Experiment on Torsion of Bars (Repaired)

7/21/2019 Experiment on Torsion of Bars (Repaired)

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UNIVERSITY OF MAURITIUS

FACULTY OF ENGINEERING

CIVIL ENGINEERING DEPARTMENT

STRUCTURES PRACTICAL

STRUCTURAL MECHANICS LABORATORY

BEng (HONS) CIVIL ENGINEERING P/T E411

YEAR 1-SEMESTER 1

MODULE: INTRODUCTION TO STRUCTURES

F!" #$%& ''%"'n# *' *%++ %n,'%g#' #$' '+#%!n&$% .'#*''n #!0'

n ng+' !2 #*% !2 3%30+ 3!&& &'3#%!n .& !2 %22''n# "#'%+&

SUBMITTED BY:

GROUP 4

1 LUC5EENARAIN Y!g'&$ 50" (S#0'n# ID:1116781)

9 MATTAPULLUT M$'n 50" (S#0'n# ID: 11196;)

6 BHUN


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TABLE OFCONTENTS

INTRODUCTION 1-9

THEORY 6

DESCRIPTION OF APPARATUS 4

E?PERIMENTAL PROCEDURES ;

RECORD AND TABULATION OF VALUES 8-=

GRAPHS AND ANALYSIS OF RESULTS 17-97

DISCUSSION 91-99

CONCLUSION 96

REFERENCES 94

INTRODUCTION TO STRUCTURES| CIVE1105


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INTRODUCTION

A torsion bar is a flexible spring that an be !o"e# abo$t its axis "ia t%isting& Torsion bars are

#esigne# an# base# on the a!o$nt of tor'$e $se# in the t%isting of the spring( the angle of the

t%ist( the o"erall #i!ensions of the torsion bar an# %hat !aterials the torsion bar is !a#e fro!&

The !ost o!!on plae to fin# a torsion bar is in the s$spension of a ar or tr$)( in !ahines

$se# for pro#$tion or in other preision #e"ies& The flexibilit* of the spring is the !ain reason

that a torsion bar is $se#& If a !ore rigi# str$t$re %ere $se# s$h as steel ro# %ere $se# too

!$h loa# bearing press$re %o$l# be plae# on the both the %heels an# the $n#er bo#* of the

"ehile&

A torsion bar %or)s b* resisting the tor'$e plae# on it& +hen one en# of the torsion bar is

affixe# to an ob,et that annot be !o"e#( the other en# of the bar is t%iste#( th$s a$sing tor'$e

to b$il# $p& +hen this happens( the torsion bar is resistant to the tor'$e an# %ill '$i)l* go

ba) to its starting position one the tor'$e is re!o"e#& In general( the ob,et that annot be

!o"e# is $s$all* a fra!e& If there is not an* fore applie# to the torsion bar( it %ill sta* at the

sa!e position $ntil fore is applie#&

An exa!ple the other en# of the bar %ill be ontate# to a ontrol ar!& The ontrol ar! !o"es in

a fixe# !anner on the fra!e an# this reates the t%isting !o"e!ent on the bar& This( in t$rn(

s$pplies the tor'$e nee#e# to !a)e a spring&

In %or)shops an# fatories( a t$rning fore is al%a*s applie# to trans!it energ* b* rotation& This

t$rning fore is applie# either to the ri! of a p$lle*( )e*e# to the shaft or at an* other s$itable

point at so!e #istane fro! the axis of the shaft& The pro#$t of this t$rning fore an# the

#istane bet%een the point of appliation of the fore an# the axis of the shaft is )no%n as

tor'$e( t$rning !o!ent or t%isting !o!ent& An# the shaft is sai# to be s$b,ete# to torsion& D$eto this tor'$e( e"er* ross-setion of the shaft is s$b,ete# to so!e shear stress&

INTRODUCTION TO STRUCTURES| CIVE1105 1


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The follo%ing ass$!ptions are !a#e %hile fin#ing o$t shear stress in a ir$lar shaft s$b,ete#

to torsion.

1& The !aterial of the shaft is $nifor! thro$gho$t&

/& The t%ist along the shaft is $nifor!

& Nor!al ross-setions of the shaft( %hih %ere plane an# ir$lar before the t%ist( re!ain

plane an# ir$lar e"en after the t%ist&

& All #ia!eters of the nor!al ross-setion( %hih %ere straight before the t%ist( re!ain

straight %ith their !agnit$#e $nhange#( after the t%ist&

A little onsi#eration %ill sho% that the abo"e ass$!ptions are ,$stifie#( if the tor'$e applie# is

s!all an# the angle of t%ist is also s!all&



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THEORY

Tor'$e is #efine# as a !o!ent that ats abo$t a !e!ber2s longit$#inal axis& A !e!ber that has

tor'$e applie# to it s$h that it #efor!s along its longit$#inal axis is sai# to be $n#er torsion& The

torsion presents itself as shear strain( 3( %hih is e'$al to the angle of t%ist along the

longit$#inal axis #enote# b* the s*!bol( 4& or a #iagra! of this relationship( see ig$re 1&

6ea$se this experi!ent $ses *lin#rial spei!ens( the theor* #is$sse# %ill pertain onl* to

!e!bers of ir$lar ross-setion&

F%g0' 1

ro! the priniple of tor'$e applie# on ir$lar shaft( the follo%ing for!$la an be #eri"e#.

4 (TL) / (G


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APPARATUS USED:

5! !eas$ring tape( loa#s of 1N to 0 N( loa# hanger( !iro!eter sre% ga$ge( open en# an#

ring spanners an# test spei!ens ro# =Al$!ini$! allo* ro#( Steel ro# an# N*lon ro#?

DESCRIPTION OF APPARATUS

A base fra!e has a la!p at one en# an# a ball bearing in a ho$sing =


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E?PERIMENTAL PROCEDURES

1& Che) ero error in !iro!eter sre% ga$ge

/& Deter!ine the !ean #ia!eter of the test spei!ens $sing the !iro!eter sre% ga$ge

an# reor#& Cal$late the polar !o!ent of inertia of the setion an# reor#&&


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RECORD AND ANALYSIS

T.+'1: R'3! !2 ,+0'& !2 %"'#'& !2 #$' #' &'3%"'n&

Lero Error in !iro!eter sre% ga$ge. M0&05

:ean #ia!eter 8 =1M/MMM5?@5 M 0&05

T' &'3%"'n& 1 9 6 4 ; M'n %"'#'/""

A+0"%n%0" ++!> &J &J &JF &J &J &K/

S#''+ ! & & & &F & &J/

N>+!n ! F&51 F&51 F&51 F&51 F&51 F&5F

T.+' 9: R'3! !2 ,+0'& 2! A+0"%n%0" R!

L! (N) T*% !2 ! 4/

O,' 477"" O,' 977 ""

0 0&0P 0&0P

5 /&0P 1&5P

10 F&0P &0P

15 &5P &5P

/0 11&0P F&0P

/5 1&0P J&0P0 1F&0P K&0P

5 1K&0P 10&5P

0 //&0P 1/&0P



9/26

T.+' 6: T.0+#%!n !2 '&0+#& 2! A+0"%n%0" R!

- Cal$lation of Tor'$e@ N!! 8 7oa#@N x ra#i$s of Torsion hea#@!!

- Con"ersion of angle of t%ist fro! #egreePto ra#ian r

4 @r8 =>@1J0P? x 4 @P

- Dia!eter of Al$!ini$! ro#. &JM 0&05 !!

L! (N) T*% !2 !4/ T!0' N/""

O,' 477"" O,' 977 ""

0 0&000 0&000 0

5 0&05 0&0/F 1J5

10 0&105 0&05/ 0

15 0&11 0&0K 555/0 0&1K/ 0&105 0

/5 0&/ 0&10 K/5

0 0&/K 0&15 1110

5 0&// 0&1J 1/K5

0 0&J 0&/0K 1J0

T.+' 4: R'3! !2 ,+0'& 2! S#''+ R!

L! (N) T*% !2 ! 4/

O,' 477"" O,' 977 ""

0 0&0P 0&0P

5 0&JP 0&5P

10 1&5P 1&0P

15 /&5P 1&5P

/0 &5P /&0P

/5 &0P /&5P

0 F&0P &0P

5 F&5P &5P

0 &0P &0P



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T.+' ;: T.0+#%!n !2 '&0+#& 2! S#''+ R!

- Cal$lation of tor'$e@ N!! 8 7oa#@N x ra#i$s of Torsion hea#@!!


4 @r8 =>@1J0P? x 4 @P

- Dia!eter of Steel ro#. & M 0&05 !!

L! (N) T*% !2 !4/ T!0'/ N""

O,' 477"" O,' 977 ""

0 0&000 0&000 0

5 0&01 0&00J 1J5

10 0&0/F 0&01 0

15 0&0 0&0/F 555/0 0&0F1 0&0 0

/5 0&00 0&0 K/5

0 0&105 0&05/ 1110

5 0&11 0&0F1 1/K5

0 0&1// 0&00 1J0

T.+' 8: R'3! !2 ,+0'& 2! N>+!n R!

L! (N) Ang+' T*% !2 !4/

O,' 477"" O,' 977 ""

0 0&0P 0&0P

1 15&0P J&5P

/ &0P 1&5P

K&5P /F&0P

F&0P &0P

5 J0&0P &0P



11/26

T.+' @: T.0+#%!n !2 '&0+#& 2! N>+!n R!

- Cal$lation of tor'$e@ N!! 8 7oa#@N x ra#i$s of Torsion hea#@!!


4 @r8 =>@1J0P? x 4 @P

- Dia!eter of N*lon ro#. F&51 M0&05 !!

L! (N) T*% !2 !4/ T!0' N/""

O,' 477"" O,' 977 ""

0 0&000 0&000 0

1 0&/F/ 0&1J / 0&5F 0&05

0&JF 0&5 111

1&11 0&5K 1J

5 1&KF 0&50 1J5

T.+' =: T.0+#%!n !2 V+0'& !2 P!+ "!"'n# !2 ' 8 //@

T' &'3%"'n& M'n %"'#'/""


12/26

A G$ !2 ng+' !2 T*% !2 A+0"%n%0" ! / !,' %n3' !2 477"" 2!" #$' 3+"

g%n T!0'/ N"" %& +!##'

0 /00 00 F00 J00 1000 1/00 100 1F00

0

0&05

0&1

0&15

0&/

0&/5

0&

0&5

0&

0&5

0

0.04

0.11

0.13

0.19

0.24

0.28

0.33

0.38

G$ !2 Ang+' !2 T*%/ g%n T!0'/N""

T!0'/N""

Ang+' !2 #*%/



13/26

Cal$lation of the Val$es of :o#$l$s of Rigi#it* of the Al$!ini$! Allo* spei!en( 9@ N!! -/

Using the graph(

=Q/( /? =1/K5( 0&/?

=Q1( 1? =0( 0?

: 8 =0&/- 0? @ =1/K5 - 0?

8 /&JF x 10-

4 (TL) / (G


14/26

A G$ !2 ng+' !2 T*% !2 A+0"%n%0" ! / !,' %n3' !2 977"" 2!" #$' 3+"

g%n T!0'/ N"" %& +!##'

0 /00 00 F00 J00 1000 1/00 100 1F000

0&05

0&1

0&15

0&/

0&/5

0

0.03

0.05

0.08

0.11

0.14

0.16

0.18

0.21

G$ O2 ng+' !2 T*%/ Ag%n T!0'/N""

T*% !2 !/

T!0'/N""



15/26

Cal$lation of the Val$es of !o#$l$s of Rigi#it* of !aterials( 9@ N!!-/

U&%ng #$' g$

=Q/( /? - =1/K5( 0&1J?

=Q1( 1? - =0( 0?

: 8 =0&1J- 0? @ =1/K5 - 0?

8 1&1 x 10-

4 (TL) / (G


16/26

A G$ !2 ng+' !2 T*% !2 S#''+ ! / !,' %n3' !2 477"" 2!" 3+" g%n

T!0'/ N"" %& +!##'

0 /00 00 F00 J00 1000 1/00 100 1F00

0

0&0/

0&0

0&0F

0&0J

0&1

0&1/

0&1

0

0.01

0.03

0.04

0.06

0.07

0.11

0.11

0.12

G$ !2 ng+' !2 T*%/ g%n T!0'/N""

T*% !2 !/

T!0'/N""



17/26

Cal$lation of the Val$es of !o#$l$s of Rigi#it* of steel ro#( 9@ N!! -/

U&%ng #$' g$

=Q/( /? - =1F0( 0&11/?

=Q1( 1? - =0( 0?

: 8 =0&11/- 0? @ =1F0 - 0?

8 J&/ x 10-5

4 (TL) / (G


18/26

A G$ !2 ng+' !2 T*% N>+!n ! / !,' %n3' !2 477"" 2!" #$' 3+" g%n

T!0'/ N"" %& +!##'

0 /0 0 F0 J0 100 1/0 10 1F0 1J0 /00

0

0&/

0&

0&F

0&J

1

1&/

1&

1&F

0

0.06

0.58

0.86

1.12

1.4

G$ !2 ng+' !2 T*%/ g%n T!0'/N""

T*% !2 !/

T!0'/N""



19/26

Cal$lation of the Val$es of !o#$l$s of Rigi#it* of N*lon ro#( 9@ N!!-/

U&%ng #$' g$

=Q/( /? - =1J( 1&11?

=Q1( 1? - =/0( 0&0J?

: 8 =1&11- 0&0J? @ =1J - /0?

8 J&10 x 10-

4 (TL) / (G


20/26

A G$ !2 ng+' !2 T*% !2 N>+!n ! / !,' %n3' !2 977"" 2!" #$' 3+"

g%n T!0'/ N"" %& +!##'

0 /0 0 F0 J0 100 1/0 10 1F0 1J0 /00

0

0&1

0&/

0&

0&

0&5

0&F

0&

0&J

0

0.15

0.31

0.45

0.59

0.75

G$ !2 ng+' !2 T*%/ g%n T!0'/N""

T*% !2 !/

T!0' N/""



21/26

Cal$lation of the Val$es of !o#$l$s of Rigi#it* of N*lon ro#( 9@N!!-/

U&%ng #$' g$

=Q/( /? - =100( 0&0?

=Q1( 1? - =0( 0?

: 8 =0&0- 0? @ =100 - 0?

8 &00 x 10-

4 (TL) / (G


22/26

T.+' 17: V+0'& !2 !,'++ M!0+0& !2 %g%%#> !2 "#'%+& G (2!" g$&)

7@ =9;? 8 gra#ient of plotte# line

Cal$lation of o"erall 9

O"erall 9@N!!-/8 =Val$e of !o#$l$s of Rigi#it* of !aterials( 9@ N!! o"er 00 !! M Val$e

of !o#$l$s of Rigi#it* of !aterials( 9@ N!! o"er /00 !!?@/

T' &'3%"'n&

V+0'& !2 "!0+0&

!2 R%g%%#> !2

"#'%+& G/ N""-9

!,' 477 ""

V+0'& !2 "!0+0&

!2 R%g%%#> !2

"#'%+& G/ N""-9

!,' 977 ""

O,'++

G

Al$!ini$! allo* /KFJ&/0 /F0&1 /F/J5&5

Steel ro# K15K1&J - K15K1&J

N*lon ro# /1&F/ /5&01 /&1



23/26

DISCUSSION

T! *$# '#'n# !'& #$' ''%"'n# ,'%2> #$' #!0' / #*% 2!"0+

ro! the #ata that %e got( the graphs plotte# sho% that the angle of t%ist against tor'$e is

inreasing linearl* for all t*pes of spei!ens( an# it is #iretl* proportional as !entione# in

theor*&

ro! the for!$la gi"en.

4 T

TL / G

Documents

Experiment on Torsion of Bars (Repaired)