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A suggested logic for trading between fire-safety measures
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A Suggested Logic for Trading
between Fire-Safety Measures
by T.Z. Harmathy
Reprinted from
Fire and Materials
Vol. 10, No. 3 & 4, September/ December 1986
p.
141 -143
(IRC Paper No. 1471)
Price $3.00
NRCC 27997
L ' a u t e u r e x p o s e une l o g i q u e s i m p l e pour e x p r i m e r l ' 6 q u i v a l e n c e d e s mesures d e s g c u r i t g i n c e n d i e . Cette l o g i q u e e s t fondGe s u r l e p r i n c i p e s u i v a n t : t o u t e combinaison d e mesures d e s g c u r i t g i n c e n d i e e s t s a t i s f a i s a n t e t a n t q u ' e l l e n ' e n t r a h e p a s d e s t a w
d e p e r t e s m a t ' e r i e l l e s ou d e d i k e s ou b l e s s u r e s s u p ' e r i e u r s a u n i v e a u a c c e p t 6 p a r l a s o c i 6 t g .
FIRE AND MATERIALS, VOL. 10, 141-143 (1986)
A
Suggested Logic for Trading between
Fire-safety Measures
T. Z. Harmathy
National Research Council Canada, Institute for Research in Construction, Ottawa, Canada
i
A simple logic is presented for expressing the equivalence of fire safety measures. It is based on the principle that anycombination of safety measures is acceptable as long as it does not lead to losses (property and human losses) above the level accepted by society.
How to trade between various passive and active measures to arrive at equivalent levels of fire safety in buildings has long been a controversial and hotly debated issue. This note suggests a coherent formulation for trade- off decisions. No effort will be made at this stage to identify all input variables. A more or less complete list of these variables will be compiled by a Delphi group.
BASIS OF TRADE-OFF DECISIONS
Since the purpose of fire safety measures is to prevent fire losses (human losses-deaths and injuries-as well as property losses) it is logical to claim that any combination of fire safety measures is permissible as long as it does not lead to losses beyond a level accepted by society. Clearly, that loss level is a function of the type of occupancy, and may also vary from region to region. Defining the sphere of applicability of a trade-off scheme is, therefore, a decision that should precede the collection of data on which the scheme is to be based.
Repugnant as it may sound to many, in an economic sense only those losses count as such that can be expressed in monetary terms. As to fire losses in buildings, a great deal of information is available through the (US) National Fire Incident Reporting System and through other data- banks. The monetary equivalent of human losses can be evaluated from statistics on injuries and deaths, and from information on the costs of medical treatment, hospitaliz- ation, and damages awarded by the courts. All the loss data relate to fires in buildings built according to regul- ations which have been in force for sometime; consequent- ly they reflect the loss level society is willing to tolerate. There have been suggestions that, thanks to continuing efforts to improve the safety of life, the loss level society is willing to tolerate will decline during the years. Yet, without prophetic sight, the designer can only speculate about such unknown variables as society's tolerance of risk and economy. There seems to be no compelling reason to factor in future trends into present-day decisions.
It may be noted that a certain proportion of the
insurance premium (probably somewhere between 20%
and 50%) that the insurance companies set aside for paying fire losses could be regarded as a rough measure of
the expected yearly fire loss for a given type of building in a given region.
LOSSES ACCORDING TO TYPES OF FIRES The expected number of ignitions per year, N, is usually described as
N=KAa (1)
where A is the total floor area of the building and
K
and u are empirical constants to be derived from statistical data.' Some information on K and u is available for various o c c ~ p a n c i e s . ~ ~ ~The loss depends on the nature of the fire that follows ignition. Figure 1 shows a scheme for classifying fires. In this figure,
P: Fires that remain in the preflashover stage. The fire
Ignition Fire remains ~n pref lashover stage Fire grows into the fully developed stage FSC FS D F N
I
I1
.
Fully developed Fully developed Non spread~ng fire spreading fire spreading fully developed by COnvection by destruction fire Figure 1. Classification of fires following ignition.
0308-0501/86/040141-03$05.00
0 1986 by John Wiley & Sons, Ltd.
Received 25 March and 14 July 1986 Accepted 19 August 1986
142 T. 2. HARMATHY
itself is confined to the compartment of origin. Pro- building in question can now be written as: perty and (possibly) human losses occur mainly in the = NPpIp
+ N(l - Pp)
compartment of origin, but occasionally (due to smoke
spread) also outside that compartment. x [(I- PFSD
-
PFNYFSC+
PFSD~FSD+ PFN~FNI
(4) F: Fires that grow into the fully developed stage. The condition of acceptability of a fire-safety system is FSC: The fire spreads by c~nvection (through a door that L should not exceed the loss level accepted by society:or window left open by the tenants or destroyed
by the fire, or perhaps through some other L S S ( 5 ) opening) to other building spaces, while the where S is the annual loss accepted by society. As non-mobile b~undaries of the compartment are mentioned earlier, it is, in general, a function of occup- still structurally Sound.* Property and ( ~ 0 s - ancy, and may vary from region to region.
sibly) human losses occur both inside and out- side of the compartment of fire origin.
FSD: The fire spreads by the destruction of one or ESnMAnON OF PROBABILITIES more non-mobile building elements (wall, ceil-
3
ing, etc.). and (possibly) If quantitative information on the Ps and Is is available forhuman losses Occur inside and the a range of conditions, Eqns (4) and (5) can be used to
compartment of origin. examine a number of systems from the point of view of FN: The lire not Wead. loss Occurs their equivalence from a fire safety point of view. (Of
in the fire course, some of these systems may prove impractical on Human loss may occur both inside and outside the basis of further cost-benefjt studies.)
the compartment (the latter due to smoke It seems extremely unlikely that statistical data will spread). ever be available in such detail that P, and PFN could be The following equations apply: reliably evaluated for any combination of situations and Given ignition, design features. It is suggested that these probabilities be P p + P F = 1 (2) looked upon as consisting of a number of contributions:
Given flashover, PP = (PP)o
+
C
(APP)~i (6)
P~~~
+
P~~~+
P~~ = I (3) PFN = ( P F ~ ) ~+
C
(APFN)ii (7)
where the Ps are probabilities of the various types of fires
indicated in the subscript, as explained in Fig. 1. where (P,), and (P,,), are probabilities related to a P,,,, the probability that destructive spread occurs reference set of conditions, and (AP,), and (APFN)! are (given flashover), can be preselected by appropriately (positive or negative) incremental probabilities associated
defining the fire resistance requirements4 with the ith factor representing some deviation from the Information on the average loss (property and human) reference conditions. Such incremental probabilities per incident for the various types of fires, I,, I,,, IF,, could be generated using the Delphi technique.
and I,,, can probably be derived from statistics to be The reference set of conditions could perhaps be defined obtained from the National Fire Incident Reporting as those characteristic of a two-storey apartment building System and other sources.+ Judgement on how to interpret in a small town, average with respect to access by the fire these loss data should, of course, be made after an department, built without combustible linings of any kind examination of the available material. One is inclined to and employing no special fire-safety measures. It is think that:
(1) I,, I,,, and IF, should be looked upon as functions of
occupancy and perhaps type of building (high-rise, Table 1. L i t of factors that may call for incremental proba-
low-rise, row, detached, etc.); and bilities (Y: dependence on factor expected, N: de-
(2) IF,, should be considered as a function of the nature of pendence not expected)
the building element destroyed by the fire (wall, PP PFN
ceiling, roof, column) as well as of occupancy and type Building height Y Y
Average compartment size Y N
of building. Dense furnishings Y N
The fire loss expectation for a one-year period, L, for the Combustible lining in compartment Y N ! Combustible lining in corridor N Y Combustible lining of building exterior N Y
Smoke detector Y N
*Convective spread is the most frequent. It usually occurs shortly after Sprinklering Y N the onset of the fully developed fire(e.g. ifadoor or window is left open or Building pressurization N Y
a window breaks), or sometime during the First 45 minutes if a door doors N Y (which, as a rule, is the weakest boundary element) is destroyed by the Access by fire department
fire. For buildings conforming to some elementary Fire resistance Y Y requirements, fire spread by the destruction of a non-mobile compart- from fire Y Y ment boundary is rare. Size of municipality Y Y 'If sufficiently detailed information on these variables is not available, Winter temperature N Y
the scheme discussed in this paper will at least give some guidance on O C C U P ~ ~ C V Y N how loss data could be more felicitously collected and broken down in
A SUGGESTED LOGIC FOR TRADING BETWEEN FIRE-SAFETY MEASURES 143 expected that for such a 'reference building' (P,), and result, the value of L will decrease. The designer may now (P,,), can be derived from statistical data. increase PFSD and still remain within the bounds imposed
A
(possibly incomplete) list of the factors the Delphi by Eqn (5). An increased value of P,,, on the other hand, group might consider in determining incremental proba- leads to a reduction in fire resistancerequirement^.^
bilities is given in Table 1. To prevent P, and P,, fromassuming unrealistic values as a result of applying incre-
mental contributions, some limitation may be imposed on STATISTICAL DATA VERSUS
their maxima and minima. For example, 0.2
<
Pp<
0.9. DELPHI DECISIONS TRADING OFF FIRE RESISTANCE. REQUIREMENTS
Rightly or wrongly, fire-resistant compartmentation is still regarded as the basic tool in achieving fire safety. The problem most commonly met in fire-safety design is, therefore, how to decide on fire resistance requirements and how to trade them off against active fire-safety measures (e.g. smoke detection).
As an example, how to trade off fire resistance require- ments against sprinklering will be discussed briefly. Equations (4) and (5) can be used to solve the problem. With the use of sprinklers, the probability that the fire will remain in the preflashover stage, P,, will greatly increase, bringing about an increase in the first term on the right- hand side of Eqn (4) and a decrease in the second term. Since I, (the loss associated with preflashover fires) is much smaller than I,,, I,,, or l,, (losses associated with fully developed fires), the decrease in the second term will greatly overshadow the increase in the first term; as a
One may object to the use of the Delphi technique in quantifying P, and P,, on the grounds that the values, even though arrived at by experts, still hide a great deal of subjectivity. Yet, as pointed out earlier,5 the use of statistical data in complex situations is not necessarily free of subjectivity either. For example, data on fire incidence may represent averages for the country, province, city or district, and the designer may choose any of these values to arrive at the result he or she had in mind all along.
Naturally, values obtained using the Delphi technique can be replaced later by statistical data if such data become available. Until then, they offer a means of codifying fire-safety design.
COST-EFFECTIVE DESIGN
With the technique outlined in this note the designer can derive a number of 'equivalent' free-safety systems. Once these equivalents are known, he or she can determine their relative economic advantages.
NOMENCLATURE
A total floor area of the building P probability of the type of fire indicated in the
K
constant subscript (see Fig. 1)1 loss (property and human) per incident for the type A P incremental probabilities
of fire indicated in the subscript (see Fig. 1) S annual loss level accepted by society L fire loss expectation for a one-year period a constant
N the expected number of fires for a one-year period
REFERENCES
1 . G . Ramachandran, A review of mathematical models for asessing ational Conference of Actuaries, Oslo (June 1972).
fire risk. Fire Prevention 28 (May 1982). 4. T . Z . Harmathy and J. R. Mehaffey, Design of buildings for
2 . R. Rutstein and R. A. Cooke, The value of fire protection in prescribed levels of structural fire safety. In T . Z.Harmathy (ad.),
builings. Home Office Scientific Advisory Branch Report No. Fire Safety: Science and Engineering ASTM STP 882, p. 160,
17/78, HMSO, UK (1978). Philadelphia (1 985).
3. G . Benktander, Claims frequency and risk premium rate as a 5. T . Z. Harrnathy, The Delphi method: a complement to research.
T h i s paper i s being d i s t r i b u t e d i n r e p r i n t form by t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n . A l i s t of b u i l d i n g p r a c t i c e and r e s e a r c h p u b l i c a t i o n s a v a i l a b l e from t h e I n s t i t u t e may be o b t a i n e d by w r i t i n g t o t h e P u b l i c a t i o n s S e c t i o n , I n s t i t u t e f o r R e s e a r c h i n C o n s t r u c t i o n , N a t i o n a l Research C o u n c i l of C a n a d a , O t t a w a , O n t a r i o ,
KlA
0R6.Ce document e s t d i s t r i b u g sous forme d e t i r e - a - p a r t p a r 1' I n s t i t u t de r e c h e r c h e e n c o n s t r u c t i o n . On peut o b t e n i r une l i s t e d e s p u b l i c a t i o n s de 1 ' I n s t i t u t p o r t a n t s u r les t e c h n i q u e s ou l e s r e c h e r c h e s
