The fundamental step in designing structures for fire safety is to verify that the fire resistance of the structure (or each part of the structure) is greater than the severity of the fire to which the structure is exposed. This verification requires that the following design equation be satisfied:
fire resistance fire severity (4.1)
4
vent spread of fire during exposure to a fire of specified severity, and fire severity is a measure of the destructive impact of a fire, or a measure of the forces or temperatures which could cause collapse or other failure as a result of the fire. There are several different definitions of fire severity and fire resistance, leading to different ways of comparing them using different units. These comparisons can be confusing if not made correctly, so it is important for designers to understand the alternatives clearly.
As shown in Table 4.1, there are three alternative methods of comparing fire severity with fire resistance. The verification may be in the time domain, the temperature domain or the strength domain, as discussed below.
4.1.1.1 Time domain
By far the most common procedure is for fire severity and fire resistance to be compared in the time domain such that:
tfail ts (4.2)
where tfail is the fire resistance, or time to failure of the element when exposed to the standard fire, and ts is the fire severity, which is the design duration of the standard fire for the building under consideration, as specified by a code or calculated. All of these times have units of minutes or hours.
The time to failure of a building element is usually given as a fire resistance rating, which may be obtained from a published listing of ratings or by calculation, as described later. The fire duration, or fire severity, is usually a time of standard fire exposure specified by a building code, or the equivalent time of standard fire exposure calculated for a real fire in the building.
4.1.1.2 Temperature domain
It is sometimes necessary to verify design in the temperature domain by ensuring that the maximum temperature (°C) in a part of the structure is no greater than the temperature (°C) which would cause failure. Failure in this context could be failure of a separating element by
excessive temperature rise, or structural collapse of a load‐bearing member. Verification in the temperature domain requires that:
Tfail Tmax (4.3)
where Tfail is the temperature which would cause failure of the element and Tmax is the maximum temperature reached in the element during the expected fire, or the temperature after a certain time of standard fire exposure, specified by the building code.
The temperature reached in the element can be calculated by a thermal analysis of the struc- tural assembly exposed to the design fire. For a separating element, the failure temperature is the temperature on the unexposed face which would allow fire to spread into the next compartment, by local ignition or radiation to other items. For a structural element, the tem- perature which would cause collapse can be calculated from the knowledge of the loads on the element, the load capacity at normal temperatures, and the effect of elevated temperatures on the structural materials, as described in Chapter 5.
The temperature domain is typically used for an element which serves an insulating or containing function, although it cannot be used to predict integrity failures. The temperature domain is less suitable for structural elements because it does not adequately consider internal thermal gradients or structural behaviour. However, some simple elements (e.g. in steel struc- tures) may be designed in this domain (CEN, 2005b).
4.1.1.3 Strength domain
Verification in the strength domain is a comparison of the applied load at the time of the fire with the load capacity of structural members throughout the fire, such that
Rf Uf (4.4)
where Rf is the minimum load capacity reached during the fire, or the load capacity at a certain time specified by the code, and Uf is the applied load at the time of the fire.
These values may be expressed in units of force and resistance for the whole building, or as internal member actions such as axial force or bending moment in individual members of the structure. The load capacity during the fire can be calculated from a thermal analysis and a structural analysis at elevated temperatures. The loads at the time of the fire can be calculated using load combinations from national loadings codes.
4.1.1.4 Example
The comparison of fire severity with fire resistance described above can be rather confusing, so the three alternative domains of verification are illustrated with a simple example.
Figure 4.1(a) shows the temperature of a steel beam during fire exposure. Calculations show that the beam will fail when the steel temperature reaches Tfail at time tfail. The building code requires that the beam should have a fire resistance of tcode or in other words the required fire severity is tcode. Verification in the time domain requires checking that the beam does not fail
prematurely, so that the time to failure tfail is greater than the fire severity specified by the code tcode [check 1 in Figure 4.1(a)]. Verification in the temperature domain requires checking that the steel temperature which would cause failure Tfail is greater than Tcode which is the tempera- ture reached in the beam at time tcode [check 2 in Figure 4.1(a)]. These two checks will give identical results because they are both based on the same process.
Figure 4.1(b) shows the load capacity of the same steel beam during the fire. The imposed load at the time of the fire is Uf. The load capacity before the fire is Rcold and the graph shows how this decreases during the fire. At the time tcode the load capacity of the beam has reduced to Rcode. Verification in the strength domain simply requires checking that the reduced load capacity is greater than the applied load [check 3 in Figure 4.1(b)]. All three of these verifica- tion checks give identical results.
tfail Time
Time Failure of steel beam tcode
tfail tcode Rcold
Rcode
Load capacity
Uf
Code fire resistance
Code fire resistance 3
(b)
Figure 4.1 Behaviour of a steel beam in fire: (a) temperature increase; (b) loss of strength
4.1.2 Fire Exposure Models
Figure 4.2 illustrates a range of alternative design situations. The left‐hand column shows three different ways in which a design fire can be specified. Fire exposure H1 represents exposure to a standard test fire for a specified period of time tcode as prescribed by a building code. This is the most common specification of fire exposure. Traditional prescriptive codes specify the required fire resistance directly, leaving little opportunity for fire engineers to calculate a specific fire severity for any particular building. Prescriptive codes usually require fire resistance to be somewhere between half an hour and 4 h, in half hour or 1 h steps, with little or no reference to the severity of the expected fire.
Fire exposure H2 represents a modified duration of exposure to the standard test fire. The equivalent time te is the time of exposure to the standard test fire considered to be equivalent to a complete burnout of a real fire in the same room. Methods of calculating equivalent fire severity are described in subsequent sections. Many performance‐based codes allow the use of time equivalent formulae as an improvement on simple prescriptive fire resis- tance requirements.
Structural response
model Elements Sub-assemblies Structures Fire
exposure model
H1 T
T
T
ISO-834
Test or calculation
Test or calculation
Calculation occasional
Calculation occasional test
Difference in schematization becomes too large
Calculation occasional test
Calculation occasional and for research Calculation unpractical
Calculation ISO-834
tcode
te
t H2
H3
S1 S2 S3
Figure 4.2 Fire models and structural response models. Reprinted from CIB (1986) with permission from Elsevier Science
single element, a sub‐assembly or a whole structure. The words in the lower boxes show that test results are only likely to be used for single elements exposed to H1 or H2 fires, with calcu- lations becoming necessary in most other cases. Verification that a member or structure has sufficient fire resistance will be by comparison of times, temperatures, or strength as described above. With reference to Figure 4.2, verification to fire exposures H1 and H2 is likely to be in the time domain, where an assigned fire resistance (in hours) is compared with the required fire resistance (also in hours). Verification using exposure to a complete burnout (H3) is more likely to be a comparison of temperatures for insulating elements or a comparison of strength for structural elements.
4.1.3 Design Combinations
The above options illustrate that several alternative methods can be used for verifying fire resistance requirements. Because of the large number of possible combinations, it is essential for designers to specify clearly which combination of exposure and resistance is being used.
Both the design and the assessment of the design can become very confusing if the selected combination is not clearly stated and used accordingly. Table 4.2 shows a list of the most common combinations, to help designers select a combination for a particular design. In very general terms, both the accuracy of the prediction and the amount of calculation effort increase downwards in the table.