deflection of beam lab report

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


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 &&


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


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+*


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*


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*


7/23

5

!ample Calc-lation:

M.* .) E*,-+-,8 ;1&

(4%*7%%3*7

−

−

= 7*4%

P7+/,1774%*7

4%*7&*7×

−

= 1%*>

D-+-./:


8/23

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


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


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*


P7.+7:


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+*



deflection*



4* T'e re+-ltin0 dial 0a-0e readin0 i+ recorded*


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=


13/23

11

Table &:

!pan5 L Lo0 (L)!lope5

/

Lo0 (

/

)

%77 &*438 7*8


14/23

12

?rom Grap' &2

Po,er for t'e +pan = Gradient of t'e +lope

=( )

( )( )7&*717%*7


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*


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 +=


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*


P7.+7:


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+*



deflection*



4* T'e re+-ltin0 dial 0a-0e readin0 i+ recorded*


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):


20/23

18

Grap' & (t=*7 mm):

Grap' (t=3*7 mm):


21/23

19

Table &:

T'ic9ne++5 t(mm) Lo0 (t)!lope5

/

Lo0 (

/

)

&*8 7*


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(

−

−−−

= "&*


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*

deflection of beam lab report

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