Flat Circular Plate - 2 Point Loads
Flat Circular Plate - 2 Point Loads
(OP)
Hello All,
I have a flat circular steel plate that has 2 point loads (in the form of lugs) spaced symmetrically and along the centerline of the circle. The edge is fixed along the circumference. I had searched through Roark's 6th Edition to find examples of how to analyze the stress on this but I couldn't find anything that fit. Maybe I'm missing something in one of the examples. Is there any reference out there that does analyze this loading condition? If it is in Roark's could you please point me in the right direction?
I tried conservatively treating the plate as a 1 in. wide beam and using the AISC beam diagrams. It neglects any help from panel action but this may be too conservative. I couldn't get the plate to work without making the plate too thick compared to the rest of the plating. Also, I only have STAAD Pro to work with as an FEA tool. I'd like to avoid using STAAD if there are some equations out there.
Thank you in advance,
Daniel...
I have a flat circular steel plate that has 2 point loads (in the form of lugs) spaced symmetrically and along the centerline of the circle. The edge is fixed along the circumference. I had searched through Roark's 6th Edition to find examples of how to analyze the stress on this but I couldn't find anything that fit. Maybe I'm missing something in one of the examples. Is there any reference out there that does analyze this loading condition? If it is in Roark's could you please point me in the right direction?
I tried conservatively treating the plate as a 1 in. wide beam and using the AISC beam diagrams. It neglects any help from panel action but this may be too conservative. I couldn't get the plate to work without making the plate too thick compared to the rest of the plating. Also, I only have STAAD Pro to work with as an FEA tool. I'd like to avoid using STAAD if there are some equations out there.
Thank you in advance,
Daniel...






RE: Flat Circular Plate - 2 Point Loads
BA
RE: Flat Circular Plate - 2 Point Loads
As pointed out by BAretired, Timoshenko solves your problem at point 64. (2nd Ed.), but there too you get an explicit expression for deflections only, the moments need be derived.
prex
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RE: Flat Circular Plate - 2 Point Loads
if it's reactions you're after (rather than deflections) maybe you could say that the shear reaction at the edge is inversely proportional to the distance from the load and that'll also setup the moment reactions.
RE: Flat Circular Plate - 2 Point Loads
Thanks again!
Daniel...
RE: Flat Circular Plate - 2 Point Loads
RE: Flat Circular Plate - 2 Point Loads
If what you are looking for is the moment at the edge, then you have from Roark the moment at the near edge due to a single eccentric load.
The contribution of the other load cannot be easily determined but...
First observation is that the ratio of deflections due to the local load to that caused by the other load (determined from Roark's formulae) at each load point is about 20 with your proportions. This result would push you at considering negligible the contribution of the other load, but that's not true.
In fact in any fully clamped circular plate, loaded at any point by a concentrated load not too close to the edge, the maximum edge moment is independent of geometry and equals P/4π
You can see that Roark's formula for the radial moment at the near edge gives this same result when the load is really a concentrated load (ro<0.5t)
In conclusion you can sum up two equal contributions for the edge moment getting Mr=P/2π (where P is a single load).
I would however be careful at your place: the assumption of a fully clamped edge is never a safe one and is often quite unrealistic. You should compare your results with those for a simply supported edge (also in Roark and even more complete).
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Flat Circular Plate - 2 Point Loads
Thanks for all of the input and insight,
Daniel...