Chapter 4 Sbvl

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Chng 4: c Trng Hnh Hc Mt Ct Ngang

1 Gii Thiu

2 Din tch-Mmen Tnh-Trng Tm Ca Hnh Phng

3 Cc Mmen Qun Tnh

4 Cng Thc Chuyn Trc Song Song

Gii Thiu1

* Kh nng chu lc ca chi tit khng nhng ph thuc vo hnhdng, kch thc mt ct ngang m cn ph thuc vo cch b tr camt ct ngang.

x

y

P

xy

P

2.1 Din tch ca hnh phng


F

F dF

2.2 Mmen tnh ca hnh phng

- i vi trc Ox: F

x ydFS

- i vi trc Oy: F

y xdFS

x

y

x

y dF

O



* Mmen tnh c th m, dng hoc bng khng

0 yx SS

* Mmen tnh ca hnh phng i vi mt trc no bng khng,trc c gi l trc trung tm. Giao im ca hai trc trung tml trng tm hnh phng.

x

y

dF

dF

y

y



* Gi C l trng tm hnh phng, cc trc Cx0 v Cy0 l hai trc trungtm

0

0

0

0

0

0

Fy

Fx

dFxS

dFyS

Ta c

0

0

yyyxxx

C

C

x

y

x

y dF

O

0y

0x0x

0y

C

Cx

Cy

FF

CF

CF

x dFydFydFyyydFS 00

FySFyS CxCx .. 0



x

y

x

y dF

O

0y

0x0x

0y

C

Cx

Cy

FxSFyS

Cy

Cx

.

.

Nu hnh phng l hnh phc tp

n

iiCy

n

iiCx

FxS

FyS

i

i

1

1

.

.

Trong : ,i iC C

x y Ta trng tm ca hnh th i

iF Din tch ca hnh th i


2.3 Trng tm ca hnh phng

n

ii

n

iiC

xC

n

ii

n

iiC

yC

F

Fy

FSy

F

Fx

FS

x

i

i

1

1

1

1

x

y

x

y dF

O

0y

0x0x

0y

C

Cx

Cy

3.1 Mmen qun tnhca hnh phng

3.2 Mmen qun tnh cc ca hnh phng i vi tm O

- i vi trc Ox: F

x dFyJ2

- i vi trc Oy: F

y dFxJ2

3 Cc Mmen Qun Tnh

x

y

x

y dF

O

F

dFJ 2

Ta thy: 222 yx yx JJJ

3.3 Mmen qun tnh ly tm ca hnhphng i vi h trc xOy

F

xy xydFJ

3 Cc Mmen Qun Tnh

x

y

x

y dF

O

* Mmen qun tnh ly tm c th m, dnghoc bng khng.

* Nu mmen qun tnh ly tm ca hnh phng ivi mt h trc no bng khng, h trc cgi l h trc qun tnh chnh.

* Nu h trc qun tnh chnh i qua trng tm mtct c gi l h trc qun tnh chnh trung tm.

x

y

dF dF

xx

3.4 Mmen qun tnh ca mt s hnh thng gp

3 Cc Mmen Qun Tnh

* Hnh ch nhtx

y

y

dy

b

h

dF

12

32/

2/

22 bhbdyydFyJh

hFx

3 3

;12 12x ybh hbJ J

x

y

dR

C

* Hnh trn4 4

2 2 4

0

2 0,12 32

R

F

R DJ dF d D

44

44

0,05 ;64

2 0,132

x y

x

DJ J D

DJ J D

3 Cc Mmen Qun Tnh

* Hnh tam gic

3 3

;12 36Cx xbh bhJ J

b

h

Cx

cxy

dydF

rb r

r

b h yb

hdF b dy

2 /3 32 2

/3

32 2

0

36

12

C

h

xF h

h

xF

b h y bhJ y dF y dyh

b h y bhJ y dF y dyh

* Bit:


x

y

x

y dF

O

0y

0x0x

0y

A

Ax

Ay

00, yx JJ

* Tm: yx JJ ,

Vi 00 //,// yyxx

Ta c

0

0

yyyxxx

A

A

F

AFF

AF

AF

x dFyydFydFydFyydFyJ 020

220

2 2

00

00

.2.

.2.2

2

yAyAy

xAxAx

SxJFxJ

SyJFyJ


x

y

x

y dF

O

0y

0x0x

0y

A

Ax

Ay

* Nu A l trng tm mt ct, Ax0 vAy0 l hai trc trung tm ca mt ctngang

000 yx SS

FxJJ

FyJJ

Ayy

Axx

.

.2

2

0

0

Ta c

* V d 1: Tnh mmen qun tnh ca hnh ch nht i vi cc trc x,y

6122

32

122

43

43

bbbJ

bbbJ

c

c

y

x

Ta c

x

y

b2

bx

y

b2

b

cx

cy

C

42

2

422

322.

2

382.

bbbJJ

bbbJJ

c

c

yy

xx

* V d 2: Tnh mmen qun tnh ca hnh tam gic i vi cc trc x

36

3bhJcxTa c

1221.

3

32 bhbhhJJcxx

xb

h

b

h Cx

cx

3

3

36

12

cx

x

bhJ

bhJ

* V d 3: Tnh mmen qun tnh ca hnh tam gic i vi cc trc x, y

12

481222

3

3

3

hbJ

bhhb

J

y

x

x

b

h

y

x

b

2h

y

2h

* V d 4: Tnh m men qun tnh chnh trung tm ca hnh phng

b b b b

x

y

(1)

(2)

3

4

22 .2

212 12x y

bbbJ J

* V d 5: Tnh cc mmen qun tnh chnh trung tm ca hnh phng

900

30

30450

450 30

y

x 1 2 3

x x x xJ J J J

1

2 3

3

423

30.90012

76626450.30 900 30 .450.30

12 2 2

x

x

x x

JJ cm

J J

1 2 3

3 34900.30 30.4502 45765

12 12y y y yJ J J J cm

* V d 6: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng

To trng tm ca hnh phng

b

b

8b

7b

b

b

8b

7b

1x

x

(1)

(2)

cy

y

2

2 21

2 2 2

1

0

4 .8 8,5 .7 6,18 7

i

C

C ii

C

ii

x

y Fb b b by b

b bF

3 32 21 2 2 2 4

3 31 2 4

. 8 7 .4 6,1 .8 8,5 6,1 .7 118,85b

12 12

8 . . 729,25

12 12

x x x

y y y

b b b bJ J J b b b b b b

b b b bJ J J b

* V d 7: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng

b

b 7b

15b

b

b7b

15b1x

y

xC

cy

2

12

1

0

3,5 .15 .7 3 .13 .6 8915 .7 13 .6 18

i

C

C ii

C

ii

x

y Fb b b b b by b

b b b bF

To trng tm ca hnh phng

3 32 21 2 4

3 31 2 4

15 . 7 13 . 689 893,5 .15 .7 3 .13 .6 118,917b12 18 12 18

7 . 15 6 . 13870,25

12 12

x x x

y y y

b b b bJ J J b b b b b b b b

b b b bJ J J b

* V d 8: Xc nh trng tm v tnh cc mmen qun tnh chnh trung tmca hnh phng

50cm

75cm

40cm70cm

50cm

75cm

40cm70cm x

y

3 34

23 34

75.70 12,5.204 2110416,66712 12

70.75 40.12,5 100 12 40.12,5 1901041,66712 36 3 2

x

y

J cm

J cm


53014 14

3609 5 5b b2b

6

6

30

22

6

50cm75cm

40cm

70cm

25cm

* V d 10: Xc nh trng tm v tnh cc mmen qun tnh chnh trungtm ca hnh phng. Khi tnh b qua cc gc ln. So snh kt qu tnh cvi tra bng thp hnh L70x70x6

70

70

6

6

* V d 11: Tnh cc mmen qun tnh chnh trung tm ca mt ct ngangnh hnh v. Mt ct ngang gm hai thp hnh L70x70x6 ghp li.

70

6

6

70


70 7

40 40 5L

40 40 5L 40 40 5L

40 40 5L

174

6

40 40 5L

184

40 40 5L

40 40 5L

40 40 5L

18I

22I xx

y

y

18I

18I

12

400

xx

y

y

18I

Documents

Chapter 4 Sbvl