fire resistance versus flame spread resistance

Fire Resistance versus Flame Spread Resistance T. Z. H A R M A T H Y Division of Building Research National Research Council of Canada

Current fire resistance tests of compartment boundary materials should be referred to as "fire spread resistance" tests. Unless additional fire protection measures have been taken, compartment boundaries are rarely able to prevent the spread of fire out of the space of origin. The true fire resistance of all key building components, therefore, must be judged on ability of those components to withstand fire exposure from two sides.

M ANY F I R E experts still regard fire resistant compar tmenta t ion as the basic measure of fire protection. In the absence of other pro-

tecting measures, fire can spread through well-compartmented, fire resistant buildings almost as easily as in other buildings. Even the experts realizing this believe tha t the fire resistant quali ty of certain s t ructural elements of the building is an essential par t of the overall fire protect ion system.

In this paper, the conventional concept of fire resistance will be examined and a newer concept introduced. A procedure will be described by which a realistic appraisal of the performance of some key s t ructural components of a building can be obtained.

F I R E R E S I S T A N C E T E S T S

In Nor th America, ASTM Method E-119 (similar to Standard Methods of Tests of Building Construction and Material, N F P A No. 251) specifies the conduct of fire resistance tests and the interpretat ion of the findings. During a fire resistance test, a representat ive sample of an element of compar tment boundary (structure) is exposed on one side to the fire of a test furnace whose temperature is programmed to follow a unique curve, steadily increasing with time. This curve is assumed to reproduce the

NOTE: Dr. Harmathy is a research officer in the Fire Research Section, Division of Building Research, National Research Council of Canada, Ottawa.

290

Fire R e s i s t a n c e a

Z

291 b

Figure t . (a) Fire exposure as impl ied by test standards. Compar tmen t boundaries are exposed to fire on one side only. (b) Realis t ic fire exposure. Some compar tmen t 5oundaries ~ are exposed to fire on both sides.

temperature history of a hypothetical, fully developed* compartment fire. The test usually is continued until the specimen fails. Three types of failure are specified by the test standard: (1) the at tainment of a critical temperature (about 325°F or 163 ° C) by the surface of the specimen opposite to the fire exposure; (2) the at tainment of a critical temperature by some load-bearing steel component in the construction (800, 1000, or 1100 ° F or 427, 538, or 593 ° C); and (3) collapse of, or serious damage to, the specimen.

The desired duration of exposure of the compartment element to the test fire is the minimum period for which fire resistance rating (expressed in hours and fractions and multiples thereof) is required by an authoritative building code. If the specimen construction withstands the simulated fire exposure for 1 ~ hr without failure, the compartment element that it represents is "rated" as 1 ~ hr fire resistant construction. A compartment built entirely from elements with fire resistance ratings not less than the minimum required by the building code for the type of building is referred to as a fire resistant compartment. Requirements usually range from

to 1 hr. Because the specimens are exposed to the test fire on one side only, the

restflts of fire resistance tests are applicable only to fires confined to a single compartment (Figure la). Indeed, the philosophy of fire resistance testing was built on the belief that fire resistant compartment boundaries are capable of preventing the spread of fire. Judging from the criteria of failure in the fire test, one can conclude that the confinement of the fire to a single compartment is believed to be satisfactorily achieved if the compartment boundaries are (a) sufficiently resistant to heat transmission to prevent the development of dangerously high temperatures in an ad-

*The period of "fully developed" fire is the vigorously burning period during which 80 to 85 percent of the combustible materials originally present in the compartment are consumed.

292 Fire Technology

jacent (horizontally or vertically) building space and (b) strong enough to withstand structural failure and, thereby, the dispersion of flames.

Assuming, for the time being, that there is no flaw in the philosophy of fire resistance testing, one can see that these tests were visualized to yield information on the ability of compartment boundaries to withstand the spread of fires in buildings and that, correctly, one should refer to them as "fire spread resistance" tests. The practice of using the test results to judge the performance of various structural elements in realistic fires, as characterized by some degree of fire spread beyond the place of origin,* is of somewhat dubious value, as will be shown.

F I R E D U R A T I O N

Once it has become established that the true meaning of the result of a fire test is a sort of fire spread resistance of an element of compar tment boundary, it becomes imperative to examine what fire spread resistance requirements one can regard as realistic. If the fire spread resistant boundaries are as effective as implied by the philosophy of fire testing, the maxi- m u m requirement need not be much higher than the time required for the complete burnout of a compartment without human intervention.

Based on hundreds of compartment burnout tests performed in several countries and on valuable earlier theoretical work by others, this author gave a comprehensive analysis of the characteristics of compar tment fires.1 The following equations, describing the duration of fully developed compar tment fires, are somewhat simplified forms of equations presented therein, t ~:

If C < 0.079 T = 0.0249/C (1)

If C >_ 0.079 7 = 0.315 (2) where

C - Aw Hw ~ (3) A~ F

C is an extremely important parameter of fully developed fires. I t will be referred to here as the "control parameter." Equat ion 1 relates to poorly ventilated "ventilation-controlled" fires, and Equat ion 2, to well-ventilated

* B y the use of some engineer ing techniques , e.g., spr inkler ing, va r ious m e t h o d s of fire isolat ion and fire dra inage, i t is possible to e l imina te or s u b s t a n t i a l l y reduce the poss ibi l i ty of fire spread. I t is a s sumed in th i s p a p e r t h a t such eng ineer ing t e c h n i q u e s are no t employed.

t T h e mean i ng of t he symbols are expla ined in A p p e n d i x B.

:~It is c u s t o m a r y to assume t h a t , a f t e r a window has been b roken by t h e fire, t he t o t a l window area is ava i lab le for t he inflow of air , essent ia l ly t h r o u g h o u t t h e en t i re period of fully developed fire. T h e r e h a v e been suggest ions, however , t h a t some b roken pieces of the pane m a y s t ay in place for some t ime and h inder airflow. T o t ake a c c o u n t of th is possibi l i ty, t he des igner m a y choose t he "ef fec t ive" window area, Aw, as s o m e w h a t smal le r t h a n t he to ta l window area or, a l t e rna t ive ly , specify w indows t h a t a u t o m a t i c a l l y swing open on exposure to fire.

Fire Resistance

TABLE 1. D u r a t i o n o f F u l l y Developed C o m p a r t m e n t F i re s

293

rain

A ~ F = 2 l b / f t ~ F = 5 l b / f t ~- F = 10 l b / f t ~ w

A r H m = H m = H w = H m = H~v = H m = H w = Hvr = Hrz = 2 . 5 [ t 5 . O f t 8 . O f t 2 . 5 f t 5 . O f t 8 . O f t 2 . 5 f t 5 . O f t 8 . O f t

0.1 19 19 19 47 33 26 94 67 53

0.125 19 19 19 38 27 21 75 53 42

0.15 19 19 19 31 22 19 63 44 35

0.175 19 19 19 27 19 19 54 38 30

0.2 19 19 19 24 19 19 47 33 26

0.225 19 19 19 21 19 19 42 30 23

0.25 19 19 19 19 19 19 38 27 21

"fuel~surface-controlled" fires. These equations have been used to calculate the values presented in Table 1.

To admit sufficient light, the total window area is usually selected to amount to at least 10 percent of the floor area.* Thus only the values in the clear area of the table are of practical significance for modern buildings. Those in the shaded area are for buildings having window areas less than 10 percent of the floor area. Since, in residential and office buildings, the average specific fire load is known to amount to about 4.5 lbs/f t ~- (22 kg/m2), 2 -4 the data in Table 1 clearly indicate that, unless the fire load is unusually high, a fully developed compartment fire is not expected to last longer than 30 rain. In fact, fires longer than I hr should usually be regarded as clear indications that the fire spread resistant boundaries did not fulfill their function. I t appears certain, therefore, that wall and floor fire spread resistance requirements well over 1 hr are often not fully justifiable. Only for poorly ventilated spaces (e.g., basements, theaters, and large halls) or for spaces that are liable to accumulate higher than average fire loads would a fire spread resistance in excess of 1 hr be appropriate.

The finding tha t fire can, and often does, spread to other building spaces in spite of fire spread resistant compartment boundaries, comes as no surprise to fire experts. I t is well known tha t fire rarely spreads by excessive heat conduction or structural damage, as is assumed by the fire test philosophy. Most often it spreads horizontally through doors tha t were left open, vertically through windows that were broken by fire, and both horizontally and vertically through improperly fire-stopped or protected openings.

*A Bri t ish survey 2 of modern office buildings indica ted tha t , if the building is well c o m p a r t m e n ted , the average value of the rat io of (actual) window area to floor area is h igher t han 0.3.

294 Fire Technology

T W O - S I D E D F I R E E X P O S U R E

The weaknesses of the principle of fire resistant compartmentat ion are clearly recognized by now. Yet, m a n y fire experts still favor the use of highly fire spread resistant compartment boundaries, but for a reason entirely incompatible with the philosophy of conventional fire testing - - to protect the structural integrity of the most vulnerable components of the building following the spread of fire.

Once the fire has spread to the neighboring compartment, the threatened compartment boundary becomes exposed to fire from two sides (Figure lb) - - a condition tha t is not covered in the standard fire test procedure. The problem is further complicated by the fact that fire exposure of the two sides is not necessarily simultaneous, and that delayed fire in a neighboring compartment m a y cause more serious structural problems than a simultaneous fire.

If it were possible to devise a single fire test tha t could clearly reveal the most adverse structural performance of building components in realistic (spreading) fires, that test could be rightfully referred to as a fire resistance test. Although such a test may never be practical, the designer mus t not be overly concerned. Thanks to substantial improvement in recent years in the understanding of material behavior at elevated temperatures and to the use of computers in heat flow analyses, the analytical appraisal of the behavior of building components in fire has become, in many cases, a dist inct alternative to fire testing. Admittedly, there are still some dif- ficulties in the stress-strain analysis of fire-exposed structures, yet these can often be circumvented by prudent design, or resolved by small-scale benchtop type testing.

In the following section, the kinds of calculations needed for the assess- ment of the performance of some key building components in fires will be described and illustrated.

H E A T F L O W A N A L Y S E S

One can usually assume that the conditions in the two (horizontally or vertically) adjacent compartments (Compartments I and 2) on either side of the building element to be analyzed are similar, so that the characteristics of fire, among them the duration of fully developed fire, are roughly identical. Under these circumstances, it is convenient to introduce a "delay factor" interpreted as

¢ = (ton - t o l ) / . ~ (4)

and carry out analyses for a number of values* of @. @ -- 0 indicates fire beginning at the same time in both compartments, p = 1 Lndicates that in Compartment 2 the fully developed period of the fire begins when it ends in

*It will be seen la te r t ha t , w i th some ins igh t in to the p rob lem, these ana lyses can be comple te ly d ispensed with, or the i r n u m b e r s u b s t a n t i a l l y reduced.

Fire Resistance

TABLE 2. Information Used in the Numerical Studies

A) Concrete slab thickness: density: thermal conductivity: specific heat:

B) Coefficients of heat transfer before fully developed fire: during decay period:

C)

l = 0.5f t o = 137 lb/ft ~ k = 0.971 Btu/hr ft ° F c = 0.310 Btu/lb ° F

hs = 2.0 Btu/hr ft ~ ° F h~ = 4.5 Btu/hr ft"- ° F

Factors affecting fire characteristics and fire severity parameters

295

Fire severity parameters F H , Aw C r. ~z~

Fire (lb/[t ~) ([t) A---~ ([P/~/lb) m~n T~ (° F) (Btu/hr f t ~)

H 6.15 6.0 0.196 0.0781 19 1600 9380 (24) (1575)

V 12.3 6.0 0.098 0.0195 75 2040 6740 (67) (1790)

D) Delay factors chosen for FireH: ~ = 0 ,1 ,2 , 0~ for FireV: ~ = 0,0.5, 1, co

C o m p a r t m e n t 1, and ¢ --~ co indicates an isolated fire in C o m p a r t m e n t 1, developing in a way similar to t h a t assumed b y the convent iona l fire tes t ing phi losophy.

T h e building e lement to be s tudied has been selected as a s imple one del ibera te ly - - a 6-in-thick re inforced concrete slab t h a t m a y be regarded as pa r t of a load-bearing wall or ceiling separa t ing C o m p a r t m e n t s 1 and 2 (assumed to be identical). All in format ion pe r t i nen t to the s t u d y is l isted in Tab l e 2.

As will be shown in Appendix A, the t e m p e r a t u r e h is tory of the slab (or a n y building e lement in fire) depends pr imar i ly on two variables; r and q~. In Tab le 2 they are referred to as "fire sever i ty pa rame te r s . "

T h e sever i ty of fires is charac ter ized by a group of three p a r a me t e r s - - the du ra t ion of ful ly developed fire, r; the average gas t e m p e r a t u r e in the c o m p a r t m e n t dur ing the period of ful ly developed fire, T~; and the "effec- t ive hea t f lux," i.e., the average hea t flux pene t ra t ing the c o m p a r t m e n t boundaries , q~, during the period of fully developed fire. T h e value of r can be calculated f rom Equa t i ons 1 to 3. Those of T~ and q~ are ob ta ined f rom the tr ial and error solut ion of two equat ions (Equat ions 51 and 62 of Reference 1). T h e values in the brackets in Ta b l e 2 re la te to exper imenta l values derived f rom the tes t resul ts of Bu t c h e r e t al. s, 6

T h e behavior of the slab will be ana lyzed under two sets of fire conditions. T h e y represent s imulat ions of two full-scale b u r n o u t tes ts f rom am on g a series conduc ted by B u t c h e r e t al. 5, 6 T h e first fire, refer red to as F i re H, is charac ter ized by a cont ro l parameter , C, v e ry close to the critical value, 0.079 (see Equa t i ons 1 to 3). T o emphasize the significance of this

296 Fire Technology

fact, at tention is directed to the full-lined curves in Figure 7 of Reference 1, which represent plots (at three specific fire loads) of the effective heat flux against the "ventilation parameter ," a variable of which the control parameter, C, used in this paper, is a normalized form. (The critical values of the ventilation parameter, indicated by arrows in the figure, correspond to the critical value of the control parameter, 0.079.) Since the maxima of qE are seen to occur always at C = 0.079, and the values of these maxima depend hardly at all on the specific fire load, and since q~ decreases sharply as C increases beyond 0.079 while ~ remains unchanged (see Equat ion 2), one can conclude that Fire H represents the most adverse conditions (or nearly so) that may occur among well-ventilated, fuel-surface-controlled fires, i.e., whenever C _> 0.079.

The second fire, referred to as Fire V in Table 2, represents a very severe fire, due to the high specific fire load and poor ventilation (and the resulting low value of the control parameter). The great severity of this fire, in relation to Fire H, is manifest from its long duration, which grossly overshadows the somewhat lower value of the effective heat flux.

The first step in evaluating the fire resistance of a construction is the calculation of its temperature history under the most adverse fire conditions tha t may arise. Because the fire severity parameters are determined by the design and contents (and, in tur-n, by the occupancy) of the building, finding the most adverse temperature history consists (in principle) of a series of heat flow studies performed for a range of values of the delay factor, ~, a t constant values of the fire severity parameters. The numerical procedure used in the studies of this paper is given in Appendix A.

The calculation procedure is different from the conventional ones. I t has been customary to use a temperature history for the compar tment (e.g., the temperature-t ime curve defined by ASTM E-119 when dealing with standard fire exposure) as the imposed reference condition. In this paper, the effective heat flux (i.e., the average heat flux penetrating the construction) is used as the imposed reference condition during the period of fully developed fire. In this way not only do the calculations become more simple (a constant rather than a variable quanti ty is used in the boundary conditions), but the results become more realistic. * The surfaces of the construction are assumed to exchange heat with the surroundings according to Newton's law before and after the period of fully developed fire.

To avoid unnecessary complications, the material properties and heat transfer coefficients have been selected as constants. Because of the neglect of the beneficial effect of moisture, the calculation errors are on the safe side.

*The con t ro l p a r a m e t e r un ique ly de t e rmines t he r a t e of bul-aing of the c o m b u s t i b l e ma te r i a l s in t h e c o m p a r t m e n t and, in tu rn , the r a t e of h e a t evo lu t ion (see R e f e r e n c e 1 for detai ls) . T h e effective h e a t flux can be ca lcu la ted as descr ibed in Re fe r ence 1, or j u s t e s t ima ted for p re l imina ry ca lcu la t ions as 10 to 50 pe rcen t of t he r a t e of h e a t evolu t ion f rom the fuel. (Higher pe rcen tage values usual ly pe r t a i n to lower va lues of t he cont ro l pa r am e t e r ) .

Fire R e s i s t a n c e lOOO , [ i ~ I r

~ ~ ~ 8 0 0 6 0 0 + I = }0 r a i n ~ : 20 ra in

400

200 42 _

O0 0 4 0 8 O-- 014 ( 08

J [ I

t = 30 rnin

i ' ' ' 04 08

+, t : 4 0 m i a

2-.

04 08

t = 5 O m i n

5~

I 0.4 08

i ( l [ t ~ 60 r a i n

I t l l

04 08

297

4 1 : 7 0 mln

"1

I i i i I 04 08

Figure 2. Temperature history of 6- in. reinforced concrete slab under exposure to Fire H. Curves: (1) ~ = O, (2) ¢z = 1, (3) ¢ = 2, (4) ~ - -~ ~ .

Some results of the two series of heat flow analyses are presented in Figures 2 and 3. • The temperature histories of the two steel reinforcing bars, assumed to be located at 1 13/64 in. from the surfaces, are shown in Figures 4 and 5.

E V A L U A T I O N O F T H E F U L L R E S I S T A N C E T O S P R E A D I N G F I R E

Once the results of heat flow analysis are available, the designer can decide whether the construction is liable to undergo thermal conditions that may endanger its stability. Unfortunately, there is no well-defined procedure that he can follow. In the case of construction containing concrete and steel, his decision may be based on the following facts: (1) the loss of ultimate and yield strengths of structural and reinforcing steels is usually insignificant below 7 0 0 ° F (371 ° C), 7 (2) the creep of steel becomes substantial above 1,000° F (538 ° C), 7 (3) the loss of compressive strength of most concretes is negligible up to about 400 ° F (204 ° C), ~, g and (4) concretes of low permeability may spall in fire at relatively low moisture content.'°

If concrete is regarded only as an insulating cover on the load-bearing steel bars, the temperatures that it may attain need not be considered. The only important consideration is that it must not be liable to spall or disintegrate under the prevailing conditions. On the other hand, if the concrete carries a substantial compressive load, that portion of the con-

Figure 3. Temperature history of 6-in. reinforced concrete stab under exposure to Fire V . Curves: (1) g, = O, (2) ~ = 0.5, (3) ¢ = 1, (4) ¢--+ ~z.

2000 -- ! + . t ~25 rain 1600

80o }

400 I~

04 0.8

1=50 m / n

I

{ 014 I 0!8

1 " , ; |

I ! ;75 rain .

04 OB

L

04 0.8

t l £

t:125 min t :150 caln

4

0.4 0.8 0 0.4 O.B

. I

I=175 rain

3

0.4 0.8

298 100 I i I t I

c u ~vEs= [i] ~ B, [~] ~= l , [3] , ~ B, [47 ~ ~ 6O0

ON SIDE I OF SLAB

500 . . . . ON SIDE 2 OF SLAB

400 I ~SIDES 1 , 2 ) ~ I

..,- - - , _ _ t -

0 10 20 30 40 50 60 70 80

T I~E, D<4IN

Figure 4. Temperature of steel reinforcing bars in Fire Ho Bars located at a depth of lI~ff~ in. from surfaces.

crete attaining temperatures in excess of 400°F (371 ° C) m a y exhibit significant plastic deformation and become the cause of an undesirable redistribution of stresses.

An inspection of Figure 4 reveaks that, in Fire H, the steel reinforcing bars did not at tain a temperature that could be considered as detr imental for any of the delay factors examined. I f the construction is s trongly re- strained, the designer may have to consider the stress build-up caused by the thermal expansion of steel and concrete. Experience obtained from standard fire tests indicates that, if the construction is exposed to fire from one side only, it can absorb much of the excess stress wi thout serious damage by deflecting toward the fire. Unfortunately, experimental information is not readily available on the more adverse si tuation when a construction is exposed to fire on both sides simultaneously.

A close examination of Figure 2 will reveal that, as the delay parameter increases (within a range that may have practical significance), the thick- hess of the layer on Side 2 (x/1 = 1) of the slab that attains a tempera ture of 400 ° F or more wilt increase slightly. Consequently, some problems may arise ff the concrete slab is loaded with a bending moment (e.go, if it rs par t of a ceiling) and if, as is usual, the compressive strength of concrete has been relied on in the design. Yet, as emphasized earlier, Fire H may be considered as representing the most adverse conditions among fuel-surface- controlled fires. In view of this and of the fact that the maximum temperatures at tained by the construction (see Figures 2 and 4) would be much

F i r e T e c h n o l o g y

J J

F i r e R e s i s t a n c e

I I t t I

c u RYES: [ l ] ~,o o, [2] *o o. 5, [B] , ~ t, [4] ~ ~

299 1400[

1200 1 ON SIDE i OF SLAB

I000 I - ON SIDE 2 OF SLAB z~-~ .,,/" ""-,. -

t l~s,DEs 1, z l ~ . / ~ . " 9 ," "'-. ; " ' .

o ~ 5 I I .1 i _ { _] 0 25 50 75 100 125 150 175 200

TIME, MIN Figure 5. Temperature of steel reinforcing bars in Fire V. Bars located at a depth of 11~ in. from surfaces.

lower had the beneficial effect of moisture been considered, one may venture to say that the designer need not be overly concerned with the structural performance in fire of conventionally designed reinforced concrete constructions in residential or office occupancies as long as the control parameter is larger than 0.079 - - i n other words, as long as the potential fires are expected to be fuel-surface-controlled. This claim is essentially a confirmation of the one made earlier by this author 1~ on the basis of less comprehensive reasoning.

As Table I shows, the value of the control parameter for Fire V is much less than the critical value, 0.079. This fire is strongly ventilation-controlled and, therefore, very severe. Figures 3 and 5 reveal that, in the case of two- sided exposure, the temperature of the entire concrete mass may rise above the critical 400 ° F (204 ° C) limit and, with substantially delayed exposure of Side 2 ( x / l = 1), the temperature of the steel reinforcing bars on that side may also rise well into the region of fast creep. To avoid possible structural failure, the designer can either change the construction (e.g., by applying insulation to both sides of the slab) or make some changes in the compartment design (e.g., increase window area or window height or both, or reduce the fire load) in order to increase the control parameter to above 0.079.

Even if the key structural element is part of the outside shell of a building, it may still be exposed to fire on both sides. The exposure of the outer surface originates from the flames issuing from the windows. The

300

qI

oi h a

i, t I ¢

o o o

n-I n

I N

0

n*l

o N?l

SIDE 2

'N h~

n a

Fire T e c h n o l o g y

Figure 6. Subdivision of concrete slab for numerical heat flow analysis.

dura t ion of the outside exposure is rough ly equal to the per iod of ful ly deve loped fire in the adjoining compar tmen t s . H e a t flux to the o u t e r surface m a y be es t imated f rom the energy released b y the fuel ou ts ide the windows, as described in Reference 1.

C O N C L U S I O N S

W h a t is usual ly refer red to as the "fire res is tance" of c o m p a r t m e n t boundar ies is, in effect, a measure of thei r abi l i ty to p r e v e n t t h e spread of fire by some mechanisms implied by the s t anda rd tes t p rocedure . In real i ty, fires spread by different mechanisms and, therefore , c o m p a r t m e n t boundar ies m a y become exposed to fire on bo th sides. T h e resu l t s of s t and a rd fire tes ts are no t appl icable to such si tuations.

T h e per fo rmance of a s imple bu t co mmo n s t ruc tura l e l ement o f a building has been ana lyzed under condit ions corresponding to two real is t ic fires. I t has been concluded t h a t convent iona l concrete-steel s t ruc tu res a r e l ikely to func t ion sat isfactor i ly in a spreading fire, p rov ided t h a t the "con t ro l p a r a m e t e r " character iz ing the na tu re of the fire is h igher t h a n a cri t ical value.

R E F E R E N C E S

i I-Iarmathy, T. Z., "A New Look at Compartment Fires - - Parts I and II," Fire Technology, Vol. 8 (1972), pp. 196 and 326.

2 Baldwin, R., Law, M., Allen, G., and Griffiths, L. G., "Survey of Fire Loads in Modern Office Buildings - - Some Preliminary Results," JFRO, Fire Research Note No. 808 (1970).

a Witteveen, J., "Brandveitighed Staalconstructies," Centrum Bouwen in Staal, Rotterdam, Holland (1966).

Nilsson, L., "Brandbelastning i Bostadslangenheter" (Fire Loads in Flats), Report No. 34:1970 of the National Swedish Institute for Building Research.

5 Butcher, E. G., Chitty, T. B., and Ashton, L. A., "The Temperatures Attained by Steel in Building Fires," JFRO Fire Research Technical Paper No. 15 (1966).

6 Butcher, E. G., Bedford, G° K., and Fardell, P. J., "Further Experiments on Temperatures Reached by Steel in Buildings," Paper 1, Proceedings of a Symposium held at the Fire Research Station, January 1967, JFRO (1968), p. 1.

A P P E N D I X A

Because the mass of steel in a convent iona l re inforced concre te s t r u c t u r e is negligible in compar i son wi th the mass of concrete, t he presence of the reinforcing bars can be disregarded in hea t flow studies. Thus , t he hea t flow th rough a re inforced concrete slab can be mode led as t h a t t h ro u g h a homogeneous concrete slab.

Fire R e s i s t a n c e 301

Figure 6 shows the subdivision of the slab into a number of elementary slabs in preparation for the numerical heat flow analysis. The reference points in the elementary slabs are numbered from 0 to N. The numerical procedure is similar to tha t described in Reference A-1 and will not be discussed here in detail. The equations used for the calculation of the temperatures at the reference points and at time level t = (j + 1) At are as follows: for point 0;

To(J + ~) = T j +

for points 1 < n < N - 1;

T~(; + ~) = T j + kA__~t p c A x 2

for point N;

T,v(~' + ~ = T~i + -

where, if to~ = 0,

q2 j = qE

2k At q 1 j AX T d + T~i + (A1)

pc Ax 2 k

T(~_ 1) ~ - 2T~J + T(~ + 1) i (A2)

2 k A t T ( N _ 1) j -- TN j + q~JAx (A3) pc Ax 2 k

i f0 < t < ~- (A4)

ha ( T ~ - T j ) i f t > (A5)

if t < ~b ~ (A6)

f i e f < t < r (¢ + 1 ) (A7)

h a ( T ~ - T,v ~) i f t > T(¢ + 1 ) (AS)

The reason for including the coefficient 2/3 in Equations A5 and A8 is as follows. After the period of fully developed fire, fresh air continues to rush into the compartment at approximately an unchanged rate, so tha t the temperature in the compartment decreases rapidly. Yet the charring remains of the fuel continue to evolve heat at a rate amounting to about 13 percent of that during the hffly developed fire. I t is estimated tha t a realistic "driving force" for the cooling of the construction during this so-called "decay period" of fire is obtained if the driving force toward a cool environment is reduced by one third.

The initial conditions are, if t = 0,

To o = T1 ° = T.~ ° = = T~ (A9)

These computations were performed with the aid of an HP9820A program- mable desk calculator.

A C =

C = F = h = H = k = l = n --

N = q = q~ =

t = At = T =

To = X =

Ax =

GREEK LETTERS

p = density, l b / f t ~

302 F i re T e c h n o l o g y

R E F E R E N C E

A-~ H a r m a t h y , T . Z., A Treatise on Theoretical Fire Endurance Rating, A S T M Special Techn ica l P u b l i c a t i o n No. 301 (Amer ican Socie ty for T e s t i n g a n d Ma te r i a l s , Ph i l ade lph ia , 1962), p. 10.

A P P E N D I X B - - N O M E N C L A T U R E

= area, "e f fec t ive" a rea (for windows), f t 2 specific heat , B t u / t b ° F control p a r a m e t e r , f t ~ 12/lb specific fire load, l b / f t 2 hea t t r ans fe r coefficient, B t u / h r f t ~ ° F height, f t t h e r m a l conduc t iv i ty , B t u / h r f t ° F th ickness of slab, f t 1 , 2 . . . . N - 1 n u m b e r of reference poin ts less one hea t flux, B t u / h r f t ~- "effect ive hea t f lux," B t u / h r f t ~ t ime, hr (min in F igures 2 to 5 for convenience) t ime inc rement , hr t e m p e r a t u r e , o F ave rage gas t e m p e r a t u r e in c o m p a r t m e n t , ° F d is tance f r o m side 1 of slab, f t d is tance be t ween reference poin ts

r = du ra t ion of ful ly deve loped fire, hr (min in Tab l e s 1 and 2 a n d Figures 2 to 5 for convenience)

= de lay factor , d imensionless

SUBSCRIPTS

b = pe r t a in ing to the t ime preceding the per iod of ful ly deve loped fire = per ta in ing to the " d e c a y per iod" of fire = of the cool e n v i r o n m e n t = of the floor = a t the n - th reference po in t

N = a t the N - t h reference po in t o = of the beg inn ing of per iod of ful ly deve loped fire; a t the 0 - th refer-

ence point ; a t t = 0 w = of the window 1 = (when used wi th t or q) for the fire in c o m p a r t m e n t 1, or for side 1

of the s lab (a t x / I = O) = (when used wi th t or q) for the fire in c o m p a r t m e n t 2, or for side 2 of

the slab (a t x / l = 1)

continued on page 330

330 Fire Technology

R E F E R E N C E S

1 Brown, Arthur A., and Davis, Kenneth P., Forest Fire; Control and Use (McGraw- Hill, New York, 1974).

2 Storey, Theodore G., and Noel, Susan M., Large Fires in the World Since 1825 (U.S. Department of Agriculture, Forest Service, Washington, D.C., 1965).

3 Storey, Theodore G., "FOCUS: A Computer Simulation Model for Fire Control Planning," Fire Technology, Vol. 8, No. 2 (May 1972), pp. 91-102.

4 U.S. Department of Agriculture, Forest Service, National Forest Fire Reports (Washington, D.C., 1971).

Kourtz, Peter H., "A System to Predict the Occurrence of Lightning Caused Forest Fires," Canadian Forest Service, Forest Fire Research Institute, Information Report FF-X-47 (March 1974), pp. 1, 6-8.

Berry, Brian J. L., "Problems of Data Organization and Analytical Methods in Geography," Journal of the American Statistical Association, Vol. 66 (June 1971), pp. 51-523.

McCutchan, Morris H., Tyan, Bill C., and Schroeder, Mark, "Meteorological Input to Fire Command and Control Systems (FCCS)," Pacific Southwest Forest and Range Experiment Station, Riverside, California (unpublished 1973), pp. 1-58.

8 Fuquay, Donald M., "Status and Problems in the Development of Lightning Risk," U.S. Department of Agriculture, Forest Service, Northern Forest Fire Labora- tory, Missoula, Montana (1974), p. 17.

Pierce, J. R., Symbols, Signals and Noise: The Nature and Process of Communi- cations (Harper and Brothers, New York, 1963).

l°Fishman, George S., and Kiviat, Philip J., "Digital Computer Simulation: Statistical Considerations," The Rand Corporation Memorandum R~vI-5387-PR (November 1967), pp. 4-10.

continued from page 302

SUPERSCRIPTS

0, j, (j + ~) a t t h e t i m e level t = 0, jar, and ( j + 1)At, r e spec t ive ly .

NOTE: This paper is a contribution from the Division of Building Research, National Research Council of Canada and is published with the approval of the Director of the Division.

fire resistance versus flame spread resistance

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