ÿþM a t e r i a By d o w i c z e D z o g r z e w n i c t w a
R o z d z i a B d o l n y - o g r z e w a n i e g r a w i t a c y j n e
t z / t p = 9 0 / 7 0 °
= ° C
= °
= °
"Á = 1 2 . 4 7 k g / m 3
"Á =
"Á =
"Á =
Q G l d v R R l £¶ Z R l + Z U w a g i
£¶
£¶
£¶
N r W k g / s m m m m / s P a / m P a P a P a
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
P i o n n r 6
O b i e g p r z e z g r z e j n i k n r 1 w p o m i e s z c z e n i u n r 1 2
"p c z = g Å" "ÁÅ" = 9 . 8 1 Å"1 2 . 4 7 Å" 2 . 9 5 = 3 6 1 P a
" = Å" "ÁÅ"h = Å" Å" =
" = Å" "ÁÅ" = Å" Å" =
" = Å" "ÁÅ" = Å" Å" =
0 . 5 Å" 3 6 1
Å"
Å"
Å"
R o r j = = 7 . 1 P a / m
= =
= =
= =
2 5 . 3
1 6 5 0 0 , 0 0 7 8 2 1 5 0 , 0 4 2 , 3 5 1 7 , 5 1 4 1 9
2 3 6 6 0 0 , 0 4 3 7 1 7 , 2 2 0 0 , 1 2 1 5 2 5 8 1 2 8 9 3 4 7
3 5 3 5 0 0 , 0 6 3 9 3 2 5 0 , 1 2 9 , 5 2 9 7 5 2 8 1
4 1 0 1 2 0 0 , 1 2 0 9 1 , 6 3 2 0 , 1 3 8 , 5 1 4 3 , 5 3 0 4 4
5 2 0 2 4 0 0 , 2 4 1 8 1 , 5 4 0 0 , 1 8 1 5 2 3 3 , 5 6 3 8 6
2 5 , 3 5 7 5 > 3 6 1
£l =
£ =
£ = £ =
£ = £ =
£ =
£ =
1 6 5 0 0 , 0 0 7 8 2 1 5 0 , 0 4 2 , 3 5 1 7 , 5 1 4 1 9
2 3 6 6 0 0 , 0 4 3 7 1 7 , 2 2 5 0 , 0 7 8 4 , 4 7 6 1 2 4 0 1 1 6 S k o r y g o w a n a [r e d n i c a
3 5 3 5 0 0 , 0 6 3 9 3 2 5 0 , 1 2 9 , 5 2 9 7 5 2 8 1
4 1 0 1 2 0 0 , 1 2 0 9 1 , 6 3 2 0 , 1 3 8 , 5 1 4 3 , 5 3 0 4 4
5 2 0 2 4 0 0 , 2 4 1 8 1 , 5 4 0 0 , 1 9 1 5 2 3 3 , 5 6 3 8 6
£ = 3 4 4 O k
3 6 1 - 3 4 4
-
-
-
´ = Å"1 0 0 % = 4 . 6 % < 1 0 %
´ = Å" = <
´ = Å" = <
´ = Å" = <
3 4 4
O b i e g p r z e z g r z e j n i k n r 6 w p o m i e s z c z e n i u n r 1 1
6 4 9 0 0 , 0 0 5 9 2 1 5 0 , 0 3 1 , 4 3 1 7 , 5 9 1 2
D z i a Bk i w s p ó l n e 2 d o 5 3 2 5
3 3 7
3 6 1 - 3 3 7
-
-
-
´ = Å"1 0 0 % = 7 . 1 % < 1 0 %
´ = Å" = <
´ = Å" = <
´ = Å" = <
3 3 7
S t r o n a 7
D z i a Bk a
M a t e r i a By d o w i c z e D z o g r z e w n i c t w a
Q G l d v R R l £¶ Z R l + Z U w a g i
£¶
£¶
£¶
N r W k g / s m m m m / s P a / m P a P a P a
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
O b i e g p r z e z g r z e j n i k n r 8 w p o m i e s z c z e n i u n r 1 1 2
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å" ( 2 . 9 5 + 3 ) = 7 2 8 P a
0 . 5 Å"( 7 2 8 - 3 4 1 )
R o r j = = 2 4 . 2 P a / m
8
7 2 5 2 0 0 , 0 3 0 1 6 1 5 0 , 1 5 3 0 1 8 0 2 2 4 2 0 4
8 4 7 0 0 , 0 0 5 6 2 1 0 0 , 0 4 5 4 , 6 9 1 7 , 5 1 8 2 7
8 2 3 1
£ =
£ =
£l = £ =
£ = £ =
£ =
£ =
D z i a Bk i w s p ó l n e 2 d o 5 3 2 5
5 5 6
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 7 2 8 - 5 5 6 = 1 7 2 P a
"
"
"
D o b r a n o k r y z 4 m m
G 2 0 . 0 0 5 6 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 4 . 0 m m K 4
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 1 7 2
"
"
"
O b i e g p r z e z g r z e j n i k n r 9 w p o m i e s z c z e n i u n r 1 1 1
9 3 4 0 0 , 0 0 4 1 2 1 0 0 , 0 3 5 2 , 5 5 1 7 , 5 1 2 1 7
D z i a Bk i w s p ó l n e 2 d o 5 , 7 5 2 9
5 4 6
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"
"( R l + Z ) = 7 2 8 - 5 4 6 = 1 8 2 P a
"
"
D o b r a n o k r y z 3 . 5 m m
G 2 0 . 0 0 4 1 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 3 . 3 m m K 3 . 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 1 8 2
"
"
"
O b i e g p r z e z g r z e j n i k n r 1 1 w p o m i e s z c z e n i u n r 2 1 2
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å"( 2 . 9 5 + 3 + 3 ) = 1 0 9 5 P a
0 . 5 Å"( 1 0 9 5 - 5 2 7 )
R o r j = = 3 5 . 5 P a / m
8
1 0 1 7 1 0 0 , 0 2 0 4 6 1 5 0 , 1 1 4 8 4 2 1 2 9 6
1 1 4 7 0 0 , 0 0 5 6 2 1 0 0 , 0 4 5 4 , 6 9 1 7 , 5 1 2 2 1
8 1 1 7
£ =
£ =
£l = £ =
£ = £ =
£ =
£ =
D z i a Bk i w s p ó l n e 2 d o 5 , 7 5 2 9
6 4 6
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 0 9 5 - 6 4 6 = 4 4 9 P a
"
"
"
D o b r a n o k r y z 3 m m
G 2 0 . 0 0 5 6 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 3 . 1 m m K 3
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 4 4 9
"
"
"
S t r o n a 8
D z i a Bk a
M a t e r i a By d o w i c z e D z o g r z e w n i c t w a
Q G l d v R R l £¶ Z R l + Z U w a g i
£¶
£¶
£¶
N r W k g / s m m m m / s P a / m P a P a P a
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
O b i e g p r z e z g r z e j n i k n r 1 2 w p o m i e s z c z e n i u n r 2 1 1
1 2 3 2 0 0 , 0 0 3 8 2 1 0 0 , 0 3 5 2 , 2 4 1 7 , 5 9 1 3
D z i a Bk i w s p ó l n e 2 d o 5 , 7 , 1 0 6 2 5
6 3 8
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 0 9 5 - 6 3 8 = 4 5 7 P a
"
"
"
D o b r a n o k r y z 2 . 5 m m
G 2 0 . 0 0 3 8 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 2 . 6 m m K 2 . 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 4 5 7
"
"
"
O b i e g p r z e z g r z e j n i k n r 1 4 w p o m i e s z c z e n i u n r 3 1 2
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å"( 2 . 9 5 + 3 + 3 + 3 ) = 1 4 6 2 P a
0 . 5 Å"( 1 4 6 2 - 6 1 4 )
R o r j = = 5 3 P a / m
8
1 3 9 2 0 0 , 0 1 1 0 6 1 5 0 , 0 5 5 4 , 6 2 8 2 4 3 2
1 4 5 6 0 0 , 0 0 6 7 2 1 0 0 , 0 5 5 6 , 6 1 3 1 7 , 5 3 0 4 3
8 7 5
£ =
£ =
£l = £ =
£ = £ =
£ =
£ =
D z i a Bk i w s p ó l n e 2 d o 5 , 7 , 1 0 6 2 5
7 0 0
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 4 6 2 - 7 0 0 = 7 6 2 P a
"
"
"
D o b r a n o k r y z 3 m m
G 2 0 . 0 0 6 7 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 3 . 0 m m K 3
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 7 6 2
"
"
"
O b i e g p r z e z g r z e j n i k n r 1 5 w p o m i e s z c z e n i u n r 3 1 1
1 5 3 6 0 0 , 0 0 4 3 2 1 5 0 , 0 3 1 2 1 7 , 5 9 1 1
D z i a Bk i w s p ó l n e 2 d o 5 , 7 , 1 0 , 1 3 6 4 3
6 5 4
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 4 6 2 - 6 4 3 = 8 1 9 P a
"
"
"
D o b r a n o k r y z 2 . 5 m m
G 2 0 . 0 0 4 3 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 2 . 3 m m K 2 . 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 8 1 9
"
"
"
S t r o n a 9
D z i a Bk a
M a t e r i a By d o w i c z e D z o g r z e w n i c t w a
Q G l d v R R l £¶ Z R l + Z U w a g i
£¶
£¶
£¶
N r W k g / s m m m m / s P a / m P a P a P a
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
O b i e g p r z e z g r z e j n i k n r 1 7 w p o m i e s z c z e n i u n r 1 0
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å" 2 . 9 5 = 3 6 1 P a
0 . 5 Å"( 3 6 1 - 2 1 1 )
R o r j = = 7 . 4 P a / m
1 0 . 2
1 6 1 6 9 0 0 , 0 2 0 2 8 , 2 2 0 0 , 0 5 5 3 , 2 2 6 8 , 5 1 5 4 1
1 7 5 1 0 0 , 0 0 6 1 2 1 0 0 , 0 5 5 , 2 1 0 1 5 1 9 2 9
1 0 , 2 D z i a Bk i w s p ó l n e 3 d o 5 , 2 1 1
£l =
£ =
£ =
£ =
2 8 2
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 3 6 1 - 2 8 2 = 7 9 P a
"
"
"
D o b r a n o k r y z 5 m m
G 2 0 . 0 0 6 1 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 5 . 0 m m K 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 7 9
"
"
"
O b i e g p r z e z g r z e j n i k n r 1 9 w p o m i e s z c z e n i u n r 1 1 0
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å" ( 2 . 9 5 + 3 ) = 7 2 8 P a
0 . 5 Å"( 7 2 8 - 2 5 2 )
R o r j = = 2 9 . 8 P a / m
8
1 8 1 1 8 0 0 , 0 1 4 1 6 1 5 0 , 0 7 7 4 2 0 , 5 1 4 3
1 9 3 6 0 0 , 0 0 4 3 2 1 0 0 , 0 3 5 2 , 7 5 1 5 1 0 1 5
8 D z i a Bk i w s p ó l n e 3 d o 5 , 1 6 2 5 2
£l =
£ =
£ =
£ =
3 1 0
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 7 2 8 - 3 1 0 = 4 1 8 P a
"
"
"
D o b r a n o k r y z 3 . 0 m m
G 2 0 . 0 0 4 3 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 2 . 8 m m K 3 . 0
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 4 1 8
"
"
"
O b i e g p r z e z g r z e j n i k n r 2 1 w p o m i e s z c z e n i u n r 2 1 0
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å"( 2 . 9 5 + 3 + 3 ) = 1 0 9 5 P a
0 . 5 Å"( 1 0 9 5 - 2 9 5 )
R o r j = = 5 0 P a / m
8
2 0 8 2 0 0 , 0 0 9 8 6 1 5 0 , 0 5 3 , 8 2 3 0 , 5 1 2 4
2 1 3 6 0 0 , 0 0 4 3 2 1 0 0 , 0 3 5 2 , 7 5 1 5 1 0 1 5
8 D z i a Bk i w s p ó l n e 3 d o 5 , 1 6 , 1 8 2 9 5
£l =
£ =
£ =
£ =
3 3 4
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 0 9 5 - 3 3 4 = 7 6 1 P a
"
"
"
D o b r a n o k r y z 2 . 5 m m
G 2 0 . 0 0 4 3 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 2 . 4 m m K 2 . 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 7 6 1
"
"
"
S t r o n a 1 0
D z i a Bk a
M a t e r i a By d o w i c z e D z o g r z e w n i c t w a
Q G l d v R R l £¶ Z R l + Z U w a g i
£¶
£¶
£¶
N r W k g / s m m m m / s P a / m P a P a P a
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
O b i e g p r z e z g r z e j n i k n r 2 2 w p o m i e s z c z e n i u n r 3 1 0
"p c z = g Å" "Á Å" h = 9 . 8 1 Å"1 2 . 4 7 Å"( 2 . 9 5 + 3 + 3 + 3 ) = 1 4 6 2 P a
0 . 5 Å"( 1 4 6 2 - 3 1 9 )
R o r j = = 7 1 P a / m
8
2 2 4 6 0 0 , 0 0 5 5 8 1 0 0 , 0 5 4 , 6 3 7 1 5 1 8 5 5
D z i a Bk i w s p ó l n e 3 d o 5 , 1 6 , 1 8 , 2 0 3 1 9
3 7 4
"P k r = "P c z - + = - =
" = " - + = - =
" = " - + = - =
" = " -
"( R l + Z ) = 1 4 6 2 - 3 7 4 = 1 0 8 8 P a
"
"
"
D o b r a n o k r y z 2 . 5 m m
G 2 0 . 0 0 5 5 2
4
4
d k r = 1 9 2 Å" = 1 9 2 Å" = 2 . 5 m m K 2 . 5
= Å" = Å" =
= Å" = Å" =
= Å" = Å" =
"p k r 1 0 8 8
"
"
"
S t r o n a 1 1
D z i a Bk a
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