent wall.The thickness az of the damaged zone and the reduced properties of the concrete should be determined separately for each rectangular part of a cross section. This means that az may be different for the flange of a T shaped, cross section, from that of the web of the same cross section [see Figure 4.9 f)].

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(6) The reduced compressive strength fcd(GM) at the point M in a member exposed to fire on both sides is

where GM is the temperature at the point M.The reduced short term modulus of elasticity at this point is

The short term value of modulus of elasticity does not take account of the effect of creep or transient strain (that part of the thermal expansion resisted by compressive stresses). Where second order effects for columns and walls need to be considered the method given in ENV 1992-1-1 should be used with this value of the modulus of elasticity and the reduced cross section of this clause. (The value of Ecd(GM) cannot be derived from Annex A where creep and transient strain are included in the data).(7) The damaged zone az is estimated for an equivalent wall exposed on both sides as follows:

a) The half thickness of the wall w is divided into n parallel zones of equal thickness, where n W 3 (see Figure 4.10).b) The temperature is calculated for the middle of each zone.c) The corresponding reductions kc(Gi) of the compressive strength of the concrete are determined.

Figure 4.9 — Reductions of strength and cross-sections found by means of equivalent walls (wall1 and wall2) exposed to fire on both sides

fcd(GM) = kc(GM) fck(20 °C) (4.13)

Ecd(GM) = (kc(GM))2 Eck(20 °C). (4.14)

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The reduced compressive strength and the damaged zone z may be estimated by means of Annex B for a standard fire exposure until the time of maximum gas temperature or by means of the following procedure.d) The mean reduction coefficient incorporating a factor (1 – 0,2/n) which allows for the variation in temperature within each zone, may be calculated using Equation (4.15):

e) The width of damaged zone for beams, slabs and members subjected to in-plane shear may be calculated using Equation (4.16):

where kc(Gm) denotes the reduction coefficient for concrete at point M.

For columns, walls and other constructions where second order effects may be calculated using Equation (4.17):

(8) The reinforcement is taken into account with reduced strength and modulus of elasticity according to the temperature of each bar, even if it is placed outside the reduced cross section, see Annex B.(9) For compression bars a strain of 0,2 % with the corresponding stress reductions should be applied. For bars in tension an increased stress as an effect of a larger strain may be taken into account. The reduction of the modulus of elasticity of a bar may be assessed as equal to the reduction of the 0,2 % stress of the bar.(10) Beams and slabs might become over-reinforced. For the analysis of this, the short term value of ¼cu,max may be assessed as

within the limits of the reduced cross section.(11) In situations where a larger strain than 0,2 % is assumed for the reinforcement, it should be verified that this larger strain occurs at the ultimate limit state under fire conditions.

Figure 4.10 — Divisions of a wall, exposed on both sides, into zones for use in calculation of strength reduction and az values

(4.15)

(4.16)

(4.17)

¼cu,max = 0,0035/kc(GM) (4.18)

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4.4 General calculation methods4.4.1 General

(1)P General calculation methods may be used for individual members, for sub-assemblies or for entire structures and for any type of cross-section.(2)P General calculation methods shall provide a realistic analysis of structures exposed to fire. They shall be based on fundamental physical behaviour leading to a reliable approximation of the expected behaviour of the relevant structural component under fire conditions.(3)P General calculation methods may include separate sub-models for the determination of:

a) the development and distribution of the temperature within structural members (thermal response model);b) the mechanical behaviour of the structure or of any part of it (mechanical response model).

(4)P Any potential failure mode not covered by the general calculation method shall be excluded by appropriate detailing (e.g. insufficient rotational capacity, spalling, local buckling of compressed reinforcement, shear and bond failure, damage to anchorage devices).(5)P General calculation method may be used in association with any heating curve, provided that the material properties are known for the relevant temperature range.

4.4.2 Thermal response

(1)P General calculation methods for thermal response shall be based on the acknowledged principles and assumptions of the theory of heat transfer.(2)P The thermal response model shall consider:

a) the thermal actions evaluated according to ENV 1991-2-2;b) the temperature dependant thermal properties of the materials as specified in relevant documents (see Annex A);c) the contribution of protective layers, if any.

(3) The influence of moisture content and of migration of the moisture within concrete or protective layers if any, may conservatively be neglected.(4) The temperature profile in a reinforced concrete element may be assessed apart from the presence of reinforcement.(5) The effects of non-uniform thermal exposure and of heat transfer to adjacent building components may be included where appropriate.

4.4.3 Mechanical response

(1)P General calculation methods for mechanical response shall be based on the acknowledged principles and assumptions of the theory of structural mechanics, taking into account the changes of mechanical properties with temperature.(2)P The deformations at ultimate limit state implied by the calculation methods shall be limited as necessary to ensure that compatibility is maintained between all parts of the structure.(3)P Where relevant, the mechanical response of the model shall also take account of geometrical non-linear effects.(4)P The effects of thermally induced strains and stresses both due to temperature rise and due to temperature differentials, shall be considered.(5) The total strain º may be assumed to be:

whereºth is the thermal strain,

ºload is the instantaneous stress-dependent strain

ºcreep is the creep strain and

ºtr is the transient strain

º = ºth + ºload + ºcreep + ºtr (4.15)

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During fire exposure the creep strain may be disregarded; its contribution may only be significant for calculation of deflections after a fire.(6) For practical calculations, deformations and indirect actions in hyperstatic structures during fire may be assessed by means of imposed strains (mean axis elongation and curvature) estimated on the basis of appropriate documents (see for example Annex D).(7) The load bearing capacity of individual members, sub-assemblies or entire structures exposed to fire may be assessed by plastic methods of analysis (ref. ENV 1992-1-1, 2.5.3).(8) The plastic rotation capacity of reinforced concrete sections should be estimated in account of the increased ultimate strains ºcu and ºsu in hot condition. ºcu will also be affected by the confinement reinforcement provided.(9) The compressed zone of a section, especially if directly exposed to fire (e.g. negative bending in continuous beams), should be checked and detailed with particular regard to spalling or falling-off of concrete cover.(10) In the analysis of individual members or sub-assemblies the boundary conditions should be checked and detailed in order to avoid failure due to the loss of adequate support to the members.

4.4.4 Validation of general calculation methods

(1)P The validity of the general calculation methods shall be verified by the following procedures:a) justification of the design assumptions shall be made on basis of relevant test results.b) sensitivity analysis of the effect of the critical parameters shall be performed.

4.5 Shear and torsion(1) The shear and torsion capacity may be calculated according to the methods given in ENV 1992-1-1 using reduced material properties and reduced prestress for each part of the section.(2) When using the simplified calculation method of 4.3, ENV 1992-1-1 may be applied directly to the reduced cross section.(3) When using the simplified calculation method of 4.3, if no shear reinforcement is provided or the shear capacity relies mainly on the reduced tensile strength of the concrete, the actual shear behaviour of the concrete at elevated temperatures must be considered.In the absence of more accurate information concerning the reduction of the tensile strength of concrete, the values of kct(G) given in Figure A.1 may be applied.(4) When using the simplified calculation method of 4.3, for elements in which the shear capacity is dependent on the tensile strength, special consideration should be given where tensile stresses are caused by non-linear temperature distributions (e.g. voided slabs, thick beams, etc). A reduction in shear strength should be taken equivalent to these tensile stresses.

4.6 Anchorage(1) Where necessary for fire purposes the anchorage capacity may be calculated according to ENV 1992-1-1 using reduced temperature related material properties [see 3.1 (4)].

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5 Protective layers

(1)P Required fire resistance can be obtained by the application of protective layers.(2) The properties and performance of the insulation material to be used for protective layers should be assessed using appropriate test procedure.(3) The test procedure should confirm that the material remains coherent and cohesive for all foreseen temperatures and deformations. It should provide information concerning

— temperature at the relevant depths of the concrete cross-section related to the fire duration, protective material and layer thickness, or— where possible equivalent concrete thickness, related to the fire duration, or— thermal material properties related to the temperature.

A further alternative is to provide a thermal analyses in accordance with the general calculation method given in 4.4.

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Annex A (informative) Additional information on material propertiesA.1 Strength and deformation properties of concrete(1) The strength and deformation properties of uniaxial stressed concrete at elevated temperatures are characterized by a set of stress-strain relationships with a shape as specified in Figure A.2.(2) For a given concrete temperature, the stress-strain curves are defined by two parameters:

— the compressive strength fc(G)— the strain ºc1(G) corresponding to fc(G).

(3) Values for each of these parameters are given in Table A.1 as a function of the concrete temperatures. For intermediate values of the temperature, linear interpolation is permitted.(4) A graphical display of the two parameters of Table A.1 is given as a function of the concrete temperatures in Figure A.3. Further illustration of the stress-strain relationships at various temperatures is given in Figure A.4.(5) The values given in Table A.1 are recommended values. Due to various ways of testing specimens, ºc1(G) shows considerable scatter, which is presented in Table A.2. Recommended values for ºcu(G) defining the range of the descending branch are also presented.(6) The stress-s train relationships include in an approximate way the effect of high temperature creep.(7) In case of natural fire simulation, particularly when considering the decreasing temperature branch, the material model given here has to be modified.(8) In all situations the ultimate tensile strength of concrete may be assumed to be zero, which is on the safe side. If it is necessary to take account of the tensile strength, when using the simplified or general method of calculation, Figure A.1 may be used.

Figure A.1 — Coefficient kct(G) allowing for decrease of tensile strength, (fctk) of concrete at elevated temperature

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Table A.1 — Values for the main parameters of the stress-strain relationships in compression of siliceous and calcareous concrete

at elevated temperatures (range I in Figure A.2)

Range I

to be chosen according to the values of Table A.1

Range II: For numerical purposes a descending branch should be adopted.

Linear and non linear models are permitted.

Figure A.2 — Model for compression stress-strain relationships of siliceous and calcareous concrete at elevated temperatures

Concrete Temperature (°C)fc(G)/fc(20 °C)

ºc1(G) × 10–3

siliceous calcareous

20 1,00 1,00 2,5100 0,95 0,97 3,5200 0,90 0,94 4,5300 0,85 0,91 6,0400 0,75 0,85 7,5500 0,60 0,74 9,5600 0,45 0,60 12,5700 0,30 0,43 14,0800 0,15 0,27 14,5900 0,08 0,15 15,0

1 000 0,04 0,06 15,01 100 0,01 0,02 15,01 200 0,00 0,00 —

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Figure A.3 — Parameters for stress-strain relationships of concrete at elevated temperatures, according to Figure A.2 and Table A.1

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Table A.2 — Recommended values for ºc1(G) and ºcu(G) and admissible range of ºc1(G)

Figure A.4 — Stress-strain relationships of siliceous concrete under uniaxial compression at elevated temperatures

Concrete Temperature (°C)

ºc1(G) × 10–3ºcu(G) × 10–3

RecommendedRange Recommended

20 2,5 2,5 20,0

100 2,5 – 4,0 3,5 22,5

200 3,0 – 5,5 4,5 25,0

300 4,0 – 7,0 6,0 27,5

400 4,5 – 10,0 7,5 30,0

500 5,5 – 15 9,5 32,5

600 6,5 – 25 12,5 35,0

700 7,5 – 25 14,0 37,5

800 8,5 – 25 14,5 40,0

900 10 – 25 15,0 42,5

1 000 10 – 25 15,0 45,0

1 100 10 – 25 15,0 47,5

1 200 — — —

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A.2 Strength and deformation properties of steel(1) The strength and deformation properties of steel at elevated temperatures are characterized by a set of stress-strain relationships with a linear elliptical shape as specified in Figure A.5.

Range I elastic

Range II non-linear

Range III plastic

Range IV For numerical purposes a descending branch should be adopted.Linear and non-linear models are permitted.

Figure A.5 — Model for stress-strain relationships of reinforcing and prestressing steels at elevated temperatures (notations for prestressing steels “p” instead of “s”)

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(2) For a given steel temperature, the stress-strain curves of Figure A.5 are defined by three parameters:— the slope of the linear elastic range for reinforcement and prestressing steels respectively,— the proportional limit Öspr(G), Öppr(G) respectively and— the maximum stress level fy(G), fpy(G) respectively.

Values for each of the above parameters are given as a function of the steel temperature for various types of reinforcing and prestressing steels in Table A.3 – Table A.6.

Table A.3 — Values for the parameters of the stress-strain relationship of hot rolled reinforcing steel

Table A.4 — Values for the parameters of the stress-strain relationship of cold worked reinforcing steel

Steel Temperature (°C)

20100200300400500600700800900

1 0001 1001 200

1,001,000,870,720,560,400,240,080,060,050,030,020,00

1,000,960,920,810,630,440,260,080,060,050,030,020,00

1,001,001,001,000,940,670,400,120,110,080,050,030,00

Steel Temperature (°C)

20100200300400500600700800900

1 0001 1001 200

1,001,000,900,800,700,600,310,130,090,070,040,020,00

1,001,000,810,610,420,360,180,070,050,040,020,010,00

1,001,001,001,001,000,780,470,230,110,060,040,020,00

Es G( ),Ep G( )

Es G( )Es 20 °C( )-----------------------

Öspr G( )

f0,2 20 °C( )-------------------------

fy G( )

f0,2 20 °C( )-------------------------

Es G( )Es 20 °C( )-----------------------

Öspr G( )

f0,2 20 °C( )-------------------------

fy G( )

f0,2 20 °C( )-------------------------

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Table A.5 — Values for the parameters of the stress-strain relationship of quenched and tempered prestressing steel

Table A.6 — Values for the parameters of the stress-strain relationship of cold worked prestressing steel

(3) A graphical display of the parameters of Table A.3 – Table A.6 is given in Figure A.7, Figure A.9,Figure A.11 and Figure A.13. Further illustration of the stress-strain relationships at various temperatures is given in Figure A.6, Figure A.8, Figure A.10 and Figure A.12.

Steel Temperature (°C)

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1 0001 1001 200

1,000,760,610,520,410,200,150,100,060,030,000.000,00

1,000,770,620,580,520,140,110,090,060,030,000,000,00

1,000,980,920,860,690,260,210,150,090,040,000,000,00

Steel Temperature (°C)

20100200300400500600700800900

1 0001 1001 200

1,000,980,950,880,810,540,410,100,070,030,000,000,00

1,000,680,510,320,130,070,050,030,020,010,000,000,00

1,000,990,870,720,460,220,100,080,050,030,000,000,00

Ep G( )Ep 20 °C( )------------------------

Öppr G( )

fp0,2 20 °C( )---------------------------

fpy G( )

fp0,2 20 °C( )---------------------------

Ep G( )Ep 20 °C( )------------------------

Öppr G( )

fp0,2 20 °C( )---------------------------

fpy G( )

fp0,2 20 °C( )---------------------------

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Figure A.6 — Stress-strain relationships of hot-rolled reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.3

Figure A.7 — Parameters for stress-strain relationships of hot-rolled reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.3

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Steel Temperature (°C)

ºp2(G) ºpu(G)

Recommended values (%)

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1 0001 1001 200

5555,566,577,588,599,5

10

10101010,51111,51212,51313,51414,515

Figure A.8 — Stress-strain relationships for cold-worked reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.4

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Figure A.9 — Parameters for stress-strain relationships of cold-worked reinforcing steels at elevated temperatures, according to Figure A.5 and Table A.4

Steel Temperature

(°C)

ºp2(G) ºpu(G)

Recommended values (%)

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1 0001 1001 200

555566,577,588,599,5

10

10101010,51111,51212,51313,51414,515

Figure A.10 — Stress-strain relationships for quenched and tempered prestressing steels (bars) at elevated temperatures, according to Figure A.5 and Table A.5

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Figure A.11 — Parameters for stress-strain relationships of quenched and tempered prestressing steels (bars) at elevated temperatures, according to Figure A.5 and Table A.5

Figure A.12 — Stress-strain relationships for cold-worked prestressing steels (wires and strands) at elevated temperatures, according to Figure A.5 and Table A.6

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(4) The stress-strain relationships include in an approximate way the effect of high temperature creep.As creep effects are not explicitly considered, this material model has only been checked for heating rates similar to those appearing under standard fire conditions. For heating rates outside the above range, the reliability of the strength and deformation properties used for steel must be demonstrated explicitly.(5) In case of natural fire simulation, particularly when considering the decreasing temperature branch, the stress-strain relationships given here may be used as a sufficiently precise approximation in case of hot-rolled steels. At the present time, verified formulations of properties for the decreasing branch are not available for other types of steel.(6) The stress-strain relationships may be applied for steel in tension as well as in compression.A.3 Thermal propertiesA.3.1 Concrete (siliceous, calcareous and lightweight aggregates)(1) The thermal elongation %l/l of concrete may be adopted according to Equations (A.1) – (A.5).

Figure A.13 — Parameters for stress-strain relationships of cold-worked prestressing steels (wires and strands) at elevated temperatures, according to Figure A.5 and Table A.6

siliceous aggregates:for 20 °C < G u 700 °C

(%l/l)c = (– 1,8 × 10–4) + (9 × 10– 6G) + (2,3 × 10–11 G3) (A.1)for 700 °C < G u 1 200 °C

(%l/l)c = 14 × 10–3 (A.2)

calcareous aggregates:for 20 °C < G u 805 °C

(%l/l)c = (– 1,2 × 10–4) + (6 × 10–6 G) + (1,4 × 10–11 G3) (A.3)

for 805 °C < G u 1 200°(%l/l)c = 12 × 10–3 (A.4)

lightweight aggregates:for 20 °C < G u 1200 °C

(%l/l)c = 8 × 10– 3(G – 20) (A.5)

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where:lc is the length at room temperature

%lc is the temperature induced elongation

G is the concrete temperature (°C)The above equations are presented graphically in Figure A.14 below.

If only an approximate answer is required (simple calculation, estimation) the coefficient of thermal elongation may be used and considered as independent of the concrete temperature:

(%l/l)c = 18 × 10–3 G for concrete with siliceous aggregates

(%l/l)c = 12 × 10–3 G for concrete with calcareous aggregates

(%l/l)c = 8 × 10–3 G for concrete with lightweight aggregates.

(2) The specific heat cc of concrete may be adopted according to Equations (A.6) and (A.7) (see Figure A.15):

In case the moisture content is not considered on the level of the heat and mass balance, the function given for the specific heat of concrete with siliceous or calcareous aggregates may be completed by a peak value situated between 100 °C and 200 °C such as

cc,peak = 1 875 J/kgK for a humidity of 2 % of concrete weight

cc,peak = 2 750 J/kgK for a humidity of 4 % of concrete weight.

If only an approximate answer is required (simple calculation, estimation), the specific heat may be considered as independent of the concrete temperature cc = 1 000 J/kgK for concrete with siliceous or calcareous aggregates.

Figure A.14 — Thermal elongation of concrete

Concrete with siliceous or calcareous aggregates:for 20 °C < G u 1 200 °C

cc = 900 + 80 G/120 – 4(G/120)2 (J/kgK) (A.6)

Concrete with lightweight aggregates:for 20 °C < G u 1 200 °C

cc = 840 (J/kgK) (A.7)

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(3) The thermal conductivity Æc of concrete may be calculated according to Equations (A.8) to (A.11):

The above Equations are presented graphically in Figure A.16.

Figure A.15 — Specific heat of concrete

Concrete with siliceous aggregates:for 20 °C < G u 1 200 °C

Æc = 2 – 0,24 G/120 + 0,012(G/120)2 (W/Mk) (A.8)

Concrete with calcareous aggregates:for 20 °C < Gc u 1 200 °C

2c = 1,6 – 0,16 G/120 + 0,008(G/120)2 (W/Mk) (A.9)

Concrete with lightweight aggregates:for 20 °C < G u 800 °C

2c = 1,0 – G/1 600 (W/Mk) (A.10)

for 800 °C < G u 1 200°2c = 0,5 (W/Mk) (A.11)

Figure A.16 — Thermal conductivity of concrete

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If only an approximate answer is required (simple calculation, estimation), the thermal conductivity may be considered as independent of the concrete temperature:

Æc = 1,60 W/Mk for concrete with siliceous aggregates

Æc = 1,30 W/Mk for concrete with calcareous aggregates

Æc = 0,80 W/Mk for concrete with lightweight aggregates

(4) The density Ôc of unreinforced concrete may be considered as independent of the concrete temperature and may be evaluated according to ENV 1992-1-2.For thermal response models the value Ôc = 2 300 kg/m3 may be adopted for normal dense concrete (siliceous or calcareous).The density may also be reduced by 100 kg/m3 after having reached 100 °C, due to the evaporation of free water.(5) The moisture content of concrete may be taken equal to the equilibrium moisture content. If these data are not available, moisture content may be considered u 2 % of the concrete weight.A high moisture content delays the heating up of concrete, but increases the risk of spalling.(6) If only an approximate answer is required (simple calculation, estimation), the thermal diffusivity of concrete ac (m2/s) may be used.It may be considered as independent of the concrete temperature:

ac = 0,69 × 10– 6 m2/s for concrete with siliceous aggregates

ac = 0,56 × 10– 6 m2/s for concrete with calcareous aggregates

dependent on the density for lightweight concrete.A.3.2 Steel (reinforcing and prestressing)(1) The thermal elongation %l/l of steel may be adopted according to Equations (A.11) – (A.15).

where:ls, lp is the length at room temperature

%ls, %lp is the temperature induced elongation (see Figure A.17)

G is the steel temperature (°C)

reinforcing steel:for 20 °C < G u 750 °C

(%l/l)s = (– 2,416 × 10–4) + (1,2 × 10–5G) + (0,4 × 10–8 G2) (A.12)

for 750 °C < G u 860 °C(%l/l)s = 11 × 10–3 (A.13)

for G W 860 °C(%l/l)s = (– 6,2 × 10–3) + (2 × 10–5 G) (A.14)

prestressing steel:for 20 °C < G u 1 200 °C

(%l/l)p = (– 2,016 × 10–4) + 10–5 G + (0,4 × 10–8 G2) (A.15)

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If only an approximate answer is required (simple calculation, estimation), the coefficient of thermal elongation may be used and considered as independent of the steel temperature:

(%l/l)s = 14 × 10–6 G for reinforcing steels

(%l/l)p = 12 × 10–6 G for prestressing steels

(2) The density Ôs of reinforcing and prestressing steel should be considered as independent from the steel temperature:

Ôs = 7 850 kg/m3

(3) Normally in both reinforced and prestressed concrete members, the thermal properties Æs, cs, and as, of steel may be ignored since the influence of the reinforcement on the temperature rise of the cross-section is of little importance.A.4 Spalling(1) Normally explosive spalling is unlikely to occur where the smaller of the cross section dimensions h or b in the compressive zones of beams, slabs, walls and columns satisfy the conditions given in Figure A.18. The compressive stress Öc,fi may be calculated for the combination of actions in the fire situation using the cross section required by ENV 1992-1-1.

Figure A.17 — Thermal elongation of steel

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Annex B (informative) Temperature profiles and reduced cross sectionB.1 Temperature profiles(1) Figure B.1 and Figure B.2 provide temperature profiles for beams and slabs. These are conservative values and are intended for use in determining the temperature of reinforcing bars and prestressing tendons.B.2 Cross section and concrete strength(1) Figure B.3 provides curves which give values of the reduction in concrete compressive strength and cross section with respect to the thickness of section.(2) The thickness of section w is assessed as follows:

— For slabs: w = h— For beams: w = " bw

— For columns or walls exposed on one side only: w = width of wall or column— For columns or walls exposed on two sides: w = " × width of wall or column— For columns exposed on four sides: w = " × the smaller section dimension

(3) The reduction in cross section az is described in 4.3.3, see Figure 4.9.(4) The reduction in strength kc(GM) is defined in 3.2.

NOTE a (in mm) is taken as the lesser of h and b.

Figure A.18 — Relationship between Öc,fi and h (or b) for risk of explosive spalling for normal weight concrete members

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Figure B.1 — Temperature profiles for beams

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Figure B.2 — Temperature profiles for slabs

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w is assessed as:

* The thickness of a slab,

* The thickness of a one sided exposed wall or column,

* Half the thickness of the web of a beam,

* Half the thickness of a two sided exposed wall or column or

* Half the smallest dimension of a four sided exposed column.

a) Reduction of compression strength for a reduced cross-section using siliceous aggregate concrete.

b) Reduction in cross-section az of a beam or slab using siliceous aggregate concrete.

c) Reduction in cross section az of a column or wall using siliceous aggregate concrete.

NOTE The values for siliceous aggregate concrete are conservative for most other aggregate concretes.

Figure B.3 — Reduction in cross section and concrete strength assuming a standard fire

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Annex C (informative) Simplified method of calculation for beams and slabsC.1 General(1) This simplified method of calculation provides an extension to the use of the tabular method for beams exposed on three sides and slabs, Table 4.4 to Table 4.8. It determines the affect on bending resistance for situations where the axis distance, a, to bottom reinforcement is less than that required by the tables.The minimum cross-section dimensions (b, bw, hs) given in Table 4.4 to Table 4.7 should not be reduced.This method uses strength reduction factors based on Curve 1 of Figure 3.2 for reinforcing steels and Figure 3.3 for prestressing steels.(2) This simplified method may be used to justify reducing the axis distance a. Otherwise the rules given in 4.2.6.1 to 4.2.6.3 should be followed. This method is not valid for continuous beams where, in the areas of negative moment, the width b or bw is less than 200 mm and the height hs is less than 2b, where b is the value given in Column 3 of Table 4.4.C.2 Simply supported beams and slabs(1) It should be verified that

(2) The loading under fire conditions Fd,fi (kN) may be determined using Equation (2.5).(3) The maximum fire design moment MSd,fi for predominantly uniformly distributed load may be calculated using Equation (C.2).

where leff is the effective length of beam or slab.(4) The moment of resistance MRd,fi for design for the fire situation may be calculated using Equation (C.3).

where:Ys is the partial material factor for steel used in ENV 1992-1-1, (normally taken to be 1,15)

Ys,fi is the partial material factor for steel under fire conditions (normally taken to be 1,0)

ks(G) is the strength reduction factor of the steel for the given temperature G under the required fire resistance. G may be taken from Figure B.1 and Figure B.2 for the chosen axis distanceMSd is the applied moment for cold design to ENV 1992-1-1

As,prov is the area of tensile steel provided

As,req is the area of tensile steel required for cold design by ENV 1992-1-1

As,prov/As,req should not be taken as greater than 1,3.

C.3 Continuous beams and slabs(1) Static equilibrium of flexural moments and shear forces should be ensured for the full length of continuous beams and slabs under the design fire conditions.(2) In order to satisfy equilibrium of fire design, moment redistribution from the span to the supports is permitted where sufficient area of reinforcement is provided over the supports to take the design fire loading. This reinforcement should extend a sufficient distance into the span to ensure a safe bending moment envelope.(3) The moment of resistance MRdSpan,fi of the section at the position of maximum sagging moment should be calculated for fire conditions in accordance with C.2 (4). The maximum free bending moment for applied loads in the fire situation (Fd,fi leff/8 for uniformly distributed load) should be fitted to this moment of resistance MRdSpan,fi such that the support moments MRd1,fi and MRd2,fi provide equilibrium as shown in Figure C.1. This may be carried out by choosing the moment to be supported at one end as equal to or less than the moment of resistance at that support [calculated using Equation (C.4)], and then calculating the moment required at the other support.

Msd,fi u MRd,fi (C.1)

MSd,fi = Fd,fileff/8 (C.2)

MRd,fi = (Ys/Ys,fi) × ks(G) × MSd (As,prov/As,req) (C.3)

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(4) In the absence of more rigorous calculations, the moment of resistance at supports for design for the fire situation may be calculated using Equation (C.4).

whereYs, MSd, Ys, Ys,fi, As,prov and As,req are defined in C.2

a is the required average axis distance given in Table 4.5 for beams and Table 4.8, Column 3 for slabs,d is the effective depth of sectionAs,prov/As,req should not be taken as greater than 1,3.

(5) Equation (C.4) is valid where the temperature of the top steel over the supports does not exceed 350 °C for reinforcing bars nor 100 °C for prestressing tendons.For higher temperatures MRd,fi should be reduced by ks(G) according to Figure 3.2, curve 1, for reinforcing bars, and by kp(G) according to Figure 3.3 for prestressing tendons.(6) The curtailment length lbnet,fi required under fire conditions should be checked. This may be calculated using Equation (C.5).

where lbnet is given in ENV 1992-1-1, Equation (5.4).The length of bar provided should extend beyond the support to the relevant contra-flexure point as calculated in C.3 (3) plus a distance equal to lb net,fi.

Annex D (informative) A procedure for assessing the structural response of reinforced concrete elements under fireD.1 General(1) This step by step procedure describes a method for assessing the structural response of reinforced concrete structures composed of typical elements (beams, columns, slabs and walls) under fire condition, by means of simple methods of statics.(2) The effective thermal strain profiles and the consequent behaviour under fire may be estimated with good approximation, in spite of the uncertainties and the inaccuracy of the physical model used.D.2 Rules for application(1) For appropriately chosen durations of the given fire, or corresponding steps of %G (eg. 50 °C or even 100 °C), the development of surface temperatures on the exposed surfaces and the “temperatures profiles” of the concrete elements should be determined (see Figure D.1).

Figure C.1 — Positioning the free bending moment diagram MSd,fi to establish equilibrium

MRd,fi = (Ys/Ys,fi) MSd (As,prov/As,req) (d – a)/d (C.4)

lbnet,fi = (Ys/Ys,fi) (Yc,fi/Yc) lbnet (C.5)

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(2) For each temperature level, determine the modified elastic modulus Ec(Gm) and elongation (%/(Gm/l)c of concrete (see Annex A).(3) Assume that the structural element is composed of independent longitudinal fibres (layers), known as thermo-elements, which are free to move axially. Under fire conditions the temperature profiles induce thermal elongations which are not distributed linearly, so that sections do not remain plane (see Figure D.2).

Figure D.1 — Temperature profiles in concrete elements. Gm is the average temperature along a horizontal section y-y

Figure D.2 — Layers of thermo-elements assumed free to move axially

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(4) The equivalent action effects N(G) and M(G) are then determined by applying a hypothetical stress Ö(G) to each layer, sufficient to cause an equal and opposite strain to its thermal strain. The forces from each layer are summed over the height of the section to give N(G), e and hence M(G) (see Figure D.3).

where:Ec(G) and (%l(G)/l)c are defined in D.2 (see also Annex A),

h is the height of the cross section,y is the distance of a thermo-element from the element axis andy1, and y2 are the distances of the upper and lower thermo-elements from the member axis.

(5) The residual internal stresses are found by combining the hypothetical stresses Ö(G) and the stresses due to N(G) and M(G), as shown in Figure D.4.(6) The effective imposed strains are equal to the sum of the thermal strains of the thermo-elements (see Figure D.2) and the mechanical strains due to the final internal stresses (see Figure D.4).Hence:

a) The mean axial strain imposed on the cross-section is given by the expression:

(D.1)

(D.2)

Figure D.3 — Hypothetical and equalising forces

(D.3)

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b) The curvature, i.e. the mean strain gradient imposed on the cross-section is given by the expression:

where:Ac is the area of the cross-section,

lc is the moment of inertia of the cross-section, subscripts 1 and 2 refer respectively to the upper and lower fibre of the cross-section.

(7) If the member is axially unrestrained (i.e. free to expand) the mean axial strain imposed on the cross-section [Equation (D.3)] will result in an overall axial deformation.If the member is free to rotate the mean strain gradient imposed on the cross-section [Equation (D.4)] will result in an overall curvature of the section.The resulting axial elongations, rotations and deflections of such unrestrained building elements do not produce any further external forces.(8) In the general case of statically indeterminate structural elements or sub-assemblies, the mean strains and curvatures developed under elevated temperatures, lead to a modification of axial deformations, deflections and rotations, as well as to redistribution of action-effects.The relevant analysis can be carried out by means of conventional methods of statics, based on moment/curvature and axial-force/elongation diagrams of selected cross-sections for a given temperature profile. Such diagrams provide all the necessary values of (variable) stiffness for every situation and corresponding level of action-effects.(9) It is also possible to evaluate the safety margin (against flexural or shear failure) and the ductility at critical sections of structural elements. In order to do this, the properties of concrete, steel and their bond characteristics should be modified to take account of the corresponding internal temperature levels.D.3 Possible further simplifications(1) In order to overcome the laborious procedure of setting up thermo-elements and calculating the internal stresses, practical diagrams may be used to obtain an approximate estimation of the effective thermal deformations (mean elongation and curvature) assuming sections remain plane under fire conditions.

(D.4)

Figure D.4 — Final internal self-equilibrating stresses

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(2) For certain shapes and dimensions of typical cross-sections, practical diagrams may be prepared using an equivalent linear temperature distribution Geff at the exposed faces of the considered cross-section, instead of the actual temperature distribution Gact. An example of such a practical diagram is given in Figure D.5. This is only valid for cross-sections similar to those shown. Using such diagrams, the redistribution of action-effects and the modification of deformations of reinforced concrete elements during fire may be analyzed using normal loads with effective imposed deformations.

(D.5)

(D.6)

Figure D.5 — Equivalent temperature values Geff for typical reinforced concrete sections exposed to a standard fire

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