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Laboratory reportThick Cylinder
Ujjwalraj Anitha (@00414004)Distribution, Transission systesand desi!ns"sc# $etroleu and !as en!ineerin!"odule co%ordinator& $ro'#Ali kadir
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Contents1. Objective......................................................................................................... 2
2. Abstract...........................................................................................................2
3. Introduction.....................................................................................................2
4. Theory............................................................................................................. 2
4.1 LAME Theory...............................................................................................2
!. Apparatus re"uired..........................................................................................!
#. $rocedure........................................................................................................ !
%. &esu'ts ( co)putation....................................................................................#
*. +iscussion.....................................................................................................1!
,. Conc'usion.....................................................................................................1!
&e-erences...........................................................................................................1#
List o- tab'es
Tab'e 1 +epth penetration /.#*............................................................................ #
Tab'e 2 +epth penetration 1.!*............................................................................ *
Tab'e 3 +epth penetration 2.2,..........................................................................1/
Tab'e 4 +epth penetration 3.#!..........................................................................12
Tab'e ! 0 error has been ca'cu'ated -or dierent penetrations..........................1!
List o- ure
iure 1 pressure in thic5 cy'inder........................................................................3
iure 2 Top vie6.................................................................................................. 3
List o- raph
7raph 1 8oop9 radia' stress :; 1;r2.....................................................................#
7raph 2 8oop and radia' strain :; 1;r2................................................................%
7raph 3 8oop and radia' stress :; r....................................................................*
7raph 4 8oop9 radia' stress :; 1;r2.....................................................................*
7raph ! 8oop and radia' strain :; 1;r2...............................................................,
7raph # 8oop and radia' stress :;s r..................................................................1/
7raph % 8oop9 radia' stress :; 1;r2...................................................................11
7raph * 8oop ( radia' strain :; 1; r2................................................................11
7raph , &adia' ( hoop stress :; r.....................................................................12
7raph 1/ 8oop9 radia' stress :; 1;r2.................................................................13
1
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7raph 11 8oop strain ( radia' strain :; 1;r2.....................................................14
7raph 12 8oop stress ( radia' stress :; r.........................................................14
1. ObjectiveTo e
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2@ Lonitudina' a
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+i!ure & To* -iew
ro) ure inner radius B &1and outer radius B&29
Cy'inder havin pressure p?interna'@ at distance r?radia'@9
The LAME= e"uation is iven by9
8oop stress 9
2
BA
r = +
Radial stressr
2r
BA
r =
Using boundary conditions,
Then the equations become,
4
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!. Apparatus re"uired
1@ A thic5 cy'inder 6ith outer dia)eter B 3/4)) ( inner dia)eterB
1!!)) attached 6ith ten strain aues at respective positions.
2@ 8ydrau'ic ra)
3@ Tapered p'u inside the bore
4@ 8ydrau'ic cy'inder to supp'y 'ubricatin oi'
!@ train aue
#@ +ata 'oer ?Solatron Schlumber3!3/@
#. $rocedure
To attain ero re-erence 'ubricatin oi' is pu)ped to the taperedp'u. The p'u is rotated at the sa)e ti)e durin the 'ubrication
to ensure uni-or)ity ti' the spira' roove is ''ed 6ith the oi'.
In case o- hydrau'ic ra)9 an initia' 6eiht 6as app'ied and
/.2#)) 6as obtained as initia' readin. o6 it is eroed and 1/
dierent channe's o- strain are initia'ised to the 'oin syste).
The operator pushed the hand pu)p do6n to -orce the hydrau'ic
ra) head ti'' the tapered p'u. i)u'taneous'y 'ubrication is done
6ith the he'p o- pu)p to ensure the uni-or)ity o- the ra) and
the oi' pu)p. ote do6n the readins o- strain.
!
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&eadins 6ere noted -or penetrations o- 4)) 6ith a step
dierence o- /.%!)). Lubrication is done si)u'taneous'y. Load
shou'd be re)oved 6hen you are ta5in the readins.
%. &esu'ts ( co)putation
a@ +epth o- penetration B /.#*
Table 1& De*th *enetration 0#./
#
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ra*h 1& oo*, radial stress 23 13r
From graph,
A= 5.4N/mm2
B= (0!"#$0#0!%&2 ' 0)= 57050N
*= !!+&mm2
By ame-s equation (theoretically%,
A=4.477.5
2
152277.5
2 = 1.545N/mm2
B=4.477.521522
15224.42 = 35711.18N
.n graph , r /& r and e , er /& &r2 are plotted
%
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ra*h & oo* and radial strain 23 13r
ra*h 5& oo* and radial stress 23 r
b@ +epth o- penetration B 1.!*
Table & De*th *enetration 1#6/
*
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ra*h 4& oo*, radial stress 23 13r
From graph,
A= 9.9N/mm2
B= (1)$#%&2'0)= 184600N
*= 10 N/mm2
ame-s eqn,
A=1077.52
152277.52 = 3.51N/mm
2
B =1077.5
2152
2
15224.4
2 = 81161.79N
3i4en graph ,
r /& r ande ,
er /& &r2 5or penetration )6 has
been plotted
,
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ra*h 6& oo* and radial strain 23 13r
ra*h .& oo* and radial stress 23s r
c@ +epth o- penetration B 2.2,
1/
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Table 5& De*th *enetration #7
ra*h 8& oo*, radial stress 23 13r
From graph,
A= 10.9N/mm2
B= (2012$")0%&2 ' 0)= 300600N
* = 20.2N(3raph%
By ame-s 5ormula,
A=20.277.5
2
152277.5
2 = 7.09N/mm2
B=20.277.5
2152
2
15224.4
2 = 163946.81N
.n graph ,
r /& r ande ,
er /& &r2 ( penetration 22% has been
dra7n belo7
11
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ra*h /& oo* 9 radial strain 23 13 r
ra*h 7& adial 9 hoo* stress 23 r
d@ +epth o- penetration B 3.#!
Table 4& De*th *enetration 5#.6
12
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ra*h 10& oo*, radial stress 23 13r
From graph,
A= 22N/mm2
B= (!1$!!62%&2'0)= 472150N
*=30N
By ame-s theory,
A=3077.5
2
152277.5
2 = 10.53N/mm2
B=3077.5
2152
2
15224.4
2 = 243485.37N
3raph o5
,
r /& r ande
,
e
r /& &r2 ( penetration "1)% has been
dra7n belo7
13
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ra*h 11& oo* strain 9 radial strain 23 13r
ra*h 1& oo* stress 9 radial stress 23 r
$ercentae error ca'cu'ations
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Table 6& : error has been calculated 'or di;erent *enetrations
*. +iscussion >hen the p'u penetration increases9 the pressure inside the
cy'inder a'so increases. >hen the depth o- penetration is /.#*))9
the interna' pressure beco)es 4.4;))29 and by increasin the
deepness to 1.!*9 2.2,9 ( 3.#!))9 the re'ated pressure va'ues are
1/9 2/.2 ( 3/;))2 respective'y. The -o''o6in strain readins -or
dierent heihts 6ou'd va'idate the increase in va'ues o- interna'
pressure.
Fy co)parin the va'ues o- theoretica' ( e
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&e-erences
Fhavi5atti9 . . Mechanics Of Solids. e6 +e'hi e6 Ae
Internationa' Ltd.9 2/1/. $rint.
8earn9 E. ?1,,%@. Mechanics of materials. O