MECHANICS AND MATERIALS LABORATORY (MEMB221) SEMESTER 2, 2015/2016
EXPERIMENT 2 : TORSION TEST
DATE PERFORMED
:
3 rd DECEMBER 2015
DUE DATE DATE
:
11th DECEMBER 2015
SECTION
:
05
GROUP
:
04
GROUP MEMBERS Mithradassa Nair A! G Dha"#dhara$ S#r$a &ai'ash A! &a$$a$ &(r())a' Ra+,,$ A! Thi-a.(.#/a' Pra.at,sh &("ar A! Ash#) &("ar Sar+aisa$ A! M($ia$d-
LAB INSTRUCTOR:
Ci) N(ras'i$da Bi$ti A$(ar
TABLE OF CONTENT
I / D NUMBER ME0%5512 ME0%55*% ME0%552 ME0%55 ME0%55*0
SUMMAR ABSTRACT
1
OBECTIE
2
TEOR
263
E7PERIMENT E8UIPMENT
36
PROCEDURE
6*
DATA AND OBSERATIONS
106%
ANA!SIS AND RESU!TS
11612
DISCUSSIONS
13614
CONC!USIONS
14615
REFERENCES
15
ABSTRACT
This experiment is performed to study the principle of torsion test and also to determine the modulus of shear, G through measurement of the applied torque and angle of twist. The variation of pure shear when a structural member is twisted is called torsion. The torsional forces produce a rotating motion about one end to another end of the member.
Two dierent specimens has been used in this experiment, specimen A and specimen B. pecimen A is bright gold in colour whereas pecimen B is silver and much more lighter than specimen A. The dimension for the both specimen is measured and recorded before the experiment begin. The torque measuring unit is calibrated !rst by inspecting the read out torque from ampli!er to be similar with the applied torque. The test is then performed. To avoid some measurement errors several measure were ta"en which can aect the results. The test specimen is place between the loading device and the torque measuring unit. The reading from the ampli!er is ta"en out each time when the load is applied. The results were ta"en and some calculations is performed using the formula given in the lab manual which is the applied torque, angle of twist, number of revolutions and the percentage error and from the results obtain a graph is plotted. The modulus can be determined when the specimen is still wor"ing under the elastic limit. Based on the results obtained, it is concluded that specimen B is more ductile than specimen A. The G value for specimen B theoretically is larger than specimen A, hence it is harder to twist than specimen B. The torque needed to twist specimen A to the same amount degree of rotation as specimen B is greater.
#
O!"#$%&"' • •
To understand the principle of torsion test. To determine the modulus of shear, G through measurement of the applied torque and angle of twist.
T"*+
Torsion is a force produced when a structural member is twisted , torsional forces produces
a rotating motion around the ob$ect. %n each test, the torque and
twisting angle are measured to determine the shear modulus, G. The shear modulus G is calculated based on this formula&' T J
=
2
Gϕ
J
L
=
π r 2
=
π d
4
32
where
Th, a$.', #9 tist; i$ radia$s; 9#r a s#'id r#($d
Tl GJ
U-. T G > ! R D
*%"
T#r=(, P#'ar "#",$t #9 i$,rtia Sh,ar "#d('(s A$.', a9t,r a//'i?ati#$ #9 t#r=(, !,$.th Radi(s Dia",t,r
The value of the torque in this experiment will be showed in the digital meter or the read out ampli!er.
( EQUIPMENT/DESCRIPTION OF EXPERIMENTAL APPARATUS
Figure 1: layout of the torsion apparatus
T"#%# "'#*%3$% 4 $" 33*$' Th, a//arat(s ?#$sists "ai$'- #9: 1@ 2@ 3@ 4@ 5@ @
!#adi$. d,+i?, ith s?a', a$d r,+#'(ti#$ ?#($t,r 9#r tisti$. a$.', ",as(r,",$t T#r=(, ",as(r,",$t ($it Ca'i
3
T"#%# D$
G,$,ra' data:6 Mai$ di",$si#$: 1400 350 300 "" ,i.ht: 25 ).
!#adi$. d,+i?,:6 #r" .,ar r,d(?ti#$ rati#: 2 R,+#'(ti#$ ?#($t,r: 5 di.it; ith r,s,t O(t/(t s?a',: 30 I$/(t s?a',: 30 I$di?at#r: Ad(sta<',
T#r=(, ",as(r,",$t ($it:6 Ra$.,: 0 30 N" Dis/'a-: di.it; !ED 14 "" T,"/,rat(r, #/,rati$. ra$.,: 0 6 50 C P#,r s(//'-: 230 ; 500
Ca'i
4 L% D"&%#"
Th, t#rsi#$a' '#adi$. is tra$s"itt,d t# th, s/,?i",$ <- a #r" .,ar a$d a ha$d h,,'@ Th,r, ar, t# r,+#'(ti#$ s?a',s; #$, is th, i$/(t s?a', #$ is #(t/(t@ At th, i$/(t sid, th,r, is a r#tati$. .,ar hi?h is (s,d t# t(r$ th, s/,?i",$ ith a$ a$.',@
T*7" M"'*"8"$ U%$
Th, s/,?i",$ is "#($t,d at #$, sid, t# th, '#adi$. d,+i?, a$d th, #th,r sid, t# th, t#r=(, ",as(r,",$t d,+i?,@ Th, t#r=(, a//'i,d t# th, s/,?i",$ i'' /r#d(?, sh,ar str,ss,s hi?h ar, d,t,?t,d <- th, strai$ .a(.,s@ Th, si.$a' #9 th, .a(.,s is ?#$diti#$,d <- a ",as(ri$. a"/'i9i,r ith a di.ita' r,ad #(t@ Strai$ .a(.,s ?a$ #$'- ",as(r, strai$@ I$ th, ?as, #9 /(r, t#rsi#$ th, "ai"(" #9 /ri$?i/a' str,ss i'' #??(r at a 45 ° t# th, aia' ais #9 th, t#rsi#$ r#d hi?h th,$ ?a(s,s S'i.ht d,9#r"ati#$ #9 th, t#rsi#$ r#d @Th(s this i'' ?a(s, a$ ,rr#r i$ th, tist a$.', ?a'?('ati#$@ Th, ,rr#r ?a$ <, r,d(?,d <-; "#+i$. th, s/,?i",$ h#'d,r #9 th, t#r=(, ",as(r,",$t ($it@ C#"/,$sati#$ ?a$ <, ?#$tr#'',d <- a dia' .a(., hi?h is '#?at,d at th, sid, #9 th, s/,?i",$ h#'d,r@ Th, #(t/(t si.$a' #9 th, strai$ .a(., ?a$ <, #
5
S3"#%8"
S/,?i",$ A H
S/,?i",$ B Ha'("i$i("
P*#"*":
I9
C%*$%
Ca'i
<,t,,$ 0 a$d 30 N"@ R,s#'(ti#$ (s,d as 2@5 N"@ Th, ?a'i
R,ad #(t #9 th, a"/'i9i,r as s,t t# ,r#@ T#r=(, ",as(r,",$t ($it as ?#$$,?t,d t# th, ",as(r,",$t a"/'i9i,r@ M,as(r,",$t a"/'i9i,r at th,
II9 C**+% $ $" "3"*%8"$:
S3"#%8" $$#8"$: 1@ T# s/,?i",$s $a",'- s/,?i",$ A a$d B ar, (s,d@ 2@ Th, "at,ria's ,r, "#($t,d i$ <,t,,$ th, '#adi$. d,+i?, a$d t#r=(, ",as(r,",$t ($it@ 3@ ,a.#$ s#?),t #9 1%"" as (s,d@ 4@ Shi9ti$. h#'d,r #9 th, '#ad d,+i?, has t# <, i$ "id /#siti#$@ 5@ Th,r, sh#('d $#t <, a /r,'#ad #$ th, s/,?i",$@ a$d h,,' at th, i$/(t ?a$ <, t(r$,d i9 $,?,ssar- ($ti' a"/'i9i,r r,ad #(t sh#s ,r#@ @ B#th i$di?at#rs at th, i$/(t a$d #(t/(t sha9t #9 th, #r" .,ar as s,t t# ,r#@ @ Dia' .a(., #9 th, ?#"/,$sati#$ ($it as ?a'i
*@ R,+#'(ti#$ ?#($t,r as r,s,t@
S3"#%8" % $$% 1@ a$d h,,' at th, i$/(t #9 th, .,ar as t(r$,d ?'#?)is, t# '#ad th, ,/,ri",$ta' "at,ria'@ It sh#s #$'- t(r$,d 9#r a d,9i$,d a$.', i$?r,",$t@ 2@ F#r th, 9irst r#tati#$; a$ i$?r,",$t #9 =(art,r r#tati#$ H%0K as ?h#s,$@ F#r th, s,?#$d a$d third r#tati#$ #9 a ha'9 =(art,r H1*0K as ?h#s,$ a$d 9#r th, 9#(rth t# t,$th r#tati#$ H30K as ?h#s,$@ 3@ Th, tist a$.', as ?a'?('at,d at th, s/,?i",$ <- di+idi$. th, r#tati#$s at th, i$/(t <- th, r,d(?ti#$ rati# #9 2@ 4@ B,t,,$ 100 a$d 200 r#tati#$; 9ra?t(r, i'' #??(r@ 5@ Th, d,9#r"ati#$ #9 th, ",as(ri$. t#rsi#$ r#d a9t,r ,a?h a$.', i$?r,",$t as ?#"/,$sat,d@ Th, ha$d h,,' #9 th, ?#"/,$sati#$ ($it sh#s t(r$,d t# a?hi,+, this ($ti' th, dia' .a(., i$di?at,d ,r#@ @ T#r=(, +a'(,s ,r, r,ad 9r#" th, dis/'a- #9 th, a"/'i9i,r a$d ,r, $#t,d ith th, i$di?at,d a$.', tist@ @ R,s('ts ,r, ta<('at,d@ *@ E/,ri",$t as r,/,at,d ith s/,?i",$ B@
)
DATA AND OBSERATIONS !,$.th #9 ',+,r L 0@5" LOAD (N)
10 20 30 40 50 0
O$"* "$, L I"* L"$, L% D%8"$"*,
∅
A33%" L T*7" R" $ T*7" (N8) (N8) 5 4@50 10 %@0 15 14@55 20 1%@40 25 24@30 30 Ta<', 1: R,adi$. 9#r ?a'i
Ta<', 2: Di",$si#$s #9 s/,?i",$s
S3"#%8" B (A8%%8) 0@15 " 0@02" 0@001"
A" $ "* %3$ ("*"")
R" $ $*7" (N8)
%0
1@40
("*"") 1@45
1*0
2@45
2@%0
20
3@%5
4@35
30
4@5
5@*1
540
@25
*@1
20
*@20
11@1
%00
*@0
14@52
10*0
%@00
1@42
4th
1440
%@40
23@23
5th
1*00
%@0
2%@03
th
210
%@*0
34@*4
th
2520
%@%0
40@5
*th
2**0
10@15
4@45
%th
3240
10@35
52@2
N9 4 R$$%
1st
2$d 3rd
10th
A" 4 $.%'$,
10@50 300 5*@0 Ta<', 2: Sh#s th, +a'(,s #
θ
S3"#%8" B (S%&"* C* M$"*%)
O(t,r !,$.th; !# L 115"" L 0@15" I$$,r !,$.th; ! i L @2"" L 0@02" Dia",t,r;
∅
L @1"" L 0@001"
A" $ "* %3$ ("*"")
R" $ $*7" (N8)
%0
0
("*"") 1@45
1*0
0@15
2@%0
20
0@25
4@35
30
0@5
5@*1
540
1@%5
*@1
20
3@15
11@1
%00
5@*5
14@52
10*0
*@35
1@42
4th
1440
11@%0
23@23
5th
1*00
12@25
2%@03
th
210
12@40
34@*4
th
2520
12@55
40@5
*th
2**0
12@0
4@45
%th
3240
12@5
52@2
N9 4 R$$%
1st
2$d 3rd
10th
A" 4 $.%'$,
12@*0 300 5*@0 Ta<', 3: Sh#s th, +a'(,s #
O'"*&$%': I$ th, <,.i$$i$.; h,$ th, ,/,ri",$t as 9irst ?#$d(?t,d t# t,st th, ?a'i
10
ANALYSIS AND RESULTS
I@
FROM CA!IBRATION CURE
Th, .radi,$t +a'(, #
P,r?,$ta., Err#r L
|
L
|
II@
|
TheoreticalValue – ExperimentalValue × 100 Theoretical Value 1.00 – 0.9651 1.00
|
× 100
=
ϕ
10@15 − 4@5 4@45 − 5@*1 4
32
ϕ J •
4
=
π × 0@001
= 1@35% × 10
32
−10
m
4
−10
m
4
P#'ar "#",$t #9 i$,rtia; L TL
•
0@133
=
Gradi,$t 9r#" th, .ra/h; π d
•
3.49
FOR SPECIMEN A
T
•
=
=
0@133 × 0@02 −10
1@35% × 10
m
4
=
4@% MPa
Sh,ar M#d('(s; G L Th,#r,ti?a' a'(,; G 9#r Brass L 3%GPa 3%@00 − 0@04% 3%@00
× 100 =
%%@*3M
P,r?,$ta., ,rr#r; L FOR SPECIMEN B
T
12@40 =
ϕ •
34@*4 4
32
ϕ J •
− 14@52
0@322
=
4
=
π × 0@001 32
= 1@35% × 10
P#'ar "#",$t #9 i$,rtia; L TL
•
5@*5
Gradi,$t 9r#" th, .ra/h; π d
•
−
=
0@322 × 0@02 1@35% × 10
−10
m
Sh,ar M#d('(s; G L Th,#r,ti?a' a'(,; G 9#r Brass L 2GPa
4
=
15@*5 MPa
P,r?,$ta.,
2@00 − 0@15% 2@00
,rr#r; L
× 100 =
%%@42M
11
Graph of Read Out Torque ! A"#$e of T%&!t #( #* )
R"02 O5$ T*75" (N8)
. , ( * * #* (* +* ,* -* .* /*
A,61" 4 T.%'$ (2"6)
19 F* S3"#%8" A
G*03 4 R"02 O5$ T*75" &' A,61" 4 T.%'$ #, #( #* )
R"02 O5$ T*75" (N8)
. , ( * *
#*
(*
+*
,*
-*
.*
A,61" 4 T.%'$ (2"6)
29 F* S3"#%8" B
12
D&!'u!!&o"
/*
#. 0rom the graph of read out ampli!er vs applied load torque it can be clearly seen that the graph is linearly proportional, which means as the applied load increase there will be an increase in read out ampli!er. The equation of the graph is 12 *.3-#4 5#.#*(. (. 0rom the graph of read out torque vs angle of twist it can be seen that at a angle of * specimen A has a higher torque because it is a more brittle material while specimen B has a lower torque value because it is a more ductile material. +. 0rom the results obtained at table #, the shear modulus, G for specimen A is 4@% MPa
15@*5 MPa
.6hereas the shear modulus for material B is . The theoretical value of shear modulus of specimen A is (/78a and for specimen B is +378a. 0rom this we can see that the experimented value of both specimen is higher than its theoretical value. This is due to random errors. . Based on the results of this experiment, material A and B has an increase of torque when the number of rotation of the hand gear increases. The percentage %%@*3M
%%@42M
error obtained for specimen A is whereas for specimen B is . ,$?, th, ,/,ri",$ts ,r, ',ss a??(rat, 9#r specimen A@ Th, +a'(, #9 th, /,r?,$ta., ,rr#r t(r$,d #(t t# <, hi.h 9#r <#th s/,?i",$; a$d this is d(, t# h("a$ ,rr#r@ M#r, t#r=(, is $,,d,d t# tist th, specimen A s/,?i",$ tha$ specimen B@ It is ?',ar that s/,?i",$ A is ',ss d(?ti', ?#"/ar,d s/,?i",$ B@
5@ Th, (sa., #9 t#rsi#$ i$ r,a' 'i9, ,$.i$,,ri$. is +,r- i"/#rta$t; this is <,?a(s, it i$+#'+,s thi$.s that r#tat,@ O$, ?#""#$ ",?ha$i?a' /art that ar, s(<,?t t# t#rsi#$ ar, th, sha9ts@ h,$ a sha9t is s(<,?t,d t# a t#r=(, #r tisti$.; a sh,ari$. str,ss is /r#d(?,d i$ th, sha9t@ Th, sh,ar str,ss +ari,s 9r#" ,r# i$ th, ais t# a "ai"(" at th, #(tsid, s(r9a?, #9 th, sha9t@a$ ,a"/', #9 sha9t (sa., ar, i$ ?ars hi?h is th, .,ar sha9t@ A$#th,r ",?ha$i?a' /art is th, <#'t@ B#'ts ar, +,r- i"/#rta$t i$ a'' t-/,s #9 a//'i?ati#$s@ , ?a$ a's# sa- shi/s $,,d <#'ts@ ith#(t <#'ts; th,r, is $# s,?(r, ?#$$,?ti#$ <,t,,$ th, <#d- /arts #9 th, shi/@ T#rsi#$ is th, tisti$. #9 th, <#'t h,$ a//'-i$. th, ti.ht,$i$. t#r=(,@ h,$ a <#'t is ti.ht,$,d it is s(<,?t,d t# t,$si', str,ss as /r,'#ad is i$tr#d(?,d <(t a's# t# t#rsi#$ str,ss as a r,s('t #9 9ri?ti#$@ Th, t#rsi#$ that .,$,rat,s 9ri?ti#$ hi?h h#'ds (/ th, <#'t s# that it d#,s $#t <,?#", '#s,@
1
E***' P*"#$%' Gra/hs #9 s/,?i",$ A a$d B ar, ,/,?t,d t# <, sa",@ , had ,rr#rs that ,99,?t,d #(r r,s('t i$ a s"a'' s?a',@ Fr#" this ,/,ri",$t; th, ,rr#r , .#t as ?a'i
C#'% I$ ?#$?'(si#$; this ,/,ri",$t is a<#(t t#rsi#$ t,st @First th, ,/,ri",$t as t,st,d <- (si$. '#ads t# ",as(r, th, r,ad #(t t#r=(,; th,$ th, .ra/h #9 ?a'i
15@*5 MPa
as a$d 9#r s/,?i",$ B as @Fr#" this , ?a$ stat, that s/,?i",$ B is a "#r, d(?ti', "at,ria' ?#"/ar,d t# s/,?i",$ A hi?h has a ',ss,r "#d('(s #9 sh,ar@ Th, %%@*3M
%%@42M
/,r?,$ta., ,rr#r 9#r s/,?i",$ A as a$d 9#r s/,?i",$ B as at th, a$.', #9 tist #9 2@%2; "at,ria' A has a r,ad #(t t#r=(, #9 2@55 h,r,as s/,?i",$ B has a r,ad #(t t#r=(, #9 0@15@ This sh#,d th, di99,r,$?, i$ /r#/,rt- #9 th, s/,?i",$ @ Bas,d #$ a'' this ?a'?('at,d +a'(,s; , ?#$?'(d,d that s/,?i",$ A has a str#$.,r a$d ',ss d(?ti', /r#/,rt- h,r,as s/,?i",$ B has a "#r, d(?ti', /r#/,rt- a$d ',ss str#$.,r /r#/,rt?#"/ar,d t# s/,?i",$ A@ Fr#" this ,/,ri",$t , ($d,rst##d that s/,?i",$ A is t# <, B*'' h,r,as s/,?i",$ B is t# <, A8%%8 , #(r ($d,rsta$di$. as
/r#d(?, a$ a$.', #9 tist hi?h is th,$ ?a'?('at,d t# )$# hi?h s/,?i",$ is "#r,
R"4"*"#" •
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15
