chapter 11- structural fire engineering design

doi: 10.1680/mosd.41448.0169

CONTENTS

11.1 Introduction 169

11.2 Compartment timetemperature response 169

11.3 Heat transfer 174

11.4 Mechanical (structural) response 178

11.5 Conclusion 180

11.6 References 180

ICE Manual of Structural Design: Buildings 2012 Institution of Civil Engineers www.icemanuals.com 169

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11.1 IntroductionThe traditional means of ensuring compliance with the require-ments of the Building Regulations for structural fire safety is to rely on the results from standard fire tests on individual elements or components. At the simplest level structural fire engineering is based on simple prescriptive rules and guidance which ensure sufficient passive fire protection is applied to structural members or that minimum dimensions are satisfied to ensure load-bearing capacity and/or the separating function is maintained for a period corresponding to the recommended fire resistance requirement from the regulatory guidance.

In this way, structural engineers have been involved in fire engineering for many years without necessarily being aware of it and most probably being unaware of the background to the development of the regulations and the guidance that under-pins them. For example, a structural engineer responsible for designing a reinforced concrete framed building will specify the overall dimensions, size and position of reinforcement dependent on the ambient temperature design considerations in terms of loading and environmental conditions. In the vast majority of cases, the structural fire engineering will simply consist of checking in the tables produced in BS 8110 Part 2 to ensure that the design meets the minimum dimensions and minimum depth of cover to the reinforcement for the specified fire resistance period.

Within this simple process there are a large number of impli-cit considerations on the likelihood of a fire occurring: the con-sequences in terms of life safety should a fully developed fire occur, the thermal exposure within the fire compartment and the consequent temperature distribution through the structural member. To a large extent structural fire engineering design simply consists of making explicit decisions rather than relying on the implicit assumptions within the prescriptive approach.

The three-stage approach to structural fire engineering design is illustrated schematically in Figure 11.1.

11.2 Compartment timetemperature responseThe first step in a structural fire engineering design is to evalu-ate an appropriate compartment timetemperature response to be used for the subsequent heat transfer and structural response calculations. This initial process can itself be further subdivided into two important preliminary tasks: the choice of appropriate design fire scenario(s) and the selection based on the design fire scenarios adopted of an appropriate design fire.

11.2.1 Design fire scenario(s)

The appropriate design fire scenarios should be determined on the basis of an overall fire risk assessment taking into account the nature and distribution of fire load within the project and the

Chapter 11

Structural fire engineering designTom Lennon Principal Consultant, BRE Global, UK

The purpose of this chapter is to explain the methodology underpinning the structural fire engineering design process. Structural fire engineering design consists of three basic components: choosing an appropriate design fire, using this information to derive the temperatures of the structural elements and assessing the structural behaviour with respect to the temperatures derived. For each element of the structural fire engineering design process there are a number of options available to the designer depending on the complexity of the project, the state of knowledge with regard to the structural material chosen and the objectives of the fire engineering design strategy. Detailed information on the design methodology in this area is available in the Institution of Structural Engineers Guide to the Advanced Fire Safety Engineering of Structures (2007).

Fire analysis (compartment timetemperature)

Heat Transfer Analysis (determination of material temperatures)

Structural analysis (determination of mechanical response)

Figure 11.1 Three stages of structural fire engineering design

Concept design

170 www.icemanuals.com ICE Manual of Structural Design: Buildings 2012 Institution of Civil Engineers

The principal choice facing the designer at this stage of the process is whether to use a nominal fire curve or a natural fire model to evaluate the compartment timetemperature response. Nominal fires are representative fire curves for the purposes of classification and comparison but bear no relation-ship to the particular characteristics of the building under con-sideration. Natural fires are calculation techniques based on a consideration of the physical parameters specific to a particu-lar building or fire compartment. Figure 11.3 illustrates the options available to the designer when choosing to model com-partment time-temperature behaviour.

11.2.2.1 Nominal fire curves

Nominal or standard fire curves are the simplest and most com-monly adopted means of representing a fire. They have been developed to allow classification and assessment of construc-tion products using commercial furnaces. Although they do not represent real fire scenarios they have been developed from experience of real fires. A number of different curves exist. The choice of curve for a particular situation will depend on the

presence of likely ignition sources and the impact of detection and suppression systems.

The design fire scenarios selected will identify specific com-partment geometries with their own associated fire loads and ven-tilation conditions and should be based on a reasonable worst case scenario. The choice of design fire scenario will dictate the choice of the design fire to be used in subsequent analysis.

To take a simple example, an appropriate design fire sce-nario within a medium rise residential building consisting of a number of separate dwellings would be a fire within a single dwelling bounded by fire resisting construction. Given the pres-ence of sufficient oxygen for combustion, sufficient fire load and an ignition source a fully developed fire within a single dwelling would be one design fire scenario to be considered.

11.2.2 Design fire

For each design fire scenario adopted, a design fire will be cho-sen that represents the likely risk within that area. Normally the design fire is only applied to one fire compartment at a time, i.e. in the example above it would not be normal practice to assume that two dwellings were fully involved in a fire at the same time. The extent of the fire to be considered will, to a large extent, be governed by the compartmentation in place within the building.

This stage of the process involves the selection of an appro-priate model representing the fire within the compartment under consideration. In many cases, the type of occupancy will play a major role in defining the type of model to be used. Given a fire load and an ignition source there are three options in terms of fire development: either (i) the fire is extinguished due to manual or automatic suppression or lack of oxygen, (ii) the fire remains localised due to a lack of oxygen or insufficient fuel load or (iii) the fire becomes fully developed. For the designer, detection and the active intervention of third parties (such as the Fire and Rescue Service) are not taken into account, therefore the chief consideration is to decide if the fire will remain local-ised or grow into a fully developed fire. In terms of structural considerations, the most serious situation is where flashover occurs within the compartment and all combustible materials become involved in the process. Such a situation would require the adoption of a post-flashover fire model.

Combustion behaviour within a fire compartment is a com-plex process involving a mass balance where the energy released from combustion of the fire load is utilised in convective heat flow through openings where hot gases inside the compartment are replaced by incoming cold air, radiated heat flow through the openings and heat losses to the compartment boundaries. For uncontrolled compartment fires this complex process can be simplified into a three phase behaviour characterised by the transition point known as flashover. Compartment fire behav-iour is illustrated schematically in Figure 11.2.

Localised fire models are available in codes and standards but are not considered further here as, for structural fire engi-neering it is the post-flashover situation which represents the most serious threat to structural stability.

Time

FLASHOVER Naturalfire curve

Tem

pera

ture

Ignition - Smouldering Heating Cooling

Standardfire curve

Figure 11.2 Three phase fire behaviour

Available fire models

Nominal (standard) fire curves suitablefor the vast majority of structures

Equivalent time of fire exposure

Parametric curves

Zone models

CFD analysis

Figure 11.3 Available options for modelling fire behaviour in order of increasing complexity

Structural fire engineering design


In addition to the problems associated with the relation-ship between the standard thermal exposure and real fires, a number of difficulties arise in extrapolating the results from standard tests to predict structural behaviour under realis-tic conditions. The geometric limitations of specimen size mean that it is not possible to simulate complicated three-dimensional structural behaviour. No allowance can be made during the test for the beneficial or detrimental effects of restraint to thermal expansion provided by the surrounding cold structure. The nature of the test means that only ideal-ised end conditions can be used and only idealised load levels and distributions are adopted. During a fire some degree of load shedding will take place from the areas affected by fire to the unheated parts of the building. In the standard test, no allowance can be made for alternative load-carrying mecha-nisms or alternative modes of failure that are a function of the building rather than the element of structure. In particu-lar, the standard fire test does not address the important role that connections play in maintaining overall global structural stability.

A reliance on the results from standard tests and, in par-ticular, the use of tabulated values for generic products has retarded our understanding of structural behaviour in fires. Structural fire engineering attempts to go beyond a blind reli-ance on prescriptive guidance, to consider the physical char-acteristics that contribute to fire development and evaluate the material and mechanical response of the structure to the increase in temperature.

Although the standard fire curve is the most well known a number of other nominal curves exist for special circum-stances. These include the external fire curve where the structural element is subject to heating from flames emerg-ing from openings. For situations such as petrochemical plants where the calorific value of combustibles is signifi-cantly higher than the cellulosic material assumed for normal building design a number of hydrocarbon fire curves exist. In recent years a number of high profile tunnel fires have caused great damage and loss of life. In such applications an even more severe exposure than the hydrocarbon curve may be appropriate to simulate the effect of a fire involving large petrol tankers in a confined space. The most onerous exposure has been developed in the Netherlands as the RWS curve which reaches temperatures of 1350C. Other curves include the German RABT curve which achieves a maxi-mum temperature of 1200C.

11.2.2.2 Natural fire models

All of the nominal fire curves discussed above are post-flashover models of fire behaviour under various conditions. They are models loosely based on observed behaviour in real fires but are not based on any physical parameters. Natural fire models are based on the physical parameters that influence fire growth and development and range from simple models for both localised fires and post-flashover fire behaviour to

end-use. Different curves are used for testing and assessment depending on whether the structural element or product is to be used in the construction of a normal building (office, dwelling, etc.), the petrochemical or offshore industry or for tunnels.

The most well known and widely adopted nominal fire curve is the so-called standard fire enshrined in National, European and international standards. The standard fire curve is based on a cellulosic (i.e. wood/paper/fabric) fire within a compartment and is described by the following equation:

g = 20 + 345 log10 (8t + 1) (11.1)As with many other nominal fire curves it is characterised by a steadily increasing temperature and does not incorporate a descending branch or cooling phase.

The standard curve has been adopted throughout the world for a number of reasons: to provide evidence of regulatory compliance; to assist in product development; and to provide a common basis for research into the effect of variables other than temperature. As such it has proved remarkably successful over a long period of time. It has the advantage of familiar-ity for designers, regulators and specifiers. The existence of a large body of test data facilitates the continuing use of the standard curve and enables tabulated data for generic materi-als to be developed. It is simple to use and clearly defined and allows for a direct comparison of the performance of products tested under nominally identical conditions.

However, the standard fire test suffers from a number of drawbacks when any attempt is made to extrapolate test results to performance in real life situations. These drawbacks arise as a consequence of simplistic assumptions regarding the thermal exposure and the support and loading conditions of the test spec-imen. Whilst the standard curve incorporates the transient nature of fire development there is no direct relationship between per-formance in a standard test and the duration of a real fire. This is a source of some confusion as many observers conclude that 60 minutes fire resistance means that the element of structure will survive for 60 minutes in a real fire. In reality, the element of construction may perform satisfactorily for a longer or shorter period depending on the severity and duration of the fire and the boundary conditions and loading present in the building at the time of the fire. The temperature within a furnace is relatively uniform compared to the temperature within a real fire com-partment. Spatial temperature differences (particularly during the growth face) may lead to longitudinal and cross-sectional thermal gradients within structural members that are not present during a furnace test which in turn could lead to deformations not observed during a standard test. For certain forms of con-struction, direct flame impingement during a real fire may have important implications which cannot be observed in a standard test. As mentioned above, a real fire consists of three distinct phases. The relative durations of these three phases may have a significant impact on the performance of elements of structure. Such behaviour cannot be addressed by an ever increasing curve where temperature rises at a decreasing rate with time.

Concept design


widely used is that in the fi re part of Eurocode 1 which is of the form:

t e,d = ( q f,d w f k b ) k c (11.3)

where:

q f,d is the design fi re load density per unit fl oor area (MJ/m ) k b is the conversion factor for the compartment thermal prop-

erties (min.m /MJ) w f is the ventilation factor

k c is a correction factor dependent on the structural material

Detailed guidance is available on the use of the method (Lennon et al ., 2006).

The time equivalent method represents a sort of halfway house between nominal and natural fi re models to describe severity in a language understood by designers, manufactur-ers and regulators. A more rational approach is to consider fi re behaviour purely in relation to the factors that infl uence fi re growth and development independent of any reference to standard test procedures. A number of simplifi ed models exist to calculate the timetemperature response caused by a fi re within a building compartment. The most commonly used and widely validated method is the parametric approach set out in the fi re part of the Eurocode 1 for Actions on Structures. The temperature-time curves in the heating phase are given by:

g = 1325(1 0.324 e 0.2 t * 0.204 e 1.7 t * 0.472 e 19 t * ) (11.4)

where:

g = temperature in the fi re compartment ( C) t* = t. (h) t = time (h)

= [ O / b ] 2 /(0.04/1160) 2 (-) b cb cb c=b c b c b c and should lie between 100 and 2200 (J/m s K) O = opening factor ( / )A hA h( /A h( /( /A h( / Av t( /v t( /( /v t( /( /A h( /v t( /A h( /( /A h( /v t( /A h( / Av tA (m

)

A v = area of ventilation openings (m ) h = height of ventilation openings (m)

A t = total area of enclosure (including openings) (m ) = density of boundary enclosure (kg/m ) c = specifi c heat of boundary enclosure (J/kgK)

= thermal conductivity of boundary (W/mK)

The theory assumes that temperature rise is independent of fi re load. In order to account for the depletion of the fuel or for the active intervention of the Fire and Rescue Service or suppres-sion systems, the duration of the fi re must be considered. This is a complex process and depends on the rate of burning of the material which itself is dependent on the ventilation and the physical characteristics and distribution of the fuel.

advanced methods based on computational fl uid dynamics. The remainder of this section deals with simple post-fl ashover calculation models for establishing compartment time temperature response.

A number of attempts have been made to utilise the simpli-city of the standard fi re curve and to relate actual fi re severity to an equivalent period within a standard test. Time equiva-lence is an extremely useful tool for demonstrating compliance with regulations in a language clearly understood by building control authorities. The basic concept considers equivalent fi re severity in terms of the temperature attained by a struc-tural element within a fi re compartment and the time taken to achieve the same temperature in a standard fi re test. The con-cept is illustrated in Figure 11.4 . Alternative formulations con-sider the normalised heat input from a standard furnace. The vast majority of the research effort into time equivalence has been initiated by the steel industry and the results are therefore largely applicable to protected steel specimens. However, if the data exist, there is no reason why the concept should not be extended to cover other forms of construction.

The concept of time equivalence relates the severity of a real compartment fi re in an actual building to an equivalent period of heating in a standard furnace test. This equivalent period is then compared with the design value of the standard fi re resist-ance of the individual structural members, which must satisfy the following relationship:

t e,d < t ,d (11.2)

where, t e,d is the design value of time equivalence and t ,d is the design value of the fi re resistance of the member. A number of methods are available to calculate time equivalence. The most

Atmosphere (fire)Atmosphere(furnace)

1200

1000

800

600

400

200

00 15 30 45 60 75 90te

Steel (fire)

Tem

pera

ture

[deg

C]

Steel (furnace)

Max. Steel Temp.

Time [mins]

Figure 11.4 Graphical representation of the concept of time equivalence (t e )



limiting values. The temperaturetime curves for the cooling phase are then given by:

g = max 625(t* t*max) for t*max 0.5(h) (11.6)

g = max 250(3 t*max)(t* t*max) for 0.5 < t*max < 2(h) (11.7)

g = max 250(t* t*max) for t*max 2(h) (11.8)The relevant input parameters for the parametric approach are illustrated schematically in Figure 11.5.

The concept of time equivalence and parametric fire expo-sure is illustrated by reference to a simple worked example below.

Time Equivalence Design information:Compartment in 4 storey office buildingFloor area: Af = 6 m 6 m = 36 mDesign fire load density: = 570 MJ/m (80% fractile value

for offices from PD 6688-1-2: 2007)Compartment construction: roof formed from hollowcore

concrete slabs, walls and floor lined with plasterboard

The parametric approach is a relatively straightforward cal-culation ideally suited for modern spreadsheets. It provides a reasonable estimate of the average timetemperature response for a wide range of compartments and represents a major advance compared to a traditional reliance on nominal fires which bear little or no relationship to a realistic fire scenario. The parametric fire curves comprise a heating phase repre-sented by an exponential curve up to a maximum temperature max occurring at a corresponding time of tmax, followed by a linearly decreasing cooling phase.

The maximum temperature in the heating phase occurs at a time given by:

tmax = max[(0.2 103 qt,d / Olim); tlim] (11.5)

where:

qt,d = qf,d Af / At

and tlim = 25 min for a slow fire growth rate, 20 min for a medium fire growth rate and 15 min for a fast fire growth rate.

For most practical combinations of fire load, compartment geometry and opening factor tmax will be in excess of these

Area of bounding

surfaces At

Area of ventilation Av

Height of ventilation openings h

Opening factor Avh/At = O

Density of compartment boundaries

Specific heat of

compartment boundaries c

Thermal conductivity

of compartment boundaries

Thermal properties b = (c)

Timetemperature response in heating phase

Fire load density qfd

Compartment floor area Af

Fire growth rateslow/medium/fast

qt,d = qf,d . Af/At tlim

tmax = max [(0.2x10-3.qt,d /O) ; tlim

Figure 11.5 Input values for parametric calculation

Concept design


The parametric time factor is a function of the opening factor O and the thermal inertia b

= ( O / b ) 2 /(0.04/1160) 2 = (0.066/945) 2 /(0.04/1160) 2 = 4.1

Fire load

q f,d = 570 MJ/m q t,d = q f,d A f /A t = 570 36/153.6 = 133.6 MJ/m Maximum temperature will be at time

t max = (0.2 10 3 q t,d / O ) = 0.2 10 3 133.6/0.066 = 0.4 hours (24min)

The heating and cooling phases can then be constructed using the relevant formulae above to give the compartment time-temperature response illustrated in Figure 11.6 .

11.3 Heat transfer Heat transfer analysis is undertaken to determine the tempera-ture rise and distribution of temperature within the structural members. Thermal models are based on the acknowledged principles and assumptions of heat transfer. They vary in complexity ranging from simple tabulated values to com-plex calculation models based on fi nite difference or com-putational fl uid dynamics. The heating conditions considered extend to cover natural fi re scenarios. However, the validity of some of the simpler methods and most of the tabular data is restricted to a fi re exposure corresponding to the standard fi re curve.

Whatever model is adopted the analysis needs to consider transient behaviour which covers:

Heat transfer within the element including conduction for solid elements but also any radiative or convective components particu-larly where the construction includes cavities and/or voids.

Moisture migration.

Chemical reactions and phase changes.

In order to undertake the analysis, knowledge of material prop-erties at elevated temperature is required specifi cally:

thermal conductivity;

specifi c heat;

density;

emissivity;

initial moisture content;

charring rate if appropriate.

As the guidance in this manual is aimed principally at practis-ing structural engineers the fundamental theory is not consid-ered and the focus is on tabulated data and simple calculation

Ventilation area A v = 3.6 m 2 m = 7.2 m Height of compartment H (m) = 3.4 m Total area of enclosure A t = (2 6 6) + (4 3.4 6) =

153.6 m Opening factor O = A v h / A t = 7.2 2 / 153.6 = 0.066 m 1 Calculation: Ventilation factor: w f = (6/ H ) 0.3 [0.62 + 90(0.4 v ) 4 ] 0.5 v = A v / A f = 7.2/36 = 0.2 (this is within the limits in the

Eurocode) giving w f = 1.95 Thermal properties of compartment linings: The factor k b is

dependent on the thermal inertia of the construction materials as defi ned by the factordependent on the thermal inertia of the construction materials

b cb cb c=b c b c b c where: = density (kg/m ) c = specifi c heat (J/kgK) = thermal conductivity (W/mK) Although no information on the thermal properties of com-

monly used construction materials is provided in the Eurocode (or the National Annex and associated NCCI), some guidance is available in the literature. Table 11.1 sets out the appropriate values for the current case taken from published data.

The b value to be used for design is a weighted average where b = b j A j /A j . Here the relevant b value = 945J/m s K . From Table B.1 of the NCCI this corresponds to a value of k b = 0.07 . Note: If no detailed information is available on the thermal properties of the compartment linings or if there are uncertainties about the fi nal construction or changes may be made over the course of the buildings design life then the default value of k b = 0.09 should be used.

The equivalent time of fi re exposure is then given by:

t e,d = 570 1.95 0.07 = 78 min (11.9)

The above example of a corner offi ce compartment is used to illustrate the parametric approach.

Design information:

Floor area A f = 36 m

Design fi re load density = q f,d = 570 MJ/m

Opening factor O = 0.066 m -1

Thermal inertia b = 945 J/m s K

Table 11.1 Thermal properties of compartment linings

Construction Material Thermal inertia (b value J/m s K with b = c )

Area (m )

Ceiling Concrete 2280 36

Floor Plasterboard 520 36

Walls Plasterboard 520 76.8



11.3.1 Concrete

For materials with a high thermal conductivity (such as steel) it is generally possible to ignore thermal gradients within the member and assume a uniform temperature. However, for concrete members having a low thermal con-ductivity and including free and chemically bound mois-ture, the calculation of heat transfer to the structure can be very complex. A number of different methods may be used to derive the temperature distribution within the member. Eurocode 2 includes a number of temperature profiles for slabs, beams and columns with the temperature profile for slabs also being applicable to walls subject to heating from one side. The temperature profiles are presented for specific fire resistance periods and are therefore applicable only to a heating regime corresponding to a standard fire exposure. In principal, the calculation methods for which the temperature profile is input data could be used to determine performance due to different thermal exposure but there are no validated test data to support this.

11.3.2 Structural steel

Steel loses both strength and stiffness with increasing tem-perature. It should be borne in mind that the determination of strength reduction factors for hot rolled steel is dependent not only on the material but also on the test method, the heat-ing rate and the strain limit used to determine steel strength. The differences between test data are significant. The British

models. The structural Eurocodes provide methods for deter-mining temperature distributions subject to certain conditions. The thermal modelling approaches set out in the Eurocodes are summarised in Table 11.2.

Heat transfer methods for materials that incorporate free moisture should consider the effect of moisture migration with time through the member in order to provide an accurate predic-tion of the temperature of the element with time. This is gener-ally accomplished through the incorporation of mass transfer in the model providing additional information on the pressure field due to steam production which, in certain cases, may influence the tendency of a material to spalling. For many simple models, the influence of moisture is either implicitly included (empiri-cal models and tabulated data) or conservatively ignored.

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20Time (hrs)

Tem

p (C

)

HeatingCooling

Figure 11.6 Parametric curve

Table 11.2 Thermal modelling options in the structural Eurocodes

Eurocode Material Tabular data

Simple model

Advanced model

EN 1992-1-2 Concrete Yes No Yes

EN 1993-1-2 Steel No Yes Yes

EN 1994-1-2 Composite (steel and concrete)

Yes Yes Yes

EN 1995-1-2 Timber No Yes No

EN 1996-1-2 Masonry Yes Yes Yes

EN 1999-1-2 Aluminium No Yes Yes

Concept design


The European fi re design standard for steel structures includes methods for calculating the temperature rise in both unprotected and protected steel assuming a uniform tempera-ture distribution through the cross-section. The increase of temperature a,t for an unprotected member during a time interval t is given by:

a t a t a t a t sh m

a aa anet dk k

A V A V mA Vm m A V m c

h t h t neh tnet dh tt d, ,, ,a t, ,a t sh, ,sh ne, ,net d, ,t dc, ,c/A V/A V A V / A V sec= = = sh = sh m = m k = k h t= h t h t = h t ne h t ne = ne h t ne t d h t t d = t d h t t d fo= fo= r 5r 5tr 5t= r 5= = r 5= t= tr 5t= t (11.10)

where

a is the unit mass of steel [kg/m 3 ];

A m is the surface area of the member per unit length [m 2 ];

A m / V is the section factor for unprotected steel members [m 1 ];

c a is the specifi c heat of steel [J/kgK];

h. net,d is the net heat fl ux per unit area [W/m 2 ];

k sh is correction factor for the shadow effect ( k sh = 1.0 if the shallow effect is ignored);

t is the time interval [seconds];

V is the volume of the member per unit length [m 3 ].

For circular or rectangular cross-sections fully engulfed by fi re the shadow effect is not relevant and k sh = 1.0 otherwise: for I sections under normal fi le actions for the other cases

k

A V

A VA V

A V

sh

m bA Vm bA V

mA VmA V

m bA Vm bA V

mA VmA V

=

09[ /A V[ /A Vm b[ /m bA Vm bA V[ /A Vm bA V ]m b]m b/A V/A V

[ /A V[ /A Vm b[ /m bA Vm bA V[ /A Vm bA V ]m b]m b/A V/A V

(11.11)

In the above equation the value of A m / V should not be used if it less than 10 m 1 . [A m / V] b is the box value of the section factor.

The k sh correction for the shadow effect accounts for the fact that members with geometry similar to I and H sections are shielded from the direct impact of the fi re in some parts of the surface.

The above method requires integration with respect to time with the calculated temperature rise substituted back into the equation for each time step. This can be realised using a simple spreadsheet based method. For greater accuracy temperature-dependent values for specifi c heat and thermal conductivity could be used (where known).

For protected members a similar procedure is adopted tak-ing into account the relevant material properties of the pro-tection material. The method is applicable to non-reactive fi re protection systems such as board or spray protection but is not appropriate for reactive materials such as intumescent coatings. Assuming a uniform temperature distribution the temperature

Steel data used in the National and European codes show that for a temperature of 550 C structural steel will retain 60% of its room temperature strength while the corresponding fi gure obtained from the ECCS relationship for the same temperature is closer to 40%. The use of the British Steel data is justifi ed by their improved correlation with large-scale beam and col-umn tests, both in terms of the heating rates and the strains developed at the defl ection limits imposed by the standard fi re resistance tests. This simplifi ed presentation does not itself take into consideration the fact that values above unity exist within the lower range of temperatures. The fi ne detail in the temperature-dependent material properties is principally of interest to those involved in the numerical modelling of mate-rial and structural behaviour. What is abundantly clear is that both strength and stiffness decrease with increasing tempera-ture and that this reduction is particularly signifi cant between 400 and 700 C.

Because of the perceived poor performance of steel ele-ments in fi re discussed above, the most common method of designing for fi re is to design the steel structure for the ambi-ent temperature loading condition and then to protect the steel members with proprietary fi re protection materials to ensure that a specifi c temperature is not exceeded or, in the light of the discussion above, that a specifi ed percentage of the ambient temperature loading capacity is retained.

Traditional fi re design methods for structural steel are based on the concept of a single critical temperature. Due to the relationship between steel strength and temperature the fi g-ure of 550 C is generally adopted as the critical temperature for steel. In reality there is no single critical temperature as the capacity of the structure is a function of the load applied at the fi re limit state. This is discussed further in the section dealing with the calculation of the mechanical response of structural elements.

The rate of increase in temperature of a steel cross-section is determined by the ratio of the heated surface area (A) to the volume (V). The ratio A/V is known as the section factor and is analogous to the earlier concept whereby the rate of tem-perature rise was related to the ratio of the heated perimeter (H p ) to the area of the section (A). A steel section with a large surface area will be subject to a greater heat fl ux than one with a smaller surface area. The greater the volume of the section the greater will be the heat sink effect. Therefore, a small thick section (such as a UC section) will heat up to a given tempera-ture more slowly than a long thin section. In terms of applying passive fi re protection the greater the section factor the greater the thickness of protection required to limit the temperature of the steel to a given temperature.

The most common method used in the UK to relate pro-tection thickness to section factor for a given fi re resistance period and a specifi ed critical temperature is the Yellow Book published by the Association for Specialist Fire Protection (2007).

Structural fi re engineering design


periods for different types of masonry. For insulation pur-poses the calculation of the temperature rise of the unexposed face is reasonably well understood and the Eurocode includes temperature-dependent material properties for use in thermal modelling. However, the issue of free and chemically bound water needs to be addressed to be able to accurately refl ect the delay in reaching temperatures signifi cantly above 100 C. Other issues that need to be considered include the presence of voids in hollow masonry blocks and ancillary products (such as metal wall ties) leading to localised areas of high conduction.

11.3.5 Aluminium

Although not readily associated with fi re resistant structural design, BS EN1999-1-2 provides guidance on the use of simple and advanced calculation models for aluminium structures subject to fi re. The code effectively utilises many of the proce-dures set out in BS EN1993-1-2 in terms of the calculation of heat transfer to external members (Annex B), and in the verifi -cation methods related to aluminium temperature development and calculation of the resistance of cross-sections. The most signifi cant difference between the two codes is that the thermal and structural material property data only extend up to 500 C at which point the strength and stiffness of aluminium is zero. The reduction in strength with temperature for aluminium depends on the specifi c alloy adopted. Figure 11.7 illustrates the lower range of values for the 0.2% proof strength ratios for the alloys covered in the Eurocode.

rise a,t of a protected steel member during a time interval t is given by:

a ta tp p

p a aag t g t a t a t

g tg t

A Vp pA Vp pd cp ad cp a

t e t e

,a t,a t, ,g t, ,g t a t, ,a t

/ / / g t,g t

/ (A V/ (A V )

( /( / )

( ) ( ) ( ) t e( )t e t e ( ) t e / ( ) /

=

t e t e ( ) ( ) t e ( ) t e t e ( ) t e

1 3( /1 3( /( /1 3( /( /+( /1 3( /+( /

( ) 1 ( ) 10 10 ( ) 10 ( )

(11.12)

With a,t 0 and

=c

cd A V

p pp p

a aa ap pd Ap pd A /

where

p is the thermal conductivity of fi re protection material [W/mK];

a,t is the steel temperature at time t [ C]; g,t is the ambient gas temperature at time t [ C]; g,t is the increase of ambient gas temperature during time

interval t [K];

a is the unit mass of steel [kg/m 3 ];

p is the unit mass of fi re protection material [kg/m 3 ];

A p / V is the section factor for steel members insulated by fi re protection material [m 1 ];

A p is the appropriate area of fi re protection material per unit length [m 2 ];

c a is the temperature-dependent specifi c heat of steel [J/kgK];

c p is the temperature-independent specifi c heat of fi re pro-tection material [J/kgK];

d p is the thickness of fi re protection material [m];

t is the time interval [seconds];

V is the volume of the member per unit length [m 3 ].

11.3.3 Composite steel and concrete construction

The European fi re design standard for composite construc-tion provides a conservative estimate of the temperature rise in composite slabs through tabulated data treating the composite slab as if it were a solid slab. The temperatures at a distance x from the underside of the exposed slab are related to specifi c standard fi re resistance periods in Table 11.3 .

11.3.4 Timber and masonry

In general there is no need to determine the temperature distri-bution through a timber structural element as capacity is related to a residual undamaged section below the char layer where the material is assumed to maintain its ambient temperature prop-erties in terms of strength and stiffness. The important aspect in this case is the calculation of the depth of charring.

The fi re part of Eurocode 6 provides tables of minimum dimensions to achieve specifi ed periods of fi re resistance; it also includes time-temperature graphs for various fi re resistance

Table 11.3 Temperature distribution in a solid normal weight concrete slab of 100 mm thickness. Data taken from BS EN 1994-1-2. Permission to reproduce extracts is granted by BSI

Depth x (mm)

Temperature c ( C) for standard fi re resistance ofR30 R60 R90 R120 R180 R240

5 535 705

10 470 642 738

15 415 581 681 754

20 350 525 627 697

25 300 469 571 642 738

30 250 421 519 591 689 740

35 210 374 473 542 635 700

40 180 327 428 493 590 670

45 160 289 387 454 549 645

50 140 250 345 415 508 550

55 125 200 294 369 469 520

60 110 175 271 342 430 495

80 80 140 220 270 330 395

100 60 100 160 210 260 305

(Note: for lightweight concrete the values may be reduced to 90% of those given) For the temperature of the reinforcement and the temperature of the steel decking the Eurocode presents a method based on the use of coeffi cients to determine the temperature for specifi c periods of fi re resistance.

Concept design


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500temperature deg C

0.2%

pr

oo

f str

engt

h ra

tio

Figure 11.7 0.2% strength ratios (lower limits) for aluminium alloys

11.4 Mechanical (structural) responseOnce the thermal analysis has been carried out to ascertain the compartment atmosphere temperatures and the heat transfer to the structure has been completed it is then necessary to assess the effect of the increased temperatures on the resistance of the structural members. In reality, steps 2 and 3 of the fire engin-eering design (heat transfer and structural response) will gen-erally be undertaken in tandem, with the rules for calculating or looking up member temperatures within the same standards as the rules for evaluating member capacities.

The most comprehensive suite of design standards for undertaking structural fire engineering design are the struc-tural Eurocodes. The fire codes cover actions on structures exposed to fire as well as design procedures for concrete, steel, composite steel and concrete, timber, masonry and alu-minium. All these codes have now been published by BSI for use in the UK along with a National Annex setting out Nationally Determined Parameters for those areas where National choice is allowed. Before looking at the methods for determining structural response it is necessary to look at the relationship between design loading at ambient tempera-ture and the design load case for the ultimate limit state for the accidental design situation of a fire. This is the subject of the next section.

11.4.1 Load effects at the fire limit state

Traditional design procedures for steel structures are based on limiting the temperature rise of the steel section to a set value generally termed the critical temperature for steel. Similarly tabulated values in the National code for the fire design of con-crete structures specify minimum cover distances to ensure that the temperature of the reinforcement does not exceed a specified limiting value. Such methods are independent of the load applied under fire conditions and offer simplified often conservative solutions to the majority of fire design scenarios.

The development of structural fire engineering has high-lighted the importance of load in determining the fire resist-ance of structural elements. A major change in the design methodology for steel structures in fire came about with the publication in 1990 of BS 5950 Part 8. Although this code is still based on an evaluation of the performance of structural steel members in the standard fire test it allows architects and engineers an alternative approach of designing for fire resist-ance through calculation procedures. It recognises that there is no single failure temperature for steel members and that structural failure is influenced not only by temperature but also by load level, support conditions and the presence or other-wise of a thermal gradient through and/or along the member. The code allows for the consideration of natural fires but does



G permanent action (dead load)

P relevant representative value of a pre-stressing action (where present)

Ad design value of an accidental action

1 factor for frequent value of a variable action

2 factor for quasi-permanent value of a variable action

Qk characteristic value of a single variable action (Qk,1 is the characteristic value of the leading variable action often the imposed load)

In the fire situation, Ad is the effect of the fire itself on the struc-ture, i.e. the effects of restrained thermal expansion, thermal gra-dients, etc. However, where the design is based on the standard fire situation then such indirect actions need not be considered.

EN 1990 allows the use of either 1 or 2 with the main vari-able action. EN 1991-1-2 recommends the use of 2. However, the UK National Annex for use with EN 1991-1-2 specifies 1 to be used in the UK. The value of the partial factors for specific types of occupancy and design situations is shown in Table 11.4.

It is important to understand the significance of the reduced partial factor for imposed loading and the effect that this has on different structural forms. Effectively a reduction in the imposed load will increase the fire resistance of the structural member. Consequently those forms of construction where the imposed load is a relatively high proportion of the total load (such as steel frame construction) may be able to reduce the levels of fire protection required by taking advantage of the spare capacity in the member. Conversely for those forms of construction (such as reinforced concrete) where the imposed load is a relatively small proportion of the total load the poten-tial benefits of a fire engineering solution taking into account residual capacity are limited. The relationship between the

not provide any detailed information or guidance. Load fac-tors and material strength factors specific to the fire limit state are given. These are partial safety factors which deal with the uncertainties inherent in probabilistic distributions for loading and material properties and represent reductions from ambient temperature design in recognition of the small probability of excessive loads being present at the same time as a fire occurs. In 2003, BS5950 Part 8 was updated to provide consistent information with the fire part of Eurocode 3.

The national code for the design of concrete structures, BS 8110 Part 2, did not reflect the important role that load level plays in determining performance under fire conditions. Load effects are allowed for in Eurocode 2 for the tabulated data for concrete structures with dimensions dependent on load level for columns and load-bearing walls.

An accurate assessment of the performance of a structural member during a fire requires knowledge of both the reduction in material properties with increasing temperature and an accu-rate assessment of the loads acting on the structure at the time of the fire. Load effects can have a significant impact on the fire resistance of a structure and this is reflected in the requirement for realistic load levels to be in place during standard fire tests. As material properties reduce with increasing temperature the load-bearing failure criterion is reached when the residual strength of the element equals the load applied. Load level can also have a significant impact on other types of construction such as timber or light steel framing that rely on sacrificial linings for fire resist-ance. Increased loading leads to increased deflections at the fire limit state which can cause gaps to open between panels thereby compromising the assumed level of fire protection.

Loads are factored and a number of load cases considered for the ambient temperature situation to account for uncertain-ties and the potential for adverse conditions. Fire in terms of the Eurocode system is an ultimate limit state accidental action and, as such, is subject to specific partial factors that reflect the reduced likelihood of the full ambient temperature design loading being present at the same time as a fire occurs. In the European system in order to determine the calculation of the load effects at the fire limit state the designer must be familiar with the Basis of Design EN 1990 which provides the required load combinations and with the fire part of the Eurocode for Actions on Structures EN 1991-1-2 which, in addition to spe-cifying the fire design to be adopted also specifies the mechan-ical actions for structural analysis. In particular, EN 1991-1-2 specifies the partial factor for imposed (assuming leading vari-able action) loading for the fire limit state. Fire loading is an ultimate limit state accidental design situation of the form:

Ed = E (Gk,j; P; Ad; (1,1 or 2,1)Qk,i) for j 1; i > 1 (11.13)

where

E the effect of actions (Ed is the design value of the effect of actions)

Table 11.4 Values of partial factors (fi) to be used for the accidental fire limit state. Data taken from BS EN 1990. Permission to reproduce extracts is granted by BSI

Action 1 2

Imposed loads in buildings 0.5 0.3

Category A: domestic, residential 0.5 0.3

Category B: office areas 0.7 0.6

Category C: congregation areas 0.7 0.6

Category D: shopping areas 0.9 0.8

Category E: storage areas 0.7 0.6

Category F: traffic area, 30 kN 0.5 0.3Category G: traffic area, 30160 kN 0 0

Category H: roofs

Snow load: H 1000m a.s.l. 0.2 0Wind loads on buildings 0.2 0

Concept design


A knowledge of the reduction in material strength and stiffness at elevated temperature and familiarity with reduction factors to be used for given temperatures.

A detailed breakdown of the various calculation methods avail-able is beyond the scope of this publication.

11.5 Conclusion Many structural engineers will be unfamiliar with the principles of structural fi re engineering design. In recent years, a number of specialist consultants have emerged offering fi re engineering solutions, largely for prestigious projects where the potential benefi ts of adopting a fi re engineering design approach out-weigh the additional design cost to the client. There is a funda-mental lack of understanding of the principles of structural fi re engineering design. In reality, the design methodology, as set out in the fi re parts of the structural Eurocodes, is based on the principles adopted for normal temperature design. One of the aims of this simplifi ed guidance is to demystify the subject so that it can be readily understood and used by structural engi-neers familiar with the underlying principles and assumptions of design for the ambient temperature condition.

11.6 References Association for Specialist Fire Protection (2007). Fire Protection for

Structural Steel in Buildings , 4th edn. Aldershot: ASFP. Institution of Structural Engineers (2007). Guide to the Advanced

Fire Safety Engineering of Structures . London: ISE. Lennon , T. , Moore , D. B. , Wang , Y. C. and Bailey , C. G. (2006).

Designers Guide to EN1991-1-2, EN1992-1-2, EN1993-1-2 and EN1994-1-2: Handbook for the Fire Design of Steel, Composite and Concrete Structures to the Eurocodes . London: Thomas Telford.

11.6.1 Standards and statutory instruments BSI (August 1985). Structural Use of Concrete Part 2: Code of

Practice for Special Circumstances . London: BSI, BS 8110- 2. BSI (May 1987). Fire Tests on Building Materials and Structures Part

20: Method for Determination of the Fire Resistance of Elements of Construction (General Principles) . London: BSI, BS 476- 20.

BSI (November 1999). Fire Resistance Tests Part 1: General Requirements . London: BSI, BS EN 1363- 1.

BSI (2002). Eurocode Basis of Structural Design . London: BSI, BS EN 1990 :2002.

BSI (November 2002). Eurocode 1: Actions on Structures Part 12: General Actions Actions on Structures Exposed to Fire . London: BSI, BS EN 1991- 1-2.

BSI (March 2003). Application of Fire Safety Engineering Principles to the Design of Buildings Part 1: Initiation and Development of Fire within the Enclosure of Origin (Sub-system 1) . London: BSI, PD 7974- 1:2003.

BSI (2003). Structural Use of Steelwork in Building Part 8: Code of Practice for Fire Resistant Design . London: BSI, BS 5950- 8:2003.

BSI (December , 2004). Eurocode 5: Design of Timber Structures Part 12: General Rules Structural Fire Design . London: BSI, BS EN 1995- 1-2:2004.

reduction factor fi and the ratio of the dead and imposed loads is illustrated in Figure 11.8 where:

fi

fik fk f i kk fi kk f

G k G k Q kG QG Qk fG Qk fk fG Qk f i kG Qi kk fi kk fG Qk fi kk fG Q G Q G k G Q G k Q kG QQ k Q k G Q Q k

=G Q+G Qk fG Qk f+k fG Qk fG Q+G Q G Q + G Q

,

, ,Q k, ,Q k

1

1 1Q k1 1Q kQ kG QQ k1 1Q kG QQ k, ,1 1, ,Q k, ,Q k1 1Q k, ,Q k (11.14)

with:

Q k,1 = characteristic value of the leading variable action (imposed load)

G k = characteristic value of a permanent action (dead load)

G = partial factor for permanent actions (1.35) Q,1 = partial factor for variable action 1 (1.5) = combination factor (= 0.5 for residential and offi ce appli-

cations from UK National Annex to EN 1991-1-2)

11.4.2 Calculation methods

A number of calculation methods are available ranging from simple tabulated data through to advanced numerical methods. Advanced numerical methods which consider nonlinear behav-iour at elevated temperature require specifi c areas of expertise and in general would not be available to practising structural engi-neers. The fi re parts of the structural Eurocodes include tabulated data and simplifi ed calculation methods which can be used by engineers familiar with ambient temperature design procedures. The nature of the calculation procedures is determined in part by the current state of knowledge with respect to the behaviour of the specifi c construction materials at elevated temperature. However, there are some common principles that apply to all materials. Simple calculation methods are based on:

A knowledge of the design procedures at ambient temperature.

An understanding of the partial factors for load effects to be used at the fi re limit state.

3.00.0 0.5 1.0 1.5 2.0 2.50.2

0.3

0.4

0.5

0.6

0.7

0.8

Q k,1/ G k

fi

Figure 11.8 Relationship between reduction factor fi and ratio of dead and imposed loads for values of the partial factor for the fi re situation fi



11.6.2 Recommended readingBuchanan, A. H. (2002). Structural Design for Fire Safety. Chichester:

John Wiley.Drysdale, D. (2002). An Introduction to Fire Dynamics, 2nd edn.

Chichester: John Wiley.Franssen, J. M. and Zaharia, R. (2005). Design of Steel Structures

Subjected to Fire. University of Liege.Lennon, T. (2011). Structural Fire Engineering Design. London:

Thomas Telford/IHS BRE Press.Purkiss, J. A. (2007). Fire Safety Engineering Design of Structures,

2nd edn. Oxford: Butterworth Heinemann.

11.6.3 Useful websiteswww.access-steel.com/www.concretecentre.com/technical_information/performance_and_

benefits/fire_resistance/concrete_fire_forum.aspx www.eurocodes.co.ukwww.istructe.org/Pages/default.aspxwww.mace.manchester.ac.uk/project/research/structures/strucfire/www.steelinfire.org.uk/

BSI (February, 2005). Eurocode 2: Design of Concrete Structures Part 12: General Rules Structural Fire Design. London: BSI, BS EN1992-1-2:2004.

BSI (April, 2005). Eurocode 3: Design of Steel Structures Part 12: General Rules Structural Fire Design. London: BSI, BS EN1993-1-2:2005.

BSI (June 2005). Eurocode 6: Design of Masonry Structures Part 12: General Rules Structural Fire Design. London: BSI, BS EN1996-1-2:2005.

BSI (December 2005). Eurocode 4: Design of Composite Steel and Concrete Structures Part 12: General Rules Structural Fire Design. London: BSI, BS EN1994-1-2:2005.

BSI (April 2007). Eurocode 9: Design of Aluminium Structures Part 12: Structural Fire Design. London: BSI, BS EN1999-1-2:2007.

BSI (June, 2007). Background Paper to the UK National Annex to BS EN1991-1-2. London: BSI, Published Document PD 6688-1-2:2007.

International Organization for Standardization (1975). Fire Resistance Test Elements of Building Construction. Geneva: ISO, ISO 834.

chapter 11- structural fire engineering design

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