View
255
Download
0
Category
Preview:
Citation preview
8/16/2019 Deflection of Beam Lab Report
1/23
UNIVERSITY COLLAGE OF TECHNOLOGY SARAWAK
SCHOOL OF ENGINEERING AND TECHNOLOGY
EEM3961
ENGINEERING LABORATORY 2
LABORATORY REPORT
LAB CODE: EEM 3961
LAB NAME: DEFLECTION OF A BEAM
NAME : JAYLE FRANCIS (BME1!9!!!"
DATE OF E#PERIMENT: 2$TH MARCH 2!16
DATE OF SUBMISSION: %TH APRIL 2!16
LECTURER&INSTRUCTOR: MS' TAHARAH
PREPARED BY: JAYLE FRANCIS
8/16/2019 Deflection of Beam Lab Report
2/23
TABLE OF CONTENT:
CONTENT PAGE
Lab Code and Experiment Title 1
DM 1(A) : Deflection ! Load 1"#
DM 1($) : Deflection ! !pan %"1&
DM 1(C) : Deflection ! Dept' 1"&1
eference &&
8/16/2019 Deflection of Beam Lab Report
3/23
1
1'! LAB CODE AND TITLE OF E#PERIMENT:
Lab Code : DM1*
Title of Experiment : Deflection of a $eam*
A' D)*+,-./ 0 L.'
O45+,-0:
To e+tabli+' t'e relation+'ip bet,een deflection and applied load to determine t'e
ela+tic mod-l-+ of t'e beam +pecimen from t'e deflection data*
T.78:
T'e mid"+pan deflection of a +impl. +-pported beam loaded ,it' a load / at mid"+pan i+
0ien b.2
EI
WL
34
=δ
e,ritin05
=
δ
W
I
L E
34
8/16/2019 Deflection of Beam Lab Report
4/23
2
6 !lope of t'e load
deflection c-re
Or5
I
L E
34
=
T'e deflection di+tance of a member -nder a load i+ directl. related to t'e +lope of t'e
deflected +'ape of t'e member -nder t'at load*
A7,:
1* A +-pport frame*
&* A pair of pinned +-pport*
* A load 'an0ar*
3* A dial 0a-0e ,it' 7*71 mm acc-rac. to mea+-rin0 deflection*
8* $eam +pecimen ,it' con+tant dept' and ,it' of t'e beam +pecimen*
#* A caliper to mea+-re t'e dept' and ,idt' of t'e beam +pecimen*
%* A meter r-ler or tape mea+-rer to mea+-re t'e +pan of t'e beam*
4* A +et of ,ei0't+*
8/16/2019 Deflection of Beam Lab Report
5/23
3
P7.+7:
1* T'e t,o 9nife ed0e +-pport+ i+ bolted to t'e +-pport frame -+in0 t'e plate and bolt
+-pplied ,it' t'e apparat-+* T'e di+tance bet,een t'e t,o +-pport+ i+ e-al to
t'e +pan of beam -+ed*
&* T'e ,idt' and t'e dept' of t'e beam i+ mea+-red and t'e readin0+ i+ recorded*
* T'e beam +pecimen i+ placed on t'e 9nife ed0e +-pport+*
3* T'e load 'an0ar i+ fixed at t'e mid"+pan of t'e beam*
8* T'e dial 0a-0e i+ po+itioned at t'e mid"+pan of t'e beam to mea+-re t'e re+-ltin0
deflection*
#* T'e dial 0a-0e readin0 i+ +et to ;ero*
%* A +-itable load i+ placed on t'e load 'an0ar*
4* T'e re+-ltin0 of t'e dial 0a-0e readin0 i+ recorded*
8/16/2019 Deflection of Beam Lab Report
6/23
4
R*,:
!pan of te+ted beam5 L = #77 mm
/idt' of beam +pecimen5 b = &8*7< mm
Dept' of beam +pecimen5 d = *7 mm
Moment of inertia of beam +pecimen = 3mm1#*84
Dial 0a-0e readin05 1 di = 7*71 mm
Table 1:1
Applied Load
(N)
Deflection (mm)
Experimental T'eoretical
di mm
1 7 7*& 7*4%
& 7*71 7*%% 7*%%3
7 1*7# 1*1#1
3 7 1*3# 1*83%
8 7*71 1*4# 1*
8/16/2019 Deflection of Beam Lab Report
7/23
5
!ample Calc-lation:
M.* .) E*,-+-,8 ;1&
(4%*7%%3*7
−
−
= 7*4%
P7+/,1774%*7
4%*7&*7×
−
= 1%*>
D-+-./:
8/16/2019 Deflection of Beam Lab Report
8/23
6
$a+ed on t'e experiment data5 a 0rap' of load er+-+ t'e experimental deflection i+
plotted* ?rom t'e 0rap'5 it i+ ob+ered t'at a+ t'e amo-nt of applied load i+ increa+ed5 t'e
re+-ltin0 di+placement or al-e of deflection al+o increa+e+ proportionall.*
T'e al-e of t'e +lope of t'e 0rap' repre+ent+ t'e al-e of t'e beam@+ Mod-l-+ of ela+ticit.5 ,'ic' i+ t'e mec'anical propert. of linear ela+tic +olid material+* t define+ t'e
relation+'ip bet,een +tre++ and +train in a material* ?or t'i+ experiment5 t'e load po+ition
i+ fixed at t'e middle of t'e +pan beca-+e different load po+ition ,ill affect t'e mod-l-+
al-e* Ot'er t'an t'at5 it i+ beca-+e t'e deflection al-e i+ max at t'e middle of t'e beam
+pan*
/'en comparin0 t'e experimental and t'eoretical data for t'e deflection of t'e
beam5 t'ere i+ a +li0't difference* T'e percenta0e error i+ ran0in0 from 8> to #>* T'i+ i+ po++ibl. ca-+ed b. t'e error+ ,'en cond-ctin0 t'e experiment* One of t'e error+ i+ t'e
'-man error* ?or example5 a +li0't error in ta9in0 t'e readin0 or t'e apparat-+ +et"-p ,ill
affect t'e data obtained*
C./+*-./:
At t'e end of t'e experiment5 t'e relation+'ip bet,een t'e deflection and applied
load i+ identified and t'e al-e of t'e ela+tic mod-l-+ of t'e beam +pecimen calc-lated
from t'e deflection data i+ able to be determined* T'e experiment@+ obBectie i+ ac'ieed*
B' D)*+,-./ 0 S/'
https://en.wikipedia.org/wiki/Linear_elasticityhttps://en.wikipedia.org/wiki/Elasticity_(physics)https://en.wikipedia.org/wiki/Elasticity_(physics)https://en.wikipedia.org/wiki/Linear_elasticity
8/16/2019 Deflection of Beam Lab Report
9/23
7
O45+,-0:
To find t'e relation+'ip bet,een deflection and +pan of t'e beam +pecimen*
T.78:
?rom t'eor.5 T'e mid +pan deflection i+ 0ien b. t'e e-ation:
EI
WL
34
=δ
n order to +t-d. t'e effect of +pan -pon deflection 5 t'e po,er for t'e +pan i+ replaced
b. n* T'-+5 t'e deflection e-ation can be ,ritten a+:
n L
EI
WL
W ×=
34
δ
or:n
LC W
∗=δ
/'ere t'e con+tant C = EI 34
1
T'e deflection e-ation can be ,ritten in lo0 from a+ belo,2
8/16/2019 Deflection of Beam Lab Report
10/23
8
c Log L Log nW
Log +=
δ
T'i+ repre+ent+ t'e e-ation of a +trai0't line* T'e +lope of t'e 0rap' repre+ent+ t'e po,er
of t'e +pan and t'e ertical intercept repre+ent+ t'e con+tant*
A7,:
1* A +-pport frame*
&* A pair of 9nife"ed0ed +-pport*
* A load 'an0ar*
3* A dial 0a-0e (,it' 7*71 mm acc-rac.)*
8* $eam +pecimen*
#* A micrometer*
%* A meter r-ler*
4* A +et of ,ei0't+*
P7.+7:
8/16/2019 Deflection of Beam Lab Report
11/23
9
1* T,o 9nife"ed0ed +-pport+ i+ bolted to t'e +-pport frame -+in0 t'e plate and bolt
+-pplied ,it' t'e apparat-+* T'e di+tance bet,een t'e t,o +-pport+ i+ e-al to t'e
+pan of t'e beam to be te+ted*
&* T'e ,idt' and dept' of t'e beam +pecimen i+ mea+-red and t'e readin0+ arerecorded* Mea+-rement i+ ta9en at different location+ and t'e aera0e readin0 i+
recorded*
* T'e beam +pecimen i+ placed on t'e 9nife"ed0ed +-pport+*
3* T'e load 'an0ar i+ fixed at t'e mid"+pan of t'e beam*
8* T'e dial 0a-0e i+ po+itioned at t'e mid"+pan of t'e beam to mea+-re t'e re+-ltin0
deflection*
#* T'e dial 0a-0e readin0 i+ +et to ;ero*
%* A +-itable load i+ placed on t'e load 'an0ar*
4* T'e re+-ltin0 dial 0a-0e readin0 i+ recorded*
8/16/2019 Deflection of Beam Lab Report
12/23
10
R*,:
$eam +pecimen dimen+ion:
/idt'5 b = &8*7< mm
Dept'5 d = *7 mm
Moment of inertia5 = 84*1# 3mm
Dial 0a-0e readin05 1di = 7*71 mm
Table 1:
Load Experimental mid"+pan deflection
!pan5 L1=%77 mm !pan5 L&=477 mm !pan5 L=
8/16/2019 Deflection of Beam Lab Report
13/23
11
Table &:
!pan5 L Lo0 (L)!lope5
/
Lo0 (
/
)
%77 &*438 7*8
8/16/2019 Deflection of Beam Lab Report
14/23
12
?rom Grap' &2
Po,er for t'e +pan = Gradient of t'e +lope
=( )
( )( )7&*717%*7
8/16/2019 Deflection of Beam Lab Report
15/23
13
C' D)*+,-./ 0 D,'
O45+,-0:
To e+tabli+' t'e relation+'ip bet,een deflection and dept' and 'ence determine t'e
ela+tic mod-l-+ for t'e beam +pecimen*
T.78:
?rom t'eor.5
T'e mid"+pan deflection i+ 0ien b. t'e e-ation:
EI
WL
34
=δ
T'e +ection mod-l-+
1&
bt
I =
T'e deflection e-ation can be re,ritten a+ follo,+:
1&
34 bt EI
WL
×=δ
n order to +t-d. t'e effect of t'ic9ne++5 t5 -pon deflection5 5 t'e po,er for t'e t'ic9ne++
i+ replaced b. n*
8/16/2019 Deflection of Beam Lab Report
16/23
14
nbt EI
WL 1&
34
×=δ
Or5
)(
34
nt
bE
WL
W
−
×=δ
Or5
)( nt C
W
−×=δ
/'ere C i+ a con+tant
T'e aboe e-ation can be ,ritten in t'e lo0 form a+ follo,+2
)()()( t nLog C Log W
Log −=δ
T'i+ repre+ent+ t'e e-ation of a +trai0't line
cmxY +=
8/16/2019 Deflection of Beam Lab Report
17/23
15
A7,:
1* A +-pport frame*
&* A pair of 9nife"ed0ed +-pport*
* A load 'an0ar*
3* A dial 0a-0e (,it' 7*71 mm acc-rac.)*
8* $eam +pecimen+ ,it' +ame ,idt' b-t different dept'*
#* A micrometer*
%* A meter r-ler*
4* A +et of ,ei0't+*
P7.+7:
8/16/2019 Deflection of Beam Lab Report
18/23
16
1* T,o 9nife"ed0ed +-pport+ i+ bolted to t'e +-pport frame -+in0 t'e plate and bolt
+-pplied ,it' t'e apparat-+* T'e di+tance bet,een t'e t,o +-pport+ i+ e-al to t'e
+pan of t'e beam to be te+ted*
&* T'e ,idt' and dept' of t'e beam +pecimen i+ mea+-red and t'e readin0+ i+recorded* Mea+-rement i+ ta9en at different location+ and t'e aera0e readin0 i+
recorded*
* T'e beam +pecimen i+ placed on t'e 9nife"ed0ed +-pport+*
3* T'e load 'an0ar i+ fixed at t'e mid"+pan of t'e beam*
8* T'e dial 0a-0e i+ po+itioned at t'e mid"+pan of t'e beam to mea+-re t'e re+-ltin0
deflection*
#* T'e dial 0a-0e readin0 i+ +et to ;ero*
%* A +-itable load i+ placed on t'e load 'an0ar*
4* T'e re+-ltin0 dial 0a-0e readin0 i+ recorded*
8/16/2019 Deflection of Beam Lab Report
19/23
17
R*,:
!pan of beam = 877 mm
/idt' of beam = &8 mm
Dial 0a-0e readin05 1 di = 7*71 mm
Table 1:
Load Experimental mid"+pan deflection
T'ic9ne++ = &*8 mm T'ic9ne++ = *7 mm T'ic9ne++ = 3*7 mm
N di mm di mm di mm
1 7 7*4 7 7*1% 7 7*74
& 7 7*%8 7 7*< 7*71 7*14
7 1*11 7 7*#& 7 7*&%
3 7*71 1*87 7 7*48 7 7*%
8 7 1*44 7 1*7# 7 7*3#
# 7 &*&8 7 1*&4 7 7*8#
Grap' 1 (t=&*8 mm):
8/16/2019 Deflection of Beam Lab Report
20/23
18
Grap' & (t=*7 mm):
Grap' (t=3*7 mm):
8/16/2019 Deflection of Beam Lab Report
21/23
19
Table &:
T'ic9ne++5 t(mm) Lo0 (t)!lope5
/
Lo0 (
/
)
&*8 7*
8/16/2019 Deflection of Beam Lab Report
22/23
20
D-+-./:
Po,er for t'e t'ic9ne++ ; !lope of t'e 0rap'
=)(
3%%*7#7&*7
)#8*7(7&&7*1(
−
−−−
= "&*
8/16/2019 Deflection of Beam Lab Report
23/23
?rom t'e experiment cond-cted5 it i+ ob+ered t'at t'e t'ic9ne++ of t'e beam i+
iner+el. proportional to t'e deflection of beam at mid"point* /'en t'e t'ic9ne++
increa+e+5 t'e deflection decrea+e+*
T'e re+-lt of t'e experiment i+ not acc-rate d-e to t'e error+ t'at mi0't 'append-rin0 cond-ctin0 t'e experiment* ?e, error+ t'at po++ibl. lead to t'i+ difference in
al-e i+ +-c' a+ t'e +en+itiit. of t'e dial 0a-0e to t'e +-rro-ndin0 enironment5 +li0't
error in apparat-+ +et -p5 or t'e t.pical '-man error ,'en cond-ctin0 t'e experiment*
C./+*-./:
At t'e end of t'e experiment5 t'e relation+'ip bet,een deflection and dept' and
'ence determine t'e ela+tic mod-l-+ for t'e beam +pecimen i+ able to be determined* T'e
experiment@+ obBectie i+ ac'ieed*
R)7/+:
1* Gere5 * M*5 F Goodno5 $* * (&71)* Mechanics of materials 8th Edition* !tamford CT:
Cen0a0e Learnin0*
&* $eer5 ?* P* (n*d*)* Mechanics of materials 7 th Edition* McGra,"ill Ed-cation5 & Penn
Pla;a5 Ne, Hor9*
Recommended