elementry stresses & stress concentration 36 ti

8/11/2019 Elementry Stresses & Stress Concentration 36 TI

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Institute of Air MF-4- SJ1

In the name of

ALLAH,the mostgracious, the most

merciful


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Institute of Air MF-4- SJ2

O my Lord! eand me my chest" #ase my tas$ for me" and %emo&e the imediment from myseech,

So they may understand what I say.


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Institute of Air MF-4- SJ

#L#M#'(A%)S(%#SS#S


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*e+nition of Stress

Stress is de+ned as theinternally distriuted forcesthat resist a change in the

ody

It is measured in Pound Per S.uare

Inch /Psi0


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Force asically starts from oint of aand runs through the 1hole ody

#ect of force on entire ody is asic c

*id the failure occur due to alied foror some other reason as 1ell5

lication of Force

F FA


7/39Institute of Air MF-4- SJ

6ross Sectional Area

'o of inner surfaces of the odyde+nes the cross sections of theody

Force is acting through the crosssectional area 6ross sections may lie

at dierent angles to the alied forut 1e 1ill restrict our discussionto sections erendicular and aralleto the alied force



Free-7ody *iagrams

6onsider ar emedded in ric$ 1all 1ith aial force F alied at its end

F

F

Free-body diagram: pictorial representation used for analysis that

shows all forces acting on an object

F

If the bar is stationary,

the wall must produce

a reaction force equaland opposite to the

applied force

FF

F

F

!ince bar is in equilibrium, e"ery portion

of the bar is also in equilibrium

L


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A;IAL, 7#'*I'



ial Stresses

Forces which try topull the body apart are

called tensile forces,resulting in stressesknown as

tensile stresses />t0 It acts on a planeperpendicular

to the Load

ensile Stress /Pulling0



If forces acting on a body arepushing against each other, body

is said to be in comression. It also acts perpendicular to the p

c9 F : A

mressi&e Stress /Pushing0



If loads are acting parallel to theplane of the structure, but not

passing through the same axis,they are known

as shear loadsand resulting

stressesare called shear stresses.

Shear

Stress/Slicing0



If forces act on a iece of materialin such a 1ay that it inducescomressi&e stress o&er one art ofcross ?section and tensile stresso&er the remaining art, the ieceis said to e in ending

ending

#c$2%%& 'roo(s)*ole, a di"ision of +homson earning, Inc +homson earningis a trademar( used herein under license



PP

6omression

(ension


http://www.avweb.com/newspics/metfatig_figure5.gif



(he t1istingaction of onesection of aody 1ith

resect to acontinuoussection is

termed astorsion

orsion

!tress distribution



P%O7L#MS


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SOL@(IO'

.ffecti"e length #/$ 0 2% ia-------#$

iameter 0 radius 3 2

4adius 0 5 inch

ia 0 562 0 7 inch

8utting "alue of ia in eqn

.ffecti"e length #/$ 0 2% 7 0 12 inch

!+4.!!08)/-----#*$

809%% lbs

/rea0

!ide / 0 2% inch

!ide ' 0 9 inch

4adius 0 5 inch


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SOL@(IO' /6O'(3*0

/rea 0 12 3 9

0 ;% inch2

8utting "alues of 8 and /rea in eqn *

< !+4.!! 0 8)/

0 9%% ) ;%

0 7& psi


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SOL@(IO'!+4.!! 0 8 ) /

8 0 1%% lbs

/rea 0 #pi$ r2

4adius #r$ 0 2 inch

!o,

/rea 0 &15 3 5

0 129; inch2

!+4.!! 0 1%% ) 129;

!+4.!! 0 =>; psi


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S(%#SS6O'6#'(%A(IO'


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hat is Stress6oncentration

A hole, cutout, 1eld Ba1, nic$s, crac$s and otherdiscontinuities in a material $no1n as CStress%aisers3 result in an increase in the a&erage

stress in the &icinity of that discontinuity $no1nas Stress 6oncentration


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ASS@MP(IO'S :LIMI(A(IO'S*IS6@SSIO' %#MAI'S

%#S(%I6(#* (O D-

6ircular and ellitical

discontinuities Memer is E-*imensional

(he eect of Stress

6oncentration factor /0 isanalyGed on the erihery of thediscontinuity and 'O( on the

ody as a 1hole

St 6 t ti i


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Stress 6oncentrations in anAirframe

Fillets

Rivets Holes


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Stress 6oncentrationFactor

9

is the Stress 6oncentration FactorH /Ma0 is the Ma Stress 1ith

discontinuity

H/A&g0 is the Stress 1ithout discontinuity

H /Ma0

H /A&g0


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Flo1 o&er a cylinder in a1ind tunnel

8o1 Stress 6oncentrationOccurs

elocity increases aroundcylinder


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8 8

Stress Lines around a hole in auniform late


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Stress 6oncentration @nderPolariGed Light

&5


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Stress 6oncentration6alculation

(he stress concentration factor C3 is al1aysgreater than K

*etermined on the asis of geometric shae Indeendent of the tye of material

is indeendent of the siGe of the discontinuity


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8o1 to 6alculate Stress6oncentration

a8

b

8

K = 1 + 2 (a/b)

a 0 side perpendicular to load

b 0 side parallel to load

Note: Formula is applicable for circular and o"al discontinuities only


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a 0 % ? b 0 1

@ 0 1

a 0 1 ? b 0 1

@ 0 &

8arallel *rac( 8erpendicular *rac( 4ound Aole

a 0 1 ? b 0 %

@ 0 B


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6onclusion

Stress concentrates locally aroundshar discontinuities in structurallyloaded memer

Sharer the discontinuity or stress

raiser greater the stressconcentration

6rac$s in a material can e stoed

y drilling a hole Stress concentration factor reduces

the material strength y the ratio:


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elementry stresses & stress concentration 36 ti

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