Đặc trưng hình học của mặt cắt ngang docx

1









 !

"#$%&&


"#'&$
(


)
$
'
'
$
*+
'
"
$
"
"








=
=
∫
∫
F
y
F
X
xdFS
ydFS
,
 
!" #$%
-
'
.-
$
*/0
1

'.$2#$3-
'
.-
$

4567*58
,


9&'.$2%:&*; 3-
'
.-
$
2%
:&*; <

&
'
()*&
+
()'.$45$%$,-5
=:<>*-
?
@A'
=:<

 . /0$%$,-12trọng tâm



B
Trọng tâm mặt cắt








=
=
F
S
y
F
S
x
x
C
y
C
C
3,45

3,45678 !" 
#$%







=
=

∫
∫
F
2
y
F
2
X
dFxJ
dFyJ
D
?
.D
$
45
0
1

'.
$.2#$345
67*58
B

E
3,45

F6
%8
∫
ρ=

F
2
P
dFJ
)
$
'
'
$
+
*+
ρ45G&!H
I6'.$8J=.
ρ
(
@'
(
K$
(

( )
∫
+=+=
F
yx
22
p
JJdFyxJ
L
3,45


3,451+-
∫
=
F
xy
xydFJ
M
3,45

N4$:/
5&2OPG/2;Q=45
9
:
$%3,455<RJ3
1

=:;Q=
459
:
$%3,45$,-

STOUGV%5&3
W2%'X;Q3
1

<

RJ0
1

2
1
'#OUGV
5&2'#2W
4Y253
1
<
Z
3,45#;6
78< =

6>?
12
hb
J
3
y
=
12
bh
J
3
x
=
[A
3,45#;6
78< =

6 4
12

bh
J
3
x
=
[[
3,45#;6
78< =

6$@
2
R
JJ
4
yx
π
==
4
4
yx
4
4
P
D05,0
64
D
JJ
D1,0
32
D

J
≈
π
==
≈
π
=
[(
3,45#;6
78< =

5G0
( ) ( )
( ) ( )
444
4
444
444
105,01
642
11,01
323232
ηη
π
ηη
πππ
−≈−===
−≈−=−=
D
DJ

JJ
D
DdD
J
P
yx
P
[,
A4B53,45

'
.
$
\OG
0
1
'
5$
F
J
i
F
J
i
y
y
x
x
=
=

[B
A4B53,45

]Y\

^\


5G0\
12
h
i
x
=
12
b
i
y
=
4
D
ii
yx
==
2
yx
1
4
D
ii α+==

[C
C,+/$%;.;.
3,45

>U7\OJD
'
.D
$
.D
'$
/)'$<
SD
?
.D
_
.D
?_
/&&)?_



+=
+=
byY
axX
[E
C,+/$%;.;.
3,45






+++=
++=
++=
abFbSaSJJ
FaaS2JJ
FbbS2JJ
yxxy
Y
X
2
yyY
2
xxX
[L
C,+/$%;.;.
3,45

RJ'.$45/
:.
-
'
@-
$
@A






+=
+=
+=
abFJJ
FaJJ
FbJJ
xy
Y
X
2
yY
2
xX

RJ'$45/
:.
-
'
@-
$
@A5D
'$
@A






=
+=
+=
abFJ
FaJJ
FbJJ
Y
X
2
yY
2
xX
[M
CD.+$%
3,45
>U7

"2*/+

`!aOJ\
*/+6D
'
.D
$
.
D
'$
8/)'$<

S

*/+/
)
[Z
CD.+$%
3,45
`=6.845=
%I&/=).
2

@'&αK$α

@b'αK$&α 68
/
)45









=
=
=
∫
∫
∫
F

uv
F
2
v
F
2
u
uvdFJ
dFuJ
dFvJ
(A
( )
α−α+αα−αα=
αα+α+α=
αα−α+α=
22
xyyxuv
xy
2
y
2
xv
xy
2
y
2
xu
JJJJ
J2JJJ
J2JJJ

&&&
&<&
&<&
α−α
−
=
α+α
−
+
+
=
α−α
−
+
+
=
2J2
2
JJ
J
2J2
2
JJ
2
JJ
J
2J2
2
JJ
2

JJ
J
xy
yx
uv
xy
yxyx
v
xy
yxyx
u
&
&
&
([
CD.+$%
3,45

>X/

:;Q'X
H7G/D

@A
$
yx
xy
JJ
J2
2tg

−
−=α
SX

/

( )
( )
2
xy
2
yx
yx
2
xy
2
yx
yx
J4JJ
2
1
2
JJ
J
J4JJ
2
1
2
JJ
J

+−−
+
=
+−+
+
=

'
((
E5F%GHI
?X

:

(,
E5F%GHI

?X=
:
a
F
yF
y
i
i
i
ii
c
3
5

3
1
3
1
==
∑
∑
=
=
(B
E5F%GHI


:
4
3
143
3
21
a
JJJJ
F
x
F
x
F
xx
=
++=
4

19
3
21
a
JJJJ
F
y
F
y
F
yy
=
++=
(C
E5F%GHI

cG
aa
F
J
i
x
x
993,1
12.3
143
2
===
aa
F

J
i
y
y
258,1
12
19
2
===