# Plane Stress

1. Aug 20, 2012

### Hassan2

Hi all,

I have a question regarding deformation analysis.

For materials with non-zero Poisson's ration, when is it justified to use plane strain analysis rather than three-dimensional? Perhaps one case is when we are going to analyze a thin sheet. Are there other cases too?

Thanks,

Hassan

2. Aug 20, 2012

### Studiot

Well did you mean plane stress (the thread title) or plane strain (in the question)?

They are different and for different circumstances. Do you understand the difference?

The short answer to when do we use one or the other is 'Whenever we can', since either simplifies the analysis.

Last edited: Aug 20, 2012
3. Aug 20, 2012

### Hassan2

Thanks. I didn't know the difference but after your emphasis , I searched and learned a little bit about them. In fact I meant "Plane Strain".

Suppose we have a hollow cylinder with a radios of 10 cm and the a height of 15 cm. the force distribution on the inner wall is normal to the surface and independent of the coordinate along the axis and I thought maybe I can use plane strain. However the height is not large enough compared with the radius, so it doesn't seem to be a case of plane strain. I have seem some papers doing the analysis in two dimensions, and I wonder if their result is valid .

Thanks.

4. Aug 20, 2012

### Studiot

OK plane strain it is.

Since you are studying mech eng here is a mech example.

Consider a roller bearing - that is a solid roller (cylinder) confined between two loading plates.

So the bearing is loaded in compression transversally to the cylindrical axis.

Consider any thin slice or section of the cylinder, except at the extreme ends.

This disk suffers two diametrically opposed point compression loads, in the plane of the disk.

However the disk is unable to expand normal to its own plane becuase of the confining effect of the material (other disks) on each side.
So to a very good approximation the disk undergoes plain strain radially.
The resulting stresses and deflections are known as Hertzian.

Does this help?

BTW You need two radii to define a hollow cylinder!

Stress analysis of such a cylinder will depend upon wall thickness as to whether we can use a membrane or hoop stresses or whether we have a thick walled pipe.

5. Aug 20, 2012

### Hassan2

It helped a lot. Thanks.

My case is the vibration analysis of and electric motor which is more complicated than your example but essentially the same.

6. Aug 20, 2012

### Studiot

Post again if you need more.