140936393 Bai Tap Suc Ben Vat Lieu

8/22/2019 140936393 Bai Tap Suc Ben Vat Lieu

1/34

Noi lc Khoa Xay Dng & C Hoc ng Dung

Bai tap sc ben vat lieu trang 1 03/2013

Chng 02

NOI LC

I) TOM TAT LY THUYET1.1. Cac thanh phan noi lc tren mat cat ngang

Phng phap mat cat xac nh noi lc: gia s ta co mot vat the can bang di tac dung

cua ngoai lc iP

. e xac nh noi lc tren mat cat ngang cha iem C thuoc vat the ta

tng tng co mot mat phang qua iem C va cat vat the thanh hai phan A va

B nh hnh 2.1. Xet s can bang cua mot phan, v du phan A . Phan A c can

bang nh noi lc cua phan B tac dung len phan A . Noi lc nay phan bo bat k trenmat cat va hp lc cua noi lc nay can bang vi ngoai lc tac dung len phan A ang

xet. Tng t neu ta xet s can bang cua phan B th phan A cung tac dung len phan

B cac noi lc tng t nhng ngc chieu nh hnh 2.1.

Thu gon he noi lc ve tam mat cat ta c mot vec t chnh noi lc R va mot mo menchnh noi lc M nh hnh 2.2.

Hnh 2.2. Hp cua noi lc tren mat cat

a)

1P

2P

3P

R

M

C A

4P

1nP

nP

M

R

C

B

I

Hnh 2.1. Phng phap mat cat va noi lc.

C

II

1P

2P

3P

4P

1nP

nP1

P

2P

3P 4P

1nP

nP

A

B


2/34



Xet bai toan thanh: at he truc toa o tai trong tam mat cat, truc z trung vi phap

tuyen cua mat cat, cac truc ,x y cung vi truc z tao thanh mot tam dien thuan.

Chieu vec t chnh noi lc R va mo men chnh noi lc M len cac truc toa o ta c

sau thanh phan noi lc nh hnh 2.3: Lc doc zN lam thanh chu keo_nen ung tam. Lc cat ,x yQ Q lam thanh chu cat. Mo men uon ,x yM M lam thanh chu uon. Mo men xoan zM lam thanh chu xoan.

1.2.Xac nh cac thanh phan noi lc tren mat cat ngangKhi at sau thanh phan noi lc vao mat cat th phan A tr nen can bang (ngoai lc

tac dung len phan A can bang vi sau thanh phan noi lc at tren mat cat). S dung sau

phng trnh can bang tnh hoc ta co the xac nh c tr so, chieu cua sau thanh phan noilc nay:

1

1

1

1

1

0

0

0

0

0

n

z i xi

n

y i yi

n

x i xi

n

x x i

i

n

y y i

i

N P

Q P

Q P

M m P

M m P

(2.1)

Hnh 2.3. Cac thanh phan noi lc

1P

2P

nP

x

zN

yQ

xQ

xMM

yM

A

C


3/34



1

0n

z z i

i

M m P

1.3. Quan he gia cac thanh phan noi lc vi cac thanh phan ng suat

Lc doc: z zFN dF

(2.2)

Lc cat : x zxFy zy

F

Q dF

Q dF

(2.3)

Momen uon: x zFy z

F

M ydF

M xdF

(2.4)

Momen xoan: z zx zyFM y x dF

(2.5)

Hnh 2.4. Cac thanh phan noi lc

1P

2P

3P

zN

Q

xQ

xM

M

M

A

x

yx


4/34



1.4. Qui c dau cua cac thanh phan noi lcNh hnh 2.5

Lc doc : N hng ra mat cat (keo) la dng. Lc cat: ,x yQ Q co xu hng lam cho phan ang xet quay cung chieu kim ong

ho la dng. Momen uon: ,x yM M lam cang (keo) phan ben di la dng. Momen xoan: khi nhn vao mat cat thay M quay cung chieu kim ong ho la

dng.

V du 1: Xac nh cac thanh phan noi lc tren mat cat ngang tai B cua dam chu lcnh hnh 2.6 a.

Bc 1 xac nh phan lc lien ket tai ngam A : at cac phan lc lien ket tai A nh hnh 2.6 b, s dung ieu kien can bang tnh hoc e xac nh cac thanh phanphan lc nay.

Hnh 2.5. Chieu dng cua noi lc.

0z

N

0yQ

0xM

0z

M

a 2aA B C

Hnh 2.6

q

2M qa

a 2aA B C

q

2M qaAY

AM

A

AY

AMxM

yQa 2aB C

q

2M qa

yQ

xM

)a)b

)c )d

1

1A

Z

BNN


5/34



2 20 .2 .2 0 5

0 .2 0 2

0 0

A A A

y A A

z A

m M q a a qa M qa

F Y q a Y qa

F Z

Bc 2 dung mat cat 1 1 qua B cat dam thanh hai phan AB va BC. Gia sdam chu lc trong mat phang z , at cac thanh phan noi lc tng ng vao

hai phan nh hnh 2.6 c va 2.6 d. Xet mot trong hai phan, gia s xet phan bentrai nh hnh 2.6 c. S dung ieu kien can bang tnh hoc e xac nh cac thanhphan noi lc nay:

2

0 0 2

0 0

0 . 0 3

y A y y A

z z

B A A x x

F Y Q Q Y qa

F N

m M Y a M M qa

Neu xet phan ben phai nh hnh 2.6 d ta c:

2 2

0 .2 0 2

0 0

0 .2 . 0 3

y y y

z z

B x x

F Q q a Q qa

F N

m M q a a qa M qa

V du 2: Cho cot AB co kch thc, lien ket va chu lc nh hnh 2.7a. Xac nh cacthanh phan noi lc tren mat cat tai A cua cot.

at cac thanh phan noi lc vao mat cat tai A nh hnh 2.7 b. S dung ieu kien canbang tnh hoc e xac nh cac thanh phan phan lc nay.

Hnh 2.7

0,5m

2100 /q kN m

1 50 /q kN m

A

B

0,5m

A

B

xMyQ

N

1R

2R

0,5

3m

0,5

2m

1

2

50.0,5 25

1100 50 .0,5 12,5

2

R kN

R kN

1 50 /q kN m

2 100 /q kN m

)a )b


6/34



1 2 1 2

1 2

0 0 25 12,5 37,5

0 0

0,5 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

V du 3: Cho khung ABCDE co kch thc, lien ket va chu lc nh hnh 2.8a. Xacnh cac thanh phan noi lc tren cac mat cat 1 1, 2 2, 3 3, 4 4 .

Bc 1 xac nh phan lc lien ket tai ngam A : at cac phan lc lien ket tai A nh hnh 2.8 b, s dung ieu kien can bang tnh hoc e xac nh cac thanh phanphan lc nay.

2 210 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

C

Hnh 2.8

q

2M qa

A

3P qa

a

)a

)c)d

B

D E

2P qa

a

a

a

C

q

2M qa

A

3P qa

a

)b

B

D E

2P qa

a

a

aA

M1 1

2

2

3 3

4

4

2

1z

34

AX

AY

AY

1yQ

1x

M1

N

X

1z M

1 1

C

2M qa

3P qa

2xM

2yQ

2z2

q

D E

2P qa

33

3yQ

3xM

a

q

E4

4

4yQ

4xM

)e )f

3ZN


7/34



Bc 2 dung mat cat 1 1 cat khung thanh hai phan, xet phan ben di. at cacthanh phan noi lc tng ng vao mat cat 1 1 nh hnh 2.8 c. S dung ieu kiencan bang tnh hoc e xac nh cac thanh phan noi lc nay:

1 1

1 1

1 1

2

1 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

Tng t cho cac mat cat khac nh hnh 2.8d,e,f, ta co c cac thanh phan noilc:

2 2

3 3 3

4 4

2

2

2

3

2

4 4

3 ; 3 .

12 ; ; 2 .

21

. ; .2

y x

y z x

y x

Q qa M qa qa z

Q qa N qa M qa z qa

Q q z M q z

V du 4: Moc ch U co kch thc va chu lc nh hnh 2.9 a. Xac nh cac thanhphan noi lc tren mat cat A A .

Dung mat cat A A cat chi tiet thanh hai phan, xet phan di. at he truc toa o vacac thanh phan noi lc tng ng nh hnh 2.9 b. S dung ieu kien can bang tnh hoc exac nh cac thanh phan phan lc nay.

0 0

0 00 .6 0 6

x x

z z z

y y y

F Q

F N P N Pm M P b M Pb

x

x

y

z

yM

C

P

b

b

2b

4b

A A

AA

Hnh 2.9

)a

)b

xQ

q


8/34



V du 5: Truc AE c tren hai o lan tai ,A E, lien ket, chu lc nh hnh 2.10a.Xac nh cac thanh phan noi lc tren mat cat tai O .

Bc 1: v truc oi xng nen 2A BY Y P . Bc 2: Dung mat cat tai O cat truc lam hai phan, xet phan ben trai. at he truc

toa o va cac thanh phan noi lc vao mat cat tai O nh hnh 2.10c. s dung cacphng trnh can bang ta xac nh c cac thanh phan noi lc:

0 2 0

0 0

0 2 . 0 2

y y y

z z z

x x x

F P P Q Q P

m M M M M

m P z P z a M M Pz P z a

V du 6: Truc AB ngam tai A , au B c han vuong goc vi thanh BC va chu lcnh hnh 2.11a. Xac nh cac thanh phan noi lc tren mat cat tai A .

Xet mat cat tai A , at he truc toa o va cac thanh phan noi lc vao mat cat tai A nhhnh 2.11b. s dung cac phng trnh can bang ta xac nh c cac thanh phan noi lc:

1m

0,3m

A B

C

150P kN

1m

0,3m

A B

C

150P kN

x

Q

zM

xM

Hnh 2.11

)a)b

zM

xM

A

Q

150P kN

B

C

1m0,3m

Hnh 2.10

M 2M M

a 2a 2a a

P2P

P

AB

C D EO

M 2M M

a 2a 2a a

P2P

P

AB

C D E

z

O

AY EY

M

P

AB

O

2AY P

x

y

xM

zM

yQ

)a )b )c

a


9/34



0 150 0 150

0 150.0,3 0 45 .

0 150.1 0 150 .

y y y

z z z

x x x

F Q Q kN

m M M kN m

m M M kN m

1.5.Bieu o noi lc1.5.1. nh ngha Bieu o noi lc la o th mo ta qui luat phan bo noi lc doc theo truc thanh. oan chu lc: la oan ma tren o ham so xac nh noi lc la mot ham lien tuc. Cach chia oan chu lc: khi co s thay oi ve lc, lien ket ta phai tien hanh chiaoan chu lc mi.

1.5.2. Ve bieu o noi lc bang phng phap mat cat bien thienTrong moi oan chu lc ta s dung mot mat cat e thiet lap cac ham noi lc cho tngoan, sau o ve cac ham so nay len he truc ta c s phan bo noi lc doc theo truc thanh.

V du 7: Ve bieu o noi lc phat sinh trong dam nh hnh 2.13 a.

Bc 1 giai phong lien ket tai ,A B va at cac phan lc lien ket tng ng nhhnh 2.12 b.

2

2

30 .2 . 2 .2 .3 0

23

0 .2 .2 . 2 . 02

A B B

B A A

m q a a qa Y a qa a Y qa

m Y a q a a qa qa a Y qa

Bc 2 thiet lap bieu thc tnh noi lc trong hai oan ,AB BCDung mat cat 1 1 cat dam lam hai phan, xet phan ben trai va at cac thanh phannoi lc tng ng nh hnh 2.12 c.

22M qa

q

A B

P qa

C

2a a

22M qa

q

A B

P qa

C

2a aAY BY

q

A 1

1zAY yQ

xM

P qa

2z

2

yQ

xM C

3

2qa

1

2qa

qa

29

8qa

2qa

2qa

yQ

xM

)a )b

)c

)d

Hnh 2.12

1

1

2

2

10 2a

20 a


10/34



1 1

2

1 11 1 1 1

30 . 0 .

2

30 . . . 0 .

2 2 2

y A y y

A x x

F Y q z Q Q qa q z

z zm Y z q z M M qa z q

Ta thay tren oan AB yQ la ham bac nhat, the 1 0z va 1 2z a ta ve c bieu o

yQ tren oan AB . Ham xM la ham bac hai nen i tm cc tr va khao sat s loi,

lom cua o th

1 1

1

3 30

2 2

xM qa qz z az

, tai 1

3

2z a ham xM at cc tr.

2

2

1

0xM

qz

ham xM loi.

Tng t dung mat cat 2 2 cat dam lam hai phan, xet phan ben phai va at cac

thanh phan noi lc tng ng nh hnh 2.10 d.

2 2 2

0 0

0 . 0 .

y y y

x x

F Q P Q qa

m M P z M qa z

Ta thay tren oan BC yQ la ham hang so, xM la ham bac nhat nen the the 2 0z

va 2z a ta ve c o th yQ , xM tren oan BC nh hnh ve.

V du 8: Ve bieu o noi lc phat sinh trong cot chu lc nh hnh 2.13 a.

Bc 1: giai phong lien ket tai ngam A va at phan lc lien ket tng ng nhhnh 2.13 b. 0 3 2 .4 0 9z A AF qa qa q a N N qa .

P qa

3P

P

q3a

a

A

B

C

Hnh 2.13

3qa

4qa6qa

9qa zN

3P

P

q3a

a

A

B

C

AN

P qa

1 1

1z

2 2 2z

A

AN

1 1

1zq

1zN

C

3P

2 2

2zq

2zN

)a )b

)c

)d)e


11/34



Bc 2: thiet lap bieu thc tnh noi lc trong hai oan ,AB BC: tren oan AB dung mat cat 1 1 cach A mot oan 1z cat cot lam hai phan, xet phan di nh

hnh 2.13c va at noi lc tng ng vao mat cat. Tng t, tren oan BC dungmat cat 2 2 cach C mot oan

2

z cat cot lam hai phan, xet phan tren nh hnh

2.13d va at noi lc tng ng vao mat cat. S dung cac phng trnh can bangta xac nh c:

1 1 19 (0 3 )ZN qz qa z a , 1ZN la ham bac nhat.

2 2 23 (0 )ZN qa qz z a , 2ZN la ham bac nhat.

V du9: Ve bieu o noi lc phat sinh trong truc chu lc nh hnh 2.14 a.

Bc 1: giai phong lien ket tai ngam A va at phan lc lien ket tng ng nhhnh 2.14 b. 0 6 .2 0 3z A Am M ma m a ma M ma .

Bc 2: thiet lap bieu thc tnh noi lc trong hai oan ,AB BC: tren oan AB dung mat cat 1 1 cach A mot oan 1z cat truc lam hai phan, xet phan ben trai

nh hnh 2.14c va at noi lc tng ng vao mat cat. Tng t, tren oan BCdung mat cat 2 2 cach C mot oan 2z cat cot lam hai phan, xet phan ben

phai nh hnh 2.14d va at noi lc tng ng vao mat cat. S dung cac phngtrnh can bang ta xac nh c:

1 13 (0 )ZM ma z a , 1ZM hang so tren oan AB .

2 2 2(0 2 )ZM ma mz z a , la ham bac nhat 2ZM .

M ma

2a

6M

A BC

m

M ma

2a

6M

A BC

mAM

ma

3ma

3ma

M

Hnh 2.14

a

a

)a

)b

)e

AM1Z

M

1

A1

C

m

M ma

2ZM

2

2

)c

)d

1

1

2

2


12/34



1.5.3. Ve bieu o noi lc bang phng phap ve nhanh.

Lien he vi phan gia momen uon, lc cat va tai trong ngang phan boXet dam chu uon phang trong mat phang yz vi tai trong la cac lc tap trung, lc phan

bo va ngau lc tap trung nh hnh 2.15. Dung hai mat cat 1 1 va 2 2 tach t oan chulc phan boBC mot phan to chieu dai dz va at cac thanh phan noi lc tng ng vao haimat cat nh hnh 2.16a.

0 0 ( )yy y y ydQ

F Q Q dQ qdz q zdz

(2.6)

Nhan xet 1:bieuo lc cat hn bieu o tai trong phan bo mot bac.

Tch phan hai ve bieu thc (2.6):C

CC B

y y y qB

B

dQ qdz Q Q S (2.7)

Nhan xet 2: khi i t trai qua phai, lc cat cuoi oan bang lc cat au oan conghp lc phan bo tren oan o (hp lc phan bo hng len dng, hng xuong am).

2

2 x x x y

.( )

0 M - (M dM ) Q dz 02

q dz

m

, bo qua ai lng vo cung bebac cao 2( )dz ta c: y

x Qdz

dM (2.8)

Nhan xet 3: bieu o mo men uon hn bieu o lc cat mot bac. Neu trong nhng

oan mo men uon co bac hai, mo men uon at cc tr tai nhng iem co 0yQ .

Tch phan hai ve bieu thc (2.8):y

CC

C B

x y x x QB

B

dM Q dz M M S (2.9)

Nhan xet 4: khi i t trai qua phai, mo men uon cuoi oan bang mo men uon au

oan cong dien tch bieu o lc cat tren oan o. Lien he gia momen uon, lc cat va tai trong ngang tap trung

Hnh2.15Dam chu lc

dz

dz

1

1

2

2

3

3

4

4 q z

M

P

B C D


13/34



Dung hai mat cat 3 3 va 4 4 tach t dam hai ben D mot phan to chieu dai dz va atcac thanh phan noi lc tng ng vao hai mat cat nh hnh 2.16b.0 0t p p t y y y y yF Q P Q Q Q P (2.10)

Nhan xet 5: khi i t trai qua phai neu tren s o tnh co lc tap trung bieu o lc

cat co bc nhay, gia tr buc nhay bang gia tr lc tap trung, chieu bc nhay cungchieu vi lc tap trung.

0 . . 02 2

t t p p

D y x y x

dz dz m Q M M Q M , bo qua thanh phan vo cung be bac cao

ta c: p tx xM M M (2.11)

Nhan xet 6: khi i t trai qua phai neu tren s o tnh co ngau lc tap trung bieu omo men uon co bc nhay, gia tr buc nhay bang gia tr ngau lc tap trung, nhayxuong khi ngau lc quay cung chieu kim ong ho, nhay len cho trng hp ngc lai.

Lien he gia lc doc va cac tai trong doc.

Dung hai mat cat 1 1 va 2 2 tach t oan chu lc phan boBC mot phan to chieu daidz va at cac thanh phan noi lc tng ng vao hai mat cat nh hnh 2.17b.

0 . 0 zz z z zdN

F N q dz N dN qdz

(2.12)

Nhan xet 7: bieu o lc doc hn bieu o tai trong phan bo mot bac.

Hnh2.16 Lien he gia tai trong ngang va noi lcdz

q

yQ

xM

y yQ dQ

x xM dM

1

1 2

2

a

3

3 4

4

t

yQtx

M

p

yQ

p

xM

b

D

M

P

dz

Hnh 2.17: Lien he gia tai trong doc va noi lc.

2

2

1

1

q z qPzN

z zN dN

dz

dz

1

1

2

2B C D

a bt

zN pzN

dz

3

3

4

4

cP

D3

3

4

4


14/34




CC B

z z qB

B

dN qdz N N S (2.13)

Nhan xet 8: lc doc cuoi oan bang lc doc au oan cong hp lc phan bo tren

oan o (hp lc phan bo gay keo dng, gay nen am).Dung hai mat cat 3 3 va 4 4 tach t thanh hai ben D mot phan to chieu dai dz vaat cac thanh phan noi lc tng ng vao hai mat cat nh hnh 2.17c.

0 0t p p t z z z z zF N P N N N P (2.14)

Nhan xet 9: neu tren s o tnh co lc tap trung bieu o lc doc co bc nhay, gia

tr bc nhay bang gia tr lc tap trung, nhay ve pha dng khi lc gay keo, nhay vepha am khi lc gay nen.

Lien he gia momen xoan va cac tai trong momen xoan.

Dung hai mat cat 1 1 va 2 2 tach t oan chu tai phan bo BC mot phan to chieu daidz va at cac thanh phan noi lc tng ng vao hai mat cat nh hnh 2.18b.

0 . 0 zz z z zdM

m M dM m dz M m

dz

(2.15)

Nhan xet 10: bieu o mo men xoan hn bieu o tai trong phan bo mot bac.


CC B

z z mB

B

dM mdz M M S (2.16)

Nhan xet 11:mo men xoan cuoi oan bang mo men xoan au oan cong hp ngau

lc phan bo tren oan o (hp mo men xoan lc phan bo cung chieu kim ong hodng, ngc chieu kim ong ho am).

Dung hai mat cat 3 3 va 4 4 tach t thanh hai ben D mot phan to chieu dai dz va

at cac thanh phan noi lc tng ng vao hai mat cat nh hnh 2.18c.0 0t p p t z z z z zm M M M M M M (2.14)

Nhan xet 12: neu tren s o tnh co mo men xoan tap trung bieu o mo men xoan

co bc nhay, gia tr bc nhay bang gia tr ngau lc tap trung, nhay ve pha dngkhi ngau lc cung chieu kim ong ho, nhay ve pha am khi ngau lc quay ngc chieukim ong ho.

Hnh 2.18: Lien he gia momen tai trong va noi lc.

2

2

1

1dz

z zM dM

zM m z

m

1

1

2

2dz

p

zM

1

1

2

2dz

t

zM3

3

4

4 BCD

M M

D

a b c


15/34



V du 10: Ve bieu o noi lc phat sinh trong cot chu nen ung tam nh hnh 2.20.

Phan lc lien ket tai ngam A : 0 .4 2 3 0 9z A AF N q a qa qa N qa Tai C co lc tap trung 3 3P qa gay nen nen bieu o co bc nhay ve pha

am (ben trai) mot oan bang 3qa t v tr khong thuoc ng chuan.

Noi lc pha tren cua mat cat tai B . 3 4B Cz ztrenN N q a qa qa qa Tai B co lc tap trung 2 2P qa gay nen nen bieu o N co bc nhay ve pha

am (ben trai) mot oan bang 2qa t gia tr 4qa nen N pha di mat cat

taiB co gia tr 4 2 6qa qa qa .

Noi lc pha tren cua mat cat tai A : .3 6 3 9A Bz ztren duoiN N q a qa qa qa

Tai A co lc tap trung 9A qa gay keo nen bieu o N co bc nhay ve phadng (ben phai) mot oan bang 9qa t gia tr 9qa nen N pha di mat cat

tai A co gia tr 9 9 0qa qa .

V du11: Ve bieu o noi lc phat sinh trong cot chu nen ung tam nh hnh 2.20.

P qa

3P

P

q3a

a

A

B

C

Hnh 2.19

3qa

4qa

6qa

9qa N

3P

P

q3a

a

A

B

C

AN

P qa

Cach ve bieu o noi lc trong thanh chu keo-nen ung tam: Bieu o lc doc hn bieu o tai trong phan bo mot bac. Neu tren s o tnh co lc tap trung bieu o lc doc co bc nhay, gia trbc nhay bang gia tr lc tap trung, nhay ve pha dng khi lc gay keo, nhayve pha am khi lc gay nen. Lc doc cuoi oan bang lc doc au oan cong hp lc phan bo tren oano (hp lc phan bo gay keo dng, gay nen am).


16/34



Phan lc lien ket tai ngam A : 0 .3 5 0z A AF N q a qa qa N qa Tai C co lc tap trung P qa gay nen nen bieu o N co bc nhay ve pha

am (ben trai) mot oan bang qa t v tr 0 thuoc ng chuan.

Noi lc pha tren cua mat cat tai B 0B C Cz z ztren duoi duoiN N N qa (oanBC khong co tai phan bo nen hang so).

Tai B co lc tap trung 5 5P qa gay keo nen bieu o N co bc nhay ve phadng (ben phai) mot oan bang 5qa t gia tr qa nen N pha di mat cat

taiB co gia tr 5 4qa qa qa .

Noi lc pha tren cua mat cat tai A : .3 4 3A Bz ztren duoiN N q a qa qa qa Tai A co lc tap trung AN qa gay nen nen bieu o N co bc nhay ve pha

am (ben trai) mot oan bang qa t gia tr qa nen N pha di mat cat tai A co

gia tr 0qa qa .

Cach ve bieu o noi lc trong truc chu xoan: Bieu o momen xoan hn bieu o tai trong phan bo mot bac. Neu tren s o tnh co ngau lc tap trung bieu o momen xoan co bc nhay,gia tr bc nhay bang gia tr ngau lc tap trung, nhay ve pha dng khi nhnvao mat cat thay ngau lc quay cung chieu kim ong ho, nhay ve pha am chotrng hp ngc lai. Momen xoan cuoi oan bang momen xoan au oan cong hp ngau lc phanbo tren oan o (hp ngau lc phan bo quay cung chieu kim ong ho dng,ngc lai la am).

Hnh 2.20

P qa

q3a

a

A

B

C

AN

P qa

q3a

a

A

B

C

2,5P2,5P2,5P2,5P

qa

4qa

N

4qa

qa


17/34



V du 12: Ve bieu o noi lc phat sinh trong truc chu xoan nh hnh 2.21 a.

Phan lc lien ket tai ngam A : at phan lc lien ket tai ngam A nh hnh 2.21 b0 6 .2 0 3z A Am M ma m a ma M ma

Tai C co ngau lc tap trung M ma cung chieu kim ong ho nen bieu o M co bc nhay ve pha dng (ben tren) mot oan bang qa t v tr 0 thuocng chuan.

Noi lc pha ben phai cua mat cat tai B :.2 2 3B Cz zphai

M M m a ma ma ma

Tai B co ngau lc tap trung 6 6M ma ngc chieu kim ong ho nen bieu oM co bc nhay ve pha am (ben di) mot oan bang 6ma t gia tr 3ma

nen M ben trai mat cat taiB co gia tr 3 6 3ma ma ma .

Noi lc pha ben phai cua mat cat tai A : 0 3A B Bz z zphai trai traiM M M ma (tren oan BA khong co tai phan bo nen M hang so).

Tai A co ngau lc tap trung 3AM ma cung chieu kim ong ho nen bieu oM co bc nhay ve pha dng (ben tren) mot oan bang 3qa t gia tr 3ma

nen M pha trai mat cat tai A co gia tr 3 3 0ma ma .

V du 13: Ve bieu o noi lc phat sinh trong truc chu xoan nh hnh 2.22a. Phan lc lien ket tai ngam A :

M ma

2a

6M

A B C

m

M ma

2a

6M

A BC

mM

ma

3ma

3ma

M

Hnh 2.21

a

a

)a

)b

)c


18/34



0 4 0 3z A Am M M M M M Tai C co ngau lc tap trung M cung chieu kim ong ho nen bieu o M co

bc nhay ve pha dng (ben tren) mot oan bang M t v tr 0 thuoc ng

chuan. Noi lc pha ben phai cua mat cat tai B : 0B C Cz z zphaiM M M M (trenoan CB khong co tai phan bo nen M hang so).

Tai B co ngau lc tap trung 4M ngc chieu kim ong ho nen bieu o M cobc nhay ve pha am (ben di) mot oan bang 4M t gia tr M nen M

ben trai mat cat taiB co gia tr 4 3M M M .

Noi lc pha ben phai cua mat cat tai A : 0 3A B Bz z zphai trai traiM M M M (tren oan BA khong co tai phan bo nen M hang so).

Tai A co ngau lc tap trung 3A

M M cung chieu kim ong ho nen bieu o M

co bc nhay ve pha dng (ben tren) mot oan bang 3M t gia tr 3M nenM pha tr mat cat taiA co gia tr 3 3 0M M .

M

2a

4M

A BC

M

2a

A BC

M

M

3M

M

a

4M

a

Hnh 2.22

)a

)b

)c


19/34



V du14: Ve bieu o noi lc phat sinh trong dam chu uon phang nh hnh 2.23 a. Phan lc lien ket tai cac goi ,A B : at cac phan lc lien ket tng ng tai ,A B

nh hnh 2.23 b.

0 3 .2 .3 02

0 .2 3 . 02

A B B

B A A

Pm Pa Pa Y a P a Y

Pm Pa Y a Pa P a Y

Ve bieu o lc cat yQ : tren oan ,AB BC khong co lc phan bo nen bieu o lc cat yQ co

dang hang so. Tai A co lc tap trung / 2AY P hng len nen bieu o yQ co bc nhay hng

len mot oan bang / 2P t v tr 0 thuoc ng chuan.

Lc cat ben trai cua mat cat tai B : 0 / 2B A Ay y ytraiQ Q Q P (tren oan AB khong co tai phan bo nen yQ hang so).

Tai B co lc tap trung / 2BY P hng len nen bieu o yQ co bc nhay hnglen mot oan bang / 2P t gia tr / 2P nen yQ ben phai mat cat tai B co gia

tr / 2 / 2P P P .

Lc cat ben trai cua mat cat tai C: 0C B By y ytrai phai phaiQ Q Q P (tren oanBC khong co tai phan bo nen yQ hang so).

Cach ve bieu o noi lc trong dam chu uon phang: Bieu o lc cat:

Bieu o lc cat hn bieu o tai trong phan bo mot bac. Khi i t trai qua phai, neu tren s o tnh co lc tap trung bieu o lc cat cobc nhay, gia tr bc nhay bang gia tr lc tap trung, chieu bc nhay cungchieu vi lc tap trung. Khi i t trai qua phai, lc cat cuoi oan bang lc cat au oan cong hp lcphan bo tren oan o (hp lc phan bo hng len dng, hng xuong am). Bieu o momen uon:

Bieu o momen uon hn bieu o lc cat mot bac. Khi i t trai qua phai, neu tren s o tnh co ngau lc tap trung bieu omomen uon co bc nhay, gia tr bc nhay bang gia tr ngau lc tap trung, nhayxuong khi ngau lc quay cung chieu kim ong ho, nhay len khi ngau lc quay

ngc chieu kim ong ho. Khi i t trai qua phai, momen uon cuoi oan bang momen uon au oancong dien tch lc cat tren oan o (Neu tren oan o momen uon la ham bachai, momen uon se at cc tr tai v tr lc cat bang khong).


20/34



Tai C co lc tap trung P hng xuong nen bieu o yQ co bc nhay hngxuong mot oan bang P t gia tr P nen yQ ben phai mat cat tai C co gia tr

0P P .

Ve bieu o mo men uonxM : (Bieu o mo men uon tren am di dng) ta a biet bieu

o momen uon xM hn bieu o lc cat yQ mot bac nen tren oan ,AB BC bieu o

momen uon xM co dang bac nhat.

Tai A co ngau lc tap trung M Pa cung chieu kim ong ho nen bieu o xM co bc nhay hng xuong mot oan bang Pa t v tr 0 thuoc ng chuan.

Momen uon ben trai cua mat cat tai B : 1

.2 22yABB A

x x Qtrai phaiM M S Pa P a Pa . Tai B co ngau lc tap trung 3M Pa ngc chieu kim ong ho nen bieu o xM

co bc nhay hng len mot oan bang 3Pa t gia tr 2Pa nen xM ben phai

mat cat taiB co gia tr 2 3Pa Pa Pa .

Momen uon ben trai cua mat cat tai C: . 0y

BCC B

x x Qtrai phaiM M S Pa P a .

a2a

P3M

A CB

a2a

P3M Pa

A CB

AY BY

M Pa

P1

2P

Pa

2PaPa

yQ

xM

Hnh 2.23

M Pa

)a

)b

)c

)d


21/34



V du 15: Ve bieu o noi lc phat sinh trong dam chu uon phang nh hnh 2.20.

Phan lc lien ket tai cac goi ,B C:2

2

50 . 2 .4 .2 .4 0

4

150 .5 2 .4 .4 .2 0

4

B C C

C B B

m qa a qa q a a Y a Y qa

m qa a qa Y a q a a Y qa

Ve bieu o lc cat yQ : tren oan AB khong co lc phan bo nen bieu o yQ tren oan

AB co dang hang so, tren oan BC lc phan bo la hang so nen bieu o yQ tren oan BC

co dang bac nhat. Tai A co lc tap trung P qa hng xuong nen bieu o yQ co bc nhay

hng xuong mot oan bang qa t v tr 0 thuoc ng chuan.

P qa22M qa

q

a 4a

A B C

P qa2

2M qaq

a 4a

A B C

BY CY

qa

11

4qa

5

4qa

225

32qa

2qa

23qa

Hnh 2.24

I


22/34



Lc cat ben trai cua mat cat tai B : 0B A Ay y ytraiQ Q Q qa (tren oan AB khong co tai phan bo nen yQ hang so).

Tai B co lc tap trung 154

BY qa hng len nen bieu o yQ co bc nhay

hng len mot oan bang15

4qa t gia tr qa nen yQ ben phai mat cat tai B

co gia tr15 11

4 4qa qa qa .

Lc cat ben trai cua mat cat tai C:

11 54

4 4

BCC B

y y qtrai phaiQ Q R qa qa qa .

Tai C co lc tap trung 54

CY qa hng len nen bieu o yQ co bc nhay hng

len mot oan bang 54

qa t gia tr 54

qa nen yQ ben phai mat cat tai C co gia

tr5 5

04 4

qa qa .

Ve bieu o mo men uonxM : (Bieu o mo men uon tren am di dng) tren oan AB

bieu o yQ co dang hang so nen tren oan AB bieu o xM co dang bac nhat, tren oan

BC bieu o yQ co dang bac nhat nen tren oan BC bieu o xM co dang bac hai, v vay

tren oan BC tai cac iem 0yQ bieu o xM at cc tr.

Tai A khong co ngau lc tap trung nen bieu o xM khong co bc nhay . Momen uon ben trai cua mat cat tai B : 20 .

y

ABB A

x x QtraiM M S qa a qa .

Tai B ngau lc tap trung 22M qa ngc chieu kim ong ho nen bieu o xM co bc nhay hng len mot oan bang 22qa t gia tr 2qa nen xM ben phai

mat cat taiB co gia tr 2 2 22 3qa qa qa .

Trong oan BC bieu o lc cat bac nhat nen bieu o mo men uon bac hai. Taimat cat I lc cat 0yQ nen tai ay xM at cc tr. V vay ta phai tm gia tr

mo men uon tai mat cat nay:

2 21 11 11 253 . .2 4 4 32y

BII B

x x QphaiM M S qa qa a qa .

Tai I khong co ngau lc tap nen bieu o xM khong co bc nhay . Momen uon ben trai cua mat cat tai B :

225 1 5 5. . 032 2 4 4y

ICC I

x x QtraiM M S qa qa a .

Tai C khong co ngau lc tap trung nen bieu o xM khong co bc nhay .


23/34



II)BAI TAP2.1-> 2.2. Xac nh cac thanh phan noi lc (tr so, phng, chieu) phat sinh tren mat catAA cua cac chi tiet chu tac dung cua lc 100P N nh hnh B.2.1 va hnh B.2.2. Cac

kch thc cho tren hnh co n v la milimet.

(Gi y: at he truc toa o tai trong tam mat cat sao cho truc z trung vi phap tuyen cuamat cat sau o at cac thanh phan noi lc tng ng e can bang vi ngoai lc tac dung)

2.3. Moc can truc mang tai trong 20kN nh hnh B2.3, mat cat ngang tai mat cat AA lahnh ch nhat. Xac nh cac thanh phan noi lc (tr so, phng, chieu) phat sinh tren matcat AA . Cac kch thc co n v la milimet.

P

25R

100

A A

Hnh B.2.1

186

40

16,67( 2 :1)AA TL

C

P

50

25

A A

Hnh B.2.2

193

22 3

8,21

C

( 2 :1)AA TL


24/34



2.4. Tay quay co kch thc va chu lc nh hnh B.2.4, mat cat ngang tai mat cat AA lahnh ch nhat. Xac nh cac thanh phan noi lc (tr so, phng, chieu) phat sinh tai trongtam cua gia tay quay. Cac kch thc co n v la milimet.

2.5. Cot hnh tru rong ng knh trong 200mm , ng knh ngoai 250mm c han vimot congxon chu mot tai tnh 20kN nh hnh B.2.5. Tam cua tai cach tam cua cot500mm . Xac nh cac thanh phan noi l c (tr so, phng, chieu) phat sinh trong cot.

2.6. Mot chi tiet may co hnh dang va kch thc nh hnh B.2.6, chu mot tai 20kN . Xacnh cac thanh phan noi lc (tr so, phng, chieu) phat sinh trong mat cat ch U .

20kN

100

20

50

150

A A

Hnh B.2.3

20kN

500

250

200

Hnh B.2.5

15kN 30kN

140

120

80

Hnh B.2.4

A

A


25/34



2.7. Lc 20P kN theo phng ngang tac dung bi day dai len mot congxon nh hnhB.2.7. Tai mot iem cach tng 75mm , mat cat ngang cua congxon co hnh ch T . Xacnh cac thanh phan noi lc (tr so, phng, chieu) phat sinh trong mat cat AA .2.8. Mot gia bang thep nh hnh B.2.8, chu tac dung cua lc keo 6kN nghieng goc 045 so

vi phng ngang. Mat cat ngang cua gia la hnh ch nhat. Xac nh cac thanh phan noilc (tr so, phng, chieu) phat sinh trong mat cat tai ngam.

2.9. Ma kep ch C nh hnh B.2.9, chu mot tai 25P kN . Mat cat ngang cua kep la hnhch nhat. Xac nh cac thanh phan noi lc (tr so, phng, chieu) phat sinh trong mat cat

,AA BB va CC.P

P

5060

90

9

12

A

A

75Hnh B.2.7

AA

61,78

C

90

20kN 20kN

20

90

30

Hnh B.2.6


26/34



2.10. Thanh cong mat cat ngang khong oi, hnh tron ng knh d , chu nen bi mot lc15P kN cach tam truc mot oan 200mm . Xac nh cac thanh phan noi lc (tr so,

phng, chieu) phat sinh trong mat cat AA .

2.11. Tay quay co kch thc va chu lc nh hnh B.2.4, mat cat ngang tai mat cat AA lahnh ch nhat. Xac nh cac thanh phan noi lc (tr so, phng, chieu) phat sinh tai trongtam cua gia tay quay. Cac kch thc co n v la milimet.2.12. Cho cot AB lam bang betong chu lc nh hnh 2.34. Biet rang betong co tronglng rieng 325 /kN m .

Ve s o tnh. Xac nh noi lc tai mat cat chan cot.

P200

AA

Hnh B.2.10 40 25

75

50

25

125

P

Hnh B.2.11

P

P

40

140

150

t

b

045

AA

B

B

C

C

Hnh B.2.9

6kN0

4575

130

56

28

Hnh B.2.8


27/34



2.13. Can thiet ke mot tay quay co hnh dang, kch thc va chu lc nhhnh 2.13, lc25P kN tac dung vuong goc vi tay quay tai O . Mat cat ngang tai mat cat AA la hnh

vuong canh b b , mat cat ngang tai mat cat BB la hnh tron ng knh d . Cac kchthc cho tren hnh co n v milimet. Xac nh cac thanh phan noi lc (tr so, phng,chieu) cua mat cat AA , BB .2.12. Thanh cng AC c gi bi he thanh nh hnh B.2.12. Xac nh ng lc trong cacthanh cua he dan.

100 20

80

250

P

Hnh 3.13

d

A

b

A B

B 80b

OO

AA

1 12P kNz

x

l 2bb

Hnh 3.12

A

B

2 3P kN

3 m

4 m

3,5 m

030

200 /N m

100P N

A

B

C

Hnh B.2.13

a a a

a

15P kNABCD

E F G

Hnh B.2.12


28/34



2.13. Cho he chu lc nh hnh B.2.13. Xac nh phan lc lien ket tai khp quay A va nglc trong thanhBC. Khi tnh bo qua be day cua cac phan t trong he.

2.14. Cac thanh ,AB DG tuyet oi cng chu lien ket khp xoay tai ,A D va c gi bicac thanh thanh giang ,BC HG nh hnh B.2.14. Xac nh ng lc trong cac thanh

,BC HG .

2.15. Cho he dan co kch thuc va chu lc nh hnh B.2.15a, B.2.15b, B.2.15c. Xac nhng lc trong cac thanh cua dan.

2.16. Cho khung chu lc nh hnh 2.16. Xac nh noi lc tai cac mat cat: Mat cat tai ngam A . Mat cat tai B thuoc cot AB , mat cat tai B thuoc cot BD va mat cat tai B thuoc

dam BC. Mat cat tai D thuoc cot BD va mat cat tai D thuoc dam DE.

a

A B C

F G

D E

7kN

7kN

7kN

7kN

7kN

H

a a a

030 030

Hnh B.2.15c

a

a

a

15P kN

A B

C

F G

Hnh B.2.15b

D E

a

a a a

a

15P kNABCD

E F G

Hnh B.2.15a

15P kN15P kN

q

3P qa

AB

C

DEFG

H

a a 2a

2a,E F

, 2E F

Hnh B.2.14

060


29/34



2.17. Xet mot oan ap bang be tong dai 1m , chu lc nh hnh B.2.17. Xac nh noi lctai mat cat chan ap. Biet rang be tong co trong lng rieng 325 /kN m .

2.18. Ve bieu o noi lc phat sinh trong cac cot nh hnh B.2.18.

1m 3m

5m

1m

Hnh B.2.17

225 /kN m

C

Hnh B.2.16

q

2M qa

A

3P qa

a

B

D E

2P qa

a

a

a

P qa

P

q4a

a

A

B

C

Pl l

P qaP

q3a

a

A

B

C

2P

l lP qaP

q2a

a

A

B

C

2P

l lP qaP

q3a

a

A

B

C

l l

Hnh B.2.18-1 Hnh B.2.18-2 Hnh B.2.18-3 Hnh B.2.18-4


30/34


31/34



2.20. Xac nh cac phan lc lien ket va ve cac bieu o noi lc phat sinh trong cac dam nhhnh B.2.20.

P

a 2a

A B C

2a

D

M Pa

a 4a

A B D

22M qaq

P=2qaq

a a a

A B C D

21

2M qa

40P kN

1m 2m

A B C

2m

D

30 .M kN m 60 .M kNm

Hnh B.2.20-1 Hnh B.2.20-2

Hnh B.2.20-3 Hnh B.2.20-4

3P

3a

A B C

2a

2M Pa 70P kN

3m

A B C

2m

20 /q kN m

Hnh B.2.20-5 Hnh B.2.20-6

22M qa

q

2a a

A B

P qa

C

Hnh B.2.20-7

P qa22M qaq

3a a

A B C

2M qa

60P kN30 .M kN m20 /q kN m

4m 1m

A B C

P qa23M qa

q

2a a

A B C

2M qa

Hnh B.2.20-8

Hnh B.2.20-9 Hnh B.2.20-10


32/34



2.21. Xac nh cac phan lc lien ket va ve cac bieu o noi lc phat sinh trong cac dam nhhnh B.2.21.

2.22. Truc AE mat cat ngang khong oi hnh tron, c at tren hai o lan tai ,A E (bo quama sat tai cac o lan). Tren truc ngi ta gan ba banh rang , ,B C D . Hai banh rang ,B D

giong nhau co cung ng knh 2 160d mm , chu tac dung cua lc vong 2 1250tF N va

lc hng tam2

455rF N . Banh rang C co ng knh 1 400d mm chu tac dung cua lc

AB C

DE

3P

/ 2PP

2P Pa a a a

2M

MM

2P

x

y

a a a

M

P 2P

M

A B CD

P2P

Hnh B.2.21-3 Hnh B.2.21-4

23M qa P qaP qa q

a 2a a

A B C D

5m 2m 2m

AB C

D

70P kN

30 .M kN m10 /q kN m

Hnh B.2.20-15 Hnh B.2.20-16

P qa 22M qaq

a 4a

A B C

Hnh B.2.20-12

P qa23M qaq

a 2a a

A B C D

Hnh B.2.20-

a2a2a

AB C

D

P 2P

M

M

Hnh B.2.21-2

a a aM

P 2PM

x

y

zA B C

D

Hnh B.2.21-1

2aa a

2

1M qa2

2 2M qaP qa

AB C D

q

Hnh B.2.20-14

2a a a

AB C

D

P qa23

2M qa

q

Hnh B.2.20-


33/34



vong1

1000tF N va lc hng tam 1 360rF N nh hnh B.22. Ve bieu o noi lc phat

sinh trong truc AE.

2.23. Truc AB ngam tai A , au B c han vuong goc vi thanh BC va chu lc nhhnh B.2.23. Ve bieu o noi lc phat sinh trong truc AB .

2.24. Cot bac ABC ngam tai A va chu lc trong mot mat phang nh hnh B.2.24. Ve s o tnh cho cot. Ve cac bieu o noi lc phat sinh trong cot.

2.25. CotAB ngam tai A va chu lc nh hnh B.2.25. Biet rang cot lam bang betong cotrong lng rieng 325 /kN m . Ve s o tnh cho cot. Ve cac bieu o noi lc phat sinh trong cot.

75P kN

15 /q kN m4m

2m

A

B

C

0,5m

35P kN

75P kN

12 /q kN m5m

3m

A

B

C

0,5m

35P kN

20P kN

0,3m

45P kN

12 /q kN m5m

3m

A

B

C

0,5m

20P kN

10P kN

0,2m

Hnh B.2.24-1 Hnh B.2.24-2 Hnh B.2.24-3

1m

0,3m

A B

C

150P kN

Hnh B.2.23

1rF1tF

2tF

2tF2rF 2rF

A B CD E

a 3a 3a a

Hnh B.2.22


34/34


2.26. Cot AB nghieng mot goc 060 so vi phng ngang, ngam tai A va chu lc trongmot mat phang nh hnh B.2.26. Ve cac bieu o noi lc phat sinh trong cot.2.27. Cot AC thang ng, ngam tai A va chu lc nh hnh B.2.27. Ve cac bieu o noi lcphat sinh trong cot.

Hnh B.2.26

060

4m

A

B

75P kN

x

y

z

A

B

C

1 55P kN

2 25P kN

045

060

2m

2m

Hnh B.2.27

5P qa

q

z

y

a 2bb

Hnh B.2.25

140936393 Bai Tap Suc Ben Vat Lieu

Documents

Transcript of 140936393 Bai Tap Suc Ben Vat Lieu