ÿþ1 . D a n e g e o m e t r y c z n e i z a Bo |e n i a w y j [c i o w e d o p r o j e k t o w a n i a :
L c o l : = 6 . 8 m - w y s o k o [ s Bu p a
a : = 2 . 3 m - w y s i g l e w e g o r y g l a
b : = 3 . 3 m - w y s i g p r a w e g o r y g l a
G : = 5 5 k N - c i |a r r u r o c i a g u
P : = 1 1 0 k N - c i |a r m e d i a
f : = 0 . 1 2 - w s p ó Bc z y n n i k t a r c i a
L o k a l i z a c j a : W r o c Ba w
g Bb o k o [ s t r e f y p r z e m a r z a n i a :
h z : = 1 . 0 m
2 . D o b ó r w y m i a r ó w p o s z c z g ó l n y c h e l e m e n t ó w :
2 . 1 S Bu p
l 0 l 0
l 0 : = 2 ×ðL c o l = 1 3 . 6 m h s 1 : = = 0 . 6 8 m h s 2 : = = 0 . 5 4 4 m
2 0 2 5
p r z y j m u j e :
h s : = 0 . 6 m b s : = h s = 0 . 6 m
2 . 2 R y g i e l :
b r : = b s = 0 . 6 m h r : = b r + 0 . 2 m = 0 . 8 m
2 . 3 S t o p a f u n d a m e n t o w a
W s t p n i e p r z y j t o w y m i a r y s t o p y f u n d a m e n t o w e j :
B : = 4 . 0 m L : = 4 . 0 m H : = 1 . 1 m
3 . Z e s t a w i e n i e o b c i |e D
3 . 1 . O b c i |e n i a s t a Be
k N
³b e t : = 2 5
- c i |a r o b j . b e t o n u
³G : = 1 . 3 5 ( 1 . 0 ) - w s p . o b l i c z e n i o w y
3
m
C i |a r w Ba s n y r y g l a
k N
g r : = h r ×ðb r ×ð³b e t ×ð³G = 1 6 . 2 ×ð
m
C i |a r w Ba s n y s Bu p a
k N
g s : = h s ×ðb s ×ð³b e t ×ð³G = 1 2 . 1 5 ×ð
m
C i |a r w Ba s n y r u r o c i g u
k N
G d : = G ×ð³G = 7 4 . 2 5 m ×ð
m
3 . 2 . O b c i |e n i a z m i e n n e
³Q : = 1 . 5 0 ( 0 . 0 ) - w s p . o b l i c z e n i o w y d l a o b c i |e n i a z m i e n n e g o
O b c i |e n i e p i o n o w e
P d : = P ×ð³Q = 1 6 5 ×ðk N - o b c i |e n i a p i o n o w e o d m e d i u m
O b c i |e n i e p o z i o m e
H d : = f ×ð + G d = 2 8 . 7 1 ×ðk N - o b c i |e n i a p o z o i m e o d t a r c i a m e d i u m o [c i a n k i r u r o c i g u
( P )
d
4 . 3 O b c i |e n i a z m i e n n e w p k t A 4 . 4 O b c i |e n i a z m i e n n e w p k t . B
4 . 5 O b c i |e n i a z m i e n n e w p k t . C
5 . Z e s t w i e n i e m a k s y m a l n y c h s i B p r z e k r o j o w y c h
5 . 1 R y g i e l l e w y
2
g r ×ða
M x . r l : = + G d ×ða + P d ×ða = 5 9 3 . 1 2 4 ×ðk N ×ðm M y . r l : = H d ×ða = 6 6 . 0 3 3 ×ðk N ×ðm
2
Q x . r l : = g r ×ða + G d + P d = 2 7 6 . 5 1 ×ðk N Q y . r l : = H d = 2 8 . 7 1 ×ðk N
5 . 2 R y g i e l p r a w y
2
g r ×ðb
M x . r p : = + G d ×ðb + P d ×ðb = 8 7 7 . 7 3 4 ×ðk N ×ðm M y . r p : = H d ×ðb = 9 4 . 7 4 3 ×ðk N ×ðm
2
Q x . r p : = g r ×ðb + G d + P d = 2 9 2 . 7 1 ×ðk N Q y . r p : = H d = 2 8 . 7 1 ×ðk N
5 . 3 S Bu p
K o m b i n a c j e d l a z g i n a n i a
I K o m b i n a c j a ( M a x y m a l n y m o m e n t M . x o r a z w a r t o [c i o d p o w i a d a j a c e )
2 2
b a
M x . s : = g r ×ð - g r ×ð + G d ×ð( b - a ) + P d ×ðb = 6 6 4 . 1 1 ×ðk N ×ðm
2 2
M y . s : = H d ×ðL c o l = 1 9 5 . 2 2 8 ×ðk N ×ðm
N s : = g r ×ð( a + b ) + g s ×ð + 3 ×ðG d + P d = 5 6 1 . 0 9 ×ðk N
( L )
c o l
Q y . s : = H d = 2 8 . 7 1 ×ðk N
I I . K o m b i n a c j a ( M a x y m a l n y m o m e n t M . y o r a z w a r t o [c i o d p o w i a d a j c e )
M y . s : = 3 H d ×ðL c o l = 5 8 5 . 6 8 4 ×ðk N ×ðm
2 2
b a
M x . s : = g r ×ð - g r ×ð + G d ×ð( b - a ) + P d ×ð( b - a ) = 2 8 4 . 6 1 ×ðk N ×ðm
2 2
N s : = g r ×ð( a + b ) + g s ×ð + 3 ×ðG d + 3 P d = 8 9 1 . 0 9 ×ðk N
( L )
c o l
Q y . s : = 3 H d = 8 6 . 1 3 ×ðk N
K o m b i n a c j e d l a s k r c a n i a
I . M a k s y m a l n y m o m e n t s k r c a j c y i o d p o w i a d a j c a m u s i Ba [c i n a j c a :
M z . s : = ( a + b ) ×ðH d = 1 6 0 . 7 7 6 ×ðk N ×ðm Q y . s : = H d = 2 8 . 7 1 ×ðk N
I I . M a k s y m a l n a s i Ba [c i n a j c a i o d p o w i a d a j c y m o m e n t s k r c a j c y :
M z . s : = ( b - a ) ×ðH d = 2 8 . 7 1 ×ðk N ×ðm Q y . s : = 3 H d = 8 6 . 1 3 ×ðk N
6 . D a n e m a t e r i a Bo w e
6 . 1 B e t o n C 3 0 / 3 7
w s p ó Bc z y n n i k b e z p i e c z e Ds t w a
³c : = 1 . 4
w y t r z y m a Bo [ c h a r a k t e r y s t y c z n a n a [c i s k a n i e b e t o n u
f c k : = 3 0 M P a
f c k
w y t r z y m a B[ o b l i c z e n i o w a n a [i s k a n i e b e t o n u
f c d : = = 2 1 . 4 2 9 ×ðM P a
³c
[r e d n i a w y t r z y m a Bo [c n a [c i s k a n i e b e t o n u
f c m : = f c k + 8 M P a = 3 8 ×ðM P a
2
3
f c k
æð öð
[r e d n i a w y t r z y m a Bo [ n a r o z c i g a n i e b e t o n u
f c t m : = 0 . 3 ×ðçð ÷ð ×ðM P a
M P a
èð øð
w y t r z y m a Bo [ c h a r a k t e r y s t y c z n a n a r o z c i g a n i e b e t o n u
f c t k : = 2 M P a
f c t k
w y t r z y m a Bo [ o b l i c z e n i o w a n a r o z c i g a n i e b e t o n u
f c t d : = = 1 . 4 2 9 ×ðM P a
³c
0 . 3
f c m
æð öð
3
[r e d n i m o d u B s p r |y s t o [c i b e t o n u
E c m : = 2 2 ×ðçð0 . 1 ×ð ÷ð ×ðM P a ×ð1 0 = 3 2 . 8 3 7 ×ðG P a
M P a
èð øð
6 . 2 S t a l z b r o j e n i o w a R B 5 0 0 W
w s p ó Bc z y n n i k b e z p i e c z e Ds t w a
³s : = 1 . 1 5
c h a r a k t e r y s t y c z n a g r a n i c a p l a s t y c z n o [c i
f y k : = 5 0 0 M P a
f y k
o b l i c z e n i o w a g r a n i c a p l a s t y c z n o [c i
f y d : = = 4 3 4 . 7 8 3 ×ðM P a
³s
w y t r z y m a Bo [ c h a r a k t e r y s t y c z n a n a r o z c i g a n i e
f t k : = 5 5 0 M P a
f t k
w y t r z y m a Bo [ o b l i c z e n i o w a n a r o z c i g a n i e
f t d : = = 4 7 8 . 2 6 1 ×ðM P a
³s
m o d u B s p r |y s t o [c i s t a l i
E s : = 2 0 0 G P a
7 . W y m i a r o w a n i e r y g l a
7 . 1 O t u l e n i e z b r o j e n i a
K l a s a e k s p o z y c j i X C 4 Z a l e c a n a k l a s a k o n s t r u k c j i : S 4
p r z y j t a [r e d n i c a z b r o j e n i a
Õ : = 2 5 m m
o t u l e n i e z e w z g l d u n a p r z y c z e p n o [
c m i n . b : = Õ = 2 5 ×ðm m
o t u l e n i e z e w z g l . n a w a r u n k i [r o d o w i s k a
c m i n . d u r : = 3 0 m m
”c d u r . ³ : = 0 m m o t u l e n i e z e w z g l . n a b e z p i e c z e Ds t w o
”c d u r . s t : = 0 m m z m n i e j s z n i e o t u l e n i a z e w z g l . n a s t a l n i e r d z e w n
”c d u r . a d d : = 0 m m z m n i e j s z e n i e o t u l e n n i a z e w z g l . n a d o d a t k o w e
z a b e z p i e c z e n i e
”c d e v : = 1 0 m m d o d a t e k z e w z g l . n a o d c h y Bk
M i n i m a l n e o t u l e n i e :
c m i n : = m a x + ”c d u r . ³ - ”c d u r . s t - ”c d u r . a d d , 1 0 m m = 3 0 ×ðm m
( c )
m i n . b , c m i n . d u r
N o m i n a l e n o t u l e n i e :
c n o m : = c m i n + ”c d e v = 4 0 ×ðm m
7 . 2 G r a n i c z n a w z g l d n a w y s o k o [ s t r e f y [c i s k a n e j
µc u 2 : = 0 . 0 0 3 5 o d k s z t a Bc e n i a w b e t o n i e [c i s k a n y m
- f y d
- 3
µy d : = = - 2 . 1 7 4 ´ð 1 0 o d k s z t a Bc e n i a w s t a l i
E s
µc u 2
æð öð
¾e f f : = = 0 . 6 1 7 w z g l d n a w y s o k o [ s t r e f y [c i s k a n e j
çð ÷ð
µc u 2 - µy d
èð øð
¾e f f . l i m : = 0 . 8 ×ð¾e f f = 0 . 4 9 3 g r a n i c z n a w z g l d n a w y s o k o [c s t r e f y [c i s k a n e j
7 . 3 W y m i a r o w a n i e r y g l a n a z g i n a n i e
M o m e n t y z g i n a j c e :
M x . r l = 5 9 3 . 1 2 4 ×ðk N ×ðm M x . r p = 8 7 7 . 7 3 4 ×ðk N ×ðm
M y . r l = 6 6 . 0 3 3 ×ðk N ×ðm M y . r p = 9 4 . 7 4 3 ×ðk N ×ðm
O b l i c z e n i e p o t r z e b n e g o z b r o j e n i a A . s 1 x
h r = 0 . 8 m w y s o k o [ r y g l a
b r = 0 . 6 m s z e r o k o [ r y g l a
d x : = h r - 0 . 5 Õ - 8 m m - c n o m = 0 . 7 4 m
w y s o k o [ u |y t e c z n a
M E d . x : = M x . r p = 8 7 7 . 7 3 4 ×ðk N ×ðm
m o m e n t o b l i c z e n i o w y
M E d . x
S c . e f f : = = 0 . 1 2 5 w s p ó Bc z y n n i k p o m o c n i c z y
2
b r ×ðd x ×ðf c d
¾e f f : = 1 - 1 - 2 ×ðS c . e f f = 0 . 1 3 4 z a s i g e f e k t y w n e j s t r e f y [c i s k a n e j
¾e f f . l i m = 0 . 4 9 3 g r a n i c z n y z a s i g s t r e f y [c i s k a n e j
¾e f f < ¾e f f . l i m = 1 W A R U N E K S P E AN I O N Y
x e f f : = d x ×ð¾e f f = 9 . 8 9 3 ×ðc m e f e k t y w n a w y s o k o [ s t r e f y [c i s k a n e j
f c d ×ðx e f f ×ðb r
2
A s 1 . x : = = 2 9 . 2 5 6 ×ðc m p o l e z b r o j e n i a
f y d
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 m i n i m a l n e g o :
k : = 0 . 6 5 w s p ó Bc z y n n i k z a l e |n y o d n a p r |e D w b e t o n i e
k c : = 0 . 4 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 n a p r |e D
2
A c t : = 0 . 5 ×ðb r ×ðh r = 0 . 2 4 ×ðm p o l e r o z c i g a n e g o p r z e k r o j u
Ãs . l i m : = 2 0 0 M P a p r z y j t e n a p r |e n i a w z b r o j e n i u p o z e r w a n i u
f c t m
2
A s . m i n . 1 : = 0 . 2 6 ×ð ×ðb r ×ðd x = 6 . 6 8 3 ×ðc m
f y k
2
A s . m i n . 2 : = 0 . 0 0 1 3 ×ðb r ×ðd x = 5 . 7 6 8 ×ðc m
k ×ðk c ×ðf c t m ×ðA c t
2
A s . m i n . 3 : = = 9 . 0 3 7 ×ðc m
Ãs . l i m
P o w i e r z c h n i a z b r o j e n i a m i n i m a l n e g o :
2
A s . m i n : = m a x = 9 . 0 3 7 ×ðc m
( A )
s . m i n . 1 , A s . m i n . 2 , A s . m i n . 3
A s 1 . x > A s . m i n = 1 W A R U N E K S P E AN I O N Y
2
P r z y j c i e z b r o j e n i a : A s 1 . x = 2 9 . 2 5 6 ×ðc m Õ : = 2 2 m m
2
À×ðÕ
2
P r z y j t o 1 1 Õ2 5 A s 1 . x . p r o v : = 1 1 ×ð = 4 1 . 8 1 5 ×ðc m
4
O b l i c z e n i e p o t r z e b n e g o z b r o j e n i a A . s 1 y
h r = 0 . 8 m w y s o k o [ r y g l a
b r = 0 . 6 m s z e r o k o [ r y g l a
d y : = b r - 0 . 5 Õ - 8 m m - c n o m = 0 . 5 4 1 m
w y s o k o [ u |y t e c z n a
M E d . y : = M y . r p = 9 4 . 7 4 3 ×ðk N ×ðm
m o m e n t o b l i c z e n i o w y
M E d . y
w s p ó Bc z y n n i k p o m o c n i c z y
S c . e f f : = = 0 . 0 1 9
2
h r ×ðd y ×ðf c d
z a s i g e f e k t y w n e j s t r e f y [c i s k a n e j
¾e f f : = 1 - 1 - 2 ×ðS c . e f f = 0 . 0 1 9
g r a n i c z n y z a s i g s t r e f y [c i s k a n e j
¾e f f . l i m = 0 . 4 9 3
W A R U N E K S P E AN I O N Y
¾e f f < ¾e f f . l i m = 1
e f e k t y w n a w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = d y ×ð¾e f f = 1 . 0 3 1 ×ðc m
f c d ×ðx e f f ×ðh r
2
p o l e z b r o j e n i a
A s 1 . y : = = 4 . 0 6 7 ×ðc m
f y d
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 m i n i m a l n e g o :
w s p ó Bc z y n n i k z a l e |n y o d n a p r |e D w b e t o n i e
k : = 0 . 7 6
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 n a p r |e D
k c : = 0 . 4
2
p o l e r o z c i g a n e g o p r z e k r o j u
A c t : = 0 . 5 ×ðb r ×ðh r = 0 . 2 4 ×ðm
p r z y j t e n a p r |e n i a w z b r o j e n i u p o z e r w a n i u
Ãs . l i m : = 2 0 0 M P a
f c t m
2
A s . m i n . 1 : = 0 . 2 6 ×ð ×ðb r ×ðd y = 4 . 8 8 9 ×ðc m
f y k
2
A s . m i n . 2 : = 0 . 0 0 1 3 ×ðh r ×ðd y = 5 . 6 2 6 ×ðc m
k ×ðk c ×ðf c t m ×ðA c t
2
A s . m i n . 3 : = = 1 0 . 5 6 6 ×ðc m
Ãs . l i m
P o w i e r z c h n i a z b r o j e n i a m i n i m a l n e g o :
2
A s . m i n : = m a x = 1 0 . 5 6 6 ×ðc m
( A )
s . m i n . 1 , A s . m i n . 2 , A s . m i n . 3
W A R U N E K N I E S P E AN I O N Y - p r z y j c i e z b r o j e n i a m i n i m a l n e g o
A s 1 . y > A s . m i n = 0
2
P r z y j c i e z b r o j e n i a :
A s 1 . y : = A s . m i n = 1 0 . 5 6 6 ×ðc m
2
À×ðÕ
2
P r z y j t o
4 Õ2 2 A s 1 . y . p r o v : = 4 ×ð = 1 5 . 2 0 5 ×ðc m
4
N o [n o [ o b l i c z e n i o w a p r z e k r o j u n a z g i n a n i e w p Ba s z c z y [n i e x :
f y d ×ðA s 1 . x . p r o v
¾e f f : = = 0 . 1 9 1
f c d ×ðb r ×ðd x
¾e f f < ¾e f f . l i m = 1
2 3
M R d . x : = f c d ×ðb r ×ðd x ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f = 1 . 2 1 6 ´ð 1 0 ×ðk N ×ðm
( 1 )
N o [n o [ o b l i c z e n i o w a p r z e k r o j u n a z g i n a n i e w p Ba s z c z y [n i e y :
f y d ×ðA s 1 . y . p r o v
¾e f f : = =
f c d ×ðh r ×ðd y
¾e f f < ¾e f f . l i m = 1
2
M R d . y : = f c d ×ðh r ×ðd y ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f = 3 4 4 . 9 0 8 ×ðk N ×ðm
( 1 )
S p r a w d z e n i e w a r u n k u n o [n o [c i n a z g i n a n i e d w u k i e r u n k o w e :
M E d . x M E d . y
W A R U N E K S P E AN I O N Y
+ = 0 . 9 9 7
M R d . x M R d . y
7 . 4 W y m i a r o w a n i e r y g l a n a [c i n a n i e
P r z e k r o j o w e s i By p o p r z e c z n e :
Q x . r l = 2 7 6 . 5 1 ×ðk N V E d . x : = Q x . r p = 2 9 2 . 7 1 ×ðk N
Q y . r l = 2 8 . 7 1 ×ðk N V E d . y : = Q y . r p = 2 8 . 7 1 ×ðk N
W y m i a r o w a n i e n a [c i n a n i e w p Ba s z c z y |n i e x :
S p r a w d z e n i e c z y w a y m a g a n e j e s t w y m i a r o w a n i e z b r o j e n i a n a [c i n a n i e
2 0 0 m m 0 . 1 8
æð1 öð
k : = m i n + , 2 = 1 . 5 2 C R d . c : = = 0 . 1 2 9
çð ÷ð
d x ³c
èð øð
3
w s p ó Bc z y n n i k i
0 . 5
f c k
æð öð
2
½m i n : = 0 . 0 3 5 ×ðk ×ðçð ÷ð ×ðM P a = 0 . 3 5 9 ×ðM P a
M P a
èð øð
2
p o l e z a s t o s o w a n e g o z b r o j e n i a n a
A s l : = A s 1 . x . p r o v = 4 1 . 8 1 5 ×ðc m
z g i n a n i e
A s l
æð öð
- 3
s t o p i e D z b r o j e n i a p r z e k r o j u
ÁL : = m i n = 9 . 4 2 4 ´ð 1 0
çð0 . 0 2 , b ÷ð
r ×ðd x
èð øð
1
3
1 0 0 ×ðÁL ×ðf c k
æð öð
o b l i c z e n i o w a n o s n o [ n a [c i n a n i e
V R d . c : = C R d . c ×ðk ×ðçð ÷ð ×ðb r ×ðd x ×ðM P a = 2 6 4 . 1 6 7 ×ðk N
e l e m e n t ó w b e z z b r o j e n i a
M P a
èð øð
V R d . c . m i n : = ½m i n ×ðb r ×ðd x = 1 5 9 . 4 0 6 ×ðk N
W A R U N E K N I E S P E AN I O N Y - w y m a g a n e w y m i a r o w a n i e z b r o j e n i a n a
V R d . c > V E d . x = 0
[c i n a n i e
S p r a w d z e n i e w a r u n k u [c i s k a n y c h k r z y |u l c ó w b e t o n o w y c h
f y w d : = f y d = 4 3 4 . 7 8 3 ×ðM P a o b l i c z e n i o w a g r a n i c a p l a s t y c z n o [c i
d x = 0 . 7 4 m w y s o k o [ u |y t e c z n a p r z e k r o j u
b r = 0 . 6 m s z e r o k o [ r y g l a
r a m i s i B w e w n e t r z n y c h
z : = 0 . 9 ×ðd x = 6 6 . 5 5 5 ×ðc m
w s p ó Bc z y n n i k z a l e |n y o d n a p r |e n i a
±c w : = 1
w p a s i e [c i s k a n y m ( k s t . n i e s p r |o n e )
f c k
æð öð
½ : = 0 . 6 ×ðçð1 - ÷ð = 0 . 5 2 8 w s p ó Bc z y n n i k r e d u k c j i w y t r z y m a Bo [c i
2 5 0 M P a
èð øð
b e t o n u z a r y s o w a n e g o p r z y [c i n a n i u
˜ : = 2 6 . 6 d e g c o t ( ˜) = 1 . 9 9 7 k t n a c h y l e n i a k r z y |ó l c ó w b e t .
m a x . s i Ba [c i n j c a j a k p r z e n o s z
±c w ×ðb r ×ðz ×ð½×ðf c d
3
V R d . m a x : = = 1 . 8 0 9 ´ð 1 0 ×ðk N k r z y z ó l c e b e t o n o w e
c o t ( ˜) + t a n ( ˜)
V R d . m a x > V E d . x = 1 W A R U N E K S P E AN I O N Y - k r z y |u l c e b e t o n o w e n i e u l e g n z m i a |d |e n i u
W y z n a c z e n i e r o z s t a w u z b r o j e n i a p o p r z e z n e g o :
± : = 9 0 d e g
k t n a c h y l e n i a s t r z e m i o n
Õs : = 8 m m
[r e d n i c a s t r z e m i o n
2
Õs
æð öð
2 p o l e p r z e k r o j u z b r o j e n i a n a [c i a n i e
A s w : = 2 ×ðÀ×ðçð ÷ð = 1 . 0 0 5 ×ðc m
( s t r z e m i o n a 2 - c i t e )
2
èð øð
A s w
s 1 : = ×ðf y w d ×ðz ×ðc o t ( ˜) = 1 9 . 8 4 6 ×ðc m D o b r a n o :
s 1 : = 1 5 c m
V E d . x
S p r a w d z e n i e r o z s t a w u i s t o p n i a z b r o j e n i a :
s I . m a x : = 0 . 7 5 d x = 5 5 . 4 6 3 ×ðc m m a k s y m a l n y r o z s t a w s t r z e m i o n
s 1 < s I . m a x = 1 W A R U N E K S P E AN I O N Y
- 1
f c k ×ðM P a
Áw . m i n : = 0 . 0 8 ×ð = 0 . 0 8 8 ×ð% m i n i m a l n y s t o p i e D z b r o j e n i a
- 1
f y k ×ðM P a
A s w
Áw : = = 0 . 1 1 2 ×ð% s t o p i e D z b r o j e n i a
b r ×ðs 1
Áw > Áw . m i n = 1 W A R U N E K S P E AN I O N Y
W y m i a r o w a n i e n a [c i n a n i e w p Ba s z c z y |n i e y :
S p r a w d z e n i e c z y w a y m a g a n e j e s t w y m i a r o w a n i e z b r o j e n i a n a [c i n a n i e
2 0 0 m m 0 . 1 8
æð1 öð
k : = m i n + , 2 = 1 . 6 0 8 C R d . c : = = 0 . 1 2 9
çð ÷ð
d y ³c
èð øð
3
w s p ó Bc z y n n i k i
0 . 5
f c k
æð öð
2
½m i n : = 0 . 0 3 5 ×ðk ×ðçð ÷ð ×ðM P a = 0 . 3 9 1 ×ðM P a
M P a
èð øð
2
p o l e z a s t o s o w a n e g o z b r o j e n i a n a
A s l : = A s 1 . y . p r o v = 1 5 . 2 0 5 ×ðc m
z g i n a n i e
A s l
æð öð
s t o p i e D z b r o j e n i a p r z e k r o j u
ÁL : = m i n = 0 . 3 4 3 ×ð%
çð0 . 0 2 , b ÷ð
r ×ðd x
èð øð
1
3
1 0 0 ×ðÁL ×ðf c k
æð öð
o b l i c z e n i o w a n o s n o [ n a [c i n a n i e
V R d . c : = C R d . c ×ðk ×ðçð ÷ð ×ðh r ×ðd y ×ðM P a = 1 9 4 . 5 6 5 ×ðk N
e l e m e n t ó w b e z z b r o j e n i a
M P a
èð øð
V R d . c . m i n : = ½m i n ×ðh r ×ðd y = 1 6 9 . 1 8 1 ×ðk N
W A R U N E K S P E AN I O N Y - n i e w y m a g a n e w y m i a r o w a n i e z b r o j e n i a n a
V R d . c > V E d . y = 1
[c i n a n i e
S p r a w d z e n i e w a r u n k u n a V b
o b l i c z e n i o w a g r a n i c a p l a s t y c z n o [c i
f y w d : = f y d = 4 3 4 . 7 8 3 ×ðM P a
w y s o k o [ u |y t e c z n a p r z e k r o j u
d y = 0 . 5 4 1 m
s z e r o k o [ r y g l a
h r = 0 . 8 m
f c k
æð öð
w s p ó Bc z y n n i k r e d u k c j i w y t z r y m a Bo [c i
½ : = 0 . 6 ×ðçð1 - ÷ð = 0 . 5 2 8
b e t o n u z a r y s o w a n e g o p r z y [c i n a n i u
2 5 0 M P a
èð øð
3
V b : = 0 . 5 ×ðh r ×ðd y ×ð½×ðf c d = 2 . 4 4 8 ´ð 1 0 ×ðk N
W A R U N E K S P E AN I O N Y - k r z y |u l c e b e t o n o w e n i e u l e g n z m i a |d |e n i u
V b > V E d . y = 1
P r z y j c i e z b r o j e n i a k o n s t r u k c y j n e g o :
Õs : = 8 m m
[r e d n i c a s t r z e m i o n
2
Õs
æð öð
2
p o l e p r z e k r o j u z b r o j e n i a n a [c i a n i e
A s w : = 2 ×ðÀ×ðçð ÷ð = 1 . 0 0 5 ×ðc m
2
èð øð
( s t r z e m i o n a 2 - c i t e )
d o b r a n y r o z s t a w s t r z e m i o n
s 1 : = 1 2 . 5 c m
m a k s y m a l n y r o z s t a w s t r z e m i o n
s I . m a x : = 0 . 7 5 d x = 5 5 . 4 6 3 ×ðc m
W A R U N E K S P E AN I O N Y
s 1 < s I . m a x = 1
- 1
f c k ×ðM P a
m i n i m a l n y s t o p i e D z b r o j e n i a
Áw . m i n : = 0 . 0 8 ×ð = 0 . 0 8 8 ×ð%
- 1
f y k ×ðM P a
A s w
s t o p i e D z b r o j e n i a
Áw : = = 0 . 1 0 1 ×ð%
h r ×ðs 1
Áw > Áw . m i n = 1 W A R U N E K S P E AN I O N Y
8 . W y m i a r o w a n i e s Bu p a
8 . 1 . D a n e i z a Bo |e n i a
b s = 0 . 6 m s z e r o k o [ s Bu p a
h s = 0 . 6 m w y s o k o [ s Bu p a
L c o l = 6 . 8 m d Bu g o [ o b l i c z e n i o w a s Bu p a
²x : = 2 ²y : = 2 w s p ó Bc z y n n i k i w y b o c z e n i o w e
m x : = 1 m y : = 1 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
r o z p a t r y w a n y e f e k t
Õ : = 3 2 m m p r z y j t a [r e d n i c a z b r o j e n i a g Bó w n e g o
n : = 1 6 p r z y j t a l i c z b a p r e t ó w
2
À Õ
2
A s : = n ×ð = 1 2 8 . 6 8 ×ðc m p o l e p r z y j t e g o z b r o j e n i a
4
Õs = 8 ×ðm m p r z y j t a [r e d n i c a s t r z e m i o n
c n o m = 4 0 ×ðm m o t u l e n i e z b r o j e n i a
d : = b s - c n o m - Õs - 0 . 5 ×ðÕ = 5 3 . 6 ×ðc m w y s o k o [ u |y t e c z n a w p Ba s z c z y |n i e x i y
a 1 : = c n o m + Õs + 0 . 5 Õ = 6 . 4 ×ðc m
o d l e g Bo [ [r o d k a c i |k o [c i z b r o j e n i a o d
a 2 : = a 1 = 6 . 4 ×ðc m k r a w d z i
8 . 2 . 1 I k o m b i n a c j : M a k s y m a l n y M . x i w a r t o [c i o d p o w i a d a j c e
M x . s : = 6 6 4 . 1 1 k N ×ðm M E d . x : = M x . s = 6 6 4 . 1 1 ×ðk N ×ðm o b l i c z e n i o w y m o m e n t z g i n a j c y
( p B. x , d ó B s Bu p a )
o b l i c z e n i o w y m o m e n t z g i n a j c y
M y . s : = 1 9 5 . 2 2 8 k N ×ðm M E d . y : = M y . s = 1 9 5 . 2 2 8 ×ðk N ×ðm
( p B. y , d ó B s Bu p a )
N s : = 5 6 1 . 0 9 k N N E d : = N s = 5 6 1 . 0 9 ×ðk N o b l i c z e n i o w a s i Ba [c i s k a j c a ( d ó B s Bu p a )
8 . 2 . 2 Z b r o j e n i e m i n i m a l n e i m a k s y m a l n e d l a s Bu p a
0 . 1 N E d
æð öð
2
A s . m i n : = m a x , 0 . 0 0 2 ×ðh s ×ðb s = 7 . 2 ×ðc m z b r o j e n i e m i n i m a l n e
çð ÷ð
f y d
èð øð
2
A s . m a x : = 4 % ×ðb s ×ðh s = 1 4 4 ×ðc m z b r o j e n i e m a k s y m a l n e
8 . 2 . 3 I n p e r f e k c j e g e o m e t r y c z n e
1
˜o : = = 0 . 0 0 5 w a r t o [ b a z o w a
2 0 0
2 2
±h : = = 0 . 7 6 7 < ±h < 1 = 1
W A R U N E K S P E AN I O N Y . w s p ó Bc z y n n i k
3
L c o l
r e d u k u j c y w y s o k o [
m
æð1 1 öð
±m : = 0 . 5 ×ð + = 1 w s p ó Bc z y n n i k 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
çð ÷ð
m x
e l e m e n t ó w
èð øð
˜l : = ˜o ×ð±h ×ð±m = 0 . 0 0 4 k t p o c h y l e n i a
l 0 . x : = ²x ×ðL c o l = 1 3 . 6 m l 0 . y : = l 0 . x = 1 3 . 6 m d Bu g o [c i e f e k t y w n e s Bu p a
˜l ×ðl 0 . x
e i . x : = = 2 6 . 0 7 7 ×ðm m i . y : = e i . x = 2 6 . 0 7 7 ×ðm m
e m i m o [r ó d i m p e r f e k c j i
2
M E d . x
e e . x : = = 1 1 8 3 . 6 0 7 ×ðm m m i m o [r ó d I r z d u w p B. x
N E d
M E d . y
e e . y : = = 3 4 7 . 9 4 4 ×ðm m m i m o [r ó d I r z d u w p B. y
N E d
b s
æð öð
e 0 . x : = m a x çð2 0 m m , e i . x + e e . x , ÷ð = 1 2 0 . 9 6 8 ×ðc m
3 0
èð øð
h s
æð öð
e 0 . y : = m a x çð2 0 m m , e i . y + e e . y , ÷ð = 3 7 . 4 0 2 ×ðc m
3 0
èð øð
8 . 2 . 4 . W s p ó Bc z y n n i k p e Bz a n i a
8 . 2 . 4 . 1 . K o Dc o w y w s p ó Bc z y n n i k p e Bz a n i a
3 2
A c : = b s ×ðh s = 3 . 6 ´ð 1 0 ×ðc m p o l e p r z e k r o j u s Bu p a
u : = 2 ×ð + h s = 2 4 0 ×ðc m o b w ó d e l e m e n t u k o n t a k t u j c e g o s i z a t m o s f e r
( b )
s
2 ×ðA c
h 0 : = = 3 0 ×ðc m m i a r o d a j n y w y m i a r e l e m e n t u
u
R H : = 5 0 w i l g o t n o [ w z g l d n a p o w i e t r z a ( % )
”t : = 2 8 w i e k b e t o n u w c h w i l i o b c i |e n i a ( d n i )
T ”t : = 1 5 t e m p e r a t u r a d o j r z e w a n i a b e t o n u ( s t . c e l . )
0 . 7
3 5 M P a
æð öð
±1 : = = 0 . 9 4 4
çð ÷ð
f c m
èð øð
w s p ó Bc z y n n i k i z a l e |n e o d w y t r z y m a Bo [c i b e t o n u
0 . 2
3 5 ×ðM P a
æð öð
±2 : = = 0 . 9 8 4
çð ÷ð
f c m
èð øð
R H
æð öð
1 -
çð ÷ð
1 0 0 w s p ó Bc z y n n i k z a l e |n y o d w p By w u w i l g o t n o [c i
ÕR H : = + ×ð±1 = 2 . 4 7 8
çð1 ÷ð×ð±2
w z g l d n e j n a p o d s t a w i e w s p ó Bc z y n n i k a p e Bz a n i a
3
çð - 1 ÷ð
0 . 1 ×ð h 0 ×ðc m
èð øð
1 6 . 8
²f c m : = = 2 . 7 2 5
- 1
f c m ×ðM P a
4 0 0 0
æð öð
- - 1 3 . 6 5
çð ÷ð
2 7 3 + T ”t
w i e k b e t o n u d o s t o s o w a n y d o t e m p e r a t u r y
èð øð
t 0 . T : = ”t ×ðe = 2 2 . 0 5
d o j r z e w a n i a 1 5 s t . C p r z e z 2 8 d n i
w y k Ba d n i k p o t e g o w y d l a c e m n e t u k l a s y N
± : = 0
±
éð ùð
öð
êðt 0 . T ×ðæð 9 úð
w i e k b e t o n u z u w z g l d n i e n i e m r o d z a j u c e m e n t u
t 0 : = m a x + 1 , 0 . 5 = 2 2 . 0 5
çð ÷ð
1 . 2
êð úð
çð ÷ð
2 + t 0 . T
ëð èð øð ûð
1
w s p ó Bc z y n n i k z a l e |n y o d w i e k u b e t o n u w c h w i l i
²t . 0 : = = 0 . 5 1 1
0 . 2
o b c i |e n i a
0 . 1 + t 0
k o Dc o w y w s p ó Bc z y n n i k p e Bz a n i a
Õo o . t o : = ÕR H ×ð²f c m ×ð²t . 0 = 3 . 4 5 2
8 . 2 . 4 . 2 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
o b l i c z e n i o w a s i Ba o d p r a w i e s t a By c h o b c i |e D
N E . g : = 0 . 8 ×ðN E d = 4 4 8 . 8 7 2 ×ðk N
( d Bu g o t r w a By c h )
M E . g . x : = 0 . 8 M E d . x = 5 3 1 . 2 8 8 ×ðk N ×ðm
w s p ó Bc z y n n i k o d o b c i |e D s t a By c h
³G s u p : = 1 . 3 5
M E . g . x
c h a r a k t e r y s t y c z n y m o m e n t o d p r a w i e s t a By c h
M E . q p . x : = = 3 9 3 . 5 4 7 ×ðk N ×ðm
³G s u p
o b c i |e D d Bu g o t r w a By c h
N E . g
c h a r a k t e r y s t y c z n a s i Ba o d p r a w i e s t a By c h o b c i |e D
N E . q p . x : = = 3 3 2 . 4 9 8 ×ðk N
³G s u p
c h a r a k t e r y s t y c z n y m o m e n t I r z d u o d p r a w i e
M 0 . E . q p . x : = M E . q p . x + N E . q p . x ×ðe i . x = 4 0 2 . 2 1 7 ×ðk N ×ðm
s t a By c h o b c i |e D
o b l i c z e n i o w y m o m e n t I r z d u o d w s z y s t k i c h
M 0 . E d . x : = M E d . x + N E d ×ðe i . x = 6 7 8 . 7 4 1 ×ðk N ×ðm
o b c i |e D
M 0 . E . q p . x
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
Õe f : = Õo o . t o ×ð = 2 . 0 4 6
M 0 . E d . x
M 0 . E . q p . x
0 . 8
= 0 . 5 9 3 = 0 . 5 9 3
M 0 . E d . x ³G s u p
W d r u g i e j p Ba s z c z y zn i e w a r t o [ e f e k t y w n e g o w s p ó Bc z y n n i k a j e s t t a k a s a m a
8 . 2 . 5 S p r a w d z e n i e c z y n a l e |y u w z g l d n i e f e k t y I I r z d u
P Ba s z c z y z n a x
3 2
A c : = b s ×ðh s = 3 . 6 ´ð 1 0 ×ðc m p o l e p r z e k r o j u s Bu p a
3
b s ×ðh s
6 4
I c . x : = = 1 . 0 8 ´ð 1 0 ×ðc m 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 s Bu p a
1 2
I c . x
i x : = = 1 7 . 3 2 1 ×ðc m p r o m i e D b e z w Ba d n o [c i
A c
²x ×ðL c o l
»x : = = 7 8 . 5 2 s m u k Bo [ s Bu p a
i x
1
A : = = 0 . 7 1
1 + 0 . 2 ×ðÕe f
A s ×ðf y d
É : = = 0 . 7 2 5 m o c z b r o j e n i a ( p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o )
A c ×ðf c d
B : = 1 + 2 ×ðÉ = 1 . 5 6 5
r m : = 1 C : = 1 . 7 - r m = 0 . 7
N E d
n a : = = 0 . 0 7 3 w z g l d n a s i Ba n o r m a l n a
A c ×ðf c d
2 0 ×ðA ×ðB ×ðC
»l i m . x : = = 5 7 . 6 6 9 s m u k Bo [c g r a n i c z n a
n a
»x > »l i m . x = 1 s Bu p s m u k By - n a l e |y u w z g l d n i e f e k t y I I r z d u
P Ba s z c z y z n a y
3 2
A c : = b s ×ðh s = 3 . 6 ´ð 1 0 ×ðc m p o l e p r z e k r o j u s Bu p a
3
b s ×ðh s
6 4
I c . y : = = 1 . 0 8 ´ð 1 0 ×ðc m 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 s Bu p a
1 2
I c . y
i y : = = 1 7 . 3 2 1 ×ðc m p r o m i e D b e z w Ba d n o [c i
A c
²y ×ðL c o l
»y : = = 7 8 . 5 2 s m u k Bo [ s Bu p a
i y
1
A : = = 0 . 7 1
1 + 0 . 2 ×ðÕe f
A s ×ðf y d
É : = = 0 . 7 2 5 m o c z b r o j e n i a ( p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o )
A c ×ðf c d
B : = 1 + 2 ×ðÉ = 1 . 5 6 5
: = : = - =
r m : = 1 C : = 1 . 7 - r m = 0 . 7
N E d
w z g l d n a s i Ba n o r m a l n a
n a : = = 0 . 0 7 3
A c ×ðf c d
2 0 ×ðA ×ðB ×ðC
s m u k Bo [c g r a n i c z n a
»l i m . x : = = 5 7 . 6 6 9
n a
s Bu p s m u k By - n a l e |y u w z g l d n i e f e k t y I I r z d u
»x > »l i m . x = 1
8 . 2 . 6 . A n a l i z a I I r z d u - m e t o d a n o m i n a l n e j k r z y w i z n y
P Ba s z c z y z n a x
N E d
w z g l d n a s i Ba n o r m a l n a
n a : = = 0 . 0 7 3
A c ×ðf c d
w a r t o [ d l a k t ó r e j o s i g a s i m a k s y m a l n y m o m e n t
n b a l : = 0 . 4
g r a n i c z n y , m o |n a p r z y j m o w a = 0 , 4
A s ×ðf y d
m o c z b r o j e n i a ( p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o )
É : = = 0 . 7 2 5
A c ×ðf c d
n u : = 1 + É = 1 . 7 2 5
n u - n a
æð öð
w s p ó Bc z y n n i k p o p r a w k o w y z a l e |n y o d s i By p o d Bu |n e j
K r : = m i n = 1
çð1 , n - n b a l ÷ð
u
èð øð
f c k »x
²' : = 0 . 3 5 + + = 1 . 0 2 3
2 0 0 ×ðM P a 1 5 0
w s p ó Bc z y n n i k u w z g l d n i a j c y p e Bz a n i e
K Õ : = m a x + ²' ×ðÕe f , 1 = 3 . 0 9 4
( 1 )
f y d
- 3
µy d : = = 2 . 1 7 4 ´ð 1 0
E s
2
À Õ
2 A s 2 . x : = A s 1 . x
A s 1 . x : = 7 ×ð = 5 6 . 2 9 7 ×ðc m
4
p o l e p r z e k r o j u z b r o j e n i a w p Ba s z c z y z n i e x
2
A s . x : = A s 1 . x + A s 2 . x = 8 5 . 5 5 4 ×ðc m
m o m e n t b e z w Ba d n o [c i c a Bk o w i t e g o z b r o j e n i a s Bu p a w z g l d e m [r o d k a c i |k o [c i
4 2
À×ðÕ
4 4
I s . x : = n ×ð + A s . x ×ð - a 1 + 4 ×ð ×ð - a 1 - 1 0 c m = 5 . 3 6 8 ´ð 1 0 ×ðc m
( 0 . 5 b ) 2 À×ðÕ ( 0 . 5 ×ðb ) 2
s s
6 4 4
I s . x
p r o m i e D b e z w Ba d n o [c i
i s : = = 2 0 . 4 2 5 ×ðc m
2
À×ðÕ
n ×ð
4
b s
s k o r y g o w a n a w y s o k o [ u |y t e c z n a
d = 5 3 . 6 ×ðc m d ' : = + i s = 5 0 . 4 2 5 ×ðc m
2
0 . 4 5 ×ðd ' 1 1
- 3
r o : = = 1 0 4 . 3 8 m = 9 . 5 8 ´ð 1 0
µy d r o m
r o
1 1 k r z y w i z n a e l e m e n t ó w o s y m e t r y c z n y m p r z e k r o j u
r : = = 3 3 . 7 4 1 m = 0 . 0 3
p o p r z e c z n y m ( w Bc z a j c z b r o j e n i e )
K r ×ðK Õ r m
p r z e k r ó j p o p r z c z n y s t a By
c : = 1 0
2
æð öð
l 0 . x
çð ÷ð
1
m i m o [r ó d I I r z d u w p Ba s z c z y zn i e x
e 2 . x : = ×ð = 5 4 . 8 1 8 ×ðc m
çð ÷ð
r c
èð øð
m i m o [r ó d c a Bk o w i t y ( I i I I r z d u + p r z y p a d k o w y )
e t o t . x : = e 0 . x + e 2 . x = 1 7 5 . 7 8 6 ×ðc m
m o m e n t c a Bk o w i t y
M E d . x . t o t : = N E d ×ðe t o t . x = 9 8 6 . 3 1 8 ×ðk N ×ðm
P Ba s z c z y z n a y
N E d
w z g l d n a s i Ba n o r m a l n a
n a : = = 0 . 0 7 3
A c ×ðf c d
w a r t o [ d l a k t ó r e j o s i g a s i m a k s y m a l n y m o m e n t
n b a l : = 0 . 4
g r a n i c z n y , m o |n a p r z y j m o w a = 0 , 4
A s ×ðf y d
m o c z b r o j e n i a ( p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o )
É : = = 0 . 7 2 5
A c ×ðf c d
n u : = 1 + É = 1 . 7 2 5
n u - n a
æð öð
w s p ó Bc z y n n i k p o p r a w k o w y z a l e |n y o d s i By p o d Bu |n e j
K r : = m i n = 1
çð1 , n - n b a l ÷ð
u
èð øð
f c k »y
²' : = 0 . 3 5 + + = 1 . 0 2 3
2 0 0 ×ðM P a 1 5 0
w s p ó Bc z y n n i k u w z g l d n i a j c y p e Bz a n i e
K Õ : = m a x + ²' ×ðÕe f , 1 = 3 . 0 9 4
( 1 )
f y d
µy d : = = 0 . 0 0 2
E s
2
À Õ
2
A s 1 . y : = 8 ×ð = 6 4 . 3 4 ×ðc m A s 2 . y : = A s 1 . y
4
p o l e p r z e k r o j u z b r o j e n i a w p Ba s z c z y z n i e y
2
A s . y : = A s 1 . y + A s 2 . y = 1 2 8 . 6 8 ×ðc m
m o m e n t b e z w Ba d n o [c i c a Bk o w i t e g o z b r o j e n i a s Bu p a w z g l d e m [r o d k a c i |k o [c i
4 2
éð ùð
À×ðÕ
4 4
êð
I s . y : = n ×ð + A s . y ×ð - a 1 + 4 ×ð ×ð - a 1 - 1 0 c m = 7 . 7 7 ´ð 1 0 ×ðc m
( 0 . 5 h ) 2 À×ðÕ ( 0 . 5 ×ðh ) 2 úð
s s
6 4 4
ëð ûð
I s . y
p r o m i e D b e z w Ba d n o [c i
i s : = = 0 . 2 4 6 m
2
À×ðÕ
n ×ð
4
h s
s k o r y g o w a n a w y s o k o [ u |y t e c z n a
d = 5 3 . 6 ×ðc m d ' : = + i s = 5 4 . 5 7 3 ×ðc m
2
0 . 4 5 ×ðd ' 1 1
r o : = = 1 1 2 . 9 6 6 m = 0 . 0 0 9
µy d r o m
r o
1 1 k r z y w i z n a e l e m e n t ó w o s y m e t r y c z n y m p r z e k r o j u
r : = = 3 6 . 5 1 7 m = 0 . 0 2 7
p o p r z e c z n y m ( w Bc z a j c z b r o j e n i e )
K r ×ðK Õ r m
p r z e k r ó j p o p r z e c z n y s t a By
c : = 1 0
2
æð öð
l 0 . y
çð ÷ð
1
m i m o [r ó d I I r z d u w p Ba s z c z y zn i e y
e 2 . y : = ×ð = 5 0 . 6 5 1 ×ðc m
çð ÷ð
r c
èð øð
m i m o [r ó d c a Bk o w i t y ( I i I I r z d u + p r z y p a d k o w y )
e t o t . y : = e 0 . y + e 2 . y = 8 8 . 0 5 3 ×ðc m
m o m e n t c a Bk o w i t y
M E d . y . t o t : = N E d ×ðe t o t . y = 4 9 4 . 0 5 7 ×ðk N ×ðm
8 . 2 . 6 . 1 . S p r a w d z e n i e c z y s Bu p n a l e |y p r o j e k t o w a j a k o j e d n o c z y d w u k i e r u n k o w o
z b r o j o n y
»x = 7 8 . 5 2 »y = 7 8 . 5 2
»x »x »y »y
W A R U N K I
= 1 < 2 = 1 = 1 < 2 = 1
»y »y »x »x
S P E AN I O N E
e t o t . x e t o t . x e t o t . y e t o t . y
b s b s h s h s
W A R U N I K I N I E
= 1 . 9 9 6 < 0 . 2 = 0 = 0 . 5 0 1 < 0 . 2 = 0
S P E AN I O N E
e t o t . y e t o t . y e t o t . x e t o t . x
h s h s b s b s
S AU P D W U K I E R U N K O W O Z B R O J O N Y
8 . 2 . 6 . 2 N o [n o [ s Bu p a
8 . 2 . 6 . 2 . 1 N o [n o [ M R d d l a p Ba s z c z y z n y x - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . x + f y d ×ðA s 1 . x
¾e f f : = = 0 . 2 5 2 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðb s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . x
çð ÷ð×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 3 9 3
e f f
2
f c d ×ðb s ×ðd + ×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . x - f y d ×ðA s 1 . x
¾' ' : = = - 0 . 4 5 8
e f f
f c d ×ðb s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 2 5 2
f y d ×ðA s 1 . x ×ð - a 2
( d )
e s 2 : = = 2 0 5 . 9 0 6 ×ðc m
N E d
2
f c d ×ðb s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . x ×ð - a 2
( 1 ) ( d )
e s 1 : = = 2 5 2 . 0 1 ×ðc m
N E d
2 ×ða 2
¾e f f < = 0
d
b s
æð öð
3
M R d . x : = f y d ×ðA s 1 . x ×ð - a 2 + N E d ×ðçð - a 2 ÷ð = 1 . 2 8 8 ´ð 1 0 ×ðk N ×ðm
( d )
2
èð øð
M E d . x . t o t = 9 8 6 . 3 1 8 ×ðk N ×ðm
8 . 2 . 6 . 2 . 2 N o [n o [ M R d d l a p Ba s z c z y z n y y - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . y + f y d ×ðA s 1 . y
¾e f f : = = 0 . 0 8 1 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðh s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . y
çð ÷ð×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 3 3 5
e f f
2
f c d ×ðh s ×ðd + ×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . y - f y d ×ðA s 1 . y
¾' ' : = = - 0 . 7 3
e f f
f c d ×ðh s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 0 8 1
f y d ×ðA s 1 . y ×ð - a 2
( d )
e s 2 : = = 2 3 5 . 3 2 1 ×ðc m
N E d
2
f c d ×ðh s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . y ×ð - a 2
( 1 ) ( d )
e s 1 : = = 2 8 6 . 7 3 9 ×ðc m
N E d
2 ×ða 2
¾e f f < = 1
d
h s
æð öð
3
M R d . y : = f y d ×ðA s 1 . y ×ð - a 2 + N E d ×ðçð - a 2 ÷ð = 1 . 4 5 3 ´ð 1 0 ×ðk N ×ðm
( d )
2
èð øð
M E d . y . t o t = 4 9 4 . 0 5 7 ×ðk N ×ðm
Z E S T A W I E N I E W Y N I K Ó W :
N E d = 5 6 1 . 0 9 ×ðk N M E d . x . t o t = 9 8 6 . 3 1 8 ×ðk N ×ðm M E d . y . t o t = 4 9 4 . 0 5 7 ×ðk N ×ðm
3 3
M R d . x = 1 . 2 8 8 ´ð 1 0 ×ðk N ×ðm M R d . y = 1 . 4 5 3 ´ð 1 0 ×ðk N ×ðm
M R d . x > M E d . x . t o t = 1 M R d . y > M E d . y . t o t = 1
8 . 2 . 6 . 2 . 3 O k r e [l e n i e n o [n o [c i s Bu p a o s i o w o [c i s k a n e g o
l i c z b a p t ó w
n = 1 6
2
À×ðÕ
2
p o w i e r z c h n i a p r t ó w z b r o j e n i a
A s . c a l : = n ×ð = 1 2 8 . 6 8 ×ðc m
4
4 N o [n o [ o b l i c z e n i o w a s Bu p a
N R d . 0 : = - A s . c a l c d + A s . c a l ×ðf y d = 1 . 3 0 3 ´ð 1 0 ×ðk N
( b ) f
s ×ðh s
[c i s k a n e g o
N E d
= 0 . 0 4 3 a : = 1 w g T a b e l a p k t . 5 . 8 . 9 E C - 2
N R d . 0
8 . 2 . 6 . 2 . 4 . O k r e [l e n i e n o [n o [c i s Bu p a d w u k i e r u n k o w o z g i n a n e g o :
a a a a
M E d . x . t o t M E d . y . t o t M E d . x . t o t M E d . y . t o t
æð öð æð öð æð öð æð öð
+ = 1 . 1 0 6 + £ð 1 = 0
çð ÷ð çð ÷ð çð ÷ð çð ÷ð
M R d . x M R d . y M R d . x M R d . y
èð øð èð øð èð øð èð øð
8 . 2 . 7 A n a l i z a I I r z d u - 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 o m i n a l n a s z t y w n o [ - p Ba s z c z y z n a x
³C E : = 1 . 2 6 4
I c . x = 1 . 0 8 ´ð 1 0 ×ðc m
E c m
E c d : = = 2 7 . 3 6 4 ×ðG P a
³C E
4 4
I s . x = 5 . 3 6 8 ´ð 1 0 ×ðc m
A s
Áx : = = 3 . 5 7 4 ×ð% Áx ³ð 0 . 0 0 2 = 1 s t o p i e D z b r o j e n i a
A c
f c k
k 1 : = = 1 . 2 2 5 w s p ó Bc z y n n i k z a l e |n y o d k l a s y c e m e n t u
2 0 ×ðM P a
N E d
n : = = 0 . 0 7 3 w z g l d n a s i Ba p o d Bu |n a
A c ×ðf c d
»x = 7 8 . 5 2 s m u k Bo [ s Bu p a
»x
æð öð
w s p ó Bc z y n n i k z a l e |n y o d s i By o s i o w e j i s m u k Bo [c i
k 2 : = m i n çðn ×ð , 0 . 2 ÷ð = 0 . 0 3 4
s Bu p a
1 7 0
èð øð
K s : = 1 w s p ó Bc z y n n i k w y r a |a j c y u d z i a B z b r o j e n i a
k 1 ×ðk 2
K c : = = 0 . 0 1 4 w s p ó Bc z y n n i k w y r a |j c y e f e k t y z a r y s o w a n i a ,
1 + Õe f
p e Bz a n i a , i t p .
2
E I : = K c ×ðE c d ×ðI c . x + K s ×ðE s ×ðI s . x = 1 1 1 . 3 5 8 ×ðM N ×ðm n o m i n a l n a s z t y w n o [ s m u k By c h e l e m e n t ó w
[c i s k a n y c h
2
À
3
N B . x : = ×ðE I = 5 . 9 4 2 ´ð 1 0 ×ðk N n o [n o [ p r z y w y b o c z e n i u u s t a l o n a p r z e z a Bo |e n i u
2
s z t y w n o [c i n o m i n a l n e j
l 0 . x
c o : = 8 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 u
2
À
²' : = = 1 . 2 3 4 z a Bo |e n i e s i n u s o i e a l n e g o r o z k Ba d u m o m e n t u I r z d u
c o
m o m e n t I r z d u u w z g l d n i a j c y e f e k t y i m p e r f e k c j i
M 0 . E d . x : = M E d . x + N E d ×ðe i . x = 6 7 8 . 7 4 1 ×ðk N ×ðm
æð1 ²' öð
M E d . x . t o t : = M 0 . E d . x ×ð + = 7 6 6 . 0 5 5 ×ðk N ×ðm m o m e n t c a Bk o w i t y
çð ÷ð
N B . x
çð ÷ð
- 1
çð ÷ð
N E d
èð øð
M E d . x . t o t
e t o t . x : = = 1 3 6 . 5 3 ×ðc m m i m o [r ó d c a Bk o w i t y
N E d
N o m i n a l n a s z t y w n o [ - p Ba s z c z y z n a y
³C E : = 1 . 2 6 4
I c . y = 1 . 0 8 ´ð 1 0 ×ðc m
E c m
E c d : = = 2 7 . 3 6 4 ×ðG P a
³C E
4 4
I s . y = 7 . 7 7 ´ð 1 0 ×ðc m
A s
Áy : = = 3 . 5 7 4 ×ð% Áy ³ð 0 . 0 0 2 = 1 s t o p i e D z b r o j e n i a
A c
f c k
k 1 : = = 1 . 2 2 5 w s p ó Bc z y n n i k z a l e |n y o d k l a s y c e m e n t u
2 0 ×ðM P a
N E d
n : = = 0 . 0 7 3 w z g l d n a s i Ba p o d Bu |n a
A c ×ðf c d
»y = 7 8 . 5 2 s m u k Bo [ s Bu p a
»y
æð öð
w s p ó Bc z y n n i k z a l e |n y o d s i By o s i o w e j i s m u k Bo [c i
k 2 : = m i n çðn ×ð , 0 . 2 ÷ð = 0 . 0 3 4
s Bu p a
1 7 0
èð øð
K s : = 1 w s p ó Bc z y n n i k w y r a |a j c y u d z i a B z b r o j e n i a
k 1 ×ðk 2
K c : = = 0 . 0 1 4 w s p ó Bc z y n n i k w y r a |j c y e f e k t y z a r y s o w a n i a ,
1 + Õe f
p e Bz a n i a , i t p .
2
E I : = K c ×ðE c d ×ðI c . y + K s ×ðE s ×ðI s . y = 1 5 9 . 3 9 6 ×ðM N ×ðm n o m i n a l n a s z t y w n o [ s m u k By c h e l e m e n t ó w
[c i s k a n y c h
2
À
N B . y : = ×ðE I = 8 5 0 5 . 5 0 7 ×ðk N n o [n o [ p r z y w y b o c z e n i u u s t a l o n a p r z e z a Bo |e n i u
2
s z t y w n o [c i n o m i n a l n e j
l 0 . y
c o : = 1 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 u
2
À
²' : = = 0 . 8 2 2 z a Bo |e n i e s i n u s o i e a l n e g o r o z k Ba d u m o m e n t u I r z d u
c o
m o m e n t I r z d u u w z g l d n i a j c y e f e k t y i m p e r f e k c j i
M 0 . E d . y : = M E d . y + N E d ×ðe i . y = 2 0 9 . 8 5 9 ×ðk N ×ðm
æð1 ²' öð
M E d . y . t o t : = M 0 . E d . y ×ð + = 2 2 2 . 0 5 ×ðk N ×ðm m o m e n t c a Bk o w i t y
çð ÷ð
N B . y
çð ÷ð
- 1
çð ÷ð
N E d
èð øð
M E d . y . t o t
e t o t . y : = = 3 9 . 5 7 5 ×ðc m m i m o [r ó d c a Bk o w i t y
N E d
8 . 2 . 7 . 1 . S p r a w d z e n i e c z y s Bu p n a l e |y p r o j e k t o w a j a k o j e d n o c z y d w u k i e r u n k o w o
z b r o j o n y
»x = 7 8 . 5 2 »y = 7 8 . 5 2
»x »x »y »y
= 1 < 2 = 1 = 1 < 2 = 1 W A R U N K I
»y »y »x »x
S P E AN I O N E
e t o t . x e t o t . x e t o t . y e t o t . y
b s b s h s h s
W A R U N I K I N I E
= 3 . 4 5 < 0 . 2 = 0 = 0 . 2 9 < 0 . 2 = 0
S P E AN I O N E
e t o t . y e t o t . y e t o t . x e t o t . x
h s h s b s b s
S AU P D W U K I E R U N K O W O Z B R O J O N Y
8 . 2 . 7 . 2 N o [n o [ s Bu p a
8 . 2 . 7 . 2 . 1 N o [n o [ M R d d l a p Ba s z c z y z n y x - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . x + f y d ×ðA s 1 . x
¾e f f : = = 0 . 2 5 2 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðb s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . x
çð ÷ð×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 3 9 3
e f f
2
f c d ×ðb s ×ðd + ×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . x - f y d ×ðA s 1 . x
¾' ' : = = - 0 . 4 5 8
e f f
f c d ×ðb s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 2 5 2
×ð ×ð -
( )
f y d ×ðA s 1 . x ×ð - a 2
( d )
e s 2 : = = 2 0 5 . 9 0 6 ×ðc m
N E d
2
f c d ×ðb s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . x ×ð - a 2
( 1 ) ( d )
e s 1 : = = 2 5 2 . 0 1 ×ðc m
N E d
2 ×ða 2
¾e f f < = 0
d
b s
æð öð
2 3
M R d . x : = f c d ×ðh s ×ðd x ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . x ×ð - a 2 - N E d ×ðçð - a 1 ÷ð = 2 . 2 7 6 ´ð 1 0 ×ðk N ×ðm
( 1 ) ( d )
x
2
èð øð
M E d . x . t o t = 7 6 6 . 0 5 5 ×ðk N ×ðm
8 . 2 . 7 . 2 . 2 N o [n o [ M R d d l a p Ba s z c z y z n y y - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . y + f y d ×ðA s 1 . y
¾e f f : = = 0 . 0 8 1 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðh s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . y
çð ÷ð×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 3 3 5
e f f
2
f c d ×ðh s ×ðd + ×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . y - f y d ×ðA s 1 . y
¾' ' : = = - 0 . 7 3
e f f
f c d ×ðh s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 0 8 1
f y d ×ðA s 1 . y ×ð - a 2
( d )
e s 2 : = = 2 3 5 . 3 2 1 ×ðc m
N E d
2
f c d ×ðh s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . y ×ð - a 2
( 1 ) ( d )
e s 1 : = = 2 8 6 . 7 3 9 ×ðc m
N E d
2 ×ða 2
¾e f f < = 1
d
h s
æð öð
3
M R d . y : = f y d ×ðA s 1 . y ×ð - a 2 + N E d ×ðçð - a 2 ÷ð = 1 . 4 5 3 ´ð 1 0 ×ðk N ×ðm
( d )
2
èð øð
M E d . y . t o t = 2 2 2 . 0 5 ×ðk N ×ðm
Z E S T A W I E N I E W Y N I K Ó W :
N E d = 5 6 1 . 0 9 ×ðk N M E d . x . t o t = 7 6 6 . 0 5 5 ×ðk N ×ðm M E d . y . t o t = 2 2 2 . 0 5 ×ðk N ×ðm
3 3
M R d . x = 2 . 2 7 6 ´ð 1 0 ×ðk N ×ðm M R d . y = 1 . 4 5 3 ´ð 1 0 ×ðk N ×ðm
M R d . x > M E d . x . t o t = 1 M R d . y > M E d . y . t o t = 1
8 . 2 . 7 . 2 . 3 O k r e [l e n i e n o [n o [c i s Bu p a o s i o w o [c i s k a n e g o
n : = 2 4 l i c z b a p t ó w
2
À×ðÕ
2
A s . c a l : = n ×ð = 1 9 3 . 0 1 9 ×ðc m p o w i e r z c h n i a p r t ó w z b r o j e n i a
4
4 n o [n o [ o b l i c z e n i o w a s Bu p a
N R d . 0 : = - A s . c a l c d + A s . c a l ×ðf y d = 1 . 5 6 9 ´ð 1 0 ×ðk N
( b ) f
s ×ðh s
[c i s k a n e g o
N E d
= 0 . 0 3 6
a : = 1 w g T a b e l a p k t . 5 . 8 . 9 E C - 2
N R d . 0
8 . 2 . 7 . 2 . 4 . O k r e [l e n i e n o [n o [c i s Bu p a d w u k i e r u n k o w o [c i s k a n e g o :
a a a a
M E d . x . t o t M E d . y . t o t M E d . x . t o t M E d . y . t o t
æð öð æð öð æð öð æð öð
+ = 0 . 4 8 9 + £ð 1 = 1
çð ÷ð çð ÷ð çð ÷ð çð ÷ð
M R d . x M R d . y M R d . x M R d . y
èð øð èð øð èð øð èð øð
8 . 3 . 1 I I k o m b i n a c j : M a k s y m a l n y M . y i w a r t o [c i o d p o w i a d a j c e
o b l i c z e n i o w y m o m e n t z g i n a j c y
M y . s : = 5 8 5 . 6 8 4 k N ×ðm M E d . y : = M y . s = 5 8 5 . 6 8 4 ×ðk N ×ðm
( p B. y , d ó B s Bu p a )
M x . s : = 2 8 4 . 6 1 k N ×ðm M E d . x : = M x . s = 2 8 4 . 6 1 ×ðk N ×ðm o b l i c z e n i o w y m o m e n t z g i n a j c y
( p B. x , d ó B s Bu p a )
N s : = 8 9 1 . 0 9 k N N E d : = N s = 8 9 1 . 0 9 ×ðk N o b l i c z e n i o w a s i Ba [c i s k a j c a ( d ó B s Bu p a )
8 . 3 . 1 . 1 A n a l i z a I I r z d u - 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 o m i n a l n a s z t y w n o [ - p Ba s z c z y z n a x
³C E : = 1 . 2 6 4
I c . x = 1 . 0 8 ´ð 1 0 ×ðc m
E c m
E c d : = = 2 7 . 3 6 4 ×ðG P a
³C E
4 4
I s . x = 5 . 3 6 8 ´ð 1 0 ×ðc m
A s
Áx : = = 3 . 5 7 4 ×ð% Áx ³ð 0 . 0 0 2 = 1 s t o p i e D z b r o j e n i a
A c
f c k
k 1 : = = 1 . 2 2 5 w s p ó Bc z y n n i k z a l e |n y o d k l a s y c e m e n t u
2 0 ×ðM P a
N E d
n : = = 0 . 1 1 6 w z g l d n a s i Ba p o d Bu |n a
A c ×ðf c d
»x = 7 8 . 5 2 s m u k Bo [ s Bu p a
»x
æð öð
w s p ó Bc z y n n i k z a l e |n y o d s i By o s i o w e j i s m u k Bo [c i
k 2 : = m i n çðn ×ð , 0 . 2 ÷ð = 0 . 0 5 3
s Bu p a
1 7 0
èð øð
K s : = 1 w s p ó Bc z y n n i k w y r a |a j c y u d z i a B z b r o j e n i a
k 1 ×ðk 2
w s p ó Bc z y n n i k w y r a |j c y e f e k t y z a r y s o w a n i a ,
K c : = = 0 . 0 2 1
1 + Õe f
p e Bz a n i a , i t p .
2
n o m i n a l n a s z t y w n o [ s m u k By c h e l e m e n t ó w
E I : = K c ×ðE c d ×ðI c . x + K s ×ðE s ×ðI s . x = 1 1 3 . 7 0 6 ×ðM N ×ðm
[c i s k a n y c h
2
À
3
n o [n o [ p r z y w y b o c z e n i u u s t a l o n a p r z e z a Bo |e n i u
N B . x : = ×ðE I = 6 . 0 6 7 ´ð 1 0 ×ðk N
2
s z t y w n o [c i n o m i n a l n e j
l 0 . x
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 u
c o : = 8
2
À
z a Bo |e n i e s i n u s o i e a l n e g o r o z k Ba d u m o m e n t u I r z d u
²' : = = 1 . 2 3 4
c o
m o m e n t I r z d u u w z g l d n i a j c y e f e k t y i m p e r f e k c j i
M 0 . E d . x : = M E d . x + N E d ×ðe i . x = 3 0 7 . 8 4 7 ×ðk N ×ðm
æð1 ²' öð
m o m e n t c a Bk o w i t y
M E d . x . t o t : = M 0 . E d . x ×ð + = 3 7 3 . 2 2 7 ×ðk N ×ðm
çð ÷ð
N B . x
çð ÷ð
- 1
çð ÷ð
N E d
èð øð
M E d . x . t o t
m i m o [r ó d c a Bk o w i t y
e t o t . x : = = 4 1 . 8 8 4 ×ðc m
N E d
N o m i n a l n a s z t y w n o [ - p Ba s z c z y z n a y
³C E : = 1 . 2 6 4
I c . y = 1 . 0 8 ´ð 1 0 ×ðc m
E c m
E c d : = = 2 7 . 3 6 4 ×ðG P a
³C E
4 4
I s . y = 7 . 7 7 ´ð 1 0 ×ðc m
A s
s t o p i e D z b r o j e n i a
Áy : = = 3 . 5 7 4 ×ð% Áy ³ð 0 . 0 0 2 = 1
A c
f c 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 c e m e n t u
k 1 : = = 1 . 2 2 5
2 0 ×ðM P a
N E d
w z g l d n a s i Ba p o d Bu |n a
n : = = 0 . 1 1 6
A c ×ðf c d
s m u k Bo [ s Bu p a
»y = 7 8 . 5 2
»y
æð öð
w s p ó Bc z y n n i k z a l e |n y o d s i By o s i o w e j i s m u k Bo [c i
k 2 : = m i n çðn ×ð , 0 . 2 ÷ð = 0 . 0 5 3
s Bu p a
1 7 0
èð øð
w s p ó Bc z y n n i k w y r a |a j c y u d z i a B z b r o j e n i a
K s : = 1
k 1 ×ðk 2
w s p ó Bc z y n n i k w y r a |j c y e f e k t y z a r y s o w a n i a ,
K c : = = 0 . 0 2 1
1 + Õe f
p e Bz a n i a , i t p .
2
n o m i n a l n a s z t y w n o [ s m u k By c h e l e m e n t ó w
E I : = K c ×ðE c d ×ðI c . y + K s ×ðE s ×ðI s . y = 1 6 1 . 7 4 4 ×ðM N ×ðm
[c i s k a n y c h
2
À
3
n o [n o [ p r z y w y b o c z e n i u u s t a l o n a p r z e z a Bo |e n i u
N B . y : = ×ðE I = 8 . 6 3 1 ´ð 1 0 ×ðk N
2
s z t y w n o [c i n o m i n a l n e j
l 0 . y
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 u
c o : = 1 2
2
À
z a Bo |e n i e s i n u s o i e a l n e g o r o z k Ba d u m o m e n t u I r z d u
²' : = = 0 . 8 2 2
c o
m o m e n t I r z d u u w z g l d n i a j c y e f e k t y i m p e r f e k c j i
M 0 . E d . y : = M E d . y + N E d ×ðe i . y = 6 0 8 . 9 2 1 ×ðk N ×ðm
æð1 ²' öð
m o m e n t c a Bk o w i t y
M E d . y . t o t : = M 0 . E d . y ×ð + = 6 6 6 . 5 8 1 ×ðk N ×ðm
çð ÷ð
N B . y
çð ÷ð
- 1
çð ÷ð
N E d
èð øð
M E d . y . t o t
m i m o [r ó d c a Bk o w i t y
e t o t . y : = = 7 4 . 8 0 5 ×ðc m
N E d
8 . 3 . 1 . 2 . S p r a w d z e n i e c z y s Bu p n a l e |y p r o j e k t o w a j a k o j e d n o c z y d w u k i e r u n k o w o
z b r o j o n y
»x = 7 8 . 5 2 »y = 7 8 . 5 2
»x »x »y »y
W A R U N K I
= 1 < 2 = 1 = 1 < 2 = 1
»y »y »x »x
S P E AN I O N E
e t o t . x e t o t . x e t o t . y e t o t . y
b s b s h s h s
W A R U N I K I N I E
= 0 . 5 6 < 0 . 2 = 0 = 1 . 7 8 6 < 0 . 2 = 0
S P E AN I O N E
e t o t . y e t o t . y e t o t . x e t o t . x
h s h s b s b s
S AU P D W U K I E R U N K O W O Z B R O J O N Y
8 . 3 . 1 . 3 N o [n o [ s Bu p a
8 . 3 . 1 . 3 . 1 N o [n o [ M R d d l a p Ba s z c z y z n y x - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . x + f y d ×ðA s 1 . x
¾e f f : = = 0 . 3 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðb s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . x
çð ÷ð×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 4 1 3
e f f
2
f c d ×ðb s ×ðd + ×ðf y d ×ðA s 1 . x
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . x - f y d ×ðA s 1 . x
¾' ' : = = - 0 . 4 1
e f f
f c d ×ðb s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 3
f y d ×ðA s 1 . x ×ð - a 2
( d )
e s 2 : = = 1 2 9 . 6 5 2 ×ðc m
N E d
2
f c d ×ðb s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . x ×ð - a 2
( 1 ) ( d )
e s 1 : = = 1 7 3 . 0 5 4 ×ðc m
N E d
2 ×ða 2
¾e f f < = 0
d
b s
æð öð
2 3
M R d . x : = f c d ×ðh s ×ðd x ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . x ×ð - a 2 - N E d ×ðçð - a 1 ÷ð = 2 . 4 4 1 ´ð 1 0 ×ðk N ×ðm
( 1 ) ( d )
x
2
èð øð
M E d . x . t o t = 3 7 3 . 2 2 7 ×ðk N ×ðm
8 . 3 . 1 . 3 . 2 N o [n o [ M R d d l a p Ba s z c z y z n y y - p r z y z n a n e j s i l e [c i s k a j c e j
N E d - f y d ×ðA s 2 . y + f y d ×ðA s 1 . y
¾e f f : = = 0 . 1 2 9 ¾e f f . l i m = 0 . 4 9 3
f c d ×ðh s ×ðd
2
æð öð
N E d + - 1 - f y d ×ðA s 2 . y
çð ÷ð×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
èð øð
¾' : = = 0 . 3 5 4
e f f
2
f c d ×ðh s ×ðd + ×ðf y d ×ðA s 1 . y
1 - ¾e f f . l i m
N E d - f y d ×ðA s 2 . y - f y d ×ðA s 1 . y
¾' ' : = = - 0 . 6 8 3
e f f
f c d ×ðh s ×ðd
¾e f f < ¾e f f . l i m = 1 ¾e f f = 0 . 1 2 9
f y d ×ðA s 1 . y ×ð - a 2
( d )
e s 2 : = = 1 4 8 . 1 7 4 ×ðc m
N E d
2
f c d ×ðh s ×ðd ×ð¾e f f ×ð - 0 . 5 ×ð¾e f f + f y d ×ðA s 2 . y ×ð - a 2
( 1 ) ( d )
e s 1 : = = 1 9 8 . 3 0 9 ×ðc m
N E d
2 ×ða 2
¾e f f < = 1
d
h s
æð öð
3
M R d . y : = f y d ×ðA s 1 . y ×ð - a 2 + N E d ×ðçð - a 2 ÷ð = 1 . 5 3 1 ´ð 1 0 ×ðk N ×ðm
( d )
2
èð øð
M E d . y . t o t = 6 6 6 . 5 8 1 ×ðk N ×ðm
Z E S T A W I E N I E W Y N I K Ó W :
N E d = 8 9 1 . 0 9 ×ðk N M E d . x . t o t = 3 7 3 . 2 2 7 ×ðk N ×ðm M E d . y . t o t = 6 6 6 . 5 8 1 ×ðk N ×ðm
3 3
M R d . x = 2 . 4 4 1 ´ð 1 0 ×ðk N ×ðm M R d . y = 1 . 5 3 1 ´ð 1 0 ×ðk N ×ðm
M R d . x > M E d . x . t o t = 1 M R d . y > M E d . y . t o t = 1
8 . 3 . 1 . 4 O k r e [l e n i e n o [n o [c i s Bu p a o s i o w o [c i s k a n e g o
l i c z b a p t ó w
n : = 2 4
2
À×ðÕ
2
p o w i e r z c h n i a p r t ó w z b r o j e n i a
A s . c a l : = n ×ð = 1 9 3 . 0 1 9 ×ðc m
4
N o [n o [ o b l i c z e n i o w a s Bu p a
4
N R d . 0 : = - A s . c a l c d + A s . c a l ×ðf y d = 1 . 5 6 9 ´ð 1 0 ×ðk N
( b ) f
s ×ðh s
[c i s k a n e g o
N E d
= 0 . 0 5 7
w g T a b e l a p k t . 5 . 8 . 9 E C - 2
a : = 1
N R d . 0
8 . 3 . 1 . 5 . O k r e [l e n i e n o [n o [c i s Bu p a d w u k i e r u n k o w [c i s k a n e g o :
a a a a
M E d . x . t o t M E d . y . t o t M E d . x . t o t M E d . y . t o t
æð öð æð öð æð öð æð öð
+ = 0 . 5 8 8 + £ð 1 = 1
çð ÷ð çð ÷ð çð ÷ð çð ÷ð
M R d . x M R d . y M R d . x M R d . y
èð øð èð øð èð øð èð øð
8 . 4 . Z b r o j e n i e n a s k r c a n i e i [c i n a n i e
8 . 4 . 1 I . k o m b i n a c j a ( m a k s y m a l n y m o m e n t s k r c a j c y i o d p o w i a d a j c a s i Ba [c i n a j c a )
M z . s : = 1 6 0 . 7 7 6 k N ×ðm T E d : = M z . s = 1 6 0 . 7 7 6 ×ðk N ×ðm
Q y . s : = 2 8 . 7 1 k N V E d : = Q y . s = 2 8 . 7 1 ×ðk N
S p r a w d z e n i e c z y z b r o j e n i e n a [c i n a n i e i s k r c a n i e j e s t k o n i e c z n e
0 . 1 8 2 0 0 m m
æð1 öð
C R d . c : = = 0 . 1 2 9 k : = m i n + , 2 = 1 . 6 1 1
çð ÷ð
³c d
èð øð
A s L
æð öð
2
A s L : = A s . x = 8 5 . 5 5 4 ×ðc m ÁL : = m i n , 2 % = 1 . 9 2 8 ×ð% 1 : = 0 . 1 5
k
çð ÷ð
b s ×ðd x
èð øð
Ãc p : = 0 M P a
1
3
2
f c k
æð öð
2
½m i n : = 0 . 0 3 5 ×ðk ×ðçð ÷ð ×ðM P a = 0 . 3 9 2 ×ðM P a
M P a
èð øð
1
éð ùð
êð úð
3
êð f c k úð
æð öð
V R d . c : =
êðC R d . c ×ðk ×ðçð1 0 0 ×ðÁL ×ð ÷ð ×ðM P a + k 1 ×ðÃc p úð×ðb s ×ðd x = 3 5 5 . 3 9 5 ×ðk N
M P a
ëð èð øð ûð
V R d . c > + k 1 ×ðÃc p s ×ðd x = 1 W A R U N E K S P E AN I O N Y
( ½ ) ×ðb
m i n
V R d . c = 3 5 5 . 3 9 5 ×ðk N > V E d = 2 8 . 7 1 ×ðk N N I E P O T R Z E B A Z B R O J E N I A N A
ZC I N A N I E
b s ×ðh s
éð ùð
t e f : = m a x
êð2 ×ða 1 , 2 ×ð + h s = 0 . 1 5 m
( b ) úð
s
ëð ûð
3 2
A k : = - t e f s - t e f = 2 . 0 2 5 ´ð 1 0 ×ðc m u k : = 2 ×ð - t e f + h s - t e f = 1 . 8 m
( b ) ×ð( h ) ( b )
s s
T R d . c : = 2 ×ðA k ×ðt e f ×ðf c t d = 8 6 . 7 8 6 ×ðk N ×ðm T R d . c < T E d = 1 N a l e |y z a s t o s o w a z b r o j e n i e n a
s k r c a n i a
M a k s y m a l n a s i Ba [c i s k a j c a [c i a n k :
T E d V E d
ÄT : = = 2 . 6 4 7 ×ðM P a ÄV : = = 0 . 0 7 2 ×ðM P a
2 ×ðA k ×ðt e f b s ×ð
( 0 . 9 ×ðd )
x
V E d . i : = + ÄV e f ×ð - t e f = 1 8 3 . 4 9 3 ×ðk N
( Ä ) ×ðt ( h )
T s
2
À×ðÕs
2
A s w : = = 0 . 5 0 3 ×ðc m
4
f c k
æð öð
½ : = 0 . 6 ×ðçð1 - ÷ð = 0 . 5 2 8 ±c w : = 1
2 5 0 M P a
èð øð
2 ×ðV E d . i
éð ùð
1
¸ : = ×ða s i n = 1 4 . 3 6 ×ðd e g c o t ( ¸) = 3 . 9 0 6 > 2
êð
2
( h ) úð
s
ëð±c w ×ð½×ðf c d ×ðt e f ×ð - t e f ûð
P r z y j t o : ¸ : = 2 6 . 6 d e g c o t ( ¸) = 1 . 9 9 7
f y w d : = f y d
A s w
s 1 : = ×ð - t e f y w d ×ðc o t ( ¸) = 1 0 . 7 0 3 ×ðc m p r z y j t o r o z s t a w : s 1 : = 1 0 c m
( h ) ×ðf
V E d . i s
A s w
V R d . s . i : = ×ð - t e f y w d ×ðc o t ( ¸) = 1 9 6 . 3 9 1 ×ðk N V R d . s . i > V E d . i = 1
( h ) ×ðf
s 1 s
±c w ×ðt e f ×ð - t e f c d
( h ) ×ð½×ðf
s
V R d . m a x . i : = = 3 0 5 . 7 6 5 ×ðk N V R d . m a x . i > V E d . i = 1
c o t ( ¸) + t a n ( ¸)
T R d . m a x : = 2 ×ð½×ð±c w ×ðf c d ×ðA k ×ðt e f ×ðs i n ( ¸) ×ðc o s ( ¸) = 2 7 5 . 1 8 8 ×ðk N ×ðm
±c w ×ðb s ×ð0 . 9 ×ðd x ×ð½×ðf c d
3
V R d . m a x : = = 1 . 8 0 9 ´ð 1 0 ×ðk N
c o t ( ¸) + t a n ( ¸)
T E d V E d
< W A R U N E K S P E AN I O N Y
+ = 0 . 6 1
T R d . m a x V R d . m a x
W y m a g a n e p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o n a s k r c a n i e :
T E d u k
2
A S L : = ×ð ×ðc o t ( ¸) = 3 2 . 8 2 ×ðc m
2 ×ðA k f y d
A S L < A s = 1
N i e t r z e b a p r z y j m o w a d o d a t k o w e g o z b r o j e n i a p o d Bu |n e g o
S p r a w d z e n i e w a r u n k ó w n a m i n i m a l n y s t o p i e D z b r o j e n i a o r a z w a r u n k ó w k o n s t r u k c y j n y c h :
2 A s w - 1
f c k ×ðM P a
Áw : = = 0 . 1 6 8 ×ð%
Áw . m i n : = 0 . 0 8 ×ð = 0 . 0 8 8 ×ð%
s 1 ×ðb s
- 1
f y k ×ðM P a
Áw > Áw . m i n = 1
u k
æð öð
s m a x : = m i n çð0 . 7 5 ×ðd x , b s , ÷ð = 2 2 . 5 ×ðc m
8
èð øð
W A R U N E K S P E AN I O N Y
s 1 < s m a x = 1
8 . 4 . 2 I I . k o m b i n a c j a ( m a k s y m a l n a s i B [c i n a j c a i o d p o w i a d a j c y m o m e n t s k r c a j c y )
M z . s : = 2 8 . 7 1 k N ×ðm T E d : = M z . s = 2 8 . 7 1 ×ðk N ×ðm
Q y . s : = 8 6 . 1 3 k N V E d : = Q y . s = 8 6 . 1 3 ×ðk N
S p r a w d z e n i e c z y z b r o j e n i e n a [c i n a n i e i s k r c a n i e j e s t k o n i e c z n e
0 . 1 8 2 0 0 m m
æð1 öð
C R d . c : = = 0 . 1 2 9 k : = m i n + , 2 = 1 . 6 1 1
çð ÷ð
³c d
èð øð
A s L
æð öð
2
A s L : = A s . x = 8 5 . 5 5 4 ×ðc m ÁL : = m i n , 2 % = 1 . 9 2 8 ×ð% 1 : = 0 . 1 5
k
çð ÷ð
b s ×ðd x
èð øð
Ãc p : = 0 M P a
1
3
2
f c k
æð öð
2
½m i n : = 0 . 0 3 5 ×ðk ×ðçð ÷ð ×ðM P a = 0 . 3 9 2 ×ðM P a
M P a
èð øð
1
éð ùð
êð úð
3
êð f c k úð
æð öð
V R d . c : =
êðC R d . c ×ðk ×ðçð1 0 0 ×ðÁL ×ð ÷ð ×ðM P a + k 1 ×ðÃc p úð×ðb s ×ðd x = 3 5 5 . 3 9 5 ×ðk N
M P a
ëð èð øð ûð
W A R U N E K S P E AN I O N Y
V R d . c > + k 1 ×ðÃc p s ×ðd x = 1
( ½ ) ×ðb
m i n
V R d . c = 3 5 5 . 3 9 5 ×ðk N > V E d = 8 6 . 1 3 ×ðk N N I E P O T R Z E B A Z B R O J E N I A N A
ZC I N A N I E
b s ×ðh s
éð ùð
t e f : = m a x
êð2 ×ða 1 , 2 ×ð + h s = 0 . 1 5 m
( b ) úð
s
ëð ûð
3 2
A k : = - t e f s - t e f = 2 . 0 2 5 ´ð 1 0 ×ðc m u k : = 2 ×ð - t e f + h s - t e f = 1 . 8 m
( b ) ×ð( h ) ( b )
s s
T R d . c : = 2 ×ðA k ×ðt e f ×ðf c t d = 8 6 . 7 8 6 ×ðk N ×ðm T R d . c < T E d = 0
N I E P O T R Z E B A Z B R O J E N I A N A
S K R C A N I E
T E d V E d
<
+ = 0 . 1 5 2 1 W A R U N E K S P E AN I O N Y
T R d . m a x V R d . m a x
S p r a w d z e n i e w a r u n k ó w n a m i n i m a l n y s t o p i e D z b r o j e n i a o r a z w a r u n k ó w k o n s t r u k c y j n y c h :
s 1 = 1 0 ×ðc m j a k d l a I k o m b i n a c j i
- 1
2 A s w f c k ×ðM P a
Áw : = = 0 . 1 6 8 ×ð% Áw . m i n : = 0 . 0 8 ×ð = 0 . 0 8 8 ×ð%
s 1 ×ðb s - 1
f y k ×ðM P a
Áw > Áw . m i n = 1
u k
æð öð
s m a x : = m i n çð0 . 7 5 ×ðd x , b s , ÷ð = 2 2 . 5 ×ðc m
8
èð øð
s 1 < s m a x = 1 W A R U N E K S P E AN I O N Y
4 . P r z y p a d k i o b c i |e n i a
4 . 1 O b c i |e n i e s t a Be ( c i |a r p o d p o r y ) 4 . 2 O b c i |e n i e s t a Be ( c i |a r r u r o c i g u )
( p o l e p r z e k r o j u z b r o j e n i a p o d Bu |n e g o )
t u t a j c o s
2 O b c i |e n i e s t a Be ( c i |a r r u r o c i g u )
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