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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 199412
August 2005
ICS 13.220.50; 91.010.30; 91.080.10; 91.080.40
Supersedes ENV 199412:1994
Incorporating corrigendum July 2008
English Version
Eurocode 4  Calcul des structures mixtes acierbéton Partie 12: Règles générales  Calcul du comportement au feu  Eurocode 4  Bemessung und Konstruktion von Verbundtragwerken aus Stahl und Beton  Teil 12: Allgemeine Regeln Tragwerksbemessung im Brandfall 
This European Standard was approved by CEN on 4 November 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Uptodate lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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© 2005 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 199412:2005: E
1Page  
Foreword  5  
Background of the Eurocode programme  5  
Status and field of application of Eurocodes  6  
National Standards implementing Eurocodes  6  
Links between Eurocodes and harmonised technical specifications (ENs and ETAs) for products  7  
Additional information specific for EN 199412  7  
National annex for EN 199412  10  
Section 1 General  11  
1.1  Scope  11  
1.2  Normative references  13  
1.3  Assumptions  15  
1.4  Distinction between Principles and Application Rules  15  
1.5  Definitions  15  
1.5.1  Special terms relating to design in general  15  
1.5.2  Terms relating to material and products properties  16  
1.5.3  Terms relating to heat transfer analysis  16  
1.5.4  Terms relating to mechanical behaviour analysis  16  
1.6  Symbols  16  
Section 2 Basis of design  26  
2.1  Requirements  26  
2.1.1  Basic requirements  26  
2.1.2  Nominal fire exposure  26  
2.1.3  Parametric fire exposure  27  
2.2  Actions  27  
2.3  Design values of material properties  27  
2.4  Verification methods  28  
2.4.1  General  28  
2.4.2  Member analysis  29  
2.4.3  Analysis of part of the structure  30  
2.4.4  Global structural analysis  31  
Section 3 Material properties  31  
3.1  General  31  
3.2  Mechanical properties  31  
3.2.1  Strength and deformation properties of structural steel  31  
3.2.2  Strength and deformation properties of concrete  33  
3.2.3  Reinforcing steels  35  
3.3  Thermal properties  36  
3.3.1  Structural and reinforcing steels  36  
3.3.2  Normal weight concrete  39  
3.3.3  Light weight concrete  41  
3.3.4  Fire protection materials  42  
3.4  Density  42 2  
Section 4 Design procedures  43  
4.1  Introduction  43  
4.2  Tabulated data  44  
4.2.1  Scope of application  44  
4.2.2  Composite beam comprising steel beam with partial concrete encasement  45  
4.2.3  Composite columns  47  
4.3  Simple Calculation Models  51  
4.3.1  General rules for composite slabs and composite beams  51  
4.3.2  Unprotected composite slabs  51  
4.3.3  Protected composite slabs  52  
4.3.4  Composite beams  53  
4.3.5  Composite columns  61  
4.4  Advanced calculation models  64  
4.4.1  Basis of analysis  64  
4.4.2  Thermal response  65  
4.4.3  Mechanical response  65  
4.4.4  Validation of advanced calculation models  65  
Section 5 Constructional details  66  
5.1  Introduction  66  
5.2  Composite beams  66  
5.3  Composite columns  67  
5.3.1  Composite columns with partially encased steel sections  67  
5.3.2  Composite columns with concrete filled hollow sections  67  
5.4  Connections between composite beams and columns  68  
5.4.1  General  68  
5.4.2  Connections between composite beams and composite columns with steel sections encased in concrete  69  
5.4.3  Connections between composite beams and composite columns with partially encased steel sections  70  
5.4.4  Connections between composite beams and composite columns with concrete filled hollow sections  70  
Annex A (INFORMATIVE)  Stressstrain relationships at elevated temperatures for structural steels  72  
Annex B (INFORMATIVE)  Stressstrain relationships at elevated temperatures for concrete with siliceous aggregate  75  
Annex C (INFORMATIVE)  Concrete stressstrain relationships adapted to natural fires with a decreasing heating branch for use in advanced calculation models  77  
Annex D (INFORMATIVE)  Model for the calculation of the fire resistance of unprotected composite slabs exposed to fire beneath the slab according to the standard temperaturetime curve  79  
D.1  Fire resistance according to thermal insulation  79  
D.2  Calculation of the sagging moment resistance M_{fi,Rd}^{+}  80  
D.3  Calculation of the hogging moment resistance M_{fi},_{Rd}^{}  82  
D.4  Effective thickness of a composite slab  84  
D.5  Field of application  85 3  
Annex E (INFORMATIVE)  Model for the calculation of the sagging and hogging moment resistances of a steel beam connected to a concrete slab and exposed to fire beneath the concrete slab.  86  
E.1  Calculation of the sagging moment resistance M_{fi,Rd}^{+}  86  
E.2  Calculation of the hogging moment resistance M_{fi,Rd}^{} at an intermediate support (or at a restraining support)  87  
E.3  Local resistance at supports  88  
E.4  Vertical shear resistance  89  
Annex F (INFORMATIVE)  Model for the calculation of the sagging and hogging moment resistances of a partially encased steel beam connected to a concrete slab and exposed to fire beneath the concrete slab according to the standard temperaturetime curve.  90  
F.1  Reduced crosssection for sagging moment resistance M_{fi} _{Rd}^{+}  90  
F.2  Reduced crosssection for hogging moment resistance M_{fi} _{Rd}^{}  94  
F.3  Field of application  95  
Annex G (INFORMATIVE)  Balanced summation model for the calculation of the fire resistance of composite columns with partially encased steel sections, for bending around the weak axis, exposed to fire all around the column according to the standard temperaturetime curve.  96  
G.1  Introduction  96  
G.2  Flanges of the steel profile  97  
G.3  Web of the steel profile  97  
G.4  Concrete  98  
G.5  Reinforcing bars  99  
G.6  Calculation of the axial buckling load at elevated temperatures  100  
G.7  Eccentricity of loading  101  
G.8  Field of application  101  
Annex H (INFORMATIVE)  Simple calculation model for concrete filled hollow sections exposed to fire all around the column according to the standard temperaturetime curve.  104  
H.1  Introduction  104  
H.2  Temperature distribution  104  
H.3  Design axial buckling load at elevated temperature  104  
H.4  Eccentricity of loading  105  
H.5  Field of application  105  
Annex I (INFORMATIVE)  Planning and evaluation of experimental models  109  
I.1  Introduction  109  
I.2  Test for global assessment  109  
I.3  Test for partial information  109 
This European Standard EN 199412: 2005, Eurocode 4: Design of composite steel and concrete structures: Part 12 : General rules – Structural fire design, has been prepared by Technical Committee CEN/TC250 « Structural Eurocodes », the Secretariat of which is held by BSI.
CEN/TC250 is responsible for all Structural Eurocodes.
This European Standard shall be given the status of a National Standard, either by publication of an identical text or by endorsement, at the latest by February 2006, and conflicting National Standards shall be withdrawn at latest by March 2010.
This Eurocode supersedes ENV 199412: 1994.
According to the CENCENELEC Internal Regulations, the National Standard Organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national 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 Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980’s.
In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement^{1} between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products – CPD  and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).
The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts:
EN 1990, Eurocode : Basis of structural design
EN 1991, Eurocode 1: Actions on structures
EN 1992, Eurocode 2: Design of concrete structures
EN 1993, Eurocode 3: Design of steel structures
^{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).
5EN 1994, Eurocode 4: Design of composite steel and concrete structures
EN1995, Eurocode 5: Design of timber structures
EN1996, Eurocode 6: Design of masonry structures
EN 1997, Eurocode 7: Geotechnical design
EN1998, Eurocode 8: Design of structures for earthquake resistance
EN1999, Eurocode 9: Design of aluminium structures
Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.
The Member States of the EU and EFTA recognise that EUROCODES serve as reference documents for the following purposes :
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents^{2} referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards^{3}. Therefore, technical aspects arising from the Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving full compatibility of these technical specifications with the Eurocodes.
The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.
The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National annex.
^{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 hENs and ETAGs/ETAs.
^{3} According to Art. 12 of the CPD the interpretative documents shall :
The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.
6The National Annex may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e. :
it may also contain:
There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works^{4}. Furthermore, all the information accompanying the CE Marking of the construction products which refer to Eurocodes shall clearly mention which Nationally Determined Parameters have been taken into account.
EN 199412 describes the Principles, requirements and rules for the structural design of buildings exposed to fire, including the following aspects:
EN 199412 is intended for clients (e.g. for the formulation of their specific requirements), designers, contractors and public authorities.
The general objectives of fire protection are to limit risks with respect to the individual and society, 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 the limitation of fire risks:
“The construction works must be designed and built in such a way, that in the event of an outbreak of fire
^{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 N°1.
^{5} see clauses 2.2, 3.2(4) and 4.2.3.3 of ID N° 2
7According to the Interpretative Document N°2 “Safety in Case of Fire^{5}” the essential requirement may be observed by following various possibilities for fire safety strategies prevailing in the Member States like conventional fire scenarios (nominal fires) or “natural” (parametric) fire scenarios, including passive and/or active fire protection measures.
The fire parts of Structural Eurocodes deal with specific aspects of passive fire protection in terms of designing structures and parts thereof for adequate load bearing resistance and for limiting fire spread as relevant.
Required functions and levels of performance can be specified either in terms of nominal (standard) fire resistance rating, generally given in national regulations or, where allowed by national fire regulations, by referring to fire safety engineering for assessing passive and active measures.
Supplementary requirements concerning, for example
are not given in this document, because they are subject to specification by the competent authority.
Numerical values for partial factors and other reliability elements are given as recommended values that provide an acceptable level of reliability. They have been selected assuming that an appropriate level of workmanship and of quality management applies.
A full analytical procedure for structural fire design would take into account the behaviour of the structural system at elevated temperatures, the potential heat exposure and the beneficial effects of active fire protection systems, together with the uncertainties associated with 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 adequate performance which incorporates some, if not all, of these parameters and to demonstrate that the 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 calls for specific periods of fire resistance, takes into account (though not explicitly), the features and uncertainties described above.
Application of this Part 12 is illustrated below. The prescriptive approach and the performancebased approach are identified. The prescriptive approach uses nominal fires to generate thermal actions. The performancebased approach, using fire safety engineering, refers to thermal actions based on physical and chemical parameters.
For design according to this part, EN 199112 is required for the determination of thermal and mechanical actions to the structure.
8Figure 0.1: Alternative design procedures
Apart from simple calculation models, EN 199412 gives design solutions in terms of tabulated data (based on tests or advanced calculation models) which may be used within the specified limits of validity.
It is expected, that design aids based on the calculation models given in EN 199412, will be prepared by interested external organizations.
The main text of EN 199412 together with informative Annexes A to I includes most of the principal concepts and rules necessary for structural fire design of composite steel and concrete structures.
9This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 199412 should have a National annex containing all Nationally Determined Parameters to be used for the design of buildings to be constructed in the relevant country.
National choice is allowed in EN 199412 through clauses:
Figure 1.1 Typical examples of concrete slabs with profiled steel sheets with or without reinforcing bars
11Figure 1.2: Composite beam comprising steel beam with no concrete encasement
Figure 1.3: Steel beam with partial concrete encasement
Figure 1.4: Steel beam partially encased in slab
Figure 1.5: Composite beam comprising steel beam with partial concrete encasement
Figure 1.6: Concrete encased profiles
Figure 1.7: Partially encased profiles
Figure 1.8: Concrete filled profiles
NOTE: The design principles and rules given in 4.2, 4.3 and 5 refer to steel surfaces directly exposed to the fire, which are free of any fire protection material, unless explicitly specified otherwise.
NOTE : Information on Concrete Strength Classes higher than C50/60 is given in section 6 of EN 199212. The use of these concrete strength classes may be specified in the National Annex.
EN 13651  Fire resistance tests for loadbearing elements – Part 1: Walls 
EN 13652  Fire resistance tests for loadbearing elements – Part 2: Floors and roofs 
EN 13653  Fire resistance tests for loadbearing elements – Part 3: Beams 13 
EN 13654  Fire resistance tests for loadbearing elements – Part 4: Columns 
EN 100251  Hotrolled products of structural steels  Part 1 : General technical delivery conditions 
EN 100252  Hotrolled products of structural steels  Part 2: Technical delivery conditions for nonalloy structural steels 
EN 100253  Hotrolled products of structural steels  Part 3: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels 
EN 100254  Hotrolled products of structural steels  Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels 
EN 100255  Hotrolled products of structural steels  Part 5: Technical delivery conditions for structural steels with improved atmospheric corrosion resistance 
EN 100256  Hotrolled products of structural steels  Part 6: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition 
EN 10080  Steel for the reinforcement of concrete  Weldable reinforcing steel General 
EN 102101  Hot finished structural hollow sections of nonalloy and fine grain structural steels – Part 1 : Technical delivery conditions 
EN 102191  Cold formed welded structural hollow sections of nonalloy and fine grain structural steels – Part 1 : Technical delivery conditions 
ENV 133811  Test methods for determining the contribution to the fire resistance of structural members – Part 1: Horizontal protective membranes 
ENV 133812  Test methods for determining the contribution to the fire resistance of structural members – Part 2: Vertical protective membranes 
ENV 133813  Test methods for determining the contribution to the fire resistance of structural members – Part 3: Applied protection to concrete members 
ENV 133814  Test methods for determining the contribution to the fire resistance of structural members – Part 4: Applied protection to steel members 
ENV 133815  Test methods for determining the contribution to the fire resistance of structural members – Part 5: Applied protection to concrete/profiled sheet composite members 
ENV 133816  Test methods for determining the contribution to the fire resistance of structural members – Part 6: Applied protection to concrete filled hollow steel columns 
EN 1990  Eurocode: Basis of structural design 
EN 1991 11  Eurocode 1 : Actions on Structures – Part 1.1: General Actions  Densities, selfweight and imposed loads 
EN 1991 12  Eurocode 1 : Actions on Structures – Part 1.2: General Actions  Actions on structures exposed to fire 14 
EN 1991 13  Eurocode 1 : Actions on Structures – Part 1.3: General Actions  Actions on structures  Snow loads 
EN 1991 14  Eurocode 1 : Actions on Structures  Part 1.4: General Actions  Actions on structures  Wind loads 
EN 199211  Eurocode 2: Design of concrete structures  Part 1.1: General rules and rules for buildings 
EN 199212  Eurocode 2: Design of concrete structures  Part 1.2: Structural fire design 
EN 199311  Eurocode 3: Design of steel structures  Part 1.1: General rules and rules for buildings 
EN 199312  Eurocode 3: Design of steel structures  Part 1.2: Structural fire design 
EN 199315  Eurocode 3: Design of steel structures  Part 1.5: Plated structural elements 
EN 199411  Eurocode 4: Design of composite steel and concrete structures  Part 1.1: General rules and rules for buildings” 
distance between the axis of the reinforcing bar and the nearest edge of concrete
isolated part of an entire structure with appropriate support and boundary conditions
members for which measures are taken to reduce the temperature rise in the member due to fire
a frame which has a sway resistance supplied by a bracing system which is sufficiently stiff for it to be acceptably accurate to assume that all horizontal loads are resisted by the bracing system
15duration of protection against direct fire exposure; that is the time when the fire protective claddings or other protection fall off the composite member, or other elements aligned with that composite member fail due to collapse, or the alignment with other elements is terminated due to excessive deformation of the composite member
any material or combination of materials applied to a structural member for the purpose of increasing its fire resistance
for a steel member, the ratio between the exposed surface area and the volume of steel; for an enclosed member, the ratio between the internal surface area of the exposed encasement and the volume of steel
for a given load level, the temperature at which failure is expected to occur in a structural steel element for a uniform temperature distribution
the temperature of the reinforcement at which failure in the element is expected to occur at a given load level
cross section of the member in structural fire design used in the effective cross section method. It is obtained by removing parts of the cross section with assumed zero strength and stiffness
for a given temperature, the stress level at which the stressstrain relationship of steel is truncated to provide a yield plateau
Latin upper case letters
A  crosssectional area or concrete volume of the member per metre of member length 
A_{a,θ}  crosssectional area of the steel profile at the temperature θ 
A_{c,θ}  crosssectional area of the concrete at the temperature θ 
A_{f}  crosssectional area of a steel flange 16 
A_{i},A_{j}  elemental area of the cross section with a temperature θ_{i}, or θ_{j} 
or the exposed surface area of the part i of the steel crosssection per unit length  
A/L_{r}  the rib geometry factor 
A_{i}/V_{i}  section factor [m^{−1}] of the part i of the steel crosssection (nonprotected member) 
A_{m}  directly heated surface area of member per unit length 
A_{m}/V  section factor of structural member 
A_{p,i}  area of the inner surface of the fire protection material per unit length of the part i of the steel member 
A_{p,i}/ V_{i}  section factor [m^{−1}] of the part i of the steel crosssection (with contour protection) 
A_{r}  crosssectional area of the stiffeners 
A_{r} / V_{r}  section factor of stiffeners 
A_{s,θ}  crosssectional area of the reinforcing bars at the temperature θ 
E  integrity criterion 
E 30  or E 60,…a member complying with the integrity criterion for 30, or 60… minutes in standard fire exposure 
E_{a}  characteristic value for the modulus of elasticity of structural steel at 20°C 
E_{a,f}  characteristic value for the modulus of elasticity of a profile steel flange 
E_{a, θ}  characteristic value for the slope of the linear elastic range of the stressstrain relationship of structural steel at elevated temperatures 
E_{a, θ, σ}  tangent modulus of the stressstrain relationship of the steel profile at elevated temperature θ and for stress σ_{i} _{θ} 
E_{c, sec, θ}  characteristic value for the secant modulus of concrete in the fire situation, given by f_{C,θ} divided by ε_{cuθ} 
E_{c0,θ}  characteristic value for the tangent modulus at the origin of the stressstrain relationship for concrete at elevated temperatures and for short term loading 
E_{c,θ,σ}  tangent modulus of the stressstrain relationship of the concrete at elevated temperature 9 and for stress σ_{i,θ} 
E_{d}  design effect of actions for normal temperature design 
E_{fi,d}  design effect of actions in the fire situation, supposed to be time independent 
E_{fi,d,t}  design effect of actions, including indirect fire actions and loads in the fire situation, at time t 
(EI)_{fi,c,z}  flexural stiffness in the fire situation (related to the central axis Z of the composite crosssection) 17 
(EI)_{fi,eff}  effective flexural stiffness in the fire situation 
(EI)_{fi,f,z}  flexural stiffness of the two flanges of the steel profile in the fire situation (related to the central axis Z of the composite crosssection) 
(EI)_{fi,s,z}  flexural stiffness of the reinforcing bars in the fire situation (related to the central axis Z of the composite crosssection) 
(EI)_{fi,eff,z}  effective flexural stiffness (for bending around axis z) in the fire situation 
(EI)_{fi,w,Z}  flexural stiffness of the web of the steel profile in the fire situation (related to the central axis Z of the composite crosssection) 
E_{k}  characteristic value of the modulus of elasticity 
E_{s}  modulus of elasticity of the reinforcing bars 
E_{s,θ}  characteristic value for the slope of the linear elastic range of the stressstrain relationship of reinforcing steel at elevated temperatures 
E_{s,θ,σ}  tangent modulus of the stressstrain relationship of the reinforcing steel at elevated temperature θ and for stress σ_{i,0} 
F_{a}  compressive force in the steel profile 
F^{+}, F^{−}  total compressive force in the composite section in case of sagging or hogging bending moments 
F_{c}  compression force in the slab 
G_{k}  characteristic value of a permanent action 
HC  hydrocarbon fire exposure curve 
I  thermal insulation criterion 
I _{i,θ}  second moment of area, of the partially reduced part i of the crosssection for bending around the weak or strong axis in the fire situation 
I 30  or I 60,… a member complying with the thermal insulation criterion for 30, or 60… minutes in standard fire exposure 
L  system length of a column in the relevant storey 
L_{ei}  buckling length of a column in an internal storey 
L_{et}  buckling length of a column in the top storey 
M  bending moment 
M_{fi,Rd}^{+}: M_{fi, Rd}^{−}  design value of the sagging or hogging moment resistance in the fire situation 
M_{fi,t,Rd}  design moment resistance in the fire situation at time t 
N  number of shear connectors in one critical length, 18 or axial load 
N_{equ}  equivalent axial load 
N_{fi,Cr}  elastic critical load (≡ Euler buckling load) in the fire situation 
N_{fi,cr,Z}  elastic critical load (≡ Euler buckling load) around the axis Z in the fire situation 
N_{fi,pi,Rd}  design value of the plastic resistance to axial compression of the total crosssection in the fire situation 
N_{fi,Rd}  design value of the resistance of a member in axial compression (≡ design axial buckling load) and in the fire situation 
N_{fi,Rd,z}  design value of the resistance of a member in axial compression, for bending around the axis Z, in the fire situation 
N_{fi,Sd}  design value of the axial load in the fire situation 
N_{Rd}  axial buckling load at normal temperature 
N_{s}  normal force in the hogging reinforcement (A_{s}. f_{sy}) 
P_{Rd}  design shear resistance of a headed stud automatically welded 
P_{fi,Rd}  design shear resistance in the fire situation of a shear connector 
Q_{k,1}  characteristic value of the leading variable action 1 
R  Load bearing criterion 
R 30  or R 60, R90, R120, R180, R240… a member complying with the load bearing criterion for 30, 60, 90, 120, 180 or 240 minutes in standard fire exposure 
R_{d}  design resistance for normal temperature design 
R_{fi,d,t}  design resistance in the fire situation, at time t 
R_{fi,y,Rd}  design crushing resistance in the fire situation 
T  tensile force 
V  volume of the member per unit length 
V_{fi,pi,Rd}  design value of the shear plastic resistance in the fire situation 
V_{fi,Sd}  design value of the shear force in the fire situation 
V_{i}  volume of the part i of the steel cross section per unit length [m^{3}/m] 
X  X (horizontal) axis 
X_{fi,d}  design values of mechanical (strength and deformation) material properties in the fire situation 19 
X_{k}  characteristic or nominal value of a strength or deformation property for normal temperature design 
X_{k,θ}  value of a material property in the fire situation, generally dependant on the material temperature 
Y  Y (vertical) axis 
Z  Z (column) central axis of the composite crosssection 
Latin lower case letters
a_{w}  throat thickness of weld (connection between steel web and stirrups) 
b  width of the steel section 
b_{1}  width of the bottom flange of the steel section 
b_{2}  width of the upper flange of the steel section 
b_{c}  depth of the composite column made of a totally encased section, or width of concrete partially encased steel beams 
b_{c,fi}  width reduction of the encased concrete between the flanges in the fire situation 
b_{c,fi,min}  minimum value of the width reduction of the encased concrete between the flanges in the fire situation 
b_{eff}  effective width of the concrete slab 
b_{fi}  width reduction of upper flange in the fire situation 
c  specific heat, or buckling curve, or concrete cover from edge of concrete to border of structural steel 
c_{a}  specific heat of steel 
c_{c}  specific heat of normal weight concrete 
c_{p}  specific heat of the fire protection material 
d  diameter of the composite column made of concrete filled hollow section, or diameter of the studs welded to the web of the steel profile 
d_{p}  thickness of the fire protection material 
e  thickness of profile or hollow section 
e_{1}  thickness of the bottom flange of the steel profile 
e_{2}  thickness of the upper flange of the steel profile 
e_{f}  thickness of the flange of the steel profile 
e_{w}  thickness of the web of the steel profile 20 
ef  external fire exposure curve 
f_{ay,θ}  maximum stress level or effective yield strength of structural steel in the fire situation 
f_{ay,θcr}  strength of steel at critical temperature θ_{cr} 
f_{ap,θ}; f_{sp,θ}  proportional limit of structural or reinforcing steel in the fire situation 
f_{au,θ}  ultimate tensile strength of structural steel or steel for stud connectors in the fire situation, allowing for strainhardening 
f_{ay}  characteristic or nominal value for the yield strength of structural steel at 20°C 
f_{c}  characteristic value of the compressive cylinder strength of concrete at 28 days and at 20°C. 
f_{c,j}  characteristic strength of concrete part j at 20°C. 
f_{c,θ}  characteristic value for the compressive cylinder strength of concrete in the fire situation at temperature θ°C. 
f_{c,θn}  residual compressive strength of concrete heated to a maximum temperature (with n layers) 
f_{c,θy}  residual compressive strength of concrete heated to a maximum temperature 
f_{fi,d}  design strength property in the fire situation 
f_{k}  characteristic value of the material strength 
f_{ry}, f_{sy}  characteristic or nominal value for the yield strength of a reinforcing bar at 20°C 
f_{sy,θ}  maximum stress level or effective yield strength of reinforcing steel in the fire situation 
f_{y,i}  nominal yield strength f_{y} for the elemental area Aj taken as positive on the compression side of the plastic neutral axis and negative on the tension side 
h  depth or height of the steel section 
h_{1}  height of the concrete part of a composite slab above the decking 
h_{2}  height of the concrete part of a composite slab within the decking 
h_{3}  thickness of the screed situated on top of the concrete 
h_{c}  depth of the composite column made of a totally encased section, or thickness of the concrete slab 
h_{eff}  effective thickness of a composite slab 
h_{fi}  height reduction of the encased concrete between the flanges in the fire situation 
design value of the net heat flux per unit area 21  
design value of the net heat flux per unit area by convection  
design value of the net heat flux per unit area by radiation  
h_{u}  thickness of the compressive zone 
h_{u,n}  thickness of the compressive zone (with n layers) 
h_{v}  height of the stud welded on the web of the steel profile 
h_{w}  height of the web of the steel profile 
k_{c,θ}  reduction factor for the compressive strength of concrete giving the strength at elevated temperature f_{c,θ} 
k_{E,θ}  reduction factor for the elastic modulus of structural steel giving the slope of the linear elastic range at elevated temperature E_{a,θ} 
k_{y,θ}  reduction factor for the yield strength of structural steel giving the maximum stress level at elevated temperature f_{ap,θ} 
k_{P;θ}  reduction factor for the yield strength of structural steel or reinforcing bars giving the proportional limit at elevated temperature f_{ap,θ} or f_{sp,θ} 
k_{r}, k_{s}  reduction factor for the yield strength of a reinforcing bar 
k_{shadow}  correction factor for the shadow effect 
k_{u,θ}  reduction factor for the yield strength of structural steel giving the strain hardening stress level at elevated temperature f_{au,θ} 
k_{θ}  reduction factor for a strength or deformation property dependent on the material temperature in the fire situation 
ℓ  length or buckling length 
ℓ_{1}, ℓ_{2}, ℓ_{3}  specific dimensions of the reentrant steel sheet profile or the trapezoidal steel profile 
ℓ_{w}  length (connection between steel profile and the encased concrete) 
ℓ_{θ}  buckling length of the column in the fire situation 
S_{s}  length of the rigid support (calculation of the crushing resistance of stiffeners) 
t  duration of fire exposure 
t_{fi,d}  design value of standard fire resistance of a member in the fire situation 
t_{fi,requ}  required standard fire resistance in the fire situation 
t_{i}  the fire resistance with respect to thermal insulation 22 
u  geometrical average of the axis distances u_{1} and u_{2} (composite section with partially encased steel profile) 
u_{1} ; u_{2}  shortest distance from the centre of the reinforcement bar to the inner steel flange or to the nearest edge of concrete 
z_{i} ; z_{j}  distance from the plastic neutral axis to the centroid of the elemental area A_{i} or A_{j} 
Greek letters upper case letters
Δ_{l}  temperature induced elongation of a member 
Δ_{l/l}  related thermal elongation 
Δ_{t}  time interval 
Δθ_{a,t}  increase of temperature of a steel beam during the time interval Δt 
Δθ_{t}  increase in the gas temperature [°C] during the time interval Δt 
Φ  configuration or view factor 
Greek letters lower case letters
α  angle of the web 
α_{c}  convective heat transfer coefficient 
α_{slab}  coefficient taking into account the assumption of the rectangular stress block when designing slabs 
γ_{G}  partial factor for permanent action G_{k} 
γ_{M,fi}  partial factor for a material property in the fire situation 
γ_{M,fi,a}  partial factor for the strength of structural steel in the fire situation 
γ_{M,fi,c}  partial factor for the strength of concrete in the fire situation 
γ_{M,fi,s}  partial factor for the strength of reinforcing bars in the fire situation 
γ_{M,fi,v}  partial factor for the shear resistance of stud connectors in the fire situation 
γ_{Q}  partial factor for variable action Q_{k} 
γ_{v}  partial factor for the shear resistance of stud connectors at normal temperature 
δ  eccentricity 
ε  strain 
ε_{a}  axial strain of the steel profile of the column 23 
ε_{a,θ}  strain in the fire situation 
ε_{ae,θ}  ultimate strain in the fire situation 
ε_{ay,θ}  yield strain in the fire situation 
ε_{ap,θ}  strain at the proportional limit in the fire situation 
ε_{au,θ}  limiting strain for yield strength in the fire situation 
ε_{c}  axial strain of the concrete of the column 
ε_{c,θ}  concrete strain in the fire situation 
ε_{ce,θ}  maximum concrete strain in the fire situation 
ε_{ce,θmax}  maximum concrete strain in the fire situation at the maximum temperature 
ε_{cu,θ}  concrete strain corresponding to f_{c,θ} 
ε_{cn,θmax}  concrete strain at the maximum concrete temperature 
ε_{f}  emissivity coefficient of the fire 
ε_{m}  emissivity coefficient related to the surface material of the member 
ε_{s}  axial deformation of the reinforcing steel of the column 
ϕ_{b}  diameter of a bar 
ϕ_{s}  diameter of a stirrup 
ϕ_{r}  diameter of a longitudinal reinforcement at the corner of the stirrups 
η  load level according to EN 199411 
η_{fi}  reduction factor applied to E_{d} in order to obtain E_{fi} _{d} 
η_{fi,t}  load level for fire design 
θ  temperature 
θ_{a}  temperature of structural steel 
θ_{a,t}  steel temperature at time t assumed to be uniform in each part of the steel crosssection 
θ_{c}  temperature of concrete 
θ_{cr}  critical temperature of a structural member 
θ_{i}  temperature in the elemental area A_{i} 24 
θ_{lim}  limiting temperature 
θ_{max}  maximum temperature 
θ_{r}  the temperature of a stiffener 
θ_{R}  the temperature of additional reinforcement in the rib 
θ_{S}  temperature of reinforcing steel 
θ_{t}  gas temperature at time t 
θ_{v}  temperature of stud connectors 
θ_{W}  temperature in the web 
λ_{a}  thermal conductivity of steel 
λ_{c}  thermal conductivity of concrete 
λ_{p}  thermal conductivity of the fire protection material 
relative slenderness  
relative slenderness of stiffeners in the fire situation  
ξ  reduction factor for unfavourable permanent action G_{k} 
ρ_{a}  density of steel 
ρ_{c}  density of concrete 
ρ_{c,NC}  density of normal weight concrete 
ρ_{c,LC}  density of lightweight concrete 
ρ_{ρ}  density of the fire protection material 
σ  stress 
σ_{a,θ}  stress of the steel profile in the fire situation 
σ_{c,θ}  stress of concrete under compression in the fire situation 
σ_{s,θ}  stress of reinforcing steel in the fire situation 
φ_{a,θ}  reduction coefficient for the steel profile depending on the effect of thermal stresses in the fire situation 
φ_{c,θ}  reduction coefficient for the concrete depending on the effect of thermal stresses in the fire situation 
φ_{s,θ}  reduction coefficient for reinforcing bars depending on the effect of thermal stresses in the fire situation 25 
X  reduction or correction coefficient and factor 
X_{z}  reduction or correction coefficient and factor (for bending around axis z) 
ψ_{0,1}  combination factor for the characteristic or rare value of a variable action 
ψ_{1.1}  combination factor for the frequent value of a variable action 
ψ_{2,1}  combination factor for the quasipermanent value of a variable action 
ψ_{fi}  combination factor for a variable action in the fire situation, given either by ψ_{1,1} or ψ_{2,1} 
NOTE 1: See for definition EN199112, chapters 1.5.1.8 and 1.5.1.9
NOTE 2: In case of a composite slab, the thermal radiation criterion is not relevant.
NOTE : See EN199112, chapters 1.5.3.5 and 3.2.2
NOTE : See EN199112, chapters 1.5.3.11 and 3.2.3
NOTE : The values of Δθ_{1} and Δθ_{2} for use in a Country may be found in its National Annex. The recommended values are Δθ_{1} = 200 K and Δθ_{2} = 240 K.
X_{fi,d} = k_{θ} X_{k}/γ_{M,fi} (2.1)
where:
X_{k}  is the characteristic or nominal value of a strength or deformation property (generally f_{k} or E_{k}) for normal temperature design according to EN 199411; 27 
k_{θ}  is the reduction factor for a strength or deformation property (X_{k,θ}/X_{k}), dependent on the material temperature, see 3.2; 
γ_{M,fi}  is the partial factor for the relevant material property, for the fire situation. 
NOTE 1: For mechanical properties of steel and concrete, the recommended values of the partial factor for the fire situation are γ_{M,fi,a} = 1,0; γ_{M,fi,s} = 1,0; γ_{M,fi,c} = 1,0 γ_{M,fi,V} = 1,0. Where modifications are required, these may be defined in the relevant National Annexes of EN 199212 and EN 199312.
NOTE 2: If the recommended values are modified, tabulated data may need to be adapted.
X_{fi,d} = X_{k,θ}/γ_{M,fi} (2.2a)
X_{fi.d} = γ_{M,fi} X_{k,θ} (2.2b)
where:
X_{k,θ}  is the value of a material property in the fire situation, generally dependent on the material temperature, see 3.3; 
γ_{M, fi}  is the partial factor for the relevant material property, for the fire situation. 
NOTE 1: For thermal properties of steel and concrete, the recommended value of the partial factor for the fire situation is y_{Mfl} = 1,0; where modifications are required, these may be defined in the relevant National Annexes of EN 199212 and EN 199312.
NOTE 2: If the recommended values are modified, tabulated data may need to be adapted.
E_{fi,d,t} ≤ R_{fi,d,t} (2.3)
where:
E_{fi,d,t}  is the design effect of actions for the fire situation, determined in accordance with EN 199112, including the effects of thermal expansions and deformations; 
R_{fi,d,t}  is the corresponding design resistance in the fire situation. 
NOTE: For verifying standard fire resistance requirement, a member analysis is sufficient.
E_{fi,d,t} = E_{fi.d} = η_{fi} E_{d} (24)
where:
E_{d}  is the design value of the corresponding force or moment for normal temperature design, for a fundamental combination of actions (see EN 1990) 
η_{fi}  is the reduction factor of E_{d} 
or for load combinations (6.10a) and (6.10b) in EN 1990 as the smaller value given by the two following expressions:
where:
Q_{k,I}  is the characteristic value of the leading variable action 1 
G_{k}  is the characteristic value of a permanent action 
γ_{G}  is the partial factor for permanent actions 
γ_{Q,i}  is the partial factor for variable action 1 
ξ  is a reduction factor for unfavourable permanent action G_{k} 
ψ_{0,1}  combination factor for the characteristic value of a variable action 29 
ψ_{fi}  is the combination factor for fire situation, given either by ψ_{1.1} (frequent value) or ψ_{2,1} (quasipermanent value) according to 4.3.1(2) of EN 199112 
NOTE 1:  An example of the variation of the reduction factor η_{fi} versus the load ratio Q_{k,1}/G_{k} for different values of the combination factor ψ_{fi} = ψ_{1.1} according to expression (2.5), is shown in Figure 2.1 with the following assumptions: γ_{G} = 1,35 and γ_{Q} = 1,5. Partial factors are specified in the relevant National Annexes of EN 1990. Equations (2.5a) and (2.5b) give slightly higher values. 
NOTE 2:  As a simplification the recommended value of η_{fi} = 0,65 may be used, except for imposed loads according to load category E as given in EN 199111 (areas susceptible to accumulation of goods, including access areas), where the recommended value is 0,7. 
Figure 2.1: Variation of the reduction factor η_{fi} with the load ratio Q_{k,1}/G_{k}
NOTE: For the rules of this standard, it is assumed that the heating rates fall within the specified limits.
Figure 3.1: Mathematical model for stressstrain relationships of structural steel at elevated temperatures
Strain Range  Stress σ  Tangent modulus 

I / elastic ε ≤_{ap,θ}  E_{a,θ} ε_{a.θ}  E_{a,θ} 
II / transit elliptical ε ap,θ ≤ ε ε ≤ ε_{ay,θ} 

III / plastic ε_{ay,θ} ≤ ε ε ≤ ε_{au,θ}  f_{ay,θ}  0 
NOTE: The strainhardening option is detailed in informative Annex A.
32NOTE: Values for ε_{au,θ} and ε_{ac,θ} defining the range of the maximum stress branches and decreasing branches according to Figure 3.1, may be taken from informative Annex A.
Steel Temperature θ_{a}[°c] 


20  1,00  1,00  1,00  1,25 
100  1,00  1,00  1,00  1,25 
200  0,90  0,807  1,00  1,25 
300  0,80  0,613  1,00  1,25 
400  0,70  0,420  1,00  
500  0,60  0,360  0,78  
600  0,31  0,180  0,47  
700  0,13  0,075  0,23  
800  0,09  0,050  0,11  
900  0,0675  0,0375  0,06  
1000  0,0450  0,0250  0,04  
1100  0,0225  0,0125  0,02  
1200  0  0  0 
NOTE: For the rules of this standard, it is assumed that the heating rates fall within the specified limits.
NOTE: Due to various ways of testing specimens, ε_{cu,θ} shows considerable scatter, which is represented in Table B.1 of informative Annex B. Recommended values for ε_{ce,θ} defining the range of the descending branch may be taken from Annex B.
NOTE: As concrete, which has cooled down after having been heated, does not recover its initial compressive strength, the proposal of informative Annex C may be used in an advanced calculation model according to 4.4.
Figure 3.2: Mathematical model for stressstrain relationships of concrete under compression at elevated temperatures.
Concrete Temperature θ_{C} [°C] 
K_{c,θ} = f_{c},θ/f_{c}  ε_{cn,θ}.10^{3} NC 


NC  LC  
20  1  1  2,5 34 
100  1  1  4,0 
200  0,95  1  5,5 
300  0,85  1  7,0 
400  0,75  0,88  10,0 
500  0,60  0,76  15,0 
600  0,45  0,64  25,0 
700  0,30  0,52  25,0 
800  0,15  0,40  25,0 
900  0,08  0,28  25,0 
1000  0,04  0,16  25,0 
1100  0,01  0,04  25,0 
1200  0  0   
NOTE: Prestressing steels will normally not be used in composite structures.
Steel Temperature θ_{s}[°C] 


20  1,00  1,00  1,00 
100  1,00  0,96  1,00 
200  0,87  0,92  1,00 
300  0,72  0,81  1,00 
400  0,56  0,63  0,94 
500  0,40  0,44  0,67 
600  0,24  0,26  0,40 
700  0,08  0,08  0,12 
800  0,06  0,06  0,11 
900  0,05  0,05  0,08 
1000  0,03  0,03  0,05 
1100  0,02  0,02  0,03 
1200  0  0  0 
Δl/l = 11.10^{−3} for 750°C < θ_{a} ≤ 860°C (3.1b)
Δl/l = –6,2. 10^{–3} + 2 . 10^{–5} θ_{a} for 860°C < θ_{a} ≤ 1200°C (3.1c)
where:
I  is the length at 20°C of the steel member 
Δl  is the temperature induced elongation of the steel member 
θ_{a}  is the steel temperature. 
Δl/l = 14.10^{–6} (θ_{a} – 20) (3.1d)
c_{a} 650 [J/kgK] for 900 < θ_{a} ≤ 1200°C (3.2d)
where:
θ_{a}  is the steel temperature 
c_{a} = 600 [J/kgK] (3.2e)
λ_{a} = 54 – 3,33. 10^{–2} θ_{a} [W/mK] for 20°C ≤ 0_{a} ≤ 800°C (3.3a)
λ_{a} = 27,3 [W/mK] for 800°C < θ_{a} ≤ 1200°C (3.3b)
where θ_{a} is the steel temperature.
λ_{a} = 45 [W/mK] (3.3c)
37Figure 3.3: Thermal elongation of steel as a function of the temperature
Figure 3.4: Specific heat of steel as a function of the temperature
Figure 3.5: Thermal conductivity of steel as a function of the temperature
Δl/l = 14.10^{–3} for 700°C < θ_{C} ≤ 1200°C (3.4b)
where:
l  is the length at 20°C of the concrete member 
Δl  is the temperature induced elongation of the concrete member 
θ_{C}  is the concrete temperature 
NOTE: For calcareous concrete, reference is made to 3.3.1(1) of EN 199212.
Δl/l = 18. 10^{–6} (θ_{c} – 20) (3.4c)
c_{c} = 900 [J/kgK] for 20°C ≤ θ_{c} ≤ 100°C (3.5a)
c_{c} = 900 + (θ_{c} –100) [J/kg K] for 100°c < θ_{C} ≤ 200°C (3.5b)
c_{c} = 1000 + (θ_{c} – 200)/2 [J/kg K] for 200°C < 0_{C} ≤ 400°C (3.5c)
c_{c} =1100 [J/kg K] for 400°C < θ_{c} ≤ 1200°C (3.5d)
where θ_{C} is the concrete temperature [°C].
NOTE: The variation of c_{c} as a function of the temperature may be approximated by:
c_{cθ} = 890 + 56,2 (θ_{c} / 100) – 3,4(θ_{c}/100)^{2} (3.5e)
c_{c} = 1000 [J/kgK] (3.5f)
Figure 3.6: Thermal elongation of normal weight concrete (NC) and lightweight concrete (LC) as a function of the temperature
Figure 3.7: Specific heat of normal weight concrete (NC) and lightweight concrete (LC) as a function of the temperature
Figure 3.8: Thermal conductivity of normal weight concrete (NC) and lightweight concrete (LC) as a function of the temperature
40The last situation may occur for hollow sections filled with concrete.
NOTE 1: The value of thermal conductivity may be set by the National Annex within the range defined by the lower and upper limits.
NOTE 2: The upper limit has been derived from tests of steelconcrete composite structural elements. The use of the upper limit is recommended.
λ_{c} = 2 – 0,2451 (θ_{c} / 100)+ 0,0107 (θ_{c} / 100)^{2} [W/mK] for 20°C ≤ θ_{c} ≤ 1200°C (3.6a)
where θ_{c} is the concrete temperature.
The lower limit of thermal conductivity λ_{c} of normal weight concrete may be determined from:
λ_{c} = 1,36 – 0,136(θ_{c} / 100)+ 0,0057 (θ_{c} / 100)^{2} [W/mK] for 20°C ≤ θ_{c} 1200°C (3.6b)
where θ_{C} is the concrete temperature.
λ_{c} = 1,60 [W/mK] (3.6c)
Δ1 / 1 = 8.10^{–6} (θ_{c} – 20) (3.7)
where:
l  is the length at room temperature of the lightweight concrete member 
Δl  is the temperature induced elongation of the lightweight concrete member 
θ_{c}  is the lightweight concrete temperature [°C]. 
c_{c} = 840 [J/kg K] (3.8)
λ_{c} = 1,0 – (θ_{c} / 1600) [W/mK] for 20°C ≤ θ_{C} ≤ 800°C (3.9a)
λ_{c} = 0,5 [W/mK] for θ_{C} < 800°C (3.9b)
ρ_{a} = 7850 [kg/m^{3}] (3.10)
NOTE: The variation of ρ_{c} in function of the temperature may be approximated by
ρ_{c,θ} = 2354 – 23,47 (θ_{c} / 100) (3.11)
ρ_{c,NC} = 2300 [kg/m^{3}] (3.12a)
ρ_{c,LC} = 1600 to 2000 [kg/m^{3}] (3.12b)
NOTE: The decision on the use of advanced calculation models in any Country may be found in the National Annex.
where:
E_{d}  is the design effect of actions for normal temperature design and 
R_{d}  is the design resistance for normal temperature design; 
load level for fire design, 
where:
E_{fi,d,t}  is the design effect of actions in the fire situation, at time t. 
NOTE: When at present classification is impossible, this is marked by “” in the tables.
the effective slab width b_{eff} does not exceed 5 m,
the additional reinforcement A_{s} is not taken into account.
Standard Fire Resistance  

R30  R60  R90  R120  R180  
1  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,3 

min b [mm] and additional reinforcement A_{s} in relation to the area of flange A_{s} / A_{f} 

1.1  h ≥ 0,9 × min b  70/0,0  100/0,0  170/0,0  200/0,0  260/0,0 
1.2  h ≥ 1,5 × min b  60/0,0  100/0,0  150/0,0  180/0,0  240/0,0 
1.3  h ≥ 2,0 × min b  60/0,0  100/0,0  150/0,0  180/0,0  240/0,0 
2  Minimum crosssectional dimensions for load level ηfi,t ≤ 0,5 

min b [mm] and additional reinforcement A_{s} in relation to the area of flange A_{s} / A_{f}  
2.1  h ≥ 0,9 × min b  80/0,0  170/0,0  250/0,0  270/0,5   
2.2  h ≥ 1,5 × min b  80/0,0  150/0,0  200/0,2  240/0,3  300/0,3 
2.3  h ≥ 2,0 × min b  70/0,0  120/0,0  180/0,2  220/0,3  280/0,3 
2.4  h ≥ 3,0 × min b  60/0,0  100/0,0  170/0,2  200/0,3  250/0,3 
3  Minimum crosssectional dimensions for load level ηfi,t ≤ 0.7 

min b [mm] and additional reinforcement A_{s} in relation to the area of flange A_{s} / A_{f}  
3.1  h ≥ 0,9 × min b  80/0,0  270/0,4  300/0,6     
3.2  h ≥ 1,5 × min b  80/0,0  240/0,3  270/0,4  300/0,6   
3.3  h ≥ 2,0 × min b  70/0,0  190/0,3  210/0,4  270/0,5  320/0,8 
3.4  h ≥ 3,0 × min b  70/0,0  170/0,2  190/0,4  270/0,5  300/0,8 
Profile Width b[mm] 
Min. Axis Distanace [mm] 
Standard Fire Resistance 

R60  R90  R120  R180  
170  u_{1} u_{2} 
100 45 
120 60 
  
  

200  u_{1} u_{2} 
80 40 
100 55 
120 60 
  

250  u_{1} u_{2} 
60 35 
75 50 
90 60 
120 60 

≥ 300  u_{1} u_{2} 
40 25^{*} 
50 45 
70 90 
60 60 
NOTE: *) This value has to be checked according to 4.4.1.2 of EN 199211
NOTE: For R30, concrete need only be placed between the flanges of the steel section.
Standard Fire Resistance  

R30  R60  R90  R120  R180  
Concrete cover c[mm]  0  25  30  40  50 
Standard Fire Resistance  

R30  R60  R90  R120  R180  R240  
1.1  Minimum dimensions h_{c} and b_{c} [mm]  150  180  220  300  350  400 
1.2  minimum concrete cover of steel section c [mm]  40  50  50  75  75  75 
1.3  minimum axis distance of reinforcing bars u_{s} [mm]  20^{*}  30  30  40  50  50 
or  
2.1  Minimum dimensions h_{c} and b_{c} [mm]    200  250  350  400   
2.2  minimum concrete cover of steel section c [mm]    40  40  50  60   
2.3  minimum axis distance of reinforcing bars u_{s} [mm]    20^{*}  20^{*}  30  40   
NOTE: *) These values have to be checked according to 4.4.1.2 of EN 199211
NOTE: For R30, concrete need only be placed between the flanges of the steel section.
Standard Fire Resistance  

R30  R60  R90  R120  R180  
Concrete cover c [mm]  0  25  30  40  50 
Standard Fire Resistance  

R30  R60  R90  R120  
Minimum ratio of web to flange thickness e_{w}/e_{f}  0,5  0,5  0,5  0,5  
1  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,28  
1.1  minimum dimensions h and b [mm]  160  200  300  400 
1.2  minimum axis distance of reinforcing bars u_{s} [mm]    50  50  70 
1.3  minimum ratio of reinforcement A_{S}/(A_{C}+A_{S}) in %    4  3  4 
2  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,47  
2.1  minimum dimensions h and b [mm]  160  300  400   
2.2  minimum axis distance of reinforcing bars u_{s} [mm]    50  70   
2.3  minimum ratio of reinforcement A_{S}/(A_{C}+A_{S}) in %    4  4   
3  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,66  
3.1  minimum dimensions h and b [mm]  160  400     
3.2  minimum axis distance of reinforcing bars u_{s} [mm]  40  70     
3.3  minimum ratio of reinforcement A_{S}/(A_{C}+A_{S}) in %  1  4     
NOTE: The values of the load level η_{fi,t} have been adapted to the design rules for composite columns in EN 199411.
NOTE: Alternatively to this method, the design rules given in 5.3.2 or 5.3.3 of EN199212 may be used, when neglecting the steel tube.
Standard Fire Resistance  

R30  R60  R90  R120  R180  
1  Minimum crosssectional dimensions for load level η_{fi,t ≤ 0,28}  
1.1  Minimum dimensions h and b or minimum diameter d [mm]  160  200  220  260  400 
1.2  Minimum ratio of reinforcement A_{s} / (A_{c} + A_{s}) in (%)  0  1,5  3,0  6,0  6,0 
1.3  Minimum axis distance of reinforcing bars u_{s} [mm]    30  40  50  60 
2  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,47  
2.1  Minimum dimensions h and b or minimum diameter d [mm]  260  260  450  450  500 
2.2  Minimum ratio of reinforcement A_{s} / (A_{c} + A_{s}) in (%)    3,0  6,0  6,0  6,0 
2.3  Minimum axis distance of reinforcing bars u_{s} [mm]    30  40  50  60 
3  Minimum crosssectional dimensions for load level η_{fi,t} ≤ 0,66  
3.1  Minimum dimensions h and b or minimum diameter d [mm]  260  450  550     
3.2  Minimum ratio of reinforcement A_{s} / (A_{c} + A_{s}) in (%)  3,0  6,0  6,0     
3.3  Minimum axis distance of reinforcing bars U_{s} [mm]  25  30  40     
NOTE: The values of the load level η_{fi,t} have been adapted to the design rules for composite columns in EN 199411.
where:
α_{slab}  is the coefficient taking into account the assumption of the rectangular stress block when designing slabs, α_{slab}= 0,85. 
f_{y,j}  is the nominal yield strength f_{y} for the elemental steel area A_{i}, taken as positive on the compression side of the plastic neutral axis and negative on the tension side; 
f_{cj}  is the design strength for the elemental concrete area A_{j} at 20°C. For concrete parts tension is ignored; 
k_{y,θ,i} or k_{c,θ,j} are as defined in Table 3.2 or Table 3.3.
where:
z_{i}, Z_{j}  is the distance from the plastic neutral axis to the centroid of the elemental area A_{i} or A_{j} 
NOTE: A method is given in D.4 of Annex D for the calculation of the effective thickness h_{eff}
Figure 4.1: Symbols for trapezoidal sheeting
Figure 4.2: Symbols for reentrant sheeting
NOTE 1: In D.1 of Annex D a method is given for the calculation of the fire resistance with respect to the criterion of thermal insulation “I”.
NOTE 2: In D.2 and D.3 of Annex D a method is given for the calculation of the fire resistance with respect to the criterion of mechanical resistance “R” and in relation to the sagging and hogging moment resistances.
NOTE: The fire resistance, with regard to the load bearing criterion “R”, of protected composite slabs is at least 30’ (see 4.3.2(5)).
NOTE: Guidance on critical crosssections is given in 6.1.1(4)P of EN199411.
NOTE: For the calculation of the vertical shear resistance of the structural steel section, a method is given in E.4 of Annex E.
NOTE 1: For partially encased beams under hogging bending, a method is given in F.2(7) of Annex F.
NOTE 2: For composite beams comprising steel beams with no concrete encasement, a method is given in E.2 and E.4 of Annex E.
or by the tension force in the steel profile given by:
NOTE: For the calculation of the longitudinal shear in the area of hogging bending, a method is given in E.2 of Annex E.
Steel beam
Figure 4.3: Elements of a crosssection
where
k_{shadow}  is a correction factor for the shadow effect (see(4))  
c_{a}  is the specific heat of steel in accordance with (4) of 3.3.1  [J/kgK] 
ρ_{a}  is the density of steel in accordance with (1)P of 3.4  [kg/m^{3}] 
A_{i}  is the exposed surface area of the part i of the steel crosssection per unit length  [m^{2}/m] 
A_{i}/V_{i}  is the section factor [m^{−1} ] of the part i of the steel crosssection  
V_{i}  is the volume of the part i of the steel cross section per unit length  [m^{3}/m] 
is the design value of the net heat flux per unit area in accordance with 3.1 of EN 19911 2  
[W/m^{2}]  
[W/m^{2}]  
[W/m^{2}]  
ε_{m}  as defined in 2.2(2)  
ε_{f}  is the emissivity of the fire according to 3.1 (6) of EN 199112  
θ_{t}  is the ambient gas temperature at time t  [°C] 
θ_{a,t}  is the steel temperature at time t [°C] supposed to be uniform in each part of the steel crosssection  
Δt  is the time interval  [sec] 
with e_{l}, b_{l}, e_{w} h_{w} e_{2}, b_{2} and cross sectional dimensions according to Figure 4.3.
NOTE: The above equation giving the shadow effect (k_{shadow}), and its use in (3), is an approximation, based on the results of a large amount of systematic calculations; for more refined calculation models, the configuration factor concept as presented in 3.1 and Annex G of EN199112 should be applied.
with
where:
λ_{p}  is the thermal conductivity of the fire protection material as specified in (1)P of 3.3.4  [W/mK] 
d_{p}  is the thickness of the fire protection material  [m] 
A_{p,i}  is the area of the inner surface of the fire protection material per unit length of the part i of the steel member  [m^{2}/m] 
C_{p}  is the specific heat of the fire protection material as specified in (1)P of 3.3.4  [J/kgK] 
ρ_{p}  is the density of the fire protection material  [kg/m^{3}] 
Δ_{t}  is the ambient gas temperature at time t  [°C] 
Δθ_{t}  is the increase of the ambient gas temperature [°C] during the time interval Δt 
for the lower flange:
A_{i}/V_{i} or A_{p,i}/V_{i} = 2(b_{l} + e_{l})/b_{l} e_{l} (4.9a)
for the upper flange, when at least 85% of the upper flange of the steel profile is in contact with the concrete slab or, when any void formed between the upper flange and a profiled steel deck is filled with noncombustible material:
A_{i}/V_{i}, or A_{p,i}/V_{i} = (b_{2} + 2e_{2})/b_{2} e_{2} (4.9b)
for the upper flange when used with a composite floor when less than 85% of the upper flange of the steel profile is in contact with the profiled steel deck:
A_{i}/V_{i} or A_{p,i}/V_{i} = 2(b_{2} + e_{2})/b_{2}e_{2} (4.9c)
where:
A_{p}  is the area of the inner surface of the box protection per unit length of the steel beam  [m^{2}/m] 
V  is the volume of the complete crosssection of the steel beam per unit length  [m^{3}/m] 
Flat concrete or steel deckconcrete slab system
NOTE: In order to determine temperatures over the thickness of the concrete slab a method is given in the Table D.5 of Annex D.
for R30 0,9 η_{fi,t} = f _{ay,θcr}/f_{ay} (4.10a)
in any other case 1,0 η_{fi,t} = f_{ay,θcr} / f_{ay} (4.10b)
where η_{fi,t} = E_{fi,d,t}/R_{d} and E_{fi,d,t} = η_{fi} E_{d} according to (7)P of 4.1 and (3) of 2.4.2.
NOTE: For the calculation of sagging and hogging moment resistances, a method is given in Annex E.
P_{fi,Rd} = 0,8 .k_{u,θ} .P_{Rd}, with P_{Rd} as obtained from equation 6.18 of EN 199411 or (4.11a)
P_{fi,Rd} = k_{c,θ} . P_{Rd}, with P_{Rd} as obtained from equation 6.19 of EN 199411 and (4.11b)
where values of k_{u,θ} and k_{c,θ} are taken from Tables 3.2 and 3.3 respectively.
NOTE: For the calculation of this reduction factor, a method is given in Annex F
NOTE: For the evaluation of this effective width, a method is given in F.1 of Annex F
Standard Fire Resistance 
Minimum Slab Thickness h_{c} [mm] 

R30  60 
R60  80 
R90  100 
R120  120 
R180  150 
Figure 4.4: Elements of a crosssection for the calculation of the sagging moment resistance
Figure 4.5: Elements of a crosssection for the calculation of the hogging moment resistance
NOTE: For the design of the web, regarding vertical shear, a method is given in F.2 of Annex F.
60NOTE: EN199411, 6.7.3.1(1), in all cases limits the relative slenderness for normal design, to a maximum of 2.
N_{fi,Rd} = χ N_{fi,pl,Rd} (4.12)
where:
χ  is the reduction coefficient for buckling curve c of 6.3.1 of EN 199311 and depending on the relative slenderness , 
N_{fi,pl,Rd}  is the design value of the plastic resistance to axial compression in the fire situation. 
where:
A_{i,θ}  is the area of each element of the crosssection (i = a or c or s), which may be affected by the fire. 
where:
I_{i,θ}  is the second moment of area, of the partially reduced part i of the crosssection for bending around the weak or strong axis, 
φ_{i,θ}  is the reduction coefficient depending on the effect of thermal stresses. 
E_{c,sec,θ}  is the characteristic value for the secant modulus of concrete in the fire situation, given by f_{c,θ} divided by ε_{cu,θ} (see Figure 3.2). 
NOTE: A method is given in G.6 of Annex G, for the evaluation of the reduction coefficient of partially encased steel sections.
where
ℓ_{θ}  is the buckling length of the column in the fire situation. 
where
N_{fi,pl,R} is the value of N_{fi,pl,Rd} according to (4) when the factors γ_{M,fi,a} γ_{M,fi,s} and γ_{M,fi,s} are taken as 1,0.
NOTE 1: Values for L_{ei} and L_{et} may be defined in the National Annex. The recommended values are 0,5 and 0,7 times the system length L.
62NOTE 2: For the buckling length reference may be made to 5.3.2(2) and 5.3.3(3) of EN199212 and to 4.2.3.2(4) of EN199312.
Figure 4.6: Structural behaviour of columns in braced frames
NOTE 1: For steel sections with partial concrete encasement, a method is given in Annex G.
NOTE 2: For eccentric loads a method is given in G.7 of Annex G.
NOTE 1: For unprotected concrete filled hollow sections, a method is given in Annex H.
NOTE 2: For eccentric loads a method is given in H.4 of Annex H.
NOTE: Compared with tabulated data and simple calculation models, advanced calculation models give an improved approximation of the actual structural behaviour under fire conditions.
Figure 5.1: Measures providing connection between the steel profile and the encasing concrete
66Figure 5.2: Arrangement of bars or studs providing connection between the steel profile and the encased concrete
NOTE : For steel sections with a profile depth h greater than 400 mm, studs and stirrups may be chosen according to Figure G.2 of Annex G.
NOTE: For the design of fire protected connections, methods are given in 4.2.1 (6) and Annex D of EN 199312.
Figure 5.3: Hogging moment connection for fire conditions
Figure 5.4: Examples of connections to a totally encased steel section of a column.
Figure 5.5: Examples of connections to a partially encased steel section
Figure 5.6: Examples of connections to a concrete filled hollow section
[informative]
Figure A.1: Graphical presentation of the stressstrain relationships for the steel grade S235 up to a strain of 2 %.
θ_{a} ≤ 300°C; f_{au,θ} = 1,25 f_{ay} (A.1)
300 < θ_{a} ≤ 400°C; f_{au,θ} = f_{ay} (2 – 0,0025 θ_{a}) (A.2)
θ_{a} ≥ 400°C; f_{au,θ} = f_{ay,θ} (A.3)
2%< ε_{a,θ} < 4% σ_{a,θ} = [(f_{au,θ} – f_{ay,θ})/0,02] ε_{a,θ} – f_{au,θ} + 2 f_{ay,θ} (A.4)
4% ≤ ε_{a,θ} ≤ 15% σ_{a,θ} = f_{au,θ} (A.5)
15% < ε_{a,θ} < 20 % σ_{a,θ} = [1  ((ε_{a,θ} – 0,15)/0,05)] f_{au,θ} (A.6)
ε_{a,θ} ≥ 20% σ_{a,θ} = 0 (A.7)
Figure A.2: Graphical presentation of the stressstrain relationships of structural steel at elevated temperatures, strainhardening included.
Figure A.3: Reduction factors k_{θ} for stressstrain relationships allowing for strainhardening of structural steel at elevated temperatures (see also Table 3.2 of 3.2.1).
[informative]
Figure B.1: Graphical presentation of the stressstrain relationships for concrete with siliceous aggregates with a linear descending branch, including the recommended values ε_{cu,θ} and ε_{ce,θ} of Table B.1.
75Concrete temperature θ_{c}[°C] 
ε_{cu,θ}. 10^{3} recommended value 
ε_{ce,θ}. 10^{3} recommended value 

20  2,5  20,0 
100  4,0  22,5 
200  5,5  25,0 
300  7,0  27,5 
400  10  30,0 
500  15  32,5 
600  25  35,0 
700  25  37,5 
800  25  40,0 
900  25  42,5 
1000  25  45,0 
1100  25  47,5 
1200     
Figure B.2: Parameters for stressstrain relationships at elevated temperatures of normal concrete (NC) and lightweight concrete (LC).
[informative]
f_{c,θ,20°C} = φ f_{c} where for (C.1)
20°c ≤ φ_{max} < 100° C; φ = K_{c,θmax} (C.2)
100°C ≤ θ_{max} < 300°C; φ = 1,0 – [0,235 (θ_{max} –100)/200] (C.3)
θ_{max} ≥ 300°C; φ = 0,9k_{c,θmax} (C.4)
Note: The reduction factor k_{c,θ max} is taken according to (4) of 3.2.2.
θ_{1} = 200°C;  f_{c} _{0}, = 0,95 . 40 = 38  [N/mm^{2}]  (C.5) 
ε_{cu,θ1} = 0,55  [%]  (C.6)  
ε_{2,5}  [%]  (C.7)  
θ_{2} = 400°C;  f_{c,θ2} = 0,75.40 = 30  [N/mm^{2}]  (C.8) 
ε_{cu,θ2} =1  [%]  (C.9)  
ε_{ce,θ2} = 3,0  [%]  (C.10) 
For a possible maximum concrete temperature of θ_{max} = 600°C;
f_{c,θ max} = 0,45. 40 = 18  [N/mm^{2}]  (C.11) 
ε_{cu,θmax} = 2,5  [%]  (C.12) 
ε_{ce,θ max} = 3,5  [%]  (C.13) 
For any lower temperature obtained during the subsequent cooling down phase as for θ_{3} = 400°C:
f_{c,θ.20°C} = (0,9 K_{c,θmax}) f_{c} = 0,9. 0,45.40 = 16,2  [N/mm^{2}  (C.14) 
f_{c,θ3} = f_{c,θ max} – [(f_{c,θ max} – f_{c,θ,20°C}) (θ_{max} – θ_{3})/(θ_{max} – 20)] = 17,4  [N/mm^{2}]  (C.15) 
ε_{cu,θ3} = ε_{cu,θmax} =2,5  [%]  (C.16) 
ε_{ce,θ3} = ε_{cu,θ3} + [(ε_{ce,θ max} – ε_{cu,θ max}) f_{c,θ3}/f_{c,θmax}] = 3,46  [%]  (C.17) 
Figure C.1: Example of concrete heating and cooling
Figure C.2: Stressstrain relationships of the concrete strength class C40/50, heated up to θ_{1}, = 200°C, θ_{2} = 400°C, θ_{max} = 600°C and cooled down to θ_{3} = 400°C.
[Informative]
where:
t_{i}  the fire resistance with respect to thermal insulation  [min] 
A  concrete volume of the rib per metre of rib length  [mm^{3}/m] 
L_{r}  exposed area of the rib per metre of rib length  [mm^{2}/m] 
A/L_{r}  the rib geometry factor  [mm] 
Φ  the view factor of the upper flange  [] 
ℓ_{3}  the width of the upper flange (see Figure D.1) [min]  [mm] 
For the factors a_{i}, for different values of the concrete depth h_{1} for both normal and lightweight concrete, refer to Figure D.1 and Table D.1. For intermediate values, linear interpolation is allowed.
Figure D.1 : Definition of the rib geometry factor A/L_{r} for ribs of composite slabs.
a_{0} [min] 
a_{1} [min/mm] 
a_{2} [min] 
a_{3} [min/mm] 
a_{4} [min mm] 
a_{5} [min] 


Normal weight concrete  −28,8  1,55  −12,6  0,33  −735  48,0 
Lightweight concrete  −79,2  2,18  −2,44  0,56  −542  52,3 
where:
θ_{a}  is the temperature of the lower flange, web or upper flange  [°C] 
For factors b_{i}, for both normal and lightweight concrete, refer to Table D.2. For intermediate values, linear interpolation is allowed.
Concrete  Fire resistance [min] 
Part of the steel sheet  b_{0} [°C] 
b_{1}[°C]. mm  b_{2} [°C]. mm 
b_{3} [°C] 
b_{4} [°C] 

Normal weight concrete 
60  Lower flange  951  −1197  −2,32  86,4  −150,7 
Web  661  −833  −2,96  537,7  −351,9  
Upper flange  340  −3269  −2,62  1148,4  −679,8  
90  Lower flange  1018  −839  −1,55  65,1  −108,1  
Web  816  −959  −2,21  464,9  −340,2  
Upper flange  618  −2786  −1,79  767,9  −472,0  
120  Lower flange  1063  −679  −1,13  46,7  −82,8  
Web  925  −949  −1,82  344,2  −267,4  
Upper flange  770  −2460  −1,67  592,6  −379,0  
Light weight concrete 
30  Lower flange  800  −1326  −2,65  114,5  −181,2 
Web  483  −286  −2,26  439,6  −244,0  
Upper flange  331  −2284  −1,54  488,8  −131,7  
60  Lower flange  955  −622  −1,32  47,7  −81,1  
Web  761  −558  −1,67  426,5  −303,0  
Upper flange  607  −2261  −1,02  664,5  −410,0  
90  Lower flange  1019  −478  −0,91  32,7  −60,8  
Web  906  −654  −1,36  287,8  −230,3  
Upper flange  789  −1847  −0,99  469,5  −313,0  
120  Lower flange  1062  −399  −0,65  19,8  −43,7  
Web  989  −629  −1,07  186,1  −152,6  
Upper flange  903  −1561  −0,92  305,2  −197,2 
where:
θ_{S}  the temperature of additional reinforcement in the rib  [°C] 
u_{3}  distance to lower flange  [mm] 
z  indication of the position in the rib (see (4))  [mm^{−0.5}] 
α  angle of the web  [degrees] 
For factors c_{i} for both normal and lightweight concrete, refer to Table D.3. For intermediate values, linear interpolation is allowed.
Concrete  Fire resistance [min]  C_{0} [°C] 
C_{1} [°C] 
c_{2} [°C]. mm^{0.5} 
c_{3} [°C]. mm 
c_{4} [°C/°] 
c_{5} [°C]. mm 

Normal weight concrete 
60  1191  −250  −240  −5,01  1,04  −925 
90  1342  −256  −235  −5,30  1,39  −1267  
120  1387  −238  −227  −4,79  1,68  −1326  
Light weight concrete 
30  809  −135  −243  −0,70  0,48  −315 
60  1336  −242  −292  −6,11  1,63  −900  
90  1381  −240  −269  −5,46  2,24  −918  
120  1397  −230  −253  −4,44  2,47  906 
Figure D.2: Parameters for the position of the reinforcement bars
u_{1}, n_{2}:  shortest distance of the centre of the reinforcement bar to any point of the webs of the steel sheet; 81 
u_{3};  distance of the centre of the reinforcement bar to the lower flange of the steel sheet. 
point I:  is situated at the central line of the rib, at a distance from the lower flange of the steel sheet and calculated as a function of the limiting temperature according to equation D.7 and D.9 of (4) and (5); 
point IV:  is situated at the central line between two ribs, at a distance from the upper flange of the steel sheet, calculated as a function of the limiting temperature according to equations D.7 and D.14 of (4) and (5); 
point II:  is situated on a line through point I, parallel to the lower flange of the steel sheet, at a distance from the web of the steel sheet, equal to that from the lower flange; 
point III:  is situated on a line through the upper flange of the steel sheet, at a distance from the web of the steel sheet, equal to the distance of point IV to the upper flange. 
The isotherm is obtained by linear interpolation between the points I, II, III and IV.
Note: The limiting temperature is derived from equilibrium over the cross section and therefore has no relation with temperature penetration
Figure D.3.a : Schématisation isotherm
82Figure D.3.b: Establishment of isotherms
where:
N_{s}  is the normal force in the hogging reinforcement  [N] 
For factors d_{i}, for both normal and lightweight concrete, refer to Table D.4 For intermediate values, linear interpolation is allowed.
Concrete  Fire resistance [min] 
d_{0} [°C] 
d_{1} [°C].N 
d_{2} [°C].mm 
d_{3}[°C]  d_{4} [°C].mm 

Normal weight concrete 
60  867  −1,9.10^{−4}  −8,75  −123  −1378 
90  1055  −2,2.10^{−4}  −9,91  −154  −1990  
120  1144  −2,2.10^{−4}  −9,71  −166  −2155  
Light weight concrete 
30  524  −1,6.10^{−4}  −3,43  −80  −392 
60  1030  −2,6.10^{−4}  −10,95  −181  −1834  
90  1159  −2,5.10^{−4}  −10,88  −208  −2233  
120  1213  −2,5.10^{−4}  −10,09  −214  −2320 
Depth × mm  Temperature θ_{c}°C after a fire duration in min. of 

30′  60′  90′  120′  180′  240′  
5 10 
535 470 
705 642 
738 

15 20 
415 350 
581 525 
681 627 
754 697 

25 30 
300 250 
469 421 
571 519 
642 591 
738 689 
740 

35 40 
210 180 
374 327 
473 428 
542 493 
635 590 
700 670 

45 50 
160 140 
289 250 
387 345 
454 454 
549 508 
645 550 

55 60 
125 110 
200 175 
294 271 
369 342 
469 430 
520 495 

80 100 
80 60 
140 100 
220 160 
270 210 
330 260 
395 305 
The cross sectional dimensions of the slab h_{1} h_{2}, ℓ_{1}, ℓ_{2}, and ℓ_{3} are given in Figures 4.1 and 4.2.
Standard Fire Resistance  Minimum effective thickness h_{eff} [mm] 

I 30  60 h_{3} 
I 60  80 h_{3} 
I 90  100 h_{3} 
I 120  120 h_{3} 
I 180  150 h_{3} 
I 240  175 h_{3} 
for reentrant steel sheet profiles  for trapezoidal steel sheet profiles  
77,0  ≤  ℓ_{1}  ≤  135,0  mm  80,0  ≤  ℓ_{1}  ≤  155,0  mm 
110,0  ≤  ℓ_{2}  ≤  150,0  mm  32,0  ≤  ℓ_{2}  ≤  132,0  mm 
38,5  ≤  ℓ_{3}  ≤  97,5  mm  40,0  ≤  ℓ_{3}  ≤  115,0  mm 
50,0  ≤  h_{1}  ≤  130,0  mm  50,0  ≤  h_{2}  ≤  125,0  mm 
30,0  ≤  h_{2}  ≤  60,0  mm  50,0  ≤  h_{2}  ≤  100,0  mm 
[informative]
Figure E.1: Calculation of the sagging moment resistance
T^{+} = [f_{ay,θ1}(b_{1} e_{1}) + f_{ay,θw}(h_{w} e_{w}) + f_{ay,θ 2} (b_{2} e_{2})] / γ_{M,fi,a}, (E.1)
with f_{ay,θ} the maximum stress level according to 3.2.1 at temperature θ defined following 4.3.4.2.2.
T^{+} ≤ N P_{fi,Rd} (E.3)
where:
N  is the smaller number of shear connectors related to any critical length of the beam and P_{fi,Rd} is the design shear resistance in the fire situation of a shear connector according to 4.3.4.2.5. 
NOTE: The critical lengths are defined by the end supports and the crosssection of maximum bending moment.
where b_{eff} is the effective width according to 5.4.1.2 of EN 199411, and f_{c} the compressive strength of concrete at room temperature.
86(h_{c} —h_{u})≥ h_{cr} with h_{cr} is the depth x according to Table D.5 corresponding to a concrete temperature below 250°C. In that situation the value of h_{u} according to equation (E.4) applies.
or (h_{c}  h_{u}) < h_{cr} ; some layers of the compressive zone of concrete are at a temperature higher than 250°C. In this respect, a decrease of the compressive strength of concrete may be considered according to 3.2.2. The h_{u} value may be determined by iteration varying the index “n” and assuming on the basis of Table D.5 an average temperature for every slice of 10 mm thickness, such as:
where:
h_{u} = (h_{c}  h_{cr}) + 10 (n–2) + h_{u,n}, [mm]
n  is the total number of concrete layers in compression, including the top concrete layer (h_{c}  h_{cr}) with a temperature below 250°C. 
y_{F} ≈ h + h_{c} – (h_{u}/2) (E.6)
and the sagging moment resistance is
M_{fi,Rd+} = T^{+} (y_{F} – y_{T}) (E.7)
with T^{+}, the tensile force given by the value of (E.5) while taking account of (E.3).
Figure E.2: Calculation of the hogging moment resistance
where :
T^{−}  is the total tensile force of the reinforcing bars, equal to the compressive force F^{−} in the steel section. 
F^{+} ≤ N × P_{fi,Rd} – T^{−} (E.8)
where:
N  is the number of shear connectors between the critical crosssection and the intermediate support (or the restraining support) and where P_{fi,Rd} is the shear resistance of a shear connector in case of fire, as mentioned in clause 4.3.4.2.5 
NOTE: Classification may be done according to 4.2.2 of EN199312.
where
k_{E,θ} and k_{y,θ} are given in Table 3.2,
is the relative slenderness at room temperature for the stiffener associated with part of web as shown in Figure E.3 and
ε is calculated according to 4.2.2 of EN199312.
where:
f_{ay,θw} and f_{ay,θr} are respectively the maximum stresses in steel at the temperature of web θ_{W} and of stiffener θ_{r};
r is equal to the root radius for a hot rolled section, or to with a the throat of fillet weld for a welded crosssection.
Figure E.3 : Stiffener on an intermediate support
Figure F.1 Calculation scheme for the sagging moment resistance.
Note to Figure F.1:
 Example of stress distribution in concrete;
 Example of stress distribution in steel
Standard Fire Resistance  Slab Reduction h_{c,fi} [mm] 

R 30  10 
R 60  20 
R 90  30 
R 120  40 
R 180  55 
Figure F.2: Thickness reduction h_{c,fi} for various types of concrete slabs
Standard Fire Resistance  Width Reduction b_{fi} of the Upper Flange [mm] 

R 30  (e_{f}/2) + (bb_{c})/2 
R 60  (e_{f}/2) + 10 + (bb_{c})/2 
R 90  (e_{f}/2) + 30 + (bb_{c})/2 
R 120  (e_{f}/2) + 40 + (bb_{c})/2 
R 180  (e_{f}/2) + 60 + (bb_{c})/2 
The bottom part h_{l} is given directly in Table F.3 for 1 < h/b_{c} < 2.
91Standard Fire Resistance 
a_{1} [mm^{2}] 
a_{2} [mm^{2}] 
h_{ℓmin} [mm] 


R30  3 600  0  20  
R60  9 500  20 000  30  
h/b_{c} ≤ 1  R 90  14 000  160 000  40 
R 120  23 000  180 000  45  
R 180  35 000  400 000  55  
R 30  3 600  0  20  
R 60  9 500  0  30  
h/b_{c} > 2  R 90  14 000  75 000  40 
R 120  23 000  110 000  45  
R 180  35 000  250 000  55  
R30  h_{ℓ} = 3 600 / b_{c}  20  
R 60  h_{ℓ} = 9 500 / b_{c} + 20 000 (e_{w} / b_{c} h) (2  h / b_{c})  30  
1 < h/b_{c} < 2  R 90  h_{ℓ} = 14 000/b_{c} + 75 000 (e_{w} / b_{c} h) + 85 000 (e_{w} / b_{c} h) (2  h / b_{c}) 
40  
R 120  h_{ℓ} = 23 000/b_{c} + 110 000 (e_{w}/b_{c}h) + 70 000 (e_{w}/ b_{c} h) (2  h / b_{c}) 
45  
R 180  h_{ℓ} = 35 000 / b_{c} + 250 000 (e_{w} / b_{c} h) + 150 000 (e_{w} /b_{c} h)(2h/b_{c}) 
55 
f_{ay,x} = f_{ay} [1 – x(1 – k_{a})/ h_{ℓ}] (F.1)
where:
k_{a}  is the reduction factor of the yield point of the lower flange given in (8). This leads to a trapezoidal form of the stress distribution in h_{ℓ} 
Standard Fire Resistance  Reduction Factor k_{a}  k_{a,min}  k_{a,max} 

R 30  [(1,12)(84/b_{c}) + (h/22b_{c})]a_{0}  0,5  0,8 
R 60  [(0,21)(26/b_{c}) + (h/24b_{c})]a_{0}  0,12  0,4 
R 90  [(0,12)(17/b_{c}) + (h/38b_{c})]a_{0}  0,06  0,12 
R 120  [(0,1)(15/b_{c}) + (h/40b_{c})]a_{0}  0,05  0,10 
R 180  [(0,03)(3/b_{c}) + (h/50b_{c})]a_{0}  0,03  0,06 
k_{r,min}  k_{r,min}  

Standard Fire Resistance  a_{3}  a_{4}  a_{5}  
R 30  0,062  0,16  0,126  
R 60  0,034  0,04  0,101  0,1  1 
R 90  0,026  0,154  0,090  
R 120  0,026   0,284  0,082  
R 180  0,024   0,562  0,076 
where:
A_{m} = 2h + b_{c} [mm]
V = hb_{c} [mm^{2}]
u = 1/[(1/u_{1}) + (1/u_{si}) + 1/(b_{c}e_{w}u_{si}.)] (F.2)
where:
U_{i}  is the axis distance [mm] from the reinforcing bar to the inner side of the flange and 
u_{si}  is the axis distance [mm] from the reinforcing bar to the outside border of the concrete (see Figure F.1). 
Figure F.3: Calculation scheme for the hogging moment resistance.
Standard Fire Resistance 
Reduction Factor k_{} 
k_{s,min}  k_{s,max} 

R 30  1  
R 60  (0,022 u) + 0,34  
R 90  (0,0275 u)0,1  0  1 
R 120  (0,022 u)  0,2  
R 180  (0,018 u)0,26 
Standard Fire Resistance  h_{fi} [mm]  h_{fi,min} [mm]  b_{c,fi} [mm]  b _{c,fi,min}[mm] 

R 30  25  25  25  25 
R 60  165(0,4b_{c})8(h/b_{c})  30  60(0,15b_{c})  30 
R90  220  (0,5bJ  8 (h / bj  45  70(0,1b_{c})  35 
R 120  290 (0,6b_{c})10(h/b_{c})  55  75(0,1b_{c})  45 
R 180  360 (0,7b_{c})10(h/b_{c})  65  85(0,1b_{c})  55 
NOTE: The symbol b_{c} is the minimum value of either the width b of the lower flange or the width of the concrete part between the flanges, web thickness e_{w} included (see Figure F.1).
Standard Fire Resistance 
Minimum Profile Height h_{c} and Minimum Width b_{r} [mm] 
Minimum Area h b_{c} [mm^{2}] 

R30  120  17500 
R60  150  24000 
R90  170  35000 
R120  200  50000 
R180  250  80000 
[informative]
Figure G.1: Reduced crosssection for structural fire design
N_{fi,Rd,Z} = χ_{z} N_{fi,pl,Rd} (G.1)
θ_{f,t} = θ_{o,t} + k_{t} (A_{m}/V) (G.2)
where:
t  is the duration in minutes of the fire exposure 
A_{m}/V  is the section factor in m^{−1}, with A_{m} = 2 (h + b) in [m] and V = h b in [m^{2}] 
θ_{o,t}  is a temperature in °C given in Table G.1 
k_{t}  is an empirical coefficient given in Table G.1. 
Standard Fire Resistance  θ_{θ,t} [°C] 
k_{t} [m°C] 

R30  550  9,65 
R60  680  9,55 
R90  805  6,15 
R120  900  4,65 
f_{ay,f,t} = f_{ay,f} k_{y,θ} and (G.3)
E_{a,f,t} = E_{a,f} k_{E,θ} with k_{y,θ} and k_{E,θ} following Table 3.2 of 3.2.1 (G.4)
N_{fi,pl,Rd,f} = 2(b e_{f} f_{ay,f,t}) / γ_{M,fi,a} and (G.5)
(EI) _{fi,f,Z} = E_{a,f,t} (e_{f} b^{3})/6 (G.6)
Standard Fire Resistance  H_{t} [mm]  

R 30  350  
R 60  770  
R 90  1100  
R 120  1250 
N_{fi,pl,Rd,w} = [e_{w} (h – 2e_{f}  2h_{w,fi}) f_{ay,w,t}]/γ_{M,fi,a} (G.9)
Standard Fire Resistance  b_{c,fi} [mm] 

R 30  4,0 
R 60  15,0 
R 90  0,5 (A_{m}/V) + 22,5 
R 120  2,0 (A_{m}/V) + 24,0 
R30  R60  R90  R120  

A_{m}/v [m^{−1}] 
θ_{c,t} [°C] 
A_{m/V} [m^{−}] 
θ_{c/t} [°C] 
A_{m}/V [m^{−1}] 
θ_{c,t} [°C] 
A_{m}/V [m^{−}] 
θ_{c,t} [°C] 
4  136  4  214  4  256  4  265 
23  300  9  300  6  300  5  300 
46  400  21  400  13  400  9  400 
    50  600  33  600  23  600 
        54  800  38  800 
            41  900 
            43  1000 
E_{c,sec,θ} = f_{c,θ} = f_{c,} K_{c,θ}/ε_{cu,θ} with K_{c,θ} and ε_{cu,θ} following Table 3.3 of 3.2.2 (G.11
where A_{s} is the crosssection of the reinforcing bars, and 0,86 is a calibration factor.
where I_{s} is the second moment of area of the reinforcing bars related to the central axis Z of the composite crosssection.
u[mm] Standard Fire Resistance 
40  45  50  55  60 

R30  1  1  1  1  1 
R60  0,789  0,883  0,976  1  1 
R90  0,314  0,434  0,572  0,696  0,822 
R120  0,170  0,223  0,288  0,367  0,436 
u[mm] Standard Fire Resistance 
40  45  50  55  60 

R30  0,830  0,865  0,888  0,914  0,935 
R60  0,604  0,647  0,689  0,729  0,763 
R90  0,193  0,283  0,406  0,522  0,619 
R120  0,110  0,128  0,173  0,233  0,285 
where
U_{1}  is the axis distance from the outer reinforcing bar to the inner flange edge  [mm] 
u_{2}  is the axis distance from the outer reinforcing bar to the concrete surface  [mm] 
99Note:
N_{fi,pi,Rd,s} = A_{s} k_{y,t} f_{sy}/γ_{M,fi,s} (G.15)
(EI)_{fi,s,z} = k_{E,t} E_{s} I_{S,Z} (G.16)
N_{fi,pl,Rd} = N_{fi,pl,Rd,f} + N_{fi,pl,Rd,w} + N_{fi,pl,Rd,c} + N_{fi,pl,Rd,s} (G.17)
(EI)_{fi,eff,z} = φ_{f,θ} (EI)_{fi,f,z} + φ_{w,θ;} (EI)_{fi,w,z} + φ_{c,θ} (EI)_{fi,c,z} + φ_{s,θ} (EI)_{fi,s,z} (G.18)
where φ_{i,θ} a reduction coefficient depending on the effect of thermal stresses. The values of φ_{i,θ} are given in Table G.7.
Standard Fire Resistance  φ_{f,θ}  φ_{w,θ}  φ_{c,θ}  θ_{s,θ} 

R30  1,0  1,0  0,8  1,0 
R60  0,9  1,0  0,8  0,9 
R90  0,8  1,0  0,8  0,8 
R120  1,0  1,0  0,8  1,0 
where:
ℓ_{θ}  is the buckling length of the column in the fire situation. 
where:
N_{fi,pl,R} is the value of N_{fi,pl,Rd} according to (1) when the factors γ_{M,fi,a}, γ_{M,fi,c} and γ_{M,fi,s} are taken as 1,0.
N_{fi,Rd,z} = X_{z} N_{fi,pl,Rd} (G.21)
100These design graphs are based on the partial material safety factors γ_{M,fi,a} = γ_{M,fi,s} = γ _{M,fi,c} = 1,0.
where:
N_{Rd} and N_{Rd,δ} represent the axial buckling load and the buckling load in case of an eccentric load calculated according to EN 199411, for normal temperature design.
buckling length ℓ_{θ}  ≤  13,5b  
230 mm  ≤  height of cross section h  ≤  1100 mm 
230 mm  ≤  width of cross section b  ≤  500 mm 
1 %  ≤  percentage of reinforcing steel  ≤  6% 
standard fire resistance  ≤  120 min 
Figure G.2: Parameters for buckling resistance of partially encased stell sections
Figure G.3.a: Buckling loads of partially encased steel sections for R60
102Figure G.3.b: Buckling loads of parially encased steel sections for R90
Figure G.3.c: Buckling loads of parially encased steel sections for R120
103[informative]
N_{fi,Rd} = N_{fi,cr} = N_{fi,pl,Rd} (H.1)
where:
N_{fi,pl,Rd} = A_{a} σ_{a,θ}/γ_{M,fi,a} + A_{c} σ_{c,θ}/γ_{M,fi,c} + A_{s} σ_{s,θ} / γ_{M,fi,s} and where (H.3)
N_{fi,cr}  is the elastic critical or Euler buckling load, 
N_{fi,pl,Rd}  is the design value of the plastic resistance to axial compression of the total crosssection 
ℓ_{θ}  is the buckling length in the fire situation, 
E_{i,θ,σ}  is the tangent modulus of the stressstrain relationship for the material i at temperature θ and for a stress σj_{i,θ}, (see Table 3.1 and Figure 3.2) 
I_{i}  is the second moment of area of the material i, 
_{i}  Arelated to the central axis y or z of the composite crosssection, 
A_{i}  is the crosssection area of material i, 
σ_{i,θ}  is the stress in material /i, at the temperature θ. 
ε_{a} = ε_{c} = ε_{s} = ε (H.4)
where:
ε  is the axial strain of the column and 
ε_{i}  is the axial strain of the material i of the crosssection. 
NOTE: The normal procedure is to increase the strain in steps. As the strain increases, E_{i,θ,σ} and N_{fi,cr} decrease and σ_{i,θ} and N_{fi,pl,Rd} increase. The level of strain is found where N_{fi,cr} and N_{fi,pl,Rd} are equal and the condition in (1) is satisfied.
N_{equ} = N_{fi,sd} / (φ.φ_{δ}) (H.5)
where:
φ_{s}  is given by Figure H.1 and φ_{δ} by Figure H.2 
b  is the size of a square section, 
d  is the diameter of a circular section, 
δ  is the eccentricity of the load. 
buckling length ℓ_{θ}  ≤  4,5 m  
140 mm  ≤  depth b or diameter d of crosssection  ≤  400 mm 
C20/25  ≤  concrete grades  ≤  C40/50 
0%  ≤  percentage of reinforcing steel  ≤  5% 
Standard fire resistance  ≤  120 min. 
Figure H.1: Correction coefficient φ_{s} as a function of the percentage of reinforcement
Figure H.2: Correction coefficient φ_{δ} as a function of the eccentricity δ
106Figure H.3 : Example of design graph for CIRCULAR HOLLOW SECTIONS (R60)
107Figure H.4 : Example of design graph for SQUARE HOLLOW SECTIONS (R90)
108[informative]