Structural Steelwork Eurocodes  Development of

a Trans-National Approach

 

 

 

 

Course: Eurocode 4

Lecture 11a: Introduction to Structural Fire Engineering

Summary:

·         Both steel and concrete suffer a progressive reduction in both strength and stiffness as their temperature increases in fire conditions.  EC3 and EC4 provide material models of stress-strain curves for both materials over an extensive range of temperatures.

·         Fire resistance of structural elements is quoted as the time at which they reach a defined deflection criterion when tested in a furnace heated according to a standard ISO834 time-temperature curve.

·         It is possible to assess the severity of a natural fire as a time-equivalent between its peak temperature and the same temperature on the ISO834 standard curve.

·         The behaviour of elements in furnace tests is very different from that in a building frame, and the only practical way of assessing whole-structure behaviour is to use advanced calculation models.

·         EC3 or EC4 calculation of fire resistance takes account of the loading level on the element.  However the safety factors applied are lower than in those used in strength design.

·         Critical temperature is calculated for all types of member of classes 1, 2 or 3 from a single equation in terms of the load level in fire.  Class 4 sections are universally assumed to have a critical temperature of 350°C.

·         It is possible to calculate the temperature growth of protected or unprotected members in small time increments, in a way which can easily be implemented on a spreadsheet.

Pre-requisites: an appreciation of

·         Simple element design for strength and serviceability according to EC3 and EC4.

·         Framing systems currently used in steel-framed construction, including composite systems.

Notes for Tutors:

·         This material is a general introduction to structural fire engineering, and may be used as the initial stage of a course which leads into EC4 design of composite structures for fire conditions.

·         The lecturer can break up the session with formative exercises at appropriate stages (calculation of member capacities in fire, and fire resistance times are suggested).


Objectives:

After completing the module the student should:

·         Understand that both steel and concrete progressively lose strength and stiffness at elevated temperatures.

·         Understand that fire resistance is quoted in relation to furnace testing using a standard time-temperature curve in which the temperature never reduces, and does not refer to actual survival in a real fire.

·         Know that EC1 specifies three such standard fire curves, of which two refer only to hydrocarbon and external fires, but also provides a method of modelling parametric natural fires if sufficient detail of fire loads, ventilation etc are known.

·         Understand the concept of time-equivalence in rating the severity of a natural fire in terms of the standard fire curve.

·         Know about traditional methods of passive fire protection of steel members.

·         Understand that other strategies may be used in fire engineering design to provide the required fire resistance, including overdesign, selection of framing systems, and use of sprinklers.

·         Understand the principles of the simple design calculations of resistance in fire conditions of beams and columns, and the concept of critical temperature.

·         Understand the methods of calculating the thermal response of protected and unprotected members to increase of atmosphere temperature in a fire.

References:

·         ENV 1991-1: Eurocode 1: Basis of Design and Actions on Structures.  Part 1: Basis of Design.

·         prEN 1991-1-2: Eurocode 1: Basis of Design and Actions on Structures.  Part 1.2: Actions on Structures Exposed to Fire.

·         ENV 1992-1-1: Eurocode 2: Design of Concrete Structures.  Part 1.1: General Rules: General Rules and Rules for Buildings.

·         ENV 1992-1-2: Eurocode 2: Design of Concrete Structures.  Part 1.2: General Rules: Structural Fire Design.

·         prEN 1993-1-1: Eurocode 3: Design of Steel Structures.  Part 1.1: General Rules: General Rules and Rules for Buildings.

·         prEN 1993-1-2: Eurocode 3: Design of Steel Structures.  Part 1.2: General Rules: Structural Fire Design.

·         prEN 1994-1-1: Eurocode 4: Design of Composite Steel and Concrete Structures.  Part 1.1: General Rules: General Rules and Rules for Buildings.

·         ENV 1994-1-2: Eurocode 4: Design of Composite Steel and Concrete Structures.  Part 1.2: General Rules: Structural Fire Design.

·         EN yyy5: Method of Test for the Determination of the Contribution to Fire Resistance of Structural Members.


Contents:

1              Introduction                                                                                                                                         

2              Temperatures in fires                                                                                                                            

3              Behaviour of beams and columns in furnace tests                                                                          

4              Fire protection methods                                                                                                                       

5              Basic structural fire resistant design of members                                                                             

5.1       Notation                                                                                                                                     

5.2       Loadings                                                                                                                                  

5.3       Basic principles of fire resistant design                                                                              

6              Material properties                                                                                                                              

6.1           Mechanical properties                                                                                                        

6.1.1       Steel strengths                                                                                                     

6.1.2       Concrete strengths                                                                                              

6.2           Thermal properties                                                                                                              

6.2.1       Thermal expansion of steel and concrete                                                         

6.2.2       Other relevant  thermal properties of steel                                                       

6.2.3       Other relevant  thermal properties of concrete                                                

7                              Thermal analysis                                                                                                                  

7.1          Unprotected steel sections                                                                                                

7.2           Steel sections with passive protection                                                                            

8              Concluding Summary                                                                                                                          

 

 

1      

 

 
Introduction

Any structure must be designed and constructed so that, in the case of fire, it satisfies the following requirements:

·         The load-bearing function of the structure must be maintained during the required time,

·         The development and spread of fire and smoke within the building  is restricted,

·         The spread of the fire to adjacent buildings is restricted,

·         People within the building must be able to leave the area safely or to be protected by other means such as refuge areas,

·         The safety of fire fighters is assured.

 

 

 

 

EC4 Part 1.2

 

 

 

 

 

 

 

 

 

 

2       Temperatures in fires

A real fire in a building grows and decays in accordance with the mass and energy balance within the compartment in which it occurs (Fig. 1).  The energy released depends upon the quantity and type of fuel available, and upon the prevailing ventilation conditions. 

Figure 1      Phases of a natural fire, comparing atmosphere temperatures with the ISO834 standard fire curve

It is possible to consider a real fire as consisting of three phases, which may be defined as growth, full development and decay.  The most rapid temperature rise occurs in the period following flashover, which is the point at which all organic materials in the compartment spontaneously combust.

Fire resistance times specified in most national building regulations relate to test performance when heated according to an internationally agreed atmosphere time-temperature curve defined in ISO834 (or Eurocode 1 Part 1.2), which does not represent any type of natural building fire.  It is characterised by an atmosphere temperature which rises continuously with time, but at a diminishing rate (Fig. 2).  This has become the standard design curve which is used in furnace testing of components.  The quoted value of fire resistance time does not therefore indicate the actual time for which a component will survive in a building fire, but is a like-against-like comparison indicating the severity of a fire which the component will survive.

Figure 2         Atmosphere temperature for ISO834 standard fire

Where the structure for which the fire resistance is being considered is external, and the atmosphere temperatures are therefore likely to be lower at any given time (which means that the temperatures of the building materials will be closer to the corresponding fire temperatures), a similar “External Fire” curve may be used.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC1 Part 1.2

4.2.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.2.3

 

In cases where storage of hydrocarbon materials makes fires extremely severe a “Hydrocarbon Fire” curve is also given.  These three “Nominal” fire curves are shown in Fig. 3.

Figure 3      EC1 Part 1.2 nominal fire curves compared with a parametric fire

Any of the normal means of establishing fire resistance times (prescriptive rules, tabulated data or calculation models) may be used against these curves.

An alternative method to the use of fire resistance times related to nominal fire curves, which may only be used directly with fire resistance calculation models, is to attempt to model a natural fire using a “parametric” fire curve for which equations are provided in EC1 Part 1.2.  This enables fairly simple modelling of fire temperatures in the heating and cooling phases of the post-flashover fire (the initial growth phase is not addressed), and the time at which the maximum temperature is attained.  It is necessary to have data on the properties (density, specific heat, thermal conductivity) of the materials enclosing a compartment, the fire load (fuel) density and ventilation areas when using these equations.  They are limited in application to compartments of up to 100m2 with mainly cellulosic (paper, wood etc ...) fire loads. 

4.2.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC1 Part 1.2

Annex A

 

 

It may be advantageous to the designer to use parametric curves in cases where the density of combustible materials is low, where using the nominal fire curves is unnecessarily conservative. 

In using a parametric curve the concept known as ‘equivalent time’ can be used both to compare the severity of the fire in consistent terms and to relate the resistance times of structural elements in a real fire to their resistance in the standard fire.  The principle is shown in Fig. 4.

Figure 4         Time-equivalent severity of natural fires

This is useful in applying calculation models which are based on the standard fire heating curve, but the important aspect of using parametric fire curves and the calculated structure temperatures which come from these is that they represent an absolute test of structural fire resistance.  The comparison is between the maximum temperature reached by the structure and its critical temperature, rather than an assessment of the way it would perform if it were possible to subject it to a standard fire time-temperature curve based on furnace testing.

3       Behaviour of beams and columns in furnace tests

Furnace testing using the standard time-temperature atmosphere curve is the traditional means of assessing the behaviour of frame elements in fire, but the difficulties of conducting furnace tests of representative full-scale structural members under load are obvious. The size of furnaces limits the size of the members tested, usually to less than 5m, and if a range of load levels is required then a separate specimen is required for each of these.  Tests on small members may be unrepresentative of the behaviour of larger members.

Figure 5  Typical beam fire test

A further serious problem with the use of furnace tests in relation to the behaviour of similar elements in structural frames is that the only reliable support condition for a member in a furnace test is simply supported, with the member free to expand axially.   When a member forms part of a fire compartment surrounded by adjacent structure which is unaffected by the fire its thermal expansion is resisted by restraint from this surrounding structure.

 

 

EC1 Part 1.2

Annex D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EN yyy5

 

This is a problem which is unique to the fire state, because at ambient temperatures structural deflections are so small that axial restraint is very rarely an issue of significance.  Axial restraint can in fact work in different ways at different stages of a fire; in the early stages the restrained thermal expansion dominates, and very high compressive stresses are generated.  However, in the later stages when the weakening of the material is very high the restraint may begin to support the member by resisting pull-in.  Furnace tests which allow axial movement cannot reproduce these restraint conditions at all; in particular, in the later stages a complete collapse would be observed unless a safety cut-off criterion is applied.  In fact a beam furnace test is always terminated at a deflection of not more than span/20 for exactly this reason.

Only recently has any significant number of fire tests been performed on fire compartments within whole structures.  Some years may pass before these full-scale tests are seen to have a real impact on design codes.  In fact full-scale testing is so expensive that there will probably never be a large volume of documented results from such tests, and those that exist will have the major function of being used to validate numerical models on which future developments of design rules will be based.  At present, Eurocodes 3 and 4 allow for the use of advanced calculation models, but their basic design procedures for use in routine fire engineering design are still in terms of isolated members and fire resistance is considered mainly in terms of a real or simulated furnace test.

4       Fire protection methods

In general for composite steel and concrete structures can be used the same fire protection methods as for steel structures.

This may be in alternative forms:

·         Boarding (plasterboard or more specialised systems based on mineral fibre or vermiculite) fixed around the exposed parts of the steel members.  This is fairly easy to apply and creates an external profile which is aesthetically acceptable, but is inflexible in use around complex details such as connections.  Ceramic fibre blanket may be used as a more flexible insulating barrier in some cases.

·         Sprays which build up a coating of prescribed thickness around the members.  These tend to use vermiculite or mineral fibre in a cement or gypsum binder.  Application on site is fairly rapid, and does not suffer the problems of rigid boarding around complex structural details.  It can, however, be extremely messy, and the clean-up costs may be high.  Since the finish produced tends to be unacceptable in public areas of buildings these systems tend to be used in areas which are normally hidden from view, such as beams and connections above suspended ceilings. They are sometimes susceptible to cracking and shrinkage.

·         Intumescent paints, which provide a decorative finish under normal conditions, but which foam and swell when heated, producing an insulating char layer which is up to 50 times as thick as the original paint film.  They are applied by brush, spray or roller, and must achieve a specified thickness which may require several coats of paint and measurement of the film thickness.

All of these methods are normally applied as a site operation after the main structural elements are erected.  This can introduce a significant delay into the construction process, which increases the cost of construction to the client.  The only exception to this is that some systems have recently been developed in which intumescents are applied to steelwork at the fabrication stage, so that much of the site-work is avoided.  However, in such systems there is clearly a need for a much higher degree than usual of resistance to impact or abrasion.

These methods can provide any required degree of protection against fire heating of steelwork, and can be used as part of  a fire engineering approach.  However traditionally thicknesses of the protection layers have been based on manufacturers’ data aimed at the relatively simplistic criterion of limiting the steel temperature to less than 550°C at the required time of fire resistance in the ISO834 standard fire.  Fire protection materials are routinely tested for insulation, integrity and load-carrying capacity in ISO834 furnace test. Material properties for design are determined from the results by semi-empirical means.

 

 

Open steel sections fully or partially encased in concrete, and hollow steel sections filled with concrete, generally do not need additional fire protection.  In fire the concrete acts to some extent as a heat-sink as well as an insulator, which slows the heating process in the steel section. 

The most recent design codes are explicit about the fact that the structural fire resistance of a member is dependent to a large extent on its loading level in fire, and also that loading in the fire situation has a very high probability of being considerably less than the factored loads for which strength design is performed.  This presents designers with another option which may be used alone or in combination with other measures.  A reduction in load level by selecting composite steel and concrete members which are stronger individually than are needed for ambient temperature strength, possibly as part of a strategy of standardising sections, can enhance the fire resistance times, particularly for beams.  This can allow unprotected or partially protected beams to be used.

The effect of loading level reduction is particularly useful when combined with a reduction in exposed perimeter by making use of the heat-sink effects of the supported concrete slab and concrete full or partial encasement. The traditional downstand beam (Fig. 6a)) gains some advantage over complete exposure by having its top flange upper face totally shielded by the slab; beams with concrete encasement (Fig. 6b)) provide high fire resistance (up to 180´), but their big disadvantage are complicated constructions of joints and the need of sheeting. Better solution is to use steel beams with partial concrete encasement (Fig. 6c)). Concrete between flanges reduces the speed of heating of the profile's web and upper flange, contributes to the load bearing resistance, when lower part of the steel beam loses its strength very quickly during the fire. The big advantage is that the partial encasement of the beam can be realised in the shop without the use of sheeting, the beam is concreted in stages in the side way position. The construction of joints is always very simple, typical joint types in common use in steel structures can be adopted also here.

The recent innovation of “Slimflor” beams (Fig. 6d)), in which an unusually shallow beam section is used and the slab is supported on the lower flange, either by pre-welding a plate across this flange or by using an asymmetric steel section, leaves only the lower face of the bottom flange exposed.

(a)                                (b)                                   (c)                          ( d)

Figure 6  Inherent fire protection to steel beams

Alternative fire engineering strategies are beyond the scope of this lecture, but there is an active encouragement to designers in the Eurocodes to use agreed and validated advanced calculation models to analyse the behaviour of the whole structure or sub-assemblies. The clear implication of this is that designs which can be shown to gain fire resistance overall by providing alternative load paths when members in a fire compartment have individually lost all effective load resistance are perfectly valid under the provisions of these codes.  This is a major departure from the traditional approach based on the fire resistance in standard tests of each component.  The preambles to Parts 1-2 of both Eurocodes 3 and 4 also encourage the use of integrated fire strategies, including the use of combinations of active (sprinklers) and passive protection. However it is acknowledged that allowances for sprinkler systems in fire resistant design are at present a matter for national Building Regulations.

5       Basic structural fire resistant design of members

Details of Eurocode structural fire resistance calculations are given in the appropriate articles on EC3 and EC4, together with an example design calculation using the simple calculation models, and so this section concentrates on the principles of these methods rather than their detail.

5.1   Notation

Eurocodes use a very systematic notation in which different symbols are used for general and particular versions of parameters.  For example an “effect of an action” is denoted in general terms as E in establishing a principle; in particular members this might become the axial force N or the internal bending moment M.  Subscripts denoting different attributes of a parameter may be grouped, using dots as separators, as in Efi.d.t which denotes the design value of the effect of an action in fire, at the required time of resistance.  Commonly used notations in the fire engineering parts of Eurocodes 1, 3 and 4 are:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

1.4

 

E =

effect of actions

 

G =

permanent action

 

Q =

variable action

 

Rfi =

load-bearing resistance

 

tfi =

standard fire resistance time of a member

 

tfi.requ =

standard fire resistance time nominal requirement

 

q =

temperature

 

qcr =

critical temperature of a member

 

g =

partial safety factor

 

y =

load combination factor

 

and the following subscript indices may be used alone or in combination:

 

 

A =

accidental design situation

 

cr =

critical value

 

fi =

relevant to fire design

 

d =

design value

 

q =

associated with certain temperature (may be replaced by value)

 

k =

characteristic value

 

t =

at certain fire exposure time (may be replaced by value)

 

1, 2 .. =

ranking order for frequency of variable actions

 

5.2   Loadings

Eurocode 1 Part 1.2 presents rules for calculating design actions (loadings) in fire, which recognise the low probability of a major fire occurring simultaneously with high load intensities.  The normal Eurocode classification of loads is as permanent and variable; in fire the characteristic permanent actions (dead loading) are used unfactored (gGA=1,0) while the principal characteristic variable action (imposed loading) is factored down by a combination factor y1.1 whose value is between 0,5 and 0,9 depending on the building usage.  The “reduction factor” or “load level for fire design” can be defined either as

 (loading in fire as a proportion of ambient-temperature design resistance),

which is relevant when global structural analysis is used, or

 (loading in fire as a proportion of ambient-temperature factored design load),

which is the more conservative, and is used in simplified design of individual members, when only the principal variable action is used together with the permanent action.  This may be expressed in terms of the characteristic loads and their factors as

                                                                                                          (1)

Typical values of the safety factors specified in Eurocode 1 are:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

Fig. 2.1

 

gGA

= 1,0

(Permanent loads: accidental design situations)

 

 

y1.1

= 0,5

(Combination factor: variable loads, office buildings)

 

 

gG

= 1,35

(Permanent loads: strength design)

 

 

gQ.1

= 1,5

(Variable loads: strength design)

 

 

5.3   Basic principles of fire resistant design

Structural fire-resistant design of a member is concerned with establishing that it satisfies the requirements of national building regulations over the designated time period when subjected to the appropriate nominal fire curve.  This can be expressed in three alternative ways:

·         The fire resistance time should exceed the requirement for the building usage and type when loaded to the design load level and subjected to a nominal fire temperature curve:

·         The load-bearing resistance of the element should exceed the design loading when it has been heated for the required time in the nominal fire:

·         The critical temperature of an element loaded to the design level should exceed the design temperature associated with the required exposure to the nominal fire:

6       Material properties

6.1   Mechanical properties

6.1.1     Steel strengths

Most construction materials suffer a progressive loss of strength and stiffness as their temperature increases.  For steel the change can be seen in EC3/4 stress-strain curves (Fig. 7) at temperatures as low as 300°C.  Although melting does not happen until about 1500°C, only 23% of the ambient-temperature strength remains at 700°C.  At 800°C this has reduced to 11% and at 900°C to 6%.

Figure 7     Reduction of stress-strain properties with temperature for S275 steel (EC4 curves)

Figure 8     EC3 Strength reduction for structural steel (SS) and cold-worked reinforcement (Rft) at high temperatures

These are based on an extensive series of tests, which have been modelled by equations representing an initial linear elastic portion, changing tangentially to a part-ellipse whose gradient is zero at 2% strain.  When curves such as these are presented in normalised fashion, with stresses shown as a proportion of ambient-temperature yield strength, the curves at the same temperatures for S235, S275 and S355 steels are extremely close to one another.  It is therefore possible to use a single set of strength reduction factors (Fig. 8) for all three grades, at given temperatures and strain levels.  In Eurocodes 3 and 4 strengths corresponding to 2% strain are used in the fire engineering design of all types of structural members.

Hot-rolled reinforcing bars are treated in Eurocode 4 in similar fashion to structural steels, but cold-worked reinforcing steel, whose standard grade is S500, deteriorates more rapidly at elevated temperatures than do the standard grades.  Its strength reduction factors for effective yield and elastic modulus are shown on Fig. 8.  It is unlikely that reinforcing bars or mesh will reach very high temperatures in a fire, given the insulation provided by the concrete if normal cover specifications are maintained.  The very low ductility of S500 steel (it is only guaranteed at 5%) may be of more significance where high strains of mesh in slabs are caused by the progressive weakening of supporting steel sections.

 

6.1.2     Concrete strengths

Concrete also loses strength properties as its temperature increases (Fig. 9), although a variety of parameters contribute to the relevant characteristics of any given concrete element in the structure.

The stress-strain curves at different temperatures for concrete have a significant difference in form from those for steel.  The curves all have a maximum compressive strength, rather than an effective yield strength, which occurs at strains which progressively increase with temperature, followed by a descending branch. Tensile strength for all concretes is normally considered to be zero. As is normal in Eurocodes, alternative material constitutive laws may be used provided that they are supported by experimental evidence.

 

Figure 9     EC4 stress-strain- temperature curves for normal-weight and lightweight concrete

For normal-weight concretes (density around 2400 kg/m3) only the lower range of strength values, corresponding to the siliceous type which is shown in Fig. 10, are tabulated in Eurocode 4 Part 1.2.  For calcareous-aggregate concrete these are also used, being inherently conservative values.  Where more detail is required designers are referred to Eurocode 2 Part 1.2.

Figure 10   EC4 Strength reduction for normal-weight siliceous concrete and lightweight concrete at elevated temperatures

Lightweight concretes are defined as those within the density range 1600-2000 kg/m3.  Although in practice they may be created using different forms of aggregate, they are treated in EC4 Part 1.2 as if they degrade similarly with temperature.  Hence the single set of strength reduction factors (Fig. 10) for lightweight concrete is again necessarily on the conservative side.

It is important to notice that concrete, after cooling down to ambient temperature does not regain its initial compressive strength.  Its residual strength fc,q,20ºC depends on the maximum temperature which was reached during the heating phase (Fig. 11).

Figure 11    Proportional loss of residual compressive strength fc,q,20ºC after heating to different maximum temperatures

During the cooling phase it is possible to define the corresponding compressive cylinder strength for a certain temperature q (qmax > q > 20ºC) by linear interpolation between fc.q.max and fc.q.20ºC   in the way illustrated in Fig. 12.

Figure 12   Stress-strain relationships of concrete C20/25 at 400ºC during the heating and cooling phases, after reaching maximum temperature 700ºC

Concrete has a lower thermal conductivity than steel and is therefore a relatively good insulator to reinforcement or embedded parts of sections.  Fire resistance of reinforced concrete members tends to be based on the strength reduction of reinforcement, which is largely controlled by the cover specification.  However, concrete is affected by spalling, which is a progressive breaking away of concrete from the fire-exposed surface where temperature variation is high, and this can lead to the exposure of reinforcement as a fire progresses.  Its behaviour at elevated temperatures depends largely on the aggregate type used; siliceous (gravel, granite) aggregates tends to cause concrete to spall more readily than calcareous (limestone) aggregates.  Lightweight concrete possesses greater insulating properties than normal-weight concrete.

6.2   Thermal properties

6.2.1     Thermal expansion of steel and concrete

In most simple fire engineering calculations the thermal expansion of materials is neglected, but for steel members which support a concrete slab on the upper flange the differential thermal expansion caused by shielding of the top flange, and the heat-sink function of the concrete slab, cause a “thermal bowing” towards the fire in the lower range of temperatures.  When more advanced calculation models are used, it is also necessary to recognise that thermal expansion of the structural elements in the fire compartment is resisted by the cool structure outside this zone, and that this causes behaviour which is considerably different from that experienced by similar members in unrestrained furnace tests.  It is therefore necessary at least to appreciate the way in which the thermal expansion coefficients of steel and concrete vary with respect to one another and with temperature.  They are shown in Fig. 13; perhaps the most significant aspect to note is that the thermal expansion coefficients of steel and concrete are of comparable magnitudes in the practical range of fire temperatures. 

Figure 13    Variation of Eurocode 3/4 thermal expansion coefficients of steel and concrete with temperature

Concrete is unlikely to reach the 700°C range at which its thermal expansion ceases altogether, whereas exposed steel sections will almost certainly reach the slightly higher temperature range within which a crystal-structure change takes place and the thermal expansion temporarily stops.

6.2.2     Other relevant  thermal properties of steel

Two additional thermal properties of steel affect its heating rate in fire.  Thermal conductivity is the coefficient which dictates the rate at which heat arriving at the steel's surface is conducted through the metal.  A simplified version of the change of conductivity with temperature, defined in EC3, is shown in Fig. 14.  For use with simple design calculations the constant conservative value of 45W/m°K is allowed. 

Figure 14 Eurocode 3 representations of the variation of thermal conductivity of steel with temperature

The specific heat of steel is the amount of heat which is necessary to raise the steel temperature by 1°C.  This varies to some extent with temperature across most of the range, as is shown in Fig. 15, but its value undergoes a very dramatic change in the range 700-800°C.  The apparent sharp rise to an "infinite" value at about 735°C is actually an indication of the latent heat input needed to allow the crystal-structure phase change to take place.  Once again, when simple calculation models are being used a single value of 600J/kg°K is allowed, which is quite accurate for most of the temperature range but does not allow for the endothermic nature of the phase change.

Figure 15  Variation of the specific heat of steel with temperature

6.2.3     Other relevant  thermal properties of concrete

The thermal conductivity lc of concrete depends on the thermal conductivity of its individual components and also on moisture content, aggregate type, mixture proportion and cement type. The aggregate type has the most significant influence on the conductivity of dry concrete.  However, as the concrete's moisture content increases its thermal conductivity increases.

Figure 16 Thermal conductivity of normal-weight (NC) and light-weight concrete (LC) as a function of temperature

EC4 gives the thermal conductivity development with temperature for both normal and light-weight concrete (Fig. 16). In simple calculation models for normal-weight concrete a constant value of thermal conductivity may be used.

The specific heat of concrete cc is also influenced by gravel type, mixture rate and moisture content.  Gravel type is significant particularly in the case of concrete with calcareous aggregate, for which the specific heat increases suddenly because of chemical changes at a temperature of about 800°C.  The moisture content is significant at temperatures up to 200°C, because the specific heat of wet concrete is twice that for dry concrete.

EC4 gives simple equations for the variation of the specific heat with temperature (Fig. 17).  However in simple calculation models a constant value may be used.  Values of specific heat  for wet concrete are given for several values of moisture content in Table 1.

 

Figure 17 Specific heat of normal-weight (NC) and light-weight concrete (LC) as a function of temperature

 

 

 

 

EC1 Part 1.2

Section 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC3 Part 1.2

3.2

Table 3.1

Fig. 3.1

EC4 Part 1.2

3.2.1; Annex A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC3 Part 1.2

Fig. 3.2

EC4 Part 1.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

Fig. B.1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

3.2.2

Annex B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Annex C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC3 Part 1.2

3.3.1.1

EC4 Part 1.2

3.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

3.2.2;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC3 Part 1.2

3.3.1.3

EC4 Part 1.2

3.3.1; 3.3.2; 3.3.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

3.3.2, 3.3.3

 

 

 

 

Water content [%]

 [J/kg°K]

 

 

 

 

2

1875

 

 

 

 

4

2750

 

 

 

 

10

5600

 

 

 

Table 1. Variation of concrete specific heat with moisture content.

 

 

7       Thermal analysis

The same calculation rules are given in both EC3 Part 1.2 and EC4 Part 1.2 for calculating the temperatures of unprotected and protected steel beams.  The temperatures of the lower and upper flanges may differ considerably, so it is very important that they should be calculated properly in order to obtain an accurate estimate of the bending moment resistance of the composite section.

The heat transfer to the member is predominantly by two mechanisms; radiation and convection.  Since the rate of heating by both mechanisms is dependent at any time on the temperatures of both the fire atmosphere and the member, the member temperature is related to time via a fairly complex differential equation.  This is dealt with in Eurocode 3 by linearising the temperature increments over small time steps, which is impractical for hand calculation but is ideal for setting up in spreadsheet software. 

7.1   Unprotected steel sections

For an unprotected steel section the temperature increase Dqa.t in a small time interval Dt (up to 5 seconds) is given by the net amount of heat which the section acquires during this time:

                                                                                                          (2)

in which

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EC4 Part 1.2

4.3.3.2

 

 

 

 =

specific heat of steel

 

 

 =

density of steel

 

 =

a “Section Factor” composed of

 

 

 =

exposed surface area of member per unit length (Fig. 22)

 

 

V  =

volume of member per unit length

 

hnet.d =

design value of net heat flux per unit area

 

The net heat flux has radiative and convective components, of which the radiative is:

                                                            (3)

in which, apart from the Stefan-Boltzmann constant of 5,67x10-8,

EC1 Part 1.2

4.1

 

 =

configuration factor (can be set to 1.0 in the absence of data)

 

 

=

resultant emissivity = emissivity of fire compartment x emissivity of member surface (0,8 . 0,625=0,5 if no specific data)

 

 

 =

environment and member surface temperatures

 

 

and the convective heat flux is:

                                                                                                                 (4)

4.1

 

in which  =

convective heat transfer coefficient (subject to NAD values, but 25W/m2°K used for Standard or External Fire curves, 50W/m2°K for Hydrocarbon Fire)

 

 

 =

environment (gas) and member surface temperatures

 

 

When forming the net heat flux from these, each may be factored in order to account for differences in national practice in fire testing, but usually they are simply added together.

The “Section Factor” Am/V uses the exposed perimeter in calculating an appropriate value of Am and this means the actual surface which is exposed to radiation and convection. In determination of the Section Factor for the case of a composite slab with profiled steel sheets the three-sided exposure case can be considered, provided that at least 90% of the upper flange is covered by the steel sheet.  If this is not the case then void-fillers made from appropriate insulating material must be used.

7.2   Steel sections with passive protection

For members with passive protection the basic mechanisms of heat transfer are identical to those for unprotected steelwork, but the surface covering of material of very low conductivity induces a considerable reduction in the heating rate of the steel section.  Also, the insulating layer itself has the capacity to store a certain, if small, amount of heat.  It is acceptable to assume that the exposed insulation surface is at the fire atmosphere temperature (since the conduction away from the surface is low and very little of the incident heat is used in raising the temperature of the surface layer of insulation material).

 

 

 

 

Figure 18  Estimation of the section factors of unprotected and protected steel beams

 

 

The calculation of steel temperature rise Dqa.t in a time increment Dt (up to 30 s) is now concerned with balancing the heat conduction from the exposed surface with the heat stored in the insulation layer and the steel section:

 but        (5)

in which the relative heat storage in the protection material is given by the term

                                                                                                                     (6)

in which

 

EC4 Part 1.2

4.3.3.2

 

 

section factor for protected steel member, where Ap is generally the inner perimeter of the protection material (Fig. 18)

 

 

specific heats of steel and protection material

 

 

thickness of fire protection material

 

 

temperatures of steel and furnace gas at time t

 

 

increase of gas temperature during the time step Dt

 

 

thermal conductivity of the fire protection material

 

 

densities of steel and fire protection material

 

 

Fire protection materials often contain a certain percentage of moisture which evaporates at about 100°C, with considerable absorption of latent heat.  This causes a “dwell” in the heating curve for a protected steel member at about this temperature while the water content is expelled from the protection layer.  The incremental time-temperature relationship above does not model this effect, but this is at least a conservative approach.  A method of calculating the dwell time is given, if required, in the European pre-standard for fire testing.

 

 

 

 

 

 

EN yyy5

 

8       Concluding Summary

·         Both steel and concrete suffer a progressive reduction in both strength and stiffness as their temperature increases in fire conditions.  EC3 and EC4 provide material models of stress-strain curves for both materials over an extensive range of temperatures.

·         Fire resistance of structural elements is quoted as the time at which they reach a defined deflection criterion when tested in a furnace heated according to a standard ISO834 time-temperature curve.

·         It is possible to assess the severity of a natural fire as a time-equivalent between its peak temperature and the same temperature on the ISO834 standard curve.

·         The behaviour of elements in furnace tests is very different from that in a building frame, and the only practical way of assessing whole-structure behaviour is to use advanced calculation models.

·         EC3 or EC4 calculation of fire resistance takes account of the loading level on the element.  However the safety factors applied are lower than in those used in strength design.

·         Critical temperature is calculated for all types of member of classes 1, 2 or 3 from a single equation in terms of the load level in fire.  Class 4 sections are universally assumed to have a critical temperature of 350°C.

·         It is possible to calculate the temperature growth of protected or unprotected members in small time increments, in a way which can easily be implemented on a spreadsheet.