Ceg 201 Lab Reportddd (Autosaved)

8/19/2019 Ceg 201 Lab Reportddd (Autosaved)

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NAME: EMENIKE-UKAH MICHAEL CHIEDOZIE

MATRIC NUMBER: 150408510

DEPARTMENT: COMPUTER ENGINEERING

CEG 201 LAB REORT

GROUP: C

DATE SUBMITTED: 17/02/2016

EPERIMENT 1!

TENSILE TESTS ON STEEL" BRASS" AND ALUMINIUM RODS!


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DATE PER#ORMED: 27$% &' ()*+), 2016.

OBJECTIVES:

i.) To determine the Young’s modulus of elasticit of steel! "rass and aluminium "arfrom tensile test.

ii.) #nother main o"$ecti%e of this e&'eriment is to measure the tensile 'ro'erties ofthree 'olmeric materials! steel! aluminium! and "rass at a constant strain rate on thetensile testing machine.

#((##T*S:

i.) The *ni%ersal Testing +achine.

ii.) Steel! aluminium! and "rass rods.

iii.) Vernier calli'er.

i%.) Steel ruler.

T,EOY:

This e&'eriment is "ased on the ,OO-ES #/ O0 E#STICITY 1hich states that! 1ithinthe elastic limit of a solid material! the deformation2strain) 'roduced " a force2stress)of an 3ind is 'ro'ortional to the force. If the elastic limit is not e&ceeded! the materialreturns to its original sha'e and si4e after the force is remo%ed! other1ise it remainsdeformed or stretched. /hen forces are a''lied to materials! the deform in reactionto those forces. The magnitude of the deformation for a constant force de'ends on the

geometr of the materials. i3e1ise! the magnitude of the force re5uired to cause agi%en deformation! de'ends on the geometr of the material. 0or these reasons!engineers de6ne stress and strain.

Stress 2engineering de6nition) is gi%en ": Stress δ =

P

A

1here ( 7 oad or force acting on the "od! and

# 7 Cross8sectional area of the "od.

The unit of stress is (ascal 2(a) 1hich is e5ual to 9 ;m< .

=e6ned in this manner! the stress can "e thought of as a normali4ed force.

Strain 2engineering de6nition) is gi%en ":

Strainε=

e

L

1here e 7 e&tensionin length of the "od! and

7 Original length of the "od.

The strain can "e thought of as a normali4ed deformation./hile the relationshi' "et1een the force and deformation de'ends on the geometr of the material! the


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relationshi' "et1een the stress and strain is geometr inde'endent. The relationshi'"et1een stress and strain is gi%en " a sim'li6ed form of ,oo3e>s a1:

stress

Strain=constant = E

1here E is a constant of 'ro'ortionalit 3no1n as Young +odulus.

.&+* M&++ &' 3)$$ E is the slo'e of the straight line 'ortion of a stressstrain cur%e. It is also called stress8strain ratio. =e'ending on the t'e of loadingre'resented " the stress8strain cur%e! modulus of elasticit ma "e re'orted as:com'ressi%e modulus of elasticit? @e&ural modulus of elasticit? shear modulus of elasticit? tensile modulus of elasticit? torsional modulus of elasticit.

PROCEDURE:

The alread 're'ared s'ecimen 2 a steel clindrical rod) 1ith a cross sectional

diameter of 9< mm and an original length of Amm 1as fastened "et1een the t1o

%ertical $a1s of the *ni%ersal Testing +achine! 1ith its length of analsis set at a

gauge length’ of


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2mm


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• Young modulus=

stress

strain

Stress ¿

force

originalarea Strain¿

extension

originallength

Stress ¿

50000 N

113.11mm2 Strain¿ 38

200

Stress ¿442.05 Strain ¿0.19

∴Young modulus=442.05

0.19

¿2326.58 N /m m2

0ailure Stress ¿

Failureload

Finalarea

¿ 4700 N

50.27m m2

0ailure Stress ¿93.5 N /mm2

DISCUSSION:

/hile man e&'erimental tests e&ist to determine the mechanical 'ro'erties ofsolid state materials! the sim'lest is this tensile test.

If one 'ulls on a material until it "rea3s! one can 6nd out lots of information a"outthe %arious strengths and mechanical "eha%iours of a material. This informationcould then "e used to deduce the 'roof load and the ultimate load ca'acit of suchmaterial 1hen used for a 'ro'osed ne1 design: a good e&am'le "eing in theconstruction of "ridges! automo"ile! 'ressure %essels.

The accurac of the dimensional measurement of the steel rod is 0.05mm .

One indirect 1a of cross chec3ing and im'ro%ing the results is to send similars'ecimens to at least t1o other testing la"oratories.

Some 'recautions I too3:

i.) The $a1s 1ere 6rml clam'ed onto the ends of the s'ecimens to 're%entsli''ing! 1hich 1ould other1ise result in e&'erimental errors.ii.) The error due to 'aralla& 1hen ta3ing measurements from the metre rule 1as

considera"l reduced " ensuring tha m line of %ision 1as incidental to %alue in5uestion.


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Tensile Test omenclature: # 'lot of the Engineering stress %ersus the Engineeringstrain.

The material test cur%es ha%e a region 1here the deformation caused " the stress iselastic. #t stresses greater than a certain %alue! a 'ortion of the strain "ecomes'ermanent or 'lastic. The stress re5uired to cause a .s a1 descri"es the stress8strain relationshi'! the elastic res'onse is the dominant deformationmechanism. ,o1e%er! man materials e&hi"it nonlinear "eha%ior at higherle%els of stress. This nonlinear "eha%iour occurs 1hen 'lasticit "ecomes the

dominant deformation mechanism. +etals are 3no1n to e&hi"it "oth elasticitand 'lasticit. The transition from elasticit to 'lasticit occurs at acritical 'oint 3no1n as the ield 'oint. Since 'lasticit is characteri4ed "'ermanent deformation! the ield 'oint is an im'ortant characteristic to 3no1.In 'ractice! the ield 'oint is the stress 1here the stress8strain "eha%iortransforms from a linear relationshi' to a non8linear relationshi'. The mostcommonl used method to e&'erimentall determine the ield 'oint is the .


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'oint 3no1n as the ultimate stress. Since failure occurs soon after nec3ing"egins! the ultimate stress is an im'ortant characteristic to 3no1.

The stress changes during this test for t1o reasons: the load increases! and thecross8sectional area decreases. Therefore! the stress can "e calculated " t1oformulae 1hich are distinguished as engineering stress and true stress.Engineering stress uses the original cross8sectional area 1hile true stress uses

the instantaneous cross8 sectional area of the s'ecimen.

PRECAUTIONS

/hen using the %ernier calli'ers! error due to 'aralla& 1as a%oided

Error due to 'aralla& 1as also a%oided 1hen loading the material in the testingmachine.

RE#ERENCES

9) Strength of +aterials " .S. -hurmi


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#I+:

i.) To determine the reactions of a and " for a sim'l su''orted "eam.

ii.) To determine the %alues of a and " as a gi%en load mo%es from one end of asim'l su''orted "eam to the other.

iii.) To determine the numeric dierences "et1een the theoretical and e&'erimentall

o"tained %alues of a and ".

#((##T*S:

i.) T1o s'ring "alances.

ii.) # long steel "eam.

iii.) /eights.

T,EOY:

This e&'eriment is "ased on the (ICI(ES O0 +O+ETS 1hich states that if asstem of co'lanar forces acting on a rigid "od is 3ee'ing it in e5uili"rium condition!the sum of all %ertical forces is 4ero! the sum of all hori4ontal forces is also e5ual to4ero! and also! the alge"raic sum of there moments is e5ual to 4ero.

+athematicall!

Ta3ing moments a"out 'oint #! ∑ ! A=0

"# ( L )−$ ( x )=0

"# L=$x

∴ "#=$x

L

Su"stituting for "# in (1) !

$ = " A+$x

L

" A=$ −$x

L

" A=$L−$x

L

∴ " A=$ ( L− x)

L % % % % % %(¿)

PROCEDURE:

The steel "eam is sus'ended almost 'erfectl hori4ontal on the hoo3s of t1o s'ring"alances 1hich are 'ositioned at e5ual length from the mid'oint of the "eam. It mustthen "e ensured that he reactions at "oth s'ring "alances are in unison.


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# load hanger is 'ositioned at the centre of the "eam! and the s'ring "alances areread! still ensuring that that the are "oth identical.0or the 6rst e&'eriment! the mass is increased in ste's of


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" A=$ ( L− x)

L

as 1as deri%ed in e5uation (¿) 2in the theor)

and$ = " A+ " #

∴ "#=$ − " A

1here / 7 the 1eight 2load) a''lied 7 G3g

7 the length of the "eam 7 9cm

x 7 the 'osition of the load 2cm)

#t 'osition cm!

" A=$ ( L− x)

L

¿8(100−0)

100

" A=8100

100

∴ " A=8 &g

"#=$ − " A

"#=8−8

∴ "#=0&g

In terms of 1eight! " A=80 N ' " #=0 N

Similarl! at 'osition 9cm!

" A=$ ( L− x)

L

¿8(100−10)

100


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" A=8 90

100

" A=8×0.9

∴ " A=7.2&g

"#=$ − " A

"#=8−7.2

∴ "#=0.8&g

In terms of 1eight! " A=72 N ' "#=8 N

*sing this same 'rocedure! # and B 1ere calculated for other 'ositionsand the follo1ing %alues 1ere o"tained

for


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Beams are usuall long! straight 'rismatic "ars. ,ori4ontal a''lications of "eams aret'icall found in "ridge and "uilding construction. The 'rimar deformation of a"eam is in "ending. Some "eams are loaded! such that onl "ending occurs. ,o1e%er!"eams can "e su"$ected to "ending and an com"ination of a&ial! shear! and torsionalloads. The distance "et1een the su''orts is called the span.# "eam normall su''orts a sla" 1hile the "eam is usuall su''orted " the column.# "eam can "e made of concrete or of steel. E%er "eam has su''orts. If it has t1osu''orts! then it is sim'l su''orted! "ut if it has more than t1o su''orts! then it iscontinuous.T3 &' B3) S+&,$

(in su''ort This t'e of su''ort has t1o reactions i.e. %ertical reaction 2 ) and hori4ontalreaction 2 ) as sho1n in 0ig. 9

Fig. 1

oller Su''ort This t'e of su''ort has onl one reactioni.e. %ertical reaction 2 ) as sho1n in 0ig.<

Fig. 2

igid Su''ort This t'e of su''ort has three

reactions i.e. %ertical reaction2 )! hori4ontal reaction 2 ) and moment reaction + as sho1n in 0ig.H

CONCLUSION:

# "eam is a structural mem"er or an element of a machine that is designed 'rimarilto su''ort forces acting 'er'endicular to the a&is ofthe mem"er. Menerall! the length 2) of a"eam is much larger than the other t1o cross8sectional dimensions! height! and 1idth. Beams can"e straight or cur%ed. # "eam 1ith a constant heightand 1idth is said to "e 'rismatic. /hen a "eam’s1idth or height 2more common) %aries! the mem"eris said to "e non8'rismatic.,ori4ontal a''lications of "eams are t'icall found in "ridge and "uildingconstruction.Vertical "eams are also found in %arious a''lications. The 'rimar deformation of a"eam is in "ending. Some "eams are loaded! such that onl "ending occurs. ,o1e%er!"eams can "e su"$ected to "ending and an com"ination of a&ial! shear! and torsionloads. /hen a slender mem"er is introduced 'rimaril to a&ial loads! it is considered

to "e a column. # %ertical mem"er found in "uilding construction that is loaded 1itha&ial com'ression and simultaneousl su"$ected to a hori4ontal 1ind or seismic load iscommonl referred to as a "eam column. In this 'ro$ect! onl straight! 'rismatic"eams are considered.


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(EC#*TIOS:

I a%oided the error due to 'aralla& 1hen ta3ing the readings.

I ensured that the "eam 1as 'erfectl hori4ontal

E0EECES:

/i3i'edia

Strenght of materials " rder.

EPERIMENT !

DE#LECTION O# SUPPORTED BEAMS

AIM: To determine the de@ection of sim'l su''orted "eams and cantile%ers.

THEOR.:

The de@ection of "eam elements is usuall calculated on the "asis of the Euler8Bernoulli "eam e5uation 1hich is also 3no1n as engineer’s "eam theor or classical

"eam theor. This theor is a sim'li6cation of the linear theor of elasticit 1hich'ro%ides a means of calculating the load carring and de@ection characteristics of"eams. It co%ers the case for small de@ections of a"eam that is su"$ected to lateralloads onl.


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#nother method is the D&+93 *$3,)$&* 3$%&!

This is suita"le for a single load

Since 1e made use of a single load! the dou"le integration method 1ill "e suita"le for

determining the de@ection

! = El d

2 (

d x2

El d(

dx=∫ !

El ) (=∬ !

#fter 'erforming the necessar o'erations! 1e o"ser%e that (

c

= $ l

3

48 E*

/here c 7 de@ection

/ 7 1eights a''lied

l 7 length "et1een the t1o su''ort

E 7 Young +odulus of the "eam

I 7 +oment of Inertia

,ence! 1e arri%ed at

Deflectionδ = $ L

3

48 E*

PROCEDURE:

The 9.


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This same 'rocedure 1as done for the


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Ta"le o"tained for the 12×12×1200mmsteel ¿̄

LOAD DE#LECTIONKG; N; D) G)+3

R3)*

;

.<


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* =1728mm4

Youngmodulus E=slo+e L

3

48 *

E=11.79×1.728×10

9

48×1728

∴Young modulus E=2)46×10 5 N /m m2

#&, $%3 25×6×1200mm steel ¿̄

slo+e=43.17 N /mm

L=1200,∴ L3=1.728×109mm3

* =7812mm4


3

48 *

E=43.17×1.728×10

9

48×7812

∴Young modulus E=2×105 N /m m2

#&, $%3 12×12×1000mmsteel ¿̄

slo+e=20 N /mm

L=1000,∴ L3=1×109mm3

* =1728mm4


3

48 *

E=20.2×1×10

9

48×1728

∴Young modulus E=2)4 ×105 N /mm2


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S&+,3 &' E,,&,:

98 /hen 1e get the reading there must "e accurac in getting it and on the other side

1e must ta3e careful " ma3e the dial gage 4ero.


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oo3ing at the second diagram! 1e can o"ser%e that the e&ternal force a''lied to the

"eam has caused a "ending moment in the "eam! there" causing a de@ection. The

%alue of this de@ection can "e calculated using the follo1ing formula

Deflection=$ L

3

48 E*

Various "eams ha%e dierent de@ected sha'es due to the 3ind of su''ort the ha%e.

Various t'es of "eams and their de@ected sha'es are outlined "elo1.

a. Sim'l su''orted "eam

". O%erhanging "eam

c. Cantile%er "eam

d. Continuous "eam

e. Beam 6&ed at one end and sim'l su''orted

at the other end

f. 0i&ed "eam


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#s 1as sho1n in the 6rst case a"o%e 2case a)! let us

consider the "eam "elo1 sim'l su''orted at "oth ends! ha%ing an e&ternal force 0

acting "et1een the t1o su''orts.

#fter deformation! it 1ill "end due to deformation it has undergone and 1ill then ha%e

the sha'e sho1n "elo1

The amount " 1hich a "eam de@ects! de'ends u'on its cross8section and the

"ending moment.

In modern design oces! there are t1o 3* ,$3,) for the de@ection of a

cantile%er or "eam

Strength

Stiness

#s 'er the strength criterion of the "eam design! it should "e strong enough to resist"ending moment and shear force. Or in other 1ords! the "eam should "e strong

enough to resist the "ending stresses and shear stresses. #nd as 'er the stiness

criterion of the "eam design! 1hich is e5uall im'ortant! it should "e sti enough to

0

0


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resist the de@ection of the "eam. Or in other 1ords! the "eam should "e sti enough

not to de@ect more than the 'ermissi"le limit.

RE#ERENCES:/i3i'edia

Strength of +aterials " .S. -hurmi

Strength of +aterials " . -. a$'ut

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Ceg 201 Lab Reportddd (Autosaved)