svojstva na beton i celik.pdf

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6. Mehani~ki i termi~ki svojstva na betonot i ~elikot 77 __________________________________________________________________________

__________________________________________________________________________Odnesuvawe na liniski konstrukcii vo uslovi na po`ar

, -

,

,

,

.

. !

,

[8, 10, 11, 19, 30, 53, 64, 65, 96, 104]. ,

- ,

. / 0,

EUROCODE 2, part 1.2 [22].

6.1

, , -

,

, ,

,

.

<

. ,

. =

,

. ,

,

,

.> ,

6



78 6. Mehani~ki i termi~ki svojstva na betonot i ~elikot __________________________________________________________________________


. ?,

,

. 0 (SiO2)

D 5000 650

0 -

-. = - . E D 1000

0

12000 - D - (-),

-. , D 6000

9000 , --

.

, ,

. > ,

, Ca(OH)2

( 44%),

. E 10000

. /

[8,10,53].

6.1.1 !"# $#!!#

,

( ) (). <

, .

!

, , -

. =

,

30 % .

> , ,

. H, ,

,

D

. I

,

. > -,

.





> !'#!(!,

!$ #)'(#*( (), . 0

,

, ..

, 0 6.1().

> !'#!(! #)'(#*(

(), ,

, 0 6.1().

> !'#!(* (25-55%

),

#)'(#*(, (). _

, 0 4.1().

, , :

E 900 D ( 10-35%). = 900 -

2000, ,

( 110% ),

. E 8000 D 50%

80%.

“-”,

(0 6.2), (Molhotra, 1956) [96].

E

. b

,

(0 6.3, 6.4 6.5), (Abrams,1971; Schneider,1982) [96].

, ,

(Molhotra, 1956).

-

(residual) . >

. =

.

E

(Molhotra, 1956; Weigler & Fischer, 1972).

=

. >,

(Abrams, 1971; Khoury et al., 1986, Molhotra, 1956,





Weigler & Fischer, 1972). >

D

.

?

(seald specimen) . >

(Lankard et al., 1971).

H

(Davis, 1967; Harada et al., 1972; Schneider,

1982).

,

. E 0 6.1()

, [1,96]:

• l ( a):

=

T .. )C ( f

)T ( f

c

c

00178 0 622 1

1

20 0 C T

C T 0

0

911350

350 20

(6.1)

• l ( b):

=

T . )C ( f

)T ( f

c

c

002 0 2

1

20 0 C T

C T 0

0

1000 500

500 20

(6.2)

6.2: ) “ +-”

, !





6.3: )

, !.

6.4: ) , !.

6.5: ) , !.





, ,

(0 6.3, 6.4 6.5). >

, ,

(0 6.6), [96].

6.6: . ,

, .

, ,

[65]. E 300-6000 - ,

600-9000 , 9000

. ? ,

, , ,

.

6.1.1.2 !%*& &#!# '!!! !,-#

E ,

,

. , ,

0 6.1() (Bennetts 1981),

. >

[65]. 0 Cruz

(1966) [8]

,

(0 6.7).





6.7:

<

- ,

.

[10],

(0 6.8).

6.8:

!

. Marechal (1972) [65]

D D

. ?

0.2, 40000 0.1. E,

, ,

[89]. Eurocode 2, part 1.2

( 2 0 .= µ ).

karbonatenbeton

lesen beton

silikatenbeton

o





6.1.1.3 !# /#0*1, #1 #/! "!#

I

[96]:

n

,

(Harada et al., 1972).

.

0 -

(Harada et al., 1972, Schneider, 1982).

/ , ,

“-”, ,

(Molhotra, 1956; Thelandersson,

1971).

l

(Schneider, 1982; Thelandersson, 1971).

(Schneider, 1982).

0 -

,

(Schneider, 1982).

.

0 6.9 [96] (FIP/CEB Committee 1978).

6.9: ) !





Eurocode 2, part 1.2 [22]

:

)C ( F )T ( F ct ct 0 20 = : C T 0 100

)T ..( )C ( F )T ( F ct ct 002 0 2 120 0

= : C T C 0 0

600 100 (6.3)

0 = )T ( F ct : C T 0 600

,

[96]:

?

(Schneider, 1981).

_

(Schneider,

1981).

(Sager et al., 1980).

>

. >

- (Schneider, 1981).

>

(Morley & Royles, 1983).

6.1.1.4 )'(#*(! '!&/1

/ -

,

, .

, ,

, , .

E 0 6.10 “-”. ,

,

( E / t =0 ), , ,

( t ). , (

1 se ), , ,

( 2 1 s s ). >

, ( r s 2 ). 0

, , “-”

(0 6.10).





6.10: ) + ( ! ): )

!; )

; ) !

l Dorn (1954) [65] “-

”, )h( , :

dt e

t RT / H c

=

0

(6.4)

:

c H - ( 1kmol J )

R - ( 118315 K kmol J )

=

Harmathy [65], ,

:

)( coshln

t / Z t t

0 2 2

10

= .const = (6.5)

:

Z t t += 0 .const = (6.6)

)mm( t 1

0 )hmm( Z 11 , -

0 6.10(). Z Zener-Hollomon- ,

:

RT / H ts

ce Z

= & (6.7)

ts & , T

(0 6.10 ).

> -

,

: .

a) b) v)





(1968) ,

5 0 6.11 [96]. 45%

,

. H 3150 -,

.

6.11: ) ! , 45%

Anderberg and Thelandersson [65,150]

:

[ ] )T ( jexpt )T ( f

b /

ccr 2932 1

1 =

(6.8)

1b j , .

Eurocode 2. part 1.2

“ “ (0 6.15),

. 0

FIRE,

(I 8).

6.1.1.5 “ “ %"0() $#!!#

, .

E 0 6.12() “ “ ( ), 0 6.12() ( ),





Harmathy & Berndt (1966) Schneider

(1977), [65]. .

, .

6.12 - :

) , )

l ,

Schneider & Haksever (1976), “ “

, .

,

(0 6.13) [96]. /

, :

1cc :

=

2

1

11c

cccc f

(6.9)

1cc > :

=

2

1

1

31c

cccc f

(6.10)

:

c f -

1c -

c -

c -

, )T ( f c

,

)T ( c1 , :

a) b)





62

1 10)04.00.6(0025.0)( ×++= T T T c (6.11)

)20()( 0 C f T f cc = : C T 0450<

=

1000

20353.2011.2)20()( 0 T

C f T f cc

: C T 0450

6.13: “ “

, Mpa f c 35 =

I , _ (6.9),

“ “ Hogenstad, CEB-FIP Model-Code 1990 [20]

Bizri H. [13] Huang Z.&Platten A. [68]:

=

2

11

2 c

c

c

ccc f

(6.13)

> [93,103],

)T ( f c (_ 6.9 6.10)

)T ( f cR ,

, -

:

)T .( )C ( f )T ( f ccR 0010 120 0 = C T 0 500

)T ..( )C ( f )T ( f ccR 00175 0 375 120 0 = C T C 0 0 700 500 (6.14)

0 = )T ( f cR C T 0 700

H )T ( c1

, _ (6.11).

(6.12)





Iding R., Bresler B and Nizamuddin Z. [72] “ “

Saenz, :

2

11

1

2 1

++

=

c

c

c

c

c

c

cc

)m(

m

f

;

sec E

E m 0 = (6.15)

l 2 =m :

2

1

1

1

2

+

=

c

c

c

c

cc f

(6.16)

Eurocode 2, part 1.2, “ “

Popovic (_ 6.17, 0 6.14) [8].

6.14: “ “ Popovic

mccc

c

c

c

) / ( m

m

f 11 1

+= 1cc (6.17)

l D :

1ccu

ccu

c

c

f

= cucc 1 (6.18)

? _ (6.17) 2 =m ( ),

“ “ Saenz (_ 6.16), Ellingwood et al. [49, 50]

FIRE, -

. :

, c f

, 1c

, cu

“ “ (0 6.15)

Eurocode 2, part 1.2 ( 6.1 0 6.15).





6.15: ) ) “ “ +

) . 7 “ “ : (1) ,

(2) , (3) )T ( c1

$& 6.1

)C ( f / )T ( f cc0 20

(00)

31 10 × )T ( c 310 × )T ( cu

20 1.00 1.00 2.5 20.0

100 0.95 0.97 3.5 22.5

200 0.90 0.94 4.5 25.0

300 0.85 0.91 6.0 27.5

400 0.75 0.85 7.5 30.0

500 0.60 0.74 9.5 32.5

600 0.45 0.60 12.5 35.0

700 0.30 0.43 14.0 37.5

800 0.15 0.27 14.5 40.0

900 0.08 0.15 15.0 42.5

1000 0.04 0.06 15.0 45.0

1100 0.01 0.02 15.0 47.5

1200 0.00 0.00 - -

a) b)





6.16: 8 : - , -+ , -, - ,

- , - ( )

0 Khoury et al. (1985) [8] D

, ,

D

, . ! D

6000, ,

. ,

(FTS) (LITS),

(transient) ,

Anderberg and Thelandersson [65,140] :

cth'

c

cctr

)C ( f b

0 2 20

= (6.19)

:ctr - (transient) (LITS);

2 b - ;

c - ;

cth - (FTS)

? ,

, .

Harmathy & Allen (1973) [8] 10000,

. /

,





(). >

(LITS). >,

, . I,

- , ,

.

, Eurocode 2, part 1.2 [22], (0 6.17),

:

a) :

31164 103.2109108.1)/( T T l l c

++= C T C 00 70020

31014)/( = cl l C T C 00 1200700

b) :

31164 104.1106102.1)/( T T l l c

++= C T C 00 80520

31012)/( = cl l C T C 00 1200805

) :

)20(108)/(

3 =

T l l c C T C

00

120020

(6.22)

6.17: ! , EC2

6.1.1.7 '&!/! '(1 $#!!#

. (spalling),

, 30-60 .,

, . l . 0

(1): kvarcen agregat(2): agregat varovnik(3): lesen agregat

(6.20)

(6.21)





,

. /

-

. 0 ,

,

. >

. Bazant et al. (1982) -

. ,

:

>

.

,

.

/

.

E

.

> -

.

0 Eurocode 2, part 1.2 [22] -

, ,

0 6.18.

6.18: ) ! ( o )

( t ,b )

!





, ,

FIRE,

.

6.1.2 () !"# $#!!#

H

, :

, .

6.1.2.1!,-#

#!'&!'(!!%!#

/ # -

,

.. D

, .

, ,

,

. /

, .

0 D,

, . E (

)

D,

,

.

0 Harmathy & Allen (1973) [8]

. E 0 6.19

. l

D

(1) (2), D (3) (4).

.

,

.





6.19: )

7+ : )

; b) ; c) d)

, FIRE

Eurocode 2, part 1.2, ,

(0 6.20) :

a) :

2)120/(012.0120/24.02 T T c +=# [ ]mK W / C T C 00 120020 (6.23)

b) :2)120/(008.0120/16.06.1 T T c +=# [ ]mK W / C T C 00 120020 (6.24)

v) :

1600/0.1 T c =# [ ]mK W / C T C 00 80020

5.0=c# [ ]mK W / C T C 00 1200800

6.20: =7+ , EC2

0 “National Research Council of Canada”, [96]:

(1): kvarcen agregat

(2): agregat varovnik(3): lesen agregat

(6.25)





a) :

5.1000625.0 += T c# [ ]mK W / C T C 00 80020

0.1=c# [ ]mK W / C T 0800>

v) :

355.1=c# [ ]mK W / C T C 00 29320

7162.1001241.0 += T c# [ ]mK W / C T 0293>

g) :

0925.000039583.0 += T c# [ ]mK W / C T C 00 60020

6875.0=c# [ ]mK W / C T 0600>

,

(0 6.21) [6].

6.21: 7+ , 7 ! !

6.1.2.2 8*# $#!!#

I . ,

20 -1000, , D,

. 0 Eurocode 2, part

1.2 , ,

:

a) :

)20(25.12300 = T c $ [ 3m / kg ] C T 0100

2200=c $ [ 3m / kg ] C T 0100

(6.26)

(6.27)

(6.28)

(6.29)





b) :

2000=c $ [ 3m / kg ] C T C 00 120020 (6.30)

6.1.2.3 '-, #!'&!# '-##

0

,

.

, :

, ,

.

6.22: +7 + ,

Collett & Tavernier (1976)

E 0 6.22 Collett

Tavernier (1976) [96],

. =

,

. = D

Eurocode 2, part 1.2, ,

(0 6.23),

:

) :

2)120/(4120/80900 T T cc += [ ]kgK J / C T C 00 120020

1875, = pik cc [ ]kgK J / ( 2%)

2750, = pik cc [ ]kgK J / ( 5%)

) :

840=cc [ ]kgK J / C T C 00 120020 (6.32)

C T C 0 0 200 100 (6.31)





6.23: +7 + , EC2

?

, “ ” -

, D 1000 2000. ?

1000, ,

. 0 2000

.

, , ,

“ c $ “,

D . I , ,

. E 0 6.24

(Harmathy & Allen,1973) [96]

. > 5000

.

6.24: F +

(1): kvarcen agregat,agregat varovnik

(2): lesen agregat





6.2

0

,

,

. . -

- ,

. , -

( )

(0.0361 C.0561).

6.2.1 !"# &!#

, (

) -

[65], :

,

. = ..

(steadu state test).

,

, . = ..

(transient test).

.

,

, . _

, .. ,

, D

, .

6.25: ) +

+ ! A36-ASTM





E 0 6.25 -

240/360 [57]. ,

(Borowski 1978) [1] (0 6.26).

6.26: . + ! ( - ; - + ! )

> ,

, ,

. > CEB-FIP Model code [20], Eurocode 3 [23],

-

. ,

FIRE Eurocode 2 & 3, part 1.2 ( 6.2).

l -

( ),

. >

. E 0 6.27

[96]. /

3500 D

,

. l 4000

. 0

D.

, -

. H





. 0

.

6.27: ( A36-ASTM)

6.2.1.1 “ “ %"0() - /(/ T.T.Lie K.H.Almand

, -

Lie T.T. and Almand K.H. [96].

:

. ! :

C T o600 :

+=

1750 900

120 T

ln

T )C ( f )T ( f o

y y

+=

1100 2000

120 T

ln

T )C ( E )T ( E o

C T o1000 600 << :

=

240

340 340 20

T

T . )C ( f )T ( f o

y y

=

5 53

690 690 20

.T

T . )C ( E )T ( E o

I :

)T ( f . )T ( E )T ( E

)T ( f . )T ( f .

)T ( y

y y

p

=

5 12

5 12 975 0

2

(6.34)

(6.33)





E :

: )T ( p = )T ( E

: )T ( p > )T ( E

)T ( f

. )T ( f . )T ( f . y

y y

2

5 12 975 0 5 12 +=

6.2.1.2 “ “ %"0() - /(/ '!(% Eurocode 2, part 1.2

Eurocode 2, part 1.2 (0 6.28 6.29),

:

)T ( E s ,

)T ( spr )T ( f y . E

D . > ( )

,

, .

I

-. l “”

_ (6.36)÷(6.39).

) , s spr T T ( ) ( ) :

s s sT E T T ( ) ( ) ( )= & (6.36)

) , spr s sT T ( ) ( ) 1 :

( )

( )

( )( ) )T ( )T ( f ))T ( )( T ( E

)T ( )T ( f c

cc ))T ( )( T ( E b

)T ( E

))T ( ( c ))T ( )( T ( E a

))T ( ( aa

)T ( b )T ( E

c )T ( aa

b )T (

spr y spr s s

spr y

spr s s

s

spr s spr s s

s s

s s s

spr s s s

=

+=

+=

=

+=

2 1

2

2 1

2

12

12

2

1

2

1

2 1

2

(6.37)

(6.35)





) , s s sT 1 2 ( ) :

s yT f T ( ) ( )= , E T s ( ) = 0 (6.38)

) D, s s suT 2 ( ) :

s

su s

su s yT

T f T ( )

( )( )=

2

(6.39)

:

( )T spr -

( )T f y -

( )T E s - Young

1 s -

su -

E 0 6.30

,

6.2.

f y(T)

spr (T)

spr s1 s2 su

s1=0.02

s2=0.15

su=0.20

6.28: J “ ” , EC2

6.29: F !-+

K , EC2





6.30: . “ “ K , EC2

$& 6.2

(0) )C ( E

)T ( E

o s

s

20

)C ( f

)T (

o.

prs

20 2 0

)C ( f

)T ( f

o.

y

20 2 0

20

100

200

300

400

500

600

700

800

900

1000

1100

1200

1.00

1.00

0.90

0.80

0.70

0.60

0.31

0.13

0.09

0.07

0.04

0.02

0.00

1.00

1.00

0.81

0.61

0.42

0.36

0.18

0.07

0.05

0.04

0.02

0.01

0.00

1.00

1.00

1.00

1.00

1.00

0.78

0.47

0.23

0.11

0.06

0.04

0.02

0.00

, , , (

) - -

[93]. = .

(1) )20(/)( 0

2,0 C f T spr

(2) )20(/)( 0C E T E s s

(3) )20(/)( 0

2,0 C f T f y





6.2.1.3 )'(#*(! /%!&6*1

0 ,

, ,

10. , ,

1.2×10-5.

0 D .

E 0 6.31

, Eurocode 3, part 1.2 [23].

?, :

C T C 00 75020 2854 s T 104.0T 102.110416 .2 )l / l ( ++=

C T C 00 860750 3 s 1011 )l / l ( = (6.40)

C T 0860 T 102102.6 )l / l ( 53 s

+=

:

l -

l - 200

6.31 ! , EC3

0 7500 8600,

, -

.





6.2.2 () !"# &!#

,

,

, . <D,

D ,

( > ?). =

FIRE,

.

:

,

.

6.2.2.1 !,-# #!'&!'(!!%!# &!#

b ,

, . ,

,

. 0 U.S.D.A. Agricultural

Handbook No.72, 1987 [96] :

C 900T C 20 00 T 022.048 s =#

C 900T 0> 2.28 s =#

:

s# - , ( )C m / W o

T - , ( C o )

6.32: =7+ , EC3

(6.41)




l Eurocode 3, part 1.2 [23]

0 6.32, :

C T C 00 80020 T 0333.054 s =#

C 1200T C 800 00 3.27 s =#

6.2.2.2 '-, #!'&!# '-## 0*# &!#

0

. l -

. E 7350,

, (0 6.33), D

, [96]. , Eurocode 3, part 1.2 :

C T C 00 60020 36 231 s T 1022.2T 1069.1T 1073.7 425c ++=

C T C 00 735600 )T 738 /( 13003666 c s +=

C T C 00 900735 )731T /( 17820545c s +=

C T C 00 1200900 650c s =

:

sc - , )C kg / J ( o

T - , ( C o )

6.33: +7 + , EC3

I ,

: )m / kg ( 7850 3

s = $ .

(6.43)

(6.42)

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