ÿþ w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
P r z y k Ba d 8 . Zc i s k a n i e - m a By m i m o [r ó d
W y z n a c z y i n a s z k i c o w a z b r o j e n i e s Bu p a m o n o l i t y c z n e g o p o k a z a n e g o n a r y s u n k u .
M = 1 5 0 k N m ; N = 1 5 0 0 k N .
E d E d
W y m i a r y p r z e k r o j u p o p r z e c z n e g o s Bu p a : b = 0 . 3 0 m , h = 0 . 4 5 m ,
p r z y j t o a = a = 0 . 0 5 m , z a t e m d = h a = 0 . 4 5 0 . 0 5 = 0 . 4 0 m , l = 3 . 0 m , w z By n i e p r z e s u w n e
1 2 1
1 . D a n e m a t e r i a Bo w e i z a Bo |e n i a w s t p n e :
N 6 . T a b . E . 1 N
W s k a z a n a ( m i n i m a l n a ) k l a s a b e t o n u d l a k l a s y e k s p o z y c j i X C 1 ’! C 2 0 / 2 5
N 6 . T a b . 3 . 1 .
p r z y j t o b e t o n k l a s y C 2 0 / 2 5 ’! f = 2 0 M P a ,
c k
f c k 2 0
f c d = = f = 1 3 . 3 3 M P a ,
c d
³ 1 . 5
c
f = 2 . 2 M P a , f = 1 . 5 M P a ,
c t m c t k
f c t k 1 . 5
f c t d = = f = 1 . 0 M P a ,
c t d
³c 1 . 5
o
µ = 3 . 5 = 0 . 0 0 3 5
c u 2
o o
S t a l : N 6 . T a b . C 1 , s t r .
s t a l k l a s y C ( g a t u n e k B 5 0 0 S P ) p a t r z p r z y k Ba d 1 : 1 8 7 i d a n e
f = 4 2 0 M P a , f = 5 0 0 M P a , f = 5 7 5 M P a , ¾ = 0 . 5 p r o d u c e n t a
y d y k t k e f f , l i m
2 . U s t a l e n i e k a t e g o r i i p r o j e k t o w e j u |y t k o w a n i a : N 1 . T a b . 2 . 1 .
P r z y j t o k a t e g o r i 4 , c o o d p o w i a d a k l a s i e k o n s t r u k c j i S 4 N 6 . T a b . 4 . 4 N
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 1 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
3 . E f e k t y w n y w s p ó Bc z y n n i k p e Bz a n i a :
w p By w p e Bz a n i a m o |n a p o m i n , j e [l i : N 6 . p k t . 5 . 8 . 4 . ( 4 ) ,
s t r . 6 3
" Õ( ", t o ) d" 2 ,
" » d"7 5 ,
M 0 E d
" e" h
N E d
M 0 E q , p
Õe f = Õ( ", t o ) Å" ;
M 0 E d
M - m a x . n a d Bu g o [c i s Bu p a m o m e n t z g i n a j c y p i e r w s z e g o r z d u w y w o Ba n y p r a w i e s t a B
0 E q , p
k o m b i n a c j o b c i |e D ( S L S ) ,
1 5 0
M 0 E q , p H" = 1 0 0 k N m ( d l a S G U a" S L S ) ;
1 . 5
M - m a x . n a d Bu g o [c i s Bu p a m o m e n t z g i n a j c y p i e r w s z e g o r z d u w y w o Ba n y o b l i c z e n i o w
0 E d
k o m b i n a c j o b c i |e D ( U L S ) ,
M 0 E d = 1 5 0 k N m ( d l a S G N a" U L S )
2 Å" A c
h o =
u
h m i a r o d a j n y w y m i a r p r z e k r o j u p o p r z e c z n e g o ,
o
u o b w ó d c z [c i p r z e k r o j u w y s t a w i o n e j n a w y s y c h a n i e ,
2 Å" 3 0 0 Å" 4 5 0
h o = = 1 8 0 m m
2 Å"( 3 0 0 + 4 5 0 )
N 6 . r y s . 3 . 1 . , s t r .
Õ( ", t o ) H" 3 . 0 > 2 . 0 , z a t e m w p By w p e Bz a n i a n a l e |y u w z g l d n i
2 8 .
1 0 0
Õe f = 3 , 0 H" 2 . 0
1 5 0
4 . S m u k Bo [ g r a n i c z n a :
I I s p o s ó b ( o b l i c z e n i a u p r o s z c z o n e ) :
N 6 . w z ó r ( 5 . 1 3 N ) ,
2 0 Å" A Å" B Å"C
s t r . 6 0
»l i m =
n
A s Å" f y d
É = ; p r z y j t o Á = 1 . 0 % ’! A = 1 2 0 0 m m 2
s
b Å" d Å" f c d
1 2 0 0 Å"4 2 0
É = = 0 . 3 1 5
3 0 0 Å"4 0 0 Å"1 3 . 3
n w z g l d n a s i Ba n o r m a l n a :
N E d
n =
A c Å"f c d
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 2 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
1 5 0 0 0 0 0
n = = 0 . 8 3 4
3 0 0 Å" 4 5 0 Å"1 3 . 3
A = 0 . 7 ; B = 1 . 1 ; C = 0 . 7 ;
2 0 Å"0 . 7 Å"1 . 1 Å"0 . 7
»l i m = = 1 1 . 8 0
0 . 8 3 4
5 . D Bu g o [ e f e k t y w n a i r z e c z y w i s t a s m u k Bo [ s Bu p a :
W e l e m e n t a c h u s z t y w n i o n y c h d Bu g o [ e f e k t y w n a :
ëø k 1 ìø k 2 öø N 6 . w z ó r ( 5 . 1 5 ) , s t r .
öø ëø
ìø
l o = 0 , 5 l
6 1
ìø1 + 0 , 4 5 + k 1 ÷ø Å"ìø1 + 0 , 4 5 + k 2 ÷ø ;
÷ø ÷ø
íø øø íø øø
0 , 5 l < l 0 < l
˜ E J
k 1 , k 2 ’! k = Å" E J = ?
M l
k , k w z g l d n e p o d a t n o [c i p o d p ó r o g r a n i c z a j c e o b r o t y w w z Ba c h ,
1 2
˜ - k t o b r o t u p o d p o r y w y w o Ba n y m o m e n t e m z g i n a j c y m M p a t r z t a k |e :
N 6 . r y s . 5 . 7 ( f ) , ( g )
E J s z t y w n o [ g i t n a e l e m e n t u [c i s k a n e g o , p a t r z t a k |e
N 6 . p k t . 5 . 8 . 3 . 2 ( 4 ) i
( 5 )
l w y s o k o [ e l e m e n t u [c i s k a n e g o w [w i e t l e p o m i d z y k o Dc o w y m i z a m o c o w a n i a m i .
N 6 . w g s c h e m a t u
p r z y j t o l 0 = 1 . 0 Å" l = 1 . 0 Å" 3 . 0 = 3 . 0 m .
5 . 7 a , s t r . 6 1
N 6 . s c h e m a t 5 . 7 a ,
s t r . 6 1
S m u k Bo [:
l o
» =
i
i p r o m i e D b e z w Ba d n o [c i n i e z a r y s o w a n e g o p r z e k r o j u |e l b e t o w e g o ,
J c
i =
A c
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 3 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
b Å" h 3 3 0 0 Å" 4 5 0 3
J c = = = 2 2 7 8 1 2 5 0 0 0 m m 4
1 2 1 2
A c = b Å"h = 3 0 0 Å" 4 5 0 = 1 3 5 0 0 0 m m 2
2 2 7 8 1 2 5 0 0 0
i = = 1 2 9 . 9 0 m m
1 3 5 0 0 0
3 0 0 0
» = = 2 3 . 0 9 > »l i m = 1 1 . 8 0 Ò! n a l e |y u w z g l d n i w p By w e f e k t ó w d r u g i e g o
1 2 9 . 9 0
r z d u .
6 . I m p e r f e k c j e g e o m e t r y c z n e :
a ) j a k o d o d a t k o w y m i m o [r ó d
N 6 . w z ó r ( 5 . 2 )
e i = 0 , 5 Å" ˜i Å" l 0 ;
s t r . 5 0
˜i = ˜0 ±h ±m ;
N 6 . w z ó r ( 5 . 1 )
1
˜0 = - w a r t o [ b a z o w a k t a p o c h y l e n i a
s t r . 4 9
2 0 0
2
±h
w s p . r e d u k c y j n y d Bu g o [c i , l u b w y s o k o [c i d" ±h d" 1 . 0
3
2
±h = l w [ m ]
l
2
±h = = 1 . 1 5 > 1 p r z y j t o ±h
= 1 . 0
3
±m
w s p . r e d u k c y j n y z e w z g l d u n a l i c z b e l e m e n t ó w p i o n o w y c h
1
ëø1 + öø,
±m = 0 . 5 Å"
ìø ÷ø
m
íø øø
m l i c z b a e l e m e n t ó w p i o n o w y c h w p By w a j c y c h n a c a By r o z p a t r y w a n y e f e k t
N 6 . w z ó r s t r . 5 0
m = 1
±m = 1 , 0
1
˜i = Å"1 . 0 Å"1 . 0 = 5 . 0 Å"1 0 - 3
2 0 0
e i = 0 , 5 Å"5 . 0 Å"1 0 - 3 Å"3 0 0 0 = 7 . 5 m m
l u b :
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 4 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
b ) j a k o d o d a t k o w a s i Ba :
N 6 . w z ó r ( 5 . 3 b ) s t r .
w e l e m e n t a c h u s z t y w n i o n y c h H i = 2 Å" ˜i Å"N E d
5 0
H i = 2 Å" 5 . 0 Å"1 0 - 3 Å"1 5 0 0 = 1 5 . 0 k N
"M H" 0 , 2 5 Å" H i Å" l = 0 , 2 5 Å"1 5 . 0 Å" 3 . 0 = 1 1 . 2 5 k N m
M + "M = 1 5 0 + 1 1 . 2 5 = 1 6 1 . 2 5 k N m - c a Bk o w i t y
0 E d
m o m e n t p i e r w s z e g o r z d u ( u w z g l d n i a j c y i m p e r f e k c j e
g e o m e t r y c z n e ) :
7 . E f e k t y d r u g i e g o r z d u :
k r y t e r i u m u p r o s z c z o n e - m e t o d a n o m i n a l n e j s z t y w n o [c i :
N 6 . w z ó r ( 5 . 2 1 )
E J = K c Å" E c d Å" J c + K S Å" E S Å" J
S
E c d - o b l i c z e n i o w a w a r t o [ m o d u Bu s p r |y s t o [c i b e t o n u
N 6 . w z ó r ( 5 . 2 0 ) , s t r .
E c m
E c d =
6 3
³
C E
3 0 0 0 0
³C E = 1 . 2 ; E c d = = 2 5 0 0 0 M P a
1 . 2
A s
d l a Á = e" 0 , 0 0 2 m o |n a p r z y j m o w a n a s t p u j c e w a r t o [c i
A c
w s p ó Bc z y n n i k ó w :
K S - w s p ó Bc z y n n i k z a l e |n y o d u d z i a Bu z b r o j e n i a
K S = 1 , 0 ;
K C - w s p ó Bc z y n n i k z a l e |n y o d w p By w u z a r y s o w a n i a , p e Bz a n i a , i t d .
k 1 Å" k 2
K C =
1 + Õe f
k - w s p ó Bc z y n n i k z a l e |n y o d k l a s y b e t o n u ,
1
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 5 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
N 6 . W z ó r ( 5 . 2 3 )
f c k 2 0
k 1 = = = 1 ;
s t r . 6 4
2 0 2 0
k - w s p ó Bc z y n n i k z a l e |n y o d w p By w u s i By p o d Bu |n e j i s m u k Bo [c i
2
»
k 2 = n d" 0 , 2 0
1 7 0
n = 0 . 8 3 4 , ( o b l i c z o n a w p k t . 3 . ) ; »= 2 3 . 0 9 ( o b l i c z o n a w p k t . 4 . )
2 3 . 0 9
k 2 = 0 . 8 3 4 Å" = 0 . 1 1 3 < 0 , 2 0
1 7 0
1 Å"0 . 1 1 3
K c = = 0 , 0 3 8
1 + 2 . 0
b Å" h 3 3 0 0 Å" 4 5 0 3
J c = = = 2 2 7 8 1 2 5 0 0 0 m m 4
1 2 1 2
2
h
ëø
J = Á Å" b Å" d Å" - a öø ,
ìø ÷ø
s
2
íø øø
w p i e r w s z y m k r o k u i t e r a c j i z a Bo |o n o Á= 0 . 0 1 = 1 . 0 %
J m o m e n t b e z w Ba d n o [c i p r z e k r o j u z b r o j e n i a w z g l d e m [r o d k a c i |k o [c i p r z e k r o j u b e t o n u
S
2
4 5 0
J S = 0 . 0 1 Å"3 0 0 Å" 4 0 0 Å"ëø - 5 0 öø = 3 6 7 5 0 0 0 0 m m 4
ìø ÷ø
2
íø øø
E J = 0 . 0 3 8 Å" 2 5 0 0 0 Å" 2 2 7 8 1 2 5 0 0 0 + 1 . 0 Å" 2 0 0 0 0 0 Å"3 6 7 5 0 0 0 0 =
2 . 1 5 Å"1 0 1 2 + 7 . 3 5 Å"1 0 1 2 = 9 . 5 Å"1 0 1 2 [ N Å" m m 2 ]
8 . W s p ó Bc z y n n i k p o w i k s z e n i a m o m e n t u :
C a Bk o w i t y m o m e n t o b l i c z e n i o w y z a w i e r a j c y m o m e n t d r u g i e g o r z d u m o |n a p r z e d s t a w i j a k o
p o w i k s z o n y m o m e n t z g i n a j c y w y n i k a j c y z a n a l i z y p i e r w s z e g o r z d u , s t o s u j c w z ó r :
N 6 . w z ó r ( 5 . 2 8 ) ,
M = M 0 E d Å" p M
E d
s t r . 6 5
²
p M = 1 + ;
N ’
- 1
N E d
2
À
² =
N 6 . w z ó r ( 5 . 2 9 )
c 0
² - w s p ó Bc z y n n i k z a l e |n y o d r o z k Ba d u m o m e n t ó w 1 - g o i 2 - g o r z d u ,
N o b l i c z e n i o w a w a r t o [ s i By p o d Bu |n e j ,
E d
N s i Ba k r y t y c z n a z e w z g l d u n a w y b o c z e n i e , o b l i c z o n a p r z y z a Bo |e n i u , |e s z t y w n o [ j e s t r ó w n a
B
n o m i n a l n e j
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 6 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
2
À
² = H" 1 , 0 3
9 . 6
' '
M = M = M = 1 6 1 . 2 5 k N m
0 E d 0 1 0 2
2 2
À E J À
E u l .
N B = N k r ( E J ) = = 9 . 5 0 Å"1 0 1 2 = 1 0 4 1 7 9 1 6 N = 1 0 4 1 8 k N
2
l o ( 3 0 0 0 ) 2
1 , 0 3
p M = 1 + = 1 . 1 7
1 0 4 1 8
- 1
1 5 0 0
M = 1 , 1 7 Å"1 6 1 . 2 5 = 1 8 9 . 1 9 k N m
E d
9 . O b l i c z e n i e p o w i e r z c h n i z b r o j e n i a s Bu p a ( m e t o d u p r o s z c z o n ) :
M 1 8 9 . 1 9
E d
e = = = 0 . 1 2 6 m = 1 2 6 m m
N E d 1 5 0 0
a ) z a Bo |e n i e m a Be g o m i m o [r o d u :
A s 1 `" A s 2
d - a 2 4 0 0 - 5 0
e s 1 = e + = 1 2 6 + = 3 0 1 m m
2 2
Ò! p r z e k r ó j j e s t [c i s k a n y z m a By m m i m o [r o d e m ( p o n i e w a | s i Ba [c i s k a j c a l e |y p o m i d z y [r o d k a m i
c i |k o [c i z b r o j e D A i A ) .
s 1 s 2
e s 2 = ( d - a 2 ) - e s 1
e s 2 = ( 4 0 0 - 5 0 ) - 3 0 1 = 4 9 m m
x e f f , l i m = ¾e f f , l i m Å" d = 0 . 5 Å" 4 0 0 = 2 0 0 m m
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 7 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
b ) o b l i c z e n i e w y s o k o [c i s t r e f y [c i s k a n e j :
= 0 Ò! f y d Å" A s 1 Å"( d - a 2 ) - f c d Å"b Å" x e f f ( 0 . 5 x e f f - a 2 ) = N E d Å"e s 2 ,
"M A s 2
p r z y c z y m x e f f > x e f f , l i m , n a l e |y o b l i c z y ¾e f f ( u w a g a : Ã = º Å" f < f ) ;
s 1 s y d y d
z a k Ba d a j c A z b l i |o n e d o m i n . :
s 1
2 [ ( 1 - ¾e f f , l i m ) Å" N Å"( - e s 2 ) + ( 1 + ¾e f f , l i m ) Å" A s 1 Å" f Å"( d - a 2 ) ]
E d y d
¾e f f = B + B 2 +
2
( 1 - ¾e f f , l i m ) Å"b Å" d Å" f c d
)
a 1 2 Å" A s 1 Å" f y d Å"( d - a 2
B = -
2
d ( 1 - ¾e f f , l i m ) Å"b Å" d Å" f c d
N E d
ñø 1 5 0 0 0 0 0
ôø0 . 1 0 f y d = 0 . 1 4 2 0 = 3 5 7 m m 2 ,
A s , m i n =
òø
ôø0 , 0 0 2 Å" A c = 0 . 0 0 2 Å" 3 0 0 Å" 4 0 0 = 2 4 0 m m 2
óø
w s t p n i e z a Bo |o n o z b r o j e n i e A z b l i |o n e d o m i n i m a l n e g o ( 2 ¦1 2 m m o A = 2 2 6 m m 2 )
s 1 s 1
5 0 2 Å" 2 2 6 Å" 4 2 0 Å"( 4 0 0 - 5 0 )
B = - = - 0 . 0 8 3
4 0 0 ( 1 - 0 . 5 ) Å"3 0 0 Å" 4 0 0 2 Å"1 3 . 3 3
2 [ ( 1 - 0 . 5 ) Å"1 5 0 0 0 0 0 Å"( 4 9 ) + ( 1 + 0 . 5 ) Å" 2 2 6 Å" 4 2 0 Å"( 4 0 0 - 5 0 ) ]
2
¾e f f = - 0 . 0 8 3 + ( - 0 . 0 8 3 ) +
( 1 - 0 . 5 ) Å" 3 0 0 Å" 4 0 0 2 Å"1 3 . 3 3
¾e f f = 0 . 6 5 7 > ¾e f f , l i m = 0 . 5 , z a t e m p r z e k r ó j [c i s k a n y z m a By m m i m o [r o d e m
x e f f = ¾e f f Å" d = 0 . 6 5 7 Å" 4 0 0 = 2 6 3 m m
c ) O b l i c z e n i e p o l a p o w i e r z c h n i z b r o j e n i a [c i s k a n e g o z :
A s 1
"M = 0 Ò! f y d Å" A s 2 Å"( d - a 2 ) + f c d Å" b Å" x e f f ( d - 0 . 5 x e f f ) = N E d Å"e s 1
N E d Å" e s 1 - f c d Å" b Å" x e f f ( d - 0 . 5 x e f f )
A s 2 =
f y d Å"( d - a 2 )
1 5 0 0 0 0 0 Å"3 0 1 - 1 3 . 3 3 Å"3 0 0 Å" 2 6 3 Å"( 4 0 0 - 0 . 5 Å" 2 6 3 )
A s 2 =
4 2 0 Å"( 4 0 0 - 5 0 )
A s 2 = 1 1 5 0 m m 2
d ) O b l i c z e n i e p o l a p o w i e r z c h n i z b r o j e n i a r o z c i g a n e g o z :
= 0 Ò! N E d = f c d Å" b w Å" x e f f + f y d 2 Å" A s 2 - ºs f y d 1 A s 1
"F x
2 ( 1 - ¾e f f )
ºs = - 1
1 - ¾e f f , l i m
2 ( 1 - 0 . 6 5 7 )
ºs = - 1 = 0 . 3 7 2
1 - 0 . 5
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 8 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
- N E d + f c d Å" b Å" x e f f + f y d 2 Å" A s 2
A s 1 =
ºs f y d 1
- 1 5 0 0 0 0 0 + 1 3 . 3 3 Å" 3 0 0 Å" 2 6 3 + 4 2 0 Å"1 1 5 0
A s 1 = = 2 3 0 m m 2
0 . 3 7 2 Å" 4 2 0
Á z a Bo |o n e ’! 0 . 0 1 = 1 . 0 %
Á ’!
Á ’!
Á ’!
( 1 1 0 8 + 2 3 0 )
Á ’! = 0 . 0 1 1 = 1 . 1 %
o b l i c z o n e
3 0 0 Å" 4 0 0
"Á = 0 . 0 1 - 0 . 0 1 1 = - 0 . 0 0 1
"Á 0 . 0 0 1
= - = 0 . 1 = 0 . 1 Ò! w s t p n i e p r a w i d Bo w o z a Bo |o n o s t o p i e D z b r o j e n i a
Áz a l o |a l o 0 . 0 1
s Bu p a
P r z y j t o :
w s t r e f i e r o z c i g a n e j : 4 ¦ 1 2 o A = 4 . 5 2 c m 2 ,
s 1
w s t r e f i e [c i s k a n e j : 4 ¦ 2 0 o A = 1 2 . 5 6 c m 2 .
s 1
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 9 / 1 0
w i c z e n i a z k o n s t r u k c j i b e t o n o w y c h P r z y k Ba d 8
U w a g a : N a l e |y p a m i t a z k t ó r e j s t r o n y p r z e k r o j u m a b y z b r o j e n i e A , a z k t ó r e j A .
s 1 s 2
2 0 1 4 - 0 5 - 0 7 d r i n |. K r y s t y n a W R Ó B E L 1 0 / 1 0
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