1. CE 808 : Structural Fire Engineering Ch 5. FIRE SEVERITY
V. Kodur, Professor
Dept of Civil and Env. Engineering
Michigan State University

2. Ch 5. FIRE SEVERITY Fire Severity Methods to Quantify Fire Severity
Standard Fires and Real Fires
Concept of Equivalent Fire Severity
CE 808 – Chapter 5

3. Burning Items in Rooms
Burning objects may behave differently when burning inside a room than in open air
The plume of hot gases above a burning object will hit the ceiling & spread horizontally to form a hot upper layer
Early in the fire, the burning rate is enhanced by radiant feedback from the hot upper layer
Later in the fire, the rate of burning may be severely reduced because of limited ventilation
CE 808 – Chapter 5

4. Fire resistance  Fire severity
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
FR is the ability of the structure to resist collapse or fire spread during exposure to a fire of specified severity
Verification may be in the:
time domain
temperature domain
strength domain
CE 808 – Chapter 5

5. Verification Fire severity is a measure of:
the destructive impact of a fire, or
the forces or temp. that may cause collapse or fire spread as a result of a fire
Table - Methods for comparing fire severity with fire resistance
CE 808 – Chapter 5

6. Verification - Time domain
The most common verification is comparing fire severity and fire resistance in time domain, i.e.:
tfail  ts
tfail - time to failure of a building element, usually a fire-resistance rating
ts - 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
CE 808 – Chapter 5

7. Verification – Temp. domain
Sometimes, verification of design is in the temp. domain, i.e.:
Tfail  Tmax
Tfail - Temp. which would cause failure of building elements (thermal or structural failure)
Tmax – Max. temp. reached in building elements during a fire or the temp. at a certain time specified by codes
Temp 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 & effect of temp. on material properties
Temp. domain is more suitable for barriers than structural elements
CE 808 – Chapter 5

8. 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 - minimum load capacity reached during a fire or the load capacity at a certain time specified by codes
Uf - applied load at the time of a fire
CE 808 – Chapter 5

9. Verification – Strength domain
The load values may be expressed in units of:
force & 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 & structural analyses at high temp., often calculated since limited fire test results are available for full burnout fires
Loads at the time of a fire can be calculated using load combinations from building codes
CE 808 – Chapter 5

10. Verification – Example
Fig - Behavior (time-temp.) of a steel beam in fire
(a) temperature increase (b) loss of strength
Calculations indicate the beam failing at time tfail when the steel temp. reaches Tfail
Codes requires a FR or required fire severity of tcode for the beam
CE 808 – Chapter 5

11. Verification – Example
Verifying time domain (check 1 - Fig (a)):
time to failure tfail  fire severity tcode
Verifying temp. domain (check 2 - Fig (a)):
steel temp. causing failure Tfail  Tcode temp. reached in the beam at time tcode
Checks 1 & 2 give the same results since they are based on the same process
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12. Verification – Example
Fig. (b) shows 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 (Rcold) decreases during fire
Load capacity of the beam reduces to Rcode at tcode
Verifying strength domain (check 3 – Fig. (b)):
Rcode  Uf at time tcode
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13. Table - Fire models and structural response models
Fire Exposure Models
Table - Fire models and structural response models
Table shows a range of design situations
The ist column shows 3 fire exposure models represent- ing 3 different design fires
Fire exposure H1 (most common) represents a std. test fire exposure for a specified period of time, tcode given by a prescriptive code
Prescriptive codes specify required fire resistance which is generally between 30 min & 4 hrs, but with no reference to the severity of fire
CE 808 – Chapter 5

14. Fire Exposure Models
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 eq. to a complete burnout of a real fire in the same room (eq. fire severity)
Performance-based codes allow the use of time eq. formulae to improve on simple prescriptive fire-resistance requirements
CE 808 – Chapter 5

15. Fire Exposure Models
Fire exposure H3 represents a realistic fire that occurs in a room with complete burnout and no fire suppression - for example Swedish curves
This Fig. 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
CE 808 – Chapter 5

16. Fire Exposure Models
Test results are mostly used for single elements exposed to H1 or H2 fires
Calculations are becoming necessary in most cases
Verifying that a member/structure has sufficient fire resistance is by comparison of time, temp. or strength
Verifying to fire exposures H1 and H2 is mostly in the time domain (assigned fire resistance versus required fire resistance)
Verification using exposure to a complete burnout (H3) is mostly a comparison of temp. for insulating elements or of strength for structural elements
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17. Table - Design combinations for verifying fire resistance
Many design combinations are possible & therefore it is essential for designers to specify clearly the combination that will be used
Common combinations are illustrated in the Table
In very general terms, both the accuracy of the prediction & the amount of calculation effort increase downwards in the table
Table - Design combinations for verifying fire resistance
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18. Fire Severity Fire severity
a measure of the destructive potential of a fire
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
CE 808 – Chapter 5

19. 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 temp.
CE 808 – Chapter 5

20. Standard Fire
Most countries assess fire performance of building materials & elements using full-size fire resistance tests
Time-temp. curves used in fire resistance tests is called the 'standard fire'
The most widely used test specifications are:
ASTM E 119 and CAN/ULC-SI01-M89 (North America)
ISO 834 (International)
British Standard BS 476 Parts 20-23
Australian Standard AS 1530 Part 4
CE 808 – Chapter 5

21. Standard Fire - Time-temp. Curves
Fig. - Standard time-temp. curves for ASTM E 119, ISO 834, Eurocode (EC1)
E 119 curve defined by a no. of discrete points
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22. Standard Fire - Time-temp. Curves
ASTM E 119 and ISO 834 curves are similar (this is true for most int. 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)
Approximate Eq. for the ASTM E119 curve for temp. T (°C) as:
T = 750[1 - e  t]  t + To
t is the time (hours), To is the ambient temp. (°C)
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23. Standard Fire - Time-temp. Curves
Eurocode hydrocarbon fire curve is intended for use where a structural member is engulfed in flames from a large pool fire
Temp, T (°C) in the hydrocarbon fire curve is given by:
T = 1080( e-0.167t e-2.5t)+ To
t is the time (min), To is the ambient temp. (°C)
The other Eurocode curve (lower temp.) is intended for designing external structural members located outside a burning compartment
Temp T (°C) for this fire is given by:
T = 660( e-0.32t e-3.8t) + To
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24. Furnace Parameters
Fire severity depends on the testing furnace characteristics
Two similarly operated furnaces may not impact test specimens with the same fire exposure severity
Temp. 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
Thermocouple measurements may be different from one furnace to another
Babrauskas and Williamson (1978) have shown that temp. differences are most significant during the first 5 minutes of the tests
CE 808 – Chapter 5

25. Furnace Parameters
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
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
Temp. increase less rapidly in furnaces lined with bricks
CE 808 – Chapter 5

26. Equivalent Fire Severity
Eq. fire severity is a concept used to relate the severity of an expected real fire exposure to the standard test fire
This relation is imp. for designers to use published fire-resistance ratings from Std. tests with estimates of real fire exposure
Methods comparing real fires to the standard test fire are:
Equal Area Concept
Maximum Temp. Concept
Minimum Load Capacity Concept
Time-equivalent formulae
CE 808 – Chapter 5

27. Equal Area Concept Fig. - Equivalent fire severity on equal area basis
Ingberg (1928) introduced the equivalency concept by stating that two fires have equivalent severity if areas under each time- temp. curve are equal
The concept is not theoretically sound
Although inadequate, the concept was used as a crude method of comparing fires
Fig. - Equivalent fire severity on equal area basis
CE 808 – Chapter 5

28. Equal Area Concept
This 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) indicated that there could be a big difference between a short hot fire & a longer cool fire
CE 808 – Chapter 5

29. Maximum Temp. Concept
The concept defines the equivalent fire severity as the time of exposure to the standard fire that would result in the same max. temp. in a protected steel member as would occur in a complete burnout of the fire compartment
This is a more realistic concept, developed by Law (1971), Pettersson et al. (1976) and others
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30. Maximum Temp. Concept
Fig. 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
Fig. - Equivalent fire severity on temp. basis
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31. Maximum Temp. Concept 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 300°C at the onset of charring of wood
The maximum temp. concept is commonly used
The concept may be misleading when max. 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
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32. Minimum Load Capacity Concept
This concept is similar to the max. temp. 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
Fig. -Equivalent fire severity on load capacity basis
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33. Minimum Load Capacity Concept
Fig. shows the load bearing capacity of a structural member exposed to a std. fire decreases continuously
The strength of the same member exposed to a real fire increases after the fire enters the decay period & the steel temp. 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 temp. start to decrease
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34. Time-equivalent formulae
Based on the max. 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
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35. Time-equivalent formulae - CIB
Derived by Pettersson (1973), published by CIB W14 (CIB, 1986)
based on ventilation parameters of the compartment & fuel load
Widely used time equivalent formula
The equivalent time of exp. to an ISO 834 fire test te (min) is given by:
te = kc w ef
ef - fuel load (MJ/m2 of floor area)
kc - a parameter to account for different linings of the compartment
w - ventilation factor (m-0.25) given by: w = Af /  Av At  Hv
Af - floor area of the compartment (m2)
Av is the total area of openings in the walls (m2)
At - total area of the internal bounding surfaces of the compartment (m2)
Hv - height of the windows (m)
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36. Time-equivalent formulae – Law
Law developed a formula, similar to CIB, for te based on tests in small-scale & large-scale compartments
te = Af ef / Hc Av (At – Av)
Hc - calorific value of the fuel (MJ/kg)
Other parameters – as defined in CIB formula
Both CIB & Law formulae
Valid only for compartments with vertical openings in the walls
Cannot be applied to rooms with openings in the roof
Give, in general, similar results (Law formula predicts slightly larger values)
CE 808 – Chapter 5

37. Time-equivalent formulae – Eurocode
Eurocode (EC1, 1994) formula:
Is a modification of CIB & Law formulae
based on empirical analysis of calculated steel temp. in a large number of fires
An important difference from the CIB formula is
Eurocode eq. time is independent of opening height, but depends on the ceiling height of the compartment
Eurocode Time Eq., te (minutes), is given as:
te = kb w ef
kb replaces kc in CIB formula
ventilation factor w is altered to allow for horizontal roof openings
CE 808 – Chapter 5

38. Time-equivalent formulae – Eurocode
The ventilation factor is given by:
w = (60/Hr)0.3[ (0.4-v)4/(1+bv ah)] > 0.5
v = Av / Ar (0.05  v  0.25)
h = Ah / Ar (h  0.20)
bv = 12.5 (1 + 10v - v2)
Hr - compartment ceiling height (m)
Af - floor area of the compartment (m2)
Av - area of vertical openings in walls (m2)
Ah - area of horizontal openings in roofs (m2)
CE 808 – Chapter 5

39. Time-equivalent formulae – CIB/Eurocode
Both CIB/Eurocode formulae
can give different results for the same room geometry
Can give similar results for small compartments with tall windows
Eurocode for. gives much lower fire severity values for large compartments with tall ceilings & low window heights
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
CE 808 – Chapter 5

40. Time-equivalent formulae – CIB/Eurocode
Table - 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)
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41. Time-equivalent formulae - Validity
Time-equivalent formulae are empirical & derived by calculation using:
a particular set of design fires
small rooms
Max. temp. concept for protected steel members with various thickness of insulation
The documents explaining formulae derivations do not describe the limitations
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42. Time-equivalent formulae - Validity
Time Eq. Formulae are crude, may not be applicable to:
other shapes of time-temp. curves
larger rooms
other types of protection
other structural materials
Applicable to protected steel & RC members
Not intended for unprotected steel or for timber construction
Based on calculations for typical concrete, steel & timber structures
Thomas et al. (1997) found formulae unsatisfactory in many real fire situations
Law (1997) also concluded that Eurocode formula is the least accurate
More precise to carry out designs using first principles to estimate post-flashover fire temp.
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43. Example 5.1
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
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: kcp = 1760 Ws0.5/m2K (medium)
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44. Example 5.1 Conversion factor: kb = 0.055
Window height: Hv = 2.0 m 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 + 10v - v2) = 43.0
Ventilation factor:
w = (6.0/3.0)3.0 [ ( )4/1(1+43.0x0)] = m-0.3
Equivalent fire severity:
te = ef kb w = 800 x x = 36.1 min
CE 808 – Chapter 5

45. Example 5.2 Ceiling opening area: Ah = 3.0 m2;
Repeat 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[ ( )4/(1+43x0.125)]
= m-0.3
Equivalent fire severity:
te = ef kb w = 800 x x = 34.0 min
CE 808 – Chapter 5

46. Example 5.3 Fuel load energy density: ef = 800 MJ/m2
Repeat Example 5.1 using the CIB formula and the Law formula.
CIB formula
Length of room: l1 = 6.0 m Width: 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
Fuel load energy density: ef = 800 MJ/m2
Total area of the internal surface:
At = 2(l1l2 + l1Hr + l2Hr) = (6x4+6x3+4x3) = 108 m2
Concrete
Thermal conductivity: k = 1.0 W/m-K
Density:  = 2200 kg/m3
Specific heat: cp = 8800 J/kg-K
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47. Example 5.3 Thermal inertia: kcp = 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
Ventilation factor
w = Af /(Av At Hv0.5)0.5 = 24/(6x108x20.5)0.5
= m-0.25
Equivalent fire severity:
te = ef kc w = 800 x 0.07 x = 44.4 min
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48. Example 5.3 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
CE 808 – Chapter 5