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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 199312
April 2005
ICS 13.220.50; 91.010.30; 91.080.10
Supersedes ENV 199312:1995
Incorporating Corrigendum
December 2005
English version
Eurocode 3: Calcul des structures en acier  Partie 12: Règles générales  Calcul du comportement au feu  Eurocode 3: Bemessung und Konstruktion von Stahlbauten  Teil 12: Allgemeine Regeln  Tragwerksbemessung für den Brandfall 
This European Standard was approved by CEN on 23 April 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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Ref. No. EN 199312:2005: E
1Page  
Foreword  4  
1.  General  9  
1.1  Scope  9  
1.2  Normative references  10  
1.3  Assumptions  11  
1.4  Distinction between principles and application rules  11  
1.5  Terms and definitions  11  
1.6  Symbols  12  
2  Basis of design  16  
2.1  Requirements  16  
2.1.1  Basic requirements  16  
2.1.2  Nominal fire exposure  16  
2.1.3  Parametric fire exposure  16  
2.2  Actions  17  
2.3  Design values of material properties  17  
2.4  Verification methods  17  
2.4.1  General  17  
2.4.2  Member analysis  18  
2.4.3  Analysis of part of the structure  19  
2.4.4  Global structural analysis  20  
3  Material properties  20  
3.1  General  20  
3.2  Mechanical properties of carbon steels  20  
3.2.1  Strength and deformation properties  20  
3.2.2  Unit mass  20  
3.3  Mechanical properties of stainless steels  23  
3.4  Thermal properties  23  
3.4.1  Carbon steels  23  
3.4.2  Stainless steels  26  
3.4.3  Fire protection materials  26  
4  Structural fire design  27  
4.1  General  27  
4.2  Simple calculation models  27  
4.2.1  General  27  
4.2.2  Classification of crosssections  28  
4.2.3  Resistance  28  
4.2.4  Critical temperature  36  
4.2.5  Steel temperature development  37  
4.3  Advanced calculation models  43  
4.3.1  General  43  
4.3.2  Thermal response  43  
4.3.3  Mechanical response  43  
4.3.4  Validation of advanced calculation models  44  
Annex A  [normative] Strainhardening of carbon steel at elevated temperatures  45  
Annex B  [normative] Heat transfer to external steelwork  47  
Annex C  [informative] Stainless steel  65  
Annex D  [informative] Joints  73 2  
Annex E  [informative] Class 4 crosssections  76 
This European Standard EN 1993, Eurocode 3: Design of steel structures, 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 October 2005, and conflicting National Standards shall be withdrawn at latest by March 2010.
This Eurocode supersedes ENV 199312.
According to the CENCENELEC internal Regulations, the National Standard Organizations of the following countries are bound to implement these 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 harmonization of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonized 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 1980s.
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 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 0:  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 
EN 1994  Eurocode 4:  Design of composite steel and concrete structures 
EN 1995  Eurocode 5:  Design of timber structures 
EN 1996  Eurocode 6:  Design of masonry structures 
EN 1997  Eurocode 7:  Geotechnical design 
EN 1998  Eurocode 8:  Design of structures for earthquake resistance 
EN 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).
4Eurocode standards recognize 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 recognize 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 harmonized 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.
The 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 contain
^{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 harmonized ENs 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.
5There is a need for consistency between the harmonized 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 should clearly mention which Nationally Determined Parameters have been taken into account.
EN 19931 2 describes the principles, requirements and rules for the structural design of steel buildings exposed to fire, including the following aspects.
EN 199312 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 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 build in such a way, that in the event of an outbreak of fire
According to the Interpretative Document N° 2 “Safety in case of fire” 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 fire regulations or 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.
^{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.
6A 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 and passive 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 in Figure 1. 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.
Where simple calculation models are not available, the Eurocode fire parts give 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 199312, will be prepared by interested external organizations.
The main text of EN 199312 together with normative Annexes includes most of the principal concepts and rules necessary for structural fire design of steel structures.
This 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 199312 should have a National annex containing all Nationally Determined Parameters to be used for the design of steel structures to be constructed in the relevant country.
National choice is allowed in EN 199312 through paragraphs:
2.3 (1)
2.3 (2)
4.1 (2)
4.2.3.6 (1)
4.2.4 (2)
Figure 0.1: Design procedure
8NOTE: This part does not include rules for separating elements.
NOTE: For the fire resistance of composite steel and concrete structures, see EN 199412.
EN 10025  Hot rolled products of structural steels; 
Text deleted  
EN 10210  Hot finished structural hollow sections of nonalloy and fine grain structural steels: 
Part 1:  Technical delivery conditions; 
EN 10219  Cold formed welded structural hollow sections of nonalloy and fine grain structural steels: 
Part 1:  Technical delivery conditions; 
EN 1363  Fire resistance: General requirements; 
EN 13501  Fire classification of construction products and building elements 
Part 2  Classification using data from fire resistance tests 
EN V 1338:  Fire tests on elements of building construction: 
Part 1:  Test method for determining the contribution to the fire resistance of structural members: by horizontal protective membranes; 
Part 2  Test method for determining the contribution to the fire resistance of structural members: by vertical protective membranes; 
Part 4:  Test method for determining the contribution to the fire resistance of structural members: by applied protection to steel structural elements; 
EN 1990  Eurocode: Basis of structural design 
EN 1991  Eurocode 1. Actions on structures: 
Part 12:  Actions on structures exposed to fire; 
EN 1993  Eurocode 3. Design of steel structures: 
Part 11:  General rules : General rules and rules for buildings; 
Part 13:  General rules : Supplementary rules for cold formed steel members and sheeting; 
Part 14:  General rules : Supplementary rules for stainless steels 
Part 18:  General Rules: Design of joints 
EN 1994  Eurocode 4. Design of composite steel and concrete structures: 
Part 12:  General rules : Structural fire design; 
ISO 1000 SI units. 
A frame may be classified as braced if its sway resistance is supplied by a bracing system with a response to inplane horizontal loads which is sufficiently stiff for it to be acceptably accurate to assume that all horizontal loads are resisted by the bracing system.
Isolated part of an entire structure with appropriate support and boundary conditions.
A nominal curve, defined in EN 135012 for representing a model of a fully developed fire in a compartment.
In this standard: steel grades according to in EN199311, except stainless steels
Any material or combination of materials applied to a structural member for the purpose of increasing its fire resistance.
All steels referred to in EN 199314.
The configuration factor for radiative heat transfer from surface A to surface B is defined as the fraction of diffusely radiated energy leaving surface A that is incident on surface B.
Convective heat flux to the member related to the difference between the bulk temperature of gas bordering the relevant surface of the member and the temperature of that surface.
Equal to absorptivity of a surface, i.e. the ratio between the radiative heat absorbed by a given surface, and that of a black body surface.
11Energy per unit time and surface area definitely absorbed by members.
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.
Ratio between the exposed surface area of a notional bounding box to the section 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.
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_{i}  an elemental area of the crosssection with a temperature θ_{i}; 
A_{m}  the surface area of a member per unit length; 
A_{m}/V  the section factor for unprotected steel members; 
C_{i}  the protection coefficient of member face i ; 
A_{p}  the appropriate area of fire protection material per unit length of the member [m^{2}/m] ; 
E_{a}  the modulus of elasticity of steel for normal temperature design; 
E_{a,θ}  the slope of the linear elastic range for steel at elevated temperature θ_{a}; 
E_{fi,d}  the design effect of actions for the fire situation, determined in accordance with EN 199112, including the effects of thermal expansions and deformations; 
F_{b,Rd}  the design bearing resistance of bolts; 
F_{b,t,Rd}  the design bearing resistance of bolts in fire; 
F_{v,Rd}  the design shear resistance of a bolt per shear plane calculated assuming that the shear plane passes through the threads of the bolt; 
F_{v,t,Rd}  the fire design resistance of bolts loaded in shear; 
F_{w,Rd}  the design resistance per unit length of a fillet weld; 
F_{w,t,Rd}  the design resistance per unit length of a fillet weld in fire; 
G_{k}  the characteristic value of a permanent action; 
I_{f}  the radiative heat flux from an opening; 
I_{z}  the radiative heat flux from a flame; 
I_{z,i}  the radiative heat flux from a flame to a column face i; 
L  the system length of a column in the relevant storey 12 
M_{b,fi,t,Rd}  the design buckling resistance moment at time t 
M_{fi,t,Rd}  the design moment resistance at time t 
M_{fi,θ,Rd}  the design moment resistance of the crosssection for a uniform temperature θ_{a} which is equal to the uniform temperature θ_{a} at time t in a crosssection which is not thermally influenced by the supports.; 
M_{Rd}  the plastic moment resistance of the gross crosssection M_{pI,Rd} for normal temperature design; the elastic moment resistance of the gross crosssection M_{eI,Rd} for normal temperature design; 
N_{b,fi,t,Rd}  the design buckling resistance at time t of a compression member 
N_{Rd}  the design resistance of the crosssection N_{pI,Rd} for normal temperature design, according to EN 199311. 
N_{fi,θ,Rd}  the design resistance of a tension member a uniform temperature θ_{a} 
N_{fi,t,Rd}  the design resistance at time t of a tension member with a nonuniform temperature distribution across the crosssection 
Q_{k,I}  the principal variable load; 
R_{fi,d,t}  the corresponding design resistance in the fire situation. 
R_{fi,d,0}  the value of R_{fi,d,t} for time t = 0; 
T_{f}  the temperature of a fire [K]; 
T_{0}  the flame temperature at the opening [K]; 
T_{x}  the flame temperature at the flame tip [813 K]; 
T_{z}  the flame temperature [K]; 
T_{z,1}  the flame temperature [K] from annex B of EN 199112, level with the bottom of a beam; 
T_{z,2}  the flame temperature [K] from annex B of EN 199112, level with the top of a beam; 
V  the volume of a member per unit length; 
V_{fi,t,Rd}  the design shear resistance at time t 
V_{Rd}  the shear resistance of the gross crosssection for normal temperature design, according to EN 199311; 
X_{k}  the characteristic value of a strength or deformation property (generally f_{k} or E_{k}) for normal temperature design to EN 199311; 
Latin lower case letters
a_{z}  the absorptivity of flames; 
c  the specific heat; 
c_{a}  the specific heat of steel; 
c_{p}  the temperature independent specific heat of the fire protection material; 
d_{i}  the crosssectional dimension of member face i; 
d_{p}  the thickness of fire protection material; 
d_{f}  the thickness of the fire protection material. (d_{f} = 0 for unprotected members.) 
f_{p,θ}  the proportional limit for steel at elevated temperature θ_{a}; 13 
f_{y}  the yield strength at 20°C 
f_{y,θ}  the effective yield strength of steel at elevated temperature θ_{a}; 
f_{y,i}  the nominal yield strength f_{y} for the elemental area A_{i} taken as positive on the compression side of the plastic neutral axis and negative on the tension side; 
f_{u,0}  the ultimate strength at elevated temperature, allowing for strainhardening. 
ḣ_{net,d}  the design value of the net heat flux per unit area; 
h_{z}  the height of the top of the flame above the bottom of the beam; 
i  the column face indicator (1), (2), (3) or (4); 
k_{b,θ}  the reduction factor determined for the appropriate bolt temperature; 
k_{E,θ}  the reduction factor from section 3 for the slope of the linear elastic range at the steel temperature θ_{a} reached at time t. 
k_{E,θ,com}  the reduction factor from section 3 for the slope of the linear elastic range at the maximum steel temperature in the compression flange θ_{a,com} reached at time t. 
k_{sh}  correction factor for the shadow effect; 
k_{θ}  the relative value of a strength or deformation property of steel at elevated temperature θ_{a}; 
k_{θ}  the reduction factor for a strength or deformation property (X_{k,θ}/X_{k}) , dependent on the material temperature, see section 3; 
k_{w;θ}  the strength reduction factor for welds; 
k_{y,0}  the reduction factor from section 3 for the yield strength of steel at the steel temperature θ_{a} reached at time t. 
k_{y,θ,com}  the reduction factor from section 3 for the yield strength of steel at the maximum temperature in the compression flange θ_{a,com} reached at time t. 
k_{y,θ,i}  the reduction factor for the yield strength of steel at temperature θ_{i},; 
k_{y,θ,max}  the reduction factor for the yield strength of steel at the maximum steel temperature θ_{a,max} reached at time t; 
k_{y,θ,web}  the reduction factor for the yield strength of steel at the steel temperature θ_{web} , see section 3. 
k_{y}  the interaction factor; 
k_{z}  the interaction factor; 
k_{LT}  the interaction factor; 
m  the number of openings on side m; 
n  the number of openings on side n; 
l  the length at 20 °C ; a distance from an opening, measured along the flame axis; 
l_{fi}  the buckling length of a column for the fire design situation; 
s  the horizontal distance from the centreline of a column to a wall of a fire compartment; 
t  the time in fire exposure; 
W_{i}  the width of an opening; 
Z_{i}  the distance from the plastic neutral axis to the centroid of the elemental area A_{i}; 
Greek upper case letters
Δt  the time interval; 
Δl  the temperature induced expansion; 
Δθ_{g,t}  the increase of the ambient gas temperature during the time interval Δt; 
ϕ_{f,i}  the configuration factor of member face i for an opening; 
ϕ_{f}  the overall configuration factor of the member for radiative heat transfer from an opening; 
ϕ_{z}  the overall configuration factor of a member for radiative heat transfer from a flame; 
ϕ_{z,i}  the configuration factor of member face i for a flame; 
ϕ_{z,m}  the overall configuration factor of the column for heat from flames on side m; 
ϕ_{z,n}  the overall configuration factor of the column for heat from flames on side n; 
Greek lower case letters
α  the convective heat transfer coefficient; 
β_{M}  the equivalent uniform moment factors; 
γ_{G}  the partial factor for permanent actions; 
γ_{M2}  the partial factor at normal temperature; 
γ_{M,fi}  the partial factor for the relevant material property, for the fire situation. 
γ_{Q,I}  the partial factor for variable action 1; 
ε_{f}  the emissivity of a flame; the emissivity of an opening; 
ε_{z}  the emissivity of a flame; 
ε_{z,m}  the total emissivity of the flames on side m; 
ε_{z,n}  the total emissivity of the flames on side n; 
ξ  a reduction factor for unfavourable permanent actions G; 
η_{fi}  the reduction factor for design load level in the fire situation; 
θ  the temperature; 
θ_{a}  the steel temperature [°C]. 
θ_{a,cr}  critical temperature of steel 
θ_{g,t}  the ambient gas temperature at time t; 
θ_{web}  the average temperature in the web of the section; 
θ_{i}  the temperature in the elemental area A_{i}. 
K  the adaptation factor; 
K_{1}  an adaptation factor for nonuniform temperature across the crosssection; 
K_{2}  an adaptation factor for nonuniform temperature along the beam; 
λ  the thermal conductivity; 15 
λ_{i}  the flame thickness for an opening i; 
λ_{p}  the thermal conductivity of the fire protection system; 
λ_{f}  the effective thermal conductivity of the fire protection material. 
μ_{0}  the degree of utilization at time t = 0. 
σ  the Stefan Boltzmann constant [5,67 × 10^{−8} W/m^{2}K^{4}]; 
ρ_{a}  the unit mass of steel; 
ρ_{p}  the unit mass of the fire protection material; 
χ_{fi}  the reduction factor for flexural buckling in the fire design situation; 
χ_{LT,fi}  the reduction factor for lateraltorsional buckling in the fire design situation; 
χ_{min,fi}  the minimum value of χ_{y,fi} and χ_{z,fi}; 
χ_{z,fi}  the reduction factor for flexural buckling about the zaxis in the fire design situation; 
χ_{y,fi}  the reduction factor for flexural buckling about the yaxis in the fire design situation; 
ψ_{fi}  the combination factor for frequent values, given either by ψ_{1,1} or ψ_{2,1} ; 
and
χ_{d,fi} = k_{θ}X_{k}/γ_{M,fi} (2.1)
where:
X_{k}  is  the characteristic value of a strength or deformation property (generally f_{k} or E_{k}) for normal temperature design to EN 199311; 
kθ  is  the reduction factor for a strength or deformation property (X_{k,θ} / X_{k}) , dependent on the material temperature, see section 3; 
γ_{M,fi}  is  the partial factor for the relevant material property, for the fire situation. 
NOTE: For the mechanical properties of steel, the partial factor for the fire situation is given in the national annex. The use of γ_{M,fi} = 1.0 is recommended.
X_{d,fi} = X_{k,θ} / γ_{M,fi} (2.2a)
X_{d,fi} = γ_{M,fi}X_{k,θ} (2.2b)
where:
X_{k,θ}  is  the value of a material property in fire design, generally dependent on the material temperature, see section 3; 
γ_{M,fi}  is  the partial factor for the relevant material property, for the fire situation. 
NOTE: For thermal properties of steel, the partial factor for the fire situation see national annex. The use of γ_{M,fi} = 1.0 is recommended.
NOTE: Where rules given in this Part 12 of EN 1993 are valid only for the standard fire exposure, this is identified in the relevant clauses.
E_{fi,d} ≤ R_{fi,d,t} (2.3)
where:
17E_{fi,d}  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 1: For member analysis, see 2.4.2;
For analysis of parts of the structure, see 2.4.3;
For global structural analysis, see 2.4.4.
NOTE 2: For verifying standard fire resistance requirements, a member analysis is sufficient.
E_{d,fi} = η_{fi}E_{d} (2.4)
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 for the design load level for the fire situation. 
or for load combination (6.10a) and (6.10b) in EN 1990 as the smaller value given by the two following expressions:
where
Q_{k,1}  is  the characteristic value of the leading variable actions; 
G_{k}  is  the characteristic value of a permanent action; 
γ_{G}  is  the partial factor for permanent actions; 
γ_{Q,1}  is  the partial factor for variable action 1; 
ψ_{fi}  is  the combination factor for values, given either by ψ_{1,1} or ψ_{2,1}, see EN199112; 
ξ  is  a reduction factor for unfavourable permanent actions G. 
NOTE 1: An example of the variation of the reduction factor η_{fi} versus the load ratio Q_{k,I}/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.
Figure 2.1: Variation of the reduction factor η_{fi} with the load ratio Q_{k,1} / G_{k}
NOTE 2: As a simplification the recommended value of η_{fi} = 0,65 may be used, except for imposed load 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.
NOTE: For the rules of this standard it is assumed that the heating rates fall within the specified limits.
  effective yield strength, relative to yield strength at 20°C:  k_{y,θ} = f_{y,θ}/f_{y} 
  proportional limit, relative to yield strength at 20°C:  k_{p,θ} = f_{p,θ}/f_{y} 
  slope of linear elastic range, relative to slope at 20°C:  k_{E,θ} = E_{a,θ}/E_{a} 
NOTE: The variation of these reduction factors with temperature is illustrated in figure 3.2.
ρ_{a} = 7850kg/m^{3}
Figure 3.1: Stressstrain relationship for carbon steel at elevated temperatures.
21Steel Temperature θ_{a}  Reduction factors at temperature θ_{a} relative to the value of f_{y} or E_{a} at 20 °C  

Reduction factor (relative to f_{y}) for effective yield strength k_{y,θ} = f_{y,θ}/f_{y} 
Reduction factor (relative to f_{y}) for proportional limit k_{p,θ} = f_{p,θ}/f_{y} 
Reduction factor (relative to E_{a} for the slope of the linear elastic range k_{E,θ} = E_{a,θ}/E_{a} 

20°C  1,000  1,000  1,000 
100°C  1,000  1,000  1,000 
200 °C  1,000  0,807  0,900 
300 °C  1,000  0,613  0,800 
400 °C  1,000  0,420  0,700 
500°C  0,780  0,360  0,600 
600 °C  0,470  0,180  0,310 
700 °C  0,230  0,075  0,130 
800 °C  0,110  0,050  0,090 
900 °C  0,060  0,0375  0,0675 
1000°C  0,040  0,0250  0,0450 
1100°C  0,020  0,0125  0,0225 
1200°C  0,000  0,0000  0,0000 
NOTE: For intermediate values of the steel temperature, linear interpolation may be used. 
Figure 3.2: Reduction factors for the stressstrain relationship of carbon steel at elevated temperatures
Δl/l = 1,2 × 10^{−5} θ_{a} + 0,4 × 10^{−8} θ_{a}^{2}  2,416 × 10^{−4} (3.1a)
Δl/l = 1,1 × 10^{−2} (3.1b)
Δl/l = 2 × 10^{−5} θ_{a}  6,2 × 10^{−3} (3.1c)
where:
l  is  the length at 20 °C; 
Δl  is  the temperature induced elongation; 
θ_{a}  is  the steel temperature [°C]. 
NOTE: The variation of the relative thermal elongation with temperature is illustrated in figure 3.3.
Figure 3.3: Relative thermal elongation of carbon steel as a function of the temperature
24c_{a} = 425 + 7,73 × 10^{−1} θ_{a} − 1,69 × 10^{−3} θ_{a}^{2} + 2,22 × 10^{−6} θ_{a}^{3} J/kgK (3.2a)
c_{a} = 650 J/kgK (3.2d)
where:
θ_{a}  is  the steel temperature [°C]. 
NOTE: The variation of the specific heat with temperature is illustrated in figure 3.4.
Figure 3.4: Specific heat of carbon steel as a function of the temperature
λ_{a} = 54  3,33 × 10^{2} θ_{a} W/mK (3.3a)
λ_{a} = 27,3 W/mK (3.3b)
where:
θ_{a}  is  the steel temperature [°C]. 
NOTE: The variation of the thermal conductivity with temperature is illustrated in figure 3.5.
Figure 3.5: Thermal conductivity of carbon steel as a function of the temperature
NOTE: These standards include a requirement that the fire protection materials should remain coherent and cohesive to their supports throughout the relevant fire exposure.
NOTE: Examples of other protection methods are water filling or partial protection in walls and floors.
NOTE: The decision on use of advanced calculation models in a Country may be found in its National Annex.
E_{fi,d} ≤ R_{fi,d,t} (4.1)
where:
E_{fi,d}  is  the design effect of actions for the fire design situation, according to EN 199112; 
R_{fi,d,t}  is  the corresponding design resistance of the steel member, for the fire design situation, at time t. 
NOTE: In 4.2.3 R_{fi,d,t} becomes M_{fi,t,Rd}, N_{fi,t,Rd} etc (separately or in combination) and the corresponding values of M_{fi,Ed}, N_{fi,Ed} etc represent E_{fi,d}.
Where:
d_{f}  is  the thickness of the fire protection material. (d_{f} = 0 for unprotected members.) 
λ_{f}  is  the effective thermal conductivity of the fire protection material. 
NOTE: As a simplification the comparison of the level of utilization within the joints and joined members may be performed for room temperature.
ε = 0,85 [235 /f_{y}] ^{0,5} (4.2)
where:
f_{y}  is  the yield strength at 20 °C 
NOTE 1: See EN199311
NOTE 2: The reduction factor 0,85 considers influences due to increasing temperature.
N_{fi,θ,Rd} = k_{y,θ}N_{Rd}[γ_{M,0} / γ_{M,fi}] (4.3)
where:
k_{y,θ}  is  the reduction factor for the yield strength of steel at temperature θ_{a}, reached at time t see section 3; 
N_{Rd}  is  the design resistance of the crosssection N_{pI,Rd} for normal temperature design, according to EN 199311. 
where:
A_{i}  is  an elemental area of the crosssection with a temperature θ_{i}; 
k_{y,θ,i}  is  the reduction factor for the yield strength of steel at temperature θ_{i}, see section 3 ; 
θ_{i}  is  the temperature in the elemental area A_{i}. 
N_{b,fi,t,Rd} = χ_{fi}A k_{y,θ}f_{y}/γ_{M,fi} (4.5)
where:
χ_{fi}  is  the reduction factor for flexural buckling in the fire design situation; 
k_{y,θ}  is  the reduction factor from section 3 for the yield strength of steel at the steel temperature θ_{a} reached at time t. 
with
and
The nondimensional slenderness for the temperature θ_{a}, is given by:
where:
k_{y,θ}  is  the reduction factor from section 3 for the yield strength of steel at the steel temperature θ_{a} reached at time t; 
k_{E,θ}  is  the reduction factor from section 3 for the slope of the linear elastic range at the steel temperature θ_{a} reached at time t. 
Figure 4.1: Buckling lengths l_{fi} of columns in braced frames
M_{fi,θ,Rd} = k_{y,θ}[γ_{M,0}/γ_{M,fi}]M_{Rd} (4.8)
where:
M_{Rd}  is  the plastic moment resistance of the gross crosssection M_{pI,Rd} for normal temperature design, according to EN 199311 or the reduced moment resistance for normal temperature design, allowing for the effects of shear if necessary, according to EN 199311; 
k_{y,θ}  is  the reduction factor for the yield strength of steel at temperature θ_{a}, see section 3 
where:
z_{i}  is  the distance from the plastic neutral axis to the centroid of the elemental area A_{i}; 
f_{y,i}  is  the nominal yield strength f_{y} for the elemental area A_{i} taken as positive on the compression side of the plastic neutral axis and negative on the tension side; 
A_{i} and k_{y,θ,i}  is  are as defined in 4.2.3.1 (2). 
M_{fi,t,Rd} = M_{fi,θ,Rd}/ (K_{1}K_{2}) (4.10)
M_{fi,θ,Rd} ≤ M_{Rd}
where:
M_{fi,θ,Rd}  is  the design moment resistance of the crosssection for a uniform temperature θ_{a} which is equal to the uniform temperature θ_{a} at time t in a crosssection which is not thermally influenced by the support.; 
k_{1}  is  an adaptation factor for nonuniform temperature across the crosssection, see (7); 
k_{2}  is  an adaptation factor for nonuniform temperature along the beam, see (8). 
M_{b,fi,t,Rd} = χ_{LT,fi} W_{p1,y} k_{y,θ,com}f_{y} / Υ_{M,fi} (4. 11)
where:
χ_{LT,fi}  is  the reduction factor for lateraltorsional buckling in the fire design situation; 
k_{y,θ,com}  is  the reduction factor from section 3 for the yield strength of steel at the maximum temperature in the compression flange θ_{a,com} reached at time t. 
NOTE: Conservatively θ_{a,com} can be assumed to be equal to the uniform temperature θ_{a}.
with
and
where:
k_{E,θ,com}  is  the reduction factor from section 3 for the slope of the linear elastic range at the maximum steel temperature in the compression flange θ_{a,com} reached at time t. 
V_{fi,t,Rd} = k_{y,θ,web.}V_{Rd}[Υ_{M,0}/Υ_{M,fi}] (4.16)
where:
V_{Rd}  is  the shear resistance of the gross crosssection for normal temperature design, according to EN 199311; 
θ_{web}  is  the average temperature in the web of the section; 
k_{y,θ,web}  is  the reduction factor for the yield strength of steel at the steel temperature θ_{web}, see section 3. 
  for a beam exposed on all four sides:  k_{1} = 1,0 
  for an unprotected beam exposed on three sides, with a composite or concrete slab on side four:  k_{1} = 0,70 
  for an protected beam exposed on three sides, with a composite or concrete slab on side four:  k_{1} = 0,85 
  at the supports of a statically indeterminate beam:  k_{2} = 0,85 
  in all other cases:  k_{2} = 1,0. 
M_{fi,t,Rd} = k_{y,θ}M_{Rd}[γ_{M,0}/γ_{M,fi}] (4.17)
where:
M_{Rd}  is  the elastic moment resistance of the gross crosssection M_{eI,Rd} for normal temperature design, according to EN 199311 or the reduced moment resistance allowing for the effects of shear if necessary according to EN 199311; 
k_{y,θ}  is  the reduction factor for the yield strength of steel at the steel temperature θ_{a}, see section 3. 
M_{fi,t,Rd} = k_{y,θ,max}M_{Rd}[γ_{M,0}/γ_{M,fi}] / (K_{1}K_{2}) (4.18)
M_{fi,θ,Rd} ≤ M_{Rd}
where:
M_{Rd}  is  the elastic moment resistance of the gross crosssection M_{e1,Rd} for normal temperature design or the reduced moment resistance allowing for the effects of shear if necessary according to EN 199311; 
k_{y,θ,max}  is  the reduction factor for the yield strength of steel at the maximum steel temperature θ_{a,max} reached at time t, text deleted ; 
K_{1}  is  an adaptation factor for nonuniform temperature in a crosssection, see 4.2.3.3 (7); 32 
k_{2}  is  an adaptation factor for nonuniform temperature along the beam, see 4.2.3.3 (8). 
M_{b,fi,t,Rd} = χ_{LT,fi} W_{el,y,} k_{y,θ,com} f_{y}/γ_{M,fi} (4.19)
where:
χ_{LT,fi}  is  as given in 4.2.3.3 (5). 
NOTE: Conservatively θ_{a,com} can be assumed to be equal to the maximum temperature θ_{a,max}.
V_{fi,t,Rd} = k_{y,θ,web}V_{Rd}[γ_{M,0}/γ_{M,fi}] (4.20)
where:
V_{Rd}  is  the shear resistance of the gross crosssection for normal temperature design, according to EN 199311. 
where:
χ_{min,fi}  is  as defined in 4.2.3.2; 
χ_{z,fi}  is  as defined in 4.2.3.2; 
χ_{LT,fi}  is  as defined in 4.2.3.3 (5); 
NOTE: For the equivalent uniform moment factors β_{M} see figure 4.2.
Figure 4.2: Equivalent uniform moment factors.
35NOTE 1: For further information see annex E.
NOTE 2: The limit θ_{crit} may be chosen in the National Annex. The value θ_{crit} = 350°C is recommended.
where μ_{0} must not be taken less than 0,013.
NOTE: Examples for values of θ_{a,cr} for values of μ_{0} from 0,22 to 0,80 are given in table 4.1.
μ_{0} = E_{fi,d}/R_{fi,d,0} (4.23)
where:
R_{fi,d,0}  is  the value of R_{fi,d,t} for time t = 0, from 4.2.3; 
E_{fi,d} and R_{fi,d,t}  are as defined in 4.2.1(1). 
μ_{0} = η_{fi}[γ_{M,fi}/γ_{M0}] (4.24)
where:
η_{fi}  is  the reduction factor defined in 2.4.2 (3) . 
μ_{0}  θ_{a,cr}  μ_{0}  θ_{a,cr}  μ_{0}  θ_{a,cr} 

0,22  711  0,42  612  0,62  549 
0,24  698  0,44  605  0,64  543 
0,26  685  0,46  598  0,66  537 
0,28  674  0,48  591  0,68  531 
0,30  664  0,50  585  0,70  526 
0,32  654  0,52  578  0,72  520 
0,34  645  0,54  572  0,74  514 
0,36  636  0,56  566  0,76  508 
0,38  628  0,58  560  0,78  502 
0,40  620  0,60  554  0,80  496 
NOTE: The national annex may give default values for critical temperatures.
where:
k_{sh}  is  correction factor for the shadow effect, see (2) 
A_{m}/V  is  the section factor for unprotected steel members [1/m]; 
A_{m}  is  the surface area of the member per unit length [m^{2}/m]; 
V  is  the volume of the member per unit length [m^{3}/m]; 
c_{a}  is  the specific heat of steel, from section 3 [J/kgK]; 
ḣ_{net,d}  is  the design value of the net heat flux per unit area [W/m^{2}]; 
Δt  is  the time interval [seconds]; 
ρ_{a}  is  the unit mass of steel, from section 3 [kg/n^{3}]. 
k_{sh} = 0.9 [A_{m}/V]_{b}/[A_{m}/V] (4.26a)
where:
[A_{m}/V]_{b}  is  box value of the section factor 
In all other cases, the value of k_{sh} should be taken as:
k_{sh} = [A_{m}/V]_{b}/[A_{m}/V] (4.26b)
37NOTE (1): For cross sections with a convex shape (e.g. rectangular or circular hollow sections) fully embedded in fire, the shadow effect does not play role and consequently the correction factor k_{sh} equals unity.
NOTE (2): Ignoring the shadow effect (i.e.: k_{sh} = 1), leads to conservative solutions.
NOTE: Some expressions for calculating design values of the section factor A_{m}/V for unprotected steel members are given in table 4.2.
Open section exposed to fire on all sides: 
Tube exposed to fire on all sides: A_{m}/V = 1/t 
Open section exposed to fire on three sides: 
Hollow section (or welded box section of uniform thickness) exposed to fire on all sides: 
Isection flange exposed to fire on three sides: A_{m}/V = (b + 2t_{f})/(bt_{f}) 
Welded box section exposed to fire on all sides: 
Angle exposed to fire on all sides: A_{m}/V = 2/t 
Isection with box reinforcement, exposed to fire on all sides: 
Flat bar exposed to fire on all sides: A_{m}/V = 2(b + t)/(bt) 
Flat bar exposed to fire on three sides: A_{m}/V = (b + 2t)/(bt) 
with:
where:
A_{p}/V  is  the section factor for steel members insulated by fire protection material; 
A_{P}  is  the appropriate area of fire protection material per unit length of the member [m^{2}/m]; 
V  is  the volume of the member per unit length [m^{3}/m]; 
c_{a}  is  the temperature dependant specific heat of steel, from section 3 [J/kgK]; 
c_{p}  is  the temperature independent specific heat of the fire protection material [J/kgK]; 
d_{p}  is  the thickness of the fire protection material [m]; 
Δt  is  the time interval [seconds]; 
θ_{a,t}  is  the steel temperature at time t[°C]; 
θ_{g,t}  is  the ambient gas temperature at time t[°C]; 
Δθ_{g,t}  is  the increase of the ambient gas temperature during the time interval Δt[K]; 
λ_{p}  is  the thermal conductivity of the fire protection system [W/mK]; 
ρ_{a}  is  the unit mass of steel, from section 3 [kg/m^{3}]; 
ρ_{p}  is  the unit mass of the fire protection material [kg/m^{3}]. 
NOTE: Some design values of the section factor A_{p}/V for insulated steel members are given in table 4.3.
Sketch  Description  Section factor (A_{p}/V) 

Contour encasement of uniform thickness  
Hollow encasement of uniform thickness)^{1}  
Contour encasement of uniform thickness, exposed to fire on three sides  
Hollow encasement of uniform thickness, exposed to fire on three sides)^{1}  
)^{1} The clearance dimensions c_{1} and c_{2} should not normally exceed h/4 
provided in both cases that there is a gap between the heat screen and the member. They do not apply if the heat screen is in direct contact with the member.
[normative]
σ_{a} = 50(f_{u,θ} − f_{y,θ}) ε + 2f_{y,θ} − f_{u,θ} (A. 1a)
σ_{a} = f_{u,θ} (A. 1b)
σ_{a} = f_{u,θ}[l − 20(ε − 0,15)] (A.1c)
σ_{a} = 0,00 (A. 1d)
where:
f_{u,θ}  is  the ultimate strength at elevated temperature, allowing for strainhardening. 
NOTE: The alternative stressstrain relationship for steel, allowing for strain hardening, is illustrated in figure A.1.
fu,θ = 1,25f_{y,θ} (A.2a)
f_{u,θ} = f_{y,θ}(2 − 0,0025 θ_{a}) (A.2b)
f_{u, θ} = f_{y,θ} (A.2c)
NOTE: The variation of the alternative stressstrain relationship with temperature is illustrated in figure A.2.
Figure A.1: Alternative stressstrain relationship for steel allowing for strainhardening
Figure A.2: Alternative stressstrain relationships for steel at elevated temperatures, allowing for strain hardening
46[normative]
σT_{m}^{4} + αT_{m} = ΣI_{z} + ΣI_{f} + 293α (B.1)
where:
σ  is  the Stefan Boltzmann constant [56,7 × 10^{−12} kW/m^{2}K^{4}]; 
α  is  the convective heat transfer coefficient [kW/m^{2}K]; 
I_{z}  is  the radiative heat flux from a flame [kW/m^{2}]; 
I_{f}  is  the radiative heat flux from an opening [kW/m^{2}]. 
Figure B.1: Member dimensions and faces
48σT_{m}^{4} + αT_{m} = I_{z} + I_{f} + αT_{z} (B.2)
where:
T_{z}  is  the flame temperature [K]; 
l_{z}  is  the radiative heat flux from the flame [kW/m^{2}]; 
I_{f}  is  the radiative heat flux from the corresponding opening [kW/m^{2}]. 
  Columns not engulfed in flame:  see B.2; 
  Beams not engulfed in flame:  see B.3; 
  Columns engulfed in flame:  see B.4; 
  Beams fully or partially engulfed in flame:  see B.5. 
Other cases may be treated analogously, using appropriate adaptations of the treatments given in B.2 to B.5.
I_{f} = ϕ_{f}ε_{f}(1  a_{z})σT_{f}^{4} (B.3)
where:
ϕ_{f}  is  the overall configuration factor of the member for radiative heat transfer from that opening; 
ε_{f}  is  the emissivity of the opening; 
a_{z}  is  the absorptivity of the flames; 
T_{f}  is  the temperature of the fire [K] from annex B of EN 199112. 
where:
ϕ_{f,i}  is  the configuration factor of member face i for that opening, see annex G of EN 199112;  
d_{i}  is  the crosssectional dimension of member face i;  
C_{i}  is  the protection coefficient of member face i as follows:

where:
ϕ_{z}  is  the configuration factor of member face i for that flame, see annex G of EN 199112. 
NOTE: Illustration are given in figure B.2
I_{z} = ϕ_{z}ε_{z}σT_{z}^{4} (B.6)
where:
ϕ_{z}  is  the overall configuration factor of the column for heat from the flame, see B. 1.4; 
ε_{z}  is  the emissivity of the flame, see B.2.2; 
T_{z}  is  the flame temperature [K] from B.2.3. 
NOTE: Illustration are given in figure B.3.
I_{z} = (ϕ_{z,m}ε_{z,m} + ϕ_{z,n}ε_{z,n})σT_{z}^{4} (B.7)
where:
ϕ_{z,m}  is  the overall configuration factor of the column for heat from flames on side m, see B. 1.4; 
ϕ_{z,n}  is  the overall configuration factor of the column for heat from flames on side n, see B. 1.4; 
ε_{z,m}  is  the total emissivity of the flames on side m, see B.2.2; 
ε_{z,n}  is  the total emissivity of the flames on side n, see B.2.2. 
NOTE: Illustration are given in figure B.4.
λ = 2h/3 (B.8a)
λ = x but λ ≤ hx/z (B.8b)
where h, x and z are as given in annex B of EN 199112.
51Figure B.2: Column positions
52Figure B.3: Column opposite opening
53Figure B.4: Column between openings
54where:
m  is  the number of openings on side m; 
n  is  the number of openings on side n; 
λ_{i}  is  the flame thickness for opening i. 
λ_{i} = w_{i} (B.10a)
λ_{i} = w_{i} + 0,4s (B.10b)
where:
w_{i}  is  the width of the opening; 
s  is  the horizontal distance from the centreline of the column to the wall of the fire compartment, see figure B.1. 
l = h/2 (B.11a)
l = 0 (B.11b)
l = sX/x (B.11c)
where X and x are as given in annex B of EN 199112.
I_{z} = ϕ_{z}ε_{z}σT_{z}^{4} (B.12)
where:
ϕ_{z}  is  the overall configuration factor for the flame directly opposite the beam, see B. 1.4; 
ε_{z}  is  the flame emissivity, see B.3.2; 
T_{z}  is  the flame temperature from B.3.3 [K]. 
I_{z} = (ϕ_{z,m}ε_{z,m} + ϕ_{z,n}ε_{z,n})σT_{z}^{4} (B.13)
where:
ϕ_{z,m}  is  the overall configuration factor of the beam for heat from flames on side m, see B.3.2; 
ϕ_{z,n}  is  the overall configuration factor of the beam for heat from flames on side n, see B.3.2; 
ε_{z,m}  is  the total emissivity of the flames on side m, see B.3.3; 
ε_{z,n}  is  the total emissivity of the flames on side n, see B.3.3; 
T_{z}  is  the flame temperature [K] , see B.3.4. 
Figure B.5: Beam not engulfed in flame
57λ = 2h/3 (B.14a)
λ = x but λ ≤ hx/z (B.14b)
where h, x and z are as given in annex B of EN 199112
where:
m  is  the number of openings on side m; 
n  is  the number of openings on side n; 
λ_{i}  is  the width of opening i. 
λ_{i} = w_{i} (B.16a)
λ_{i} = w_{i} + 0,4s (B.16b)
where:
w_{i}  is  the width of the opening; 
s  is  the horizontal distance from the wall of the fire compartment to the point under consideration on the beam, see figure B.5. 
l = h/2 (B.17a)
l = 0 (B.17b)
l = sX/x (B.17c)
where X and x are as given in annex B of EN 199112.
with:
I_{z,1}  =  C_{1} ε_{z,1} σT_{z}^{4} 
I_{z,2}  =  C_{2} ε_{z,2} σT_{z}^{4} 
I_{z,3}  =  C_{3} ε_{z,3} σT_{o}^{4} 
I_{z,4}  =  C_{4} ε_{z,4} σT_{z}^{4} 
where:
I_{z,i}  is  the radiative heat flux from the flame to column face i; 
ε_{z,i}  is  the emissivity of the flames with respect to face i of the column; 
i  is  the column face indicator (1), (2), (3) or (4); 
C_{i}  is  the protection coefficient of member face i, see B. 1.4; 
T_{z}  is  the flame temperature [K]; 
T_{o}  is  the flame temperature at the opening [K] from annex B of EN 199112. 
Figure B.6: Column engulfed in flame
60l = h/2 (B.19a)
l = (λ_{3} + 0,5d_{1})X/x but l ≤ 0,5 hX/z (B.19b)
where h, X, x and z are as given in annex B of EN 199112.
where ε_{z,1}, ε_{z,2} and ε_{z,3} are the emissivities of the flame for column faces 1, 2, and 3.
where:
I_{z,i}  is  the radiative heat flux from the flame to beam face i; 
i  is  the beam face indicator (1), (2), (3) or (4). 
I_{z,1} = C_{1} ε_{z,1} σT_{o}^{4} (B.22a)
I_{z,2} = C_{2} ε_{z,2} σT_{z,2}^{4} (B.22b)
I_{z,3} = C_{3} ε_{z,3} σ(T_{z,1}^{4} + T_{z,2}^{4})/2 (B.22c)
I_{z,4} = C_{4} ε_{z,4} σ(T_{z,1}^{4} + T_{z,2}^{4})/2 (B.22d)
where:
ε_{z,i} is the emissivity of the flame with respect to face i of the beam, see B.5.2; T_{o} is the temperature at the opening [K] from annex B of EN 199112; T_{z,1} is the flame temperature [K] from annex B of EN 199112, level with the bottom of the beam; T_{z,2} is the flame temperature [K] from annex B of EN 199112, level with the top of the beam.
Figure B.7: Beam engulfed in flame
63I_{z,1} = C_{1} ε_{z,1} σT_{o}^{4} (B.23a)
I_{z,2} = 0 (B.23b)
I_{z,3} = (h_{z}/ d_{2}) C_{3} ε_{z,3} σ(T_{z,1}^{4} + T_{x}^{4})/2 (B.23c)
I_{z,4} = (h_{z}/ d_{2}) C_{4} ε_{z,4} σ(T_{z,1}^{4} + T_{x}^{4})/2 (B.23d)
where:
T_{x}  is  the flame temperature at the flame tip [813 K]; 
h_{z}  is  the height of the top of the flame above the bottom of the beam. 
NOTE: Illustrations are given in figure B.7.
I_{z,1} = C_{1} ε_{z,1} σT_{o}^{4} (B.24a)
I_{z,2} = C_{2} ε_{z,2} σT_{z,2}^{4} (B.24b)
I_{z,3} = C_{3} ε_{z,3} σ(T_{z,1}^{4} + T_{z,2}^{4})/2 (B.24c)
I_{z,4} = C_{4} ε_{z,4} σ(T_{z,1}^{4} + T_{z,2}^{4})/2 (B.24d)
I_{z,1} = C_{1} ε_{z,1} σT_{o}^{4} (B.25a)
I_{z,2} = ϕ_{z,2} C_{2} ε_{z,2} σT_{z,2}^{4} (B.25b)
I_{z,3} = ϕ_{z,3} C_{3} ε_{z,3} σ(T_{z,1}^{4} + T_{z,2}^{4})/2 (B.25c)
I_{z,4} = 0 (B.25d)
where ϕ_{z,i} is the configuration factor relative to the upper surface of the flame, for face i of the beam, from annex G of EN 199112.
a_{z} = 1  e^{0,3h} (B.26)
where:
h  is  the height of the opening. See figure B.7b) (height is noted as λ_{1}). 
[informative]
NOTE: For other stainless steels according to EN 199314 the mechanical properties given in 3.2 may be used. The thermal properties may be taken from this annex.
NOTE: For the rules of this standard it is assumed that the heating rates fall within the specified limits.
  slope of linear elastic range, relative to slope at 20°C:  k_{E,θ}  =  E_{a,θ}/ E_{a} 
  proof strength, relative to yield strength at 20 °C:  k_{0,2p,θ}  =  f_{0,2p,θ}/ f_{y} 
  tensile strength, relative to tensile strength at 20°C:  k_{u,θ}  =  f_{u,θ}/ f_{u} 
f_{y,θ} = f_{0,2p,θ} + k_{2%,θ} (f_{u,θ}  f_{0,2p,θ}) (C.1)
  slope at proof strength, relative to slope at 20 °C:  k_{Ect,θ}  =  E_{Ct,θ}/ E_{a} 
  ultimate strain:  ε_{u,θ} 
ρ_{a} = 7850kg/m^{3}
65Figure C.1: Stressstrain relationship for stainless steel at elevated temperatures.
66Steel Temperature θ_{a} 
Reduction factor (relative to E_{a}) for the slope of the linear elastic range k_{E,θ} = E_{a,θ} / E_{a} 
Reduction factor (relative to f_{y}) for proof strength k_{0,2p,θ} = f_{0,2p,θ}/ f_{y} 
Reduction factor (relative to f_{u}) for tensile strength k_{u,θ} = f_{u,θ}/ f_{u} 
Factor for determination of the yield strength f_{y,θ} k_{2%,θ} 
Grade 1.4301  
20  1,00  1,00  1,00  0,26 
100  0,96  0,82  0,87  0,24 
200  0,92  0,68  0,77  0,19 
300  0,88  0,64  0,73  0,19 
400  0,84  0,60  0,72  0,19 
500  0,80  0,54  0,67  0,19 
600  0,76  0,49  0,58  0,22 
700  0,71  0,40  0,43  0,26 
800  0,63  0,27  0,27  0,35 
900  0,45  0,14  0,15  0,38 
1000  0,20  0,06  0,07  0,40 
1100  0,10  0,03  0,03  0,40 
1200  0,00  0,00  0,00  0,40 
Grade 1.4401 / 1.4404  
20  1,00  1,00  1,00  0,24 
100  0,96  0,88  0,93  0,24 
200  0,92  0,76  0,87  0,24 
300  0,88  0,71  0,84  0,24 
400  0,84  0,66  0,83  0,21 
500  0,80  0,63  0,79  0,20 
600  0,76  0,61  0,72  0,19 
700  0,71  0,51  0,55  0,24 
800  0,63  0,40  0,34  0,35 
900  0,45  0,19  0,18  0,38 
1000  0,20  0,10  0,09  0,40 
1100  0,10  0,05  0,04  0,40 
1200  0,00  0,00  0,00  0,40 
Grade 1.4571  
20  1,00  1,00  1,00  0,25 
100  0,96  0,89  0,88  0,25 
200  0,92  0,83  0,81  0,25 
300  0,88  0,77  0,80  0,24 
400  0,84  0,72  0,80  0,22 
500  0,80  0,69  0,77  0,21 
600  0,76  0,66  0,71  0,21 
700  0,71  0,59  0,57  0,25 
800  0,63  0,50  0,38  0,35 
900  0,45  0,28  0,22  0,38 
1000  0,20  0,15  0,11  0,40 
1100  0,10  0,075  0,055  0,40 
1200  0,00  0,00  0,00  0,40 67 
Grade 1.4003  
20  1,00  1,00  1,00  0,37 
100  0,96  1,00  0,94  0,37 
200  0,92  1,00  0,88  0,37 
300  0,88  0,98  0,86  0,37 
400  0,84  0,91  0,83  0,42 
500  0,80  0,80  0,81  0,40 
600  0,76  0,45  0,42  0,45 
700  0,71  0,19  0,21  0,46 
800  0,63  0,13  0,12  0,47 
900  0,45  0,10  0,11  0,47 
1000  0,20  0,07  0,09  0,47 
1100  0,10  0,035  0,045  0,47 
1200  0,00  0,00  0,00  0,47 
Grade 1.4462  
20  1,00  1,00  1,00  0,35 
100  0,96  0,91  0,93  0,35 
200  0,92  0,80  0,85  0,32 
300  0,88  0,75  0,83  0,30 
400  0,84  0,72  0,82  0,28 
500  0,80  0,65  0,71  0,30 
600  0,76  0,56  0,57  0,33 
700  0,71  0,37  0,38  0,40 
800  0,63  0,26  0,29  0,41 
900  0,45  0,10  0,12  0,45 
1000  0,20  0,03  0,04  0,47 
1100  0,10  0,015  0,02  0,47 
1200  0,00  0,00  0,00  0,47 
Steel Temperature θ_{a} 
Reduction factor (relative to E_{a}) for the slope of the linear elastic range k_{Ect,θ} = E_{ct,θ}/ E_{a} 
Ultimate strain ε_{u,θ} [] 
Grade 1.4301  
20  0,11  0,40 
100  0,05  0,40 
200  0,02  0,40 
300  0,02  0,40 
400  0,02  0,40 
500  0,02  0,40 
600  0,02  0,35 
700  0,02  0,30 
800  0,02  0,20 
900  0,02  0,20 
1000  0,02  0,20 
1100  0,02  0,20 
1200  0,02  0,20 
Grade 1.4401 /1.4404  
20  0,050  0,40 
100  0,049  0,40 
200  0,047  0,40 
300  0,045  0,40 
400  0,030  0,40 
500  0,025  0,40 
600  0,020  0,40 
700  0,020  0,30 
800  0,020  0,20 
900  0,020  0.20 
1000  0,020  0,20 
1100  0,020  0,20 
1200  0,020  0,20 
Grade 1.4571  
20  0,060  0,40 
100  0,060  0,40 
200  0,050  0,40 
300  0,040  0,40 
400  0,030  0,40 
500  0,025  0,40 
600  0,020  0,35 
700  0,020  0,30 
800  0,020  0,20 
900  0,020  0,20 
1000  0,020  0,20 
1100  0,020  0,20 
1200  0,020  0,20 69 
Grade 1.4003  
20  0,055  0,20 
100  0,030  0,20 
200  0,030  0,20 
300  0,030  0,20 
400  0,030  0,15 
500  0,030  0,15 
600  0,030  0,15 
700  0,030  0,15 
800  0,030  0,15 
900  0,030  0,15 
1000  0,030  0,15 
1100  0,030  0,15 
1200  0,030  0,15 
Grade 1.4462  
20  0,100  0,20 
100  0,070  0,20 
200  0,037  0,20 
300  0,035  0,20 
400  0,033  0,20 
500  0,030  0,20 
600  0,030  0,20 
700  0,025  0,15 
800  0,025  0,15 
900  0,025  0,15 
1000  0,025  0,15 
1100  0,025  0,15 
1200  0,025  0,15 
Δl/l = (16 + 4,79 × 10^{−3} θ_{a} − 1,243 × 10^{−6} θ_{a}^{2}) × (θ_{a} −20) 10^{−6} (C.1)
where:
l  is  the length at 20 °C; 
Δl  is  the temperature induced expansion; 
θ_{a}  is  the steel temperature [°C]. 
NOTE: The variation of the thermal elongation with temperature is illustrated in figure C.2.
Figure C.2: Thermal elongation of stainless steel as a function of the temperature
c_{a} = 450 + 0,280 × θ_{a} − 2,91 × 10^{−4} θ_{a}^{2} + 1,34 × 10^{−7} θ_{a}^{3} J/kgK (c.2)
where:
θ_{a} is the steel temperature [°C].
NOTE: The variation of the specific heat with temperature is illustrated in figure C.3.
71Figure C.3: Specific heat of stainless steel as a function of the temperature
λ_{a} = 14,6 + 1,27 × 10^{−2} θ_{a} W/mK (C.3)
where:
θ_{a} is the steel temperature [°C].
NOTE: The variation of the thermal conductivity with temperature is illustrated in figure C.4.
Figure C.4: Thermal conductivity of stainless steel as a function of the temperature
72[informative]
where
k_{b,θ}  is the reduction factor determined for the appropriate bolt temperature from Table D. 1; 
F_{v,Rd}  is the design shear resistance of the bolt per shear plane calculated assuming that the shear plane passes through the threads of the bolt (table 3.4 of EN 199318); 
γ_{M2}  is the partial factor at normal temperature; 
γ_{M,fi}  is the partial factor for fire conditions. 
where
F_{b,Rd}  is determined from table 3.4 EN 19931.8, 
k_{b,θ}  is the reduction factor determined for the appropriate bolt temperature from Table D.1 
where
F_{t,Rd}  is determined from table 3.4 of EN 199318, 
k_{b,θ}  is the reduction factor determined for the appropriate bolt temperature from Table D. l 
Temperature θ_{a} 
Reduction factor for bolts, k_{b,θ} (Tension and shear)  Reduction factor for welds, k_{w,θ} 
20  1,000  1,000 
100  0,968  1,000 
150  0,952  1,000 
200  0,935  1,000 
300  0,903  1,000 
400  0,775  0,876 
500  0,550  0,627 
600  0,220  0,378 
700  0,100  0,130 
800  0,067  0,074 
900  0,033  0,018 
1000  0,000  0,000 
where
k_{w,θ}  is obtained form Table D.1 for the appropriate weld temperature; 
F_{w,Rd}  is determined from clause 4.5.3. EN 199318 
θ_{h} = 0,88θ_{o} [1  0,3(h/D)] (D.5)
where
θ_{h} is the temperature at height h (mm) of the steel beam (Figure D. 1); θ_{o} is the bottom flange temperature of the steel beam remote from the joint; h is the height of the component being considered above the bottom of the beam in (mm); D is the depth of the beam in (mm).
θ_{h} = 0,88θ_{0} (D.6)
θ_{h} = 0,88θ_{o} [1 + 0,2 (1 2h/D)] (D.7)
where
θ_{o} is the bottom flange temperature of the steel beam remote from the joint; h is the height of the component being considered above the bottom of the beam in (mm); D is the depth of the beam in (mm).
Figure D.1 Thermal gradient within the depth of a composite joint
[informative]
  design yield strength , relative to yield strength at 20°C:  k_{p0,2,θ}  =  f_{p0,2,θ}/ f_{y} 
  slope of linear elastic range, relative to slope at 20°C:  k_{E,θ}  =  E_{a,θ}/ E_{a} 
NOTE: These reductions factors are illustrated in figure E.1.
Steel Temperature θ_{a} 
Reduction factor (relative to f_{y}) for the design yield strength of hot rolled and welded class 4 sections k_{0,2p,θ} = f_{p0,2,θ}/f_{y} 
Reduction factor (relative to f_{yb}) for the design yield strength of cold formed class 4 sections k_{p0,2,θ} = f_{p0,2,θ}/f_{yb} 
20 °C  1,00  
100 °C  1,00  
200 °C  0,89  
300 °C  0,78  
400 °C  0,65  
500 °C  0,53  
600 °C  0,30  
700 °C  0,13  
800 °C  0,07  
900 °C  0,05  
1000 °C  0,03  
1100 °C  0,02  
1200 °C  0,00  
NOTE 1: For intermediate values of the steel temperature, linear interpolation may be used.  
NOTE 2: The definition for f_{yb} should be taken from EN 199313 
Figure E.2: Reduction factors for the stressstrain relationship of cold formed and hot rolled class 4 steel sections at elevated temperatures
78 79