In plane loading of a thin plate

[tejanojim]

So here's my problem. I need to calculate the stresses in a thin circular plate. The plate has a hole in the center that is welded to a flange, and that flange transmits a load that acts within the plane of the plate. The plate has four small circular cut outs near the outer edge, and is welded to a circular ring that supports it. FEA methods are not available to me, so I will need to do this via mathcad/by hand. I have looked at Roark's formulas and online, and the only cases I can find involve loading normal to the plane of the plate. So I'm pretty stuck. Any advice/suggestions? Also, this is my first time to post here, so if this question would be better posed in a different forum/area, I can definitely do that. Thanks!

 

[rb1957]

is this a Kt concern ? or basic stress analysis of a plate ?

is the loading shear or tension/compression ?

 

[tejanojim]

rb1957 - Take a circular plate with a hole in the middle. Stand it upright. Weld it to a support structure around its outer edge. Weld a flange to the hole in the middle, then apply a downward force to the flange. The load is in the plane of the plate, so there is no imposed bending moment. It seems to me that the resulting stresses will include tensile, compressive, bending and shear, but that's just my intuition.

I don't know what a "Kt concern" is, but yes, I'm trying to determine the stresses in the plate. Thanks for your help!

 

[EnergyMix]

A picture might help.

 

[Cockroach]

Yeah, I see it.

I would use the Roark formula with loading at the bore thru of the plate, the position of where the flange sits. I would use a bearing load to the hole thru as the plate is held rigidly along the OD as support. This would give you the initial stress in the plate prior to the onset of movements.

But if the flange weight or load thereof is unguided, your assumption that the load is contained parallel to the plate and within the boundries thereof, would not be valid. At the beginning yes, but after a little bit of motion, there would be a bending. And that would be a nightmare to solve by hand. So I would just consider the simplified case as you have stated it.

Interesting problem. Good luck with it.

Regards,
Cockroach

 

[rb1957]

ok, you have an in-plane load from the hole (i guess that last part wasn't clear).

i'd start by looking at how the plate applys the load to "the rest of the world" ... i'd expect two in-plane shear reactions, or maybe the round plate is completely atttached along it's edges, so it'd be a classic shear flow reaction (yes?)

 

[GregLocock]

Personally I'd cheat and use FEA and then perform a hand calc of increasing complexity until I got close enough to the FEA result.

The linear range will be a small fraction of the failure load since the lower half of the plate will buckle, leaving you with a combined shear and tension support, which is going to be a cute problem to solve analytically.

Is there some reason you can't post the exact problem here?


Cheers

Greg Locock


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[chicopee]

What will be the application of this device as I am visualizing a sheave with multiple wraps?

 

[prex]

Well, it all depends on how the forces are reacted from the outer ring.
This seems a problem similar to the analysis of a bicycle wheel: see here. However the distribution of stresses is strongly related to the stiffness of the rim (the outer ring) and to how this one is supported by the external world.
The contribution of compressive stresses (the spokes are not actually under compression as they are pretensioned) is dominant in the wheel, but this is due to the way it is supported on the road.
I don't think that buckling is of importance here, as the tensioned portion of the plate will prevent the compressed portion from buckling.
Also, as the stresses go necessarily down from the center to the periphery (here there's a substantial difference with respect to the bicycle), I would only check the periphery of the inner hole for bearing.
And of course I agree on the comment that there will be no bending only if the inner hub (or flange) is suitably guided.

prex
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[GregLocock]

It won't physically destructively buckle, but it will not support load. I can't remember the proper term for that but softening of structures due to loads was my final year project.

Cheers

Greg Locock


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[rb1957]

sounds like diagonal tension, werner beam maybe, elastic buckling,