ÿþP O L I T E C H N I K A R Z E S Z O W S K A
i m . I g n a c e g o Au k a s i e w i c z a
W y d z i a B B u d o w n i c t w a i I n |y n i e r i i Zr o d o w i s k a
K A T E D R A I N {Y N I E R I I M A T E R I A AO W E J
I T E C H N O L O G I I B U D O W N I C T W A
P r o j e k t b e t o n u z w y k Be g o
T e m a t : P By t a d r o g o w a .
I Z a Bo |e n i a t e c h n i c z n o t e c h n o l o g i c z n e :
- r o d z a j e l e m e n t u : p By t a d r o g o w a ,
- w y m i a r y :
g r u b o [: 0 , 1 5 m
s z e r o k o [: 1 , 5 m
d Bu g o [: 3 , 0 m
- z b r o j e n i e :
2 x p r t f i 8 m m l = 2 9 0 c m
f i 6 m m # 6 x 1 4 0 c o 2 0 c m
- k l a s a b e t o n u : C 2 5 / 3 0
- z a g s z c z e n i e m i e s z k a n k i : m e c h a n i c z n e z a p o m o c w s t r z s a r k i
- w a r u n k i d o j r z e w a n i a : n a t u r a l n e ²= 1 , 0
- l i c z b a p r o j e k t o w a n y c h e l e m e n t ó w : 1 5 0 s z t u k
- p o j e m n o [ t e o r e t y c z n a b e t o n i a r k i : V = 5 0 0 d m 3
B
- k l a s a e k s p o z y c j i : X C 2
I I U s t a l e n i a w s t p n e :
k o n s y s t e n c j a : g s t o p l a s t y c z n a V - 2 ( w g V e - B e P N - E N - 2 0 6 - 1 )
K - 2 ( w g P N - 8 8 / B - 0 6 2 5 0 )
z a l e c a n a i l o [ z a p r a w y : 4 5 0 ÷ 5 5 0 d m 3 / m 2
I I I D o b ó r s k Ba d n i k ó w m i e s z a n k i b e t o n o w e j :
1 . C e m e n t
P r z y j t o c e m e n t p o r t l a n d z k i C E M I 3 2 , 5 ( n p . w g T A B . I - 1 I - 2 P N - 8 8 / B - 0 6 2 5 0 )
g s t o [ o b j t o [c i o w a : f = 3 , 1 k g / d m 3
c
w o d o |d n o [ c e m e n t u : W = 0 , 2 5 d m 3 / k g ( d l a k o n s y s t e n c j i g s t o p l a s t y c z n e j
c
w g T A B . 9 - 2 2 , , P o r a d n i k l a b o r a n t a b u d o w l a n e g o )
2 . K r u s z y w o
K g r u b e ( b a z a l t o w e Ba m a n e ) o w i l g o t n o [c i n a t u r a l n e j W = 2 % i g s t o [c i o b j t o [c i o w e j f =
1 n | |
2 , 6 5 k g / d m 3
K d r o b n e o w i l g o t n o [c i n a t u r a l n e j W = 5 % i g s t o [c i o b j t . f = 2 , 6 5 k g / d m 3
2 n p p
3 . W o d a
W o d a o d p o w i a d a w y m a g a n i o m P N - E N 1 0 0 8
I V U s t a l e n i e s t o s u n k u c e m e n t o w o - p i a s k o w e g o i p r o p o r c j i z m i e s z a n i a k r u s z y w a
g r u b e g o - K i d r o b n e g o - K m e t o d p u n k t u p i a s k o w e g o :
1 2
1 . U s t a l e n i e s t o s u n k u C / W É
f
C C
c m
= + 0 , 5 < 2 , 5
d l a
W A 1 W
f = 1 , 2 * f * ²
c m c k
f = 3 0 M P a
c k
f = 1 , 2 * 3 0 * 1 , 0
c m
f = 3 6
c m
A = 2 0 n a p o d s t a w i e T a b l i c y 7 . 4
1
C 3 6
= Ĉ0 , 5
W 2 0
C
< 2 , 5
É= 2 , 3 s p e Bn i a z a Bo |e n i e
W
2 . U s t a l e n i e p u n k t u p i a s k o w e g o k r u s z y w a P P
W g T A B 9 - 1 8 , , P o r a d n i k a l a b o r a n t a b u d o w l a n e g o p r z y j t o P P = 3 0 %
3 . U s t a l e n i e s t o s u n k u z m i e s z a n i a k r u s z y w a K : K = X
1 2
P P - p u n k t p i a s k o w y k r u s z y w a g r u b e g o ( k r u s z y w o b a z a l t o w e Ba m a n e ) K - 0 %
z 1
P P
p - p u n k t p i a s k o w y k r u s z y w a d r o b n r g o K - 9 7 , 0 8 %
2
P P - p u n k t p i a s k o w y s t o s u o k r u c h o w e g o - 3 0 %
P i a s e k K r u s z y w o g r u b e S t o s o k r u c h o w y W o d o |d n o [
F r a k c j a
- - % W X %
i
% % % % % % % % W
i
( 4 * X ) ( 6 + 2 ) ( 7 / ( X + 1 ) ( 8 * 1 0 )
1 2 3 4 5 6 7 8 9 1 0 1 1
0 - 0 , 1 2 5 5 , 9 4 5 , 9 4 0 0 0 5 , 9 4 1 , 8 3 1 , 8 3 0 , 2 1 5 0 , 3 9 5
0 , 1 2 5 - 0 , 2 5 9 , 4 1 1 5 , 3 5 0 0 0 9 , 4 1 2 , 9 1 4 , 4 7 0 , 1 0 9 0 , 3 1 7
0 , 2 5 - 0 , 5 4 0 , 8 4 5 6 , 3 5 0 0 0 4 0 , 8 4 1 2 , 6 2 1 7 , 3 6 0 , 0 7 6 0 , 9 5 9
0 , 5 - 1 2 8 , 2 2 8 4 , 4 1 0 0 0 2 8 , 2 2 8 , 7 2 2 6 , 0 8 0 , 0 5 3 0 , 4 6 2
1 , 0 - 2 , 0 1 2 , 6 7 9 7 , 0 8 0 0 0 1 2 , 6 7 3 , 9 2 3 0 0 , 0 3 9 0 , 1 5 3
2 , 0 - 4 , 0 2 , 9 2 1 0 0 0 , 6 6 0 , 6 6 1 , 4 7 6 4 , 3 9 6 1 , 3 6 3 1 , 3 6 0 , 0 2 9 0 , 0 3 9
4 , 0 - 8 , 0 2 4 , 5 7 2 5 , 2 3 5 4 , 9 3 9 5 4 , 9 3 9 1 6 , 9 8 4 8 , 3 4 0 , 0 2 3 0 , 3 9
8 , 0 - 1 6 , 0 7 4 , 7 7 1 0 0 1 6 7 , 1 8 6 1 6 7 , 1 8 6 5 1 , 6 6 1 0 0 0 , 0 1 8 0 , 9 3 0
P P - P P
p
X =
X = 2 , 2 3 6
P P - P P |
T r z e b a w z i 2 , 2 3 6 c z [c i m a s o w e k r u s z y w a g r u b e g o K i 1 c z [ m a s o w k r u s z y w a
1
d r o b n e g o K
2
V U s t a l e n i e w o d o |d n o [c i k r u s z y w a :
1 . W o d o |d n o [ f r a k c j i d r o b n y c h ( 0 ÷ 2 , 0 m m )
W ' = "f * W
p i i
W ' = 2 , 2 8 6 d m 3 / k g
p
D o m i e s z a n k i u |y t o c e m e n t u p o r t l a n d z k i e g o C E M I 3 2 , 5 w i c w s k a zn i k k o r y g u j c y
w o d o |d n o [ f r a k c j i d r o b n e j w y n o s i :
S = 1 , 0
o s t a t e c z n i e :
W = W ' * S
K 2 K 2
W = 2 , 2 8 6 * 1 , 0 = 2 , 2 8 6 d m 3 / k g
K 2
2 . W o d o |d n o [ f r a k c j i g r u b y c h ( 2 ÷ 1 6 m m )
W = "f * W
K 1 i i
W = 1 , 3 5 9 d m 3 / k g
K 1
3 . W o d o |d n o [ k r u s z y w a
W ĈW
K 2 K 1
W =
k
1 0 0
2 , 2 8 6 Ĉ1 , 3 5 9
W =
k
1 0 0
W = 0 , 0 3 6 5 d m 3 / k g
k
V I U s t a l e n i e m a s y s k Ba d n i k ó w n a 1 m 2
m i e s z k a n k i b e t o n o w e j m e t o d B u k o w s k i e g o
( s u c h e s k Ba d n i k i )
( r e c e p t a l a b o r a t o r y j n a ) :
1 . K r u s z y w o
1 0 0 0
K =
0
W
Îà 1
k
Ĉ1 Ĉ
žà Ÿà
1 - W "Îà f f
c c k
1 0 0 0
K =
0
0 , 0 3 6 5 2 , 5 1
Ĉ1 Ĉ
žà Ÿà
1 - 0 , 2 5 " 2 , 5 3 , 1 2 , 6 5
K = 1 7 9 9 , 9 5 k g / m 3
0
R o z b i c i e n a k r u s z y w o g r u b e i d r o b n e :
{
= 2 , 3 7
P
{+ P = 1 7 9 9 , 9 5 k g / m 3
P = 4 8 6 , 1 2 k g / m 3
{ = 1 3 1 3 , 8 3 k g / m 3
2 . W o d a
W
k
W = "K 0
0
1 - W "É
c
0 , 0 3 6 5
W = "1 7 9 9 , 9 5
0
1 - 0 , 2 5 "2 , 5
W = 1 7 5 , 2 d m 3 / m 3
0
3 . C e m e n t
C 0 = É"W
0
C 0 = 2 , 5 "1 7 5 , 2
C = 4 3 8 k g / m 3
0
V I I S p r a w d z e n i e p o p r a w n o [c i w y k o n a n y c h o b l i c z e D:
1 . R ó w n a n i e s z c z e l n o [c i
C K
0 0
+ + W = 1 0 0 0 d m 3 ± 5 d m 3
0
f f
c k
4 3 8 1 7 9 9 , 9 5 Ĉ1 7 5 , 2 = 9 9 5 , 7 2 d m 3
Ĉ
3 , 1 2 , 6 5
2 . R ó w n a n i e k o n s y s t e n c j i ( c i e k Bo [c i )
C 0 "W + K 0 "W = W
c k 0
4 3 8 * 0 , 2 5 + 1 7 9 9 , 9 5 * 0 , 0 3 6 5 = 1 7 5 , 2 d m 3 / m 3
V I I I S p r a w d z e n i e w a r u n k ó w n o r m o w y c h :
1 . P N - 8 8 / B - 0 6 2 5 0 ( n i e o b o w i z u j c a )
m i n i m a l n a i m a k s y m a l n a i l o [ c e m e n t u w g T A B 2 . d l a b e t o n u o s Bo n i t e g o p r z e d
d z i a Ba n i e m c z y n n i k ó w a t m o s f e r y c z n y c h
C m i n = 2 2 0 k g / m 3
C m a x = 4 5 0 k g / m 3
2 2 0 k g / m 3 < 4 3 8 k g / m 3 < 4 5 0 k g / m 3
W
0
m a x †à0 , 6 0
n a j w i k s z a d o p u s z c z a l n a w a r t o [
C
0
W
0
= 0 , 4 †à0 , 6 0
C
0
z a l e c a n a i l o [ z a p r a w y Z
w g T A B 3 . Z m i n = 4 5 0 d m 3 / m 3
Z m a x = 5 5 0 d m 3 / m 3
P P "K C 0
0
Z = + + W
0
1 0 0 " f f
k c
Z = 5 2 1 , 0 3 d m 3 / m 3
2 . P N - E N 2 0 6 - 1 ( T A B F 1 z a l e c a n e w a r t o [c i g r a n i c z n e d l a k l a s y e k s p o z y c j i X C 2 ;
d o t y c z y s k Ba d u b e t o n u )
- m a k s y m a l n e
W
0
†à0 , 6 0
C
0
W
0
= 0 , 4 0 †à0 , 6 6
C
0
m i n i m a l n a z a w a r t o [ c e m e n t u k g / m 3
C m i n = 2 8 0 k g / m 3
C = 4 3 8 k g / m 3 > 2 8 0 k g / m 3
0
m i n i m a l n a k l a s a c e m e n t u
C 2 5 / 3 0
I X O b l i c z e n i e i l o [c i s k Ba d n i k ó w n a 1 m 3
z u w z g l d n i e n i e m w i l g o t n o [c i n a t u r a l n e j
k r u s z y w a :
W = 4 %
n |
W = 3 %
n p
1 . C e m e n t
C = C = 4 3 8 k g / m 3
z 0
2 . K r u s z y w o
k r u s z y w o g r u b e
W
n |
{ = { 1 +
z 0
( )
1 0 0
5
{ = 1 2 6 9 , 1 1 Ĉ = 1 3 6 6 , 3 8 k g / m 3
z
žà Ÿà
1 0 0
k r u s z y w o d r o b n e
W
n p
P = P 0 1 +
z
( )
1 0 0
P = 5 0 0 , 7 0 k g / m 3
z
3 . W o d a
W W
n | n p
W = W - { " - P 0 "
z 0 0
( ) ( )
1 0 0 1 0 0
W = 1 0 8 , 0 6 d m 3 / m 3
z
X U s t a l e n i e i l o [c i s k Ba d n i k ó w n a 1 z a r ó b w b e t o n i a r c e
( r e c e p t a r o b o c z a ) :
V = 5 0 0 d m 3 = 0 , 5 m 3 ( p o j e m n o [ t e o r e t y c z n a )
B t
V = 0 , 8 5 "5 0 0 d m 3 = 0 , 4 2 5 m 2 ( p o j e m n o [ u |y t k o w a )
B u
1 . C e m e n t
C = C "V = 1 8 6 , 1 5 k g / 1 z a r ó b
B z B u
2 . W o d a
W = 4 5 , 6 0 d m 3 / 1 z a r ó b
B
3 . K r u s z y w o
{ = { "V = 5 8 0 , 7 1 k g / 1 z a r ó b
g r u b e
B z B u
P B = P "V = 2 1 2 , 8 0 k g / 1 z a r ó b
d r o b n e
z B u
X I O b l i c z e n i e s k Ba d n i k ó w n a 1 e l e m e n t :
V - o b j t o [ e l e m e n t u [ m 3 ]
e
V = h * a * b = 0 , 1 5 * 1 , 5 * 3 = 0 , 6 7 5 m 3
e
- p o m i j a m y o b j t o [ z b r o j e n i a
1 . C e m e n t
C e = C "V = 4 3 8 "0 , 6 7 5 = 2 9 5 , 6 5 k g / 1 e l e m e n t
z e
2 . W o d a
W = W "V = 1 0 8 , 6 "0 , 6 7 5 = 7 3 , 3 1 d m 3 / 1 e l e m e n t
e z e
3 . K r u s z y w o
k r u s z y w o g r u b e
{e = { "V = 1 3 6 6 , 3 8 "0 , 6 7 5 = 9 2 2 , 3 1 k g / 1 e l e m e n t
z e
k r u s z y w o d r o b n e
P e = P "V = 5 0 0 , 7 0 "0 , 6 7 5 = 3 3 7 , 9 7 k g / 1 e l e m e n t
z e
X I I O b l i c z e n i e i l o [c i s k Ba d n i k ó w n a 1 5 0 s z t e l e m e n t ó w :
1 . C e m e n t
C 1 5 0 = C e "1 5 0 = 2 9 5 , 6 5 "1 5 0 = 4 4 3 4 7 , 5 k g / 1 5 0 e l e m e n t ó w
2 . W o d a
W = W "1 5 0 = 7 3 , 3 1 "1 5 0 = 1 0 9 9 6 , 5 d m 3 / 1 5 0 e l e m e n t ó w
1 5 0 e
3 . K r u s z y w o
k r u s z y w o g r u b e
{1 5 0 = { "1 5 0 = 9 2 2 , 3 1 "1 5 0 = 1 3 8 3 4 6 , 5 k g / 1 5 0 e l e m e n t ó w
e
k r u s z y w o d r o b n e
P 1 5 0 = P e "1 5 0 = 3 3 7 , 9 7 "1 5 0 = 5 0 6 9 5 k g / 1 5 0 e l e m e n t ó w
X I I I O b l i c z e n i e i l o [c i z a r o b ó w n a w y k o n a n i e w s z y s t k i c h 1 5 0 e l e m e n t ó w :
C
4 4 3 4 7 , 5
1 5 0
= = 2 3 8 , 2 4 z a r o b ó r
C 1 8 6 , 1 5
B
N a w y k o n a n i e 1 5 0 s z t . e l e m e n t ó w p o t r z e b a 2 3 8 , 2 4 z a r o b ó w .
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