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Time equivalence

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Contents
  1. 1Concept and purpose
  2. 2The Eurocode formula
  3. 3Worked example
  4. 4Use in design and regulation
  5. 5Limits and uncertainty
  6. 6Common misconceptions
  7. 7See also
  8. 8Notes
  9. 9References

Time equivalence is a method that expresses the severity of a real compartment fire as the time of exposure in a standard fire resistance test that would have the same effect on a building element.[1][2] The result is called the equivalent time of exposure or the equivalent fire severity. It can be compared directly with the fire resistance of an element, which is also given in minutes of exposure to the standard fire curve.[1][3] A widely used formula, from the Eurocode for actions on structures exposed to fire, combines the fire load density with a factor for the thermal properties of the enclosure and a factor for its openings.[1][4] The correlation was derived from tests and calculations of insulated steel beams exposed to a range of real fires.[1]

The method is popular because it needs only a hand calculation and leads to fire resistance levels that can be checked with standard tests.[5] In New Zealand it is one of three permitted ways to design for a full burnout fire, with a minimum of 20 minutes.[6] A major limitation is that one number represents a whole burnout, so the method cannot show when during a fire an element would fail.[7]

Concept and purpose

The basic check in structural fire design is that the fire resistance of each part of a structure exceeds the severity of the fire to which it is exposed.[3] Fire resistance is the ability of a structure to resist collapse, fire spread or other failure during exposure to a fire of specified severity. Fire severity is a measure of the potential destructive impact of a burnout of all the available fuel in a compartment. It is most often expressed as a period of exposure to the standard test fire.[8] Assemblies with a fire resistance equal to or greater than the equivalent severity are generally expected to withstand a complete burnout of the compartment.[1] In a probabilistic view, a room fails when its fire resistance is lower than the fire severity, with both quantities expressed in units of time.[9]

Building elements receive their rating in a furnace that follows a standard temperature–time relation.[10] Real fires differ. Their severity varies with the quantity of combustible material, the area of the openings and the dimensions of the room, and it can differ from room to room.[11] Damage to a structure depends largely on the heat it absorbs. Because heat transfer from post-flashover fires is mainly radiative and grows with the fourth power of absolute temperature, severity depends on both the temperatures reached and their duration.[3] Time equivalence translates such a fire into the language of the furnace test.

Equivalence can be defined in different ways. The common formula looks for the time in the ISO 834 test that produces the same maximum temperature in a protected steel member as the real fire, assuming burnout.[2] A review by Wade and co-workers did not examine this approach in detail, because such equivalence can only be established if the maximum temperatures are actually reached. The review recommended an energy-based alternative, building on the equivalent absorbed energy method of Kodur and co-workers.[12] Introduction to Fire Safety Engineering likewise notes that the thermal energy of a temperature–time curve can be compared with that of a natural fire.[13]

Schematic chart: steel temperature under a real fire peaks; under the standard fire it reaches the same value at the equivalent time.
The equivalent time is the time of standard fire exposure at which a protected steel member reaches the same maximum temperature as in the real fire. Based on Ministry of Business, Innovation and Employment (2013), p. 79.

A third option compares the times at which a chosen target element reaches the same temperature under both heating regimes.[14] In a worked case in the Australian Data Sheets, an element reached 454 °C after 63 minutes in the standard test but after 45 minutes in a parametric design fire. Its failure time in that scenario was therefore taken as 45 minutes.[15]

The Eurocode formula

The Eurocode formula is given in Annex F of EN 1991-1-2:2002. It multiplies three factors to obtain the equivalent time te,d in minutes. These are the design fire load density per unit floor area, qf,d, a conversion factor kb for the enclosure linings and a factor wf for the openings:[4][16]

te,d=qf,dkbwf

The factor wf depends on the height of the compartment and on the areas of the vertical and horizontal openings relative to the floor area. Larger openings lower its value, but it is never taken lower than 0.5. The Australian Data Sheet and the International Fire Engineering Guidelines give it as follows:[16][17]

Line chart: w_f falls from about 2.9 to 0.8 as the window-to-floor ratio rises from 0.025 to 0.25; the 5 m room lies below the 3 m room.
The factor wf of the Eurocode time equivalence formula against the ratio of window area to floor area, without roof openings, for room heights of 3 m and 5 m. Based on Ministry of Business, Innovation and Employment (2025b), p. 24.

wf=(6.0H)0.3[0.62+90(0.4−αv)41+bvαh]≥0.5,αv=AvAf,αh=AhAf,bv=12.5(1+10αv−αv2)≥10

The Australian Data Sheet allows a simpler factor for small rooms without roof openings and with a floor area below 100 m2. It uses the opening factor O, which is the vertical opening area times the square root of the average window height, divided by the total internal area. For enclosures larger than 100 m2, the Data Sheet recommends the general formula together with Kirby's values of kb:[16]

wf=O−1/2AfAt,O=AvheqAt,0.02<O<0.20

The conversion factor kb reflects how much heat the walls, floor and ceiling absorb. It is chosen from the b-factor of the linings, the square root of the product of thermal conductivity, density and specific heat.[16] Published values differ between documents, as the table shows.[17][18] In New Zealand, C/VM2 (second edition, 2025) adds a fourth factor, km, for the structural material. It equals 1.0 for reinforced concrete, protected steel and timber, while for unprotected steel it rises with the opening factor, but never below 1.0.[19]

Document kb for high b-factor (dense linings) kb for medium b-factor kb for low b-factor (insulating linings)
EN 1991-1-2:2002, as given by the Australian Data Sheet 0.04 (b above 2,500) 0.055 (b from 720 to 2,500) 0.07 (b below 720)
Kirby recommendation, as given by the Australian Data Sheet 0.05 0.07 0.09
International Fire Engineering Guidelines (2005) 0.045 (above 2,500) 0.055 (720 to 2,500) 0.080 (below 720)
C/VM2 (2025), New Zealand 0.04 (above 2,500, thin sheet steel); 0.065 (1,700, normal-weight concrete ceilings) 0.08 (1,100, lightweight concrete ceilings) 0.09 (700, plasterboard); 0.10 (400, very light insulating materials)
Symbol Description Unit
te,d equivalent time of exposure to the standard fire min
qf,d design fire load density per unit floor area MJ/m2
kb conversion factor for the thermal properties of the linings min·m2/MJ
wf ventilation factor of the Eurocode formula dimensionless
H height of the compartment m
Af floor area m2
Av area of vertical openings (windows and doors) m2
Ah area of horizontal openings in the roof m2
αv, αh vertical and horizontal opening areas relative to the floor area dimensionless
bv auxiliary factor dimensionless
O opening factor m1/2
heq weighted average height of the windows m
At total area of walls, floor and ceiling, including openings m2
km material factor in C/VM2 dimensionless

Worked example

Consider an office of 8 m by 6 m with a ceiling height of 3 m, a reinforced concrete structure and one window of 4.0 m by 1.5 m, without roof openings. In New Zealand, C/VM2 (second edition, 2025) gives a design fire load energy density of 800 MJ/m2 for offices.[20] For structural elements in an unsprinklered firecell the modification factor is 1.0.[6] For normal-weight concrete ceilings, kb is 0.065, and for reinforced concrete km is 1.0.[19][18]

The opening ratio is αv = 6.0/48 = 0.125, within the permitted range of 0.025 to 0.25, and αh is zero.[19] The formula then gives wf = (6.0/3)0.3 × [0.62 + 90 × (0.4 − 0.125)4] = 1.231 × 1.135 = 1.40. The equivalent time is te = 800 × 0.065 × 1.0 × 1.40 = 72.6 minutes, which rounds up to 73 minutes. A fire resistance rating of at least that value is required.[6][19] In its own worked examples, the 2013 commentary rounds such results up to the next 30-minute step, from 25.1 to 30 and from 50.2 to 60 minutes. Applied here, that practice would give 90 minutes.[21]

The result depends on the inputs. With sprinklers, the modification factor for structural elements of 0.5 halves the result to 36.3 minutes.[6] For a structural system without dependable deformation capacity in an unsprinklered firecell, the factor of 1.25 raises it to 90.8 minutes.[6] The 2013 commentary expects most reinforced concrete, reinforced masonry, steel and composite elements to develop such capacity, unlike cast iron in tension or bending.[22]

The concrete lining has a b-factor of about 2,012 J/(m2·s1/2·K), calculated from the properties in Introduction to Fire Safety Engineering.[23] With the Eurocode value of kb = 0.055 for that range, the same fire load gives 61.5 minutes, and with Kirby's 0.07 it gives 78.2 minutes.[16] The choice of document alone therefore shifts the answer by about 17 minutes.

Bar chart of equivalent time for one office: 36, 62, 73, 78 and 91 minutes for different factors.
Equivalent time for the office in the worked example (800 MJ/m², wf = 1.40) with different conversion factors and modification factors. Based on Ministry of Business, Innovation and Employment (2025b), pp. 22–25, and Australian Building Codes Board (2020a), Data Sheet B3, p. 37.

At the low end, the 20-minute minimum can govern. In a worked example in the 2013 commentary, a hotel guest room of 6 m by 4 m with a window of 3.0 m by 1.2 m gave 15.6 minutes. The commentary therefore used the minimum of 20 minutes.[21]

Use in design and regulation

Time equivalence condenses the usual three design stages into one. These stages are the fire exposure, the thermal response of the element and its structural or functional response.[24] The severity is expressed as a single test duration, assuming that all the fire load is consumed. The fire resistance level of the element is then compared with that duration.[24] When this method is used, the fire resistance of building elements can be shown with full-scale standard tests or with calculations under the standard temperature–time curve.[25]

Flowchart: three design stages in a row, with a shortcut arrow from fire load and ventilation to an equivalent time compared with a tested rating.
Two routes in structural fire design: the full three-stage analysis and the time equivalence shortcut, which compares one equivalent time with a tested fire resistance level. Based on Australian Building Codes Board (2020a), Data Sheet B3, pp. 32–33.

In Australia, the Fire Safety Verification Method Data Sheets list several advantages of the approach. A simple hand calculation yields a single parameter, and the required performance can be specified as fire resistance levels and verified with the standard fire test. This gives product developers and suppliers a clearly defined pathway. Structural design codes such as AS 4100, AS 3600 and AS 1720.4 also provide methods for calculating the fire resistance level of elements.[5]

In New Zealand, C/VM2 (second edition, 2025) offers three ways to model the full burnout design fire. They are the time equivalence formula with a minimum of 20 minutes, a parametric time versus gas temperature formula, or a heat release rate curve combined with a fire model.[6] According to the 2013 commentary on the first edition, most fire resistance calculations rely on the time equivalence option. The other options usually need both a structural engineer and a fire engineer, and their cost is normally justified only for large, complex buildings.[26] Where a space contains interconnected floors, C/VM2 requires separate calculations for the whole space and for each floor. The greatest severity then applies to all levels, unless the structure is designed to prevent collapse dependably.[27]

In Australia, the Fire Safety Verification Method Data Sheets present Annex F as a typical time equivalence method, with guidance for its use. The Eurocode states that the method is material dependent and not applicable to composite steel and concrete or to timber construction. Within the comparative approach of the verification method, a broader application may be justified case by case.[28] For compliance with the National Construction Code, the fire load adjustments of Annex E of EN 1991-1-2 must not be used, and the method should be limited to mainly cellulosic fire loads.[28] Where the timing of failure matters, for instance for evacuation or firefighting, the Data Sheets recommend deriving a time-dependent exposure such as a parametric fire curve.[29]

Equivalent times also appear in fire risk models. In one such model, the real fire duration follows from the fuel load divided by the rate of combustion, and a CIB formula gives the equivalent time. The fire resistance rating of a barrier is then scaled by the ratio of real to equivalent time.[30] An older correlation by Margaret Law expresses severity as an equivalent furnace duration. It is proportional to the fuel load and inversely proportional to the square root of the opening area times the enclosure surface area.[3]

Limits and uncertainty

The method has well-known weaknesses. It cannot model the behaviour of a structure through a fire scenario, so the failure time in the real fire is not predicted and cannot be compared with evacuation or fire brigade intervention. It also does not show directly the effect of heating rates and maximum temperatures. Elements that are sensitive to these may therefore be assessed unconservatively.[5] Most correlations were validated with steel protected by non-reactive insulation that stayed in place. The Data Sheets therefore advise caution for intumescent coatings and exposed timber, and note a lack of validation for penetrations, doors and lightweight structures.[5][29]

Kirby and co-workers found the method sensitive to the thickness and thermal properties of the protection and to the critical temperature adopted.[31] Without roof openings, the Eurocode limits the formula to floor areas below 100 m2. The uniform-temperature assumption has been questioned for larger or long and narrow enclosures, where a travelling fire may occur.[4] Law's correlation was developed from wood crib fires in compartments with thermally thick walls. It should not be used for compartments without openings, or with an opening smaller than about 0.4 m2.[32]

The fire load itself is uncertain. Fire severity varies from room to room and over time and is best treated as a random variable.[9] If an 80-percentile fire load is used, there is a probability of 0.2 that the equivalent time is underpredicted. The Australian Data Sheets therefore prefer to describe such a design as one that limits the probability of structural failure to an acceptable level.[33]

Common misconceptions

The equivalent time is not the duration of the fire. The 2013 commentary on C/VM2 warns that a time equivalence calculation gives an equivalent time, which is not necessarily the duration of a burnout in real time.[22] A real fire may be shorter and hotter, or longer and cooler, than the standard test exposure it is compared with, because the openings govern both its duration and its intensity.[34]

A second misconception is that an element rated for the equivalent time cannot fail. The calculation assumes complete burnout, but it does not determine when an element would fail if its resistance were exceeded.[7] Because the fire load is also uncertain, the equivalent time is a statistical estimate rather than a guaranteed limit.[33]

A third source of confusion is the term ventilation factor. In the Eurocode formula it means the dimensionless factor wf, which falls as the openings grow. In compartment fire dynamics, the ventilation factor usually means the product of the opening area and the square root of its height.[16][35]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 National Research Council of Canada et al. (2005), p. 2.6-3.
  2. ↑ 2.0 2.1 Ministry of Business, Innovation and Employment (2013), p. 79.
  3. ↑ 3.0 3.1 3.2 3.3 Iqbal and Salley (2004), p. 13-8.
  4. ↑ 4.0 4.1 4.2 Australian Building Codes Board (2020a), Data Sheet B3, p. 36.
  5. ↑ 5.0 5.1 5.2 5.3 Australian Building Codes Board (2020a), Data Sheet B3, p. 33.
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 Ministry of Business, Innovation and Employment (2025b), p. 23.
  7. ↑ 7.0 7.1 Australian Building Codes Board (2020a), Data Sheet C8, p. 228.
  8. ↑ Buchanan (2001), as cited in Iqbal and Salley (2004), p. 13-8.
  9. ↑ 9.0 9.1 Ramachandran (2002a), p. 5-110.
  10. ↑ Lie (2002), p. 4-206.
  11. ↑ Ramachandran (2002a), pp. 5-109–5-110.
  12. ↑ Wade et al. (2014) and Kodur et al. (2010), as cited in Australian Building Codes Board (2020a), Data Sheet C8, pp. 228–229.
  13. ↑ Van Rossum (2027), §8.6.
  14. ↑ England (2014), as cited in Australian Building Codes Board (2020a), Data Sheet C8, p. 229.
  15. ↑ Australian Building Codes Board (2020a), Data Sheet C8, p. 233.
  16. ↑ 16.0 16.1 16.2 16.3 16.4 16.5 Australian Building Codes Board (2020a), Data Sheet B3, p. 37.
  17. ↑ 17.0 17.1 National Research Council of Canada et al. (2005), p. 2.6-5.
  18. ↑ 18.0 18.1 Ministry of Business, Innovation and Employment (2025b), p. 25.
  19. ↑ 19.0 19.1 19.2 19.3 Ministry of Business, Innovation and Employment (2025b), p. 24.
  20. ↑ Ministry of Business, Innovation and Employment (2025b), p. 22.
  21. ↑ 21.0 21.1 Ministry of Business, Innovation and Employment (2013), pp. 225–226.
  22. ↑ 22.0 22.1 Ministry of Business, Innovation and Employment (2013), p. 77.
  23. ↑ Van Rossum (2027), §5.5.
  24. ↑ 24.0 24.1 Australian Building Codes Board (2020a), Data Sheet B3, p. 32.
  25. ↑ National Research Council of Canada et al. (2005), p. 2.6-6.
  26. ↑ Ministry of Business, Innovation and Employment (2013), p. 75.
  27. ↑ Ministry of Business, Innovation and Employment (2025b), pp. 23–24.
  28. ↑ 28.0 28.1 Australian Building Codes Board (2020a), Data Sheet B3, p. 35.
  29. ↑ 29.0 29.1 Australian Building Codes Board (2020a), Data Sheet B3, p. 34.
  30. ↑ Ramachandran (2002c), p. 3-392.
  31. ↑ Kirby et al. (1994), as cited in Australian Building Codes Board (2020a), Data Sheet B3, p. 35.
  32. ↑ Iqbal and Salley (2004), p. 13-10.
  33. ↑ 33.0 33.1 Australian Building Codes Board (2020a), Data Sheet B1, p. 15.
  34. ↑ Lie (2002), p. 4-205.
  35. ↑ Walton and Thomas (2002), p. 3-174.

References

  • Australian Building Codes Board. (2020a). Data sheets: Fire Safety Verification Method (Handbook annex, Print version 1.1).
  • Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
  • Lie, T. T. (2002). Fire temperature-time relations. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-201–4-208). National Fire Protection Association; Society of Fire Protection Engineers.
  • Ministry of Business, Innovation and Employment. (2013). Commentary for Building Code clauses C1–C6 and Verification Method C/VM2.
  • Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
  • National Research Council of Canada, International Code Council, Department of Building and Housing, & Australian Building Codes Board. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
  • Ramachandran, G. (2002a). Extreme value theory. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 5-105–5-111). National Fire Protection Association; Society of Fire Protection Engineers.
  • Ramachandran, G. (2002c). Stochastic models of fire growth. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-381–3-401). National Fire Protection Association; Society of Fire Protection Engineers.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
  • Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.
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