Equivalent concrete layer thickness of a fire protection insulation layer

ELSEVIER

Fire Safety Journal 26 (1996) 295-302 Copyright ~) 1996 Elsevier Science Limited

Printed in Northern Ireland. All rights reserved 0379-7112/96/$15.00

P i I : S 0 3 7 9 - 7 1 1 2 ( 9 6 ) 0 0 0 2 3 - 9

Equivalent Concrete Layer Thickness of a Fire Protection Insulation Layer

U. Wickstr6m & E. Hadziselimovic

Swedish National Testing and Research Institute, Fire Technology, Box 857, S-501 15 Bor~s, Sweden

(Received 21 September 1995; revised version received 25 January 1996: accepted 23 February 1996)

A BS TRA CT

The reinforcement bars in a concrete structure are usually protected against fire only by the concrete cover layer. In some cases an additional protection is needed and hence protective layers are applied, which consist o f light-weight insulation materials. The theoretical analysis outlined in this paper shows that: (a) the thermal protection capacity o f a protection layer can indeed be expressed as an equivalent concrete layer; and (b) a simple relation can be established between the thermal resistance (R = 6 /k ) o f the protection layer and the thickness o f an equivalent concrete protection. The equivalent concrete thickness yields the same time for reinforcement bars to reach 500°C as the correspond- ing thermal protection layer when the structure is exposed to the standard ISO 834 fire. All the analyses have been carried out with the finite element temperature analysis computer program TASEF. Copyright © 1996 Elsevier Science Ltd.

1 I N T R O D U C T I O N

Reinforced concrete structures lose their load-bearing capacity when the re inforcement (steel bars, pre-stressing bars, strands or wires) becomes hot. The re inforcement is usually thermally protected only by the concrete cover layer. However , sometimes it may be preferable to apply an additional insulating fire protect ion material on the concrete surface to obtain bet ter fire resistance without adding too much structural weight.

A furnace test me thod has been draf ted by E G O L F and submit ted to C E N / T C 127 (p rENV YYY5, Part 3, 1995) on how to de termine the

295

296 U. WickstrOm, E. Hadziselimovic

contr ibut ion of such protect ion systems. It is entirely based on the s tandard ISO 834 fire exposure and expresses results in terms of t empera ture at various depths and times of exposure.

In this paper it is shown, based on numerical calculations, that the thermal contr ibut ion of fire protect ion systems can be expressed in terms of an equivalent concrete cover depth. The results of one- dimensional t empera ture calculations were plot ted systematically and it was found that the thermal resistance of the protect ion layer R = ~5/k corresponds to an equivalent concrete layer thickness. ~ and k are the thickness and the conductivity, respectively, of the protect ion layer. The influence of the density of the protect ion layer was found to be negligible. The thermal resistance is the same parameter as can be used to determine the capacity of insulation products for steel structures, as detailed in Wickstr~m' and C E N / T C 1 2 7 / E N V YYY5 Part 4, 1995. Thus in principle a protect ion system need not to be tested for both concrete and steel. Only one test is needed to obtain the thermal resistance value R. In general it must, however , be noted that systematic tests have not yet been carried out to experimental ly verify the theory outl ined in this paper.

2 T E M P E R A T U R E A N A L Y S I S O F P R O T E C T E D C O N C R E T E S T R U C T U R E S

The tempera tures in concrete structures were calculated by considering fire exposure as defined in the international s tandard ISO 834. The heat transfer to the surface of the structure q was assumed according to eqn (1)"

q=6"o'(T?- T~)+/3(T~ ~)~ (1)

where the emissivity coefficient 6" was assumed to be equal to 0.8 and the convective heat transfer coefficient /3 and power Y equal to 1.0 W/m2/K and 1.33+ respectively. It must be noted that the analysis is not at all sensitive to the choice of the convective heat transfer model, as the heat transfer is dominated by the contr ibution by radiation. One-dimensional models according to the configurations in Fig. 1 were analyzed with T A S E F 2. The effects of moisture evaporat ion or other physical phenomena in the insulation as well as of any seal be tween the insulation and the concrete face were neglected.

The tempera ture was calculated in both the unprotec ted and protected structures. It was found that an equivalent concrete layer thickness d~, could be defined which gave the same protect ion to a

Fire protection insulation 297

protection layer

D

m - - . D - -

- - 4 D . - D

fire fire D

D

- - D P - ="

- - I P , - i

LL! d &~"a

Fig. 1. One-dimensional configuration of unprotected and protected concrete structures.

re inforcement bar, acting as fire protect ion insulation and thus prevent- ing it f rom reaching a critical temperature . The equivalent thickness d~, was found to be proport ional to the thermal resistance R of the protect ion insulation, independent of the concrete cover depth a of the re inforcement .

Propert ies of normal weight concrete as suggested in the T A S E F manual were assumed i.e. density p = 2300 kg /m 3 and the specific heat Cp = 1000J /kg/K, were kept constant for simplicity. The variation of thermal conductivity with tempera ture was assumed as shown in Fig. 2. Fur ther details about the calculations can be found in Wickstr6m et al?.

Tempera tu res at various depths can be calculated as a function of

Fig. 2.

1.8

1 . 6 -

v 1 . 4 -

• ~ 1 . 2 -

1- O

0 . 8 -

E 0 . 6 - ¢ -

I - -

0 .4

The thermal conductivity of normal calculations.

weight concrete

I i i ] i I i ] i i i I I i I i i I I i I

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0

Tempera tu re (°C)

assumed in the

298 U. WickstrOm, E. Hadziselimovic

Fig. 3.

800-

O

' 6 0 0 -

E 4 0 0 -

I - -

I I / J o d:30 2 0 0 / / / / , , d-40

/ ~ o d = 5 0 m m

0 , , , , i , , , , i , , , , i , , , , i , , , , i ~ , , , i , , , , i , , , ,

0 0 .5 1 1.5 2 2.5 3 3.5 4 Time (h)

Tempera tu re rise in an unprotected concrete structure at var ious depths as a funct ion of t ime.

time as shown in Fig. 3 for an unprotected structure and as shown in Fig. 4 for structures protected with thermal protection layers.

3 T H E C R I T I C A L T E M P E R A T U R E (500°C)

This analysis deals with determining the time elapsed before the reinforcement at a certain depth reaches a temperature of about 500°C.

Fig. 4.

. . . . I . . . . I , , , , I , , , , 1 , , , , I , , , I , , , , I , , , ,

k = 0 . 3 W / m K

F u l l l i n e s : 5 = 1 0 m r n a n d R = 0 . 0 3 3 m 2 K / W

8 0 0 - D a s h e d l i n e s : 8 = 4 0 m m a n d R = 0 . 1 3 3 m 2 K / W

O

°v600-

~-400- _ . . . . . . . . ..-~ .... E . . - - . - - - ' - . - E } - ' (3} _ - - - ' " . . 0 . - " ' ' - " . . o f - - ' "

200- o

0 ' ' ' ' I ' ' ' ' I ' ' ' ' L ' ' ' ' I ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 . . . .

0 0 .5 1 1,5 2 2 .5 3 3 .5 4 Time (h)

Temperature rise in protected concrete structures at various depths as a function of time.


Steel gradually loses most of its strength at this temperature. If another temperature had been chosen a similar analysis could have been carried out; however, this would have produced slightly different results.

The time to reach this temperature at various depths was compared for unprotected and protected structures. It was then noted that the thermal effect of the protection could be expressed as an equivalent concrete layer thickness d~ (de = d - a). It was also discovered that there was a linear relation between de and the thermal resistance R = 6 / k for the protection layer.

To obtain this relationship a great number of calculations were performed using the TASEF program in which the temperature histories in protected and unprotected structures were compared. Figure 5 shows how the t ime-temperature curves intercept close to the critical temperature for a protected and unprotected structure, indicat- ing that R = 0.03/0.3 = 0.1 (W/m2/K) corresponds to de = 60 mm.

When analyzing the results of several calculations it appears that the equivalent concrete layer does not depend on the assumed depth a of the reinforcement bar, but instead only on the thermal resistance R of the protection layer. Thus the diagram shown in Fig. 6 can be plotted, which displays the interdependence between R and d,.

The linear relation obtained by regression analysis is

d~ = 9 + 500R (mm) (2)

Equation (2) has been proven to be valid for the following intervals of

Fig. 5.

5 0 0 ~ ~ . . . . . . ~ . . . . I , , ~ ~ I ~ , , , I . . . . . . . . 4oo_! i i i.! ?

E 3 0 0 -

200 -

I - - ~ = 0 . 3 W / m K and a--O m i n i

1 O0 - ...... ~ , i " | . . . . . . . . . u n p r o t e c t e d s t r u c t u r e I[

. - - i I d=6O m~ I

0 . . . . I . . . . . . . . i . . . . i . . . . I . . . . i . . . . 0 0 . 5 1 . 5 2 2 . 5 3 3 . 5

T i m e ( h )

The temperature reaches 500°C at approximately the same time for a protected and unprotected structure.

300 U. WickstrOrn, E. Hadziselirnovic

E E E 0 . 1 2

0 .10 ~ 9

c -

-~ 0 .08 ¢ -

0 . 0 6

0 . 0 4 0 C

0

o 0 . 0 2 ¢ -

_.o

.-> 0

u- 0 LU

__~ , , , , , , , , , , , , , , , ! , i - E . "

: x . . . - -

Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X .,.:-[ . . . . . . . . . . . . . . . . . . . . . . . . X . ' "

X ' "

X,' XXX

. . . . . . . . . . . ~ : - X " : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

,)< x

i i , i i i I i i i i L i J i i

0 . 0 5 0 . 1 0 . 1 5 0 . 2

T h e r m a l r e s i s t a n c e , R ( m 2 K / W )

Fig. 6. Equivalent concrete thickness d, as a function of thermal resistance R = 6/k of the protection layer. The discrete points represents values obtained by numerical

calculations. The linear relation is obtained by regression analysis.

the protect ion layer thicknesses and thermal conductivities:

0.2-<k ~-0.6 ( W / m / K )

1 0 ~ 8 - < 4 5 (ram)

0.02-< R -< 0.225 (W/m2/K)

Equat ion (2) has been obta ined assuming constant thermal propert ies for the protect ion layer. The equivalent concrete layer thickness can, however , also be used for real insulation products where the conductivities change with temperature .

Calculations assuming the thermal conductivity is tempera ture de- pendent , as in the case for real products, have been carried out ~ and it has been found that eqn (2) could be applied as a good approximation if the conductivity at a t empera ture of 800°C was assumed.

4 T W O - D I M E N S I O N A L S F R U C T U R E S

A rectangular corner of a concrete structure exposed to the standard ISO 834 fire was analyzed as well (Fig. 7). A limited number of the two-dimensional calculations were per formed with the tempera tures being determined at diagonal points in the concrete, at the depth a


!1 l°

11

T

fi re

Fig. 7. Rectangular corner with protection layer.

under the protect ion layer. The conclusion is that the same relation as eqn (2) is valid, but with slightly changed coefficients.

5 E Q U I V A L E N T C O N C R E T E L A Y E R T H I C K N E S S C O N C E P T

In Eurocode 2, tables and diagrams are presented for the determinat ion of t empera tures in concrete structures. These can now be easily used for concrete structures protec ted by an insulation layer. As an example, for a concrete structure insulated with a 10 mm thick protect ion layer with a thermal conductivity of 0.1 W/m/°C at 800°C the equivalent concrete thickness can be obta ined as follows.

The thermal resistance R = 0.01/0.1 = 0.1 W/m2/K and from eqn (2) or Fig. 6 the equivalent concrete layer thickness is obta ined as d~ = 59 mm. Thus the time to reach 500°C at a point of say 20 mm (must be in the range 10-45 mm) into the structure is the same as for a point at a depth of 79 mm in an unpro tec ted structure. Further details of the calculations are presented in the full repor t from SP ~.

6 C O N C L U S I O N S

The contr ibut ion of a thermal protect ion layer to a concrete structure can be expressed in terms of an equivalent concrete layer. As a mat ter of fact it has been found by this s tudy that there is approximately a linear relationship be tween the thermal resistance of the protect ion layer (6/k) and the equivalent concrete layer thickness d~, when the structure is exposed to the s tandard fire curve according to ISO 834. The influence of the density of the protect ion layer was found to be negligible. The thermal conductivity of the protect ion layer at the t empera tu re of 800°C should be used.

302 u. Wickstrom, E. Hadziselimovic

Thus the thermal protect ion capacity, expressed as equivalent concrete thickness, can be obta ined from basic material properties. Exactly the same propert ies may be used for expressing the ability of products to protect steel structures ' .

Two-dimensional structures were also analyzed and a limited number of calculations showed that the relationship which was valid in the one-dimensional case can be used with slightly different coefficients for the two-dimensional condition as well.

R E F E R E N C E S

1. WickstrOm, U., Temperature analysis of heavily insulated steel structures exposed to fire. Fire Safety J., 9(3) (1985) 281-285.

2. Sterner, E. & Wickstr/Sm, U., TASEF: temperature analysis of structures exposed to fire--user's manual. Bor~s, SP Report, 1990.

3. Wickstr6m, U., Bengtsson, B.-O. & Hadziselimovic, E., Equivalent concrete thickness of a fire protection layer--a theoretical study. SP report (in press).

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Equivalent concrete layer thickness of a fire protection insulation layer