Normal stresses
Normal stresses
(OP)
Should there by sigma y and sigma z stresses in this plate due to poisons ratio effects? How would I go about finding exactly what they are?
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RE: Normal stresses
RE: Normal stresses
Many will disagree with me I’m sure!
RE: Normal stresses
RE: Normal stresses
If you remove the hole and constrain the plate in the y and/or z direction there will be stresses. It's a simple calculation. With the hole it gets more complicated and no constraints are required to get stresses.
Any FEMsoftware should be able to show you this. And I would not consider is "only" a theoretical issue.
Thomas
RE: Normal stresses
I’m not sure how to explain why there are sigmay stresses, or show what they should be in hand calcs
RE: Normal stresses
RE: Normal stresses
I see that you posted something new while I updated my post.
Remove the hole, add load on the short side (like you hve it now) and constrain in the perpendicular direction. You will obviously have stresses in xdirection sigma x = P / (100 mm * t).
You will also have stresses in the ydirection, sigma y = poissons ratio * sigma x. The same should apply for sigma z but that will not work if you use plate elements (plane stress means sigma z = 0).
The hole makes it more complicated to verify by a simple hand calculation.
Thomas
RE: Normal stresses
RE: Normal stresses
A simple example: Plate 500 mm x 200 mm x 20 mm.
Load in xdirextion: 100 kN gives sigma x = 100000/(0.2*0.02) = 25 MPa
Poissons ratio (steel) 0.3: sigma y = 0.3 * 25 = 7.5 MPa
Thomas
RE: Normal stresses
RE: Normal stresses
You have two effects to consider. The hole and Poissons effect. Set Poissons ratio = 0 and that effect dissapears.
Thomas
RE: Normal stresses
There’s clearly something a little different going on here than poissons*sigmax which can be identified by looking at the stress contours I posted
RE: Normal stresses
Below you see another figure. It is a platee with a 2d tensor plot showing the Major and Minor stresses with orientation.
At the left and right edge of the plate tha stresses are fairly uniform. In the middle they are definetly not uniform. But notice thar the stress near the hole (left and right edge) is small. That "stress" has moved sideways resulting in a sigma y component.
If you look at sigma y (not included here) the difference in results with Poisson = 0.3 and 0.0 is fairly small. That is as expected since the plate is not constrained in that direction.
/Thomas
RE: Normal stresses
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RE: Normal stresses
RE: Normal stresses
Over the years I have more than once met situations where a hole in a plate in tension has been required. That is the reason why I did the first simple analysis, to show a "pure" example of Poisson effect. It's not that difficult to understand if you keep the example clean.
My second example with vectors was intended to show why sigma y differs from zero. The stresses/forces has to "move" sideways which results in a sigma y component, this has little to do with Poisson effects. Hopefully not that hard to see either. It also shows that stress=force/area on the sides doesn't work. There will be effects due to excentricity.
The question in DonMises latest post also made me think of a school assigment.
Thomas