mos2-150817134311-lva1-app6892

7/21/2019 mos2-150817134311-lva1-app6892

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TORSION

A SEMINAR ON

SHREE SAD VIDYAMANDAL INSTITUTE OF

TECHNOLOGY BHARUCH

CIVIL ENGINEERING DEPARTMENT

SUB : MECHANICS OF SOLIDS

PREPARED BY

PATEL MOHAMMED ASFAK (140453106007

PATEL NIRMAL

(14045310600!

RANA SAMIR

(140453106013

RANA HETAL

(14045310601"

YADAV DIVYA

(140453106016

GUIDED BY :

ER# N#P#SONI

1$7$161

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TORSION OF CIRCULAR SHAFT

TOR%UE OR TURNING MOMENT OR T&ISTINGMOMENT :'

I )*+,-./ *2 -.- *), / 82 ,- ,.*9/,.; ).-9 - 2 ,- -,. 2#

T- ,.*9/, , .; * ,8./ )-.+ / *</2 /,. ,-, ./9 -) * 8<<; ;2 ,- , *), -. ,- *; -,.8/,*=< -/, *, -9 2/,*+ ).-9 , *>/ -) , *),#

T 9-9, -) +-8< *+,/ - , *), / +*<<2 ,-.?8 -.,8./ 9-9, -. ,/,/ 9-9,#

7/21/2019 mos2-150817134311-lva1-app6892


T-.?8 @ ,8./ )-.+ > 2/*9,. -) *),

T @ F > "R

. : T@T-.?8 F@T8./ )-.+ S@R*2/8 -) , *),

U/, -) T-.?8(T / N#99 -. N#99

R

F

F

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ANGLE OF T&IST (

& , *), / 8=+,2 ,- T-.?8 (T-/, A- , 8.)*+ -) , *), +-9 ,- A -/,/-#

T *< AOA *, , +,. -) , *), / +*<<2

, *< -) ,/,#

AOA@ @A< -) ,/,

A< -) ,/, / 9*8.2 / .*2/*#

A

-A

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SHEAR STRESS IN SHAFT:(

& * *), / 8=+,2 ,- ?8*< *2 --/,2 +-8< - *> +-/+/2 /, , *>/ -), *), , *), / */2 ,- = / 8. ,-./-*2 *, *; -/, / , +,/- -) , *), ,./<< = /28+2#

T*, ,. / +*<<2 *. ,. / *),#

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STRENGTH OF SHAFTS

M*>/989 ,-.?8 -. -. , *), +* ,.*9/,).-9 - 8<<; ,- *-,. / +*<<2 ,., -) *),#

(* F-. -</2 +/.+8<*. *),:

M*>/989 ,-.?8 (T/ / =; :

. D @ 2/*# -) , *),

@*. ,. / , *),

3

16 DT ××= τ

π

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(B )-. -<<- +/.+8<*. *),

9*>/989 ,-.?8 (, / / =;#

&. 2@ -8,. 2/* -) *), 2@/. 2/* -) *),#

D

d DT

44

16

−××= τ

π

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ASSUMPTION IN THE THEORY OF TORSION:

T )-<<-/ *89,/- *. 9*2 /< 2/-8, *. ,. / * +/.+8<*. *), 8=+,2 ,-,-./-#

1 T 9*,./*< -) *), / 8/)-.9 ,.-8-8, ,<,#

" T ,/, *<- , *), / 8/)-.9#

3 T *), / -) 8/)-.9 +/.+8<*. +,/- ,.-8-8,, <,#

4 C.- +,/- -) , *), /+ *. <* =)-.,/, .9*/ <*/ *),. ,/,#

5 A<< .*2// /+ *. ,.*/, =)-. ,/, .9*/,.*/, *),. ,/,#

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POLLAR MOMENT OF INERTIA : (

T 9-9, -) /.,/* -) * <* *.* /,.+, ,- * *>/ .2/+8<*. ,- , <* -), 8. / +*<<2 -<*. 9-9, -) /.,/*#

A . , .2/+8<*. *>/ ,-.9#

J I I I YY XX ZZ

=+=

44

6464 D D ×+×=

π π

4

32 D J ×=

π

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THEORY OF TORSION AND TORSION E%UATION

C-/2. * *), >2 *, - 2 8=+,2,- ,-.?8 *, , -,. 2#

L, T@ T-.?8

<@ <, -) , *),

R@R*2/8 -) , *),

A * .8<, -) ,-.?8 .; +.-'+,/- -), *), /<< = 8=+,2 ,- *. ,.#

L/ CA - , 8.)*+ -) , *), /<< =2)-.9 ,- CA *2 OA ,- OA * - /

8.# L, ACA@*. ,.*/

AOA@*< -) ,/,

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TORSION RIGIDITY

L, ,/,/ 9-9, P.-28+ * ,/, .*2/* /<, L#

)-. / *), , ,/, / ,.)-. .--.,/-*<,- , ,/,/ 9-9, T#

I * =*9 , =2/ 9-9, .-28+2+,/- / , *9 9*. * ,-.?8 .-28+

* ,/, / *), # T ?8*,/,; C ,*2 )-. , ,-.?8 .?8/.2 ,-

.-28+ * ,/, -) 1 .*2/* . 8/, -) , *),#

T ?8*,/,; C +-..-2/ ,- * /9/<*. EI /

>./- )-. 2+,/- -) =*9 EI / - *

L

C

J

T θ .

=

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EJAMPLE FOR SHAFT

EJAMPLE 1:' C*<+8<*, 2/*9,. -) *), ,- ,.*9/, 10 K& *, * 2

-) 15 H# T 9*>/989 *. ,. -8<2 -, >+2 609*#

P @ 10

N @ 15 H @ 15 +;+<$+ @ 15 > 60 .9

@ !00 .9

@ 60 M*

60

T N2P π

=

60

T90021010

3 ××=×

π

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T @ 106#10 N#9

-

D @ "0#0 99

3

16T D××= τ

π

33

60161010.106 D××=×

π

0.90063= D

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EJAMPLE ":'

A *), -) 60 99 2/*9,. .-,*, /, 10 .9# I).9//=< *. ,. / 100 M* 2 ,-.?8 *2 -./ K&#

S-<8,/-:'

D @ 60 99

N @ 10.9

@ 100 M*

3D16

××= τ π

T

360100

16××=

π

T @ 4"40 N#99

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N-

@ 7!!""#11*,,

P @ 7!#!" K

60

42401802P

××=

π

60

T N2P

π =

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EJAMPLE NO:' 3

E>,.*< *2 /,.*< 2/*9,. -) * .-<<. *),*. 40099 *2 "0099 .+,/<;# F/2 9*>/989 *.,. 2<-2 / , +.- +,/- * ,/,/9-9, -) 50#M / *</2# T* 9-28<8 -) .//2/,;

#/) * -) *), / 49*<- 2 ,/,/

*< -) *),#

S-<8,/-:

D @ 40099

D @ "0099 T @ 50 KN#9

L @ 49

23 N/mm108.0C ×=

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N-

@ 0#00106 .*2/*

D

d DT

44

16

−××= τ

π

400

200400

161050

446 −

××=× τ π

2 N/mm24.4=τ

l

C θ τ =

R

mm D

R 2002

400

2===

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EJAMPLE'4 :'

C*<+8<*, , 2/*9,. -) , *), .?8/.2 ,- ,.*9/,45 *, 1"0 .9# T 9*>/989 ,-.?8 / </<; ,- >+2, 9* =; 30 )-. * 9*>/989 .9//=< *. ,.-) 55 #C*<+8<*, *<- , *< -) ,/, )-. * <,-) "9 #

S-<8,/- :P @ 45 K

N @ 1"0.9

@ 55

2 N/mm

2 N/mm

60

12021045 3 T ××

=×π

60

T N2P

××

=

π

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T @350#! N#9

@ 1#30 > 350#!

@ 4655#" N#9

@ 4655" N#99

D @ 75#54 99

minmax T30.1T ×=

3355

16104655.28 D××=×

π

3

max D

16T ××= τ

π

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N- 8/ , .<*,/-

@ 0#0364 .*2/*

l

C θ τ =

R

77.37

55

2000

10803

=×× θ

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EJAMPLE 5 :'

A *), * ,- ,.*9/, 105 -. *, 160 .9# I)

, *. ,. / -, ,- >+2 , ,/,/ * <, -) 3#5 9 98, -, ,- >+2 1 2.# F/28/,*=< 2/*9,.# T*

P @ 105

N @ 160 .9

@

L @ 3500 99

N-

2 N/mm65

N.mm106266.72T 3

×=

2

N/mm65

24 N/mm108G ×=

60

T N2P

π =

60

T160210105

3 ××=×

π

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1 F-. ,.,

D @ 7#! 99

N.mm106266.72T 3

×=

3D

16××= τ

π T

3365

161072.6266 D××=×

π

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" F-. ,/Q

N-

D @ 11"#55 99

l

θ C

J

T=

3500

0174.0108

J

1072.626643××

=×

46mm1015.756J ×=

4

D32

J ×=

π

46

321015.756 D×=×

π

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EJAMOLE 6 :'

A -</2 *), ABC / >2 *, A *2 ). *, C *2 ,-.?8 -) !00 N#9 /*</2 *, B# T <, -) BC / "9 *2 ,*, -) BC / 19# T2/*9,. -) AB / 4099 *2 ,*, -) BC / "099# I) , *), /9*2 8 -) *9 9*,./*< 2 , *< -) ,/,; / .*2/8 *, ,). 2 C#

S-<8,/- :

A . / 2*,*

,/, /<< -++8. / , *), AB *2 ,. /<< = .- ,/, / *), BC#

T ,-.?8 /<< *+, -<; - *., AB#

N.mm10900T

mm1000

mm2000

mm20d

mm40d

3

B

2

1

2

1

×=

=

=

=

=

l

l

N.mm10600T 3×=

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& - ,*,

@ 0#0!6 .*2/* ,/, *, *., B#

l

θ C

J

T=

46

4

mm10251.0

4032

J

×=

×=π

2000

1080

10251.0

109003

6

3θ ××

=

×

×

radians0896.0== C B θ θ

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SHAFT COUPLING

& <, -) *), .?8/.2 / .; <*. 28 ,- -**/<*=/</,; -) * /< *), -) .?8/.2 <, /, =+-9+*.; ,- +-+, ,- *), ,-,.# T/ / 88*<<;2- =; 9* -) *2 +-8</ * - =<-

T * -) ,- *), *. -/2 ,-,. =; =-<, 8, -../, *2 , ,-.?8 / , ,.*)..2 ).-9 - *), ,-*-,. ,.-8 , +-8</#

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A , ,-.?8 / ,.*)..2 ,.-8 , =-<, /<< =8=+,2 ,- *. ,.# A , 2/*9,. -) =-<, / 9*<<

* +-9*.2 ,- , 2/*9,. -) , * ,.)-. *.,. / *892 ,- = 8/)-.9 / , =-<,#

1 D/ -) =-<, :

& - ,*, ,-.?8 ,.*9/,,2 =; , *),

&. @ *. ,. / *),

2 @ 2/*9,. -) *),

N-

T-.?8 .,2 =; - =-<,

@ ( *.* > *. ,. > .*2/8 -) =-<, +/.+<

3

D16T ××= τ

π

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&.

,-,*< ,-.?8 ./,2 =; =-<,

'''''''''''''' ("

F.-9 ?8*,/- (1 *2 ("

Ddb4

2

Ddb

4

R db4

2

b2

b2

×××=

×××=

×××=

bτ

π

τ

π

τ π

Ddbn b2

××××= τ τ

Ddb8

nd16

b23

××××=×× τ π

τ π

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DESIGN OF KEYS

A * / *,,*+2 ,- , *), =; 9* -) * ;# A.+,*< -,+ / +8, - , +/.+89).+ -) , *), *2* /9/<*. -,+ / +8, - , /. /2 -) , *# T* / , <*+2 -. , *), / 8+ * *; ,*, ,,- -,+ ).-9 * .+,*8<*. -<# A .+,*8<*. ; /, /.,2 / ,- , -< *2 , * / */2 ,- =;2 ,- , *),#

T-.?8 / ,.*9/,,2 =; , *), ,- * ,.-8, ;# K; / 8=+,2 ,- , *. ,.#

KEY

SHAFTFLANGE

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EJAMPLE OF KEYS

EJAMPLE '7:' A *2 +-8</ +-+,/ ,- <, -) -</2

+/.+8<*. *), * 6 - -) "0 99 2/*9,. =-<, ?8*<<;*+2 *<- * /,+ +/.+< -) "40 99 2/*9,.# D,.9/, *), /) , *.* *. ,. / , =-<, / ,- = ,

*9 * 9*>/989 *. ,. / , *),#S-<8,/- :

@ 6 N-

2 @ "0 99

D @ "40 99

& - ,*,

T-.?8 ,.*9/,,2 =; *), @ T-.?8 ./,2 =; =-<,

τ τ =b

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N-

sa!"#$! diamm104.82d

24020

8

6d

16

Ddb8

nd16

23

23

=∴

××××=××∴

××××=××

τ π

τ π

τ τ

τ π

b

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EJAMPLE ' :' T *), *+ -) 100 99 2/*9,. *. ,- = +-+,2 ,- ,2 =; * =-<,2 +-8</# I) , 9*>/989 *. ,. / , *), / 0M* *2 / , =-<, / 70 M* 2 , 89=. -) "0 99 2/*9,.=-<, .?8/.2 )-. , +-8</# T* 2/*9,. -) =-<, +/.+< * "00 99#

S-<8,/- :

& - ,*,

T-.?8 ,.*9/,,2 =; , *), @ ,-.?8 .,2 =; , =-<,

200mmD

mm20d

N/mm70

80N/mm

100mmd

b

2

2

=

=

=

=

=

bτ

τ

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N-

B$%" N$s8n&a#

N$s.7.143n

20070208

n1008016

Ddb8

nd16

23

23

=

=∴

××××=××

××××=××

π π

τ π

τ π

b

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EJAMPLE OF DESIGN OF SHAFT

EJAMPLE ! :'

A *), 100 / 2/*9,. / ,.*9/,,2 ,-.?8 -) 6000N#9 =; 9* -) ; "00 99 <- *2 "5 99 /2# F/2, ,. 2<-2 / *),#

2@ 100 99

T @ 6000 N#9

L @ "00 99

@ *. ,. / *),

2

6

3

N/mm56.30

5010817.9

106000

R J

T

=

=

×

×

=

τ

τ

τ

mm502

100R

10817.9J

10032

d32

J

6

44

==

×=

×=×=π π

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E>*9< '10 :'

T- *), -) 2/*9,. 50 99 *. -/2 =; * .//2 *

+-8</ *2 ,.*9/, * ,-.?8 / 8+ * *; ,*, , *. ,./ *), 2- -, >+2 # I) /> =-<, *. 82 ,- -/, * *2 , =-<, +/.+< / 150 99 / 2/*9,.# D,.9/ ,2/*9,. -) , =-<, /) , .9/,,2 *. ,. / , =-<, /

# #

S-<8,/- :

2@ 5099

@

@ 6 N-D @ 150 99

& - ,*,

T-.?8 ,.*9/,,2 =; , *), @ T-.?8 ./,2 =; =-<,#

2 N/mm80=b

τ

2 N/mm100

2 N/mm100

2 N/mm80=bτ

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N-

b$%".$! amm......di32.9d

15080db8

65010016

Ddb8

nd16

b

23

23

=

××××=××

××××=××

π π

τ τ

τ π

b

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TORSION VEDIO

7/21/2019 mos2-150817134311-lva1-app6892


TH ANK YOU

mos2-150817134311-lva1-app6892

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