Why do textbooks say Plane Stress is for thin components? 1

[DerbyEngineer]

Hi everyone,

I'm struggling with another concept - this time plane stress...

From my understanding, plane stress occurs when in-plane loads are applied to a structure such that stress through the thickness is zero. So far, so good. However, my textbooks state that plane stress occurs in thin components without any explanation as to why. A typical example is given in the attached PDF. As far as I can tell, plane stress would occur for very thick components too. What am I missing?

Any information appreciated.

Thanks again,

Martin

 

[rb1957]

a thick section provides constraint for out-of-plane deformation, so you get stresses in the 3 directions.

a thin section doesn't provide this constraint, so you get strains in three directions. this is really clearly seen at crack tips in thin sheets, you can easily see the yield zone ahead of the crack, and the deformation out-of-plane (ie the outer surfaces dish inwards).

for either state you need a pretty special state of loads/constraints. you should be able to see how things work out using poission's effects. the two states (plane stress and plane strain) are ideal (just like a fixed support), but using poission equations you can see the 3D stresses that are required to develop 2D strain (or the 3D strains that result from 2D stresses).

clear as mud ?

Quando Omni Flunkus Moritati

 

[DerbyEngineer]

Thanks rb1957. I think I've got it now

 

[dvd]

The plane of strain lies mainly in the grain.

 

[GregLocock]

http://www.youtube.com/watch?v=uVmU3iANbgk

Cheers

Greg Locock


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