Fire Severity Design Notes (NRC)

1Winter 2003 Fire Severity 1

FIRE SEVERITY

Winter 2003 Fire Severity 3-2

OVERVIEW

This section will: provide an overview of basic methods for designing

structures for fire safety describe methods for quantifying the severity of post-

flashover fires for comparison with fire resistance describe the standard fire used for fire resistance testing describe the concept of equivalent fire severity which is

used to compare real fires with standard fires


FIRE SEVERITY AND FIRE RESISTANCE

Verification Fire Exposure Models Design Combinations


Verification

The fundamental step in designing structures for fire safety is to verify that the fire resistance of the structure is greater than the severity of the fire to which the structure is exposed, i.e.,

Fire resistance Fire severity

Fire resistance is the ability of the structure to resist collapse or fire spread during exposure to a fire of specified severity


Verification

Fire severity is a measure of: the destructive impact of a fire, or the forces or temperatures that may cause collapse or

fire spread as a result of a fire

Below is a table showing methods for comparing fire severity with fire resistance


Verification

Methods for comparing fire severity with fire resistance

Domain Units Fire Resistance Fire SeverityTime minutes or hours Time to failure Fire duration as calculated or

specified by codesTemperature C Temperature to cause

failure Maximum temperature reachedduring the fire

Strength kN or kN-m Load capacity at elevatedtemperature

Applied load during the fire

2Winter 2003 Fire Severity 3-7

Verification

The verification may be in the: time domain temperature domain strength domain


Verification - Time domain

The most common verification is comparing fire severity and fire resistance in time domain, i.e.:

tfail ts tfail is the time to failure of a building element,

usually a fire-resistance rating ts is the fire duration or fire severity, usually a

time of standard fire exposure or an equivalent time of standard fire exposure calculated for a real fire in a building


Verification - Temperature domain

Sometimes, verification of design is in the temp. domain, i.e.:

Tfail Tmax Tfail is the temp. which would cause failure of

building elements (thermal or structural failure) Tmax is the maximum temp. reached in building

elements during a fire or the temp. at a certain time specified by codes


Verification - Temperature domain

Temperatures in elements can be calculated by thermal analyses of assemblies exposed to fire

For barriers, failure temp. is the unexposed side temp. causing fire spread to other areas

For structural elements, temp. causing collapse can be calculated based on loads on elements and elevated temp. effect on material properties

Temperature domain is more suitable for barriers than structural elements


Verification - Strength domain

Verifying strength domain is comparing applied loads at the time of fire with the load capacity of structural members throughout the fire, i.e.:

Rf Uf Rf is the minimum load capacity reached during a

fire or the load capacity at a certain time specified by codes

Uf is the applied load at the time of a fire


Verification - Strength domain

The load values may be expressed in units of: force and resistance for the whole building internal member actions such as axial force or bending

moment in individual structural members Load capacity in a fire can be calculated using

thermal and structural analyses at high temp., (limited structural tests available for full burnouts)

Loads at the time of a fire can be calculated using load combinations from national building codes


Verification - Example

Behaviour of a steel beam in fire(a) temperature increase (b) loss of strength



Figure (a) shows the time-temperature of a steel beam during fire exposure

Calculations indicate the beam failing at time tfailwhen the steel temperature reaches Tfail

The code requires a fire resistance or required fire severity of tcode for the beam



Verifying time domain (check 1 - Figure (a)):time to failure tfail fire severity tcode

Verifying temp. domain (check 2 - Figure (a)):steel temperature causing failure Tfail Tcodetemperature reached in the beam at time tcode

Checks 1 & 2 give the same results since they are based on the same process



Figure (b) shows the load capacity of the same steel beam during the fire

Applied load at the time of the fire is Uf Load capacity before the fire is Rcold, which

decreases during the fire Load capacity of the beam reduces to Rcode at

tcode Verifying strength domain (check 3 - Figure (b)):

Rcode Uf at time tcode


Fire Exposure ModelsFire models and structural response models


Fire Exposure Models

The Figure shows a range of design situations The first column shows three fire exposure

models representing three different design fires Fire exposure H1 (most common) represents a

standard test fire exposure for a specified period of time, tcode given by a prescriptive code

Prescriptive codes specify required fire resistance (30 min to 4 hrs), no reference to the fire severity



Fire exposure H2 represents a modified duration of exposure to the standard test fire

The equivalent time, te is the exposure time to the standard test fire considered to be equivalent to a complete burnout of a real fire in the same room (equivalent fire severity)

Performance-based codes allow the use of time equivalent formulae to improve on simple prescriptive fire-resistance requirements



Fire exposure H3 represents a realistic fire that occurs in a room with complete burnout and no fire suppression - for example Swedish curves

The figure also shows that the fire resistance may be assessed considering a single element, a sub-assembly or a whole structure

For each category, the method of assessment is indicated - testing or calculation


Design Combinations

Many design combinations are possible and therefore it is essential for designers to specify clearly the combination that will be used

The Table below illustrates the most common combinations

In very general terms, both the accuracy of the prediction and the amount of calculation effort increase downwards in the table


Design Combinations

Design combinations for verifying fire resistance

Combination Fire exposure model Assessment of fireresistance

Verificationdomain

1 Prescriptive code(H1)

Listed rating orcalculation

Time

2 Time-equivalent formula(H2)

Listed rating orcalculation

Time

3 Predicted real fire(H3)

Calculation Temperature orstrength


FIRE SEVERITY

Fire severity is a measure of the destructive potential of a fire

Fire severity is usually defined as the period of exposure to the standard test fire, but this is not appropriate for real fires which are different

In prescriptive codes, the design of fire severity is usually prescribed

In performance-based codes, the design fire severity is usually a complete burnout fire or the equivalent time of a complete burnout fire


FIRE SEVERITY

The equivalent time of a complete burnout is the time of exposure to a standard test fire that results in an equivalent impact on an element

Damage to a structure is mainly dependent on the heat absorbed by the structural elements

The severity of a fire is mainly dependent on the level and duration of the high temperatures


STANDARD FIRE

Fire performance of building elements is assessed using full-size fire resistance tests

Time-temperature curves used in fire resistance tests is called the 'standard fire'

The most widely used test specifications are: ASTM E 119 and CAN/ULC-S101-M89 (North America) ISO 834 (International) British Standard BS 476 Parts 20-23 Australian Standard AS 1530 Part 4


Time-temperature CurvesStandard time-temperature curves


Time-temperature Curves

The figure shows standard time-temperature curves for ASTM E 119 (ULC-S101), ISO 834, Eurocode (EC1)

ASTM E 119 and ISO 834 curves are similar (this is true for most international standards curves)

ISO 834 specifies the temperature T (C) as:T = 345 log10 (8t+1) + To

t is the time (min), To is the ambient temp. (C)



ASTM E 119 curve is defined by a number of discrete points

The following is an approximate equation of the ASTM E119 curve for temperature T (C) as:

T = 750[1 - e-3.79553 t] + 170.41 t + To t is the time (hours), To is the ambient temp. (C)



The following table shows temperature values for ASTM E119 and ISO 834

Time(minutes)

ASTM EI19Temperature (C)

ISO 834Temperature (C)

0 20 205 538 57610 704 67830 843 84260 927 945120 1010 1049240 1093 1153480 1260 1257



The Eurocode hydrocarbon fire curve is intended for use where a structural member is engulfed in flames from a large pool fire

The temperature T (C) in the hydrocarbon fire curve is given by:

T = 1080(1 - 0.325e-0.167t - 0.675e-2.5t)+ To t is the time (min), To is the ambient temp. (C)



The other Eurocode curve (lower temperatures) is intended for designing external structural members located outside a burning compartment

The temperature T (C) for this fire is given by: T = 660(1 - 0.687e-0.32t - 0.313e-3.8t) + To

t is the time (min), To is the ambient temp. (C)


Furnace Parameters

Fire severity depends on the testing furnace characteristics

Two similarly-operated furnaces may not impact test specimens with the same fire severity

Temperatures are not always uniform throughout the furnace (may severely impact test specimens)

Even with similar curves, tests can be considered to give only roughly equivalent thermal exposure


Furnace Parameters

Thermocouple measurements may be different from one furnace to another

Temp. differences are most significant during the first 5 minutes of the tests

Significant differences may exist between heating conditions in various furnaces, depending on the furnace size, fuel type and furnace lining material

These differences affect the heat transfer to the furnace walls and to the test specimens


Furnace Parameters

Most common wall lining materials are fire bricks or ceramic fibre blankets, which have different thermal properties, hence different rates of heat transfer to the test specimens

Temperatures increase less rapidly in furnaces lined with bricks


EQUIVALENT FIRE SEVERITY

Real Fire Exposure Equal Area Concept Maximum Temperature Concept Minimum Load Capacity Concept Time-equivalent formulae


Real Fire Exposure

The equivalent fire severity is a concept used to relate the severity of an expected real fire to the standard test fire

This relation is important for designers who want to use published fire-resistance ratings from standard tests with estimates of real fire exposure

Below is a description of the methods comparing real fires to the standard test fire


Equal Area Concept

Ingberg (1928) introduced the equivalency concept by stating that two fires have equivalent severity if areas under each time-temp. curve are equal

The figure below shows the concept The concept is not theoretically sound Although inadequate, the concept was used as a

crude method of comparing fires


Equal Area Concept

Equivalent fire severity on equal area basis


Equal Area Concept The equal area concept is used to correct results

of standard fire-resistance tests if the standard curve is not exactly followed within tolerances

A problem with the equal area concept is that it can give a poor comparison of heat transfer for fires with different shaped time-temp. curves

Babrauskas and Williamson (1978) commented that there could be a big difference between a short hot fire and a longer cool fire


Maximum Temperature Concept

This is a more realistic concept, developed by Law (1971), Pettersson et al. (1976) and others

The concept defines the equivalent fire severity as the time of exposure to the standard fire that would result in the same maximum temperature in a protected steel member as would occur in a complete burnout of the fire compartment

The following figure shows the concept



Equivalent fire severity on temperature basis



The figure compares temp. in a protected steel beam exposed to a standard fire with those when the same beam is exposed to a particular real fire

This concept is applicable to insulating elements when the temp. on the unexposed

face is used instead of the steel temp. materials which have a limiting temp. such as the 300C

temperature of charring onset of wood



The maximum temp. concept is commonly used The concept may be misleading when maximum

temp. used in the derivation of a time-equivalent formula are: greater than those causing failure in a building lower than those causing failure in a building


Minimum Load Capacity Concept

The minimum load capacity concept is similar to the maximum temperature concept

In this concept, the equivalent fire severity is the time of exposure to a standard fire resulting in the same load bearing capacity as the minimum that would occur in a complete burnout of a compartment

The following figure shows the concept



Equivalent fire severity on load capacity basis



The Figure shows the load bearing capacity of a structural member exposed to a standard fire decreases continuously

The strength of the same member exposed to a real fire increases after the fire enters the decay period and the steel temperatures decrease



The concept is the most realistic time equivalent concept for the design of load bearing members

However, the concept is difficult to apply for a material which does not show a well defined minimum load capacity

For example, wood members where charring can continue after fire temperatures start to decrease


Time-equivalent formulae

Based on the maximum temp. concept, many empirical time-equivalent formulae have been developed

These formulae are based on maximum temp. of protected steel members exposed to real fires and include: CIB formula Law formula Eurocode formula


Time-equivalent formulae -CIB formula

Widely used time equivalent formula (published by CIB W14 group (CIB, 1986)

Formula derived by Pettersson (1973) based on the ventilation parameters of the compartment and the fuel load



The equivalent time of exposure to an ISO 834 fire test te (min) is given by:

te = kc w ef ef is the fuel load (MJ/m2 of floor area) kc is a parameter to account for different linings

of the compartment



w is the ventilation factor (m-0.25) given by: w = Af / Av At Hv

Af is the floor area of the compartment (m2) Av is the total area of openings in the walls (m2) At is the total area of the internal bounding

surfaces of the compartment (m2) Hv is the height of the windows (m)


Time-equivalent formulae -Law formula

Similar to CIB formula, Law developed a formula based on tests in small-scale and large-scale compartments

The formula is given by:

te = Af ef / Hc Av (At Av) Hc is the calorific value of the fuel (MJ/kg)


Time-equivalent formulae -CIB/Law formulae

CIB and Law formulae are only valid for compartments with vertical openings in the walls

CIB and Law formulae cannot be applied to rooms with openings in the roof

CIB and Law formulae give, in general, similar results (Law formula predicts slightly larger values)


Time-equivalent formulae -Eurocode formula

Eurocode (1994) formula is a modification of CIB and Law formulae

The formula give te (minutes) as: te = kb w ef

kb replaces kc in CIB formula and the ventilation factor w is altered to allow for horizontal roof openings

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The ventilation factor is given by:w = (6.0/Hr)0.3[0.62+90(0.4-v)4/(1+bv h)] > 0.5

v = Av / Af (0.05 v 0.25)h = Ah / Af (h 0.20)bv = 12.5 (1 + 10v - v2)



Hr is the compartment ceiling height (m) Af is the floor area of the compartment (m2) Av is the area of vertical openings in walls (m2) Ah is the area of horizontal openings in roofs (m2)


Time-equivalent formulae -CIB/Eurocode formulae

The Eurocode formula comes from an empirical analysis of calculated steel temperatures in a large number of fires

An important difference from the CIB formula is that the Eurocode equivalent time is independent of opening height, but depends on the ceiling height of the compartment



The two formulae can give different results for the same room geometry

The two formulae give similar results for small compartments with tall windows

The Eurocode formula gives much lower fire severity values for large compartments with tall ceilings and low window heights



Values of kc and kb are given in the table below Values of kc and kb depend on materials of the

compartment The general case is used for compartments with

unknown materials kc and kb have slightly different values and units

because of the different ventilation factors in the respective formulae


Time-equivalent formulae

The table below gives values of kc or kb in the time equivalent formulae

k is thermal conductivity (W/m-K), is density (kg/m3), cp is specific heat (J/kg-K)

b = ( k cp)High Medium Low

Formula Term Units > 2500 720-2500 < 720 GeneralCIB WI4 kc min m2.25/MJ 0.05 0.07 0.09 0.10Eurocode kb min m2/MJ 0.04 0.055 0.07 0.07Large compartments kb min m2/MJ 0.05 0.07 0.09 0.09

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WORKED EXAMPLE 1

Calculate the equivalent fire severity using the Eurocode formula for a room 4.0 m x 6.0 m in area, 3.0 m high, with one window 3.0 m wide and 2.0 m high. The fire load is 800 MJ/m2 floor area. The room is constructed from concrete.

Length of room: l1 = 6.0 m Width of room: l2 = 4.0 m Floor area: Af = l1 x l2 = 6.0 x 4.0 = 24.0 m2


WORKED EXAMPLE 1

Height of room: Hr = 3.0 m Fuel load energy density: ef = 800 MJ/m2

For concrete Thermal conductivity: k = 1.6 W/m-K Density: = 2200 kg/m3 Specific heat: cp = 880 J/kg-K Thermal inertia: kcp = 1760 Ws0.5/m2K (medium)


WORKED EXAMPLE 1 Conversion factor: kb = 0.055 Window height: Hv = 2.0 m Window width: B = 3.0 m Window area: Av = Hv B = 2.0 x 3.0 = 6.0 m2

Horizontal vent area:Ah = 0 (no ceiling opening) v = Av / Af = 6.0/24.0 = 0.25 h = Ah / Af = 0 bv = 12.5(1 + 10v - v2) = 43.0


WORKED EXAMPLE 1

Ventilation factor:w = (6.0/3.0)0.3 [0.62+90(0.4-0.25)4/(1+43.0x0)]

= 0.820 m-0.3

Equivalent fire severity:te = ef kb w = 800 x 0.055 x 0.820 = 36.1 min


WORKED EXAMPLE 2 Repeat Worked Example 1 with an additional

ceiling opening of 3.0 m2.

Ceiling opening area:Ah = 3.0 m2; h = Ah / Af = 3.0/24.0 = 0.125

Ventilation factor:w = (6.0/3.0)0.3[0.62+90(0.4-0.25)4/(1+43x0.125)]

= 0.772 m-0.3 Equivalent fire severity:

te = ef kb w = 800 x 0.055 x 0.772 = 34.0 minWinter 2003 Fire Severity 3-66

WORKED EXAMPLE 3 Repeat Worked Example 1 using the CIB

formula and the Law formula.

CIB formula Length of room: l1 = 6.0 m Width of room: l2 = 4.0 m Floor area: Af = l1 x l2 = 6.0 x 4.0 = 24.0 m2

Height of room: Hr = 3.0 m

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WORKED EXAMPLE 3

Fuel load energy density: ef = 800 MJ/m2

Total area of the internal surface:At = 2(l1l2 + l1Hr + l2Hr) = (6x4+6x3+4x3) = 108 m2

For concrete Thermal conductivity: k = 1.0 W/m-K Density: = 2200 kg/m3 Specific heat: cp = 880 J/kg-K


WORKED EXAMPLE 3

Thermal inertia: kcp = 1391 Ws0.5/m2K (medium) Conversion factor: kc = 0.07 min-m2.25/MJ Window height: Hv = 2.0 m Window width: B = 3.0 m Window area: Av = Hv B = 2.0 x 3.0 = 6.0 m2


WORKED EXAMPLE 3 Ventilation factor

w = Af /(Av At Hv0.5)0.5 = 24/(6x108x20.5)0.5

= 0.793 m-0.25

Equivalent fire severity:te = ef kc w = 800 x 0.07 x 0.793 = 44.4 min


WORKED EXAMPLE 3

Law formula Net calorific value of wood: Hc = 16 MJ/kg Equivalent fire severity:

te = ef Af / [Hc (Av (At - Av))0.5]= 800x24/[16x(6(108-6))0.5] = 48.6 min


Time-equivalent formulae -Validity

Time-equivalent formulae are empirical and have been derived by calculation using: a particular set of design fires small rooms maximum temp. concept for protected steel members

with various thickness of insulation Formulae are crude, may not be applicable to:

other shapes of time-temperature curve larger rooms other types of protection other structural materials


Time-equivalent formulae -Validity

Time equivalent formulae are applicable to protected steel and reinforced concrete members

Time equivalent formulae are not intended for unprotected steel or for timber construction

It is more accurate to carry out designs using first principles to estimate post-flashover fire temp.

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