Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la
première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Research Paper (National Research Council of Canada. Division of Building
Research); no. DBR-RP-622, 1974
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.
https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=5a42dfb4-01fa-4b9d-85cf-de28d5d4a4b9
https://publications-cnrc.canada.ca/fra/voir/objet/?id=5a42dfb4-01fa-4b9d-85cf-de28d5d4a4b9
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.
https://doi.org/10.4224/40001756
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Fire resistance of reinforced concrete columns
Fire Resistance of Reinforced Concrete Columns Resistance au feu des colonnes en beton arm6 Feuerwiderstand von Stahlbetonstiitzen
T.T. LIE D.E. A L L E N
Division of Building Research National Research Council of Canada
Ottawa, Canada
In the p a s t , the f i r e r e s i s t a n c e of s t r u c t u r a l m e m b e r s could only be d e t e r - mined by subjecting t h e m to s t a n d a r d f i r e t e s t s . Now i t i s possible to d e t e r m i n e the f i r e r e s i s t a n c e of v a r i o u s s t r u c t u r a l m e m b e r s by calculation.
A n u m e r i c a l p r o c e d u r e h a s been developed (1) to calculate the f i r e r e s i s - tance of s q u a r e r e i n f o r c e d c o n c r e t e columns and h a s b e e n checked w i t h the r e s u l t s of a c t u a l f i r e t e s t s . T h e p r o c e d u r e has b e e n u s e d to calculate f i r e r e s i s t a n c e under both s t a n d a r d AST M t e s t conditions (1) and under conditions
that m o r e c l o s e l y r e s e m b l e those e n c o u n t e r e d i n p r a c t i c e (2).
Under s t a n d a r d t e s t conditions, t h e f i r e r e s i s t a n c e , e x p r e s s e d i n time to f a i l u r e , i s calculated a s a function of type of a g g r e g a t e , column s i z e , cover thickness to s t e e l , amount of s t e e l , e c c e n t r i c i t y of loading, d e s i g n s a f e t y factor and equivalent buckling length.
T h e s t a n d a r d ASTM t e s t conditions ( 3 ) a s s u m e that the column i s f r e e t o expand, w h e r e a s i n f a c t a column i s often r e s t r a i n e d by t h e s u r r o u n d i n g s t r u c - t u r e and t h e r e b y a t t r a c t s m o r e load t h a n a s s u m e d . T o examine t h e influence of r e s t r a i n t on the behaviour of the c o l u m n s , calculations of f i r e r e s i s t a n c e have b e e n made f o r c o l u m n s under v a r i o u s d e g r e e s of a x i a l r e s t r a i n t .
Another condition i n which t e s t and p r a c t i c e d i f f e r i s the t e m p e r a t u r e c o u r s e of the f i r e to which the column i s exposed ( i n p r a c t i c e f i r e s e v e r i t i e s c a n v a r y o v e r a wide range). T o study t h i s , f i r e - r e s i s t a n c e c a l c u l a t i o n s have b e e n made f o r columns e x p o s e d to heating a c c o r d i n g to v a r i o u s t e m p e r a t u r e c u r v e s that a r e c h a r a c t e r i s t i c of those of a c t u a l f i r e s .
M a t e r i a l P r o p e r t i e s
T h e t e m p e r a t u r e r i s e i n a column i s d e t e r m i n e d f o r the h e a t flow equations a s a function of two p r o p e r t i e s of the c o n c r e t e , t h e r m a l conductivity a n d t h e r m a l capacity. T h e s e p r o p e r t i e s a r e s t r o n g l y dependent o n the type of aggregate. Q u a r t z a g g r e g a t e , which h a s the highest t h e r m a l diffusivity of a l l c o n c r e t e s , w a s s e l e c t e d f o r d e t e r m i n i n g t h e s e p r o p e r t i e s f o r n o r m a l weight; c r y s t a l l i n e
246 I V - F I R E RESISTANCE OF REINFORCED CONCRETE COLUMNS
expanded s h a l e a g g r e g a t e w a s chosen f o r lightweight c o n c r e t e . Values of the p r o p e r t i e s a r e given i n r e f e r e n c e ( 4 ) .
T h e m o s t i m p o r t a n t m e c h a n i c a l p r o p e r t i e s that d e t e r m i n e the s t r e n g t h of r e i n f o r c e d c o n c r e t e a r e the c o m p r e s s i v e s t r e n g t h and modulus of e l a s t i c i t y of the c o n c r e t e , and the yield s t r e n g t h and modulus of e l a s t i c i t y of the s t e e l r e i n - forcing. Approximate a n a l y t i c a l r e l a t i o n s , which give t h e s e p r o p e r t i e s as a function of t e m p e r a t u r e , have been d e r i v e d f o r nor ma1 weight c o n c r e t e , light- weight c o n c r e t e and s t e e l using existing d a t a ( 5 - 7 ) . T h e r e l a t i o n s h i p s a r e shown in F i g u r e 1. I I I / I [ C O I . I P % l T i l V L I r i i N G l W I I H O R r l * L ( Y i l G i 4 l C C l N C P l l I - Y I E L D 7 0 1 1 1 1 O r < ! i l l - - I I I l l In t h o s e p a r t s of t h e s t u d i e s that included a p e r i o d of decaying f i r e t e m -
,
,
p e r a t u r e , the following a s s u m p t i o n sw e r e made r e g a r d i n g the change of 0. 8
m a t e r i a l p r o p e r t i e s a s they cool down.
0.6
F o r c o n c r e t e it w a s a s s u m e d that the
m a t e r i a l p r o p e r t i e s a r e unchanged 0.4
d u r i n g cooling and a r e e q u a l to those
c o r r e s p o n d i n g to the m a x i m u m t e m - g
-
0 . 2p e r a t u r e r e a c h e d . F o r s t e e l i t was u
-
4a s s u m e d that the s a m e r e l a t i o n s h i p s z
z
o1 . 2 -
hold f o r cooling a s well a s f o r heating.
2
I I l l 1 I I- D e f o r m a t i o n s of c o n c r e t e and s t e e l due to t e m p e r a t u r e change w e r e a s s u m e d ( 2 ) b a s e d on e x i s t i n g infor- 0 . 6 - mation. Q u a r t z a g g r e g a t e c o n c r e t e w a s c h o s e n b e c a u s e o t h e r a g g r e g a t e s , e s p e c i a l l y lightweight a g g r e g a t e s , ex- pand l e s s with i n c r e a s i n g t e m p e r a t u r e . o , 2 - - Calculation of F i r e R e s i s t a n c e 0 I I I I I I 0 I00 200 1 0 0 400 5 0 0 6 0 0 7 0 0 800 9 0 0 Column t e m p e r a t u r e s a r e cal- T E M P E R A T U R E , "C culated by a n u m e r i c a l method (8). F i g u r e 1: Effect of T e m p e r a t u r e T h e method a s s u m e s r a d i a t i v e heat on Material P r o p e r t i e s t r a n s f e r f r o m the f i r e to the s u r f a c e
of the column. In the column the
heat t r a n s f e r p r o c e e d s by conduction. T h e t e m p e r a t u r e dependence of the
t h e r m a l p r o p e r t i e s of the m a t e r i a l a r e taken into a c c o u n t in the calculation. During a f i r e , l a r g e t e m p e r a t u r e g r a d i e n t s , hence l a r g e s t r e s s g r a d i e n t s ,
o c c u r i n the column c r o s s - s e c t i o n . F i g u r e 2, b a s e d on a n a n a l y s i s of the
s t r e s s e s and s t r a i n s o c c u r r i n g in the c o l u m n d u r i n g f i r e ( 2 ) , s h o w s how s t r e s s d i s t r i b u t i o n changes i n a c o l u m n s e c t i o n d u r i n g a f i r e . E a r l y i n a f i r e , very high s t r e s s e s occur n e a r the outside of the s e c t i o n and c r a c k s a p p e a r i n the inner a r e a , which i s under t e n s i l e s t r a i n . As the f i r e p r o g r e s s e s , the outer c o n c r e t e l o s e s i t s s t r e n g t h , the t e m p e r a t u r e g r a d i e n t s become l e s s s t e e p , and the extent of c r a c k i n g i n the i n n e r a r e a i s reduced. As f a i l u r e i s approached, the c r a c k s i n the c e n t r a l a r e a d i s a p p e a r a s the r e d u c e d effective c r o s s -section b e c o m e s s t r e s s e d to capacity throughout. T h i s de m o n s t r a t e s t h a t f i r e r e s i s - t a n c e c a n be calculated o n the b a s i s of u l t i m a t e capacity of the c r o s s - s e c t i o n , which a s s u m e s full s t r e s s r e d i s t r i b u t i o n a t f a i l u r e .
T.T. LIE - D.E. ALLEN 247 F i g u r e 2: S t r e s s D i s t r i b u t i o n in C o n c r e t e Section During F i r e (20 c m S q u a r e , 4.970 S t e e l , 1. 25 c m Cover, Calculated F i r e R e s i s
-
tance 54 m i n . ) T h e s t r e n g t h of rein- f o r c e d c o n c r e t e columns a t e l e v a t e d t e m p e r a t u r e s has b e e n d e t e r m i n e d by the s a m e method as the ACI method ( 9 ) f o r room t e m p e r a t u r e , by r e p l a c i n g the r e l e v a n t mate- r i a l p r o p e r t i e s by t h e i r t e m - p e r a t u r e - d e p e n d e n t values given i n F i g u r e 1. T o do t h i s t h e c r o s s - s e c t i o n was divided into s m a l l e l e m e n t s , the p r o p e r t i e s f o r e a c h e l e m e n t d e t e r m i n e d for the c o r r e s p o n d i n g t e m p e r a t u r e , and t h e effects integratedo v e r t h e section. F i g u r e 3,
a t y p i c a l i n t e r a c t i o n d i a g r a m of a x i a l and bending strength, shows how f i r e r e d u c e s the s e c t i o n s t r e n g t h with time. In the c a s e of long c o l u m n s , the r e s i s t a n c e a l s o depends o n the buckling
load, which i s a function of the s t i f f n e s s . T h e s t i f f n e s s i s likewise d e t e r m i n e d
by i n t e g r a t i n g the t e m p e r a t u r e - d e p e n d e n t stiffness of e l e m e n t s . T h e stiffness of the c o n c r e t e , however, i s reduced d u e
to c r a c k i n g and this i s approximated by ? O D I I I
means of a reduction f a c t o r . F i g u r e 3
-
-S H O P , C O L U M N
shows how buckling effects d u r i n g f i r e r e d u c e the s t r e n g t h of a n i n t e r m e d i a t e column and that of a s h o r t column.
In T a b l e I the calculation method i s c o m p a r e d to a c t u a l t e s t r e s u l t s of axially loaded q u a r t z a g g r e g a t e columns ( 1 0 ) ; t h e s e t e s t s w e r e c a r r i e d out under well defined heating and loading con-
ditions. It i s s e e n that the calculation 0 . 5
1 . 0 1 . 5 2 . 0 2 . 5
p r o c e d u r e gives a c o n s i s t e n t , although 4 L I I O I N G M O M E N , A T F A , L U P I , Lrr . A,
somewhat c o n s e r v a t i v e , e s t i m a t e of the f i r e r e s i s t a n c e s of r e i n f o r c e d c o n c r e t e
columns under known load conditions
$
2 0 6:
h
A X I A L LoAD O N L Y . 5 H o I . r C O L U M Nr
i
o v e r a c o n s i d e r a b l e r a n g e of s l e n d e r n e s s f o , e 2 5 cu - ~ r r i i a r . * c a ~ , < r r \ C O L U h l N r a t i o s . T h e d i f f e r e n c e s , which a r e in 'IENDIIIC E - 0 2 o,,,, \ the o r d e r of 10 to 20 p e r c e n t , a r e p r o b - z
-
\.
0----
__
ably mainly due to c o n s e r v a t i v e n e s s i n : o 20 1 0 d o 80 1 0 0
T I M I . M I N U T E 5
the m a t e r i a l p r o p e r t i e s used and in the
calculation a s s u m p t i o n s . F i g u r e 3: Effect of F i r e o n Column
Standard F i r e R e s i s t a n c e of S q u a r e Columns Strength ( 1 5 c m x 15 c m ,
N o r m a l Weight Concrete
F i g u r e 4 shows the calculated f i r e 3. 570 R e i n f o r c i n g , 1. 25
r e s i s t a n c e of s q u a r e columns under ASTM c m Cover)
I V - FIRE RESISTANCE OF REINFORCED CONCRETE COLUMNS
T A B L E I
-
COMPARISON O F CALCULATED F I R E RESISTANCESWITH TEST RESULTS
c a s e d e s c r i b e d a s follows. T h e column, designed a c c o r d i n g to ACI 318-63 (adopted f o r the National Building Code of Canada), w a s pin-ended, 3 m long, and subjected to full d e s i g n dead load plus l i v e load. It w a s a l s o subjected to the minimum e c c e n t r i c i t y specified i n ACI-318 (0. 1 of the s i z e of the column o r 2. 5 c m , whichever i s the g r e a t e r ) ; t h i s c o r r e s p o n d s t o a typical i n t e r i o r lower s t o r e y column.
T h e m a i n p a r a m e t e r s affecting f i r e r e s i s t a n c e a r e column s i z e , cover and type of a g g r e g a t e . F i g u r e 4 shows that a n i n c r e a s e of cover i n c r e a s e s the f i r e r e s i s t a n c e , a s expected, owing to t h e r m a l protection. This i n c r e a s e , however, l e v e l s off when the cover r e a c h e s 1/4 of c o l u m n s i z e ( t ) . It i s fol- lowed by a d e c r e a s e , c a u s e d by a d e c r e a s e i n the m o m e n t - r e s i s t i n g l e v e r a r m due to a weakening of the o u t e r l a y e r s of c o n c r e t e . F o r l a r g e , lightly r e i n - f o r c e d s e c t i o n s and s m a l l c o v e r , the influence of the c o v e r i s negligible b e c a u s e the c o n c r e t e c a r r i e s the e n t i r e load at f a i l u r e .
Specimen
O t h e r f a c t o r s that affect the f i r e r e s i s t a n c e of a column a r e the length of the column, e c c e n t r i c i t y ( o r moment) and the safety f a c t o r . Studies ( 1 ) showed that a n i n c r e a s e of s a f e t y f a c t o r o r a l i v e load l e s s than the full d e s i g n live
load, may significantly i n c r e a s e the f i r e r e s i s t a n c e . T h e r e s u l t s a l s o show
that a n i n c r e a s e i n e c c e n t r i c i t y d e c r e a s e s the f i r e r e s i s t a n c e , e s p e c i a l l y when the p e r c e n t a g e of s t e e l i s s m a l l ( 1 to 2%). T h e d e c r e a s e , however, i s generally not of p r a c t i c a l i m p o r t a n c e b e c a u s e e c c e n t r i c i t y i n a c o l u m n under f i r e will b e
C o m p r e s s i v e s t r e n g t h of c o n c r e t e , ~ / m m
"
R a t i o time to f a i l u r e , ~ e s t / ~ a l c . T e s t load, kN ( i ) 15 c m x 15 c m-
4 c o r n e r b a r s 2 c m d i a . , c o v e r 1 . 2 c m T i m e to f a i l u r e , minutes 2 3 4 5 T e s t 38 3 1 3 1 3 1 273 273 273 27 3 Calculated ( i i ) 20 c m x 20 c m-
4 c o r n e r b a r s 2 c m d i a . , c o v e r 2.9 c m 6 4 69 63 6 6 3 4 5 6 57 5 5 55 55 3 2 32 43 43 1 . 1 2 1. 25 1. 1 5 1 . 2 0 ( i i i ) 30 c m x 30 c m - 4 c o r n e r b a r s 2.1 c m dia. , 4 mid-face b a r s 2. 2 c m dia.,
c o v e r 3 c m 464 464 59 8 598 107 105 107 107 89 89 8 8 88 147 11 1 . 2 0 1. 18 1. 22 1. 22 1708 1. 12 4 6 165T.T. LIE - D.E. ALLEN C O Y t Y C I , L O i [ l i l L O \ i i C t , F i g u r e 4: F i r e R e s i s t a n c e of Reinforced C o n c r e t e Columns a s a Function of Cover T h i c k n e s s to S t e e l for V a r i o u s Column and S t e e l Slzes ( C o l u m n Length: 3 m; Min E c c e n t r i c i t y : 2. 5 c m o r 0. I t ; Full L i v e Load) g r e a t l y r e d u c e d f r o m the design e c c e n t r i c i t y a s s u m e d f o r calculation ( 1 ) . It w a s a l s o found that the f i r e r e s i s t a n c e d e c r e a s e s with i n c r e a s e of s l e n d e r n e s s r a t i o ; t h i s generally affects only t a l l s l e n d e r columns
A d 1 with a s m a l l p e r c e n t a g e of steel. 2 4 ' 8 C O V L R C h L O V I P C M T h e r e s u l t s given i n F i g u r e 4 P S I C E L A R C , C O L U M N i R L i l l * i I - - - L I G l l l l l t l r H l C ~ I I C ~ ~ I ~ and in R e f e r e n c e 1 f o r s q u a r e - 11OPtI L I I I G I I I C O 1 I C P I I I columns c a n b e e x p r e s s e d i n the
following s i m p l e d e s i g n r u l e s f o r m i n i m u m column s i z e ( t c m ) a n d cover
*
min' ( C m i n , c m ) i n t e r m s of r e q u i r e d f i r e r e s i s t a n c e ( R , h r ) : t . = 10f(R t 1) f o r n o r m a l weight c o n c r e t e min t . = 7 . 5 f ( R t 1) f o r lightweight c o n c r e t e min C . = 2 . 5 R f o r R
<
2 h r min C . = 1 . 2 5 R t 2 . 5 f o r R>
2 h r minw h e r e f , a f a c t o r that t a k e s into account o v e r - d e s i g n , equivalent buckling length ( k h ) and p e r c e n t a g e of s t e e l ( p ) , i s given a s follows:
*
W i r e m e s h i n c o v e r i s r e c o m m e n d e d i f c o v e r i s g r e a t e r than 3 . 7 5 c m O v e r - d e s i g n f a c t o r 1.00 1 . 2 5 1. 50 Values of f k h5
3 m 1 . 0 0 . 9 0 . 8 k h = 6 m t5
30 c m P<
370 1 . 2 1 . 1 1 . 0 All o t h e r c a s e s 1.0 0 . 9 0. 8I V - F I R E RESISTANCE O F R E I N F O R C E D C O N C R E T E C O L U M N S
T h e s e r e s u l t s indicate l o w e r r a t i n g s o n d i m e n s i o n s f o r n o r m a l weight c o n c r e t e s than existing r a t i n g s cited i n the National Building Code of Canada, and about the s a m e f o r lightweight c o n c r e t e s . The lower r a t i n g s a r e attributed to a d e c r e a s e i n d e s i g n s a f e t y factor ( e x i s t i n g r a t i n g s w e r e based on t e s t s
c a r r i e d out i n 1920
-
1921), a c o n s i d e r a t i o n of m i n i m u m e c c e n t r i c i t y that o c c u r si n p r a c t i c e , and a m o r e a c c u r a t e s i m u l a t i o n of the h e a t t r a n s f e r conditions i n a f i r e .
I n t e r a c t i o n With Building S t r u c t u r e
D e t e r m i n a t i o n of f i r e r e s i s t a n c e , w h e t h e r by s t a n d a r d f i r e t e s t o r by t h e above c a l c u l a t i o n s , i s b a s e d o n the a s s u m p t i o n of a pin-ended column with no i n t e r a c t i o n with the s u r r o u n d i n g building s t r u c t u r e . Actually, a c o l u m n expands during f i r e and, b e c a u s e of the r e s i s t a n c e of the s u r r o u n d i n g s t r u c t u r e to this expansion, m o r e than t h e a s s u m e d dead load plus l i v e load i s a t t r a c t e d to the column. It t h e r e f o r e a p p e a r s , f o r the s i n g l e column exposed to f i r e , t h a t the s t a n d a r d p r o c e d u r e e r r s o n the unsafe side.
F i g u r e 5 shows the r e s u l t s of
a n i n t e r a c t i o n study of a column with a typical r e i n f o r c e d c o n c r e t e build- ing s t r u c t u r e . T h e c u r v e s i n the top g r a p h show how the applied l o a d , in- cluding the effect of i n t e r a c t i o n , c o m p a r e s with the calculated column
s t r e n g t h . T h e different c u r v e s label-
led "n s l a b s " r e f e r to t h e n u m b e r of floor s l a b s above the column that r e s i s t expansion of the column; "0 s l a b " c o r r e s p o n d s to no interaction. Curves in the bottom g r a p h show the c o r r e s p o n d i n g column lengthening and l a t e r a l deflection of the column a t mid-height.
As the v e r t i c a l s t i f f n e s s of the s u r r o u n d i n g s t r u c t u r e i n c r e a s e s f r o m 0 to 3 s t o r e y s ( o r s l a b s ) , the applied load i n c r e a s e s and the f i r e r e s i s t a n c e i s d e c r e a s e d , a s s e e n by c o m p a r i n g
column movements. T h e d e c r e a s e ,
however, i s not l a r g e and the r e - sulting f i r e r e s i s t a n c e i s n e v e r much l e s s than that calculated f r o m
Equation ( 1 ) . T h i s i s b e c a u s e a r e d u c t i o n i n end moments due to i n c r e a s e d column flexibility c o m - p e n s a t e s f o r the i n c r e a s e d column load due to i n t e r a c t i o n . As the v e r t i c a l s t i f f n e s s i s i n c r e a s e d f u r t h e r to 5 s t o r e y s , h o w e v e r , a change t a k e s place. What happens i s that the i n c r e a s e d
TIME, hllNUTES F i g u r e 5: C o l u m n - S t r u c t u r e I n t e r - a c t i o n During F i r e (30 c m x 30 c m S q u a r e Column, 4. 370 S t e e l , 3. 7 5 c m Cover, 3 m long.)
T.T. LIE - D.E. ALLEN 25 1
applied load c a u s e s l a t e r a l bending to take place, followed by c h o r d s h o r t e n i n g between the column ends and relief of the applied load, s o that f a i l u r e does not take place. Eventually, the column b e c o m e s s h o r t e r than it w a s i n i t i a l l y and, owing to load t r a n s f e r to adjacent s u p p o r t s , the f i r e r e s i s t a n c e i s i n c r e a s e d beyond that f o r an isolated column. F o r v e r y s t i f f r e s i s t a n c e ( 1 5 s t o r e y s ) , the column bends o r buckles quite e a r l y , but the column d o e s not fail. If the s t r u c - t u r e c a n t r a n s f e r the total load to o t h e r s u p p o r t s , the column w i l l n e v e r fail.
T h e r e s u l t s in F i g u r e 5, t h e r e f o r e , indicate that i n t e r a c t i o n effects with
the s u r r o u n d i n g s t r u c t u r e due to column expansion a r e not likely to reduce the f i r e r e s i s t a n c e of i s o l a t e d columns, and i n s o m e c a s e s may i n c r e a s e i t sub- stantially. Another m o r e c r i t i c a l i n t e r a c t i o n effect, r e v e a l e d i n the r e c e n t St. Louis f i r e , however, i s the effect of l a r g e l a t e r a l expansion of t h e slab above the f i r e floor causing s h e a r f a i l u r e of columns. T h i s r e q u i r e s f u r t h e r investigation.
F i r e R e s i s t a n c e Under Actual F i r e Conditions
T h e s t a n d a r d f i r e t e m p e r a t u r e c u r v e initially r i s e s a t a p r e s c r i b e d r a t e and then d r o p s suddenly to ambient t e m p e r a t u r e ( 3 ) . In actual f i r e s the t e m - p e r a t u r e r e a c h e d i n the p e r i o d of t e m p e r a t u r e r i s e c a n be much h i g h e r or l o w e r than the s t a n d a r d t e m p e r a t u r e s . In addition, i n s t e a d of a sudden d r o p to a m - bient t e m p e r a t u r e , t h e r e i s , i n actual p r a c t i c e , a g r a d u a l d e c r e a s e of the f i r e t e m p e r a t u r e a f t e r the p e r i o d of t e m p e r a t u r e r i s e .
A wide v a r i e t y of t e m p e r a t u r e c o u r s e s a r e p o s s i b l e , depending on the f i r e load, ventilation and o t h e r c h a r a c t e r i s t i c s of t h e e n c l o s u r e ( 1 ) . The m o s t
s e v e r e a r e the ventilation controlled f i r e s , i. e.
,
t h e r a t e of burning of thecombustible m a t e r i a l s i n the e n c l o s u r e i s d e t e r m i n e d by the d i m e n s i o n s of the openings through which the a i r n e c e s s a r y f o r combustion can be supplied. F o r m u l a e d e s c r i b i n g the t e m p e r a t u r e c o u r s e of ventilation-controlled f i r e s ( 1 1 ) have b e e n adopted to calculate f i r e r e s i s t a n c e of r e i n f o r c e d c o n c r e t e columns ( 2 ) .
As shown i n F i g u r e 6 , two major p a r a m e t e r s d e t e r m i n e the t e m p e r a t u r e
c o u r s e of ventilation-controlled f i r e s
- -
t h e window opening and the f i r e load( Q ) , a s defined in F i g u r e
6. T h e l a r g e r the open-
ing f a c t o r ( F ) the g r e a t e r
the t e m p e r a t u r e r i s e and the s h o r t e r the duration. T h e f i r e load affects only
the d u r a t i o n of the f i r e
- -
the h i g h e r the f i r e load the longer the d u r a t i o n of
the f i r e . In s t u d i e s a t D B R / N R C ( 2 ) , t h r e e c h a r a c t e r i s t i c t e m p e r a - t u r e c u r v e s , c o r r e s p o n - ding to F = 0 . 0 2 , F = 0 . 0 5 ( s t a n d a r d c a s e ) , TlhlE. H O U R S and F = 0 . 1 , w e r e F i g u r e 6: C h a r a c t e r i s t i c T e m p e r a t u r e Curves chosen.
F o r Various F i r e Loads Q and Opening
252 I V - F I R E RESISTANCE O F R E I N F O R C E D CONCRETE COLUMNS when Q
>
Q c r i t , the t i m e to F i g u r e 7: S t r e n g t h - T i m e C u r v e s f o r 30 c m f a i l u r e v e r y quickly a p p r o a c h e s x 30 c m Column ( 2 . 27'0 S t e e l a c o n s t a n t value, R , obtained 3.75 c m Cover) by a s s u m i n g a n unlimited f i r e 2400 I I I I I 1 - S T A N D A R D i l l € Tr?AllPAIUI'I - - - - - - C H i r s * C I E I I 5 T I C F l X t I t l , ~ L L * T U R l S - 0 I N L G M' - - - - D [ s I G N L C , D - - \ - - a---
3 0-
- * 400 - - - - I load. T h e time to f a i l u r e , R , i s a function of the opening f a c t o r : the g r e a t e r the openings, the g r e a t e r the r a t e of h e a t r i s e , and the s h o r t e r the t i m e to f a i l u r e . On the o t h e r hand, Qcrit i n c r e a s e s with a n i n c r e a s e of opening f a c t o r s i n c e m o r e of the h e a t e s c a p e s the f i r e c o m p a r t m e n t .F i g u r e 7 c o m p a r e s , f o r a t y p i c a l c a s e , c o l u m n s t r e n g t h vs t i m e f o r different c h a r a c t e r i s t i c t e m p e r a t u r e c u r v e s with that f o r the stan- d a r d c u r v e . T h e c u r v e s show that f o r a f i r e l o a d l e s s than a c r l t i c a l value, Q c r i t , no f a i l u r e of the column takes p l a c e ; i n other w o r d s below a c e r t a i n c r i t i c a l v a l u e of the f i r e load t h e r e i s insufficient c o m b u s t i b l e content t o heat
F i g u r e 8 shows the r e l a t i o n s h i p between Qcrit, R , and d i m e n s i o n s for a cover of 3 . 7 5 c m . T h e m a j o r v a r i a b l e s affecting c r i t i c a l f i r e load w e r e found ( 2 ) to be column s i z e , c o v e r and opening f a c t o r ; p e r c e n t a g e of s t e e l h a s only a
minor effect. T h e following a p p r o x i m a t e r e l a t i o n s h i p between c r i t i c a l f i r e
load, Q c r i t , and f i r e r e s i s t a n c e based o n the s t a n d a r d f i r e t e s t ( t i m e to failure f o r F = 0. 0 5 ) , R s , w a s d e t e r m i n e d f r o m the r e s u l t s f o r n o r m a l weight s q u a r e
c o n c r e t e columns: Q c r i t = 4
+
10 Rs ( s m a l l , m e d i u m openings)= 4
+
16 Rs ( l a r g e openings) ( 2 )I 5 o loo 150 200 250 '0° the column to f a i l u r e . Above
11\16 M I N U T E S the c r i t i c a l f l r e load, i. e . , T h i s r e l a t i o n s h i p i s helpful i n a s s e s s i n g Code 60 I I I I I I 6 I I I j l l - C R I I I C A L rlltc L O A D oCll, - - I ~ M E TO F , \ I L U R E F O R a=.ocR,,- f i r e r e s i s t a n c e r e q u i r e - ,.? / ments s i n c e Q c r i t c a n be 5 50 - /- / r e l a t e d to m e a n f i r e load / - f o r a given occupancy, a m , a s follows: ( 3 ) Q c r i t = k Qm w h e r e k i s a d e s i g n s a f e t y f a c t o r . T h e d e s i g n f i r e s a f e t y f a c t o r i s r e l a t e d to the r i s k of f a i l u r e which - c a n be d e t e r mined a s a O I O
'
I3b
I4b
50 O I Oj0
j0
4b
50 function of the b a s i c r e - C O L U ~ ~ N S I Z ~ C M q u i r e m e n t s of life s a f e t y and economic l o s s ( 5 ) ; f o r F i g u r e 8: F i r e R e s i s t a n c e P a r a m e t e r s F o rT.T. L I E - D.E. ALLEN 253
of k i s r e q u i r e d f o r t a l l buildings f o r r e a s o n s of l i f e s a f e t y and e c o n o m i c l o s s
t h a n f o r low buildings. T h u s , by u s i n g E q u a t i o n s ( 2 ) and ( 3 ) t h e r e q u i r e d f i r e
r e s i s t a n c e , R s , c a n b e r e l a t e d to the b a s i c r e q u i r e m e n t s of l i f e s a f e t y and e c o n o m i c l o s s .
S u m m a r v and Conclusions
T h e f i r e r e s i s t a n c e of s q u a r e , r e i n f o r c e d c o n c r e t e columns h a s been s t u d i e d u n d e r both s t a n d a r d ASTM t e s t conditions and u n d e r c o n d i t i o n s that m o r e c l o s e l y r e s e m b l e t h o s e m e t i n p r a c t i c e . F i r e r e s i s t a n c e s a r e d e t e r m i n e d by n u m e r i c a l c a l c u l a t i o n b a s e d on the t h e r m a l and s t r u c t u r a l p r o p e r t i e s of
m a t e r i a l s a t high t e m p e r a t u r e s . C o m p a r i s o n s w i t h f u r n a c e t e s t s of columns
show t h a t the c a l c u l a t e d f i r e r e s i s t a n c e s a r e c o n s i s t e n t with t h o s e m e a s u r e d but a r e about 10 to 20 m i n u t e s l e s s , the d i f f e r e n c e being a t t r i b u t a b l e mainly to c o n s e r v a t i v e n e s s i n the m a t e r i a l p r o p e r t i e s used.
U n d e r s t a n d a r d ASTM t e s t c o n d i t i o n s , the f i r e r e s i s t a n c e i n t i m e to f a i l - u r e i s c a l c u l a t e d a s a function of type of a g g r e g a t e , c o l u m n s i z e , c o v e r , p e r - c e n t a g e of s t e e l , e c c e n t r i c i t y of load, d e s i g n s a f e t y f a c t o r and b u c k l i n g length. B a s e d on c a l c u l a t e d r e s u l t s , s i m p l e d e s i g n r u l e s a r e given ( E q u a t i o n ( 1 ) ) .
T h e s t a n d a r d ASTM t e s t conditions a s s u m e t h a t a column i s f r e e to e x p a n d , w h e r e a s i n f a c t a column i s r e s t r a i n e d by the s u r r o u n d i n g s t r u c t u r e and t h e r e b y a t t r a c t s m o r e load t h a n a s s u m e d . A n u m e r i c a l s t u d y of a r e s t r a i n e d column d u r i n g f i r e ( F i g . 5) i n d i c a t e s , h o w e v e r , t h a t the a s s u m p t i o n of no r e s t r a i n t i s g e n e r a l l y c o n s e r v a t i v e .
B a s e d on the u s e of m o r e r e a l i s t i c f i r e t e m p e r a t u r e c u r v e s t h a n the s t a n - d a r d ASTM c u r v e , f i r e r e s i s t a n c e w a g c a l c u l a t e d i n t e r m s of c r i t i c a l f i r e l o a d ( a m o u n t of c o m b u s t i b l e s ) below which no f a i l u r e t a k e s p l a c e , and t i m e to f a i l u r e if the f i r e load i s g r e a t e r than c r i t i c a l . Although the c r i t i c a l f i r e l o a d i n c r e a s e s with i n c r e a s e d ventilation, the t i m e to f a i l u r e d e c r e a s e s c o n s i d e r a b l y with i n c r e a s e d ventilation. E q u a t i o n s ( 2 ) and ( 3 ) p r o v i d e a n a p p r o x i m a t e r e l a t i o n - s h i p b e t w e e n s t a n d a r d f i r e r e s i s t a n c e of c o n c r e t e c o l u m n s and c r i t i c a l f i r e l o a d ; t h i s i s useful in r e l a t i n g Code f i r e r e s i s t a n c e r e q u i r e m e n t s to t h e fun- d a m e n t a l r e q u i r e m e n t s of life s a f e t y a n d e c o n o m i c l o s s .
T h i s p a p e r i s a contribution f r o m t h e Division of Building R e s e a r c h of the National R e s e a r c h Council of Canada and i s published w i t h the a p p r o v a l of the D i r e c t o r of the Division.
R e f e r e n c e s
( 1 ) L i e , T . T . and D. E . Allen. C a l c u l a t i o n of t h e F i r e R e s i s t a n c e of Rein-
f o r c e d C o n c r e t e C o l u m n s . National R e s e a r c h Council of C a n a d a ,
D i v i s i o n of Building R e s e a r c h , T e c h . P a p e r No. 378 (NRCC 12797), 1972.
( 2 ) Allen, D. E . and T . T . L i e . F u r t h e r Studies of t h e F i r e Resistance of
R e i n f o r c e d C o n c r e t e Columns. In p r e s s .
( 3 ) S t a n d a r d Methods of F i r e T e s t s of Building C o n s t r u c t i o n and M a t e r i a l s .
ASTM D e s i g n a t i o n E l 1 0 - 7 1 , 1971 Book of ASTM S t a n d a r d s , P a r t 14, p. 431-448.
( 4 ) H a r m a t h y , T . Z . T h e r m a l P r o p e r t i e s of C o n c r e t e a t E l e v a t e d T e m p e r -
a t u r e s . ASTM J o u r n a l of M a t e r i a l s , Vol. 5, No. 1 , M a r c h 1 9 7 0 , p. 4 7 - 7 4 ( N R C 11266).
254 I V - F I R E RESISTANCE O F R E I N F O R C E D CONCRETE COLUMNS
( 5 ) L i e , T . T . F i r e and Buildings. London, Applied S c i e n c e P u b , L t d . , 1972.
( 6 ) A b r a m s , M. S. C o m p r e s s i v e S t r e n g t h of C o n c r e t e a t T e m p e r a t u r e s to
1000 F. T e m p e r a t u r e and C o n c r e t e , ACI P u b l i c a t i o n Sp 25, 1968, p. 33-58.
( 7 ) H a r m a t h y , T . Z . and J. E . B e r n d t . Hydrated P o r t l a n d Cement a n d Light-
weight C o n c r e t e a t E l e v a t e d T e m p e r a t u r e s . J o u r n a l , A m e r i c a n C o n c r e t e I n s t i t u t e , Vol. 63, No. 1 , 1966, p. 93-112. ( N R C 8847) ( 8 ) L i e , T . T . and T. Z . H a r m a t h y . A N u m e r i c a l P r o c e d u r e to C a l c u l a t e t h e T e m p e r a t u r e of P r o t e c t e d S t e e l C o l u m n s E x p o s e d to F i r e . N a t i o n a l R e s e a r c h Council of C a n a d a , D i v i s i o n of Building R e s e a r c h , (NR C 12535), 1972.
(9) ACI Building Code R e q u i r e m e n t s f o r R e i n f o r c e d C o n c r e t e . A m e r i c a n
C o n c r e t e I n s t i t u t e , ACI S t a n d a r d 31 8-7 1 , 1971.
( 1 0 ) B e c k e r , W. and J.. Stanke. B r a n d v e r s u c h e a n Stahlbetonfertigstutzen.
D e u t s c h e r A u s s c h u s s f u r S t a h l b e t o n , Heft 215, B e r l i n , 1970. ( 1 1 ) L i e , T . T . C h a r a c t e r i s t i c T e m p e r a t u r e C u r v e s f o r V a r i o u s F i r e
S e v e r i t i e s . In p r e s s .
