Stress transformation question

[shimo1989]

I have normal stresses in x, y, and z along with shear stress in x-y. I am rotating the coordinates about the z axis, so the normal stress in the z direction should be the same in the new coordinate system as in the old.

My question is, since the stress in z does not change, and since all the other stresses are in the x-y plane, can I use the stress transformation equations attached? They are clearly labeled as being useful for "plane stress and plane strain" situations only(

http://en.wikipedia.org/wiki/Stress...sformation_in_plane_stress_and_plane_strain),

but the stress in Z really doesn't seem to have anything to do with the other stresses here.

Any help is appreciated.

 

[GregLocock]

The answer is implicit in the section Transformation rule of the stress tensor in that wiki article.

I leave the maths to you.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[rb1957]

i haven't read the wiki article, but ... plane stress and plane strain are "just" two extreme stress states ... plane stress, typically for thin panels, has 2D stress (ie no stress thru the thickness) and 3D strain (due to poission); plane strain, typically thick plates, has 2D strain and 3D stress since the thick plate creates stiffness thru the thickness.

your equations are correct for rotating stresses in-plane.

 

[Cockroach]

Yes you are correct.

These equations are simply Mohr's Circle.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada