1 . D O B R W Y M I A R W K O N S T R U K C J I
1 . 1 S AU P
L c o l : = 7 . 1 m
l 0 : = 2 "L c o l = 1 4 . 2 m
h s : = 0 . 6 5 m
b s : = 0 . 6 5 m
l 0 l 0
= 2 1 . 8 4 6 = 2 1 . 8 4 6
h s b s
l 0 l 0
w a r u n e k s p e Bn i o n y w a r u n e k s p e Bn i o n y
2 0 d" = 1 2 0 d" = 1
h s b s
l 0 l 0
w a r u n e k s p e Bn i o n y w a r u n e k s p e Bn i o n y
2 5 e" = 1 2 5 e" = 1
h s b s
1 . 2 R Y G I E L
b r : = b s
a : = 3 . 2 m b : = 2 . 2 m
1 1
h r : = "a = 0 . 6 4 m h r : = "a = 0 . 8 m
5 4
P r z y j t o :
h r : = 0 . 6 5 m
1 . 3 S T O P A F U N D A M E N T O W A
L : = 3 . 5 m
B : = 3 . 5 m
h f : = 0 . 2 5 "L = 0 . 8 7 5 m h f : = 0 . 5 "L = 1 . 7 5 m
P r z y j t o :
h f : = 1 . 0 m
2 . Z E S T A W I E N I E O B C I [E C
2 . 1 W A R T O ZC I C H A R A K T E R Y S T Y C Z N E
2 . 1 . 1 C I [A R W AA S N Y P O D P O R Y
k N
B : = 2 5
m 3
- s Bu p
h r
g s : = L c o l - "b s "h s "B = 7 1 . 5 6 1 "k N
2
- r y g i e l l e w y
d : = 0 . 3 m
g r l : = ( a + d ) "b r "h r "B = 3 6 . 9 6 9 "k N
- r y g i e l p r a w y
d : = 0 . 3 m
g r p : = ( b + d ) "b r "h r "B = 2 6 . 4 0 6 "k N
- s t o p a f u n d a m e n t o w a
g s t : = L "h f "B "B = 3 0 6 . 2 5 "k N
G p : = g s + g r l + g r p + g s t = 4 4 1 . 1 8 6 "k N
2 . 1 . 2 O B C I [E N I E S T A AE R U R O C I G W
G : = 6 0 k N
2 . 1 . 3 O B C I [E N I E Z M I E N N E O D T R A N S P O R T O W A N E G O M E D I U M
P : = 1 1 0 k N
2 . 1 . 4 O B C I [E N I E Z M I E N N E O D S I AY P O Z I O M E J W Y W O AA N E J T E M P E R A T U R
M E D I U M
: = 0 . 1 4
H : = "( G + P ) = 2 3 . 8 "k N
2 . 2 W A R T O ZC I O B L I C Z E N I O W E
2 . 2 . 1 C I [A R W AA S N Y P O D P O R Y
f : = 1 . 1
- s Bu p
g s d : = g s "f = 7 8 . 7 1 7 "k N
- r y g i e l l e w y
g r l d : = g r l "f = 4 0 . 6 6 6 "k N
- r y g i e l p r a w y
g r p d : = g r p "f = 2 9 . 0 4 7 "k N
- s t o p a f u n d a m e n t o w a
g s t d : = g s t "f = 3 3 6 . 8 7 5 "k N
G p : = g s d + g r l d + g r p d + g s t d = 4 8 5 . 3 0 5 "k N
2 . 2 . 2 O B C I [E N I E S T A AE R U R O C I G W
f : = 1 . 1
G d : = G "f = 6 6 "k N
2 . 1 . 3 O B C I [E N I E Z M I E N N E O D T R A N S P O R T O W A N E G O M E D I U M
f : = 1 . 1
P d : = P "f = 1 2 1 "k N
2 . 1 . 4 O B C I [E N I E Z M I E N N E O D S I AY P O Z I O M E J W Y W O AA N E J T E M P E R A T U R
M E D I U M
: = 0 . 1 4
H d : = " + P d = 2 6 . 1 8 "k N
( G )
d
3 . S T A T Y K A K O N S T R U K C J I
3 . 1 R Y G I E L
- m o m e n t
M y R : = + P d + g r l d = 7 2 8 . 5 3 "k N "m
( G ) "a
d
M z R : = H d "a = 8 3 . 7 7 6 "k N "m
- s i Ba t n c a
V z R : = G d + P d + g r l d = 2 2 7 . 6 6 6 "k N
V y R : = H d = 2 6 . 1 8 "k N
3 . 2 S AU P
3 . 2 . 1 K o m b i n a c j a 1 : N m a x , M x o d p , M y o d p
h B : = 0 . 0 5 "m
h r
L o b l : = L c o l + h B +
2
g r l d g r p d
M y B 1 : = - P d "a - G d + "a + P d "b + G d + "b = - 2 2 0 . 1 1 3 "k N "m
2 2
M x B 1 : = H d "0 - H d "0 = 0 "k N "m
M z B 1 : = H d "a - H d "b = 2 6 . 1 8 "k N "m
g r l d g r p d
M y D 1 : = - P d "a - G d + "a + P d "b + G d + "b = - 2 2 0 . 1 1 3 "k N "m
2 2
M x D 1 : = 3 "H d "L o b l = 5 8 7 . 0 8 7 "k N "m
M z D 1 : = H d "a - H d "b = 2 6 . 1 8 "k N "m
N m a x 1 : = 3 "P d + 3 "G d + g r l d + g r p d = 6 3 0 . 7 1 2 "k N
3 . 2 . 2 K o m b i n a c j a 2 : N o d p , M x m a x , M y o d p
g r l d g r p d
M y B 2 : = - P d "a - G d + "a + P d "b + G d + "b = - 2 2 0 . 1 1 3 "k N "m
2 2
M x B 2 : = H d "0 - H d "0 = 0 "k N "m
M z B 2 : = H d "a - H d "b = 2 6 . 1 8 "k N "m
g r l d g r p d
M y D 2 : = - P d "a - G d + "a + P d "b + G d + "b = - 2 2 0 . 1 1 3 "k N "m
2 2
M x D 2 : = 3 "H d "L o b l = 5 8 7 . 0 8 7 "k N "m
M z D 2 : = H d "a - H d "b = 2 6 . 1 8 "k N "m
N m a x 2 : = 3 "P d + 3 "G d + g r l d + g r p d = 6 3 0 . 7 1 2 "k N
3 . 2 . 3 K o m b i n a c j a 3 : N o d p , M x o d p , M y m a x
3 . 2 . 3 . 1 P r z y p a d e k I
g r l d g r p d
M y B 3 1 : = - P d "a - G d + a + G d + "b = - 4 8 6 . 3 1 3 "k N "m
2 2
M x B 3 1 : = H d "0 = 0 "k N "m
M z B 3 1 : = H d "a = 8 3 . 7 7 6 "k N "m
g r l d g r p d
M y D 3 1 : = - P d "a - G d + a + G d + "b = - 4 8 6 . 3 1 3 "k N "m
2 2
M x D 3 1 : = 2 H d "L o b l = 3 9 1 . 3 9 1 "k N "m
M z D 3 1 : = H d "a = 8 3 . 7 7 6 "k N "m
N m a x 3 1 : = 2 "P d + 3 "G d + g r l d + g r p d = 5 0 9 . 7 1 2 "k N
3 . 2 . 3 . 2 P r z y p a d e k I I
g r l d g r p d
M y B 3 2 : = - P d "a - G d + a + G d + "b = - 4 8 6 . 3 1 3 "k N "m
2 2
M x B 3 2 : = H d "0 = 0 "k N "m
M z B 3 2 : = H d "a = 8 3 . 7 7 6 "k N "m
g r l d g r p d
M y D 3 2 : = - P d "a - G d + a + G d + "b = - 4 8 6 . 3 1 3 "k N "m
2 2
M x D 3 2 : = H d "L o b l = 1 9 5 . 6 9 6 "k N "m
M z D 3 2 : = H d "a = 8 3 . 7 7 6 "k N "m
N m a x 3 2 : = P d + 3 "G d + g r l d + g r p d = 3 8 8 . 7 1 2 "k N
3 . 2 . 2 K o m b i n a c j a 4 : T m a x , V o d p
V y B 4 : = H d = 2 6 . 1 8 "k N
V y D 4 : = H d = 2 6 . 1 8 "k N
M z m a x 4 : = H d "a + H d "b = 1 4 1 . 3 7 2 "k N "m
3 . 2 . 3 K o m b i n a c j a 5 : T o d p , V m a x
V y B 5 : = 3 H d = 7 8 . 5 4 "k N
V y D 5 : = 3 H d = 7 8 . 5 4 "k N
M z o d p 5 : = H d "a - H d "b = 2 6 . 1 8 "k N "m
4 . D A N E D O W Y M I A R O W A N I A
" B E T O N C 3 0 / 3 7
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
f c k : = 3 0 M P a
w y t r z y m a Bo [ o b l i c z e n i o w a n a [c i s k a n i e
f c d : = 2 0 M P a
w y t r z y m a Bo [ [r e d n i a n a r o z c i g a n i e
f c t m : = 2 . 9 M P a
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 c t d : = 1 . 3 3 M P a
m o d u B s p r \y s t o [c i
E c m : = 3 2 G P a
" S T A L A - I I I N ( R B 5 0 0 W )
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 s c i s t a l i
f y k : = 5 0 0 M 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 s t a l i
f y d : = 4 2 0 M P a
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
g r a n i c z n a w a r t o [ w z g l d n e j w y s o k o [c i
e f f . l i m : = 0 . 5
s t r e f y [c i s k a n e j d l a s t a l i A - I I I
" S T A L A - I
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 s c i s t a l i
f y k s : = 2 4 0 M 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 s t a l i
f y d s : = 2 1 0 M P a
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
g r a n i c z n a w a r t o [ w z g l d n e j w y s o k o [c i
e f f . l i m s : = 0 . 6 2
s t r e f y [c i s k a n e j d l a s t a l i A - I I I
" K l a s a e k s p o z y c j i w z a l e \n o [c i o d w a r u n k w [r o d o w i s k a
[r o d o w i s k o c y k l i c z n i e m o k r e i s u c h e C X 4
" G r u b o [ o t u l e n i a
< 3 2 m m
: = 2 8 m m
C m i n e" - z w a r u n k u p r z e k a z a n i a s i B p r z y c z e p n o [c i o r a z n a l e \y t e g o
u Bo \e n i a i z a g s z c z e n i a b e t o n u
C m i n : = 2 5 m m - z w a r u n k u o c h r o n y p r z e d k o r o z j
"C : = 1 0 m m - o d c h y Bk a d o p u s z c z a l n a
C n o m : = C m i n + "C = 0 . 0 3 5 m
5 . W Y M I A R O W A N I E R Y G L A
5 . 1 W Y M I A R Y P R Z E K R O J U R Y G L A
b r = 0 . 6 5 m h r = 0 . 6 5 m
A c : = b r "h r = 4 . 2 2 5 1 0 3 "c m 2
5 . 2 ZR E D N I C A P R T W Z B R O J E N I A
[r e d n i c a p r t w g B w n y c h
: = 2 8 m m
[r e d n i c a s t r z e m i o n
s : = 1 0 m m
w a r u n e k
C n o m e" = 1
5 . 3 W Y M I A R O W A N I E R Y G L A " a " N A Z G I N A N I E
5 . 3 . 1 P o l e p r z e k r o j u z b r o j e n i a n a z g i n a n i e
5 . 3 . 1 . 1 W p Ba s z c z y \n i e x - z
" w y s o k o [ u \y t e c z n a p r z e k r o j u w p Ba s z c z y zn i e x - z
d z : = h r - C n o m - s - = 5 9 . 1 "c m
2
M y R
" m o m e n t s t a t y c z n y
S c . e f f : = = 0 . 1 6
f c d "b r "d z 2
" w z g l d n a w y s o k o [ s t r e f y s c i s k a n e j p r z e k r o j u
e f f : = 1 - 1 - 2 "S c . e f f = 0 . 1 7 6
" g r a n i c z n a w a r t o [ w z g l d n e j w y s o k o [c i s t r e f y [c i s k a n e j
e f f . l i m : = 0 . 5
" s p r a w d z e n i e w a r u n k u
p r z e k r j j e s t p o j e d y Dc z o z b r o j o n y
e f f d" e f f . l i m = 1
" e f e k t y w n a w y s o k [ s t r e f y [c i s k a n e j
x e f f : = e f f "d z = 0 . 1 0 4 m
" o b l i c z e n i o w e p o l e z b r o j e n i a
f c d "b r "x e f f
A s 1 y : = = 3 2 . 1 8 1 "c m 2
f y d
" p r z y j c i e p o w i e r z c h n i z b r o j e n i a
A s 1 y . p r o v : = 4 9 . 2 6 "c m 2
" z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "b r "d z " = 5 . 7 9 3 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "b r "d z = 4 . 9 9 4 "c m 2
- w s p Bc z y n n i k p r z y z g i n a n i u
k c : = 0 . 4
- w s p Bc z y n n i k o d w y m u s z e n i a
k : = 1 . 0
- p o l e r o z c i g a n e j s t r e f y p r z y z g i n a n i u
A c t : = 0 . 5 "b r "h r = 0 . 2 1 1 "m 2
- [r e d n i a w y t r z y m a Bo [ b e t o n u n a r o z c i g a n i e w c h w i l i z a r y s o w a n i a
f c t . e f f : = f c t m
- n a p r \e n i e w z b r o j e n i u r o z c i g a n y m n a t y c h a m i a s t p o z a r y s o w a n i u
s . l i m : = 2 0 0 M P a
A c t
A s . m i n 3 : = k c "k "f c t . e f f " = 1 2 . 2 5 3 "c m 2
s . l i m
A s . m i n : = m a x = 1 2 . 2 5 3 "c m 2
( A , A s . m i n 2 , A s . m i n 3 )
s . m i n 1
w a r u n e k j e s t s p e Bn i o n y
A s 1 y . p r o v e" A s . m i n = 1
5 . 3 . 1 . 2 W p Ba s z c z y zn i e x - y
" w y s o k o [ u \y t e c z n a p r z e k r o j u w p Ba s z c z y zn i e x - z
d y : = b r - C n o m - s - = 5 9 . 1 "c m
2
M z R
" m o m e n t s t a t y c z n y
S c . e f f : = = 0 . 0 1 8
f c d "h r "d y 2
" w z g l d n a w y s o k o [ s t r e f y s c i s k a n e j p r z e k r o j u
e f f : = 1 - 1 - 2 "S c . e f f = 0 . 0 1 9
" g r a n i c z n a w a r t o [ w z g l d n e j w y s o k o [c i s t r e f y [c i s k a n e j
e f f . l i m : = 0 . 5 3
" s p r a w d z e n i e w a r u n k u
p r z e k r j j e s t p o j e d y Dc z o z b r o j o n y
e f f d" e f f . l i m = 1
" e f e k t y w n a w y s o k [ s t r e f y [c i s k a n e j
x e f f : = e f f "d y = 1 . 1 0 1 "c m
" o b l i c z e n i o w e p o l e z b r o j e n i a
f c d "h r "x e f f
A s 1 z : = = 3 . 4 0 7 "c m 2
f y d
" p r z y j c i e p o w i e r z c h n i z b r o j e n i a
A s 1 z . p r o v : = 1 2 . 3 2 c m 2
" z b r o j e n i e m i n i m a l n e
f c t m
0 . 2 6 "h r "d y " = 5 . 7 9 3 "c m 2
f y k
0 . 0 0 1 3 "h r "d y = 4 . 9 9 4 "c m 2
- w s p Bc z y n n i k p r z y z g i n a n i u
k c : = 0 . 4
- w s p Bc z y n n i k o d w y m u s z e n i a
k : = 1 . 0
- p o l e r o z c i g a n e j s t r e f y p r z y z g i n a n i u
A c t : = 0 . 5 "b r "h r = 0 . 2 1 1 "m 2
- [r e d n i a w y t r z y m a Bo [ b e t o n u n a r o z c i g a n i e w c h w i l i z a r y s o w a n i a
f c t . e f f : = f c t m
- n a p r \e n i e w z b r o j e n i u r o z c i g a n y m n a t y c h a m i a s t p o z a r y s o w a n i u
s . l i m : = 2 0 0 M P a
A c t
A s . m i n 3 : = k c "k "f c t . e f f " = 1 2 . 2 5 3 "c m 2
s . l i m
A s . m i n : = m a x = 1 2 . 2 5 3 "c m 2
( A , A s . m i n 2 , A s . m i n 3 )
s . m i n 1
w a r u n e k j e s t s p e Bn i o n y
A s 1 z . p r o v e" A s . m i n = 1
5 . 3 . 2 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
5 . 3 . 2 . 1 W p Ba s z c z y \n i e x - z
a 1 : = C n o m + s + = 0 . 0 5 9 m
2
A s 1 y . p r o v "f y d
e f f : = = 0 . 2 6 9
b r "d z "f c d
w a r u n e k j e s t s p e Bn i o n y
e f f d" e f f . l i m = 1
s : = f y d = 4 2 0 "M P a
e f f
M R d y : = d z 2 "b r "f c d "e f f "1 - = 1 . 0 5 8 1 0 3 "k N m
2
5 . 3 . 2 . 2 W p Ba s z c z y \n i e x - y
a 1 : = C n o m + s + = 0 . 0 5 9 m
2
A s 1 z . p r o v "f y d
e f f : = = 0 . 0 6 7
h r "d y "f c d
w a r u n e k j e s t s p e Bn i o n y
e f f d" e f f . l i m = 1
s : = f y d = 4 2 0 "M P a
e f f
M R d z : = d y 2 "h r "f c d "e f f "1 - = 2 9 5 . 5 0 9 "k N m
2
5 . 3 . 2 . 3 S p r a w d z e n i e w a r u n k u n o [n o [c i
M y R M z R
+ = 0 . 9 7 2
M R d y M R d z
M y R M z R
w a r u n e k j e s t s p e Bn i o n y
+ d" 1 = 1
M R d y M R d z
5 . 4 . W Y M I A R O W A N I A R Y G L A " a " N A ZC I N A N I E
5 . 4 . 1 W p Ba s z c z y \n i e x - z
" s i Ba [c i n a j c a
V z R = 2 2 7 . 6 6 6 "k N
" [r e d n i c a s t r z e m i e n i a
s : = 1 0 m m
s 2
"
" p o l e s t r z e m i o n c z t e r o c i t y c h
A s w 1 : = 4 = 3 . 1 4 2 "c m 2
4
" 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 s t a l i
f y d s = 2 . 1 1 0 8 "P a
" p o l e p r z e k r o j u r y g l a
A c : = b r "h r = 0 . 4 2 3 m 2
" r a m i e s i B w e w n t r z y c h
z : = 0 . 9 "d z
f c k
" w s p Bc z y n n i k
: = 0 . 6 "1 - = 0 . 5 2 8
2 5 0 "M P a
1 . 6 m - d z
" w s p Bc z y n n i k
k : = = 1 . 0 0 9 k : = m a x ( k , 1 ) = 1 . 0 0 9
1 m
A s 1 y . p r o v
" s t o p i e D z b r o j e n i a p o d Bu \n e g o
L : = = 0 . 0 1 3
b r "d z
" s t o p i e D z b r o j e n i a p o d Bu \n e g o
L : = m i n
( )
L , 0 . 0 1 = 0 . 0 1
5 . 4 . 1 . 1 N o [n o [ o d c i n k w p i e r w s z e g o r o d z a j u
V S d : = V z R = 2 2 7 . 6 6 6 "k N
" N o [n o [ V R d 1
V R d 1 : = 0 . 3 5 k "f c t d " + 4 0 L r "d z = 2 8 8 . 6 9 "k N
( 1 . 2 ) "b
w a r u n e k s p e Bn i o n y
V S d < V R d 1 = 1
" N o [n o [ V R d 2
V R d 2 : = "f c d "b r "z = 3 . 6 5 1 1 0 3 "k N
w a r u n e k j e s t s p e Bn i o n y
V S d < V R d 2 = 1
5 . 4 . 1 . 2 P r z y j c i e r o z s t a w u s t r z e m i o n
" 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 p r z y j t o z w a r u n k w k o n s t r u k c y j n y c h
s m a x : = m i n , 4 0 0 m m = 4 0 "c m
( 0 . 7 5 d )
z
" P r z y j t o r o z t a w s t r z e m i o n
o d c i n k i I - e g o r o d z a j u - s 1 : = 2 5 c m
" S t o p i e D z b r o j e n i a s t r z e m i o n a m i
A s w 1
w : = = 1 . 9 3 3 1 0 - 3
s 1 "b r
f c k
0 . 0 8
M P a
w . m i n : = = 1 . 8 2 6 1 0 - 3
f y k s
M P a
w . m i n < w = 1
w a r u n e k j e s t s p e Bn i o n y - s t r z e m i o n a n i e m a j a w p By w u n a
n o s n o [c n a [c i n a n i e
5 . 4 . 2 W p Ba s z c z y \n i e x - y
" s i Ba [c i n a j c a
V y R = 2 6 . 1 8 "k N
" [r e d n i c a s t r z e m i e n i a
s = 1 0 "m m
s 2
"
" p o l e s t r z e m i o n c z t e r o c i t y c h
A s w 1 : = 4 = 3 . 1 4 2 "c m 2
4
" 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 s t a l i
f y d s = 2 1 0 "M P a
" p o l e p r z e k r o j u r y g l a
A c : = b r "h r = 0 . 4 2 3 m 2
" r a m i e s i B w e w n t r z y c h
z : = 0 . 9 "d y
f c k
" w s p Bc z y n n i k
: = 0 . 6 "1 - = 0 . 5 2 8
2 5 0 "M P a
1 . 6 m - d y
" w s p Bc z y n n i k
k : = = 1 . 0 0 9 k : = m a x ( k , 1 ) = 1 . 0 0 9
1 m
A s 1 z . p r o v
L : = = 3 . 2 0 7 1 0 - 3
" s t o p i e D z b r o j e n i a p o d Bu \n e g o
h r "d y
3
" s t o p i e D z b r o j e n i a p o d Bu \n e g o
L : = m i n
( )
L , 0 . 0 1 = 3 . 2 0 7 1 0 -
5 . 4 . 2 . 1 N o [n o [ o d c i n k w p i e r w s z e g o r o d z a j u
V S d : = V y R = 2 6 . 1 8 "k N
" N o [n o [ V R d 1
V R d 1 : = 0 . 3 5 k "f c t d " + 4 0 L r "d y = 2 3 9 . 6 6 4 "k N
( 1 . 2 ) "h
w a r u n e k s p e Bn i o n y
V S d < V R d 1 = 1
" N o [n o [ V R d 2
V R d 2 : = "f c d "h r "z = 3 . 6 5 1 1 0 3 "k N
w a r u n e k j e s t s p e Bn i o n y
V S d < V R d 2 = 1
5 . 4 . 2 . 2 P r z y j c i e r o z s t a w u s t r z e m i o n
" 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 p r z y j e t o z w a r u n k w k o n s t r u k c y j n y c h
s m a x : = m i n , 4 0 0 m m = 4 0 "c m
( 0 . 7 5 d )
y
" P r z y j t o r o z t a w s t r z e m i o n
o d c i n k i I - e g o r o d z a j u - s 1 : = 2 5 c m
" S t o p i e D z b r o j e n i a s t r z e m i o n a m i
A s w 1
w : = = 1 . 9 3 3 1 0 - 3
s 1 "h r
f c k
0 . 0 8
M P a
w . m i n : = = 1 . 8 2 6 1 0 - 3
f y k s
M P a
w . m i n < w = 1
w a r u n e k j e s t s p e Bn i o n y - s t r z e m i o n a n i e m a j a w p By w u n a
n o s n o [c n a [c i n a n i e
6 . W Y M I A R O W A N I E S AU P A
6 . 1 W Y M I A R Y P R Z E K R O J U S AU P A
h s = 0 . 6 5 m b s = 0 . 6 5 m
A c s : = b s "h s = 4 . 2 2 5 1 0 3 "c m 2
6 . 2 ZR E D N I C A P R T W Z B R O J E N I A
[r e d n i c a p r t w g B w n y c h
: = 2 8 m m
[r e d n i c a s t r z e m i o n
s : = 1 0 m m
6 . 3 O D L E G AO Z ZR O D K A C I [K O ZC I Z B R O J E N I A
o d k r a w d z i r o z c i g a n e j
a 1 : = C n o m + s + = 0 . 0 5 9 m
2
a 2 : = C n o m + s + = 0 . 0 5 9 m
o d k r a w d z i m n i e j r o z c i g a n e j ( [c i s k a n e j )
2
6 . 4 W Y S O K O Z U [Y T E C Z N A P R Z E K R O J U
w p Ba s z c z y zn i e z - x
d x : = b s - a 1 = 0 . 5 9 1 m
w p Ba s z c z y zn i e z - y
d y : = h s - a 1 = 0 . 5 9 1 m
6 . 5 W Y M I A R O W A N I E S AU P A
6 . 5 . 1 K o m b i n a c j a 1 i 2
6 . 5 . 1 . 1 Z b r o j e n i e n a [c i s k a n i e
6 . 5 . 1 . 1 . 1 W p Ba s z c z y zn i e z - y
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
h s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a y 1 : = " + = 0 . 0 2 4 m
6 0 0 n
h s
e a y 2 : = = 0 . 0 2 2 m
3 0
e a y 3 : = 0 . 0 1 m
e a y : = m a x , e a y 2 , e a y 3 = 0 . 0 2 4 m
( e )
a y 1
" M i m o [r o d k o n s t r u k c y j n y
M x D 1
e e y : = = 0 . 9 3 1 "m
N m a x 1
" M i m o [r o d p o c z t k o w y
e o y : = e a y + e e y = 0 . 9 5 4 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 1 = 6 3 0 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 1 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
( )
A s 1 p : = 2 8 " 1 0 - 4 m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 1 . 9 8 1 1 0 - 4 m 4
s s 1 p
e o y l o
1
e y : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 1 . 4 6 8
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 2 . 7 2 7 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 3 0 1
N m a x 1
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 1 . 2 4 2 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 1
e f f : = = 0 . 0 8 2
f c d "b s "d y
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
e f f e" = 0
w a r u n e k n i e s p e Bn i o n y
d y
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 y : = d y - 0 . 5 "h s + e t o t y = 1 . 5 0 8 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 1 " - d y + 0 . 5 "x e f f
( e )
s 1 y
A s 1 x : = = 2 7 . 5 3 9 "c m 2
f y d " - a 2
( d )
y
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 x : = A s 1 x = 2 7 . 5 3 9 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
A s x : = A s 1 x + A s 2 x = 5 5 . 0 7 9 "c m 2
" Z b r o j e n i e m i n i m a l n e
N m a x 1
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 5 6 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k s p e Bn i o n y
A s x e" A s m i n = 1
d" =
w a r u n e k s p e Bn i o n y
A s x d" A s . m a x = 1
A s x - A s . z a B
= 1 . 6 7 2 "%
A s x
A s x - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s x
" P r z y j t e z b r o j e n i e
z b r o j e n i e r o z c i g a n e ( )
A s 1 x : = 2 8 " 1 0 - 4 m 2
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 x : = 2 8 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y x : = A s 1 x + A s 2 x = 5 6 "c m 2
6 . 5 . 1 . 1 . 2 W p Ba s z c z y zn i e z - x
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
b s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a x 1 : = " + = 0 . 0 2 4 m
6 0 0 n
b s
e a x 2 : = = 0 . 0 2 2 m
3 0
e a x 3 : = 0 . 0 1 m
e a x : = m a x , e a x 2 , e a x 3 = 0 . 0 2 4 m
( e )
a x 1
" M i m o [r o d k o n s t r u k c y j n y
M y D 1
e e x : = = 0 . 3 4 9 "m
N m a x 1
" M i m o [r o d p o c z t k o w y
e o x : = e a x + e e x = 0 . 3 7 3 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 1 = 6 3 0 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 1 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p : = 1 4 c m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 9 . 9 0 6 1 0 - 5 m 4
s s 1 p
e o x l o
1
e x : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 0 . 5 7 3
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 2 . 3 6 9 1 0 3 "k N
2 "k l t 0 . 1 + e x
l o 2
1
: = = 1 . 3 6 3
N m a x 1
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 0 . 5 0 8 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 1
e f f : = = 0 . 0 8 2
f c d "h s "d x
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
w a r u n e k n i e s p e Bn i o n y
e f f e" = 0
d x
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 x : = d x - 0 . 5 "b s + e t o t x = 0 . 7 7 4 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 1 " - d x + 0 . 5 "x e f f
( e )
s 1 x
A s 1 y : = = 6 . 8 2 8 "c m 2
f y d " - a 2
( d )
x
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 y : = A s 1 y = 6 . 8 2 8 "c m 2
A s y : = A s 1 y + A s 2 y = 1 3 . 6 5 7 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
" Z b r o j e n i e m i n i m a l n e
N m a x 1
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 1 5 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k n i e s p e Bn i o n y
A s y e" A s m i n = 1
w a r u n e k s p e Bn i o n y
A s y d" A s . m a x = 1
A s y - A s . z a B
= 9 . 8 3 5 "%
A s y
A s y - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s y
" P r z y j t e z b r o j e n i e
( )
A s 1 y : = 7 . 5 " 1 0 - 4 m 2
z b r o j e n i e r o z c i g a n e
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 y : = 7 . 5 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y : = A s 1 y + A s 2 y = 1 5 "c m 2
6 . 5 . 1 . 2 N o [n o [
6 . 5 . 1 . 2 . 1 W p Ba s z c z y zn i e z - y
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d y z : = 1 . 2 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p x : = 9 6 c m 2
A s 1 p x
A s 1 x : = = 4 8 "c m 2
2
A s 1 p x
A s 2 x : = = 4 8 "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 6 . 7 9 3 1 0 4 "c m 4
s s 1 p x
e o y l o 0 . 0 1 "f c d
e y : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 1 . 4 6 8
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 7 . 0 2 2 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 2 0 6
N R d y z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 1 . 1 5 1 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 y : = e t o t y + 0 . 5 "h s - a 1 = 1 . 4 1 7 m
e s 2 y : = e t o t y - 0 . 5 "h s + a 2 = 0 . 8 8 5 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 y
B : = 1 - = - 1 . 3 9 8
d y
A s 1 x "e s 1 y "f y d
s 1 : = = 0 . 6 2 9
b s "d y 2 "f c d
A s 2 x "e s 2 y "f y d
s 2 : = = 0 . 3 9 3
b s "d y 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 y > d y - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 6
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d y
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - y
f y d "A s 1 x " - a 2
( d )
y
N R d y : = = 1 . 2 1 2 1 0 3 "k N
e s 2 y
N R d y - N R d y z
= 0 . 9 6 5 "%
N R d y z
6 . 5 . 1 . 2 . 1 W p Ba s z c z y zn i e z - x
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d x z : = 1 . 2 8 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p y : = 3 6 c m 2
A s 1 p y
A s 1 y : = = 1 8 "c m 2
2
A s 1 p y
A s 2 y : = = 1 8 "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 2 . 5 4 7 1 0 4 "c m 4
s s 1 p y
e o x l o 0 . 0 1 "f c d
e : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 0 . 5 7 3
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 3 . 7 5 8 1 0 3 "k N
2 "k l t 0 . 1 + e
l o 2
1
: = = 1 . 5 1 7
N R d x z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 0 . 5 6 5 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 x : = e t o t x + 0 . 5 "b s - a 1 = 0 . 8 3 1 m
e s 2 x : = e t o t x - 0 . 5 "b s + a 2 = 0 . 2 9 9 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 x
B : = 1 - = - 0 . 4 0 6
d x
A s 1 y "e s 1 x "f y d
s 1 : = = 0 . 1 3 8
h s "d x 2 "f c d
A s 2 y "e s 2 x "f y d
s 2 : = = 0 . 0 5
h s "d x 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 x > d x - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 7 9
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d x
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - x
f y d "A s 1 y " - a 2
( d )
x
N R d x : = = 1 . 3 4 4 1 0 3 "k N
e s 2 x
N R d x - N R d x z
= 5 . 0 3 7 "%
N R d x z
6 . 5 . 1 . 2 . 3 N o [n o [ N R d 0
" 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 [c i s k a n e g o
2
N R d o : = f c d "b s "h s + 2 "A s 1 x + 2 " A s 1 y - 4 "" "f y d = 1 . 1 9 3 1 0 4 "k N
4
1
= 6 7 3 . 2 6 5 "k N
1 1 1
+ -
N R d x N R d y N R d o
O k r e [l e n i e w s p Bc z y n n i k a m n
"
e x b s
w a r u n e k n i e s p e Bn i o n y
0 . 5 < " < 2 = 0
e y h s
N m a x 1
w a r u n e k n i e s p e Bn i o n y
0 . 1 5 < < 0 . 5 = 0
f c d "b s "h s
m n : = 1
m n "N m a x 1 = 6 3 0 . 7 1 2 "k N
" S p r a w d z e n i e w a r u n k u n o [n o [c i
1
w a r u n e k z o s t a B s p e Bn i o n y
m n "N m a x 1 < = 1
1 1 1
+ -
N R d x N R d y N R d o
" S p r a w d z e n i e s t o p n i a z b r o j e n i a
2
A s 1 x "2 + A s 1 y "2 - 4 ""
4
s : = = 2 . 5 4 1 "%
b s "h s
m n "N m a x 1
= 0 . 9 3 7
1
1 1 1
+ -
N R d y N R d x N R d o
W y k o r z y s t a n o 9 3 , 7 % n o [n o [c i s Bu p a .
6 . 5 . 2 K o m b i n a c j a 3 - p r z y p a d e k 1
6 . 5 . 2 . 1 Z b r o j e n i e n a [c i s k a n i e
6 . 5 . 2 . 1 . 1 W p Ba s z c z y zn i e z - y
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
h s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a y 1 : = " + = 0 . 0 2 4 m
6 0 0 n
h s
e a y 2 : = = 0 . 0 2 2 m
3 0
e a y 3 : = 0 . 0 1 m
e a y : = m a x , e a y 2 , e a y 3 = 0 . 0 2 4 m
( e )
a y 1
" M i m o [r o d k o n s t r u k c y j n y
M x D 3 1
e e y : = = 0 . 7 6 8 "m
N m a x 3 1
" M i m o [r o d p o c z t k o w y
e o y : = e a y + e e y = 0 . 7 9 2 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 3 1 = 5 0 9 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 3 1 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
( )
A s 1 p : = 2 0 " 1 0 - 4 m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 1 . 4 1 5 1 0 - 4 m 4
s s 1 p
e o y l o
1
e y : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 1 . 2 1 8
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 2 . 2 9 7 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 2 8 5
N m a x 3 1
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 1 . 0 1 7 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 3 1
e f f : = = 0 . 0 6 6
f c d "b s "d y
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
e f f e" = 0
w a r u n e k n i e s p e Bn i o n y
d y
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 y : = d y - 0 . 5 "h s + e t o t y = 1 . 2 8 3 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 3 1 " - d y + 0 . 5 "x e f f
( e )
s 1 y
A s 1 x : = = 1 7 . 1 3 7 "c m 2
f y d " - a 2
( d )
y
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 x : = A s 1 x = 1 7 . 1 3 7 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
A s x : = A s 1 x + A s 2 x = 3 4 . 2 7 4 "c m 2
" Z b r o j e n i e m i n i m a l n e
N m a x 3 1
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 3 6 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k s p e Bn i o n y
A s x e" A s m i n = 1
w a r u n e k s p e Bn i o n y
A s x d" A s . m a x = 1
A s x - A s . z a B
= 5 . 0 3 5 "%
A s x
A s x - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s x
" P r z y j t e z b r o j e n i e
z b r o j e n i e r o z c i g a n e ( )
A s 1 x : = 1 8 " 1 0 - 4 m 2
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 x : = 1 8 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y x : = A s 1 x + A s 2 x = 3 6 "c m 2
6 . 5 . 2 . 1 . 2 W p Ba s z c z y zn i e z - x
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
b s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a x 1 : = " + = 0 . 0 2 4 m
6 0 0 n
b s
e a x 2 : = = 0 . 0 2 2 m
3 0
e a x 3 : = 0 . 0 1 m
e a x : = m a x , e a x 2 , e a x 3 = 0 . 0 2 4 m
( e )
a x 1
" M i m o [r o d k o n s t r u k c y j n y
M y D 3 1
e e x : = = 0 . 9 5 4 "m
N m a x 3 1
" M i m o [r o d p o c z t k o w y
e o x : = e a x + e e x = 0 . 9 7 8 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 3 1 = 5 0 9 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 3 1 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p : = 3 5 c m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 2 . 4 7 6 1 0 - 4 m 4
s s 1 p
e o x l o
1
e x : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 1 . 5 0 4
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 3 . 1 6 1 1 0 3 "k N
2 "k l t 0 . 1 + e x
l o 2
1
: = = 1 . 1 9 2
N m a x 3 1
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 1 . 1 6 6 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 3 1
e f f : = = 0 . 0 6 6
f c d "h s "d x
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
w a r u n e k n i e s p e Bn i o n y
e f f e" = 0
d x
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 x : = d x - 0 . 5 "b s + e t o t x = 1 . 4 3 2 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 3 1 " - d x + 0 . 5 "x e f f
( e )
s 1 x
A s 1 y : = = 2 0 . 5 2 5 "c m 2
f y d " - a 2
( d )
x
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 y : = A s 1 y = 2 0 . 5 2 5 "c m 2
A s y : = A s 1 y + A s 2 y = 4 1 . 0 5 1 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
" Z b r o j e n i e m i n i m a l n e
N m a x 3 1
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 4 3 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k n i e s p e Bn i o n y
A s y e" A s m i n = 1
w a r u n e k s p e Bn i o n y
A s y d" A s . m a x = 1
A s y - A s . z a B
= 4 . 7 4 9 "%
A s y
A s y - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s y
" P r z y j t e z b r o j e n i e
( )
A s 1 y : = 2 1 . 5 " 1 0 - 4 m 2
z b r o j e n i e r o z c i g a n e
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 y : = 2 1 . 5 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y : = A s 1 y + A s 2 y = 4 3 "c m 2
6 . 5 . 2 . 2 N o [n o [
6 . 5 . 2 . 2 . 1 W p Ba s z c z y zn i e z - y
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d y z : = 1 . 1 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p x : = 6 6 c m 2
A s 1 p x
A s 1 x : = = 3 3 "c m 2
2
A s 1 p x
A s 2 x : = = 3 3 "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 4 . 6 7 1 0 4 "c m 4
s s 1 p x
e o y l o 0 . 0 1 "f c d
e y : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 1 . 2 1 8
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 5 . 2 0 3 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 2 6 8
N R d y z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 1 . 0 0 4 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 y : = e t o t y + 0 . 5 "h s - a 1 = 1 . 2 7 m
e s 2 y : = e t o t y - 0 . 5 "h s + a 2 = 0 . 7 3 8 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 y
B : = 1 - = - 1 . 1 4 8
d y
A s 1 x "e s 1 y "f y d
s 1 : = = 0 . 3 8 8
b s "d y 2 "f c d
A s 2 x "e s 2 y "f y d
s 2 : = = 0 . 2 2 5
b s "d y 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 y > d y - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 3 4
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d y
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - y
f y d "A s 1 x " - a 2
( d )
y
N R d y : = = 9 9 9 . 4 5 5 "k N
e s 2 y
N R d y - N R d y z
= 9 . 1 4 "%
N R d y z
6 . 5 . 2 . 2 . 1 W p Ba s z c z y zn i e z - x
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d x z : = 1 . 1 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p y : = 8 4 c m 2
A s 1 p y
A s 1 y : = = 4 2 "c m 2
2
A s 1 p y
A s 2 y : = = 4 2 "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 5 . 9 4 4 1 0 4 "c m 4
s s 1 p y
e o x l o 0 . 0 1 "f c d
e : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 1 . 5 0 4
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 6 . 2 5 6 1 0 3 "k N
2 "k l t 0 . 1 + e
l o 2
1
: = = 1 . 2 1 3
N R d x z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 1 . 1 8 6 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 x : = e t o t x + 0 . 5 "b s - a 1 = 1 . 4 5 2 m
e s 2 x : = e t o t x - 0 . 5 "b s + a 2 = 0 . 9 2 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 x
B : = 1 - = - 1 . 4 5 7
d x
A s 1 y "e s 1 x "f y d
s 1 : = = 0 . 5 6 4
h s "d x 2 "f c d
A s 2 y "e s 2 x "f y d
s 2 : = = 0 . 3 5 8
h s "d x 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 x > d x - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 3 6
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d x
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - x
f y d "A s 1 y " - a 2
( d )
x
N R d x : = = 1 . 0 2 1 0 3 "k N
e s 2 x
N R d x - N R d x z
= 7 . 3 0 6 "%
N R d x z
6 . 5 . 2 . 2 . 3 N o [n o [ N R d 0
" 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 [c i s k a n e g o
2
N R d o : = f c d "b s "h s + 2 "A s 1 x + 2 " A s 1 y - 4 "" "f y d = 1 . 2 6 8 1 0 4 "k N
4
1
= 5 2 5 . 6 4 4 "k N
1 1 1
+ -
N R d x N R d y N R d o
O k r e [l e n i e w s p Bc z y n n i k a m n
"
e x b s
w a r u n e k s p e Bn i o n y
0 . 5 < " < 2 = 1
e y h s
N m a x 3 1
w a r u n e k n i e s p e Bn i o n y
0 . 1 5 < < 0 . 5 = 0
f c d "b s "h s
m n : = 1
m n "N m a x 3 1 = 5 0 9 . 7 1 2 "k N
" S p r a w d z e n i e w a r u n k u n o [n o [c i
1
w a r u n e k z o s t a B s p e Bn i o n y
m n "N m a x 3 1 < = 1
1 1 1
+ -
N R d x N R d y N R d o
" S p r a w d z e n i e s t o p n i a z b r o j e n i a
2
A s 1 x "2 + A s 1 y "2 - 4 ""
4
s : = = 2 . 9 6 7 "%
b s "h s
m n "N m a x 3 1
= 0 . 9 7
1
1 1 1
+ -
N R d y N R d x N R d o
W y k o r z y s t a n o 9 7 , 0 % n o [n o [c i s Bu p a .
6 . 5 . 3 K o m b i n a c j a 3 - p r z y p a d e k 2
6 . 5 . 3 . 1 Z b r o j e n i e n a [c i s k a n i e
6 . 5 . 3 . 1 . 1 W p Ba s z c z y zn i e z - y
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
h s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a y 1 : = " + = 0 . 0 2 4 m
6 0 0 n
h s
e a y 2 : = = 0 . 0 2 2 m
3 0
e a y 3 : = 0 . 0 1 m
e a y : = m a x , e a y 2 , e a y 3 = 0 . 0 2 4 m
( e )
a y 1
" M i m o [r o d k o n s t r u k c y j n y
M x D 3 2
e e y : = = 0 . 5 0 3 "m
N m a x 3 2
" M i m o [r o d p o c z t k o w y
e o y : = e a y + e e y = 0 . 5 2 7 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 3 2 = 3 8 8 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 3 2 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
( )
A s 1 p : = 1 8 " 1 0 - 4 m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 1 . 2 7 4 1 0 - 4 m 4
s s 1 p
e o y l o
1
e y : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 0 . 8 1 1
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 2 . 3 8 1 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 1 9 5
N m a x 3 2
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 0 . 6 3 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 3 2
e f f : = = 0 . 0 5 1
f c d "b s "d y
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
e f f e" = 0
w a r u n e k n i e s p e Bn i o n y
d y
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 y : = d y - 0 . 5 "h s + e t o t y = 0 . 8 9 6 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 3 2 " - d y + 0 . 5 "x e f f
( e )
s 1 y
A s 1 x : = = 6 . 3 3 2 "c m 2
f y d " - a 2
( d )
y
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 x : = A s 1 x = 6 . 3 3 2 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
A s x : = A s 1 x + A s 2 x = 1 2 . 6 6 3 "c m 2
" Z b r o j e n i e m i n i m a l n e
N m a x 3 2
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 1 4 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k s p e Bn i o n y
A s x e" A s m i n = 0
w a r u n e k s p e Bn i o n y
A s x d" A s . m a x = 1
A s x - A s . z a B
= 1 0 . 5 5 6 "%
A s x
A s x - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s x
" P r z y j t e z b r o j e n i e
z b r o j e n i e r o z c i g a n e ( )
A s 1 x : = 7 " 1 0 - 4 m 2
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 x : = 7 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y x : = A s 1 x + A s 2 x = 1 4 "c m 2
6 . 5 . 3 . 1 . 2 W p Ba s z c z y zn i e z - x
" W y z n a c z e n i e d Bu g o [c i o b l i c z e n i o w e j s Bu p a
L c o l : = 7 . 1 m
: = 2
l o : = "L c o l = 1 4 . 2 m
" W a r u n e k s m u k Bo [c i
l o
> 7
= 2 1 . 8 4 6 - s Bu p s m u k By
b s
" M i m o [r o d n i e z a m i e r z o n y
n : = 1
L c o l 1
1
e a x 1 : = " + = 0 . 0 2 4 m
6 0 0 n
b s
e a x 2 : = = 0 . 0 2 2 m
3 0
e a x 3 : = 0 . 0 1 m
e a x : = m a x , e a x 2 , e a x 3 = 0 . 0 2 4 m
( e )
a x 1
" M i m o [r o d k o n s t r u k c y j n y
M y D 3 2
e e x : = = 1 . 2 5 1 "m
N m a x 3 2
" M i m o [r o d p o c z t k o w y
e o x : = e a x + e e x = 1 . 2 7 5 m
" U w z g l e d n i e n i e s m u k Bo [c i
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
t 0 : = 2 8
w i l g o t n o [ w z g l d n a p o w i e t r z a
R H : = 8 0 %
p o l e p r z e k r o j u e l e m e n t u
A c s = 0 . 4 2 3 "m 2
o b w d p r z e k r o j u p o d d a n y d z i a Ba n i u p o w i e t r z a
u : = 2 "b s + 2 "h s = 2 . 6 "m
A c s
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 e l e m e n t u
h o : = 2 " = 3 2 5 "m m
u
k o Dc o w y w s p Bc z y n n i k p e Bz a n i a
: = 1 . 7 7
( ", t )
0
s i Ba p o d Bu \n a w y w o Ba n a d z i a Ba n i e m d Bu g o t r w a Be j c z [c i o b c i a \e D
N s d . l t : = N m a x 3 2 = 3 8 8 . 7 1 2 "k N
N s d . l t
k l t : = 1 + 0 . 5 " " = 1 . 8 8 5
( ", t )
N m a x 3 2 0
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p : = 2 5 c m 2
m o m e n t b e z w Ba d n o [c i p r z y j t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 1 . 7 6 9 1 0 - 4 m 4
s s 1 p
e o x l o
1
e x : = m a x , 0 . 5 - 0 . 0 1 " - 0 . 0 1 "f c d " , 0 . 0 5 = 1 . 9 6 1
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 2 . 4 4 3 1 0 3 "k N
2 "k l t 0 . 1 + e x
l o 2
1
: = = 1 . 1 8 9
N m a x 3 2
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 1 . 5 1 6 m
" O b l i c z e n i e p o l a p r z e k r o j u z b r o j e n i a
N m a x 3 2
e f f : = = 0 . 0 5 1
f c d "h s "d x
w a r u n e k s p e Bn i o n y
e f f d" e f f . l i m = 1
2 "a 2
w a r u n e k n i e s p e Bn i o n y
e f f e" = 0
d x
w y s o k o [ s t r e f y [c i s k a n e j
x e f f : = 2 "a 2 = 0 . 1 1 8 m
r a m i e s i By [c i s k a j c e j
e s 1 x : = d x - 0 . 5 "b s + e t o t x = 1 . 7 8 2 m
" O b l i c z e n i o w e p o l e z b r o j e n i a r o z c i g a n e g o
N m a x 3 2 " - d x + 0 . 5 "x e f f
( e )
s 1 x
A s 1 y : = = 2 1 . 7 4 4 "c m 2
f y d " - a 2
( d )
x
p o l e z b r o j e n i a o b l i c z e n i o w e m n i e j r o z c i g a n e g o
A s 2 y : = A s 1 y = 2 1 . 7 4 4 "c m 2
A s y : = A s 1 y + A s 2 y = 4 3 . 4 8 9 "c m 2
c a Bk o w i t e p o l e z b r o j e n i a s Bu p a
" Z b r o j e n i e m i n i m a l n e
N m a x 3 2
A s m i n : = m a x = 1 2 . 6 7 5 "c m 2
0 . 1 5 " f y d , 0 . 0 0 3 "A c
" Z b r o j e n i e m a k s y m a l n e
A s . m a x : = 4 % "b s "h s = 1 6 9 "c m 2
" Z b r o j e n i e z a Bo \o n e
A s . z a B : = 4 4 "c m 2
" S p r a w d z e n i e w a r u n k w
w a r u n e k n i e s p e Bn i o n y
A s y e" A s m i n = 1
w a r u n e k s p e Bn i o n y
A s y d" A s . m a x = 1
A s y - A s . z a B
= 1 . 1 7 5 "%
A s y
A s y - A s . z a B
w a r u n e k s p e Bn i o n y
d" 2 0 % = 1
A s y
" P r z y j t e z b r o j e n i e
( )
A s 1 y : = 2 2 " 1 0 - 4 m 2
z b r o j e n i e r o z c i g a n e
z b r o j e n i e m n i e j r o z c i g a n e ( [c i s k a n e ) ( )
A s 2 y : = 2 2 " 1 0 - 4 m 2
p o l e p r z e k r o j u z b r o j e n i a
A s . y : = A s 1 y + A s 2 y = 4 4 "c m 2
6 . 5 . 3 . 2 N o [n o [
6 . 5 . 3 . 2 . 1 W p Ba s z c z y zn i e z - y
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d y z : = 0 . 9 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p x : = 3 6 c m 2
A s 1 p x
A s 1 x : = = 1 8 "c m 2
2
A s 1 p x
A s 2 x : = = 1 8 "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "h - a 1 ) 2 "A = 2 . 5 4 7 1 0 4 "c m 4
s s 1 p x
e o y l o 0 . 0 1 "f c d
e y : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 0 . 8 1 1
h s h s 1 M P a
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 b e t o n o w e g o
b s "h s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 3 . 5 1 8 1 0 3 "k N
2 "k l t 0 . 1 + e y
l o 2
1
: = = 1 . 3 4 4
N R d y z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t y : = "e o y = 0 . 7 0 8 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 y : = e t o t y + 0 . 5 "h s - a 1 = 0 . 9 7 4 m
e s 2 y : = e t o t y - 0 . 5 "h s + a 2 = 0 . 4 4 2 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 y
B : = 1 - = - 0 . 6 4 9
d y
A s 1 x "e s 1 y "f y d
s 1 : = = 0 . 1 6 2
b s "d y 2 "f c d
A s 2 x "e s 2 y "f y d
s 2 : = = 0 . 0 7 4
b s "d y 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 y > d y - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 2 5
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d y
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - y
f y d "A s 1 x " - a 2
( d )
y
N R d y : = = 9 0 9 . 2 7 3 "k N
e s 2 y
N R d y - N R d y z
= 1 . 0 3 "%
N R d y z
6 . 5 . 3 . 2 . 1 W p Ba s z c z y zn i e z - x
" Z a k Ba d a m y n o [n o [ s Bu p a
N R d x z : = 0 . 8 "1 0 3 k N
" O b l i c z e n i e r z e c z y w i s t e j n o [n o [c i s Bu p a
p r z y j t o p o w i e r z c h n i e z b r o j e n i a
A s 1 p y : = 8 4 c m 2
A s 1 p y
A s 1 y : = = "c m 2
2
A s 1 p y
A s 2 y : = = "c m 2
2
m o m e n t b e z w Ba d n o [c i r z e c z y w i s t e g o z b r o j e n i a
I s : =
( 0 . 5 "b - a 1 ) 2 "A = 5 . 9 4 4 1 0 4 "c m 4
s s 1 p y
e o x l o 0 . 0 1 "f c d
e : = m a x , 0 . 5 - 0 . 0 1 " - , 0 . 0 5 = 1 . 9 6 1
b s b s 1 M P a
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 b e t o n o w e g o
h s "b s 3
I c : = = 0 . 0 1 5 m 4
1 2
E c m "I c 0 . 1 1
9
N c r i t : = " + 0 . 1 + E s "I s = 6 . 1 7 1 0 3 "k N
2 "k l t 0 . 1 + e
l o 2
1
: = = 1 . 1 4 9
N R d x z
1 -
N c r i t
" M i m o [r d c a Bk o w i t y
e t o t x : = "e o x = 1 . 4 6 5 m
" O b l i c z e n i e w a r t o [c i N . R d y
e s 1 x : = e t o t x + 0 . 5 "b s - a 1 = 1 . 7 3 1 m
e s 2 x : = e t o t x - 0 . 5 "b s + a 2 = 1 . 1 9 9 m
- w s p Bc z y n n i k i p o m o c n i c z e
e s 1 x
B : = 1 - = - 1 . 9 2 8
d x
A s 1 y "e s 1 x "f y d
s 1 : = = 0 . 6 7 2
h s "d x 2 "f c d
A s 2 y "e s 2 x "f y d
s 2 : = = 0 . 4 6 6
h s "d x 2 "f c d
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e s 1 x > d x - a 2 = 1
e f f : = B + B 2 + 2 " - s 2 = 0 . 1 0 4
( )
s 1
- s p r a w d z e n i e w a r u n k u
w a r u n e k s p e Bn i o n y
e f f < e f f . l i m = 1
"
2 "a 2
w a r u n e k s p e Bn i o n y
e f f < = 1
d x
" N o [n o [ s Bu p a w p Ba s z c z y zn i e z - x
f y d "A s 1 y " - a 2
( d )
x
N R d x : = = 7 8 2 . 9 1 3 "k N
e s 2 x
N R d x - N R d x z
= 2 . 1 3 6 "%
N R d x z
6 . 5 . 3 . 2 . 3 N o [n o [ N R d 0
" 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 [c i s k a n e g o
2
N R d o : = f c d "b s "h s + 2 "A s 1 x + 2 " A s 1 y - 4 "" "f y d = 1 . 1 4 2 1 0 4 "k N
4
1
= 4 3 6 . 7 7 6 "k N
1 1 1
+ -
N R d x N R d y N R d o
O k r e [l e n i e w s p Bc z y n n i k a m n
"
e x b s
w a r u n e k n i e s p e Bn i o n y
0 . 5 < " < 2 = 0
e y h s
N m a x 3 2
w a r u n e k n i e s p e Bn i o n y
0 . 1 5 < < 0 . 5 = 0
f c d "b s "h s
m n : = 1
m n "N m a x 3 2 = 3 8 8 . 7 1 2 "k N
" S p r a w d z e n i e w a r u n k u n o [n o [c i
1
w a r u n e k z o s t a B s p e Bn i o n y
m n "N m a x 3 2 < = 1
1 1 1
+ -
N R d x N R d y N R d o
" S p r a w d z e n i e s t o p n i a z b r o j e n i a
2
A s 1 x "2 + A s 1 y "2 - 4 ""
4
s : = = 2 . 2 5 7 "%
b s "h s
m n "N m a x 3 2
= 0 . 8 9
1
1 1 1
+ -
N R d y N R d x N R d o
W y k o r z y s t a n o 8 9 , 0 % n o [n o [c i s Bu p a .
6 . 5 . 4 K o m b i n a c j a 4
6 . 5 . 1 . 1 Z b r o j e n i e n a [c i s k a n i e p r z y j e d n o c z e s n y m s k r c a n i u
- m o m e n t s k c a j c y s Bu p
M z m a x 4 = 1 4 1 . 3 7 2 "k N m
- s i Ba p o p r z e c z n a s Bu p a
V y D 4 = 2 6 . 1 8 "k N
- s i Ba [c i s k a j c a s Bu p
N m a x 1 = 6 3 0 . 7 1 2 "k N
" N o [n o [ V R d 2
- [r e d n i e n a p r \e n i e [c i s k a j c e w b e t o n i e
N m a x 1
c p : = = 1 . 4 9 3 "M P a
A c
c p d" 0 . 2 5 f c d = 1
c p
- w s p Bc z y n n i k
c : = + = 1 . 0 7 5
1 f c d
- k t n a c h y l e n i a k r z y \u l c w b e t o n o w y c h
: = 2 6 . 6 d e g c o t ( ) = 1 . 9 9 7
w a r u n e k s p e Bn i o n y
1 d" c o t ( ) d" 2 = 1
- r a m i e s i B w e w n t r z y c h
z : = 0 . 9 d y = 0 . 5 3 2 m
f c k
- w s p Bc z y n n i k
: = 0 . 6 "1 - = 0 . 5 2 8
2 5 0 "M P a
- n o [n o [ o b l i c z e n i o w a n a [c i n a n i e z e w z g l g u n a [c i s k a n i e b e t o n u
z b r o j e n i e n a [c i n a n i e w y Bc z n i e z e s t r z e m i o n p r o s t o p a d By c h d o o s i e l e m e n t u
c o t ( )
V R d 2 : = "f c d "b s "z " = 1 . 4 6 2 1 0 3 "k N
1 + c o t ( ) 2
V R d 2 . r : = c "V R d 2 = 1 . 5 7 1 1 0 6 N
" N o [n o [ T R d 1
- c a Bk o w i t a p o w i e r z c h n i a p r z e k r o j u e l e m e n t u z a w a r t e g o w e w n t r z o b w o d u u
A : = b s "h s = 0 . 4 2 3 m 2
- o b w d z e w n t r z n y p r z e k r o j u
u : = 2 " + h s = 2 . 6 m
( b )
s
A
- g r u b o [ z a s t p c z a [c i a n k i p r z e k r o j u
t z a s : = = 0 . 1 6 3 m
u
- m i n i m a l n a g r u b o [ z a s t p c z a [c i a n k i p r z e k r o j u
t : = 2 "C n o m = 0 . 0 7 m
A
w a r u n e k s p e Bn i o n y
e" t z a s > t = 1
u
- p o l e p r z e k r o j u d l a t . z a s
A k : = - t z a s s - t z a s = 0 . 2 3 8 m 2
( b ) "( h )
s
- o b w d r d z e n i a
u k : = 2 " - t z a s + - t z a s = 1 . 9 5 m
( b ) ( h )
s s
- n o [n o [ o b l i c z e n i o w a n a s k r c a n i e
c o t ( ) + c o t ( 9 0 d e g )
T R d 1 : = 2 ""f c d "t z a s "A k " = 3 2 6 . 5 5 3 "k N m
1 + c o t ( ) 2
" W a r u n e k o g r a n i c z a j c y
M z m a x 4 2 V y D 4 2
w a r u n e k s p e Bn i o n y
+ d" 1 = 1
T R d 1 V R d 2 . r
" O b l i c z e n i e r o z t a w u s t r z e m i o n n a s k r c a n i e
- p o l e p r z e k r o j u j e d n e j g a Bz i s t r z e m i e n i a 2 r a m i e n n e g o
s 2
a s g : = " = 0 . 7 8 5 "c m 2
4
f y w d : = f y d s = 2 1 0 "M P a
- r o z t a w s z t r z e m i o n p r z y s k r c a n i u
a s g "f y w d
s t : = 2 "A k " "c o t ( ) = 0 . 1 1 1 m
M z m a x 4
- p r z y j t y r o z t a w s t r z e m i o n - z b r o j e n i e k o n s t r u k c y j n e
s 1 : = m i n , 4 0 "c m , b s , h s = 2 8 "c m
( 1 0 " )
- p o l e p r z e k r o j u s t r z e m i o n
s 2
A s w : = 2 " = 1 . 5 7 1 "c m 2
4
" p r z y j t o r o z t a w s t r z e m i o n
s V : = 1 1 "c m
s V < s t = 1
A s w
w : = = 2 . 4 5 7 1 0 - 3
s V "h s "s i n ( 9 0 )
0 . 0 8 " f c k "M P a
w . m i n : = = 1 . 8 2 6 1 0 - 3 w > w . m i n = 1
f y k s
w a r u n e k s p e Bn i o n y
" O b l i c z e n i e 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
- n o [n o [ o b l i c z e n i o w a n a s k r c a n i e z u w a g i n a z b r o j e n i e
T R d 2 : = M z m a x 4 = 1 4 1 . 3 7 2 "k N m
- p o l e z b r o j e n i a p o d Bu z n e g o n a s k r c a n i e
T R d 2 "u k
A s l : = "c o t ( ) = 2 7 . 5 7 6 "c m 2
2 "A k "f y d
P r z y j t o 2 8 c m 2 r o z m i e s z c z o n e r w n o m i e r n i e p o o b w o d z i e s Bu p a .
p o l e z b r o j e n i a p o d Bu z n e g o s Bu p a n a s k r c a n i e
A s l . p r o v : = 2 8 c m 2
w a r u n e k s p e Bn i o n y
A s m i n d" A s l . p r o v e" A s l = 1
6 . 5 . 5 K o m b i n a c j a 5
6 . 5 . 5 . 1 Z b r o j e n i e n a [c i s k a n i e p r z y j e d n o c z e s n y m s k r c a n i u
- m o m e n t s k c a j c y s Bu p
M z o d p 5 = 2 6 . 1 8 "k N m
- s i Ba p o p r z e c z n a s Bu p a
V y D 5 = 7 8 . 5 4 "k N
- s i Ba [c i s k a j c a s Bu p
N m a x 1 = 6 3 0 . 7 1 2 "k N
" N o [n o [ V R d 2
- [r e d n i e n a p r \e n i e [c i s k a j c e w b e t o n i e
N m a x 1
c p : = = 1 . 4 9 3 "M P a
A c
c p d" 0 . 2 5 f c d = 1
c p
- w s p Bc z y n n i k
c : = + = 1 . 0 7 5
1 f c d
- k t n a c h y l e n i a k r z y \u l c w b e t o n o w y c h
: = 2 6 . 6 d e g c o t ( ) = 1 . 9 9 7
w a r u n e k s p e Bn i o n y
1 d" c o t ( ) d" 2 = 1
- r a m i e s i B w e w n t r z y c h
z : = 0 . 9 d y = 0 . 5 3 2 m
f c k
- w s p Bc z y n n i k
: = 0 . 6 "1 - = 0 . 5 2 8
2 5 0 "M P a
- n o [n o [ o b l i c z e n i o w a n a [c i n a n i e z e w z g l g u n a [c i s k a n i e b e t o n u
z b r o j e n i e n a [c i n a n i e w y Bc z n i e z e s t r z e m i o n p r o s t o p a d By c h d o o s i e l e m e n t u
c o t ( )
V R d 2 : = "f c d "b s "z " = 1 . 4 6 2 1 0 3 "k N
1 + c o t ( ) 2
V R d 2 . r : = c "V R d 2 = 1 . 5 7 1 1 0 6 N
" N o [n o [ T R d 1
- c a Bk o w i t a p o w i e r z c h n i a p r z e k r o j u e l e m e n t u z a w a r t e g o w e w n t r z o b w o d u u
A : = b s "h s = 0 . 4 2 3 m 2
- o b w d z e w n t r z n y p r z e k r o j u
u : = 2 " + h s = 2 . 6 m
( b )
s
A
- g r u b o [ z a s t p c z a [c i a n k i p r z e k r o j u
t z a s : = = 0 . 1 6 3 m
u
- m i n i m a l n a g r u b o [ z a s t p c z a [c i a n k i p r z e k r o j u
t : = 2 "C n o m = 0 . 0 7 m
A
w a r u n e k s p e Bn i o n y
e" t z a s > t = 1
u
- p o l e p r z e k r o j u d l a t . z a s
A k : = - t z a s s - t z a s = 0 . 2 3 8 m 2
( b ) "( h )
s
- o b w d r d z e n i a
u k : = 2 " - t z a s + - t z a s = 1 . 9 5 m
( b ) ( h )
s s
- n o [n o [ o b l i c z e n i o w a n a s k r c a n i e
c o t ( ) + c o t ( 9 0 d e g )
T R d 1 : = 2 ""f c d "t z a s "A k " = 3 2 6 . 5 5 3 "k N m
1 + c o t ( ) 2
" W a r u n e k o g r a n i c z a j c y
M z o d p 5 2 V y D 5 2
w a r u n e k s p e Bn i o n y
+ d" 1 = 1
T R d 1 V R d 2 . r
" O b l i c z e n i e r o z t a w u s t r z e m i o n n a s k r c a n i e
- p o l e p r z e k r o j u j e d n e j g a Bz i s t r z e m i e n i a 2 r a m i e n n e g o
s 2
a s g : = " = 0 . 7 8 5 "c m 2
4
f y w d : = f y d s = 2 1 0 "M P a
- r o z t a w s z t r z e m i o n p r z y s k r c a n i u
a s g "f y w d
s t : = 2 "A k " "c o t ( ) = 0 . 5 9 8 m
M z o d p 5
- p r z y j t y r o z t a w s t r z e m i o n - z b r o j e n i e k o n s t r u k c y j n e
s 1 : = m i n , 4 0 "c m , b s , h s = 2 8 "c m
( 1 0 " )
- p o l e p r z e k r o j u s t r z e m i o n
s 2
A s w : = 2 " = 1 . 5 7 1 "c m 2
4
s V : = 1 1 "c m
" p r z y j t o r o z t a w s t r z e m i o n
s V < s t = 1
A s w
w : = = 2 . 4 5 7 1 0 - 3
s V "h s "s i n ( 9 0 )
0 . 0 8 " f c k "M P a
w . m i n : = = 1 . 8 2 6 1 0 - 3 w > w . m i n = 1
f y k s
w a r u n e k s p e Bn i o n y
" O b l i c z e n i e 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
- n o [n o [ o b l i c z e n i o w a n a s k r c a n i e z u w a g i n a z b r o j e n i e
T R d 2 : = M z o d p 5 = 2 6 . 1 8 "k N m
- p o l e z b r o j e n i a p o d Bu z n e g o n a s k r c a n i e
T R d 2 "u k
A s l : = "c o t ( ) = 5 . 1 0 7 "c m 2
2 "A k "f y d
P r z y j t o 1 6 c m 2 r o z m i e s z c z o n e r w n o m i e r n i e p o o b w o d z i e s Bu p a .
p o l e z b r o j e n i a p o d Bu z n e g o s Bu p a n a s k r c a n i e
A s l . p r o v : = 1 6 "c m 2
d" e" =
w a r u n e k s p e Bn i o n y
A s m i n d" A s l . p r o v e" A s l = 1
O S T A T E C Z N I E P R Z Y J T O Z B R O J E N I E P O P R Z E C Z N E W S AU P I E
A . s x = 5 5 , 4 2 c m 2 _ 9 f i 2 8
A . s y = 4 9 , 2 6 c m 2 _ 8 f i 2 8
7 . W Y M I A R O W A N I E S T O P Y F U N D A M E N T O W E J
7 . 1 Z A AO [E N I A
" G Bb o k o [ p o s a d o w i e n i a
D : = 1 . 5 "m
" W y m i a r y p r z e k r o j u
- s z e r o k o [ s t o p y
B : = 4 . 0 "m
- d Bu g o [ s t o p y
L : = 5 . 2 "m
- w y s o k o [ s t o p y
h f : = 1 "m
" P r z y j t a [r e d n i c a z b r o j e n i a
: = 2 8 "m m
" G r u b o [ o t u l e n i a
c m i n : = 4 0 "m m
"c : = 1 0 "m m
c n o m : = c m i n + "c = 5 0 "m m
" D Bu g o [ z a k o t w i e n i a i z a k Ba d u p r t w w s t o p i e
- p o w i e r z c h n i a z b r o j e n i a o b l i c z o n a
A s r e q : = 2 0 8 "c m 2
- p o w i e r z c h n i a z b r o j e n i a p r z y j t a
A s p r o v : = 2 0 9 . 3 6 "c m 2
- w s p Bc z y n n i k u w z g l d n i a j c y e f e k t y w n o [ a : = 1 . 0
z a k o t w i e n i a
f b d : = 3 . 0 M P a
- g r a n i c a p r z y c z e p n o [c i
- p o d s t a w o w a d Bu g o [ z a k o t w i e n i a
f y d
l b : = " = 0 . 9 8 m
4 f b d
- m i n i m a l n a d Bu g o [ z a k o t w i e n i a
l b m i n 1 : = 0 . 6 l b = 0 . 5 8 8 m
l b m i n 2 : = 1 0 " = 0 . 2 8 m
l b m i n 3 : = 1 0 0 "m m
l b m i n : = m a x = 0 . 5 8 8 m
( l , l b m i n 2 , l b m i n 3 )
b m i n 1
A s r e q
l b d : = a "l b " = 0 . 9 7 4 m
A s p r o v
w a r u n e k s p e Bn i o n y
l b d > l b m i n = 1
- w s p Bc z y n n i k
1 : = 1 . 0
- d Bu g o [ z a k Ba d u p r e t w
l s : = l b d "1 = 0 . 9 7 4 m
: = " " =
- m i n i m a l n a d Bu g o [ z a k Ba d u
l s m i n : = 0 . 3 a "1 "l b = 0 . 2 9 4 m
w a r u n e k s p e Bn i o n y
l s m i n e" 2 0 0 "m m = 1
- p r z y j t a d Bu g o [ z a k Ba d u
l s : = 1 0 0 "c m
w a r u n e k s p e Bn i o n y
l s e" l s m i n = 1
7 . 2 Z e s t a w i e n i e o b c i \e D
w a r t o [ c h a r a k t e r y s t y c z n a w a r t o [ o b l i c z e n i o w a
c i e \a r w Ba s n y s t o p y
k N
g 1 k : = 2 5 B "L "h f g 1 d : = 1 . 1 "g 1 k = 5 7 2 "k N
m 3
k N
c i \a r g r u n t u n a d s t o p
g 2 k : = 1 8 - h f - h s "b s g 2 d : = 1 . 2 "g 2 k = 2 2 0 . 0 7 7 "k N
( D ) "( L "B )
m 3
g k : = g 1 k + g 2 k = 7 0 3 . 3 9 8 "k N g d : = g 1 d + g 2 d = 7 9 2 . 0 7 7 "k N
R A Z E M
7 . 3 S P R A W D Z E N I E W A R U N K U N O ZN O ZC I P O D AO [A
7 . 3 . 1 M i m o [r d p o Bo \e n i a [r o d k a c i \k o [c i s Bu p a w z g l d e m [r o d k a c i \k o [c i s t o p y
g r l d g r p d
M e 1 : = P d "a + G d + "a - "b = 6 3 1 . 5 1 3 "k N "m
2 2
g r p d g r l d
M e 2 : = - P d "b - G d + "b + "a = - 3 7 8 . 2 8 7 "k N "m
2 2
N e : = P d + G d + g r l d + g r p d + g s d = 3 3 5 . 4 3 "k N
M e 1
e 1 : = = 1 . 8 8 3 m
N e
M e 2
e 2 : = = - 1 . 1 2 8 m
N e
e 1 - e 2
e s : = = 0 . 3 7 7 m
2
7 . 3 . 2 O b c i \e n i a
7 . 3 . 2 . 1 K o m b i n a c j a I
- s i Ba p i o n o w a w d o l n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
N 1 g : = N m a x 1 + g s d + g 2 d = 9 2 9 . 5 0 7 "k N
N 1 d : = N m a x 1 + g d + g s d = 1 . 5 0 2 1 0 3 "k N
- s i Ba p o z i o m a n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H L 1 : = 0 k N
- s i Ba p o z i o m a n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H B 1 : = V y D 5 = 7 8 . 5 4 "k N
- m o m e n t n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
: = - = "
M B 1 : = - M y D 1 = 2 2 0 . 1 1 3 "k N m
- m o m e n t n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
M L 1 : = M x D 1 = 5 8 7 . 0 8 7 "k N m
7 . 3 . 2 . 2 K o m b i n a c j a I I
- s i Ba p i o n o w a w d o l n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
N 2 g : = 2 "G d + 2 "P d + g r l d + g r p d + g s d + g 2 d = 7 4 2 . 5 0 7 "k N
N 2 d : = 2 "G d + 2 "P d + g r l d + g r p d + g s d + g d = 1 . 3 1 5 1 0 3 "k N
- s i Ba p o z i o m a n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H L 2 : = 0 k N
- s i Ba p o z i o m a n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H B 2 : = 2 "H d = 5 2 . 3 6 "k N
- m o m e n t n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
g r l d g r p d
M B 2 : = P d "a + G d + "a - "b = 6 3 1 . 5 1 3 "k N m
2 2
- m o m e n t n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
M L 2 : = M x D 3 1 = 3 9 1 . 3 9 1 "k N "m
7 . 3 . 2 . 3 K o m b i n a c j a I I I
- s i Ba p i o n o w a w d o l n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
N 3 g : = N 2 g = 7 4 2 . 5 0 7 "k N
N 3 d : = N 2 d = 1 . 3 1 5 1 0 3 "k N
- s i Ba p o z i o m a n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H L 3 : = 0 k N
- s i Ba p o z i o m a n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
H B 3 : = 2 "H d = 5 2 . 3 6 "k N
- m o m e n t n a k i e r u n k u L , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
g r p d g r l d
M B 3 : = - P d "b - G d + "b + "a = - 3 7 8 . 2 8 7 "k N m
2 2
- m o m e n t n a k i e r u n k u B , n a g r n e j p o w i e r z c h n i s t o p y f u n d a m e n o w e j
M L 3 : = 2 "H d "L o b l = 3 9 1 . 3 9 1 "k N "m
7 . 3 . 3 S p r a w d z e n i e c z y w y p a d k o w a o b c i \e D z n a j d u j e s i w r d z e n i u p o d s t a w y
7 . 3 . 3 . 1 K o m b i n a c j a I
- w y m i a r y p r z e k r o j u
- s z e r o k o [ s t o p y
B 1 : = 4 . 0 "m
- d Bu g o [ s t o p y
L 1 : = 5 . 2 "m
- w y s o k o [ s t o p y
h f . 1 : = 1 "m
- m i m o [r d s i By n a k i e r u n k u B
M L 1 + H B 1 "h f . 1
e B 1 : = = 0 . 4 4 3 m
N 1 d
B 1
= 0 . 6 6 7 m
6
B 1
w a r u n e k s p e Bn i o n y
e B 1 < = 1
6
- m i m o [r d s i By n a k i e r u n k u L
- N 1 g "e s
( M + H L 1 "h f . 1 )
B 1
e L 1 : = = - 0 . 0 8 7 "m
N 1 d
L 1
= 0 . 8 6 7 "m
6
L 1
w a r u n e k s p e Bn i o n y
e L 1 < = 1
6
0 , 6
0 , 5
0 , 4
0 , 3
0 , 2
0 , 1
0
0 0 , 2 0 , 4 0 , 6 0 , 8
L / 6
e . L
r d z e D e . L e . B
7 . 3 . 3 . 2 K o m b i n a c j a I I
- w y m i a r y p r z e k r o j u
- s z e r o k o [ s t o p y
B 2 : = 4 . 0 "m
- d Bu g o [ s t o p y
L 2 : = 5 . 2 "m
- w y s o k o [ s t o p y
h f . 2 : = 1 "m
- m i m o [r d s i By n a k i e r u n k u B
M L 2 + H B 2 "h f . 2
e B 2 : = = 0 . 3 3 8 m
N 2 d
B 2
= 0 . 6 6 7 m
6
B 2
w a r u n e k s p e Bn i o n y
e B 2 < = 1
6
- m i m o [r d s i By n a k i e r u n k u L
M B 2 + H L 2 "h f . 2 - N 2 g "e s
e L 2 : = = 0 . 2 6 7 m
N 2 d
e . B
L 2
= 0 . 8 6 7 "m
6
L 2
w a r u n e k s p e Bn i o n y
e L 2 < = 1
6
0 , 6
0 , 5
0 , 4
0 , 3
0 , 2
0 , 1
0
0 0 , 2 0 , 4 0 , 6 0 , 8
L / 6
e . L
r d z e D e . L e . B
7 . 3 . 3 . 3 K o m b i n a c j a I I I
- w y m i a r y p r z e k r o j u
- s z e r o k o [ s t o p y
B 3 : = 4 . 0 "m
- d Bu g o [ s t o p y
L 3 : = 5 . 2 "m
- w y s o k o [ s t o p y
h f . 3 : = 1 "m
- m i m o [r d s i By n a k i e r u n k u B
M L 3 + H B 3 "h f . 3
e B 3 : = = 0 . 3 3 8 m
N 3 d
B 3
= 0 . 6 6 7 m
6
B 3
w a r u n e k s p e Bn i o n y
e B 3 < = 1
6
e . B
- m i m o [r d s i By n a k i e r u n k u L
M B 3 + H L 3 "h f . 3 - N 3 g "e s
e L 3 : = = - 0 . 3 8 9 m
N 3 d
- m i m o [r d s i By p i o n o w e j w p Ba s z c z y zn i e p o d s t a w y s t o p y w z g l d e m [r o d k a
c i e \k o [c i s t o p y
L 3
= 0 . 8 6 7 "m
6
L 3
w a r u n e k s p e Bn i o n y
e L 3 < = 1
6
0 , 6
0 , 5
0 , 4
0 , 3
0 , 2
0 , 1
0
0 0 , 2 0 , 4 0 , 6 0 , 8
L / 6
e . L
r d z e D e . L e . B
7 . 3 . 4 O b l i c z a n i e n a p r z e D k r a w d z i o w y c h
e . B
7 . 3 . 4 . 1 K o m b i n a c j a I
M f L 1 : = M L 1 + H B 1 "h f . 1 = 6 6 5 . 6 2 7 "k N "m
M f B 1 : = M B 1 - e s "N 1 g = - 1 3 0 . 7 4 4 "k N "m
N 1 d M f L 1 M f B 1
q A 1 : = + + = 1 1 2 . 9 3 7 "k P a
B 1 "L 1 B 1 2 "L 1 B 1 "L 1 2
6 6
N 1 d M f L 1 M f B 1
q B 1 : = + - = 1 2 7 . 4 4 3 "k P a
B 1 "L 1 B 1 2 "L 1 B 1 "L 1 2
6 6
N 1 d M f L 1 M f B 1
q C 1 : = - - = 3 1 . 4 3 9 "k P a
B 1 "L 1 B 1 2 "L 1 B 1 "L 1 2
6 6
N 1 d M f L 1 M f B 1
q D 1 : = - + = 1 6 . 9 3 3 "k P a
B 1 "L 1 B 1 2 "L 1 B 1 "L 1 2
6 6
N A P R [E N I A K R A W D Z I O W E
1 4 0
1 2 7 , 9
1 1 2 , 9
1 2 0
1 0 0
8 0
6 0
4 0
3 1 , 4
1 6 , 9
2 0
0
A B C D
7 . 3 . 4 . 2 K o m b i n a c j a I I
M f L 2 : = M L 2 + H B 2 "h f . 2 = 4 4 3 . 7 5 1 "k N "m
M f B 2 : = M B 2 - e s "N 2 g = 3 5 1 . 2 4 2 "k N "m
N 2 d M f L 2 M f B 2
q A 2 : = + + = 1 1 4 . 6 8 3 "k P a
B 2 "L 2 B 2 2 "L 2 B 2 "L 2 2
6 6
N 2 d M f L 2 M f B 2
q B 2 : = + - = 7 5 . 7 1 4 "k P a
B 2 "L 2 B 2 2 "L 2 B 2 "L 2 2
6 6
N 2 d M f L 2 M f B 2
q C 2 : = - - = 1 1 . 7 1 2 "k P a
B 2 "L 2 B 2 2 "L 2 B 2 "L 2 2
6 6
N 2 d M f L 2 M f B 2
q D 2 : = - + = 5 0 . 6 8 1 "k P a
B 2 "L 2 B 2 2 "L 2 B 2 "L 2 2
6 6
q [ k P a ]
N A P R [E N I A K R A W D Z I O W E
1 4 0
1 1 4 , 7
1 2 0
1 0 0
7 5 , 7
8 0
6 0 5 0 , 7
4 0
1 1 , 7
2 0
0
A B C D
7 . 3 . 4 . 3 K o m b i n a c j a I I I
M f L 3 : = M L 3 + H B 3 "h f . 3 = 4 4 3 . 7 5 1 "k N "m
M f B 3 : = M B 3 - e s "N 3 g = - 6 5 8 . 5 5 8 "k N "m
N 3 d M f L 3 M f B 3
q A 3 : = + + = 5 8 . 6 6 6 "k P a
B 3 "L 3 B 3 2 "L 3 B 3 "L 3 2
6 6
N 3 d M f L 3 M f B 3
q B 3 : = + - = 1 3 1 . 7 3 1 "k P a
B 3 "L 3 B 3 2 "L 3 B 3 "L 3 2
6 6
N 3 d M f L 3 M f B 3
q C 3 : = - - = 6 7 . 7 2 9 "k P a
B 3 "L 3 B 3 2 "L 3 B 3 "L 3 2
6 6
N 3 d M f L 3 M f B 3
q D 3 : = - + = - 5 . 3 3 6 "k P a
B 3 "L 3 B 3 2 "L 3 B 3 "L 3 2
6 6
q [ k P a ]
N A P R [E N I A K R A W D Z I O W E
1 4 0
1 3 1 , 7
1 2 0
1 0 0
8 0 5 8 , 7
6 7 , 7
6 0
4 0
2 0
- 5 , 3
0
A B C D
- 2 0
7 . 3 . 5 S p r a w d z e n i e I s t a n u g r a n i c z n e g o
7 . 3 . 5 . 1 K o m b i n a c j a I
- n a p r \e n i e m a k s y m a l n e d o p u s z c z a l n e
q f : = 1 9 0 "k P a
- w s p Bc z y n n i k k o r e k c y j n y
m : = 0 . 9
- j e d n o s t k o w y o p r p o d Bo \a
N 1 d
q s : = d" m "q f = 1
B 1 "L 1
q m a x : = m a x = 1 2 7 . 4 4 3 "k P a
( q )
A 1 , q B 1 , q C 1 , q D 1
q m a x d" 1 . 2 "m "q f = 1
7 . 3 . 5 . 2 K o m b i n a c j a I I
- n a p r \e n i e m a k s y m a l n e d o p u s z c z a l n e
q f : = 1 9 0 "k P a
- w s p Bc z y n n i k k o r e k c y j n y
m : = 0 . 9
- j e d n o s t k o w y o p r p o d Bo \a
N 2 d
q s : = d" m "q f = 1
B 2 "L 2
q m a x : = m a x = 1 1 4 . 6 8 3 "k P a
( q )
A 2 , q B 2 , q C 2 , q D 2
q [ k P a ]
q m a x d" 1 . 2 "m "q f = 1
7 . 3 . 5 . 3 K o m b i n a c j a I I I
- n a p r \e n i e m a k s y m a l n e d o p u s z c z a l n e
q f : = 1 9 0 "k P a
- w s p Bc z y n n i k k o r e k c y j n y
m : = 0 . 9
- j e d n o s t k o w y o p r p o d Bo \a
N 3 d
q s : = d" m "q f = 1
B 3 "L 3
q m a x : = m a x = 1 3 1 . 7 3 1 "k P a
( q )
A 3 , q B 3 , q C 3 , q D 3
q m a x d" 1 . 2 "m "q f = 1
7 . 4 W Y M I A R O W A N I E S T O P Y F U N D A M E N T O W E J N A Z G I N A N I E
- m e t o d w s p o r n i k w p r o s t o k t n y c h
P r z y j t o z b r o j e n i e :
2
: = 1 6 m m A : = A = 2 . 0 1 1 "c m 2
4
d x : = h f - c n o m - d x = 9 4 . 2 "c m
2
7 . 4 . 1 K o m b i n a c j a I
" z b r o j e n i e n a k i e r u n e k L
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "B 1 "d x " = 5 6 . 8 2 1 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "B 1 "d x = 4 8 . 9 8 4 "c m 2
A s . m i n : = m a x = 5 6 . 8 2 1 "c m 2
( A , A s . m i n 2 )
s . m i n 1
k g
q s L 1 : = q A 1 "B 1 = 4 . 5 1 7 1 0 5
s 2
L 1 b s 2
+ e s -
2 2
M B 1 : = q s L 1 " = 1 . 5 8 9 1 0 3 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M B 1
n : = n = 2 2 . 1 9 7 n 1 : = 3 0
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s L : = n 1 "A = 6 0 . 3 1 9 "c m 2
A s L > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
B 1 - 2 "c n o m -
r 1 : = = 1 2 . 9 4 7 "c m
n 1
" z b r o j e n i e n a k i e r u n e k B
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "L 1 "d x " = 7 3 . 8 6 8 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "L 1 "d x = 6 3 . 6 7 9 "c m 2
A s . m i n : = m a x = 7 3 . 8 6 8 "c m 2
( A , A s . m i n 2 )
s . m i n 1
q A 1 + q B 1
k g
q s B 1 : = "L 1 = 6 . 2 5 1 0 5
2
s 2
B 1 h s 2
-
2 2
M L 1 : = "q s B 1 = 8 7 6 . 7 3 9 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M L 1
n : = n = 1 2 . 2 4 6 n 1 : = 3 8
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s B : = n 1 "A = 7 6 . 4 0 4 "c m 2
A s B > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
L 1 - 2 "c n o m
r 1 : = = 0 . 1 3 4 m
n 1
7 . 4 . 2 K o m b i n a c j a I I
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "B 2 "d x " = 5 6 . 8 2 1 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "B 2 "d x = 4 8 . 9 8 4 "c m 2
A s . m i n : = m a x = 5 6 . 8 2 1 "c m 2
( A , A s . m i n 2 )
s . m i n 1
k g
q s L 2 : = q A 2 "B 2 = 4 . 5 8 7 1 0 5
s 2
L 2 b s 2
+ e s -
2 2
M B 2 : = q s L 2 " = 1 . 6 1 4 1 0 3 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M B 2
n : = n = 2 2 . 5 4 n 1 : = 3 0
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s L : = n 1 "A = 6 0 . 3 1 9 "c m 2
A s L > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
B 2 - 2 "c n o m -
r 2 : = = 1 2 . 9 4 7 "c m
n 1
" z b r o j e n i e n a k i e r u n e k B
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "L 2 "d x " = 7 3 . 8 6 8 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "L 2 "d x = 6 3 . 6 7 9 "c m 2
A s . m i n : = m a x = 7 3 . 8 6 8 "c m 2
( A , A s . m i n 2 )
s . m i n 1
q A 2 + q B 2
k g
q s B 2 : = "L 2 = 4 . 9 5 1 0 5
2
s 2
B 2 h s 2
-
2 2
M L 2 : = "q s B 2 = 6 9 4 . 4 3 9 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M L 2
n : = n = 9 . 7 n 1 : = 3 8
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s B : = n 1 "A = 7 6 . 4 0 4 "c m 2
A s B > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
L 2 - 2 "c n o m
r 2 : = = 0 . 1 3 4 m
n 1
7 . 4 . 3 K o m b i n a c j a I I I
" z b r o j e n i e n a k i e r u n e k L
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "B 3 "d x " = 5 6 . 8 2 1 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "B 3 "d x = 4 8 . 9 8 4 "c m 2
A s . m i n : = m a x = 5 6 . 8 2 1 "c m 2
( A , A s . m i n 2 )
s . m i n 1
k g
q s L 3 : = q B 3 "B 3 = 5 . 2 6 9 1 0 5
s 2
L 3 b s 2
+ e s -
2 2
M B 3 : = q s L 3 " = 1 . 8 5 4 1 0 3 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M B 3
n : = n = 2 5 . 8 9 1 n 1 : = 3 0
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s L : = n 1 "A = 6 0 . 3 1 9 "c m 2
A s L > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
B 3 - 2 "c n o m -
r 3 : = = 1 2 . 9 4 7 "c m
n 1
" z b r o j e n i e n a k i e r u n e k B
- Z b r o j e n i e m i n i m a l n e
f c t m
A s . m i n 1 : = 0 . 2 6 "L 3 "d x " = 7 3 . 8 6 8 "c m 2
f y k
A s . m i n 2 : = 0 . 0 0 1 3 "L 3 "d x = 6 3 . 6 7 9 "c m 2
( )
A s . m i n : = m a x = 7 3 . 8 6 8 "c m 2
( A , A s . m i n 2 )
s . m i n 1
k g
q s B 3 : = q B 3 "L 3 = 6 . 8 5 1 0 5
s 2
B 3 h s 2
-
2 2
M L 3 : = "q s B 3 = 9 6 0 . 9 2 9 m "k N
2
- p o t r z e b n a l i c z b a p r t w :
W s t p n i e p r z y j t o :
M L 3
n : = n = 1 3 . 4 2 2 n 1 : = 3 8
0 . 9 "d x "f y d "A
- p r z y j t o z b r o j e n i e
A s B : = n 1 "A = 7 6 . 4 0 4 "c m 2
A s B > A s . m i n = 1
- r o z s t a w w y n i k a j c y z l i c z b y p r z y j t y c h p r t w :
L 3 - 2 "c n o m
r 3 : = = 0 . 1 3 4 m
n 1
O S T A T E C Z N I E P R Z Y J T O :
- n a k i e r u n k u L : c o 1 3 c m
A s L 3 0 ""1 6
- n a k i e r u n k u B : c o 1 3 c m
A s B 3 8 ""1 6
7 . 5 . S P R A W D Z E N I E S T O P Y N A P R Z E B I C I E
L = 5 . 2 m
- d Bu g o [ s t o p y f u n d a m e n t o w e j
B = 4 m
- s z e r o k o [ s t o p y f u n d a m n e t o w e j
h f = 1 m
- w y s o k o [ s t o p y
h s = 0 . 6 5 m
- w y s o k o [ s Bu p a
b s = 0 . 6 5 m
- s z e r o k o [ s Bu p a
d : = h f - c n o m - - 0 . 5 " = 0 . 9 2 6 m
- w y s o k o [ u \y t e c z n a s t o p y
( ) ( )
- p o l e p o w i e r z c h n i w i e l o k t a
A : = - 0 . 5 "
B "0 . 5 "( L - h s - 2 "d ) ( B - b s - 2 "d ) 2 = 4 . 2 7 4 m 2
b 1 : = h s = 0 . 6 5 m
- m i n i m a l n y z a s i g s t r e f y p r z e b i c i a
b 2 : = b s + 2 "d = 2 . 5 0 2 m
- m a k s y m a l n y z a s i g s t r e f y p r z e b i c i a
b 1 + b 2
- [r e d n i a a r y t m e t y c z a z a s i e g w s t r e f y p r z e b i c i a
b m : = = 1 . 5 7 6 m
2
N 1 d 6 "e 1
- m a k s y m a l n y k r a w d z i o w y o d p r p o d Bo \a
q f m a x : = "1 + = 2 2 9 . 0 0 5 "k P a
B "L L
p o d f u n d a m e n t e m
w a r u n e k s p e Bn i o n y
q f m a x "A d" f c t d "b m "d = 1
K O N I E C O B L I C Z E C
N : = n e w t o n
k N : = 1 0 3 N
k N m : = k N "m
M P a : = 1 0 6 "P a k N : = 1 0 3 "N
M N : = 1 0 6 N
k N : = 1 0 3 N
M P a : = 1 0 6 P a
k N
f c k : =
D a n e d o p r o j e k t u :
m b : = m E : = 1 . 5 "1 0 7
m
M N : = 1 0 6 N
m
M P a : = 1 "1 0 6 P a
g = 9 . 8 0 7
s 2
t : = 1 0 3 "k g
k P a : = 1 0 3 P a
k P a : = 1 0 3 "P a
k N : = 1 0 0 0 N
m 4 = 1 m 4
N : = 1 N
m 2 = 1 m 2
1 0 6 "N
m
M P a : = m = 1 m
N : = k g "
m 2 c m : = 0 . 0 1 "m
s 2
G P a : = 1 0 9 P a
c m 4 = 1 1 0 - 8 m 4
k N
k N m : = k N "m
k P a : =
m 2
N
P a : =
m 2
k g "m
2
s
P a : =
m 2
N R d i : = e f f "h s "d y "f c d + A s 2 "f y d - A s 1 "f y d = "k N
A s 2
N R d i : = e f f "h s "d y "f c d + A s 2 "f y d - A s 1 "f y d = "k N
A s 2
M B 3 : = - 2 3 1 "k N "m
M B 3 : = - 3 7 8 . 2 8 7 "k N "m
k N
m 2
Wyszukiwarka
Podobne podstrony:
Mathcad SŁUP PROJEKT#Mathcad SŁUP PROJEKTMathcad SŁUP PROJEKTMathcad stal projekt 2 RŁ5 OBCIĄŻENIA NAWIERZCHNI PRZEZ RUCH DROGOWY I OKREŚLANIE RUCHU OBLICZENIOWEGO DO PROJEKTOWANIA NAWI3 WYMAGANIA OGÓLNE PROJEKTOWANIA SKRZYŻOWAŃ Kopiaprojekt2 skrypt KopiaMathcad projekt2 xmcdMATHCAD instrukcja uzupelniona KopiaMathcad Projekt metal 3Kopia E1C1S1 proj1 Projekt lpcMathcad projekt 22Mathcad projekt mw calosc od michala do drukuMathcad projekt, zestawienie obciążeńMathcad Projekt4 Elementy węzła drogowego i zasady ich projektowania Kopiawięcej podobnych podstron