asi lab man sak

8/16/2019 asi lab man sak

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AE 6411 AIRCRAFT STRUCTURES LABORATORY –IL T P C

0 0 3 2 OBJECTIVES

• To study the properties of materials used in Aircraft structure.• To study the failure of di erent component under di erent loading conditions

Expt. No.: 1

!t!"#$%&t$o% o' Yo(%)*+ ,o-( (+ 'o" ,!t& $/,&t!"$& +

A$#:

To nd the defection of given simply supported beam with central point load and to

calculate Young’s modules for given material

App&"&t(+ R! ($"!-:

1. Simply supported beam

. !ial gauge

". #agnetic stand

$. %eight pan with weights

&. #easuring scale

Fo"#( & U+!-:

!e'ection of simply supported beam with central point load

1. Y ( wl") $* +,

. + ( wl") $* y,

%here-

+ Young’s #odules in /)mm

, #oment of ,nertia in mm$

l 0ength of the beam in mm

w 0oad in /


2/37


3/37

Expt. No.: 2

!t!"#$%&t$o% o' !x("& +t"!%)t7 o' #!t& $/ #&t!"$&

A$#:

To determine the 'e7ural strength and study of fracture pattern of the given mildsteel specimen.

T7!o"8

T8p!+ o' '"&/t("! $% t!%+$o%:

There are two 8inds of fracture to the distinguished in tension of a single critical

specimen with a material such as roc8 salt- we have brittle fracture withoutsubstantial plastic

deformation and fracture occurs when the magnitude of normal n anyone of theprinciple planes

reach critical values. This is called cohesive fracture. Single critical specimens ofmetal usually

show large plastic deformations along certain crystal planes. This is 8nown as shearfracture.

The relation between resistance to separation and resistance to sliding do notremain

constant for the same material. ,t depends on temperature of specimen at which

the test made.,n case of polycrystalline specimen there are two 8inds of fracture as given as-

6rittle fracture

Shear fracture

,n the rst case fracture occur practically without plastic deformation over a crosssection

perpendicular to the cross sectional a7is of the specimen. ,n the second case thefractured

occurs with plastic deformation.

These are two 8inds of fracture can again be forwarded based on the twocharacteristics

the resistance to sliding and the resistance to separation. The up and low fractureoccurs only


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5/37

. !iameter of mild steel specimen(

R!+( t:

The fracture pattern of the given cast iron specimen is observed -

The ultimate strength of mild steel specimen ( 5555..

Expt. No.: 2

!t!"#$%&t$o% o' !x("& +t"!%)t7 o' #!t& $/ #&t!"$&'"&/t("! +t"!%)t7 &%- '"&/t("! p&tt!"% o' -(/t$ ! #&t!"$&

A$#:

To determine the fracture strength and study of fracture pattern of the given mildsteel

specimen.

T7!o"8

T8p!+ o' '"&/t("! $% t!%+$o%:

There are two 8inds of fracture to the distinguished in tension of a single critical

specimen with a material such as roc8 salt- we have brittle fracture withoutsubstantial plastic

deformation and fracture occurs when the magnitude of normal n anyone of theprinciple planes

reach critical values. This is called cohesive fracture. Single critical specimens of

metal usuallyshow large plastic deformations along certain crystal planes. This is 8nown as shearfracture.

The relation between resistance to separation and resistance to sliding do notremain


6/37

constant for the same material. ,t depends on temperature of specimen at whichthe test made.

,n case of polycrystalline specimen there are two 8inds of fracture as given as-

6rittle fracture

Shear fracture

,n the rst case fracture occur practically without plastic deformation over a crosssection

perpendicular to the cross sectional a7is of the specimen. ,n the second case thefractured

occurs with plastic deformation.

These are two 8inds of fracture can again be forwarded based on the twocharacteristics

the resistance to sliding and the resistance to separation. The up and low fractureoccurs only

after a considerable uniform stretching and subse9uent local reduction of the crosssectional

of the specimen.

The stress distribution in the nec8 has been increased and it will be found that near

thetensile force in longitudinal ber has directional indication by arrows. The hori:ontal

component produces radial and tangent stresses so as to the decimal elementshaving

ma7imum shear stresses the constant tension test of plastic 'ow a7ially. Thespecimen has

ma7imum stress distribution as shown in gure by shaded area. The magnitude of,ma7 and

,min depends on radius of minimum cross section and radius of curvature ;. of thenec8 and

are given by formula.

App&"&t(+ R! ($"!- 4

1.


7/37

. #ild steel Specimen

Fo"#( & U+!-:

1.


8/37

!e'ection of simply supported beam with eccentric point load is given by-

1. Yc ( %a b ) "+,l

%here-

+( 1.* @1 &/)mm, ( bd" ) 1 mm$

b( breadth of the beam in mm

d( depth of the beam in mm

,( #oment of inertia in mm$

+( Young’s #odules /) mm

P"o/!-("!:1.#easure the length- breadth- depth of the given beam.

.The young’s #odules value can assumed to be 1.* @1 &/)mm - through our early

e9uipment on beams.

".#ar8 a point on the beam at a distance Ba’ from one end and Bb’ from other end.

$.Add weights and note the de'ection at mar8ed while loading and unloading.

&.Also nd the theoretical e9uation value for the given load by using formula and

compare the e7perimental value with the theoretical value.

TABULATION :

S.NO

LOA I% )

EFLECTION

LOA IN

I% ##

EFLECTION

UNLOA IN $% ##

AV $% ##

T;EORETICALVALUE

EFLECTION $% ##


9/37

R!+( t: The de'ection of the simply supported beam with eccentric point load has beenfound out

thus and has been compared with theoretical value

Expt. No.: 4 EFLECTION OF CANTILEVER BEA,

A$#:<

To nd the de'ection of the cantilever beam.

=o" ,&t!"$& R! ($"!-:

?antilever beam

T!+t ,&t!"$& R! ($"!-:

!ail gauge

0oads

Scale


10/37

T7!o"8:

A beam 7ed at one end and free at the other end is 8nown as cantilever beam and

when ever a cantilever beam is being loaded de'ects from the original position. The

amount of beam de'ection depends upon the cross section and the 6ending

moment =6.#>. The parameters in the basic design of cantilever are the following.

Strength Sti ness As there are many methods for nding the slope and de'ection at

a section in the loaded cantilever beam the following are widely used methods to

nd the de'ection.

1. o(9 ! $%t!)"&t$o% #!t7o-

2. ,o#!%t &"!& #!t7o-.

OUBLE INTE RATION ,ET;O :<

The bending moment at a point is given by . d7 d y # ( +, /ow integrating C (

# d7 dy +,. Again integration CC +,.y ( # 2irst e9uation gives slope- later one gives

de'ection

2. ,O,ENT AREA ,ET;O :<

This method gives the slope and de'ection of the beam. , method4 The change of

slope between any two points on an elastic curve is e9ual to the net area of 6.#

diagram between these points divided by +, ,( A ) +, ,, method4 The intercept

=between> ta8en on a given vertical reference line of tangents at any points on an

elastic curve is e9ual to the moment of 6.# diagram between these points about

the reference line divided by +, Y(A=7>)+,

PROCE URE


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#easure the dimensions of the given cantilever beam.

2i7 the de'ection angle gauge of some speci ed position and vary the loads ofthe free end of beam.

6y applying suitable conditions increasing loads at the free end note down thede'ections reading at the speci ed position.

/ow in second e7periment- reverse the position of the load and de'ection gaugerespectively.

/ote down the corresponding de'ections for the varying loads.

ANALYSIS:

The cantilever is being tested for the design criteria i.e.- for its strength and thesti ness purpose. ,t should be strong enough to resist the bending loads. Shear

stress and the de'ection of the beam-APPLICATIONS:

6uilding constructions

Aircraft design and fabrication of all structural elements

,ndustrial applications

!esigning of huge and medium structures D;+?A get the initial readings of the gauge to :ero

?arefully note the de'ection reading

CALCULATIONS:

0ength of the 6eam l ( FFFFFF


12/37

Theoretical deflection G ( FFFFFF

RESULT:

!e'ection of the cantilever beam is FFFFF


13/37

Expt. No.: >

V!"$?/&t$o% o' ,&x@! R!/$p"o/& t7!o"!#

A$#:

To verify the #a7well’s reciprocal theorem using given beam

App&"&t(+ R! ($"!-:

1. !ialH gauge

. 3ernier caliper

". #easuring scale

$. %eight pan with weights

&. Simply supported 6eamT7!o"8

#a7well ;eciprocal theorem4

,n an beam- the de'ection at any point B !’ due to a point load Bw’ at a point B?’other

than B!’ in the beam will be same as the de'ection at Bc’ due to the load at B!’.

P"o/!-("!:

1. 2irst the points B!’ and B?’ are mar8ed on the beam at e9ual distances from theends.

. The loads are rst applied at a appoint B!’ and the de'ections corresponding tothe load

are measured at point B?’

". Similarity readings are noted for unloading the loads

$. The average de'ections are calculated

&. /ote the loads and dial gauge is interchanged between the points and de'ectionsat B!’

are noted.

I. A graph between applied load and de'ection is drawn.


14/37

T&9( &t$o% :

R!+( t:

1. The #a7well ;eciprocal theorem was veri ed for given beam. Slopes of two graphs ate found to be same


15/37

Expt. No.: 6 B(/ $%) o&- !+t$#&t$o% o' + !%-!"!//!%t"$/ /o (#%+

A$#:

To determine the critical load of a column using south well plot.

T7!o"8:

The need to ma8e use of materials with high strength to weight ratio in aircraftdesign has

resulted in using of slender structure components that fail more often by instabilitythe simplest

e7ample is a slender column. ,deal column under small compressive load is slightlydisturbed

and return to original position after removal for particular loading- it ta8esneighboring column

e9uilibrium position this is neutral e9uilibrium. The instability occurs at +uler load orcritical

The ideal column de'ection occurs suddenly- but in actual column it appears as

soon as load applied.

South well should have a relation between applied load and corresponding

de'ection- which can be used to determine critical load- eccentrically by a

graphical procedure without destroying the specimen.

The well 8nown formula for critical load is-

Dcr( F + , ) J 0 - where

J is a const. depending on the end condition of the column+ Young’s modulus of the material-, #oment of ,nertia-

0 0ength of section.2or a column which is always imperfect- the de'ections are determinate at all loads.2orthe de'ection are determinate at all loads- for +7ample- the de'ection of a simplysupportedbeam = SS6> column at its middle due to load B D’ can be written as

,t can be written as 55555555555555.


16/37

App&"&t(+ R! ($"!- 4

1. ?olumn testing apparatus

. Specimen

". Screw Kauge

$. 3ernier ?aliper

&. %eights

P"o/!-("!:1. The given column is aligned on the column testing apparatus with its longitudinala7is vertical.

. The dial gauge is placed at the mid point of the column.

". /ew loads are applied gradually in steps.

$. The corresponding de'ections of a dial gauge are noted and tabulated.

&. /ew 5. ;ation is calculated and the graph of 55 3s... Dlotted.

I. The inverse slope of the load curve gives the critical load of the material for givendimensions.

S.NO LOA P $%)

EFLECTION $% ##

LOA 5EFLECTION

$% )5##


17/37

R!+( t:

Thus the crippling load was determined e7perimentally and the theoretical valuewas

veri ed for mild steel aluminum and 6rass.

Expt. No.: /o%+t"(/t$o% o' So(t7


18/37

soon as load applied.

South well should have a relation between applied load and corresponding

de'ection- which can be used to determine critical load- eccentrically by a

graphical procedure without destroying the specimen.

The well 8nown formula for critical load is-

Dcr( F + , ) J 0

%here J is a const. depending on the end condition of the column

+ Young’s modulus of the material-

, #oment of ,nertia- 0 0ength of section.

2or a column which is always imperfect- the de'ections are determinate at all loads.2or

the de'ection are determinate at all loads- for +7ample- the de'ection of a simplysupported

beam = SS6 > column at its middle due to load B D’ can be written as

,t can be written as 55555555555555.

App&"&t(+ R! ($"!- 41. ?olumn testing apparatus

. Specimen

". Screw Kauge

$. 3ernier ?aliper

&. %eights

P"o/!-("!:

1. The given column is aligned on the column testing apparatus with its longitudinal

a7is

vertical.


19/37

. The dial gauge is placed at the mid point of the column.

". /ew loads are applied gradually in steps.

$. The corresponding de'ections of a dial gauge are noted and tabulated.

&. /ew 5. ;ation is calculated and the graph of 55 3s... Dlotted.

I. The inverse slope of the load curve gives the critical load of the material for given

dimensions

TABULATION :

S.NO LOA P $%)

EFLECTION $% ##

LOA 5EFLECTION

$% )5##

,o-& )"&p7:


20/37

,n L a7is- ta8e de'ection column

,n Y a7is- ta8e load)de'ection column

R!+( t:

Thus the critical load of column is found using south well’s plot

Expt. No.: S;EAR FAILURE OF BOLTE AN RIVETE JOINTS

A$#:

To analy:e the strength of the riveted Moint

+9uipment4 universal testing machine- riveted Moint- specimen

!imension4

Al sheet of si:e (

Al rivets diameter (

T7!o"8:

A riveted Moint may fail in any of the following manner

6y tearing of the plate between the rivet hole and the edge of the plate

6y tearing of the plates between rivets .The safe tensile load that the plate canwithstand

for one pitch length is called the tearing strength

Tearing strength per pitch length ( D 7 t

Dt ( 2t 7 net area of the plate

Dt ( 2t =p d> t

2ailure due to shearing of rivet for a lap Moint if load )pitch length is large it ispossible

that the rivet may shear o


21/37

Ds( 2s 7 Nd )$

,n general in a lap Moint if rivets are covered load per pitch length would be

Ds( n 7 2s 7 Nd )$

where n ( number of rivets per pitch length. 2ailure by bearing or crushing of rivet or plate .The safe load on rivet

Db( 2b7dt where

Db( allowance bearing stress

2b ( bearing value of rivet

E /$!%/8 o' & Do$%t:

0et Dt- Ds- Db be the safe load per pitch length from tearing- shearing and bearingconsiderations.

0et p be the pitch of the rivets and t is the thic8ness of the plate

Safe pull on a solid plate for a length would be

P"o/!-("!:

Dlace the riveted Moint in the universal testing machine.

#a8e sure that plates are held at e9ual distance from both ends

Kradually apply tensile load

/ote the readings from universal testing machine at which rivet Moint fails Ebserve the type of failure

P"!/&(t$o%+:

?hec8 that the plates are rmly gripped without any slip

C& /( &t$o%+:

!iameter of the rivet d (

Ditch p (

Thic8ness of the plate t (

Tearing strength Dt (

Shearing strength Dt (

?rushing or 6earing strength Db (

Solid plate strength D (


22/37

+fficiency of the rivet- O (

R!+( t:

2ailure of riveted Moint is due to the FFFFFFFFFFFFFFFFFFFFFFFFF

FAILURE STRE NT; OF BOLTE JOINT

A$#:<

To analy:e the strength of the bolted Moint.

E ($p#!%t:<


23/37

,n general in a lap Moint n no. of bolts are covered load per pitch length would be

D ( 2t . D.t

O ( least of Dt - Ds- Db)D

P"o/!-("!:<

Dlace the lap Moint in the


24/37

R!+( t+:<

2ailure of bolted Moint is due to the FFFFFFFFFFFFF..

Expt. No.: STU Y OF NON ESTRUCTIVE TESTINPROCE URES

I%t"o-(/t$o%:

!efects of many types and si:es may be introduced to a material or a component

during

manufacture and the e7act nature and si:e of any defects will in'uence the sub

salient

performance of the component. Ether defects such as fatigue crac8s or corrosion

crac8s- may be

generated within a material service. ,t is therefore necessary to have reliable meansfor detecting

the presence of defects at the manufacturing stage and also for detecting

monitoring the rate of

growth of defects during the service life of a component or assembly.

A nondestructive test is an e7amination of an obMect in any manner which will not

impair the

future usefulness of the obMect. Although in most cases nondestructive tests do not

provide adirect measurement of mechanical properties- they are very valuable in locating

material defects

that could impair the performance of a machine member when placed in service.

Such a test is


25/37

used to detect faulty material before it is formed or machined into component parts-

to detect

faulty components before assembly- to measure the thic8ness of metal or other

materials- to

determine level of solid or li9uid contents in opa9ue containers- to identify and sortmaterials- and

to discover defects that may have developed during processing or use. Darts may

also e7amined in

There are ve basic elements in any non destructive test.

1. Source4 A source which provides some probing medium- namely- a medium thatcan be used

to inspect the item under test.

. #odi cation4 This probing medium must change or be modi ed as a result of thevariations or

discontinuities within the obMect being tested.

". !etection4 A detector capable of determining the changes in the probing medium.

$. ,ndication4 A means of indicating or recording the signals from the detector.

&. ,nterpretation4 A method of interpreting these indications. %hile there are a largenumber of

nondestructive tests in use- this section will concentrate on the most commonmethods and on one

recent development. The most common methods of nondestructive testing orinspection are4

R&-$o)"&p78

#agnetic particle inspection

2luorescent Q penetrant inspection.


26/37

thic8ness of metal. Kamma rays may be obtained from a naturally radioactivematerial such as

radium or a radioactive isotope such as cobalt I . Kamma radiation is morepenetrating than that

of 7 ray but the inferior sensitivity limits its application. There is no way that thesource may be

regulated for constrast or variable thic8ness- and it usually re9uires much longere7posure times

than the 7 ray method.

L Q rays are produced when matter is bombarded by a rapidly moving stream ofelectrons.

%hen electrons are suddenly stopped by matter- a part of their 8inetic energy isconverted to

energy of radiation- or L Q rays. The essential conditions for the generation of Lrays are =1> a

lament =cathode> to provide the source of electrons proceeding towards the target-= > a target

=anode> located in the path of electrons-="> a voltage di erence between thecathode and anode

which will regulate the velocity of the electrons stri8ing the target and thus regulatethe

wavelength L rays produced- and =$> a means of regulating tube current to controlthe number of

electrons stri8ing the target. The rst two re9uirements are usually incorporated inan L ray tube.

The use of L rays for the e7amination of a welded plate is shown schematically in2ig. L Qrays

are potentially dangerous- and ade9uate safeguards must be employed to protectoperating

personnel.

A ;adiograph is a shadow picture of a material more or less transparent toradiation. The L Q

rays dar8en the lm so that regions of lower density which readily permitpenetration appear dar8

on the negative as compared to regions of higher density which absorb more of theradiation.


27/37

Thus a hole or crac8 appears as a dar8er area- where as copper inclusions inaluminum alloy

appear as lighter areas.

%hile the radiography of metals has been used primarily for the inspection of

castings andwelded products- it may also be used to measure the thic8ness of materials. 2igshows a simple

radiation thic8ness gauge. The radiation from the source is in'uenced by thematerial being

tested. As the thic8ness increases the radiation intensity reaching the detectordecreases. ,f the

response of the detector is calibrated for 8nown thic8nesses- the detector readingcan be used to

indicate the thic8ness of the inspected material. %ith the suitable feedbac8 circuitthe detector

may be used to control the thic8ness between predetermined limits.

,&)%!t$/ – p&"t$/ ! $%+p!/t$o% ,&)%& (x : This is the method of detectingthe presence of

crac8s- laps- tears- seams- inclusions- and similar discontinuities in ferromagneticmaterials such

as iron and steel. The method will detect surface discontinuities too ne to be seen

by the na8edeye and will also detect discontinuities which lie slightly below the surface. ,t is notapplicable to

nonmagnetic materials.

#agnetic particle inspection may be carried out in several ways. The piece to beinspected may

be magneti:ed and then covered with the ne magnetic particles =iron powder>. This is 8nown as

the residual method. Er- the magneti:ation and application of the particles mayoccur

simultaneously. This is 8nown as the continuous method. The magnetic particlesmay be held in

suspension in a li9uid that is 'ushed over the piece- or the piece may be immersedin the


28/37

suspension =wet method>. ,n some applications- the particles- in the form of a nepowder- are

dusted over the surface of the wor8 piece =dry method>. The presence of adiscontinuity is

shown by the formation and adherence of a particle pattern on the surface of thewor8 piece over

the discontinuity. This pattern is called an indication and assumes the appro7imateshape of the

surfaces proMection of the discontinuity. The magnaglo method developed by the#agna 2lu7

?orporation is a variation of the magna 'u7 test. The suspension 'owed over themagneti:ed

wor8 piece is then viewed under blan8 light- which ma8e the indications stand out

more clearly.%hen the discontinuity is open to the surface- the magnetic eld lea8s to thesurface and form

small north and poles that attract the magnetic particles =see g>.

%hen ne discontinuities are under the surface- some part of the eld may still bede'ected to the

surface- but the lea8age is less and fewer particles are attracted- so that theindication obtained is

much wea8er. ,f the discontinuity is far below the surface- no lea8age of the eld willbe obtained

and conse9uently no indication. Droper use of magneti:ing methods is necessary toensure that

the magnetic eld set up will be perpendicular to the discontinuity and give theclearest

indication.

As shown in g.- for longitudinal magneti:ation- the magnetic eld may be producedin a

direction parallel to the long a7is of the wor8 piece by placing the piece in a coile7cited by an

electric current so that the long a7is of the piece is parallel to the a7is of the coil. The metal part

then becomes the core of an electromagnet and is magneti:ed by induction fromthe magnetic


29/37

eld created in the coil. 3ery long parts are magneti:ed in steps by moving the coilalong the

length. ,n the case of circular magneti:ation also shown in g. magnetic eldtransverse to the

long a7is of the wor8 piece is readily produced by magneti:ing current through thepiece along

the a7is

!irect current- Alternating current and ;ecti ed alternating current are all used formagneti:ing

purposes .!irect current is more sensitive than Alternating current for detectingdiscontinuities

that are not open to the surface. Alternating current will detect discontinuities opento the surface

and is used when the detection of this type of discontinuity is the only interest.%hen Alternating

current is recti ed it provides a more penetrating magnetic eld.

The sensitivity of the magnetic particle inspection is a ected by many factors-including

strength of the indicating suspension- time in contact with the suspension- timeallowed for

indications to form- time subMect to magneti:ing current- strength of the

magneti:ing current.Some e7amples of the crac8s detectable by magna 'u7 or magnaglo are shown in

g-

All machine parts that have been magneti:ed for inspection must be put through a

demagneti:ing-they will attract lings- grindings- chips and other steel particleswhich may cause

scoring of bearings and other engine parts. !etection of parts which have not beendemagneti:ed

is usually accomplished by 8eeping a compass on the assembly bench.U t"&+o%$/ $%+p!/t$o%: The use of sound waves to determine defects is a veryancient method. ,f

a piece of metal is struc8 by a hammer- it will radiate certain audible notes- of whichthe pitch and


30/37

damping may be in'uenced by the presence of internal 'aws. owever thistechni9ue of

hammering and listening is useful only for the determination of the large defects.

A more re ned method consists of utili:ing sound waves above the audible range

with afre9uency of 1 to & million : =cycles per second> Q hence the term ultrasonic.


31/37

a meter- or some other indicator. ,f the ultrasonic wave- travels through thespecimen without

encountering any 'aw- the signal received is relatively large .if there is a 'aw in thepath of the

ultrasonic wave- part of the energy will be re'ected and the signal received by thereceiving

transducer will be reduced.

T7! p( +!< !/7o #!t7o- : uses only one trasducer which serves as bothtransmitter and receiver.

The pattern on an oscilloscope for the pulse echo method would loo8 similar to thatshown in

g.- As the sound wave enters the material being testedH part of it is re'ected bac8to the crystal

where it is converted bac8 to an electrical impulse. This impulse is ampli ed andrendered visible

as an indication or pip on the screen of the oscilloscope. %hen the sound wavereaches the other

side of the material it is re'ected bac8 and shows as another pip on the screenfarther to the right

of the rst pip. ,f there is a 'aw between the front and bac8 surfaces of the material-

it will showas a third pip on the screen between the two indications for the front and bac8surfaces- since the

indication on the oscilloscope screen measures the elapsed time between re'ectionof the pulse

from the front and bac8 surfaces- the distance between indications is a measure ofthe thic8ness of

the material. The location of a defect may therefore be accurately determined fromthe indication

on the screen.

,n general- smooth surfaces are more suitable for the higher fre9uency testing pulseand there

by permit the detection of smaller defects. Droper transmission of the ultrasonicwave has a great


32/37

in'uence on the reliability of the test results. 2or a large part- a lm of oil ensuresproper contact

between the crystal searching unit and the test piece. Smaller parts must be placedin a tan8 of

water- oil- or glycerin. The crystal searching unit transmits sound waves through themedium

and into the material being e7amined. ?lose e7amination of the oscilloscope in thispicture shows

the presence of three pips. The left pip indicates the front of the piece- the right pipthe bac8 of

the piece- and smaller center pip is an indication of a 'aw.


33/37

e7amined.

(& $t8 o' $%+p!/t$o%:<

%hen /!T systems are used- care must be ta8en processes controlled so that notonly

9ualitative but 9uantitative information is received and this information is bothaccurate and

useful. ,f /!T is in mind that /! inspection is carried out for most part by humanbeings and

number of people will perform same tas8 all the time. ence decision must beestimated from

statistical data.

B!%!?t+ o' N T:<

?lear bene ts of /!T is the identi cation of defects which if they remainedundetected-

could result in a catastrophic failure which would be very costly.


34/37

Expt. No.: 10 VERIFICATION OF PRINCIPLE OF SUPERPOSITION

AI,

To !"$'8 t7! p"$%/$p ! o' +(p!"po+$t$o% (+$%) & /&%t$ ! !" 9!.

T;EORY

Drinciple of superposition states that VSeparate e ects of various loads or strainson a

structure or a body- applied singly- can be superimposed or algebraically added togive the total

e ects of all the loads- applied at the same timeW.

This principle is applicable to most of the elastic deformation problems providedthe

load deformation relation is linear and deformation due to each load is too small toproduce a

mar8ed change in the geometry of the structure and the de'ections measured inthe same

direction in which the loads are applied.

The principle of superposition has wide applications in the analysis and design of

Structures

APPARATUS RE UIRE :

!ial gauges- weights- meter scale- steel beam specimen

P"$%/$p ! o' S(p!"po+$t$o%

2or a linearly elastic structure- the load e ects caused by two or more loadings arethe

sum of the load e ects caused by each loading separately.


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2or a linearly elastic structure- load- D- and deformation- F- are related throughsti ness-

J- as shown4

2or an initial load on the structure we have4

D1 ( J XF1

,f we instead we had applied D we would have gotten4

D ( J X F

/ow instead of applying D separately to D1 we apply it after D1 is already applied.

The nalforces and de'ections are got by adding the e9uations4


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This result- though again deceptively Bobvious’- tells us that4

!e'ection caused by a force can be added to the de'ection caused by anotherforce to

get the de'ection resulting from both forces being appliedH

The order of loading is not important = D or 1 D could be rst>H

0oads and their resulting load e ects can be added or subtracted for a structure.

/ote that the principle is limited to4

0inear material behaviour onlyH

Structures undergoing small deformations only =linear geometry>.

D;+S+/TAT,E/ E2 !ATA

A. ?A/T,0+3+; 6+A#

S.%o

LOA G) EFLECTIONS ,,


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6. S,#D0Y S

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