00785251.PDF

DD ENV 1992-1-2:1996

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 pages
This 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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DD ENV 1992-1-2:1996

Contents of

National Application Document

Page

Introduction

Scope

Partial factors, combination factors and other values

Tabulated data

Reference standards

Additional recommendations

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

Table N4.1 — Minimum dimensions and axis distances for reinforced

concrete columns; rectangular and circular section

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

Table N4.5 — Minimum dimensions and axis distances for simply

supported beams made with reinforced and prestressed concrete

vii

Table N4.6 — Minimum dimensions and axis distances for

continuous beams made with reinforced and prestressed concrete

vii

Table N4.7 — Reinforced and prestressed concrete continuous I

beams: increased beam width and web thickness for conditions

according to Table N4.6

viii

Table N4.8 — Minimum dimensions and axis distances for reinforced

and prestressed concrete simply supported one-way and two-way slabs

viii

Table N4.9 — Minimum dimensions and axis distances for reinforced

and prestressed concrete flat slabs

viii

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

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

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DD ENV 1992-1-2:1996

Introduction

This 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 Scope

This 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 values

a) 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 data

Tables 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 dimensions

Column width

min

/axis distance

Column exposed on more than one side

Exposed on one side

= 0.2

= 0.5

= 0.7

R 30

R 60

R 90

R 120

R 180

R 240

150/10

180/10

200/40

240/50

300/50

150/10

180/10

210/10

250/40

320/50

400/50

150/10

200/10

240/35

280/40

360/50

450/50

100/10

120/10

140/10

160/45

200/60

300/60

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

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DD ENV 1992-1-2:1996

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 resistance

Minimum wall thickness

EI 30

EI 60

EI 90

EI 120

EI 180

EI 240

100

120

150

175

Standard fire

resistance

Minimum dimensions

Wall thickness/axis distance for

= 0.35

= 0.7

Wall exposed on one

side

Wall exposed on two

sides

Wall exposed on one

side

Wall exposed on two

sides

REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

100/10

110/10

120/20

150/25

180/35

230/45

120/10

140/10

160/25

200/35

250/45

120/10

130/10

140/25

160/35

210/45

270/55

120/10

140/10

170/25

220/35

250/45

300/55

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

Standard fire

resistance

Minimum dimensions

Possible combinations of member width

min

/axis

distance

R 30

R 60

R 90

R 120

R 180

R 240

80/25

120/40

150/55

200/65

240/80

280/90

200/10

300/25

400/45

500/45

600/60

700/70

NOTE For prestressed members the increase of axis distance according

to 4.2.2(4) should be noted.

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DD ENV 1992-1-2:1996

vii

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 dimensions

Possible combinations of

a and b

min

where a is the average axis

distance and

min

is the width of beam

Web thickness

R 30

min

120

160

200

R 60

min

120

160

200

300

100

R 90

min

150

200

250

400

100

R 120

min

200

240

300

500

120

R 180

min

240

300

400

600

140

R 240

min

280

350

500

160

= 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 a

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 b

min

greater than that given in column 4 no increase of a is required.

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

Standard fire resistance

Minimum dimensions

Possible combinations of

a and b

min

where a is the average

axis distance and

min

is the width of beam

Web thickness

R 30

min

160

200

R 60

min

120

200

300

100

R 90

min

150

250

400

100

R 120

min

180

300

450

120

a 55

R 180

min

225

350

550

140

a 70

R 240

min

275

450

650

160

a 80

= 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 a

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 b

min

greater than that given in column 3 no increase of a is required.

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DD ENV 1992-1-2:1996

viii

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

min

and web

thickness

R 120

220

R 180

380

R 240

480

Standard fire resistance

Minimum dimensions

Slab thickness

Average axis-distance

One way

Two way:

u 1.5

1.5

u l

u 2

REI 30

REI 60

REI 90

100

REI 120

120

REI 180

150

REI 240

175

NOTE 1 l

and l

are the spans of a two-way slab (two directions at right angles) where l

is the longer span

NOTE 2 The minimum cover of any bar should not be less than half of required average axis distance, a

m’

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.

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

Standard fire resistance

Minimum dimensions

Slab thickness

Axis-distance

REI 30

REI 60

REI 90

110

REI 120

125

REI 180

150

REI 240

170

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DD ENV 1992-1-2:1996

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

Possible combinations of width of

ribs

min

and axis distance a

Slab thickness

and axis

distance

a, in span

REI 30

min

W 80

REI 60

min

100

120

W 200

REI 90

min

120

160

W 250

100

REI 120

min

140

190

W 300

120

REI 180

min

170

260

W 410

150

REI 240

min

200

350

W 500

175

= a + 10 mm

NOTE 1 For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4)
NOTE 2 a

denotes the distance measured between the axis of the reinforcement and the lateral surface of the

rib exposed to fire.

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

Standard fire resistance

Minimum dimensions

Possible combinations of width of ribs

min

and

axis distance

Slab thickness

and axis distance

a, in span

REI 30

min

W 80

REI 60

min

100

120

W 200

REI 90

min

120

160

W 250

100

REI 120

min

140

190

W 300

120

REI 180

min

175

300

W 400

150

REI 240

min

200

400

W 500

175

= a + 10 mm

NOTE 1 For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).
NOTE 2 a

denotes the distance measured between the axis of the reinforcement and the lateral surface of the

rib exposed to fire.

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DD ENV 1992-1-2:1996

4 Reference standards

Supporting standards including materials specifications and standards for construction are listed in

Table 2 of this NAD.

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

5 Additional recommendations

5.1 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 Û

= 400 °C;

15 mm for prestressing wires and strands, corresponding to Û

= 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 %a

in equation (4.6) may be assumed as follows:

c) Clause 4.2.7.1(4) — addition
The effective thickness, h

, of hollow concrete slabs should be obtained by considering the total solid

part of the cross-section area as follows:

= h

. M

0.7

(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

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

is the total thickness of concrete slab (See Figure 4.7 of EC2-1.2);

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 a

prospective standard for provisional application. The period of validity of this

ENV is limited initially to three years. After two years the members of CEN

will be requested to submit their comments, particularly on the question

whether the ENV can be converted into an European Standard (EN).
CEN members are required to announce the existence of this ENV in the same

way as for an EN and to make the ENV available promptly at national level in

an appropriate form. It is permissible to keep conflicting national standards in

force (in parallel to the ENV) until the final decision about the possible

conversion of the ENV into an EN is reached.
CEN members are the national standards bodies of Austria, Belgium,

Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy,

Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and

United Kingdom.

CEN

European Committee for Standardization

Comité Européen de Normalisation

Europäisches Komitee für Normung

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

countries to CEN and its members

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

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ENV 1992-1-2:1995

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 6
D-10787 Berlin
Phone:(+49) 30 2601 2501
Fax:(+49) 30 2601 1231

or to your national standards organisation
National 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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ENV 1992-1-2:1995

Contents

Page

Foreword

General

1.1

Scope

1.2

Distinction between principles

and application rules

1.3

Normative References

1.4

Definitions

1.5

Symbols

1.6

Units

Basic principles

2.1

Performance requirements

2.2

Actions

2.3

Design values of material properties

2.4

Verification methods

2.4.1 General

2.4.2 Global structural analysis

2.4.3 Analysis of parts of the structure

2.4.4 Member analysis

2.4.5 Testing

Material properties

3.1

General

3.2

Concrete

3.3

Steel

Structural fire design

4.1

General

4.2

Tabulated data

4.2.1 Scope

4.2.2 General design rules

4.2.3 Columns

4.2.4 Walls

4.2.5 Tensile members

4.2.6 Beams

4.2.7 Slabs

4.3

Simplified calculation method

4.3.1 General

4.3.2 Temperature profiles

4.3.3 Reduced cross section

4.4

General calculation methods

4.4.1 General

4.4.2 Thermal response

4.4.3 Mechanical response

4.4.4 Validation of general calculation method 36
4.5

Shear and torsion

Page

4.6

Anchorage

Protective layers

Annex A (informative) Additional

information on material properties

Annex B (informative) Temperature

profiles and reduced cross section

Annex C (informative) Simplified method

of calculation for beams and slabs

Annex D (informative) A procedure for

assessing the structural response of

reinforced concrete elements under fire

Figure 2.1 — Variation of ½

as a function

of ß = Q

for different values of Ó

1,1

Figure 3.1 — Coefficient k

(G) allowing

for decrease of compressive strength (f

)

of silicious concrete at elevated temperature

Figure 3.2 — Coefficient k

(G) allowing for

decrease of characteristic strength (f

) of

reinforcing steels at elevated

temperature

Figure 3.3 — Coefficient k

(G) allowing

for decrease of characteristic strength (f

)

of prestressing steels at elevated

temperature

Figure 4.1 — Sections through

structural members, showing nominal

axis distance a, and nominal concrete

cover c to reinforcement

Figure 4.2 — Dimensions used to

calculate average axis distance a

Figure 4.3 — Exposure of built-in columns

Figure 4.4 — Definition of dimensions

for different types of beam section

Figure 4.5 —

-shaped beam with increasing

web width b

satisfying the requirements

of an imaginary cross-section

Figure 4.6 — Envelope of resisting bending

moments over supports in fire conditions

Figure 4.7 — Concrete slab with floor finishes

Figure 4.8 — Slab systems for which minimum

reinforcement areas according to 4.2.7.3 (3)

should be provided

Figure 4.9 — Reductions of strength and

cross-sections found by means of

equivalent walls (wall1 and wall2) exposed

to fire on both sides

Figure 4.10 — Divisions of a wall, exposed

on both sides, into zones for use in

calculation of strength reduction

and a

values

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ENV 1992-1-2:1995

Page

Figure A.1 — Coefficient k

(G) allowing

for decrease of tensile strength, (f

ctk

) of

concrete at elevated temperature

Figure A.2 — Model for compression

stress-strain relationships of siliceous

and calcareous concrete at elevated

temperatures

Figure A.3 — Parameters for stress-strain

relationships of concrete at elevated

temperatures, according to Figure A.2

and Table A.1

Figure A.4 — Stress-strain relationships

of siliceous concrete under uniaxial

compression at elevated temperatures

Figure A.5 — Model for stress-strain

relationships of reinforcing and prestressing

steels at elevated temperatures (notations

for prestressing steels “p” instead of “s”)

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

Figure A.8 — Stress-strain relationships

for cold-worked reinforcing steels at

elevated temperatures, according to

Figure A.5 and Table A.4

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

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

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

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

Page

Figure A.14 — Thermal elongation of concrete

Figure A.15 — Specific heat of concrete

Figure A.16 — Thermal conductivity of concrete 51
Figure A.17 — Thermal elongation of steel

Figure A.18 — Relationship between Ö

c,fi

and h (or b) for risk of explosive spalling

for normal weight concrete members

Figure B.1 — Temperature profiles for beams

Figure B.2 — Temperature profiles for slabs

Figure B.3 — Reduction in cross section and

concrete strength assuming a standard fire

Figure C.1 — Positioning the free bending

moment diagram M

Sd,fi

to establish equilibrium 59

Figure D.1 — Temperature profiles in concrete

elements. G

is the average temperature

along a horizontal section y-y

Figure D.2 — Layers of thermo-elements

assumed free to move axially

Figure D.3 — Hypothetical and equalising

forces

Figure D.4 — Final internal self-equilibrating

stresses

Figure D.5 — Equivalent temperature

values G

eff

for typical reinforced concrete

sections exposed to a standard fire

Table 4.1 — Minimum dimensions and

axis distances for reinforced concrete

columns; rectangular and circular section

Table 4.2 — Minimum wall thickness of

non load-bearing walls (partitions)

Table 4.3 — Minimum dimensions and

axis distances for load-bearing reinforced

concrete walls

Table 4.4 — Minimum dimensions and axis

distances for reinforced and prestressed

concrete tensile members

Table 4.5 — Minimum dimensions and axis

distances for simply supported beams

made with reinforced and prestressed concrete 26
Table 4.6 — Minimum dimensions and axis

distances for continuous beams made with

reinforced and prestressed concrete

Table 4.7 — Reinforced and prestressed

concrete continuous

-beams; increased

beam width and web thickness for

conditions according to 4.2.6.3 (6)

Table 4.8 — Minimum dimensions and axis

distances for reinforced and prestressed

concrete simply supported one-way

and two-way slabs

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ENV 1992-1-2:1995

Page

Table 4.9 — Minimum dimensions and

axis distances for reinforced and

prestressed concrete flat slabs

Table 4.10 — Minimum dimensions and

axis distance for two-way spanning, simply

supported ribbed slabs in reinforced or

prestressed concrete

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

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)

Table A.2 — Recommended values

for º

(G) and º

(G) and admissible range

of º

(G)

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

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

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ENV 1992-1-2:1995

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 Definitions

1.4.1

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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ENV 1992-1-2:1995

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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ENV 1992-1-2:1995

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

considered

NOTE 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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ENV 1992-1-2:1995

1.5 Symbols

The 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)

d,fi

design effect of actions in the fire situation

design effect of actions for normal temperature design

d,fi

design load bearing capacity (resistance) in the fire situation R

d,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

exposure
E 30 or E 60,... a member meeting the integrity criterion for 30, or 60... minutes in standard fire

exposure
I 30 or I 60,... a member meeting the thermal insulation criterion for 30, or 60... minutes in standard

fire exposure
X

characteristic value of a strength or deformation property for normal temperature design

d,fi

design strength or deformation property in the fire situation

axis distance of the steel from the nearest exposed surface

specific heat (characteristic value) [J/kgK]

(G) characteristic value of compressive strength of concrete at temperature G for a specified strain

(G) characteristic value of strength of prestressing steel at temperature G for a specified strain

(G) characteristic strength of reinforcing steel at temperature G for a specified strain

(G) = X

,(G)/X

reduction factor to describe a strength or deformation property at temperature G

time of fire exposure (min)

M,fi

partial safety factor for a material in fire design

= E

d,fi

ratio of design effect of actions in the fire situation to that in normal design

s,fi

strain of the reinforcing or prestressing steel at temperature G.

thermal conductivity (characteristic value) [W/mK]

= E

d,fi

(0) ratio of design effect of actions in the fire situation to the design resistance of the

structural element at time t = 0
Ö

c,fi

compressive stress of concrete in fire situation

s,fi

steel stress in fire situation

temperature [°C]

critical temperature [°C]

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ENV 1992-1-2:1995

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 I
loadbearing only: R
separating 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 (X

d,fi

) are defined as follows:

— thermal properties for thermal analysis
if 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

where

(G) is the characteristic value of a material property in fire design, generally dependent on the

material temperature
X

is the characteristic value of a strength or deformation property (e.g. f

and f

) for normal

temperature design to ENV 1992-1-1
k

(G) = X

(G)/X

is the reduction factor for a strength or deformation property dependent on the material

temperature — see 3.2 and 3.3
Y

M,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

d,fi

= X

(G)/Y

M,fi

(2.1)

d,fi

= X

(G) Y

M,fi

(2.2)

d,fi

= k(G) X

M,fi

(2.3)

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ENV 1992-1-2:1995

M,fi

=|1,0|

2.4 Verification methods

2.4.1 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

where

d,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 actions
R

d,fi

(t) is the corresponding design resistance at elevated temperatures

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 Ó

1,i

are given in ENV 1991-1. Equation (2.6) is graphically represented presented in Figure 2.1.

(5) As a simplification ½

=|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.

d,fi

(t) u R

d,fi

(t)

(2.4)

d,fi

= ½

(2.5)

is the design effect of actions from ultimate limit state design to ENV 1992-1-1 using the

fundamental combination
½

is a reduction factor, depending on ß = Q

, which is the ratio between the main variable and

permanent actions applied to the structure, see ENV 1991-2-2:
½

= ([1,0] + Ó

1,1

,ß)/(Y

+ Y

.ß)

(2.6)

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ENV 1992-1-2:1995

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 k

(G) for which:

(2) In the absence of more accurate information the following k

(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 k

(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 k

(G) for which:

(3) Where k

(G) and k

(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 k

(G) values should be used for reinforcement

(see Figure 3.2).

(G) = k

(G) f

(20 °C)

(3.1)

(G) = 1,0

for 20 °C u G u 100 °C

(G) = (1 600 – G)/1 500

for 100 °C u G u 400 °C

(G) = (900 – G)/625

for 400 °C u G u 900 °C

(G) = 0

for 900 °C u G u 1 200 °C

(G) = k

(G)f

(20 °C)

(3.2)

(G) = k

(G)f

(20 °C)

(3.3)

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ENV 1992-1-2:1995

For tension reinforcement in beams and slabs where º

s,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 º

s,fi

< 2 % when using the simplified or general calculation methods.

(5) In the absence of more accurate information the following k

(G) values should be used for prestressing

steel (see Figure 3.3).
For prestressing steel bars:

For prestressing steel wires and strands:

(G) = 1,0

for 20 °C u G u 350 °C

(G) = (6 650 – 9G)/3 500

for 350 °C u G u 700 °C

(G) = (1 200 – G)/5 000

for 700 °C u G u 1 200 °C

(G) = 1,0

for 20 °C u G u 100 °C

(G) = (1 100 – G)/1 000

for 100 °C u G u 400 °C

(G) = (8 300 – 12 G)/5 000

for 400 °C u G u 650 °C

(G) = (1 200 – G)/5 500

for 650 °C u G u 1 200 °C

(G) = 1,0

for 20 °C u G u 100 °C

(G) = (1 600 – G)/1 500

for 100 °C u G u 250 °C

(G) = (700 – G)/500

for 250 °C u G u 650 °C

(G) = (1 000 – G)/3 500

for 650 °C u G u 1 000 °C

(G) = 0

for 1 000 °C u G u 1 200 °C

(G) = 1,0

for 20 °C u G u 100 °C

(G) = (850 – G)/750

for 100 °C u G u 250 °C

(G) = (650 – G)/500

for 250 °C u G u 600 °C

(G) = (1 000 – G)/4 000

for 600 °C u G u 1 000 °C

(G) = 0

for 1 000 °C u G u 1 200 °C

Figure 3.1 — Coefficient k

(G) allowing for decrease of compressive strength (f

) of

silicious concrete at elevated temperature

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ENV 1992-1-2:1995

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 data

4.2.1 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/m

the reduction may

be |20 %|, except for non-load bearing walls (see 4.2.4.1). For densities between|1 200|kg/m

and |2 000|kg/m

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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ENV 1992-1-2:1995

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:

d,fi

is the design effect of actions in the fire situation.

d,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 G

= 500 °C. G

is the critical temperature of reinforcement at which yielding becomes

imminent under the actual steel stress Ö

s,fi

. This assumption corresponds approximately to E

d,fi

= 0,7E

and Y

= 1,15 [see Equation (4.2)] where E

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 G

= 400 °C

15 mm for prestressing wires and strands, corresponding to G

= 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 Ö

s,fi

for the actions in a fire situation (E

d,fi

) using Equation (4.2).

where:

b) evaluate the critical temperature of reinforcement G

, corresponding to the reduction

factor k

(G) = Ö

s,fi

(20 °C) using Figure 3.2 (Curve 1) for reinforcement or k

(G) = Ö

p,fi

(20 °C)

using Figure 3.3 for prestressing steel.
c) adjust the minimum axis distance given in the Tables, for the new critical temperature, G

, 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 < G

< 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 G

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).

d,fi

u 1,0

(4.1)

(4.2)

is the partial safety factor for reinforcing steel;

= 1,15 (see 2.3.3.2 of ENV 1992-1-1)

s,req

is the area of reinforcement required for ultimate limit

state according to ENV 1992-1-1
A

s,prov

is the area of reinforcement provided

d,fi

may be assessed using 2.4.3 (4) and (5).

%a = 0,1 (500 – G

) (mm)

(4.3)

mod

W b

min

+ 0,8 (400 – G

) (mm)

(4.4)

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ENV 1992-1-2:1995

where b

min

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 f

and f

respectively, the average

axis distance a

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:

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

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

When reinforcement consists of steels with different characteristic strength A

should be replaced

by A

yki

(or A

pki

) in Equation (4.5).

Figure 4.1 — Sections through structural members, showing nominal axis distance

and nominal concrete cover

c to reinforcement

(4.5)

Figure 4.2 — Dimensions used to calculate average axis distance a

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ENV 1992-1-2:1995

(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 È

has been introduced accounting for load combinations

and the design column resistance to compression and, possibly, bending, including second order effects.

The effective length l

, is assumed to be equal to the actual column length l

col

(notation as in

ENV 1992-1-1, 4.3.5).
È

may be taken as|0,7|in all cases. However, a more accurate value may be obtained using Equation (4.7):

where:

= E

d,fi

[see 2.4.3 (4)];

d,fi

(0) denotes the design resistance calculated according to ENV 1992-1-1 with l

= l

col

, Y

= 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 A

W|0,02|A

, 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.

i,nom

= a

– %a

(4.6)

is the actual axis distance of the tendon considered

is an allowance for the different critical temperatures of reinforcing and prestressing steel.

may be assumed as follows:

= 10 mm for prestressing bars
= 15 mm for prestressing wires and strands

= E

d,fi

(0) = ½

d,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 b

min

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/b

min

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 l

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

min

/axis distance

Column exposed on more than one side

Exposed on one

side

= 0,2

= 0,5

= 0,7

R 30

|150/10|

|100/10|

R 60

|150/10|

|180/10|

|200/10|

|120/10|

R 90

|180/10|

|210/10|

|240/35|

|140/10|

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|

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

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Table 4.2 — Minimum wall thickness of non

load-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 2b

min

, where b

min

is the minimum member

width given in Table 4.4.

Standard fire resistance

Minimum wall thickness (mm)

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

= 0,35

= 0,7

wall exposed on one

side

wall exposed on two

sides

wall exposed on one

side

wall exposed on two

sides

REI

|100/10|

|120/10|

REI

|110/10|

|120/10|

|130/10|

|140/10|

REI

|120/20|

|140/10|

|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|

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

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ENV 1992-1-2:1995

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 d

eff

of the bottom flange of

-shaped beams with varying webs [Figure 4.4 (c)] should

not be less than:

where b

min

is the minimum value of beam width according to Table 4.5

This 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

min

/axis distance

R 30

|80/25|

|200/10|

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.

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

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

eff

= d

+ 0,5 d

W b

min

(4.8)

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ENV 1992-1-2:1995

(6) Where the actual width of the bottom flange b exceeds the limit 1,4 b

, [b

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:

eff

is given by Equation (4.8)

min

is the minimum beam width given in Table 4.5.

(7) For flanges with b > 3,5 b

[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 A

= 2b

min

where b

min

is given

by Table 4.5 below.
(9) Higher temperature concentrations occur at the bottom corners of beams. For this reason the axis

distance a

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 of

Table 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 —

-shaped beam with increasing web width b

satisfying the

requirements of an imaginary cross-section

(4.9)

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ENV 1992-1-2:1995

(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:

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

eff

)

s,req

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

s,req

(x) is the minimum area of top reinforcement required in the section considered but not less than

(x) required by ENV 1992-1-1.

Where l

eff

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

s,req

(x) = A

s,req

(0) × (1 – 2,5x/l

eff

)

(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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ENV 1992-1-2:1995

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 b

min

where a is the average axis

distance and

min

is the width of beam

Web thickness

R 30

min

= |80|

|120|

|160|

|200|

|80|

|25|

|15|

|10|

R 60

min

= |120|

|160|

|200|

|300|

|100|

|40|

|35|

|30|

|25|

R 90

min

= |150|

|200|

|250|

|400|

|100|

|55|

|45|

|40|

|35|

R 120

min

= |200|

|240|

|300|

|500|

|120|

|65|

|55|

|50|

|45|

R 180

min

= |240|

|300|

|400|

|600|

|140|

|80|

|70|

|65|

|60|

R 240

min

= |280|

|350|

|500|

|160|

|90|

|80|

|75|

|70|

= a + 10 mm

(see note below)

For prestressed beams the increase of axis distance according to 4.2.2(4) should be noted.

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 b

min

greater than that given in Column 4 no increase of a is required.

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

Standard fire

resistance

Minimum dimensions (mm)

Possible combinations of

a and b

min

where a is the average axis distance

and

min

is the width of beam

Web thickness b

R 30

min

= |80|

|160|

|200|

|80|

|12|

R 60

min

= |120|

|200|

|300|

|100|

|25|

|12|

R 90

min

= |150|

|250|

|400|

|100|

|35|

|25|

R 120

min

= |220|

|300|

|500|

|120|

|45|

|35|

R 180

min

= |380|

|400|

|600|

|140|

|60|

|50|

R 240

min

= |480|

|500|

|700|

|160|

|70|

|60|

= a + 10 mm (see note below)

For prestressed beams the increase of axis distance according to 4.2.2(4) should be noted.

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 b

min

greater than that given in Column 3 no increase of a is required.

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

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(5) The web thickness of

-shaped continuous beams b

[see Figure 4.4 (c)] should not be less than the

minimum value b

min

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), and
b) V

> 2/3 V

Rd2

at the first intermediate support, where V

Rd2

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

-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 b

min

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 h

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

min

(mm) and web

thickness

(mm)

R 120

|220|

R 180

|380|

R 240

|480|

= 2b

min

(4.11)

Explanation:
(1) Concrete slab
(2) Flooring (non-combustible)
(3) Sound insulation (possibly combustible)
h

+ h

= h

as given in

Table 4.8

Figure 4.7 — Concrete slab with floor finishes

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ENV 1992-1-2:1995

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 A

W|0,005|A

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

(mm)

axis-distance

one way

two way:

u 1,5

1,5 <

u 2

REI 30

|60|

|10|

REI 60

|80|

|20|

|10|

|15|

REI 90

|100|

|30|

|15|

|20|

REI 120

|120|

|40|

|20|

|25|

REI 180

|150|

|55|

|30|

|40|

REI 240

|175|

|65|

|40|

|50|

and l

are the spans of a two-way slab (two directions at right angles) where l

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.

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

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ENV 1992-1-2:1995

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

axis-distance

REI 30

|150|

|10|

REI 60

|200|

|15|

REI 90

|200|

|25|

REI 120

|200|

|35|

REI 180

|200|

|45|

REI 240

|200|

|50|

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

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ENV 1992-1-2:1995

(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

min

and

axis distance

slab thickness

and

axis distance

a in span

REI 30

min

= |W 80|

= |80|

|15|

= |10|

REI 60

min

= |100|

|120|

|W 200|

= |80|

|35|

|25|

|15|

= |10|

REI 90

min

= |120|

|160|

|W 250|

= |100|

|45|

|40|

|30|

= |15|

REI 120

min

= |160|

|190|

|W 300|

= |120|

|60|

|55|

|40|

= |20|

REI 180

min

= |W 220|

|260|

|W 410|

= |150|

|75|

|70|

|60|

= |30|

REI 240

min

= |280|

|W 500|

= |175|

|90|

|70|

= |40|

= a +|10|

For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).

denotes the distance measured between the axis of the reinforcement lateral surface of the rib

exposed to fire.

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

Licensed copy:Heriot Watt University, 20/04/2004, Uncontrolled Copy, © BSI

ENV 1992-1-2:1995

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 method

4.3.1 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

min

and axis

distance

slab thickness

and axis distance

in span

REI 30

min

= |W 80|

= |80|

|10|

= |10|

REI 60

min

= |100|

|120|

|W 200|

= |80|

|25|

|15|

|10|

= |10|

REI 90

min

= |120|

|160|

|W 250|

= |100|

|35|

|25|

|15|

= |15|

REI 120

min

= |160|

|190|

|W 300|

= |120|

|45|

|40|

|30|

= |20|

REI 180

min

= |310|

|600|

= |150|

|60|

|50|

= |30|

REI 240

min

= |450|

|700|

= |175|

|70|

|60|

= |40|

= a +|10|

For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 4.2.2(4).

denotes the distance measured between the axis of the reinforcement lateral surface of the rib exposed to fire.

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

(G) = k

(G) f

(20 °C).

(4.12)

Licensed copy:Heriot Watt University, 20/04/2004, Uncontrolled Copy, © BSI

ENV 1992-1-2:1995

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 a

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 a

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 a

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 a

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 a

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)].

Licensed copy:Heriot Watt University, 20/04/2004, Uncontrolled Copy, © BSI

ENV 1992-1-2:1995

(6) The reduced compressive strength f

) at the point M in a member exposed to fire on both sides is

where G

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 E

) cannot be

derived from Annex A where creep and transient strain are included in the data).
(7) The damaged zone a

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 k

) 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

) = k

) f

(20 °C)

(4.13)

) = (k

))

(20 °C).

(4.14)

Licensed copy:Heriot Watt University, 20/04/2004, Uncontrolled Copy, © BSI

ENV 1992-1-2:1995

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 k

) 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 ¼

cu,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 a

values

(4.15)

(4.16)

(4.17)

cu,max

= 0,0035/k

)

(4.18)

ENV 1992-1-2:1995

4.4 General calculation methods

4.4.1 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:

where

is the thermal strain,

load

is the instantaneous stress-dependent strain

creep

is the creep strain and

is the transient strain

º = º

+ º

load

+ º

creep

+ º

(4.15)

ENV 1992-1-2:1995

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 º

and º

in hot condition. º

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 k

(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)].

ENV 1992-1-2:1995

Annex A (informative)

Additional information on material properties

A.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 f

(G)

— the strain º

(G) corresponding to f

(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, º

(G)

shows considerable scatter, which is presented in Table A.2. Recommended values for º

(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 k

(G) allowing for decrease of tensile strength, (f

ctk

) of

concrete at elevated temperature

ENV 1992-1-2:1995

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)

(G)/f

(20 °C)

(G) × 10

–3

siliceous

calcareous

1,00

2,5

100

0,95

0,97

3,5

200

0,90

0,94

4,5

300

0,85

0,91

6,0

400

0,75

0,85

7,5

500

0,60

0,74

9,5

600

0,45

0,60

12,5

700

0,30

0,43

14,0

800

0,15

0,27

14,5

900

0,08

0,15

15,0

1 000

0,04

0,06

15,0

1 100

0,01

0,02

15,0

1 200

0,00

—

ENV 1992-1-2:1995

Table A.2 — Recommended values for º

(G) and º

(G) and

admissible range of º

(G)

Figure A.4 — Stress-strain relationships of siliceous concrete under uniaxial

compression at elevated temperatures

Concrete

Temperature

(°C)

(G) × 10

–3

(G) × 10

–3

Recommended

Range

Recommended

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

—

ENV 1992-1-2:1995

(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 Ö

spr

(G), Ö

ppr

(G) respectively and

— the maximum stress level f

(G), f

(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)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

1,00

0,87

0,72

0,56

0,40

0,24

0,08

0,06

0,05

0,03

0,02

0,00

1,00

0,96

0,92

0,81

0,63

0,44

0,26

0,08

0,06

0,05

0,03

0,02

0,00

1,00

0,94

0,67

0,40

0,12

0,11

0,08

0,05

0,03

0,00

Steel Temperature

(°C)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

1,00

0,90

0,80

0,70

0,60

0,31

0,13

0,09

0,07

0,04

0,02

0,00

1,00

0,81

0,61

0,42

0,36

0,18

0,07

0,05

0,04

0,02

0,01

0,00

1,00

0,78

0,47

0,23

0,11

0,06

0,04

0,02

0,00

( )

(

)

-----------------------

spr

( )

0,2

(

)

-------------------------

( )

0,2

(

)

-------------------------

( )

(

)

-----------------------

spr

( )

0,2

(

)

-------------------------

( )

0,2

(

)

-------------------------

ENV 1992-1-2:1995

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)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

1,00

0,76

0,61

0,52

0,41

0,20

0,15

0,10

0,06

0,03

0,00

0.00

0,00

1,00

0,77

0,62

0,58

0,52

0,14

0,11

0,09

0,06

0,03

0,00

1,00

0,98

0,92

0,86

0,69

0,26

0,21

0,15

0,09

0,04

0,00

Steel Temperature

(°C)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

1,00

0,98

0,95

0,88

0,81

0,54

0,41

0,10

0,07

0,03

0,00

1,00

0,68

0,51

0,32

0,13

0,07

0,05

0,03

0,02

0,01

0,00

1,00

0,99

0,87

0,72

0,46

0,22

0,10

0,08

0,05

0,03

0,00

( )

(

)

------------------------

ppr

( )

p0,2

(

)

---------------------------

( )

p0,2

(

)

---------------------------

( )

(

)

------------------------

ppr

( )

p0,2

(

)

---------------------------

( )

p0,2

(

)

---------------------------

ENV 1992-1-2:1995

Steel

Temperature

(°C)

(G)

Recommended

values

(%)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

5,5

6,5

7,5

8,5

9,5

10,5

11,5

12,5

13,5

14,5

Figure A.8 — Stress-strain relationships for cold-worked reinforcing steels at elevated

temperatures, according to

Figure A.5 and Table A.4

ENV 1992-1-2:1995

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)

(G)

Recommended

values

(%)

100

200

300

400

500

600

700

800

900

1 000

1 100

1 200

6,5

7,5

8,5

9,5

10,5

11,5

12,5

13,5

14,5

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

ENV 1992-1-2:1995

(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 properties
A.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)

= (– 1,8 × 10

–4

) + (9 × 10

– 6

G) + (2,3 × 10

–11

)

(A.1)

for 700 °C < G u 1 200 °C

(%l/l)

= 14 × 10

–3

(A.2)

calcareous aggregates:

for 20 °C < G u 805 °C

(%l/l)

= (– 1,2 × 10

–4

) + (6 × 10

–6

G) + (1,4 × 10

–11

)

(A.3)

for 805 °C < G u 1 200°

(%l/l)

= 12 × 10

–3

(A.4)

lightweight aggregates:

for 20 °C < G u 1200 °C

(%l/l)

= 8 × 10

– 3

(G – 20)

(A.5)

ENV 1992-1-2:1995

where:

is the length at room temperature

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)

= 18 × 10

–3

G for concrete with siliceous aggregates

(%l/l)

= 12 × 10

–3

G for concrete with calcareous aggregates

(%l/l)

= 8 × 10

–3

G for concrete with lightweight aggregates.

(2) The specific heat c

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

c,peak

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

c,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 c

= 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

= 900 + 80 G/120 – 4(G/120)

(J/kgK)

(A.6)

Concrete with lightweight aggregates:

for 20 °C < G u 1 200 °C

= 840 (J/kgK)

(A.7)

ENV 1992-1-2:1995

If only an approximate answer is required (simple calculation, estimation), the thermal conductivity may

be considered as independent of the concrete temperature:

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

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

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

(4) The density Ô

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 Ô

= 2 300 kg/m

may be adopted for normal dense concrete

(siliceous or calcareous).
The density may also be reduced by 100 kg/m

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 a

/s) may be used.

It may be considered as independent of the concrete temperature:

= 0,69 × 10

– 6

/s for concrete with siliceous aggregates

= 0,56 × 10

– 6

/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:

, l

is the length at room temperature

, %l

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)

= (– 2,416 × 10

–4

) + (1,2 × 10

–5

G) + (0,4 × 10

–8

)

(A.12)

for 750 °C < G u 860 °C

(%l/l)

= 11 × 10

–3

(A.13)

for G W 860 °C

(%l/l)

= (– 6,2 × 10

–3

) + (2 × 10

–5

(A.14)

prestressing steel:

for 20 °C < G u 1 200 °C

(%l/l)

= (– 2,016 × 10

–4

) + 10

–5

G + (0,4 × 10

–8

)

(A.15)

ENV 1992-1-2:1995

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)

= 14 × 10

–6

G for reinforcing steels

(%l/l)

= 12 × 10

–6

G for prestressing steels

(2) The density Ô

of reinforcing and prestressing steel should be considered as independent from the steel

temperature:

= 7 850 kg/m

(3) Normally in both reinforced and prestressed concrete members, the thermal properties Æ

, c

, and a

, 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

in the compressive zones of beams, slabs, walls and columns satisfy the conditions given in Figure A.18.

The compressive stress Ö

c,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

ENV 1992-1-2:1995

Annex C (informative)

Simplified method of calculation for beams and slabs

C.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, b

, h

) 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 b

is less than 200 mm and the height h

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 F

d,fi

(kN) may be determined using Equation (2.5).

(3) The maximum fire design moment M

Sd,fi

for predominantly uniformly distributed load may be calculated

using Equation (C.2).

where l

eff

is the effective length of beam or slab.

(4) The moment of resistance M

Rd,fi

for design for the fire situation may be calculated using Equation (C.3).

where:

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

s,fi

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

(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 distance
M

is the applied moment for cold design to ENV 1992-1-1

s,prov

is the area of tensile steel provided

s,req

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

s,prov

s,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 M

RdSpan,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 (F

d,fi

eff

/8 for uniformly distributed load) should be fitted to this moment of

resistance M

RdSpan,fi

such that the support moments M

Rd1,fi

and M

Rd2,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.

sd,fi

u M

Rd,fi

(C.1)

Sd,fi

= F

d,fi

eff

(C.2)

Rd,fi

= (Y

s,fi

) × k

(G) × M

s,prov

s,req

)

(C.3)

ENV 1992-1-2:1995

(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).

where

, M

, Y

s,fi

, A

s,prov

and A

s,req

are defined in C.2

is the required average axis distance given in Table 4.5 for beams and Table 4.8, Column 3 for slabs,

is the effective depth of section

s,prov

s,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 M

Rd,fi

should be reduced by k

(G) according to Figure 3.2, curve 1, for reinforcing

bars, and by k

(G) according to Figure 3.3 for prestressing tendons.

(6) The curtailment length l

bnet,fi

required under fire conditions should be checked. This may be calculated

using Equation (C.5).

where l

bnet

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 l

b net,fi

Annex D (informative)

A procedure for assessing the structural response of reinforced concrete

elements under fire

D.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

Sd,fi

to establish equilibrium

Rd,fi

= (Y

s,fi

) M

s,prov

s,req

) (d – a)/d

(C.4)

bnet,fi

= (Y

s,fi

) (Y

c,fi

) l

bnet

(C.5)

ENV 1992-1-2:1995

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

where:

is the area of the cross-section,

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

DD ENV

1992-1-2:1996

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