Flat Circular Plate - 2 Point Loads 4

[starcasm]

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...

 

[BAretired]

I am not sure I understand your exact situation, but I believe you could find the answer in "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger.

BA

 

[prex]

My Roark's 5th Ed. has it as Case 19 of table 24: it is called 'Uniform load over a small eccentric circular area of radius ro; edge fixed' and of may be used to solve your problem. However only 2 values of the radial moment are given, but you can obtain the bending moments from the deflection, though this would require some analytical computing effort.
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

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

 

[rb1957]

Roark's solution is for a load at the center of the plate, no? maybe, depending on geometry, that's a reasonably conservative assumption ??

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.

 

[starcasm]

Thank you for the responses. I will have to look up the Timoshenko when I get a chance. I have tried the 'Uniform load over a small eccentric circular area of radius ro; edge fixed' in Roark's but I can't justify using it. I have 2 point loads and they are about 2-1/2 in. from the edges on a 17-3/4 in. diameter flat circular plate. The loads are in line on the centerline of the circular plate. Intuitively, the bending moment and reactions will not be uniform around the circumference. I would expect the reactions to be higher at the edges closest to the lugs. Perhaps this is why there is no simple formula for this load case. It's not a annular or uniform load.

Thanks again!
Daniel...

 

[miecz]

I think your selection of a 1 inch wide beam is too conservative. The question is: how wide a beam is reasonable? Seeing that your load is 2-1/2" from the edge, spreading the load at a 45 degree angle to the support would give a 5 inch wide beam. I think it would be conservative to use a 5 inch beam for this case.

 

[prex]

Roark can tell you much more than that.
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/4[π]
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 (r_o<0.5t)
In conclusion you can sum up two equal contributions for the edge moment getting M_r=P/2[&pi;] (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

 

[starcasm]

I know about analyizing anything with a fixed end. But I need the boundary conditions to size my groove welds. Otherwise, yes, I would use 'simply supported' to analyze the plate. I ended up suming the point loads and putting that force on a small circular area in the center. I have to increase the thickness of the plate but only 1/4 in.

Thanks for all of the input and insight,
Daniel...