stresses in plates

[Bharathsf]

Hi,
This question is bugging me a lot and I have not found a convincing answer.Consider a plate in the x-y plane .If I apply a normal stress in the x-direction, will there be a stress in the y-direction due to poisson's effect? I am sure in a beam problem there will be a transverse strain without any stress, but what about in the plate problem?

 

[rb1957]

If I apply a normal stress in the x-direction, will there be a stress in the y-direction due to poisson's effect?

poisson identifed the strain effect in the transverse direction (required to maintain the volume of the structureplate).
if there is no restraint in the transverse direction then the structureplate will deflect (accounting the the strain predicted by poisson). if there is restain, then the plate is prevented from deflecting (as it'd like to) and stress develops (sort of like thermal stresses, yes??)

Quando Omni Flunkus Moritati

 

[jayrod12]

I think rb has it right. If you restrain movement in the y plane, and/or the z plane, you will have stresses develop. if they are free to move (expand) then marginal stresses would develop. I think.

 

[charliealphabravo]

If the plate is in the XY plane how can a stress in the X-direction be normal to the plate?

 

[rb1957]

i assumed "normal stress in the x-direction" was tension on the plate

Quando Omni Flunkus Moritati

 

[TLHS]

rb, I would agree with you given a constant axial force through the entire cross section.

Given a large width plate, with an axial stress that isn't constant across the full width I would expect you have some sort of transverse stress due to Poisson. Say you have a very wide plate with a point axial load of some sort at the centre of the cross section. Your axial load will not be constant across the cross section of the plate, so the centre part of your cross section will see deformation due to Poisson and the outer parts will not. To maintain continuity of the section, the former will push/pull the latter and you'll get a stress. To keep the thermal expansion analogy, it would be like applying a thermal gradient to a section. The plate ends up partially restraining itself.

I haven't checked this in the literature and I've never actually worried about it, but that's how I would expect such a loading scenario to work.