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Rib Design - Stress on a rectangular plate

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jb1008

Petroleum
Nov 16, 2010
6
Hello,

I have been designing, in brief, a rectangular box that has to take relatively high pressures and have hit a rather big snag on the way.

I am using Aluminium LM6 and have 16mm wall thickness and have calculated the deflection (Roark's deflection on a rectangular plate fixed on all sides, Machinists Handbook 28) only to find that I will get 21mm deflection. (flat face is 540x340mm)

I would like to keep the wall thickness at 16mm but add ribs to prevent any permanent deformation at 50Bar.

I am having no end of trouble trying to calculate these ribs, is there a basic rule of thumb or a 'simple' rule to follow to give me width, depth, draft, radius etc.

To make it a bit more interesting, there can be a variety of holes machined into this face. These will be combinations of a window, 100x100 and numerous Ø20 holes. These are not in a fixed position and could in any place dissect a rib.

I have attached a couple of pictures showing the lid in its worse possible form.

Thanks in advance.
James
 
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i don't believe Roark's equation is valid for deflection > 0.5*thickness ... it assumes zero in-plane load, and that the plate only reacts the bending moment imposed by the pressure with an internal bending stress distribution.

i'd assume pinned edges, unless you have a dble row of fasteners. then i'd assume the pressure is reacted by both bending and in-plane membrane load ...

assume a deflection of say 0.5*thickness. use Roark to find out how much pressure is required to get this deflection, this is the portion of pressure load reacted by bending. then make an arc of the deflected side. apply the remainng pressure and determine your hoop stress (pR/t). combine the stresses
 
I think you're in Timoshenko territory. Try to find his book "Theory of Plates and Shells". Sorry it's above my level of mathematics, and I don't have a copy, but given the number of rerefences to this document, you should be able to find it with relatively little searching. Some members of the forum could point you in the right direction if you have trouble locating it.


Steven Fahey, CET
 
As rb1957 pointed out, with deflections beyond half t you are beyond the scope of the tables in Roark's. In the text adjacent to the tables you'll find a discussion as well as an iterative solution - though I'm not sure it covers your boundary conditions.

Certainly the holes cut into the plate are not amenable to any form of hand calc's. You are into nonlinear FEA territory - even if the material stays linear. Getting your product design right will be well worth a modest fee to an experienced and qualified consultant. Just do it. No, I don't moonlight - nothing in this for me.

jt
 
Assuming you don't want to go FEA for whatever reason, then I think a linear analysis is good enough, since your max deflection is not really a large proportion of the span, and ignoring the mebrane forces is conservative.

What I'd do is spend a pleasant afternoon cutting card or kraftwood up and sticking a model together with a glue gun. Or even use Meccano like a real engineer.
Even if it is not wonderfully accurate I bet you could quickly generate some rules of thumb for a better hand analysis.





Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
The assumption of clamped edges is far from being correct for that type of construction, as already noted above. On the contrary the use of Roark's formulae for large deflections stays on the safe side, contrary to what was noted above. In the first site below, under Plates->Large defo->Rectangular->Supported (or Supp.+Held if you have in plane holding) you could test the contribution of in plane forces under large deflections.
Anyway, coming back to your original question, as you don't seem to be able to accept the situation as is: to calculate the ribs you have two possible approaches.
1) The ribs are in one direction only (presumably along the short span): you take each rib with the contributing portion of the cover (deducting the holes) and treat it as a beam.
2) The ribs are closely spaced and in both directions (to be noted that it will be difficult to make the intersections strong enough): you derive an equivalent thickness by equating the stiffness of the ribbed plate to that of a flat one.
And of course if you dissect a rib, then that one is lost and of no use.

prex
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