8/18/2019 Analysis of Stress Concentration

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Concept of Stress Concentration

Theoretical stress

concentration factor,K 

t 

Maximum stress at the discontinuit

!ominal stress, max stress

"ith no discontinuit

K t  is used for normal

stresses and K ts for

shear stresses.

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Concept of Stress Concentration

#onsider an elliptical hole in an infinitel large plate loaded in uniform

tension. Using the theor of elasticit the theoretical stress concentration

factor is gi$en % the euation %elo".

Elliptical hole

'b

'a

( )or a circular hole K t  * +

( The euation can %e applied to a longitudinal crac "here b -- a

8/18/2019 Analysis of Stress Concentration

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

Stress concentration factor is found using experimental methods.

( hotoelasticit / a plane polari0ed light is passed thru aphotelastic material 1all transparent plastics2 resulting in a

colorful fringe pattern indicating the intensit of the stress. 

8/18/2019 Analysis of Stress Concentration

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

( 3rittle #oating / a speciall

prepared lacuers are usuallapplied % spraing on the actual

part. After air dring, the part is

su%4ected to stress. A pattern of

small cracs appear on the surface.

5ata could %e used to locate strain

gages for precise measurement ofthe stress. The method is sensiti$e

to temperature and humidit.

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

( Electrical strain gauges 

The method is the most popular and "idel accepted for strain measurements and

stress analsis. The strain gauge consists of a grid of strain6sensiti$e metal foil

%onded to a plastic %acing material. 7hen the gauge is su%4ected to a mechanical

deformation, its electrical resistance changes proportionall. The change in $oltage

is con$erted to strain and the stress is calculated from the strain.

8/18/2019 Analysis of Stress Concentration

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Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

( )inite Element method

The #A5 model is su%di$ided into man small pieces of simple

shapes called elements.

)EA program "rites the euations go$erning the %eha$ior of each

element taing into consideration its connecti$it to other elements.

These euations relate the unno"ns, for example displacements in

stress analsis, to no"n material properties, restraints and loads.

The program assem%les the

euations into a large set of

simultaneous alge%raic

euations 1thousands or e$en

millions2. These euations are then

sol$ed % the program to

o%tain the stress distri%ution

for the entire model.

8/18/2019 Analysis of Stress Concentration

7/9Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

8/18/2019 Analysis of Stress Concentration

8/9Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

8ound section"ith a fillet

8/18/2019 Analysis of Stress Concentration

9/9Ken Youssefi Mechanical & Aerospace Engr., SJSU

Stress Concentration Factor 

)lat plate

"ith a hole