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CEN/TC 250/SC2 N ???

Ref. No. prEN 1992-1-2: (July 2001)

EUROPEAN STANDARD

NORME EUROPÉENNE

EUROPÄISCHE NORM

prEN 1992-1-2 (2nd draft)

July 2001

ICS 00.000.00 Supersedes ENV 1992-1-2

Descriptors: Buildings, concrete structures, 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 ducomportement au feu

Eurocode 2: Planung von Stahlbeton- undSpannbetontragwerken - Teil 1-2: Allgemeine

Regeln – Tragwerksbemessung für den Brandfall

This European Standard was approved by CEN on 199?-??-??. CEN members are bound to comply with the CEN/CENELECInternal Regulations which stipulate the conditions for giving this European Standard the status of a national standardwithout any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to theCentral Secretariat or to any CEN member.

The European Standards exist in three official versions (English, French, German). A version in any other language made bytranslation under the responsibility of a CEN member into its own language and notified to the Central Secretariathas the same status as the official versions.

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

CEN

European Committee for StandardizationComité Européen de NormalisationEuropäishes Komitee für Normung

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


Ref. No. EN 1992-1 (July 2001)

FOREWORD

This European Standard EN 1992-1-2 , “Design of concrete structures - Part 1-2 General rules -Structural fire design", has been prepared on behalf of Technical Committee CEN/TC250”Structural Eurocodes”, the Secretariat of which is held by BSI. CEN/TC250/SC 2 is responsiblefor ”Eurocode 2: Design of concrete structures”.

The text of the draft standard was submitted to the formal vote and was approved by CEN asEN 199x-1-2 on YYYY-MM-DD.

[Reference to superseded ENV 1992-1-2 is made on the CEN cover page]

Background of the Eurocode programme

In 1975, the Commission of the European Community decided on an action programme in thefield of construction, based on article 95 of the Treaty. The objective of the programme was theelimination of technical obstacles to trade and the harmonisation of technical specifications.Within this action programme, the Commission took the initiative to establish a set of harmonisedtechnical rules for the design of construction works which, in a first stage, would serve as analternative to the national rules in force in the Member States and, ultimately, would replace them.

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

In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis ofan agreement1 between the Commission and CEN, to transfer the preparation and thepublication of the Eurocodes to the CEN through a series of Mandates, in order to provide themwith a future status of European Standard (EN). This links de facto the Eurocodes with theprovisions of all the Council’s Directives and/or Commission’s Decisions dealing with Europeanstandards (e.g. the Council Directive 89/106/EEC on construction products - CPD - and CouncilDirectives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalentEFTA Directives initiated in pursuit of setting up the internal market).

The Structural Eurocode programme comprises the following standards generally consisting ofa number of Parts:

EN 1990 Eurocode: Basis of Structural DesignEN 1991 Eurocode 1: Actions on structuresEN 1992 Eurocode 2: Design of concrete structuresEN 1993 Eurocode 3: Design of steel structuresEN 1994 Eurocode 4: Design of composite steel and concrete structuresEN 1995 Eurocode 5: Design of timber structuresEN 1996 Eurocode 6: Design of masonry structuresEN 1997 Eurocode 7: Geotechnical designEN 1998 Eurocode 8: Design of structures for earthquake resistanceEN 1999 Eurocode 9: Design of aluminium structures

1 Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the

work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89).


Ref. No. prEN 1992-1-2 (July 2000)

Eurocode standards recognise the responsibility of regulatory authorities in each Member Stateand have safeguarded their right to determine values related to regulatory safety matters atnational level where these continue to vary from State to State.

STATUS AND FIELD OF APPLICATION OF EUROCODES

The Member States of the EU and EFTA recognise that Eurocodes serve as referencedocuments for the following purposes :

– as a means to prove compliance of building and civil engineering works with the essentialrequirements of Council Directive 89/106/EEC, particularly Essential Requirement N°1 –Mechanical resistance and stability – and Essential Requirement N°2 – Safety in case of fire ;

– as a basis for specifying contracts for construction works and related engineering services ; – as a framework for drawing up harmonised technical specifications for construction products

(ENs and ETAs) The Eurocodes, as far as they concern the construction works themselves, have a directrelationship with the Interpretative Documents2 referred to in Article 12 of the CPD, althoughthey are of a different nature from harmonised product standards3. Therefore, technical aspectsarising from the Eurocodes work need to be adequately considered by CEN TechnicalCommittees and/or EOTA Working Groups working on product standards with a view toachieving full compatibility of these technical specifications with the Eurocodes.

The Eurocode standards provide common structural design rules for everyday use for thedesign of whole structures and component products of both a traditional and an innovativenature. Unusual forms of construction or design conditions are not specifically covered and thedesigner in such cases will require additional expert consideration.

NATIONAL STANDARDS IMPLEMENTING EUROCODES

The National Standards implementing Eurocodes will comprise the full text of the Eurocode(including any annexes), as published by CEN, which may be preceded by a National title pageand National foreword, and may be followed by a National annex.

The National annex may only contain information on those parameters which are left open inthe Eurocode for national choice, known as Nationally Determined Parameters, to be used forthe design of buildings and civil engineering works to be constructed in the country concerned,i.e. :

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

2 According to Art. 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of

the necessary links between the essential requirements and the mandates for harmonised ENs and ETAGs/ETAs. 3 According to Art. 12 of the CPD the interpretative documents shall :

a) give concrete form to the essential requirements by harmonising the terminology and the technical bases and indicating classes or levels for eachrequirement where necessary ;

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

c) serve as a reference for the establishment of harmonised standards and guidelines for European technical approvals.The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.


Ref. No. EN 1992-1 (July 2001)

– values to be used where a symbol only is given in the Eurocode,– country specific data (geographical, climatic, etc.), e.g. snow map,– the procedure to be used where alternative procedures are given in the Eurocode,– decisions on the application of informative annexes,– references to non-contradictory complementary information to assist the user to apply the

Eurocode.

LINKS BETWEEN EUROCODES AND PRODUCTS HARMONISED TECHNICALSPECIFICATIONS (ENS AND ETAS)

There is a need for consistency between the harmonised technical specifications forconstruction products and the technical rules for works4. Furthermore, all the informationaccompanying the CE Marking of the construction products which refer to Eurocodes shouldclearly mention which Nationally Determined Parameters have been taken into account.

ADDITIONAL INFORMATION SPECIFIC TO EN 1992-1-2

EN 1992- 1-2 describes the Principles, requirements and rules) for the structural design ofbuildings exposed to fire, including the following aspects. Safety requirements EN 1992-1-2 is intended for clients (e.g. for the formulation of their specific requirements),designers, contractors and relevant authorities. The general objectives of fire protection are to limit risks with respect to the individual andsociety, neighbouring property, and where required, environment or directly exposed property,in the case of fire. Construction Products Directive 89/106/EEC gives the following essential requirement for thelimitation of fire risks: "The construction works must be designed and build in such a way, that in the event of anoutbreak of fire

- the load bearing resistance of the construction can be assumed for a specified periodof time

- the generation and spread of fire and smoke within the works are limited - the spread of fire to neighbouring construction works is limited - the occupants can leave the works or can be rescued by other means - the safety of rescue teams is taken into consideration". According to the Interpretative Document N° 2 "Safety in case of fire" the essential requirementmay be observed by following various possible fire safety strategies prevailing in the MemberStates such as conventional fire scenarios (nominal fires) or “natural” (parametric) firescenarios, including passive and active fire protection measures. The fire parts of Structural Eurocodes deal with specific aspects of passive fire protection interms of designing structures and parts thereof for adequate load bearing resistance and forlimiting fire spread as relevant. 4 see Art.3.3 and Art.12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.


Ref. No. prEN 1992-1-2 (July 2000)

Required functions and levels of performance can be specified either in terms of nominal(standard) fire resistance rating, generally given in National Fire Regulations or by referring to firesafety engineering for assessing passive and active measures. This Part 1-2, together with EN 1991-1-2 "Actions on structures exposed to fire" gives thesupplements to EN 199x-1-1, which are necessary so that structures designed according to thisset of Structural Eurocodes may also comply with structural fire resistance requirements. Supplementary requirements concerning, for example

- the possible installation and maintenance of sprinkler systems, - conditions on occupancy of building or fire compartment,- the use of approved insulation and coating materials, including their maintenance,

are not given in this document, because they are subject to specification by the competentauthority. Numerical values for partial factors and other reliability elements are given as recommendedvalues that provide an acceptable level of reliability. They have been selected assuming that anappropriate level of workmanship and of quality management applies. Design procedures A full analytical procedure for structural fire design would take into account the behaviour of thestructural system at elevated temperatures, the potential heat exposure and the beneficialeffects of active and passive fire protection systems, together with the uncertainties associatedwith these three features and the importance of the structure (consequences of failure). At the present time it is possible to undertake a procedure for determining adequateperformance which incorporates some, if not all, of these parameters and to demonstrate thatthe structure, or its components, will give adequate performance in a real building fire. However,where the procedure is based on a nominal (standard) fire the classification system, which callfor specific periods of fire resistance, takes into account (though not explicitly), the features anduncertainties described above. Application of this Part 1-2 is illustrated below. The prescriptive approach and the performance-based approach are identified. The prescriptive approach uses nominal fires to generatethermal actions. The performance-based approach, using fire safety engineering, refers tothermal actions based on physical and chemical parameters. For design according to this part, EN 1991-1-2 is required for the determination of thermal andmechanical actions to the structure. Design aids Where simple calculation models are not available, the Eurocode fire parts give designsolutions in terms of tabular data (based on tests or advanced calculation models), which maybe used within the specified limits of validity.


Ref. No. EN 1992-1 (July 2001)

It is expected, that design aids based on the calculation models given in EN 199x-1-2, will beprepared by interested external organisations. The main text of EN 1992-1-2, together with informative Annexes A, B, C, and D, includes mostof the principal concepts and rules necessary for structural fire design of concrete structures.

NATIONAL ANNEX FOR EN 1992-1-2

This standard gives alternative procedures, values and recommendations for classes with notesindicating where national choices may have to be made. Therefore the National Standardimplementing EN 1992-1-2 should have a National annex containing the Eurocode all NationallyDetermined Parameters to be used for the design of buildings, and where required andapplicable, for civil engineering works to be constructed in the relevant country. [To Projectteam: Do we delete civil engineering works or do we keep this?] National choice is allowed in EN 1992-1-2 through clauses: - 2.3 (2)P [list of clauses to be completed following later decisions] Figure from Model Clauses to be added

[Figure from Model Clauses]

Alternative proposal from Project Team for discussion:

[Figures 1a, b and c from TH]


Ref. No. prEN 1992-1-2 (July 2000)

Contents List

1 General1.1 Scope1.2 Normative references1.3 Definitions1.4 Symbols

1.4.1 Supplementary symbols to EN 1992-1-11.4.2 Supplementary subscripts to EN 1992-1-1

1.5 Units

2 Basis principles and rules2.1 Performance requirements

2.1.1 General2.1.2 Nominal fire exposure2.1.3 Parametric fire exposure

2.2 Actions2.3 Design values of material properties2.4 Assessment methods

2.4.1 General2.4.2 Member analysis2.4.3 Analysis of parts of the structure2.4.4 Global structural analysis

3 Material properties3.1 General3.2 Strength and deformation properties at elevated temperatures

3.2.1 General3.2.2 Concrete

3.2.2.1 Concrete under compression3.2.2.2 Tensile strength

3.2.3 Reinforcing steel3.2.4 Prestressing steel

3.3 Residual mechanical properties3.3.1 Concrete3.3.2 Reinforcing and prestressing steel

3.3.2.1 Thermal elongation3.3.2.2 Specific heat3.3.2.3 Thermal conductivity

3.4 Thermal properties3.4.1 Concrete with siliceous, calcareous and lightweight aggregates

3.4.1.1 Thermal elongation3.4.1.2 Specific heat3.4.1.3 Thermal conductivity

3.4.1 Reinforcing and prestressing steel3.4.2.1 Thermal elongation3.4.2.2 Specific heat3.4.2.3 Thermal conductivity


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4 Design methods4.1 General4.2 Simplified calculation method

4.2.1 General4.2.2 Temperature profiles4.2.3 Reduced cross-section4.2.4 Strength reduction

4.2.4.1 General4.2.4.2 Concrete4.2.4.3 Steel

4.3 General calculation methods4.3.1 General4.3.2 Thermal response4.3.3 Mechanical response

4.4 Shear and torsion4.5 Anchorage4.6 Spalling4.7 Joints4.8 Protective layers

5 Tabulated data5.1 Scope5.2 General design rules5.3 Columns5.4 Walls

5.4.1 Non load-bearing walls (partitions)5.4.2 Load-bearing solid walls

5.5 Tensile members5.6 Beams

5.6.1 General5.6.2 Simply supported beams5.6.3 Continuous beams5.6.4 Beams exposed on all sides

5.2.7 Slabs5.7.1 General5.7.2 Simply supported slabs5.7.3 Continuous slabs5.7.4 Flat slabs5.7.5 Ribbed slabs

6 High strength concrete6.1 General6.2 Spalling6.3 Thermal properties

6.3.1 Thermal conductivity6.3.2 Specific heat

6.4 Temperature field6.5 Structural design

6.5.1 Calculation of load-carrying capacity6.5.2 Structural systems


Ref. No. prEN 1992-1-2 (July 2000)

6.5.3 Simplified calculation method6.5.4 HSC columns and walls6.5.5 Beams and slabs

Informative annexes

A Temperature profiles

B Simplified calculation methods

C Buckling of columns under fire conditions

D Simplified calculation method for beams and slabs


Ref. No. EN 1992-1 (July 2001)

SECTION 1 GENERAL

1.1 SCOPE

(1)P This Part 1.2 of EN 1992 deals with the design of concrete structures for the accidentalsituation of fire exposure and intended to be used in conjunction with EN 1992-1-1 andEN 1991-1-2. This part 1.2 only identifies differences from, or supplements to, normaltemperature design.

(2)P This Part 1.2 of EN 1992 deals only with passive methods of fire protection. Activemethods are not covered.

(3)P This Part 1.2 of EN 1992 applies to concrete structures that, for reasons of general firesafety, are required to fulfil certain functions when exposed to fire, in terms of:- avoiding premature collapse of the structure (load bearing function)- limiting fire spread (flame, hot gases, excessive heat) beyond designated areas

(separating function)

(4)P This Part 1.2 of EN 1992 gives principles and application rules (see EN 1991-1-2) fordesigning structures for specified requirements in respect of the aforementioned functionsand the levels of performance.

(5)P This Part 1.2 of EN 1992 applies to structures, or parts of structures, that are within thescope of EN 1992-1-1 and are designed accordingly. However, it does not cover:

- structures with prestressing by external tendons- shell structures

(6)P The methods given in this Part 1.2 of EN 1992 are applicable to concrete strength classesup to C90/105 and LC55/60. Additional and alternative rules for strength classes aboveC50/60 are given in section 6.

1.2 Normative references

The following normative documents contain provisions that, through reference in thistext, constitute provisions of this European Standard. For dated references, subsequentamendments to, or revisions of, any of these publications do not apply. However, partiesto agreements based on this European Standard are encouraged to investigate thepossibility of applying the most recent editions of the normative documents indicatedbelow. For undated references, the latest edition of the normative document referred toapplies.

EN … Drafting note: to be checked later

EN 1363 … Fire resistance: General requirements;

ENV 13381 Fire tests on elements of building construction:


Ref. No. prEN 1992-1-2 (July 2000)

Part 1:Test method for determining the contribution to the fire resistance ofstructural members: by horizontal protective membranes;Part 2:Test method for determining the contribution to the fire resistance ofstructural members: by vertical protective membranes;Part 3:Test method for determining the contribution to the fire resistance ofstructural members: by applied protection to concrete structural elements;

EN 13501-2 Fire classification of construction products and building elementsPart 2 Classification using data from fire resistance tests, excluding ventilation services

EN 1991 Eurocode 1. Basis of design and actions on structures:Part 1.2: Actions on structures exposed to fire;

EN 1992 Eurocode 2. Design of concrete structures:Part 1.1: General rules : General rules and rules for buildings

ISO 1000 SI units.

1.3 Assumptions

(1) Design which employs the Principles and Application Rules is deemed to meet the

requirements provided the assumptions given in EN 1990 to EN 1999 are satisfied(see Section 2).

(2) The general assumptions of this part 1.2 of EN 199x are : - The choice of the structural system and the design of the structure is made

by appropriately qualified and experienced personnel. - The choice of the relevant fire design scenario is made by appropriate

qualified and experienced personnel, or is given by the relevant nationalregulation, (new, compare to EN 1990)

– Execution is carried out by personnel having the appropriate skill andexperience.

– Adequate supervision and quality control is provided during execution ofthe work, i.e. in design offices, factories, plants, and on site.

– The construction materials and products are used as specified in EN 1990or in ENs 1991 and 199x or in the relevant execution standards, orreference material or product specifications.

– The structure will be adequately maintained.– The structure will be used in accordance with the design assumptions. Note : There may be cases when the above assumptions need to be

supplemented.


Ref. No. EN 1992-1 (July 2001)

1.4 Distinction between principles and application rules

(1) Rules given in EN 1990 apply.

1.5 Definitions

For the purposes of this Part 1.2 of EN 1992, the definitions of EN 1990 and of EN 1991-1.2 apply with the additional definitions:

Critical temperature of reinforcement : The temperature at which failure is expected tooccur in reinforcement at a given load level.*Design fire: A specified fire development assumed for design purposes.Effective cross section: Cross section of the member in structure fire design used inthe effective cross section method. It is obtained from the residual cross section byremoving parts of the cross section with assumed zero strength and stiffness.*Fire compartment: A space within a building, extending over one or several floors,which is enclosed by separating elements such that fire spread beyond the compartmentis prevented during the relevant fire exposure.Fire protection material: Any material or combination of materials applied to a structuralmember for the purpose of increasing its fire resistance.*Fire resistance: The ability of a structure, a part of a structure or a member to fulfil itsrequired functions (load bearing function and/or separating function) for a specified fireexposure and for a specified period of time.*Global structural analysis (for fire): An analysis of the entire structure, when either theentire structure, or only parts of it, are exposed to fire. Indirect fire actions are consideredthroughout the structure.*Indirect fire actions: Internal forces and moments caused by thermal expansion.*integrity (E): The ability of a separating element of building construction, when exposedto fire on one side, to prevent the passage through it of flames and hot gases and toprevent the occurrence of flames on the unexposed side*insulation (I): The ability of a separating element of building construction when exposedto fire on one side, to restrict the temperature rise of the unexposed face to belowspecified levels.*Load bearing function (R): The ability of a structure or a member to sustain specifiedactions during the relevant fire, according to defined criteria.Maximum stress level: For a given temperature, the stress level at which the stress-strain relationship of steel is truncated to provide a yield plateau*Members analysis (for fire): The thermal and mechanical analysis of a structuralmember exposed to fire in which the member is assumed as isolated, with appropriate

Drafting note: Horizontal Group Fire agreed that general definitions have to beput only in EN 1991-1-2. However, those used in this draft are given below,identified by a *, but should disappear in the final version. A reference numberwill be added for each definition


Ref. No. prEN 1992-1-2 (July 2000)

support and boundary conditions. Indirect fire actions are not considered, except thoseresulting from thermal gradients.Normal temperature design: Ultimate limite state design for ambient temperaturesaccording to Part 1-1 of EN 1992 to 1996 or ENV 1999Part of structure: isolated part of an entire structure with appropriate support andboundary conditions.Protected members: Members for which measures are taken to reduce the temperaturerise in the member due to fire.*Separating function: The ability of a separating element to prevent fire spread (e.g. bypassage of flames or hot gases - cf integrity) or ignition beyond the exposed surface (cfinsulation) during the relevant fire.*Separating element: Load bearing or non-load bearing element (e.g. wall or floor)forming part of the enclosure of a fire compartment.*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 theexposure to heating according to the standard temperature-time curve for a stated periodof time.*Standard temperature-time curve: A nominal curve, defined in EN 13501-1 forrepresenting a model of a fully developed fire in a compartment*Structural members: The load-bearing members of a structure including bracings.*Temperature analysis: The procedure of determining the temperature development inmembers on the basis of the thermal actions (net heat flux) and the thermal materialproperties of the members and of protective surfaces, where relevant.*Temperature-time curves: Gas temperature in the environment of member surfaces asa function of time. They may be:- 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.*Thermal actions: Actions on the structure described by the net heat flux to the

members.1.4 Symbols

1.4.1 Supplementary symbols to EN1992-1-1

(1)P The following supplementary symbols are used:

Latin upper case letters

Ed,fi design effect of actions in the fire situation

Drafting note: To be checked and completed later


Ref. No. EN 1992-1 (July 2001)

Ed design effect of actions for normal temperature design

Rd,fi design resistance in the fire situation; Rd,fi(t) at a given time t.

R 30 or R 60,... fire resistance class for the load-bearing criterion for 30, or 60... minutes instandard fire exposure

E 30 or E 60,... fire resistance class for the integrity criterion for 30, or 60... minutes instandard fire exposure

I 30 or I 60,... fire resistance class for the thermal insulation criterion for 30, or 60...minutes in standard fire exposure

T temperature [K] (cf θ temperature [oC]);

Xk characteristic value of a strength or deformation property for normal temperaturedesign

Xd,fi design strength or deformation property in the fire situation

Latin lower case letters

a axis distance of reinforcing or prestressing steel from the nearest exposed surface

c specific heat [J/kgK]

fck(θ) characteristic value of compressive strength of concrete at temperature θ for aspecified strain

fpk(θ) characteristic value of strength of prestressing steel at temperature θ for a specifiedstrain

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

k(θ)= Xk(θ)/Xk reduction factor for a strength or deformation property dependent on thematerial temperature θ

t time of fire exposure (min)

Greek lower case letters

γM,fi partial safety factor for a material in fire design

ηfi = Ed,fi/Ed reduction factor for design load level in the fire situation

εs,fi strain of the reinforcing or prestressing steel at temperature θ

λ thermal conductivity [W/mK]


Ref. No. prEN 1992-1-2 (July 2000)

σc,fi compressive stress of concrete in fire situation

σs,fi steel stress in fire situation

θ temperature [oC]

θcr critical temperature [0C]

1.4.2 Supplementary to EN 1992-1-1, the following subscripts are used:

fi value relevant for the fire situation

t dependent on the time

θ dependent on the temperature

1.5 Units

(1)P SI units shall be used in conformity with ISO 1000.

(2) Supplementary to EN 1992-1-1, the following units are recommended :

- temperature : °C;

- absolute temperature : K;

- temperature difference : K;

- specific heat : J/kgK;

- coefficient of thermal conductivity : W/mK.


Ref. No. EN 1992-1 (July 2001)

SECTION 2 BASIC PRINCIPLES AND RULES

2.1 Performance requirements

2.1.1 General

(1)P Where mechanical resistance in the case of fire is required, concrete structures shall bedesigned and constructed in such a way that they maintain their load bearing functionduring the relevant fire exposure - Criterion “R”.

(2)P Where compartmentation is required, the elements forming the boundaries of the firecompartment, including joints, shall be designed and constructed in such a way that theymaintain their separating function during the relevant fire exposure, i.e. when requested:

- no integrity failure in order to prevent the passage through it of flames and hotgases and to prevent the occurrence of flames on the unexposed side - Criterion"E"

- no insulation failure in order to restrict the temperature rise of the unexposed faceto below specified levels - Criterion "I"

- limitation of the thermal radiation from the unexposed side.

Note: There is no need to consider the thermal radiation with an unexposed surface temperature below300°C (see EN 1361-2 § 8.1)

(3)P Deformation criteria shall be applied where the means of protection, or the design criteriafor separating elements, require consideration of the deformation of the load bearingstructure.

(4) Consideration of the deformation of the load bearing structure is not necessary inthe following cases, as relevant:- the efficiency of the means of protection has been evaluated according to 4.9,- the separating elements have to fulfil requirements according to nominal fire

exposure.

2.1.2 Nominal fire exposure

(1)P With the standard fire exposure, members shall comply with criteria R, E and I as follows:- separating only: integrity (criterion E) and, when requested, insulation (criterion I)- load bearing only: mechanical resistance (criterion R)

- separating and load bearing: criteria R, E and, when requested I

(2) Criterion “R” is assumed to be satisfied where the load bearing function ismaintained during the required time of fire exposure.

(3) Criterion “I” may be assumed to be satisfied where the average temperature riseover the whole of the non-exposed surface is limited to 140 K, and the maximumtemperature rise at any point of that surface does not exceed 180 K

(4) With the external fire exposure curve the same criteria should apply, however the

reference to this specific curve should be identified by the letters "ef".


Ref. No. prEN 1992-1-2 (July 2000)

(5) With the hydrocarbon fire exposure curve the same criteria should apply, howeverthe reference to this specific curve should be identified by the letters "HC"

(6) Where a vertical separating element with or without load-bearing function have to

comply with impact resistance requirement (criterion M), the element should resista horizontal concentrated load as specified in EN 1363 Part 2. (rule to beincorporated only in EC2 and EC6)

2.1.3 Parametric fire exposure

(1) The load-bearing function is ensured when collapse is prevented during thecomplete duration of the fire including the decay phase or during a required periodof time.

(2) The separating function with respect to insulation is ensured when:- the average temperature rise over the whole of the non-exposed surface is

limited to 140 K, and the maximum temperature rise of that surface does notexceed 200 K at the time of the maximum gas temperature,

- and the average temperature rise over the whole of the non-exposed surfaceis limited to 180 K, and the maximum temperature rise of that surface does notexceed 240 K during the decay phase of the fire or up to a required period oftime.

2.2 Actions

(1)P The thermal and mechanical actions shall be taken from EN 1991-1-2.

(2) In addition to EN 1991-1-2, the emissivity related to the concrete surface should beequal to 0,8.

Drafting note: Emissivity for concrete is 0,7 in prEN 1994-1-2.

2.3 Design values of material properties

(1)P Design values of mechanical (strength and deformation) material properties Xd,fi aredefined as follows:

Xd,fi = kθ Xk / γM,fi (2.1)

where:Xk is the characteristic value of a strength or deformation property (generally fk

or Ek) for normal temperature design to EN 199x-1-1;

kθ is the reduction factor for a strength or deformation property (Xk,θ / Xk),dependent on the material temperature, see 3.2.1;

γM,fi is the partial safety factor for the relevant material property, for the firesituation.

(2)P Design values of thermal material properties Xd,fi are defined as follows:


Ref. No. EN 1992-1 (July 2001)

- if an increase of the property is favourable for safety:

Xd,fi = Xk,θ /γM,fi (2.2a)

- if an increase of the property is unfavourable for safety:

Xd,fi = γM,fi Xk,θ (2.2b)

where:

Xk,θ is the value of a material property in fire design, generally dependent onthe material temperature, see section 3;

γM,fi is the partial safety factor for the relevant material property, for the firesituation.

Note: For thermal properties of concrete and reinforcing and prestressing steel, the recommended value ofpartial safety factor for the fire situation is:γM,fi = 1,0

For mechanical properties of concrete and reinforcing and prestressing steel, the recommendedvalue of partial safety factor for the fire situation is:γM,fi = 1,0

2.4 Assessment methods

2.4.1 General

(1)P The model of the structural system adopted for design to this Part 1.2 of EN 1992 shallreflect the expected performance of the structure in fire.

(2)P The structural analysis for the fire situation may be carried out using one of the following:- member analysis, see 2.4.2;- analysis of part of the structure, see 2.4.3;- global structural analysis, see 2.4.4.

Note 1: Thermal expansion may cause large action effect remote from the fire source.Note 2: For verifying standard fire resistance requirements, a member analysis is sufficient

(3)P It shall be verified for the relevant duration of fire exposure that

Ed,fi ≤ Rd,t,fi (2.2)

whereEd,fi is the design effect of actions for the fire situation, determined in

accordance with EN 1991-1-2, including effects of thermal expansions anddeformations

Rd,t,fi is the corresponding design resistance in fire situation..

(4) Where application rules given in this Part 1.2 are valid only for the standardtemperature-time curve, this is identified in the relevant clauses


Ref. No. prEN 1992-1-2 (July 2000)

(5) Tabulated data given in Section 5 are based on the standard temperature-timecurve.

(6)P As an alternative to design by calculation, fire design may be based on the results of firetests, or on fire tests in combination with calculations, see EN 1990 clause 5.2.

Note: For further details see EN 1990 clause 5.2.

(7) For direct application of fire resistance tests, EN 13501-2 applies.

(8) Extended application of fire test results should be based on assessment of testsand calculations.

Note: Standards for extended application are under preparation in CEN/TC 127.

2.4.2 Member analysis

(1) As an alternative to carrying out a structural analysis for the fire situation at time t =0, the reactions at supports and internal forces and moments may be obtained froma structural analysis for normal temperature design by using:

Ed,fi = ηfi Ed (2.3)

WhereEd is the design value of the corresponding force or moment for normal

temperature design, for a fundamental combination of actions (seeEN 1990);

ηfi is the reduction factor for the design load level for the fire situation.

(3) The reduction factor for the design load level for the fire situation ηfi for loadcombination (6.10) in EN 1990 is given by:

ηfi = QGQG

k,1Q,1kG

k,11,1kGA

+ + γγψγ

(2.4)

or the smaller of the values given by the two following expressions for loadcombinations from Expressions (6.10 a) and (6.10b) of EN 1990:

ηfi = QG

QGk,11,0Q,1kG

k,11,1kGA

+ +

ψγγψγ

(2.5a)

ηfi = Q + G

Q + G 1,1

k,1Q,1kG

k,1kGA

γξγψγ

(2.5b)

wherewhere

Qk,1 is the principal variable load;


Ref. No. EN 1992-1 (July 2001)

γGA is the partial factor for permanent actions in accidental designsituations;ψfi is the combination factor for frequent values given either by ψ1,1 or

ψ2,1 , see EN1991-1-2

Drafting note: The choice of ψ1,1 or ψ2,1 is under discussion in SC 1. It will possiblybe Nationally Determined Parameter.

Note: Regarding equation (2.5), examples of the variation of the reduction factor ηfi versus the load ratioQk,1/Gk for Expression (2.4) and different values of the combination factor ψ1,1 are shown in Figure2.1 with the following assumptions: γGA = 1,0, γG = 1,35 and γQ = 1,5. Expressions (2.5a) and (2.5b)give slightly higher values. Partial factors are specified in the relevant National Annexes of EN1990. Note that Expressions (2.5 a) and (2.5b) below give slightly higher values.

Figure 2.1: Variation of the reduction factor ηηηηfi with the load ratio Qk,1 / Gk

(3) The reduction factor ηfi for load combination (6.10a) and (6.10b) in EN 1990 isthe smaller value given by the two following expressions:

ηfi = QG

QG

k,11,0Q,1kG

k,1kGA

ψγγψγ

+ + fi (2.5a)

ηfi = Q + G

Q + G fi

k,1Q,1kG

k,1kGA

γξγψγ

(2.5b)

whereξ is a reduction factor for unfavourable permanent actions G.

Note: As a simplification a recommended value of ηfi = 0,7 may be used.

0 1 1 2 2 3 30

0

0

1

1

1

1

Qk,1/Gk

ψ1,1 = 0,9

ψ1,1 = 0,7

ψ1,1 = 0,5

ψ1,1 = 0,2

ηfi

0,0 0,5 1,0 1,5 2,0 3,02,5

0,5

0,7

0,8

0,2

0,3

0,4

0,6


Ref. No. prEN 1992-1-2 (July 2000)

(4) Only the effects of thermal deformations resulting from thermal gradients acrossthe cross-section need be considered. The effects of axial or in-plain thermalexpansions may be neglected.

(5) The restraint conditions at supports and ends of member, applicable at time t = 0,are assumed to remain unchanged throughout the fire exposure.

(6) Tabulated data, simplified or general calculation methods given in 4.2, 4.3 and 4.4respectively are suitable for verifying members under fire conditions.

2.4.3 Analysis of parts of the structure

(1) As an alternative to carrying out a global structural analysis for the fire situation attime t = 0 the reactions at supports and internal forces and moments atboundaries of part of the structure may be obtained from structural analysis fornormal temperature as given in 2.4.2

(2) The part of the structure to be analysed should be specified on the basis of thepotential thermal expansions and deformations such, that their interaction withother parts of the structure can be approximated by time-independent support andboundary conditions during fire exposure.

(3) Within the part of the structure to be analysed, the relevant failure mode in fireexposure, the temperature-dependent material properties and memberstiffnesses, effects of thermal expansions and deformations (indirect fire actions)shall be taken into account

(3) The restraint conditions at supports and forces and moments at boundaries of partof the structure, applicable at time t = 0, are assumed to remain unchangedthroughout the fire exposure

2.4.4 Global structural analysis

(1)P When global structural analysis for the fire situation is carried out, the relevant failuremode in fire exposure, the temperature-dependent material properties and memberstiffnesses, effects of thermal expansions and deformations (indirect fire actions) shall betaken into account.


Ref. No. prEN 1992-1-2: (July 2001)

SECTION 3 MATERIAL PROPERTIES

3.1 General

(1)P The values of material properties given in this section shall be treated as characteristicvalues, see 2.3 (1).

(2) The values may be used with the simplified (see 4.3) and the general calculationmethod (see 4.4).

Alternative formulations of material laws may be applied, provided the solutionsare within the range of experimental evidence.

(3)P The mechanical properties of concrete, reinforcing and prestressing steel at 20°C shallbe taken as those given in EN 1992-1-1 for normal temperature design.

3.2 Strength and deformation properties at elevated temperatures

3.2.1 General

(1)P Numerical values on strength and deformation properties given in this section are basedon steady state as well as transient state tests and sometimes a combination of both. Ascreep effects are not explicitly considered, the material models have only been checkedfor heating rates between 2 and 50 K/min. For heating rates outside the above range,the reliability of the strength and deformation properties shall be demonstrated explicitly.

3.2.2 Concrete

3.2.2.1 Concrete under compression

(1)P The strength and deformation properties of uniaxially stressed concrete at elevatedtemperatures shall be obtained from the stress-strain relationships as presented in Figure3.1.

(2) The stress-strain relationships given in Figure 3.1 are defined by two parameters:- the compressive strength fc,θ- the strain εc1,θ corresponding to fc,θ.

(3) Values for each of these parameters are given in Table 3.1 as a function ofconcrete temperatures. For intermediate values of the temperature, linearinterpolation may be used.

(4) The parameters specified in Table 3.1 may be used for normal weight concretewith siliceous or calcareous (containing at least 80% calcareous aggregate byweight) aggregates and lightweight aggregate concrete with densities in the rangeof 1600 to 2000 kg/m3.

(5) Values for εcu,θ defining the range of the descending branch may be taken fromTable 3.1, Column 4 for normal weight concrete with siliceous aggregates,


Ref. No. prEN 1992-1-2: (July 2001)

Column 7 for normal weight concrete with calcareous aggregates and Column 10for lightweight aggregate concrete.

(6) For thermal actions in accordance with 4.3 of EN 1991-1-2 (natural firesimulation), particularly when considering the descending temperature branch, themathematical model for stress-strain relationships of concrete specified in Figure3.1 should be modified.

(7) The tensile strength of concrete may be assumed to be zero, which is on safeside. If it is necessary to take account of the tensile strength, when using thesimplified or general calculation method, 3.2.2.2 may be used.

ε c1,θ cu,θε

σ

ε

fc,θ

Range Stress σ(θ)

εε ≤ θ,1c

��

�

�

��

�

�

��

��

�3

θ,1cθ,1c

θ,c

2

3

ε+ε

fε

ε

εεε θ,cu)θ(1c≤< umerical purposes a descending branch should be

adopted. Linear or non-linear models arepermitted.

Figure 3.1: Mathematical model for stress-strain relationships of concrete undercompression at elevated temperatures.


Ref. No. prEN 1992-1-2: (July 2001)

Table 3.1: Values for the main parameters of the stress-strain relationships ofnormal weight concrete with siliceous or calcareous aggregates andlightweight aggregate concrete at elevated temperatures.

Concrete Siliceous aggregates Calcareous aggregates Lightweight aggregatestemp.θ fc,θ / fck εc1,θ εcu,θ fc,θ / fck εc1,θ εcu,θ fc,θ / fck εc1,θ εcu,θ

[°C] [-] [-] [-] [-] [-] [-] [-] [-] [-]1 2 3 4 5 6 7 8 9 10

20 1,00 0,0025 0,0200 1,00 0,0025 0,0200 1,00 0,0020 0,0100

100 1,00 0,0040 0,0225 1,00 0,0040 0,0225 0,75 0,0025 0,0105

200 0,95 0,0055 0,0250 0,97 0,0055 0,0250 0,73 0,0040 0,0120

300 0,85 0,0070 0,0275 0,91 0,0070 0,0275 0,73 0,0060 0,0140

400 0,75 0,0100 0,0300 0,85 0,0100 0,0300 0,72 0,0090 0,0170

500 0,60 0,0150 0,0325 0,74 0,0150 0,0325 0,70 0,0125 0,0205

600 0,45 0,0250 0,0350 0,60 0,0250 0,0350 0,65 0,0160 0,0240

700 0,30 0,0250 0,0375 0,43 0,0250 0,0375 0,55 0,0225 0,0305

800 0,15 0,0250 0,0400 0,27 0,0250 0,0400 0,25 0,0270 0,0350

900 0,08 0,0250 0,0425 0,15 0,0250 0,0425 0,10 0,0295 0,0375

1000 0,04 0,0250 0,0450 0,06 0,0250 0,0450 0,05 0,0305 0,0385

1100 0,01 0,0250 0,0475 0,02 0,0250 0,0475 0,02 0,0315 0,0395

1200 0,00 - - 0,00 - - 0,01 0,0320 0,040

3.2.2.2 Tensile strength

(1) The tensile strength of concrete may be assumed to be zero, which is on safeside. If it is necessary to take account of the tensile strength, when using thesimplified or general calculation method, 3.2.2.2 may be used.

(2) The reduction of the characteristic tensile strength of concrete is allowed for bythe coefficient kc,t,θ for which

fck,t(θ) = kck,t(θ) fck,t (3.1)

(3) In absence of more accurate information the following kck,t(θ) values should beused (see Figure 3.2):

kck,t(θ) = 1,0 for 20 °C ≤ θ ≤ 100 °C

kck,t(θ) = 1,0 � 1,0 ⋅ (θ -100)/500 for 100 °C < θ ≤ 600 °C


Ref. No. prEN 1992-1-2: (July 2001)

Figure 3.2: Coefficient kck,t(θθθθ) allowing for decrease of tensile strength (fck,t) ofconcrete at elevated temperatures

3.2.3 Reinforcing steel

(1)P The strength and deformation properties of reinforcing steel at elevated temperatures shallbe obtained from the stress-strain relationships specified in Figure 3.3 and Table 3.2.

(2) The stress-strain relationships given in Figure 3.3 are defined by threeparameters:- the slope of the linear elastic range Es,θ- the proportional limit fsp,θ- the maximum stress level fsy,θ

(3) Values for the parameters in (2) for hot rolled and cold worked reinforcing steel atelevated temperatures are given in Table 3.2. For intermediate values of thetemperature, linear interpolation may be used.

(4) The formulation of stress-strain relationships may also be applied for reinforcingsteel in compression.

(5) In case of thermal actions according to section 4.3 of EN 1991-1-2 (natural firesimulation), particularly when considering the decreasing temperature branch, thevalues specified in Table 3.2 for the stress-strain relationships of reinforcing steelmay be used as a sufficiently precise approximation.

0 100 200 300 400 500 6000

0

0

1

1

1

kck,t(θθθθ)

0,8

0,6

0,4

0,2

1,0

0,0100 200 300 400 5000 600

Temperature θθθθ [°C]


Ref. No. prEN 1992-1-2: (July 2001)

αE = tan (α )s,θ

σ

fsy,θ

fsp,θ

εε st,θεsp,θ εsu,θεsy,θ

Range Stress σ(θ) Tangent modulus

εε sp,θ< εE s,θEs,θ

εεε sy,θsp,θ ≤≤ fsp,θ − c + (b/a)[a2 −(εsy,θ − ε)2]0,5

( )��

�� −−

−

εεaa

εεb

sp,θ22

5,0sy,θ )(

εεε st,θsy,θ << fsy,θ 0

εεε su,θst,θ <≤ fsy,θ [1−(ε − εt,θ)/(εu,θ − εt,θ)] -

εε su,θ= 0,00 -

Parameter *) εsp,f = fsp,θ / Es,θ εsy,θ = 0,02 εst,θ = 0,15 εsu,θ = 0,20

Functions a2 = (εsy,θ − εsp,θ)(εsy,θ − εsp,θ +c/Es,θ)

b2 = c (εsy,θ − εsp,θ) Es,θ + c2

( )( ) ( )ffEεε

ffcsp,θsy,θs,θsp,θsy,θ

sp,θsy,θ2

2 −−−−

=

*) Values for the parameters εpt,θ and εpu,θ for prestressing steel may be taken from Table 3.3

Figure 3.3: Mathematical model for stress-strain relationships of reinforcing andprestressing steel at elevated temperatures (notations for prestressingsteel “p” instead of “s”)


Ref. No. prEN 1992-1-2: (July 2001)

Table 3.2: Values for the parameters of the stress-strain relationship of hotrolled and cold worked reinforcing steel at elevated temperatures

Steel Temperature fsy,θ / fyk fsp,θ / fyk Es,θ / Es

θ [°C] hot rolled cold worked hot rolled cold worked hot rolled cold worked

1 2 3 4 5 6 7

20 1,00 1,00 1,00 1,00 1,00 1,00100 1,00 1,00 1,00 0,96 1,00 1,00200 1,00 1,00 0,81 0,92 0,90 0,87300 1,00 1,00 0,61 0,81 0,80 0,72400 1,00 0,94 0,42 0,63 0,70 0,56500 0,78 0,67 0,36 0,44 0,60 0,40600 0,47 0,40 0,18 0,26 0,31 0,24700 0,23 0,12 0,07 0,08 0,13 0,08800 0,11 0,11 0,05 0,06 0,09 0,06900 0,06 0,08 0,04 0,05 0,07 0,051000 0,04 0,05 0,02 0,03 0,04 0,031100 0,02 0,03 0,01 0,02 0,02 0,021200 0,00 0,00 0,00 0,00 0,00 0,00

3.2.4 Prestressing steel

(1) The strength and deformation properties of prestressing steel at elevatedtemperatures may be obtained by the same mathematical model as thatpresented in 3.2.3 for reinforcing steel.

(2) Values for the parameters in section 3.2.3 (2) for cold worked (wires and strands)and quenched and tempered (bars) prestressing steel at elevated temperaturesare given in Table 3.3. For intermediate values of the temperature, linearinterpolation may be used.

(3) In case of thermal actions according to section 4.3 of EN 1991-1-2 (natural firesimulation), particularly when considering the decreasing temperature branch, thevalues specified in Table 3.3 for the stress-strain relationships of prestressingsteel may be used as a sufficiently precise approximation.


Ref. No. prEN 1992-1-2: (July 2001)

Table 3.3: Values for the parameters of the stress-strain relationship of coldworked (cw) (wires and strands) and quenched and tempered (q & t)(bars) prestressing steel at elevated temperatures

Steel temp. fpy,θ / (0,9 fpk) fpp,θ / (0,9 fpk) Ep,θ /Ep εpt,θ [-] εpu,θ [-]

θ [°C] cw q & t cw q & t cw q & t cw, q&t cw, q&t

1 2 3 4 5 6 7 8 9

20 1,00 1,00 1,00 1,00 1,00 1,00 0,0050 0,0100100 0,99 0,98 0,68 0,77 0,98 0,76 0,0050 0,0100200 0,87 0,92 0,51 0,62 0,95 0,61 0,0050 0,0100300 0,72 0,86 0,32 0,58 0,88 0,52 0,0055 0,0105400 0,46 0,69 0,13 0,52 0,81 0,41 0,0060 0,0110500 0,22 0,26 0,07 0,14 0,54 0,20 0,0065 0,0115600 0,10 0,21 0,05 0,11 0,41 0,15 0,0070 0,0120700 0,08 0,15 0,03 0,09 0,10 0,10 0,0075 0,0125800 0,05 0,09 0,02 0,06 0,07 0,06 0,0080 0,0130900 0,03 0,04 0,01 0,03 0,03 0,03 0,0085 0,01351000 0,00 0,00 0,00 0,00 0,00 0,00 0,0090 0,01401100 0,00 0,00 0,00 0,00 0,00 0,00 0,0095 0,01451200 0,00 0,00 0,00 0,00 0,00 0,00 0,0100 0,0150

3.3 Thermal properties

3.3.1 Concrete with siliceous, calcareous and lightweight aggregates

3.3.1,1 Thermal elongation

(1) The thermal strain εc(θ) of concrete may be determined from the following withreference to the length at 20°C :

Siliceous aggregates:

εc(θ) = -1,8 × 10-4 + 9 × 10-6θ + 2,3 × 10-11θ 3 for 20°C ≤ θ ≤ 700°Cεc(θ) = 14 × 10-3 for 700°C < θ ≤ 1200°C

Calcareous aggregates:

εc(θ) = -1,2 × 10-4 + 6 × 10-6θ + 1,4 × 10-11θ 3 for 20°C ≤ θ ≤ 805°Cεc(θ) = 12 × 10-3 for 805°C < θ ≤ 1200°C

Lightweight aggregates:

εc(θ) = 8 × 10-6(θ � 20) for 20°C ≤ θ ≤ 1200°C

where θ is the concrete temperature (°C)


Ref. No. prEN 1992-1-2: (July 2001)

(2) The variation of the thermal elongation with temperatures is illustrated in Figure3.5.

Curve (1): Siliceous aggregate

Curve (2): Calcareous aggregate

Curve (3): Lightweight aggregate

Figure 3.5 Total thermal elongation of concrete

3.3.1.2 Specific heat

(1) The specific heat cpθ of dry concrete may be determined from the following:

Siliceous and calcareous aggregates:

cpθ = 900 (J/kgK) for 20°C ≤ θ ≤ 100°Ccpθ = 900 + (T - 100) (J/kgK) for 100°C < θ ≤ 200°Ccpθ = 1000 + (T - 200) (J/kgK) for 200°C < θ ≤ 400°Ccpθ = 1100 (J/kgK) for 400°C < θ ≤ 1200°C

where θ is the concrete temperature (°C). cpθ is illustrated in Figure 3.6a.

(2) Where the moisture content is not considered explicitly the function given for thespecific heat of concrete with siliceous or calcareous aggregates may be modelledby a peak value situated between 100°C and 115°C such as

cp.peak = 1470 J/kgK for moisture content of 1,5 % of concrete weightcp.peak = 2020 J/kgK for moisture content of 3,0 % of concrete weight

The peaks of specific heat are illustrated in Figure 3.6a.

(3) The variation of density with temperature is influenced by water loss and isdefined as follows

ρθ = ρ20°C for 20°C ≤ θ ≤ 115°Cρθ = 0,98 ρ20°C for 115°C < θ ≤ 200°C

0 200 400 600 800 1,000 1,2000

2

4

6

8

10

12

14

16

8

2

10

0


12

34

6

12

14

1000200 800400 120020 600

(∆∆∆∆l/l)c(10 )-3


Ref. No. prEN 1992-1-2: (July 2001)

ρθ = 0,95ρ20°C for 200°C < θ ≤ 400°Cρθ = 0,88ρ20°C for 400°C < θ ≤ 1200°C

(4) The variation of the product density and cpθ is illustrated in Figure 3.6b forsiliceous concrete with a moisture content of 3% by weight and a density of 2300kg/m3.

a) Specific heat, cpθθθθ,,,, as function oftemperature at 3 different moisturecontents, 0, 1,5 and 3 % forsiliceous concrete

b) cv= ρρρρθ θ θ θ ⋅⋅⋅⋅ cpθθθθ (volumetric specific heat)as function of temperature at amoisture content of 3% and a densityof 2300 kg/m3 for siliceous concrete

Figure 3.6: Volumetric specific heat

3.3.1,3 Thermal conductivity

(1) The thermal conductivity λc of concrete may be determined from the following:

Siliceous aggregates:

λc = 1,5 - 0,7(θ-20)/180 for 20°C ≤ θ ≤ 200°Cλc = 0,8 - 0,3(θ -200)/800 for 200°C < θ ≤ 1000°Cλc = 0,5 for 1000°C < θ ≤ 1200°C

where θ is the concrete temperature (°C)

(2) The variation of the thermal conductivity with temperatures is illustrated in Figure3.7.

0 200 400 600 800 1000 12000

0,20,40,60,8

11,21,41,61,8

22,2

Temperature θ [°C]

cp (θ) [kJ/kg°C]

u = 1,5%

u = 0%

u = 3%

0 500 1000 15000

1000

2000

3000

4000

5000


cv [kJ/m3°C]


Ref. No. prEN 1992-1-2: (July 2001)

Figure 3.7: Thermal conductivity of siliceous concrete

3.3.2 Reinforcing and prestressing steel

3.3.2.1 Thermal elongation

(1) The thermal strain εs(θ) of steel may be determined from the following withreference to the length at 20°C :

Reinforcing steel:

εs(θ) = -2,416 × 10-4 + 1,2x10-5 θ + 0,4 × 10-8 θ 2 for 20°C ≤ θ ≤ 750°Cεs(θ) = 11 × 10-3 for 750°C < θ ≤ 860°Cεs(θ) = -6,2 × 10-3 + 2 × 10-5 θ for 860°C < θ ≤ 120°C

Prestressing steel:

εp(θ) = -2,016 × 10-4 + 10-5 θ + 0,4 × 10-8 θ 2 for 20°C ≤ θ ≤ 1200°C

where θ is the steel temperature (°C)

(2) The variation of the thermal elongation with temperatures is illustrated in Figure3.8.

0 200 400 600 800 1000 12000

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6


Thermal conductivity [W/m°C]


Ref. No. prEN 1992-1-2: (July 2001)

Curve (1): Reinforcing steel

Curve (2): Prestressing steel

Figure 3.8 Total thermal elongation of steel

20 200 400 600 800 1000 12000

2

4

6

8

10

12

14

16

18


1

2

(∆l/l)s(10 )-3


Ref. No. EN 1992-1 (July 2001)

SECTION 4 DESIGN METHODS

4.1 General

(1)P This Part 1-2 of EN 1992 deals with the following alternative design methods asindicated in 2.4.1:- detailing according to recognised design solutions (tabulated data), see section 5- simplified calculation methods (bending and axial forces only) [Drafting note:shear and torsion still under discussion, limitation here is in contradictionwith 4.4 shear and torsion] for specific types of members, see 4.2

- general calculation methods for simulating the behaviour of structural members,parts of the structure or the entire structure, see 4.2.

Note 1: For insulation function (I) the ambient temperature is normally assumed to be 20°C.

Note 2: When calculation methods are used, reference is made to 4.7 for integrity function (E)

Note to the PT: The two above notes are recommended in HGF Model clauses.

(2)P Where necessary, spalling shall be avoided by appropriate measures or theinfluence of spalling on performance requirements (R and/or EI) shall be taken intoaccount, see 4.6.

(3) For prestressed members with unbonded tendons the danger of progressivecollapse should be considered which can occur from excessive steel elongation dueto heating (see appropriate documents). Special precautions should be taken toprotect the anchorages.

4.2 Simplified calculation method

4.2.1 General

(1) Simplified cross-section calculation methods for bending moments and axialforces only described in Annex B may be used to determine the ultimate load-bearing capacity of a heated cross section and to compare the capacity with therelevant combination of actions, see 2.4.2.

(2) The methods in Annex B are applicable to structures subjected to a standard fireexposure and also for any other exposure such as parametric fires.

(3) A simplified method for the design of beams and slabs where the loading ispredominantly uniformly distributed and where the design at normal temperaturehas been based on linear analysis is given in Annex D

4.2.2 Temperature profiles

(1) Temperatures in a concrete structure exposed to a fire may be determined fromtests or by calculation.

(2) The temperature profiles given in Annex A are acceptable for determining thetemperatures in cross-sections with siliceous aggregate and exposed to a


Ref. No. EN 1992-1 (July 2001)

standard fire up to the time of maximum gas temperature. The profiles areconservative for most other aggregates.

4.2.3 Reduced cross-section

(1) Depending on the simplified method used the cross-section may be reduced inaccordance with either of the two methods which are described in Annex B.

(2) The methods are described in Annex B1 based on the hypothesis that concreteexposed to more than 500 °C can be neglected in the calculation of load-bearingcapacity, while concrete with lower temperature can be assumed to retain itsstrength. This method, which follows a cross-section reduced in accordance to the500 °C isotherm, is applicable to a reinforced and prestressed concrete sectionwith respect to axial load, bending moment and their combinations.

(3) The method described in Annex B2 is based on the principle that the fire damagedcross-section is reduced by ignoring a damaged zone at the fire-exposedsurfaces. The calculation should follow a specific procedure. The method isapplicable to a reinforced and prestressed concrete section with respect to axialload, bending moment and their combinations.

4.2.4 Strength reduction

4.2.4.1 General

(1) Values for the reduction of the characteristic compressive strength of concrete, andof the characteristic strength of reinforcing and prestressing steels are given in thissection. They may be used with the simplified cross-section calculation methodsdescribed in section 4.2.3.

(2) The values for strength reduction given in 4.2.4.2 and 4.2.4.3 below should only beapplied for heating rates similar to those appearing under standard fire exposureuntil the time of the maximum temperature.

(3) Alternative values for strength reduction (e.g. for parametric fires) may be applied,provided solutions are within the range of appropriate experimental evidence.

4.2.4.2 Concrete

(1) The reduction of the characteristic compressive strength of concrete as a functionof the temperature θ may be used as given in Table 3.1, Column 2 for siliceousaggregates and Column 5 for calcareous aggregates (see Figure 4.10).


Ref. No. EN 1992-1 (July 2001)

Curve (1): Normal weightconcrete with siliceousaggregates

Curve (2): Normal weightconcrete with calcareousaggregates

Figure 4.10: Coefficient kc(θθθθ) allowing for decrease of characteristic strength (fck)of concrete

4.2.4.3 Steel

(1) The reduction of the characteristic strength of a reinforcing steel as a function of thetemperature θ may be used as given in Table 3.2. For tension reinforcement inbeams and slabs where εs,fi ≥ 2%, the strength reduction may be used as given inTable 3.2, Column 2 for hot rolled and Column 3 for cold worked reinforcing steel(see Figure 4.11, curve 1 and 2).

For compression reinforcement in columns and compressive zones of beams andslabs the strength reduction at 0,2% proof strain should be used as given below.This also applies for tension reinforcement where εs,fi < 2% when using the cross-section calculation methods (see Figure 4.11, curve 3).

ks(θ) = 1,0 for 20°C ≤ θ ≤ 100°Cks(θ) = 0,7 + 0,3 ⋅ (400 – θ )/300 for 100°C < θ ≤ 400°Cks(θ) = 0,1+ 0,6 ⋅ (700 – θ )/300 for 400°C < θ ≤ 700°Cks(θ) = 0,1 ⋅ (1200 – θ )/500 for 700°C < θ ≤ 1200°C

(2) The reduction of the characteristic strength of a prestressing steel as a function ofthe temperature θ may be taken from Table 3.3, Column 2 for cold worked andColumn 3 for quenched and tempered prestressing steel (see Figure 4.12).

0,8

1

0

1

2

0,6

0,2

0,4

1000200 800400 12000 600

kc(θ θ θ θ )



Ref. No. EN 1992-1 (July 2001)

Curve (1): Tension reinforcement(hot rolled) for strains εs,fi ≥ 2%

Curve (2): Tension reinforcement(cold worked) for strains εs,fi ≥ 2%

Curve (3): Compressionreinforcement and tensionreinforcement for strains εs,fi < 2%

Figure 4.11: Coefficient ks(θθθθ) allowing for decrease of characteristic strength (fyk)of tension and compression reinforcement

Curve (1): Cold workedprestressing steel (wires andstrands)

Curve (2): Quenched andtempered prestressing steel(bars)

Figure 4.12: Coefficient kp(θθθθ) allowing for decrease of characteristic strength(0.9⋅⋅⋅⋅fpk) of prestressing steel

0,8

1

0

1

2

3

0,6

0,2

0,4

1000200 800400 12000 600

ks(θ θ θ θ )

Temperature θ θ θ θ [°C]

0,8

1

0

1

20,6

0,2

0,4

1000200 800400 12000 600

kp(θ θ θ θ )



Ref. No. EN 1992-1 (July 2001)

4.3 General calculation methods

4.3.1 General

(1)P General calculation methods can be used for individual members, for parts of the structureor 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 reliableapproximation of the expected behaviour of the relevant structural component under fireconditions.

(3)P The general calculation method shall be based on well-established thermal andmechanical material models for steel and concrete, verified on a scientific level and wellsuited for the concrete and steel materials to be used.

(4)P The procedures of the general calculation method shall be verified on a scientific level,by relevant comparisons with full-scale test data.

(5)P The state of equilibrium shall be checked and verified by control calculations

(6) General calculation methods may include separate sub-models for thedetermination 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 (mechanicalresponse model).

(7)P Any potential failure mode not covered by the general calculation method shall beexcluded by appropriate means (e.g. insufficient rotational capacity, spalling, local bucklingof compressed reinforcement, shear and bond failure, damage to anchorage devices).

(8) General calculation method may be used in association with any heating curve,provided that the material properties are known for the relevant temperature rangeand the relevant rate of heating.

4.3.2 Thermal response

(1)P General calculation methods for thermal response shall be based on the acknowledgedprinciples and assumptions of the theory of heat transfer.

(2)P The thermal response model shall consider:

a) the thermal actions evaluated according to EN 1991-1-2;

b) the temperature dependent thermal properties of the materials as specified in relevantdocuments (see Annex A);


Ref. No. EN 1992-1 (July 2001)

c) the contribution of protective layers, if any.

(3) The influence of moisture content and of migration of the moisture within concreteor protective layers if any, may conservatively be neglected.

(4) The temperature profile in a reinforced concrete element may be assessed apartfrom the presence of reinforcement.

(5) The effects of non-uniform thermal exposure and of heat transfer to adjacentbuilding components may be included where appropriate.

4.3.3 Mechanical response

(1)P General calculation methods for mechanical response shall be based on theacknowledged principles and assumptions of the theory of structural mechanics, takinginto account the changes of mechanical properties with temperature.

(2)P The deformations at ultimate limit state implied by the calculation methods shall be limitedas 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 ofgeometrical non-linear effects.

(4)P The effects of thermally induced strains and stresses both due to temperature rise and dueto temperature differentials, shall be considered.

(5) The total strain ε may be assumed to be:

ε = εth + εσ + εcreep + εtr (4.15)

whereεth is the thermal strain,εσ is the instantaneous stress-dependent strainεcreep is the creep strain andεtr is the transient strain

(6) For practical calculations, deformations and indirect actions in hyperstatic structuresduring fire may be assessed by means of imposed strains (mean axis elongationand curvature.

(7) The load bearing capacity of individual members, sub-assemblies or entirestructures exposed to fire may be assessed by plastic methods of analysis (see EN1992-1-1, Section 5).

(8) The plastic rotation capacity of reinforced concrete sections should be estimated inaccount of the increased ultimate strains εcu and εsu in hot condition. εcu will also beaffected by the confinement reinforcement provided.


Ref. No. EN 1992-1 (July 2001)

(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 withparticular regard to spalling or falling-off of concrete cover.

(10) In the analysis of individual members or sub-assemblies the boundary conditionsshould be checked and detailed in order to avoid failure due to the loss of adequatesupport to the members.

4.4 Shear and torsion

(1) The shear and torsion capacity may be calculated according to the methods givenin EN 1992-1-1 using reduced material properties and reduced prestress for eachpart of the cross section.

(2) When using the simplified calculation method of 4.2, EN 1992-1-1 may be applieddirectly to the reduced cross section.

(3) When using the simplified calculation method of 4.2, if no shear reinforcement isprovided or the shear capacity relies mainly on the reduced tensile strength of theconcrete, the actual shear behaviour of the concrete at elevated temperatures mustbe considered.

In the absence of more accurate information concerning the reduction of the tensilestrength of concrete, the values of kct(θ) given Figure 3.2 may be applied.

(4) When using the simplified calculation method of 4.2, for elements in which theshear capacity is dependent on the tensile strength, special consideration should begiven where tensile stresses are caused by non-linear temperature distributions(e.g. voided slabs, thick beams, etc). A reduction in shear strength should be takenin accordance with these increased tensile stresses.

(5) Members designed in accordance with Section 5 and the tabulated data for axisdistance to main longitudinal reinforcement and minimum cross sectiondimensions, may be assumed to have sufficient strength with respect to shearaction effects in a fire situation.

4.5 Anchorage

(1) Where necessary for fire resistance purposes the anchorage capacity may becalculated according to EN 1992-1-1 using reduced temperature related materialproperties (see 3.1(4)).

(2) Members designed in accordance with Section 5 and the tabulated data for axisdistance to main longitudinal reinforcement and minimum cross sectiondimensions, may be assumed to have sufficient strength with respect toanchorage in a fire situation.


Ref. No. EN 1992-1 (July 2001)

4.6 Spalling

(1)P Explosive spalling shall be avoided, or the influence of explosive spalling on performancerequirements (R and/or EI) shall be taken into account.

(2) When the moisture content of the concrete is less than 3% by weight explosivespalling is unlikely to occur. Above 3% more accurate assessments, moisturecontent, type of aggregate, permeability of concrete and heating rate should beconsidered.

(3) It may be assumed that where members are designed to exposure class X0 andXC1, Table 4.1 of EN 1992-1-1, the moisture content of that member is less than3% by weight.

(4) The tabulated data take into account requirements for explosive spalling in (1)P forall exposure classes given in Table 4.1 of EN 1992-1-1 and no further check isrequired.

Note : Some lightweight aggregates concrete are susceptible to explosive spalling. For suchconcrete, documentation of relevant fire tests should be used to determine the minimum membersize and additional precautions.

(5) The influence of explosive spalling on load-bearing function R may be assessed byassuming local loss of cover to reinforcement and by calculation of the reducedload-bearing capacity. This verification is unnecessary for any structural member forwhich the correct behaviour with relation to explosive spalling has been checkedexperimentally or for which complementary protection is applied and verified bytesting.

(6) Where the number of bars is large enough, it may be assumed that an acceptableredistribution of stress is possible without loss of the stability (R). This includes:• solid slabs with evenly distributed bars,• beams with width larger than 400 mm and containing more than 8 bars in the

tensile area

(7) Risk of falling off of concrete in the latter stage of fire exposure should be avoided,or taken into account when considering the performance requirements (R and/orEI).

(8) Where the nominal concrete cover to the reinforcement is 70 mm or more and testshave not been carried out to show that falling-off does not occur, then surfacereinforcement should be provided. The surface reinforcement mesh should have aspacing not greater than 100 mm, and a diameter not less than 4 mm.

4.7 Joints

(1)P The design of joints shall be based on an overall assessment of the structural behaviourin fire.

(2)P Joints shall be detailed in such a way that they comply with the R and EI criteria requiredfor the joined structural members and ensure sufficient stability of the total structure.


Ref. No. EN 1992-1 (July 2001)

(3) Joint components of structural steel shall be designed for fire resistance inaccordance with EN 1993-1-2.

(4) With reference to the I-criterion, the width of gaps in joints is deemed to satisfy thelimit of 20 mm and they should not be deeper than half the minimum thickness daccording to 4.2, of the actual separating component, see Figure 4.13.

Note: Bars in the corner zones against the gap need not be considered as corner bars with reference totabulated data.

Figure 4.13: Width of gap at joints

4.8 Protective layers

(1)P Required fire resistance can also be obtained by the application of protective layers.

(2) The properties and performance of the material for protective layers should beassessed using appropriate test procedure.

For horizontal membrane protection ENV 13381-1 applies, for vertical membraneprotection ENV 13381-2 applies, and for applied protection to concrete membersENV 13381-3 applies.

A further alternative is to provide a thermal analysis in accordance with thegeneral calculation method.

d>d/2

≤ 20 mm


Ref. No. prEN 1992-1-2: (July 2001)

5 Tabulated data

5.1 Scope

(1) This section gives recognised design solutions for the standard fire exposure up to240 minutes, see 4.1. The rules refer to member analysis according to 2.4.2.

Note: The tables have been developed on an empirical basis confirmed by experience andtheoretical evaluation of tests. Therefore, this data is derived from approximate conservativeassumptions for the more common structural elements. More specific tabulated data can be found inthe product standards for some particular types of concrete products or developed on the basis ofthe calculation in accordance with 4.2 and 4.4.

(2) The values given in the tables apply to normal weight concrete (2000 to 2600kg/m3, see EN 206-1) made with siliceous aggregates.

If calcareous aggregates are used in beams and slabs either the minimumdimension of the cross-section or the minimum value of the axis distance a ofreinforcement may be reduced by 10%.

For lightweight aggregate concrete with an oven dry density of up to 1200 kg/m3 thereduction may be 20%, except for non-load bearing walls (see 5.4.1). For densitiesbetween 1200 kg/m3 and 2000 kg/m3 linear interpolation is permitted.

(3) When using tabulated data no further checks are required concerning shear andtorsion capacity (see 4.4) and anchorage details (see 4.5).

(4) When using tabulated data no further checks are required concerning spalling,except for surface reinforcement, see 4.6 (8)

(5) For prestressed members with unbonded tendons the danger of progressivecollapse should be considered which could occur from excessive steel elongationdue to heating (see appropriate documents). Special precautions should be takento protect the anchorages.

5.2 General design rules

(1) Requirements for separating function (Criterion E and I, see 1.4) may beconsidered satisfied where the minimum thickness of walls or slabs accords withTable 5.3. For joints, see 4.7.

(2) For load bearing function (Criterion R), the minimum requirements concerningsection sizes and axis distance of steel have been set up in the tables so that

Ed,fi/Rd,fi ≤ 1,0 (5.1)

where:Ed,fi is the design effect of actions in the fire situation.Rd,fi is the design load-bearing capacity (resistance) in the fire situation.


Ref. No. prEN 1992-1-2: (July 2001)

(3) Tabulated data in this section is based on the reduction factor for the design loadlevel for the fire situation ηfi = 0,7, unless otherwise stated in the relevant clauses.

Note: Where the partial safety factors specified in the National Annexes of EN 1990 deviateconsiderably from those indicated in 2.4.2, the above value ηfi = 0,7 may not be valid. This is asubject for National Annexes of this Part 1-2 of EN 1992.

(4) In order to ensure the necessary axis distance in tensile zones of simply supported

members, the Tables 5.5, 5.6 and 5.9, Column 3 (one way), are based on a criticalsteel temperature of θcr = 500°C. This assumption corresponds approximately toEd,fi = 0,7Ed and γs = 1,15 (see Expression (5.2)) where Ed denotes the design effectof actions according to EN 1992-1-1.

(5) For prestressing tendons the critical temperature for bars is assumed to be 400°Cand for strands and wires to be 350°C. If no special check according to (6) is madein prestressed tensile members, beams and slabs the required axis distance ashould be increased by:10 mm for prestressing bars, corresponding to θcr = 400°C15 mm for prestressing wires and strands, corresponding to θcr = 350°C

(6) For tensile and simply supported bending members, except for those withunbonded tendons, modification of the required axis distance a, given in the tables5.5, 5.6 and 5.9, Column 3, for critical temperatures of reinforcement other than500oC may be carried out as follows:

a) evaluate the steel stress σs,fi for the actions in a fire situation (Ed,fi) usingExpression (5.2).

AA

γf

EEσ

s,prov

s,req

s

yk

d

d,fis,fi x

)C20( x =

°(5.2)

where:γs is the partial safety factor for reinforcing steel;

γs = 1,15 (see 2.3 of EN 1992-1-1)As,req is the area of reinforcement required for ultimate limit state according

to EN 1992-1-1As,prov is the area of reinforcement provided

Ed,fi/Ed may be assessed using 2.2 (2), (3) and (4).

b) evaluate the critical temperature of reinforcement θcr, corresponding to thereduction factor ks(θcr) = σs,fi/fyk(20oC) using Figure 5.1 (Curve 1) forreinforcement or kp(θcr) = σp,fi/fpk(20oC) using Figure 5.1 (Curve 2 or 3) forprestressing steel.

c) adjust the minimum axis distance given in the tables, for the new criticaltemperature, θcr, using the approximate Equation (5.3), where ∆a is the changein the axis distance in millimetres:

∆a = 0,1 (500 - θcr) (mm) (5.3)


Ref. No. prEN 1992-1-2: (July 2001)

(1) reinforcing steel(hot rolled and cold worked)

(2) prestressing steel(quenched & tempered bars)

(3) prestressing steel(cold worked wires and strands)

Figure 5.1: Critical temperature of reinforcing and prestressing steel θθθθcrcorresponding to the reduction factor ks(θθθθcr) = σσσσs,fi/fyk(20oC) or kp(θθθθcr) =σσσσp,fi/fpk(20oC)

(7) The above approximation is valid for 350oC<θcr<700oC and for modification of theaxis distance given in the tables only. For temperatures outside these limits, andfor more accurate results temperature profiles should be used. For prestressingsteel, Expression (5.2) may be applied analogously.

For unbonded tendons critical temperatures greater than 350°C should only beused where more accurate methods are used to determine the effects ofdeflections, see 4.1 (3).

(8) For tensile members or beams where the design requires θcr to be below 400oC thecross sectional dimensions should be increased by increasing the minimum width ofthe tensile member or tensile zone of the beam according to Expression (5.4).

bmod ≥ bmin + 0,8 (400 - θcr) (mm) (5.4)

where bmin is the minimum dimension b given in the tables, related to the requiredstandard fire resistance.

An alternative to increasing the width according to Expression (5.4) may be toadjust the axis distance of the reinforcement in order to obtain the temperaturerequired for the actual stress. This requires using a more accurate method such asthat given in Annex A.

0,8

1

0

1

2

3

0,6

0,2

0,4

1000200 800400 12000 600

ks(θθθθcr), kp(θθθθcr)



Ref. No. prEN 1992-1-2: (July 2001)

(9) Values given in the tables provide minimum dimensions for fire resistance inaddition to the detailing rules required by EN 1992-1-1. Some values of the axisdistance of the steel, used in the tables are less than that required by EN 1992-1-1and should be considered for interpolation only.

(10) Linear interpolation between the values given in the tables may be carried.

(11) In situations for which the tables do not apply, reference should be made toappropriate documents.

(12) Symbols used in the tables are defined in Figure 5.2.

Figure 5.2: Sections through structural members, showing nominal axis distancea, and nominal concrete cover c to reinforcement

(13) Axis distances a to a steel bar, wire or tendon are nominal values. Allowance fortolerance need not be added.

(14) When reinforcement is arranged in several layers as shown in Figure 5.3, andwhere it consists of either reinforcing or prestressing steel with the samecharacteristic strength fyk and fpk respectively, the average axis distance amshould not be less than the axis distance a given in the Tables. The average axisdistance may be determined by Expression (5.5).

AaA

AAAaAaAaAa

si

isi

sn2s1s

nsn22s11sm Σ

Σ = + ..... + + + ..... + + = (5.5)

where:Asi is the cross sectional area of steel bar (tendon, wire) "i"ai is the axis distance of steel bar (tendon, wire) "i" from the

nearest exposed surface.

When reinforcement consists of steels with different characteristic strength Asishould be replaced by Asi fyki (or Asi fpki) in Expression (5.4).

(15) Where reinforcing and prestressing steel is used simultaneously (e.g. in a partiallyprestressed member), the axis distances of reinforcing and prestressing steelshould be determined separately.

h > b

ba c

a

b

a

c


Ref. No. prEN 1992-1-2: (July 2001)

Note: Use of temperature graphs and simplified calculation methods is recommended.

Figure 5.3: Dimensions used to calculate average axis distance am

(16) The minimum axis distance for any individual bar should not be less than either thatrequired for R 30 for bars in a single layer or half the average axis distance for barsin multiple layers (see Expression (5.4)).

5.2.1 Columns

(1) Fire resistance of reinforced concrete columns may be satisfied by the use of Table5.2 and the following rules. Further information is given in Annex C.

(2) Table 5.2 is valid only for columns in no-sway structures. The variables used in thetable and also in Annex C are:n denotes the load level at normal temperature conditions (see EN 1992-1-1,

5.8)n = N0Ed /(Ac fcd + As fyd)

e denotes the first order eccentricity under fire conditionse = M0Ed,fi / N0Ed,fi

λfi denotes the slenderness of the column under fire conditionsλfi = i / l0,fi

lo,fi denotes the effective length of the column under fire conditionsl denotes the actual length of the columnb denotes the minimum dimension of the section on rectangular columns or

the diameter on circular columnsNo,Ed,fi, Mo,Ed,fi denotes the Axial load and first order Moment under fire conditionsω denotes the mechanical reinforcement ratio at normal temperature

conditions

cdc

yds

fAfA

ω =

(3) In Table 5.2 the load level of the column at normal temperature accounting for axialload and first order flexural bending (see EN 1992-1-1, 5.8) has been introduced byusing Expressions (5. 5 a) and (5.5 b). Second order effects have been taken intoaccount.

n = N0Ed /(Ac fcd + As fyd) (5.5a)

a4

a ,2

a3

a7 a6a ,5

a3

a1

a2

1 2 3 4

5 76


Ref. No. prEN 1992-1-2: (July 2001)

e / b = M0Ed,fi / (N0Ed,fi · b) (5.5 b)

e / b has been taken as ≤ 0,25 with emax = 100 mmλfi has been taken as ≤ 30, which covers the majority of columns in normal buildingsηfi has been taken as 0,7 in all cases.

Note: Slenderness ratio λfi under fire conditions can be assumed as equal to λ at normaltemperature in all cases. For no-sway building structures where the required Standard fireexposure is higher than 60 min, the effective length l0 can be taken as 0,5 l for intermediate floorsand 0,5 l ≤ l0,fi ≤ 0,7 l for the upper floor.

(4) In columns where As ≥ 0,02 Ac , distribution of the bars along the sides of the cross-section is required for a fire resistance higher than 90 minutes.

(5) For concrete made with calcareous or lightweight aggregate, no reduction of theminimum column width b (see 5.1(2)) given in Table 5.2 is permitted.

Table 5.2: Minimum column size with appropriate axis distance and minimum coverwith appropriate column size for reinforced concrete columns exposed onmore than one side. Rectangular and circular section.

Standard fire Mechanicalreinforcement

Minimum dimensions (mm). Column width bmin/axis distance a

resistance ratio ωωωω n = 0,15 n = 0,3 n = 0,5 n = 0,71 3 4 5 6 7

R 30

R 60

R 90

R 120

R 180

R 240

0,1000,5001,000

0,1000,5001,000

0,1000,5001,000

0,1000,5001,000

0,1000,5001,000

0,1000,5001,000

150/25*150/25*150/25*

150/30:200/25*150/25*150/25*

200/40:250/25*150/35:200/25*

200/25*

250/50:350/25*200/45:300/25*200/40:250/25*

400/50:500/25*300/45:450/25*300/35:400/25*

500/60:550/25*450/45:500/25*400/45:500/25*

150/25*150/25*150/25*

200/40:300/25*150/35:200/25*150/30:200/25*

300/40:400/25*200/45:300/25*200/40:300/25*

400/50:550/25*300/45:550/25*250/50:400/25*

500/60:550/25*450/50:600/25*450/50:550/25*

550/40:600/25*550/55:600/25*500/40:600/30

200/30:250/25*150/25*150/25

300/40:500/25*250/35:350/25*250/40:400/25

500/50:550/25*300/45:550/25*250/40:550/25*

550/25*450/50:600/25450/45:600/30

550/60:600/30500/60:600/50500/60:600/45

600/75600/70600/60

300/30:350/25*200/30:250/25*200/30:300/25

500/25*350/40:550/25*300/50:600/30

550/40:600/25*550/50:600/40500/50:600/45

550/60:600/45500/60:600/50

600/60

(1)600/75

(1)

(1)(1)(1)

* Normally the cover required by EN 1992-1-1 will control.(1) Requires width greater than 600 mm. Particular assessment for buckling is required.


Ref. No. prEN 1992-1-2: (July 2001)

5.2.2 Walls

5.2.2.1 Non load-bearing walls (partitions)

(1) Where the fire resistance of a partition is only required to meet the thermalinsulation criterion I and integrity criterion E, the minimum wall thickness should notbe less than that given in Table 5. 3 below. Requirements of axis distance may bedisregarded.

(2) If calcareous or lightweight aggregates are used the minimum wall thickness givenin Table 5. 3 may be reduced by 10%.

(3) To avoid excessive thermal deformation and subsequent failure of integrity betweenwall and slab, the ratio of clear height of wall lw to wall thickness t should notexceed 40,

Table 5.3: Minimum wall thickness of non load-bearing walls (partitions)

Standardfire resistance

Minimum wall thickness(mm)

1 2EI 30

EI 60

EI 90

EI 120

EI 180

EI 240

60

80

100

120

150

175

5.2.2.2 Load-bearing solid walls

(1) Adequate fire resistance of load-bearing reinforced concrete walls may be assumedif the data given in Table 5.4 and the following rules are applied.

(2) The minimum wall thickness values given in Table 5.4 may also be used for plainconcrete walls (see EN 1992-1-1, Section 11).

(3) 5.3(2), (3) and (6) also apply for load-bearing solid walls.


Ref. No. prEN 1992-1-2: (July 2001)

Table 5.4: Minimum dimensions and axis distances for load-bearing reinforcedconcrete walls

Standardfire

resistance

Minimum dimensions (mm)

Wall thickness/axis distance for

ηf = 0,35 ηf = 0,7

wall exposedon one side

wall exposedon two sides

wall exposedon one side

wall exposedon two sides

1 2 3 4 5REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

100/10*

110/10*

120/20*

150/25

180/40

230/55

120/10*

120/10*

140/10*

160/25

200/45

250/55

120/10*

130/10*

140/25

160/35

210/50

270/60

120/10*

140/10*

170/25

220/35

270/55

350/60

* Normally the cover required by EN 1992-1-1 will control.

5.2.2.3 Fire walls

(1) Where a fire wall has to comply with an impact resistance requirement (criterion M,see 2.1.2 (6)), the minimum thickness for normal weight concrete should not be lessthan:

200 mm for non reinforced wall140 mm for reinforced load-bearing wall120 mm for reinforced non load bearing wall

and the axis distance of the load-bearing wall should not be less than 25 mm.

5.5 Tensile members

(1) Fire resistance of reinforced or prestressed concrete tensile members may beassumed adequate if the data given in Table 5.5 and the following rules are applied.

(2) Where excessive elongation of a tensile member affects the load bearing capacityof the structure it may be necessary to reduce the steel temperature in the tensilemember to 400oC. In such situations the axis distances in Table 5.5 should beincreased by using Table 5.1 given in 5.2 (4). For the assessment of the reducedelongation reference should be made to appropriate documents.


Ref. No. prEN 1992-1-2: (July 2001)

(3) The cross-section of tensile members should not be less than 2bmin2, where bmin is

the minimum member width given in Table 5.5.

Table 5.5: Minimum dimensions and axis distances for reinforced and prestressedconcrete tensile members

Standardfire

resistance


Possible combinations of member width b/axisdistance a

1 2 3R 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

For prestressed members the increase of axis distance accordingto 5.2(4) should be noted.


5.6 Beams

5.6.1 General

(1) Adequate fire resistance of reinforced and prestressed concrete beams may beassumed if the data given in Tables 5.6 to 5.8 together with the following rules areused.

(2) The Tables apply to beams which can be exposed to fire on three sides, i.e. theupper side is insulated by slabs or other elements which continue their insulatingfunction during the whole fire resistance period. For beams, exposed to fire on allsides, 5.6.4 applies.

(3) Values in the Tables are valid for the cross-sections shown in Figure 5.4.Application rules (5) to (8) ensure adequate cross-sectional dimensions to protectthe reinforcement.

(4) For beams with varying width (Figure 5.4b) the minimum value b relates to thecentroid of the tensile reinforcement.


Ref. No. prEN 1992-1-2: (July 2001)

(5) The effective height deff of the bottom flange of -shaped beams with varying webs(Figure 5.4c) should not be less than:

deff = d1 + 0,5 d2 ≥ bmin (5.6)

where bmin is the minimum value of beam width according to Table 5.7.

(a) Constant width (b) Variable width (c) Ι - section

Figure 5.4: Definition of dimensions for different types of beam section

This rule does not apply if an imaginary cross section ((a) in Figure 5.5) which fulfilsthe minimum requirements with regard to fire resistance and which includes thewhole reinforcement can be drawn inside the actual cross section.

(a) : Imaginary cross section

Figure 5.5: I-shaped beam with increasing web width bw satisfying therequirements of an imaginary cross-section.

(6) Where the actual width of the bottom flange b exceeds the limit 1,4 bw , (bw denotesthe actual width of web, see Figure 5.4(c)), the axis distance to the reinforcing orprestressing steel should be increased to:

abb

bdaa ) - (1,85 = w

min

effeff ≥ (5.7)

where:deff is given by Expression (5.6)bmin is the minimum beam width given in Table 5.6.

b b b

bw

d1

d2x deff

A

A

B

B A - A B - B

bw

deff deff

a


Ref. No. prEN 1992-1-2: (July 2001)

(7) For flanges with b > 3,5 bw (see (6) above for definitions) 5.6.4 applies.

(8) Holes through the webs of beams do not affect the fire resistance provided that theremaining cross-sectional area of the member in the tensile zone is not less thanAc = 2b2

min where bmin is given by Table 5.6.

(9) Higher temperature concentrations occur at the bottom corners of beams. For thisreason the axis distance asd to the side of beam for corner bar (tendon or wire) in thebottom of beams with only one layer of reinforcement, should be increased by 10mm for widths of beam up to that given in Column 4 of Table 5.6 for simplysupported beams, and Column 3 of Table 5.7 for continuous beams, for the relevantstandard fire resistance.

5.6.2 Simply supported beams

(1) Table 5.6 provides minimum values of axis distance to the soffit and sides of simplysupported beams together with minimum values of the width of beam, for standardfire resistances of R 30 to R 240,

5.6.3 Continuous beams

(1) Table 5.7 provides minimum values of axis distance to the soffit and sides ofcontinuous beams together with minimum values of the width of beam, for standardfire resistance of R 30 to R 240,

(2) Table 5.7 and the following rules apply for beams where the moment redistributionaccording to EN 1992-1-1 does not exceed 15 %. In the absence of a more rigorouscalculation and where the redistribution exceeds 15%, or the detailing rules of thisPart 1-2 are not followed, each span of a continuous beam should be assessedusing Table 5.6 for simple supported beams.

(3) The area of top reinforcement over each intermediate support for standard fireresistance of R90 and above, for up to a distance of 0,3leff (as defined in 5.3.2 ofEN 1992-1-1) from the centre line of support should not be less than (see Figure5.6):

As,req(x) = As,req(0) ⋅ (1 - 2,5x/leff) (5.8)

where:x is the distance from the section considered to the centre line of the

support (x ≤ 0,3leff)As,req(0) is the area of top reinforcement required over the support,

according to EN 1992-1-1As,req(x) is the minimum area of top reinforcement required in the section

considered but not less than As(x) required by EN 1992-1-1.

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


Ref. No. prEN 1992-1-2: (July 2001)

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 EN 1992-1-1(3) Diagram of bending moments in fire conditions(4) Envelope line of resisting bending moments according to Expression (5.7)

Figure 5.6: Envelope of resisting bending moments over supports in fireconditions.

0,3l eff 0,4l eff 0,3l eff

2

1 1

23

43

4

2


Ref. No. prEN 1992-1-2: (July 2001)

Table 5.6: Minimum dimensions and axis distances for simply supported beamsmade with reinforced and prestressed concrete

Standard fireresistance Minimum dimensions (mm)

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

beam

Web thicknessbw

1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

bmin= 80a = 25

bmin= 120a = 40

bmin= 150a = 55

bmin= 200a = 65

bmin= 240a = 80

bmin= 280a = 90

12020

16035

20045

24060

30070

35080

16015*

20030

30040

30055

40065

50075

20015*

30025

40035

50050

60060

70070

80

100

110

130

150

170

asd = a + 10mm (see note below)

For prestressed beams the increase of axis distance according to 5.2(4) should benoted.

asd is the axis distance to the side of beam for the corner bars (or tendon or wire) ofbeams with only one layer of reinforcement. For values of bmin greater thanthat given in Column 4 no increase of asd is required.



Ref. No. prEN 1992-1-2: (July 2001)

Table 5.7: Minimum dimensions and axis distances for continuous beams madewith reinforced and prestressed concrete (see also Table 5.8).

Standardfire

resistanceMinimum dimensions (mm)

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

beam

Web thicknessbw

1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

bmin= 80a = 15*

bmin= 120a = 25

bmin= 150a = 35

bmin= 220a = 45

bmin= 380a = 55

bmin= 480a = 65

16012*

20012*

25025

30035

40050

50060

40025

45035

55050

65060

45025

50030

60040

70050

80

100

110

130

150

170

asd = a + 10mm (see note below)

For prestressed beams the increase of axis distance according to 5.2(4) should benoted.

asd is the axis distance to the side of beam for the corner bars (or tendon or wire) ofbeams with only one layer of reinforcement. For values of bmin greater than thatgiven in Column 3 no increase of asd is required.


(4) Table 5.7 applies to continuous beams using unbonded tendons only, if the totalhogging moment over intermediate supports under fire conditions is resisted bybonded reinforcement.

(5) The web thickness of -shaped continuous beams bw (see Figure 5.4c) should notbe less than the minimum value bmin in Table 5.7, Columns 2 to 4, for a distanceof 2h from an intermediate support unless it can be shown that explosive spallingwill not occur (see 5.7).


Ref. No. prEN 1992-1-2: (July 2001)

(6) In order to prevent a concrete compression or shear failure of a continuous beamat the first intermediate support, the beam width and web thickness should beincreased for standard fire resistances R120 - R 240 in accordance with Table5.8, if both the following conditions exist:

(a) no bending resistance is provided at the end support, either by the joint orbeam (for the purposes of this clause 5.4.2.1.2 (1) of EN 1992-1-1 does providemoment resistance when incorporated in a joint which can transfer moment), and

(b) VSd > 2/3VRd2 at the first intermediate support,

where VRd2 is the design shear resistance of the compression struts according to4.3.2 EN 1992-1-1.

Table 5.8: Reinforced and prestressed concrete continuous -beams; increasedbeam width and web thickness for conditions according to 5.6.3 (6)

Standardfire resistance

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

1 2

R 120

R 180

R 240

220

380

480

5.6.4 Beams exposed on all sides

(1) Tables 5.6, 5.7 and 5.8 apply: however

- the height of the beam should not be less than the minimum width required for therespective fire resistance period,

- the cross-sectional area of the beam should not be less than

Ac = 2b2min (5.9)

where bmin is given by Tables 5.6 to 5.8.

5.7 Slabs

5.7.1 General

(1) Fire resistance of reinforced and prestressed concrete slabs may be consideredadequate if the values in Tables 5.9 together with the following rules are applied.


Ref. No. prEN 1992-1-2: (July 2001)

(2) The minimum slab thickness hs given in Table 5.9 ensures adequate separatingfunction (Criterion E and I). Floor-finishes will contribute to the separating function inproportion to their thickness (see Figure 5.7). If load-bearing function (Criterion R)is required only the necessary slab thickness assumed for design to EN 1992-1-1may be taken.

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

hs = h1 + h2 (Table 5.10)

Figure 5.7: Concrete slab with floor finishes

(3) The rules given in 5.7.2 and 5.7.3 also apply for the flanges of T- or TT-shapedbeams.

5.7.2 Simply supported solid slabs

(1) Table 5.9 provides minimum values of axis distance to the soffit of simply supportedslabs 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 thelower layer.

h1

h 2

h1

h 2

1

2 3

2

1


Ref. No. prEN 1992-1-2: (July 2001)

Table 5.9: Minimum dimensions and axis distances for reinforced and prestressedconcrete simply supported one-way and two-way solid slabs

Standard fireresistance Minimum dimensions (mm)

slabthicknesshs (mm)

axis-distance a

one way two way:ly/lx ≤ 1,5 1,5 < ly/lx ≤ 2

1 2 3 4 5

REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

60

80

100

120

150

175

10*

20

30

40

55

65

10*

10*

15*

20

30

40

10*

15*

20

25

40

50

lx and ly are the spans of a two-way slab (two directions at right angles)where ly is the longer span.

For prestressed slabs the increase of axis distance according to 5.2(4)should be noted.

The axis distance a in Column 4 and 5 for two way slabs relate to slabssupported at all four edges. Otherwise, they should be treated asone-way spanning slab.


5.7.3 Continuous solid slabs

(1) The values given in Table 5.9 (Columns 2 and 4) also apply to one-way or two-waycontinuous slabs.

(2) Table 5.9 and the following rules apply for slabs where the longitudinal momentredistribution does not exceed 15% for ambient temperature design. In theabsence of a more rigorous calculation and where the redistribution exceeds 15%,or detailing rules of this Part 1.2 are not followed, each span of a continuous slab

Drafting Note: Further consideration is necessary to ensure against the riskof brittle failure of a continuous slab over supports.


Ref. No. prEN 1992-1-2: (July 2001)

should be assessed as a simply supported slab using Table 5.9 (Columns 2, 3, 4 or5 respectively).

The rules in 5.6.3 (3) for continuous beams also apply to continuous slabs. If theserule are not followed each span of a continuous slab should be assessed as asimply supported slab as above.

(3) A minimum negative reinforcement As ≥ 0,005 Ac over intermediate support shouldbe provided if any of the following conditions apply:

a) Type A ductility steel is used (see EN 1992-1-1, 3.2.3.2)

b) in two-span continuous slabs, no restraint to bending at end supports is providedby design provisions according to EN 1992-1-1 and/or by adequate detailing (see,for example, EN 1992-1-1, 9.2.2.2(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 takeninto account in the design (see Figure 5.8).

(A) Spanning direction, l(B) Extent of system without cross walls orbeams, > l(C) Danger of brittle failure(D) No rotational restraint provided

Section A - A

Figure 5.8: Slab systems for which minimum reinforcement areas according to5.7.3 (3) should be provided.

5.7.4 Flat slabs

(1) The following rules apply to flat slabs where the moment redistribution according to2.5.3.5.4 of EN 1992-1-1, does not exceed 15%. Otherwise axis distances shouldbe taken as for one-way slab (Column 3 in Table 5.9) and the minimum thicknessfrom Table 5.10.

AB

C

D

A A


Ref. No. prEN 1992-1-2: (July 2001)

(2) For fire ratings of REI 90 and above, at least 20% of the total top reinforcement ineach direction over intermediate supports, required by EN 1992-1-1, should becontinuous over the full span. This reinforcement should be placed in the columnstrip.

(3) Minimum slab-thicknesses should not be reduced (e.g. by taking floor finishes intoaccount).

(4) The axis distance a denotes the axis distance of the reinforcement in the lowerlayer.

Table 5.9: Minimum dimensions and axis distances for reinforced and prestressedconcrete solid flat slabs

Standard fire resistance


slab-thickness hs axis-distance a1 2 3

REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

150

200

200

200

200

200

10*

15*

25

35

45

50


5.7.5 Ribbed slabs

(1) For the assessment of the fire resistance of one-way reinforced and prestressedribbed slabs, 5.6.2, 5.6.3 for the ribs and 5.7.3, Table 5.10, Columns 2 and 5, forthe flanges apply.

(2) For two-way reinforced and prestressed ribbed slabs, adequate fire resistance maybe assumed if the values in Tables 5.11 and 5.12, together with the following rules,apply.

(3) The values in Tables 5.11 and 5.12 are valid for ribbed slabs subjected topredominantly uniformly distributed loading.

(4) For ribbed slabs with reinforcement placed in several layers, 5.6.1(4) applies.

(5) In continuous ribbed slabs, the top reinforcement should be placed in the upper halfof the flange.


Ref. No. prEN 1992-1-2: (July 2001)

(6) Table 5.11 is valid for simply supported, two-way spanning ribbed slabs. It is alsovalid for two-way spanning ribbed slabs with at least one restrained edge andstandard fire resistances lower than REI 180 where the detailing of the upperreinforcement does not meet the requirements in 5.6.3(3).

(7) Table 5.12 is valid for two-way spanning ribbed slabs with at least one restrainededge. For the detailing of the upper reinforcement, 5.6.3(3) applies for all standardfire resistances.

Table 5.11: Minimum dimensions and axis distance for two-way spanning, simplysupported ribbed slabs in reinforced or prestressed concrete.

Standard FireResistance


Possible combinations of width of ribs bminand axis distance a

slab thickness hsand

axis distance ain span

1 2 3 4 5REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

bmin = ≥80a = 15*

bmin = 100a = 35

bmin = 120a = 45

bmin = 160a = 60

bmin = ≥220a = 75

bmin = 280a = 90

12025

16040

19055

26070

35075

≥20015*

≥25030

≥30040

≥41060

≥50070

hs = 80a = 10*

hs = 90a = 10*

hs = 100a = 15*

hs = 120a = 20

hs = 150a = 30

hs = 175a = 40

asd = a + 10

For prestressed ribbed slabs, the axis-distance a should be increased in accordancewith 5.2(4).

asd denotes the distance measured between the axis of the reinforcement lateralsurface of the rib exposed to fire.



Ref. No. prEN 1992-1-2: (July 2001)

Table 5.12: Minimum dimensions and axis distances for two-way spanning ribbedslabs in reinforced or prestressed concrete with at least one restrainededge.

Standard FireResistance


possible combinations of width of ribsbmin and axis distance a

slab thickness hs andaxis distance ain span

1 2 3 4 5

REI 30

REI 60

REI 90

REI 120

REI 180

REI 240

bmin = ≥80a = 10*

bmin = 100a = 25

bmin = 120a = 35

bmin = 160a = 45

bmin = 310a = 60

bmin = 450a = 70

12015*

16025

19040

60050

70060

≥20010*

≥25015*

≥30030

hs = 80a = 10*

hs = 90a = 10*

hs = 100a = 15*

hs = 120a = 20

hs = 150a = 30

hs = 175a = 40

asd = a + 10

For prestressed ribbed slabs, the axis-distance a should be increased in accordance with 5.2(4).

asd denotes the distance measured between the axis of the reinforcement lateral surface of the rib exposed to fire.* Normally the cover required by EN 1992-1-1 will control


Ref. No. prEN 1992-1-2: (July 2001)

SECTION 6 HIGH STRENGTH CONCRETE (HSC)

6.1 General

(1)P This section gives additional rules for the design of structural elements at elevatedtemperature made with high strength normal weight concrete. It does not cover thedesign of structural elements made with high strength lightweight concrete. It does notapply to hydro-carbon fires.

(2)P Structural elements shall be designed at elevated temperature with the characteristics ofthat type of concrete and the risk of spalling shall be taken into account.

(3) Characteristics and recommendations against spalling are given for two ranges ofHSC.• Classes C ≥ 55/67 to C ≤ 80/95• Classes C > 80/95 to C ≤ 90/105

(4) Characteristics and recommendations are given only for fire exposurecorresponding to standard temperature-time curve.

(5) The ratio fc,Θ/ fck for siliceous concrete, given in Section 3, Table 3.1, are applicablefor classes C ≥ 55/67 to C ≤ 80/95

(6) For classes C > 80/95 to C ≤ 90/105, values of fc,θ/ fck are given in Table 6.1.

Table 6.1: Reduction of strength at elevated temperature

Concrete temperatureθ °C

fc,θ/ fckC > 80/95 to C ≤ 90/105

20 1,0100 0,75200 0,70300 0,65400 0,50500 0,45600 0,30700 0,20800 0,15900 0,081000 0,041100 0,011200 0,00

Note to the PT: According to Berlin minutes, it was agreed to add a column with somestrength reduction in region of 200 to 400 degrees also for the lower strength class.

6.2 Spalling

(1) For classes C 55/67 to C 80/95 the rules given in 4.6 apply, provided that themaximum content of silica fume is less than 6% by weight of cement.


Ref. No. prEN 1992-1-2: (July 2001)

0 200 400 600 800 10000

0,5

1,0

1,5

2,0


λλλλc [W/mk]

2

1

(2) For classes 80/95 < C ≤ 90/105 there is a risk of spalling and at least one of thefollowing should be provided:• a reinforcement mesh with a nominal cover of 15 mm. This mesh should

have wires with a diameter ≥ 2 mm with a pitch ≤ 50 x 50 mm. The nominalcover to the main reinforcement should be ≥ 40 mm.

• a type of concrete for which it has been demonstrated (by local experienceor by testing) that no spalling of concrete occurs under fire exposure.

• protective layers for which it is demonstrated that no spalling of concreteoccurs under fire exposure.

• include in the concrete mix more than 2 kg / m3 of monofilament propylenefibres.

6.3 Thermal properties

6.3.1 Thermal conductivity

(1) Thermal conductivity of the concrete, λc, may be calculated as follows:

λc = 1,8 - 0,7 (θ -20)/180 [ W/(m K) ] for 20°C ≤ θ ≥ 200°Cλc = 1,1 - 0,3 (θ -200)/800 [ W/(m K) ] for 200°C ≤ θ ≥ 1000°Cλc = 0,8 [ W/(m K) ] for 1000°C ≤ θ ≥ 1200°C

Where θ is the temperature of the concrete (°C)

This is compared with normal strength concrete (NSC) in Figure 6.1

(1) HSC (≤ C90/105)

(2) NSC (≤ C60/75)

Figure 6.1: Comparison of thermal conductivity for normal and high strengthconcrete


Ref. No. prEN 1992-1-2: (July 2001)

6.3.2 Specific heat

(1) The specific heat for dried out concrete with silica fume may be calculated usingExpression (6.2).

2

c ��

��

�−+=120

4120

80900p,Θθθ [ J/(kg K) ] (6.2)

(2) Extra heating is required to vaporise the moisture in the concrete. When themoisture content is not considered for the heat and mass balance thisphenomenon may be included by inserting a peak on the curve for specific heatbetween 100 and 200°C, see Figure 6.2

cp,θ [kJ/(kg K)]Temperature[°C] 40% RH 60% RH0 0,9 0,9

100 1,0 1,0120 1,8 2,3200 1,0 1,0400 1,1 1,1600 1,2 1,2800 1,25 1,251200 1,3 1,3

(1) 40% RH (2) 60% RH

Figure 6.2: Specific heat at high temperatures denoted for HSC at the relativehumidities 40% and 60% of air.

(3) Expression 6.3 may be used to determine the maximum specific heat point at120°C for vaporisation of the moisture in the concrete.

( )p,Θ

w3

p,max ∆001.01105000

cρc +⋅−⋅

=θ

θ[ J/(kg K) ] (6.3)

wherecp,max is the maximum value on the specific heat curve considering

vaporisation, [J/(kg K)],ρw is the water content by weight, [-]∆θ is the temperature interval where the vaporisation is generated, [K]cp,θ is the specific heat calculated from Expression (6.2) at temperature

θ , [J/(kg K)].

0 200 400 600 800 10000

0,5

1,0

1,5

2,0


1

2

2,5cp,θ [kJ/kg°C]


Ref. No. prEN 1992-1-2: (July 2001)

(4) For HSC with a water cement ratio of 0,3, a micro-silica/cement ratio of 0,1 and arelative humidity of 40%, the evapourable moisture content by mass of cement isapproximately 0,105. The corresponding value for 60% relative humidity is 0,155.

(5) The specific heat at elevated temperatures has been determined for concrete witha water cement ratio of 0,3, a cement weight of 465 kg/m3, 10% silica fume ofcement, concrete density of 2450 kg/m3 and the relative humidities of 40 and60%. The curves are shown in Figure 6.2. The comparison between normal andhigh strength concrete is shown in Figure 6.3.

(1) High Strength concrete

(2) Normal strength concrete

Figure 6.3 Comparison of specific heat for normal and high strength concrete

6.4 Temperature field

(1) The difference in temperature field between HSC and NSC may be considered tobe negligible for a preliminary design under the standard temperature � timecurve.

(2) For other cross-sections or under different heating regimes the temperature field ofa member may be calculated. When undertaking heat transfer calculations it isessential that relevant thermal properties of materials and heat transfer coefficientsat the boundaries are defined for the entire temperature interval.

6.5.1 HSC columns and walls

(1) Verification of the load-carrying capacity of columns and walls in the fire situationmay be conducted for a reduced cross-section, using the methods applicable fornormal design, e.g. Annex B.

0 200 400 600 800 10000

0,5

1,0

1,5

2,0


1

2

2,5cp,θ [kJ/kg°C]


Ref. No. prEN 1992-1-2: (July 2001)

(2) The reduced cross-section shall be derived on the basis of the simplified methodof Annex B, however incorporating an enhanced deduction of the fire damagedconcrete due to the influence of instability phenomena.

(3) In calculation of the effective cross-section the deducted concrete thickness shallbe equal to the depth of the 500 °C isotherm, a500, enlarged by 35%. Theenlargement approximately converts the 500°C isotherm depth into the 400°Cditto. Hence in calculation of the reduced cross-section for columns and walls adeduction thickness described by Expression (5.4) should be employed.

az = 1,3 az, 500 (6.4)

(4) Calculation of moment capacity for cross-sections subjected to combined bendingand axial loading may be undertaken by employing Method B2, Zone Method,taking account Ec,fi (θ ) = kc

2(θ )·Ec if relevant.

(5) The Tabulated method for columns and walls in Section 4 may also be used forHSC if the axis distance is increased by 35%.

(6) Time heat regimes which do not comply with the criteria of the simplified methodrequire a separate comprehensive analysis which accounts for the relativestrength of the concrete as function of the temperature.

6.5.2 HSC beams and slabs

(1) The moment capacity of beams and slabs in the fire situation may be calculatedbased on the effective cross-section, defined in Annex A, using the methodsapplicable for normal design.

(2) HSC beams and slabs furthermore require an additional reduction of thecalculated moment capacity. Hence,

Md,fi = M500 ×η (6.5)

whereMd,fi design moment capacity in the fire situationM500 calculated moment capacity based on the effective cross-section,

defined by the 500°C isothermη reduction factor in accordance with Table 6.3

(3) For slab thickness in the range of 50 to 120 mm, with fire exposure on the tensionside, the reduction factor may be obtained from linear interpolation.

(4) Time heat regimes which do not comply with the criteria of the simplified methodrequire a separate comprehensive computer analysis which accounts for therelative strength of the concrete as function of the temperature.

(5) Tabulated data of Section 4.2 for beams and slab may also be used for HSC if theaxis distance is increased by 10%.


Ref. No. prEN 1992-1-2: (July 2001)

Table 6.3: Moment capacity reduction factors for beams and slabs.

Item ηBeams 0,95Slabs exposed to fire in the compression zone 0,95Slabs exposed to fire in the tension side, t ≥ 120 mm 0,95Slabs exposed to fire in the tension side, t = 50 mm 0,85


Ref. No. prEN 1992-1-2: (July 2001)

Annex A (informative)

Temperature profiles

(1) Figures A.2 and A.3 to A.6 provide temperature profiles for slabs and beamsrespectively. The temperature values are based on thermal properties of concrete givenin Section 3 and a moisture content of 1,5%. The temperature graphs will beconservative if the moisture content is higher than 1,5%.

(2) Figures A.7 – A.10 provide temperature profiles for beams. Figure A.11 provides the500°C isotherm for a beam, h x b = 0,3 x 0,16 m. Figures A.12 to A.15 provide temperature profiles for rectangular columns. Figure A.16provides the 500 0C isotherm for a column, h x b = 0,3 x 0,3 m.Figures A.17 to A.20 provide temperature profiles for circular columns. Figure A.21provides the 500 0C isotherm for a circular column, φ = 0,3m.

The temperature values are based on thermal properties of concrete given in Section 3.

(3) Figure A.1 shows how the temperature profiles represent the temperature in the cross-section taking symmetry into account.

(1) Area of temperature profile

(2) Full cross section

Figure A.1: Area of cross-section for which the temperature profiles are presentedx

y1

2


Ref. No. prEN 1992-1-2: (July 2001)

0

200

400

600

800

1000

1200

0 10 20 30 40 50 60 70 80 90 100a (mm)

Tem

pera

ture

(°C

)

6090

240

120

30

180

Figure A.2: Temperature profile for slabs (height h = 200 mm) for 60 - 240 minstandard fire exposure, a = axis distance

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

100

200

300

300

400

400500

600

600

700

700

800

800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

100

200

300

400

500

500 600 700

800 900 900

a) R60 b) R90

Figure A.3: Temperature profile for a beam h x b = 0,6 x 0,3 m


Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

100

200

300

400

500

600

600 700

700

800

800 900 9001000 1000

Figure A.4 Temperature profile for a beam h x b = 0,6 x 0,3 m - R120

0 0.04 0.08 0.12 0.16 0.2 0.240

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

100

200

200 300

400

400 500 500 600 700 800 800

900

900

0 0.04 0.08 0.12 0.16 0.2 0.240

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

100

200

300 400

500

500

600

600 700 700

800

800

900

900

1000

1000 1000

a) R90 b) R120.Figure A.5: Temperature profile for a beam h x b = 0,8 x 0,5 m


Ref. No. prEN 1992-1-2: (July 2001)

0 0.04 0.08 0.12 0.16 0.2 0.240

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

100

200

300

300 400

500 600

600 700

800

800

900

9001000 1000

0 0.04 0.08 0.12 0.16 0.2 0.240

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.4

200

300

400

500

500

600

600

700

700

800

800 900 900

1000

10001100 1100

a) R180 b) R240Figure A.6: Temperature profile for a beam h x b = 0,8 x 0,5 m

0 0.01 0.02 0.03 0.040

0.01

0.02

0.03

0.04

0.05

0.06

0.07

800

700

600500

400

300

Figure A.7: Temperature profile for a beam, h x b = 0,15 x 0,08 m - R30


Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.080

0.02

0.04

0.06

0.08

0.1

0.12

0.14

100

200

300

300400

500

500

600

600

700

700

0 0.02 0.04 0.06 0.080

0.02

0.04

0.06

0.08

0.1

0.12

0.14

200

400500

600

700

700

800

800

900

a) R30 b) R60

Figure A.9: Temperature profile for a beam, h x b = 0,3 x 0,16 m

0 0.02 0.04 0.06 0.080

0.02

0.04

0.06

0.08

0.1

0.12

0.14

400

500

600

700

800

800 900

900

a) R90

Figure A.10: Temperature profile for a beam, h x b = 0,3 x 0,16 m


Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.080

0.02

0.04

0.06

0.08

0.1

0.12

0.14

R90

R60

R30

Figure A.11: 500°°°°C isotherm for a beam, h x b = 0,3 x 0,16 m

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

100

200

300400 400

500

500

600

600700 700

Figure A.12: Temperature profile for a column, h x b = 0,3 x 0,3 m - R30


Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

800700

600500

400

300

200

100


0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

900800

700

600500

400

300

200

100



Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1000

800

900

700600

500

400

300

200


0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

R120

R90

R60

R30

Figure A.16: 500 0C isotherm for a column, h x b = 0,3 x 0,3 m


Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

100

200300

400

500

500

600

600

700

Figure A.17: Temperature profile for a circular column, φφφφ = 0,3 m - R30

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

200

300

400

400

500

600

700

700

800

800



Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

200

300

400

500

600 700

800

800

900

900


0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

300

400

500 600

700

700

800

900

900

1000



Ref. No. prEN 1992-1-2: (July 2001)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

R120

R90

R60

R30

Figure A.21: 500 0C isotherm for a circular column, φφφφ = 0,3 m


Ref. No. prEN 1992-1-2: (July 2001)

ANNEX B (Informative)

Simplified calculation methods

This annex provides two alternative methods, “500°C isotherm” and “Zone”, for calculating theresistance to bending moments and axial forces. In addition, the cross-section should bechecked for shear (see 4.5) and spalling (see 4.7).

B.1 500°C isotherm method

B.1.1 Principle and field of application

(1)This method is applicable to standard fire exposure and any other time heat regimes,which cause similar temperature fields in the fire exposed member. Time heat regimeswhich do not comply with this criteria, require a separate comprehensive analysis whichaccounts for the relative strength of the concrete as function of the temperature.

(2) This method is valid for minimum width of cross-section given in table B1.

Table B1: Minimum width of cross-section as function of fire resistance (for standard fireexposure) and fire load density (for parametric fire exposure)

a) Fire resistance.Fire resistance R 60 R 90 R120 R180 R240Minimum widthof cross-section mm 90 120 160 280 200

b) Fire load density.Fire load density MJ/m2 200 300 400 600 800Minimum widthof cross-section mm 100 140 160 200 240

(3) The simplified calculation method comprises a general reduction of the cross-sectionsize with respect to a heat damaged zone at the concrete surfaces. The thickness of thedamaged concrete, a500, is made equal to the average depth of the 500°C isotherm inthe compression zone of the cross-section.

(4) Damaged concrete, i.e. concrete with temperatures in excess of 500°C, is assumed notto contribute to the load-carrying capacity of the member, whilst the residual concretecross-section retains its initial values of strength and modulus of elasticity.

(5) For a rectangular beam exposed to fire on three sides, the effective cross-section in thefire situation will be in accordance with Figure B1.


Ref. No. prEN 1992-1-2: (July 2001)

B.1.2 Design procedure of a reinforced concrete cross-section, exposed to bendingmoment and axial load

(1) On the basis of the above reduced cross-section approach, the procedure for calculatingthe resistance of a reinforced concrete cross-section in the fire situation may be carriedout as follows:

(a) Determine the isotherm of 500°C for the specified fire exposure, standard fire orparametric fire,

(b) Determine a new width bfi and a new effective height dfi of the cross-section byexcluding the concrete outside the 500°C isotherm (see Figure B.1),

(c) Determine the temperature of reinforcing bars in the tension and compression zones.The temperature of the individual reinforcing bar can be evaluated from thetemperature profiles in Annex A or handbooks and is taken as the temperature in thecentre of the bar,

(d) Determine the design strength due to the temperature for the tension andcompression reinforcement (see Figure 3.2 or Annex A: Figures 2 - 4); for thecompression reinforcement, it is recommended to use the tension strength dividedby 1,2,

(e) Use conventional calculation methods for the reduced cross-section for thedetermination of the ultimate load bearing capacity with stresses of the reinforcingbars, as obtained in (d), and

(f) Compare the ultimate load-bearing capacity with the design load effect or,alternatively, the evaluated fire resistance with the required resistance.

(2) Some of the reinforcing bars may fall outside the reduced cross-section, as shown inFigure B.1. Despite this, they may be included in the calculation of the ultimate load-bearing capacity of the fire exposed cross-section. The rounded corners of isotherms canbe regarded by approximating the real form of the isotherm to a rectangle or a square, asindicated in Figure B.1


Ref. No. prEN 1992-1-2: (July 2001)

T -Tension C - Compression

a) fire exposure on three sideswith the tension zone exposed

b) fire exposure on three sides withthe compression zone exposed

c) fire exposure on four sides (beam or column)

Figure B.1. Reduced cross-section of reinforced concrete beam and column

(3) Figure B.2 is shows the calculation of load-bearing capacity of a cross-section withtension as well as compression reinforcement.

bfi

b

dfi = d500 °C

T

C

bfi

b

dfi

50500 °C

d

C

T

dfi d

bfi

b

500 °C

bfi

b

hhfi500 °C


Ref. No. prEN 1992-1-2: (July 2001)

b original widthbfi width of effective cross-sectionh original heighthfi height of effective cross-sectiondfi effective height of effective cross-sectionz lever arm between tension and compression reinforcementz' lever arm between tension reinforcement and concrete

λ and x are defined in EN 1992-1

Figure B.2. Stress distribution at ultimate limit state for a rectangular concrete cross-section with compression reinforcement.

(4) If all reinforcement bars are positioned in layers and have the same area the followingexpressions may be used in calculating the axis distance, a (see Figure B.2).

The average reduced strength of a reinforcement layer with respect to increasedtemperatures, is calculated in accordance with Expression (B.1).

νν

θΣθnkk )()( i= (B.1)

where, θ temperature in reinforcement bar i k(θi) reduction of the strength of the reinforcement bar i due to the temperature

θi which is obtained from Figure 4.11kν(θ) average strength of reinforcement layer ν nν number of reinforcement bars in layer ν

(5) The axis distance, a, from bottom surface of the effective cross-section to the centroid ofthe reinforcement layers may be calculated using Expression (B.2).

)()(

θΣθΣ

ν

νν

kkaa = (B.2)

Where

As

As'

z' dfi

bfi

z

fcd

λxbfifcd

As1fsd,fi

z'

Fs = As2fsd,fi(Θm)

Fs = As'fscd,fi(Θm)

Mu2Mu1

x λx


Ref. No. prEN 1992-1-2: (July 2001)

aν is the axis distance from the bottom surface of the effective cross-section toreinforcement layer ν

(6) If only two layers exist the axis distance may be calculated using Expression (B.3)

a = √(a1a2) (B.3)

(7) If the reinforcement bars have different areas and are distributed arbitrary the followingprocedure must be used.

The average steel strength of a reinforcement group, with respect to increasedtemperatures, may be calculated using Expression (B.4)

( )( )[ ]

A

Afkfk

s

ii

isd,iiifi,sd Σ

Σ θϑ = (B.4)

Wherefsd,i design strength of reinforcement bar iAi cross-section area of reinforcement bar i

The axis distance, a (see Figure B.2), from the effective cross-section to the centroid ofthe reinforcement group is calculated in accordance with Expression (B.5).

a = [ ][ ]Afk

Afka

ii,sdisi

ii,sdisii

)(

)(

θ

θΣ

Σ (B.5)

Whereai is the axis distance from effective cross-section to reinforcement bar i

(8) The bending moment calculation of the cross-section is illustrated as follows:

fimfi,sd1s1u )( dfAM θ= 2

1 kω− (B.6)

cdfifi

mfi,sd1sk

)(fdb

fAω

θ= (B.7)

´)( mfi,sc2s2u zfAM ⋅= θ (B.8)

As = As1+As2 (B.9)

Where As total reinforcement area

fsd,fi design tensile strength of reinforcementfsc,fi design strength for compressive reinforcementωk design strength ratio of reinforcement for the fire-exposed cross-sectionbfi width of the fire exposed cross-sectiondfi efficient height of the fire exposed cross-sectionfcd design compressive strength of concrete (at normal temperature)


Ref. No. prEN 1992-1-2: (July 2001)

z´ lever between tension and compression reinforcementθm mean temperature of the reinforcement layer

When the moment contributions are assessed as shown above the total momentcapacity is obtained from

Mu = Mu1 + Mu2 (B.10)

B.2 Zone method

(1) The method of subdividing the cross-section into several zones is described below. Thismethod, although more laborious, provides a more accurate method than the 500°Cisotherm method especially for columns. The method is applicable to the standardtemperature-time curve only.

(2) The cross-section is divided into a number (n ≥ 3) of parallel zones of equal thickness(rectangular elements) where the mean temperature and the corresponding meancompressive strength fcd(θ) and modulus of elasticity (if applicable) of each zone isassessed.

(3) The fire damaged cross-section is represented by a reduced cross-section ignoring adamaged zone of thickness az at the fire exposed sides, see Figure B.3. For arectangular cross-section exposed to fire on one face only, the width is assumed to be w,see Figure B.3 (c). When two opposite sides are exposed to fire the width is assumed tobe 2w, see Figure B.3 (a), (b), (d), (e) and the web of (f). The flange of Figure B.3 (f) isrelated to the equivalent wall in figure B.3 (d), and the web to the equivalent wall inFigure B.3 (a).

(4) For the bottom and ends of rectangular members exposed to fire, where the width is lessthan the height, the value of az is assumed to be the same as the calculated values forthe sides, Figure B.3 (b), (e), (f).

The reduction of the cross-section is based on a damaged zone of thickness az at the fireexposed surfaces which is calculated as follows:

(5) The damaged zone, az, is estimated as follows for an equivalent wall exposed bothsides:

a) The half thickness of the wall is divided into n parallel zones of equal thickness,where n ≥ 3 (see Figure B.4),

b) The temperature is calculated for the middle of each zone.

c) The corresponding compressive strength reduction, kc(θi) is determined (see FigureB.5).


Ref. No. prEN 1992-1-2: (July 2001)

Figure B.3. Reduction of strength and cross-section for sections exposed to fire

Figure B.4. Division of a wall, with both sides exposed to fire, into zones for use incalculation of strength reduction and az values

kc(ΘM)

kc(Θ)

kc(Θ1111)

kc(Θ2)

kc(Θ3)

w w

az1

w1

az1

w1

az1

kc(ΘM1)M2kc(ΘM2)

w2

az2

w2

az2

M2

kc(ΘM1)

az1

w1

az1

w1

az1w1

az1

w1

az1

M1

kc(ΘM1)

w1

az2

w2

az1

az1

kc(ΘM2)

kc(ΘM1)

kc(ΘM2)

az2

w2

a) b) c)

d) e) f)


Ref. No. prEN 1992-1-2: (July 2001)

(5) The mean reduction coefficient for a particular zone, incorporating a factor (1- 0,2/n)which allows for the variation in temperature within each zone, may be calculated byExpression (B.11)

)()/2,01(ic

n1im,c θΣ k

nnk

=

−= (B.11)

wheren is the number of parallel zones in width ww is half the widthm is the zone number

(6) The width of the damaged zone for beams, slabs or members in plane shear may becalculated using Expression

��

��

�−=

)(1

Mc

m,cz θk

kwa (B.12)

Where kc(θM) denotes the reduction coefficient for concrete of zone m at point M.

(7) For columns, walls and other constructions where second order effects may becalculated using Expression (B.13).

( ) ��

�

�

��

�

�

��

�

�−=

3,1

Mc

m,cz 1

θkk

wa (B.13)

(8) When the reduced cross-section is found and the new strength and modulus of elasticityare determined the fire design follows the cold design procedure similar to that shown inFigure B.2.


Ref. No. prEN 1992-1-2: (July 2001)

w is assessed as:

• The thickness of a slab,• The thickness of a one sided exposed wall orcolumn,• Half the thickness of the web of a beam,• Half the thickness of a two sided exposed wallor column or• Half the smallest dimension of a four sidedexposed column.

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

b) Reduction in cross-section a, of abeam or slab using siliceousaggregate concrete.

c) Reduction in cross section a, of acolumn or wall using siliceousaggregate concrete.

Note: The value for siliceous aggregate concrete are conservative for most other aggregates

Figure B.5: Reduction in cross section and concrete strength assuming standardtemperature-time curve


Ref. No. prEN 1992-1-2: (July 2001)

Annex C (informative)

C.1 Buckling of columns under fire conditions

(1) This Annex deals with columns in which the structural behaviour is significantlyinfluenced by second order effects under fire conditions.

(2) Under fire conditions, the damage of the outer layers of the member due to hightemperatures, combined with the drop of the elasticity modulus at the inner layers,results in a decrease of the stiffness of structural members under fire conditions.On account of this, second order effects can be significant on columns although atambient temperature conditions their effect is negligible.

(3) The assessment of a column under fire conditions as an isolated member may bemade by the method based on estimation of curvature (see 5.8.8 of EN 1992-1) ifthe following rules are applied.

(4) For non-sway building structures, indirect fire actions need not be considered if thedecrease of the first order moments due to the decrease of stiffness of the columnis not taking into account.

(5) The effective length l0,fi under fire conditions may be taken as equal to l0 at normaltemperature as a safe simplification. For a more accurate estimation the increaseof the relative reaction at the ends of the column, due to the decrease of itsstiffness can be taking into account. For this purpose a reduced cross-section ofthe column given by B.2 method of Annex B may be used. It should be noted thatthe reduction factor for the calculation of equivalent width should be kc

2 (θ) notkc (θ).

For non-sway building structures where the required Standard fire exposure ishigher than 60 min, the effective length l0 can be taken as 0,5 l for intermediatefloors and 0,5 l ≤ l0,fi ≤ 0,7 l for upper floors.

C.2 Assessment of a reinforced concrete cross-section, exposed to bending momentand axial load by the method based on estimation of curvature.

(1) This method is valid only for the assessment of columns in non-sway structures.

(2) Determine the isotherm curves for the specified fire exposure, standard fire orparametric fire.

(3) Divide the cross section into zones with approximate mean temperature of 20ºC,100ºC, 200ºC, 300ºC ... up to 1100ºC. See Figure C.1.

(4) Determine the width wij, area Acij and co-ordinates xij yij of the centre of each zone.

(5) Determine the temperature of reinforcing bars as in simplified calculationmethods.


Ref. No. prEN 1992-1-2: (July 2001)

Figure C.1: Dividing cross-section of column into zones with approximateuniform temperature

(6) Determine the moment-curvature diagram for Nd,fi using for each reinforcing bar

and for each concrete zone the relevant stress-strain diagram according to 3.2.2,3.2.3 and eventually 3.2.4.

(7) Use conventional calculation methods for the determination of the ultimatebending moment for Nd,fi and the nominal second order moment at correspondingelongation.

(8) Determine the ultimate bending capacity for the specified fire exposure and Nd,fi asthe difference between ultimate bending moment and nominal second ordermoment so calculated.

(9) Compare the ultimate bending capacity with the design first order bendingmoment at fire conditions Md,fi.

C.3 Minimum dimensions and axis distances for reinforced concrete columns.

(1) Tables C.1 to C.9 allow useful information for assessing columns width up to 600mm and slenderness up to λ = 80 for standard fire exposure. Notations are as in5.2.1.

(2) Linear interpolation between the different column tables within this Annex ispermitted.

Ac,ij

x,i,j

y ,i,j

εεεεsup

εεεεinf

εεεεij

εεεεs1

εεεεs2

εεεεs3

Sectors defined by Isotherm curves


Ref. No. prEN 1992-1-2: (July 2001)

Table C.1 : Minimum dimensions and axis distances for reinforced concretecolumns; rectangular and circular section. Reinforcement capacity ratioωωωω = 0,1. Low first order moment: e = 0,025 b ≥≥≥≥ 10 mm.

Standard fire Minimum dimensions (mm) Column width bmin/axis distance a

resistance λ Column exposed on more than one siden = 0,15 n = 0,3 n = 0,5 n = 0,7

1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*150/25*150/25*200/25*

200/30:250/25*

150/25*150/35:200/25*

200/25*200/35:250/25*

250/25*250/30:300/25*

200/25*250/25*250/25*250/25*

250/50:300/25*300/25*

250/25*250/25*

250/50:300/25*300/40:350/25*350/30:400/25*400/30:450/25*

250/25*300/25*350/25*400/25*450/25*50025*

150/25*150/25*150/25*150/25*150/25*200/25*

150/25*150/25*200/25*

200/40:250/25*250/30:300/25*250/40:300/25*

200/25*200/30:250/25*

250/25*250/40:300/25*300/35:350/25*350/35:400/25*

250/25*250/25*300/25*350/25*400/25*

450/40:500/25*

250/25*300/30:350/25*350/50:400/25*

450/25*500/25*

550/45/600/25*

350/25*400/25*450/25*

500/60:550/25*600/25*600/80

150/25*150/25*150/25*200/25*250/25*

250/30:300/25*

200/25*200/25*250/25*

250/40:300/25*300/40:350/25*400/30:450/25*

200/50:250/25*250/25*300/25*

350/35:400/25*400/45:550/25*550/40:600/25*

250/25*300/25*

350/50:400/25*450/400:500/25*500/60:550/25*

600/45

350/25*400/25*

450/40:500/25*550/40:600/25

600/80(1)

450/25*500/25*

550/50:600/25*600/80

(1)(1)

150/25*150/25*200/25*250/25*300/25*350/25*

200/30:250/25*250/25*300/25

350/30:400/25*450/35:550/25*550/60:600/35

250/30:300/25*300/25

350/50:400/25*50/50:550/25*

600/40(1)

300/45:350/25400/25*

450/50:500/25*550/50

(1)(1)

400/50:450/25*450/50:500/25*550/60:600/35

(1)(1)(1)

500/40:550/25*600/25*

(1)(1)(1)(1)

* Normally the cover required by EN 1992-1-1 will control.(1) Requires a width greater than 600 mm. Particular assessment for buckling is required.


Ref. No. prEN 1992-1-2: (July 2001)

Table C.2 : Minimum dimensions and axis distances for reinforced concretecolumns; rectangular and circular section. Reinforcement capacity ratioωωωω = 0,1. Moderate first order moment: e = 0,25 b < 100 mm.



1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25150/25*200/25*250/25*

150/30:200/25*200/30:250/25*200/40:300/25*250/35:400/25*300/40:500/25*400/40:550/25*

200/40:250/25*250/40:350/25*300/40:500/25*300/50:550/25*400/50:550/25*500/60/600/25*

250/50:350/25*300/50:500/25*400/50:550/25*500/50:550/25*500/60:600/25*550/50:600/25*

400/50:500/25*500/50:550/25*

550/25*550/50:600/25*

600/55600/70

500/60:550/25*550/25*

550/60:600/25*600/60600/80

(1)

150/25*150/30:200/25*200/40:250/25*

300/25*350/40:500/25*

550/25*

200/40:300/25*300/35:350/25*350/45:550/25*450/50:550/25*550/30:600/25*

600/30

300/40:400/25*350/50:550/25*500/60:550/25*550/45:600/25*

600/45(1)

400/50:550/25*500/50:550/25*550/50:600/25*550/55:600/50

600/60(1)

500/60:550/25*550/50:600/25*

600/60600/80

(1)(1)

550/40:600/25*600/60600/80

(1)(1)(1)

200/30:250/25*300/25*

350/40:500/25*550/25*

550/30:600/25*(1)

300/40:500/25*450/50:550/25*550/30:600/30

600/35600/80

(1)

500/50:550/25*550/35:600/25*

600/40(1)(1)(1)

550/25*550/50:600/25

600/60(1)(1)(1)

550/60:600/30600/80

(1)(1)(1)(1)

600/75(1)(1)(1)(1)(1)

300/30:350/25*500/40:550/25*

550/25*600/30

(1)(1)

500/25*550/40:600/25*

600/55(1)(1)(1)

550/40:600/25*600/50

(1)(1)(1)(1)

550/60:600/45(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

* Normally the cover required by prEN 1992-1-1 will control.(1) Requires a width greater than 600 mm. Particular assessment for buckling is required.


Ref. No. prEN 1992-1-2: (July 2001)

Table C.3 : Minimum dimensions and axis distances for reinforced concretecolumns; rectangular and circular section. Reinforcement capacity ratioωωωω = 0,1. High first order moment: e = 0,5 b ≤≤≤≤ 200 mm.



1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*200/25*

250/30:300/25*300/40:550/25*400/40:550/25*

550/25

300/35:500/25*350/40:550/25*450/50:550/25*

550/30550/35550/40

350/50:550/25*500/60:600/30

550/40550/50:600/45550/60:600/50

600/70

550/40:600/30550/50:600/45550/55:600/50550/60:600/50

600/70(1)

550/50550/60600/70

(1)(1)(1)

600/70(1)(1)(1)(1)(1)

400/40:550/25*550/25*

550/30:600/25*600/50

(1)(1)

500/50:550/25*550/40:600/30550/50:600/40

600/80(1)(1)

550/45:600/40550/60:600/50

600/80(1)(1)(1)

550/50600/70

(1)(1)(1)(1)

600/80(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

550/25*550/35:600/30

(1)(1)(1)(1)

550/50:600/40(1)(1)(1)(1)(1)

600/80(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)




1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*150/25*150/25*150/25*

150/35:200/25*

150/25*150/25*

150/40:200/25*200/25*

200/35:250/25*200/45:250/25*

150/35:200/25*200/25*

200/40:250/25*200/50:250/25*250/35:300/25*250/45:300/25*

200/45:250/25*250/25*

250/35:300/25*300/40:350/25*

350/25*400/30:450/25*

250/25*250/40:300/25*350/30:400/25*400/35:450/25*450/30:500/25*500/40:550/25*

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*

150/35:200/25*200/30:250/25*200/35:250/25*250/30:300/25*

150/40:200/25*200/35:250/25*200/45:250/25*250/35:300/25*250/45:350/25*250/50:400/25*

200/40:250/25*250/25*

250/45:300/25*300/45:350/25*350/45:450/25*400/50:550/25

250/35:300/25*300/45:350/25*350/45:400/25*

450/25*500/40:550/25*500/55:600/45

350/25*400/45:450/25*450/50:500/25*500/50:600/25*550/75:600/50

600/70

150/25*150/25*150/25*150/25*200/25*

200/30:250/25*

150/30:200/25*200/25*

200/40:250/25*250/30:300/25*250/40:350/25*300/40:500/25*

200/40:250/25*250/30:300/25*250/45:350/25*300/45:400/25*350/45:600/25*400/50:600/35

250/45:300/25*300/45:350/25*350/45:450/25*400/50:550/25*500/50:600/40500/60:600/45

350/45:400/25*450/25*

500/40:550/25500/60:600/55

600/65600/80

450/45:500/25*500/60:550/25*550/70:600/55

600/75(1)(1)

150/25*150/25*200/25*

200/30:250/25*250/25*300/25*

200/35:250/25*250/30:300/25*250/40:350/25*300/40:450/25350/45:600/25450/50:600/35

250/40:300/25*300/40:400/25*350/45:550/25*400/50:600/35550/50:600/45

600/60

350/45:500/25*400/50:550/25*450/50:600/25*500/60:600/35

600/45600/60

450/45:500/25*500/55:600/50

600/65600/80

(1)(1)

550/65:600/50600/75

(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)

Table C.5 : Minimum dimensions and axis distances for reinforced concretecolumns; rectangular and circular section. Reinforcement capacity ratioωωωω = 0,500. Moderate first order moment: e = 0,25 b < 100 mm.



1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*

150/30:200/25*150/35:200/25*200/30:300/25*200/35:300/25*

150/35:200/25*200/35:250/25*200/40:300/25*200/50:400/25300/35:500/25*300/40:600/25*

200/45:300/25*200/50:350/25*250/45:450/25*300/50:500/25*350/50:550/25*400/50:600/25*

300/45:450/25*350/50:500/25*450/50:500/25*500/50:600/25*500/55:600/35500/60:600/55

450/45:500/25*450/50:550/25*500/55:600/25*550/55:600/40

600/60600/70

150/25*150/25*150/25*150/25*

150/35:200/25*200/30:250:25*

150/35:200/25*200/30:300/25*200/40:350/25*250/40:500/25*300/40:500/25*350/40:600/25*

200/45:300/25*250/45:500/25*300/45:550/25*350/50:600/25*400/50:600/35500/55:600/40

300/45:550/25*350/50:550/25*450/50:600/25*500/45:600/40500/50:550/45500/55:550/50

450/50:600/25*500/50:600/25*500/60:600/50550/60:600/55

600/65600/75

550/55:600/25600/50600/65600/75

(1)(1)

150/25*150/25*

200/30:250/25*250/30:300/25*350/30:400/25400/40:500/25

250/35:350/25*300/35:500/25*300/45:550/25*400/45:600/30500/40:600/35550/55:600/40

300/45:550/25*350/50:600/25*500/50:600/35550/50:600/45

600/50600/80

450/50:600/25*500/50:600/40500/55:550/45550/60:600/60

600/75(1)

500/60:600/50600/60600/70

(1)(1)(1)

600/70600/80

(1)(1)(1)(1)

200/30:250/25*300/45:350/25*350/40:450/25*500/30:550/25*550/35:600/30

600/50

350/40:550/25450/50:600/30500/50:600/35

600/45600/80

(1)

500/50:600/40550/50:600/45

600/55(1)(1)(1)

500/60:600/50600/55600/80

(1)(1)(1)

600/75(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)




1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/30:200/25*150/35:250/25*200/35:300/25*200/40:500/25*200/40:550/25*250/40:600/25*

250/40:450/25*200/50:500/25*250/45:550/25*250/50:550/30300/50:550/35350/50:600/35

250/50:550/25*300/50:600/25*400/50:550/35450/50:600/40500/50:550/45550/50:600/45

500/45:550/30500/50:600/40500:60:550/50

550755550/60600/60

550/50:600/45550/60:600/55

600/65600/70600/75600/80

150/25*150/30:200/25*200/30:250/25*200/35:300/25*250/40:400/25*300/40:500/25*

200/40:450/25*250/40:500/25*300/45:550/25*400/40:600/30500/40:550/35500/45:600/35

300/50:500/25*350/50:550/35500/45:550/40500/50:550/45550/50:600/45550/60:600/50

500/50:550/40500/55:550/45500/60:600/45

550/50550/60:600/55

600/70

550/55550/60600/70600/75

(1)(1)

600/70600/75

(1)(1)(1)(1)

250/35:300/25*300/35:450/25*400/40:500/25*450/50:550/25*500/40:600/30550/50:600/40

450/50:550/30500/40:550/35500/55:550/40550/50:600/45

600/60(1)

500/55:600/40550/60:600/50

600/60600/80

(1)(1)

550/50550/60:600/55

600/80(1)(1)(1)

600/75(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

500/40:550/25*550/30

550/50:600/40(1)(1)(1)

550/50:600/40600/60

(1)(1)(1)(1)

600/80(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)




1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*150/25*150/25*150/25*

150/30:200/25*

150/25*150/25*

150/35:200/25*150/40:250/25*200/35:250/25*200/40:250/25*

150/40:200/25*200/30:250/25*200/40:250/25*200/45:250/25*

250/25*250/35:300/25*

200/50:250/25*250/25*

250/30:300/25*250/40:350/25*300/45:400/25*350/40:450/25*

250/25*250/40:350/25*350/30:400/25*350/45:450/25*400/50:500/25*450/45:550/25*

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*

150/30:200/25*150/40:250/25*200/35:250/25*200/40:300/25*

200/25*200/35:250/25*200/40:250/25*250/55:300/25*300/35:350/25*300/40:500/25

200/45:250/25*250/25*

250/35:300/25*250/45:400/25*350/35:450/25*350/40:550/25*

300/25*300/45:350/25*350/40:450/25*350/50:500/25*450/45:600/35550/50:600/40

350/40:400/25*400/50:450/25*450/45:550/25*500/50:600/35500/60:600/45550/60:600/50

150/25*150/25*150/25*15025*

150/30/200/25*200/30:250/25*

150/25*200/30:250/25*200/40:250/25*250/35:300/25*250/40:400/25*300/40:550/25*

200/40:250/25*250/35:350/25*250/45 400/25*300/45:550/25*350/45:600/35350/50:600/40

250/40:400/25*300/45:400/25*350/40:55025*400/50:600/25*550/40:600/35550/50:600/45

350/45:450/25*450/45:550/25*450/50:600/40550/55:600/50550/70:600/65

600/75

500/40:600/25*500/60:600/40550/55:600/50

600/70(1)(1)

150/25*150/25*

150/30:200/25*200/30:250/25*

250/25*250/30:300/25*

200/40:300/25*250/35:350/25*250/40:350/25*300/40:600/25*350/40:450/35350/45:450/40

250/45:600/25*300/45:600/30350/45:600/35400/50:600/40550/50:600/45550/65:600/55

400/40:600/25*400/50:600/30550/45:600/40550/60:600/50

600/70(1)

500/50:600/45550/60:600/55

600/70600/80

(1)(1)

550/70:600/60600/75

(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)

Table C.8 : Minimum dimensions and axis distances for reinforced concretecolumns; rectangular and circular section. Reinforcement capacity ratioωωωω = 1,0. Moderate first order moment: e = 0.25 b < 100 mm.



1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/25*150/25*

150/30:200/25*150/35:200/25*200/30:250/25

200/25*200/30:250/25*200/35:300/25*200/40:400/25200/45:450/25*200/50:500/25*

200/40:250/25200/45:300/25*250/40:400/25*250/50:450/25*300/40:500/25*300/50:550/25*

300/35:400/25*300/40:450/25*400/40:500/25*400/45:550/25*400/50:600/30500/45:600/35

400/45:500/25*450/45:550/25*450/50:600/25*500/45:600/35500/50:600/40500/60:600/45

150/25*150/25*150/25*150/25*150/25*

150/30:250/25*

150/30:200/25*150/40:250/25*200/35:400/25*200/40:450/25*240/40:550/25*300/40:550/25

200/40:300/25*200/50:400/25*250/50:550/25*300/45:600/25*300/50:600/35400/50:600/35

250/50:400/25*300/40:500/25*400/40:550/25*400/50:500/35500/45:600/35500/60:600/40

450/50:550/25*500/40:600/30500/45:600/35500/55:600/45500/65:600/50

600/70

500/40:600/30500/55:600/40500/65:600/45550/70:600/55

600/75(1)

150/25*150/25*200/25*

200/30:250/25*250/35:300/25*300/35:500/25*

200/40:400/25*250/40:500/25*300/40:600/25*400/40:600/30450/45:500/35500/50:600/40

250/40:550/25*300/50:600/35400/50:600/40500/50:600/45550/55:600/50

600/55

450/45:600/30500/50:600/35550/50:600/45

600/55(1)(1)

500/60:600/45550/65:600/60

600/75(1)(1)(1)

600/60600/80

(1)(1)(1)(1)

200/30:300/25250/30:450/25*300/35:500/25*400/40:550/25*500/35:600/30500/60:600/35

��0/50:600/30400/50:600/35500/45:600/40550/40:600/40

600/60600/80

500/50:600/45500/60:600/50

600/55600/70

(1)(1)

600/60(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)




1 2 3 4 5 6

R 30

R 60

R 90

R 120

R 180

R 240

304050607080

304050607080

304050607080

304050607080

304050607080

304050607080

150/25*150/25*150/25*150/25*150/25*150/25*

150/25*150/30:200/25*150/35:250:25*200/30:350/25*250/30:450/25*250/55:500/25*

200/35:300/25*200/40:450/25*200/45:500:25*200/50:550/25*250/45:600/30250/50:500/35

200/50:450/25*250/50:500/25*300/40:550/25*350/45:550/25*450/40:600/30450/45:600/30

350/45:550/25*450/45:600/30450/50:600/35500/45:600/40500/50:600/40500/55:600/45

500/40:600/35500/50:600/40500/55:600/45500/60:600/45500/70:600/50550/60:600/55

150/25*150/25*

150/30:200/25*200/30:250/25*200/30:300/25*250/30:350/25*

200/35:450/25*200/40:500/25*250/40:550/25*300/40:600/25*350/40:600/30450/40:500/35

250/50:550/25*300/50:600/30350/50:600/35450/50:600/40500/50:600/45500/55:600/45

450/450:600/25*500/40:600/30500/50:600/35500/60:600/40550/60:600/50

600/65

500/45:600/40500/60:600/45500/70:600/55550/70:600/65

600/75(1)

550/55:600/50550/65:600/55

600/70(1)(1)(1)

200/30:300/25*250/30:450/25*300/35:500/25*350/40:500/25*450/50:550/25*500/35:600/30

350/40:600/30450/50:500/35500/40:600/35500/50:600/40550/50:600/45

600/70

500/50:600/40500/55:600/45

550/50600/60600/80

(1)

550/55:600/50600/65

(1)(1)(1)(1)

600/80(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

500/30:550/25500/40:600/30

550/35550/50

(1)(1)

550/45:600/40600/60600/80

(1)(1)(1)

600/70(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)

(1)(1)(1)(1)(1)(1)



Ref. No. prEN 1992-1-2: (July 2001)

ANNEX D (Informative)

Simplified calculation method for beams and slabs

D.1 General

(1) This simplified method only applies where the loading is predominantly uniformlydistributed and the design at ambient temperature has been based on linear analysis orlinear analysis with limited redistribution as described in 5.4 and 5.5 of EN1992-1.

(2) This simplified method of calculation provides an extension to the use of the tabularmethod for beams exposed on three sides and slabs, Tables 4.5 to 4.11. It determinesthe affect on bending resistance for situations where the axis distance, a, to bottomreinforcement is less than that required by the tables.

The minimum cross-section dimensions (bmin, bw, hs) given in Tables 4.5 to 4.11 shouldnot be reduced.

This method uses strength reduction factors based on Curve 1 of Figure 3.2 forreinforcing steels and Figure 3.3 for prestressing steels.

(3) This simplified method may be used to justify reducing the axis distance a. Otherwise therules given in 4.2.6 and 4.2.7 should be followed. This method is not valid for continuousbeams where, in the areas of negative moment, the width bmin or bw, is less than 200 mmand the height hs, is less than 2b, where bmin is the value given in Column 5 of Table 4.5.

D.2 Simply supported beams and slabs

(1) It should be verified that

MEd,fi ≤ MRd,fi (D.1)

(2) The loading under fire conditions may be determined using Expression (2.1).

(3) The maximum fire design moment MEd,fi for predominantly uniformly distributed load maybe calculated using Expression (D.2).

MEd,fi = wSd,fi leff2 / 8 (D.2)

wherewSd,fi is the uniformly distributed load (kN/m) under fire conditionsleff is the effective length of beam or slab

(4) The moment of resistance MRd.fi for design for the fire situation may be calculated usingExpression (D.3).

MRd,fi = (γs /γE,fi ) × ks(Θ) × MEd (As,prov /As,req) (D.3)

where:


Ref. No. prEN 1992-1-2: (July 2001)

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

γE,fi is the partial material factor for steel under fire conditions (normally taken tobe 1,0)

ks(Θ) is the strength reduction factor of the steel for the given temperature Θunder the required fire resistance. Θ may be taken from Annex B for thechosen axis distance

MEd is the applied moment for cold design to ENV 1992-1 -1As,prov is the area of tensile steel providedAs,req is the area of tensile steel required for the design at ambient temperature to

EN1992-1

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

D.3 Continuous beams and slabs

(1) Static equilibrium of flexural moments and shear forces should be ensured for the fulllength of continuous beams and slabs under the design fire conditions.

(2) In order to satisfy equilibrium for fire design, moment redistribution from the span to thesupports is permitted where sufficient area of reinforcement is provided over the supportsto take the design fire loading. This reinforcement should extend a sufficient distance intothe span to ensure a safe bending moment envelope.

(3) The moment of resistance MRd,fi,Span of the section at the position of maximum saggingmoment should be calculated for fire conditions in accordance withD.2 (4). The maximum free bending moment for applied loads in the fire situation foruniformly distributed load, MSd,fi = wSd,fi leff

2 / 8, should be fitted to this moment ofresistance such that the support moments MRd1,fi and MRd2,fi provide equilibrium asshown in Figure D.1. This may be carried out by choosing the moment to be supported atone end as equal to or less than the moment of resistance at that support (calculatedusing Expression (D.4)), and then calculating the moment required at the other support.

(4) In the absence of more rigorous calculations, the moment of resistance at supports fordesign for the fire situation may be calculated using Expression (D.4).

MRd,fi = (γs /γE,fi ) MEd (As,prov /As,req) (d-a)/d (D.4)

whereγs, γE,fi, MEd, As,prov, As,req are as defined in D.2a is the required average bottom axis distance given in Table 4.5,

Column 5 for beams and Table 4.8, Column 3 for slabsd is the effective depth of sectionAs,prov /As,req should not be taken as greater than 1,3.


Ref. No. prEN 1992-1-2: (July 2001)

1 Free moment diagram for uniformlydistributed load under fire conditions

Figure D. 1: Positioning the free bending moment diagram MEd.fi to establishequilibrium.

(5) Expression (D.4) is valid where the temperature of the top steel over the supports doesnot exceed 350°C for reinforcing bars nor 100°C for prestressing tendons.

For higher temperatures MRd,fi should be reduced by ks(Θ) according to Figure 3.2, Curve1, for reinforcing bars, and by kp(Θ) according to Figure 3.3 for prestressing tendons.

(6) The curtailment length lbd,fi required under fire conditions should be checked. This maybe calculated using Expression (D.5).

lbd,fi = (γs /γE,fi ) (γc,fi /γc) / lbd (D.5)where lbd is given in Expression (5.4) of EN 1992-1.

The length of bar provided should extend beyond the support to the relevantcontra-flexure point as calculated in D.3 (3) plus a distance equal to lbd,fi.

Rd1,fi

M Rd,fi,Span

M Rd2,fi

M

M = w l / 8Ed,fi d,fi eff

1