Stress vs Strain

7/25/2019 Stress vs Strain

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STRESS AND

STRAIN


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INTRODUCTION (Cont)Objective Understand diferent methods that used to

analyse stress and strain in solid body Apply various principles to solve problems

in solid mechanics

Analyse orces o solid body cause by

e!ternal orce Analyse the result o solid mechanics

e!periments


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INTRODUCTION (Cont)"earnin# Outcome Apply the concepts o stress$ strain$ torsion and

bendin# and de%ection o bar and beam inen#ineerin# &eld

E!plain the stress$ strain$ 'alculate and determine the stress$ strain and

bendin# o solid body that subjected to e!ternal andinternal load

Use solid mechanic apparatus and analyse the

e!periments result

(or) in*#roup that relates the basictheory +ithapplication o solid mechanics


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TOPICS Topic cover Stress and strain Introduction to stress and strain, stress strain diagram

Elasticity and plasticity and Hookes law

Shear Stress and Shear strain

Load and stress limit

Axial force and deection of ody


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TOPICS (Cont)Topic cover Shear Force and bending moment Introduction, types of eam and load

Shear force and ending moment

!elation etween load, shear force and ending moment

Bending Stress Introduction, Simple ending theory

Area of "ndmoment, parallel axis theorem #eection of composite eam


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REFERENCES! "ames #! $ere (%&&') #echanics o #ateria*s+! 'thEdition, Thom-son%! R!C! .ibbe*er (%&&/) #echanics o #ateria*s+! 0thEdition, Prentice .a**

/! Ra1mond Parnes (%&&), So*id #echanics in Engineering+! "ohn 2i**e1and Son


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Stress and strainDIRE'T STRESS

2hen a orce is a--*ied to an e*astic bod1, the bod1 deorms! The 3a1in 3hich the bod1 deorms de-ends 4-on the t1-e o orce a--*ied to it!

Compression force makes the body shorter.

A tensile force makes the body longer


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Tensile and compressive forces are called DIRECT FORCE

tress is the force per !nit area !pon "hich it acts.

#.. $nit is %ascal &%a' or

(ote) *ost of engineering fields !sed k%a+ *%a+ ,%a.

& imbol - igma'A

F

Area

ForceStress ===

2/mN


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DIRECT TRAI( +

In each case+ a force F prod!ces a deformation . In engineering+ "e

!s!ally change this force into stress and the deformation into strain

and "e define these as follo"s)train is the deformation per !nit of the original length.

The

symbol

train has no !nit/s since it is a ratio of length to length. *ost

engineering materials do not stretch very m!sh before they becomedamages+ so strain val!es are very small fig!res. It is 0!ite normal to

change small n!mbers in to the eponent for 1234& micro strain'.

called E%I5O(

L

x

Strain ==


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MODULUS OF ELASTICITY (E)

Elastic materials al"ays spring back into shape "hen released.

They also obey 6OO7E/s 5A8.

This is the la" of spring "hich states that deformation is directly

proportional to the force. F9 : stiffness : k(9m

The stiffness is different for the different material and different si;es of

the material. 8e may eliminate the si;e by !sing stress and straininstead of force and deformation)

If F and is refer to the direct stress and strain + then

hence andAF = Lx =L

A

x

F

=

=

Ax

FL


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The stiffness is no" in terms of stress and strain only and this

constant is called the *OD$5$ of E5ATICIT< &E'

A graph of stress against strain "ill be straight line "ithgradient of E. The !nits of E are the same as the !nit of

stress.

ULTIMATE TENSILE STRESS If a material is stretched !ntil it breaks+ the tensile stress has

reached the absol!te limit and this stress level is called the

!ltimate tensile stress.

=E

=

Ax

FL


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STRESS STRAIN DIAGRAM


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Elastic behavio!r The c!rve is straight line tro!gh o!t most of the region tress is proportional "ith strain *aterial to be linearly elastic

%roportional limit The !pper limit to linear line The material still respond elastically The c!rve tend to bend and flatten o!t

Elastic limit $pon reaching this point+ if load is remove+ the

specimen still ret!rn to original shape


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STR5IN .5RDENIN$ 2hen 1ie*ding has ended, 4rther *oad a--*ied, res4*ting in a c4r6e

that rises contin4o4s*1

Become 7at 3hen reached U8TI#5TE STRESS

The rise in the c4r6e 9 STR5IN .5RDENIN$

2hi*e s-ecimen is e*ongating, its cross sectiona* 3i** decrease

The decrease is air*1 4niorm

NEC:IN$ 5t the 4*timate stress, the cross sectiona* area begins its *oca*ised

region o s-ecimen

it is ca4sed b1 s*i- -*anes ormed 3ithin materia* 5ct4a* strain -rod4ced b1 shear strain

5s a res4*t, nec;+ tend to orm

Sma**er area can on*1 carr1 *esser *oad, hence c4r6e don3ard

S-ecimen brea; at FR5CTURE STRESS


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SHEAR STRESS

hear force is a force applied side"ays on the material &transversely

loaded'.

8hen a pair of shears c!t a material

8hen a material is p!nched

8hen a beam has a transverse load


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hear stress is the force per !nit area carrying the load.

This means the cross sectional area of the material being

c!t+ the beam and pin.

and symbol is called Ta! hear stress+

The sign convention for shear force and stress is based on ho" it

shears the materials as sho"n belo".

A

F=


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SHEAR STRAIN

The force ca!ses the material to deform as sho"n. The shear strain

is defined as the ratio of the distance deformed to the height

. ince this is a very small angle + "e can say that )

& symbol called

,amma'

hear strain

L

x

Lx=


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ULTIMATE SHEAR STRESS

If a material is sheared beyond a certain limit and it becomes

permanently distorted and does not spring all the "ay back to

its original shape+ the elastic limit has been eceeded.

If the material stressed to the limit so that it parts into t"o+ the

!ltimate limit has been reached.

The !ltimate shear stress has symbol and this val!e is !sed

to calc!late the force needed by shears and p!nches.


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DOUBLE SHEAR

Consider a pin >oint "ith a s!pport on both ends as sho"n.This is called C5E?I and C5E?I %I(

@y balance of force+ the force in the t"o s!pports is F9 each The area sheared is t"ice the cross section of the pin o it takes t"ice as m!ch force to break the pin as for a case

of single shear

Do!ble shear arrangements do!bles the maim!m force

allo"ed in the pin


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LOAD AND STRESS LIMIT

DEI,( CO(IDERATIO( 8ill help engineers "ith their important task in Designing

str!ct!ral9machine that is AFE and ECO(O*ICA55< perform for

a specified f!nction

DETER*I(ATIO( OF $5TI*ATE TRE(,T6 An important element to be considered by a designer is ho" the

material that has been selected "ill behave !nder a load This is determined by performing specific test &e.g. Tensile test'

$5TI*ATE FORCE &%$': The largest force that may be applied to

the specimen is reached+ and the specimen either breaks or

begins to carry less load

$5TI*ATE (OR*A5 TRE&$' : $5TI*ATE FORCE&%$' 9AREA


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SELECTION OF F.S.

1. ?ariations that may occ!r in the properties of the member !nderconsiderations

. The n!mber of loading that may be epected d!ring the life of the

str!ct!ral9machine

B. The type of loading that are planned for in the design+ or that may

occ!r in the f!t!re

. The type of fail!re that may occ!r

. $ncertainty d!e to the methods of analysis

4. Deterioration that may occ!r in the f!t!re beca!se of poor

maintenance 9 beca!se of !npreventable nat!ral ca!ses

. The importance of a given member to the integrity of the "hole

str!ct!re


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WORKED EXAMPLE 8

0.6 m


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SOLUTION


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SOLUTION


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SELF ASSESSMENT NO.


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AXIAL FORCE ! DEFLECTION OF BODY

Deformations of members !nder aial loading If the res!lting aial stress does not eceed the proportional limit of

the material+ 6ooke/s 5a" may be applied Then deformation & 9 ' can be "ritten as

AE

FL=

E=

Stress vs Strain

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