Chapter 2 Sbvl

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1 nh Ngha Ni Lc Cch Xc nh Ni Lc

2 Cc Thnh Phn Ni Lc

3 Lin H Gia ng Sut v Cc Thnh Phn Ni Lc

4 Qui c Du Ca Ni Lc

5 Biu Ni Lc

6 Bi Tp

1.1 nh Ngha Ni Lc


* Ni lc l lng thay i lc lin kt gia ccphn t trong mt chi tit do s thay i hnh dng,kch thc ca vt di tc ng ca ngoi lc.

1.2 Cch xc nh ni lc: s dng phng phpmt ct

1P

2P

3P

4P

nP

C I

II

1P

2P

3P

4P

nP

C

1P2P

3P

A4P

nP B

Noi lc => Ni lc l lc phtsinh trn mt ct.


* Ni lc l lc pht sinh trn mt ct.

1P2P

3P

A4P

nP B

Noi lc

* Ni lc ph thuc vo v tr ca mt ct, tng im trnmt ct v ngoi lc tc dng ln vt.

* Ni lc cn bng vi ngoi lc tc dng ln vt.

2 Cc Thnh Phn Ni Lc

* Thu gn h ni lc phn b trn mt ct v tm mt ct ta c

1P

2P

3P

C A

4P

nP

B

C

R

RM

M

: Vct chnh ni lc

M

: Mmen chnh ni lc

R

* Cc thnh phn ni lc

+ Mmen xon zM

+ Mmen un yx MM ,

+ Lc dc zN Ko-nn

+ Lc ct yx QQ , Ct

Xon

Un1P

2P

nP

y

x

zzN

yQ

xQ

xMzM

yM

A

C

2 Cc Thnh Phn Ni Lc

ZN

ZN

ZN

ZN

* Ko Nn ng tm

2 Cc Thnh Phn Ni Lc

* Nhng thanh c xem l lin kt thanh cng (thanh khngkhi lng) chu ko hay nn ng tm.

2 Cc Thnh Phn Ni Lc

2 Cc Thnh Phn Ni Lc

zM

zM

* Xon

2 Cc Thnh Phn Ni Lc

2 Cc Thnh Phn Ni Lc

* Un

2 Cc Thnh Phn Ni Lc

1P

2P

nP

y

x

zzN

yQ

xQ

xMzM

yM

A

C

* Trong mt phng (yz)

xzy MNQ ,,

* Trong mt phng (xz)

yzx MNQ ,,* Trong mt phng (xy)

zyx MQQ ,,

1P

2P

nP

y

x

zzN

yQ

xM AC

1P

2P

nP

y

x

zzN

xQyM

A

C

1P

2P

nP

y

x

z

yQxQ

zM AC

2 Cc Thnh Phn Ni Lc

* Xc nh Cc Thnh Phn Ni Lc

1P

2P

nP

y

x

zzN

yQxQ

xMzM

yM

A

C

0

0

0

0

0

0

ziz

yiy

xix

zz

yy

xx

MPm

MPm

MPm

NP

QP

QP

Ni lc cn bng vi ngoi lc

* Cho thanh chu lc nh hnh v. Xc nh ni lc ca mt ct ti ngm

P

x

y

l

Pq

xy

z

l

P

q

lM

xy

z


2P kN40cm

Dt

A

B DC

* Cho cn trc chu lc nh hnh v. Xc nh ni lc ca mt ct ti A, Bv C

* Cho h chu lc nh hnh v. Xc nh ni lc ca mt ct ti ngm A

1m

0,3m

A B

C

75P kN


P

l

* Cho h chu lc nh hnh v. Xc nh ni lc ca mt ct ti chn ct

200P N

260 /p N m

xy

z

5m

1,5m

1,8m

0,9m


m

2a

aA

B

C

P

* Cho h chu lc nh hnh v. Xc nh ni lc ca mt ct A-A

P

100

20

50150

A A

Hnh B.8.11

AA

40

* Cho h chu lc nh hnh v. Xc nh ni lc ca mt ct ti ngm

1T

2T

1T

2T

020

d

l

P

1 2200 ; 120150 ; 0, 3

T N T NP N l m

2 Cc Thnh Phn Ni Lc

1

1

.0.0

zqPNNzqPF

z

zz

* Cho thanh chu lc nh hnh v. Xc nh ni lc ti mt ct 1-1:

P

1z

q

11

z

zN

P

q1z

P

q

1z 1z

P

q

zN

1 11 1

2 Cc Thnh Phn Ni Lc

MMMMm

z

zz

00


1zy

x

z

M

1

1

1zy

x

z

M

z

y

x

zM

A B11

1zlx

z

y

M

A 11

1zx

z

y

M

xz

y

zM

2 Cc Thnh Phn Ni Lc

11 .0.0

00

zPMMzPm

PQQPF

xxx

yyy

y

z

x

C

P

lz

1

1y

z

x

C

P

z

z

x

y

yQ

xM

P

A B11

zl

y

zP

A 11

zy

zyQ

xM


2 Cc Thnh Phn Ni Lc

11 .0.0

00

zPMMzPm

PQQPF

yyy

xxx

y

z

x

CP

l1z

y

z

x

CP

1z

z

x

y

xQyM

PA B1

1

1zl

x

z

P

A 11

1z

x

z

xQ

yM


2 Cc Thnh Phn Ni Lc

20

2.0

002zqPzMMzqzzPm

qzPQQqzPF

xxx

yyy

y

z

x

C

P

lz

q

1

1 y

z

x

C

P

z

z

x

yyQ

xM

q

P

A B11

zl

y

z

q P

A 11

zy

zyQ

xMq


xz

5,5by P q

2 Cc Thnh Phn Ni Lc

* Cho thanh chu lc nh hnh v. Xc nh ni lc ti mt ct A-A:

P

b

b

4b

A A

AA

)a

q

z

y

x

b3

zN

yM

2 Cc Thnh Phn Ni Lc

PbMMbPm

PNNPF

yyy

zzx

5,505,5.0

00

* Cho thanh chu lc nh hnh v. Xc nh ni lc ti mt ct A-A:

P

b

b

4b

A A

AA

)a

q

z

y

x

b3

P

b

A A

AA

b3

z

x

x

y

zN

yMb5,5

2 Cc Thnh Phn Ni Lc

mmkNMMm

kNNNF

xxx

zzz

.20000100.200

200200

* Cho mc chu lc nh hnh v. Xc nh ni lc ti mt ct A-A:

20kN

100

20

50150

A A

z

y

zNxM

20kN

100

20

50150

A A

y

x

2 Cc Thnh Phn Ni Lc

* Dm ch I trng lng P c nng ln nh hnh v. Xc nh nilc ti mt ct 1-1, 2-2, 3-3:

030 030

5m 8m 5m

kNPT 8,1

q

mkNPq /1,018/

m2 m4

1

1

2

2

3

3

5m 8m 5m

kNPT 8,1

q

mkNPq /1,018/

m2 m4

11 2

030 0302 33

y

y

xx

2 Cc Thnh Phn Ni Lc

5m 8m 5m

kNPT 8,1

q

mkNPq /1,018/

m2 m4

11 2

030 0302 33

y

y

xx

11

m2y

zyQ

xMmkNq /1,0

mkNMMm

kNQQF

xx

yyy

.2,001.2.1,00

2,002.1,00

1

22

m5y

zyQ

xMmkNq /1,0

mkNMMm

kNQQF

xx

yyy

.25,105,2.5.1,00

5,005.1,00

2

2 Cc Thnh Phn Ni Lc

5m 8m 5m

kNPT 8,1

q

mkNPq /1,018/

m2 m4

11 2

030 0302 33

y

y

xx

A 22

m5y

z

yQ

xMmkNq /1,0 kNF 8,1

030

zN

mkNMMm

kNNNF

kNQQF

xx

zzz

yyy

.25,105,2.5.1,00

56,1030cos8,10

4,0030sin8,15.1,00

2

0

0

2 Cc Thnh Phn Ni Lc

5m 8m 5m

kNPT 8,1

q

mkNPq /1,018/

m2 m4

11 2

030 0302 33

y

y

xx

mkNMMm

kNNNF

QQF

xx

zzz

yyy

.45,004.30sin8,15,4.9.1,00

56,1030cos8,10

0030sin8,19.1,00

02

0

0

Am5

y

z

kNF 8,1

030

yQ

xM

zN

mkNq /1,0

m4

2 Cc Thnh Phn Ni Lc

* Cho ct chu lc nh hnh v. Xc nh ni lc ca mt ct ti chnct.

0,5m

2 100 /q kN m

1 50 /q kN m

A

B

0,5m

A

B

xMyQ

zN

1R

2R

0,53

m0,52

m

1

2

50.0,5 251 100 50 .0,5 12,52

R kN

R kN

1 50 /q kN m

2 100 /q kN m

1 2 1 2

1 2

0 0 25 12,5 37,5

0 00,5 0,5 250 . . 0 .2 3 3

y y y

z z

A x x

F Q R R Q R R kN

F N

m M R R M kN m

2 Cc Thnh Phn Ni Lc

* Cho khung chu lc nh hnh v. Xc nh ni lc trn cc mt ct 1-1, 2-2, 3-3, 4-4

C

q

2M qa

A

3P qa

a

B

D E2P qa

a

a

a1 1

2

2

3 3

4

4

2z

1z

3z4z

C

q

2M qa

A

3P qa

a

B

D E2P qa

a

a

aAM

AX

AY2 210 3 . 2 .2 . . 02 2

0 3 . 0 4

0 2 0 2

A A A

y A A

x A A

am M qa a qa qa a q a M qa

F Y qa q a Y qa

F X qa X qa

2 Cc Thnh Phn Ni Lc

* Mt ct 1-1

AY

1yQ

1xM

1zN

AX

1zAM1 1

C

2M qa

3P qa

2xM

2yQ

2z 2

1 1

1 1

1 1

21 1 1 1

0 0 2

0 0 4

10 . 0 2 .2

y A y y A

z A z z A

A A x x

F X Q Q X qa

F Y N N Y qa

m M X z M M qa qa z

* Mt ct 2-22 2

2 2

2 22 2 2 2

0 3 0 3

0 3 . 0 3 .y y y

x x

F qa Q Q qa

m qa qa z M M qa qa z

2 Cc Thnh Phn Ni Lc

* Mt ct 3-3

qE

44z

4yQ

4xM

q

D E2P qa

33z

3yQ

3xM

a3Z

N

3 3

3 3

3 3

23 3 3 3

0 2 0 2

0 0

10 2 . . 0 2 .2 2

y y y

z z z

x x

F qa Q Q qa

F N qa N qa

am M qa z qa M qa qa z

* Mt ct 4-4

4 4

4 4

4 4

2 24 4

4 4

0 . 0

0 02 2

y y y

x x

F Q q z Q qz

z qzm M q M

2 Cc Thnh Phn Ni Lc

* Ct thp c lin kt, chu lc v c kch thc nh hnh v. V s tnh v tnh ni lc pht sinh trn mt ct 1-1, 2-2

z

x

yB

A

1P

2P2P1l a a

2l

C

A

B

C

x

x

y y

1 1

2 2

1 1

2 2

1q

2q

2P2P

1P

2l

1l

2b

2h

x

xy

1b

1h yaa

2 Cc Thnh Phn Ni Lc

A

B

C

1 1

2 2

1q

2q

2P2P

1P

2l

1l1z 1q

1P

1zN

1 1111

111

.0.

0

zqPNNzqP

F

z

z

z

B

C

2 2

1q

2q

2P2P

1P

2z

1l

2zN

222111

222111

.2.0.2.

0

zqPlqPNNzqPlqP

F

z

z

z

2 Cc Thnh Phn Ni Lc

A

B

C

1 1

2 2

1q

2q

2P2P

1P

2l

1l

111

111

.

0.

0

lqPN

NlqP

F

t

t

Bz

Bz

z

1l

1q

1P

tBzN

B

B

C

1q2P2P

1P

1l

2zN

2111

2111

2.

02.

0

PlqPNNPlqP

F

d

d

Bz

Bz

z

3 Lin H Gia ng Sut v Cc Thnh Phn Ni Lc

* ng sut ti mt im:

dFqd

FqU

FA

lim0

1P

2P

nP

y

x

zzN

yQ

xQ

xMzM

yM

A

C

x

yzzyzx

z zF

N dF + Lc dc

x zxF

y zyF

Q dF

Q dF

+ Lc ct

x zF

y zF

M ydF

M xdF

+ Mmen un

z zx zyF

M y x dF + Mmen xon

1P

2P

3P

Vi phn ni lcq

F Vi phn din tchA

4 Qui c Du Ca Ni Lc

0zN

0yQ

y y

0xM

y y

0zM

* Khi nhn vo mt ct thy Nzhng ra mt ct (ko) ldng.

* Qx , Qy lm cho phn angxt quay cng chiu kim ngh l dng.

* Mx , My lm cng (ko) phnbn di l dng.

* Khi nhn vo mt ct thy Mzquay cng chiu kim ng hl dng.

5 Biu Ni Lc

5.1. nh Ngha

* Biu ni lc l th m t qui lut phn b ca ni lc dc trcthanh

qzPN z

P

q

z z

P

q

zN

1 11 1

l

A

B BP

ql

A

B P

qlP

z

zN0

5 Biu Ni Lc

5.2. V Biu Ni Lc Bng Phng Php Mt Ct

A B11

zl1

x

1z

1y

M

A 11

z

Mz

y

zM

x1x

1z

1y

zMM

z0 MM z

5 Biu Ni Lc

5.2. V Biu Ni Lc Bng Phng Php Mt Ct

P

A 11

zy

z

yQ

xMq

2

2zqPzM

qzPQ

x

y

P

A B11

zl

1y

1z

q

yQz

P qlP 0

xM

z0

2/2qlPl

5 Biu Ni Lc

5.2. V Biu Ni Lc Bng Phng V Nhanh

* Thanh chu ko-nn ng tm

A

BC

q

PD

A

B

C1 1

q

PD

22dz

P

1zN

dzC

2zN

1 1

2 2

A

B

C

q

PD

33dz z

N

dz

zz dNN

4 4

q3 3

4 4

PNN zz 12

ABq

Az

Bz

z

RNN

qdz

dN

5 Biu Ni Lc

PNN zz 12

ABq

Az

Bz RNN

qdz

dN z Nz hn lc phn b mt bc

Nu trn s tnh c lc tp trung,biu Nz c bc nhy, gi tr bcnhy bng gi tr lc tp trung. Nhy vdng khi lc gy ko, nhy v m khilc gy nn

Nz cui on bng Nz u on cnghp lc phn b trn on (lcphn b ko dng, nn m)

0zN

5 Biu Ni Lc

V d: V biu ni lc pht sinh trong ct nhhnh v

P qaP

3a

a

A

B

CP

l l P qaP

2q3a

a

A

B

CP

l lq

5 Biu Ni Lc

3P

P

A

B

C

Pll

m3

m1

3P

P

A

B

C

PNA 5

Pll

m3

m1

P3

P5

zN

V d: V biu ni lc pht sinh trong ct nh hnh v

5 Biu Ni Lc


3P

P

q3a

a

A

B

C

P qa

3qa

4qa6qa

9qa zN

P qa

3P

P

q3a

a

A

B

C

qaNA 9

5 Biu Ni Lc


qa

4qa

qazN

P qa

q3a

a

A

B

C

2,5P2,5P

q3a

a

A

B

C

qaNA

P qa

2,5P 2,5P

5 Biu Ni Lc

MMM zz 12

ABm

Az

Bz RMM

mdz

dM z Mz hn ngu lc phn b mt bc

Nu trn s tnh c ngu lc tptrung, biu Mz c bc nhy, gi trbc nhy bng gi tr ngu lc tptrung. Nhy v dng khi ngu lc quaycng chiu kim ng h, nhy v m khingu lc quay ngc chiu kim ng h

Mz cui on bng Mz u on cnghp ngu lc phn b trn on (ngu lc phn b cng chiu kimng h dng, ngc chiu kim ngh m)

0zM* Thanh chu xon thun ty

5 Biu Ni Lc

V d: V biu ni lc pht sinh trong trc nh hnh v

M

a

2a

3MA

B

C

5 Biu Ni Lc


a 2aA

BC

m

5 Biu Ni Lc


M

2a

4M

A B C

a

M

3M

zM

M

2a

A B C

4M

a

MM A 3

5 Biu Ni Lc


M ma

2a

6MA B C

m

a

ma3ma

3ma

zM

M ma

2a

6M

A B C

m

a

maM A 3

5 Biu Ni Lc


AB C

DE

a a a a

2M

MM

zM

M2M

A B D

a 2a a

M ma m 3M ma

C

zM

ma3ma

5 Biu Ni Lc

* Un phng thanh thng

MMM

PQQt

xp

x

ty

py

P

A B

1y

1z

q

C D

M

P

A B 11

1y

1z

q

C Ddz

22

P

11

Cdz

22

pyQ

pxM

tyQ

txM

M M

ABQ

Ax

Bx

yx

ABq

Ay

By

y

ySMM

Qdz

dMRQQ

qdz

dQ

P

A B

1y

1z

q

C D3

dz

43 4

M3

Cdz

44

yQ

xM 3

y yQ dQ

xx dMM q

5 Biu Ni Lc

PQQ typ

y

ABq

Ay

By RQQ

qdz

dQ y Qy hn lc phn b mt bc

Khi i t tri qua phi, nu trn s tnh c lc tp trung, biu Qy cbc nhy, gi tr bc nhy bng gitr lc tp trung. Chiu bc nhy cngchiu vi lc tp trung

Khi i t tri qua phi, Qy cui onbng Qy u on cng hp lc phnb trn on (lc phn b hngln dng, hng xung m)

* V biu lc ct

5 Biu Ni Lc

MMM txp

x

ABQ

Ax

Bx y

SMM

yx Q

dzdM

Mx hn Qy mt bc

Khi i t tri qua phi, nu trn s tnh c ngu lc tp trung, biu Mxc bc nhy, gi tr bc nhy bnggi tr ngu lc tp trung. Nhy xungkhi ngu lc quay cng chiu, nhy lnkhi ngu lc quay ngc chiu kimng h

Khi i t tri qua phi, Mx cui onbng Mx u on cng din tch biu lc ct trn on

* V biu m men un

5 Biu Ni Lc

V d: V biu ni lc pht sinh trong dm nh hnh v

5P qaq

a

A B

3a

P

a

A B

3a

5 Biu Ni Lc


1 2P qaq

a

A B

3aa

2P qa2 P

a

A B

3aa

P

5 Biu Ni Lc


A B

q

l

P

/ 5lA B

P P P PP

/ 5l / 5l / 5l / 5l

5 Biu Ni Lc


P

A Bl

P

A Bl

q

5 Biu Ni Lc


30P kN

AB

4l m

25 /q kN m

5 Biu Ni Lc


a2a

PA CB

a2a

A CBAY BY

P

P

P5,0

yQ

Pa

xM

32

2

B

A

PY

PY

5 Biu Ni Lc


a2a

P

A CB

PaM 5,0

A CBAY

P

a2a CY

PaM 5,0

6/P

yQ

6/5P

Pa

xM

3/4Pa

56

6

C

A

PY

PY

5 Biu Ni Lc


P qa22M qa q

a 4a

A CB

P qa 22M qa q

a 4aA B C

BY CY

qa

114

qa

54

qa

225 / 32qa

2qa

23qa

I

xM

yQ

Chapter 2 Sbvl

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