Estimating Effect of Stiffners

Hi,
Just wondering how you guys go about estimating of stiffeners.
Say I've got a circular plate restrained at the edge with a uniform
pressure applied over the whole plate.
I've solved the nice equation in Roarks and the plate is thick and therefore heavy because I'm interested in keeping the deflection down.
So instead I want to go for a lighter design by using geometry, ie thinner plate with back stiffners, say in a star pattern. How do you estimate the deflection and stress?
Previously I've taken the approach of making up imaginery T beams and applying all the load through these with the top flange of the T beam being part of the circular plate (I usually make this flange 2*width of the stiffner) This normally brackets the results, between a beam and a flat plate.
I've been thinking there must be a better solution without having to go to FEA to get "the answer"
Anyways, please tell me your thoughts and methods.
Kind Regards, Tony Mulholland
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snipped-for-privacy@xtranospam.co.nz (Tony) writes:

You have to ensure that the inner flange of the stiffeners don't buckle as well, should they be on the compression side, so make them sufficiently thick by estimating the compression in them, or go the whole hog with two thin shells, spaced by a stiffening web to transfer the shear between the "inside" and "outside" surfaces. The structure becomes a set of intersecting I-beams of variable flange width.
A first approximation is to asssume that the flanges of those I-beams aren't joined except at the centre and periphery. They actually are; so the stiffness of the structure is probably (I haven't worked it out!) an order of magnitude greater.
The stiffness of the structure is close to that of a solid shell of equivalent thickness; with the advantage of allowing the "outside" shell to be quite thin and light because it's essentially in pure tension.
Once you've figured out how light you can make it; the next task is to figure out how to make it. :-)

That will unfortunately limit the quality of your answer.
--
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OP wrote:

YEARS ago, I helped my boss with the experimental investigation of a cylindrical shell made of Isogrid.
While I was only involved in the experimental side he did explain enough about the material (geometry) for me to remember some if it.
Isogrid is a plate material stiffened by triangular stiffening elements. Based on the plate & stiffener geometry one can develop "smeared / average" plate properties.
That is, based on the stiffener pattern you get an "effective" thickness, density & modulus that can be used in uniform plate analysis.
I didn't check these links out very carefully but they might be some help
http://analyst.gsfc.nasa.gov/FEMCI/isogrid /
http://www.engineering.sdsu.edu/~satchi/papers/stiff_panel_compare.pdf
http://www.osss.com/products/spaceframe.html
If you don't find what you need I can probably get the info from him. As I recall the calcs to obtain the "average' properitie were farily simple & could be programed in a spreadsheet to do parameter studies rather quickly
Bob
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Tony, in all wisdom, typed:

I had the exact same problem some years ago (high temperature water-cooled pressure chamber with flat endcaps) and took a conservative approach.
For deflection analysis, calculate the momemt of area (I) of the base plate with stiffeners. Once you have that, back-out the equivalent thickness of a plain flat plate. Use this equivalent flat plate for deflection analysis.
Lance *****
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Lance,
Could you give me an example of how this would work? Say I have a 12 mm Mild Steel Plate of Diameter 1.6m and have four 80 x 12 ribs welded to the back of it in a star pattern as below (ribs seperated by 45 degrees). It is fixed around the outside edge and carries a uniform pressure p.
\ | / - - - / | \
Where do you calc the moment of area? And how do you then backout equivelant plate thickness? An example would be cool.
Regards, Tony.
wrote:
snip

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Tony top-posted & wrote:

> Lance, > > Could you give me an example of how this would work? Say I have a 12 > mm Mild Steel Plate of Diameter 1.6m and have four 80 x 12 ribs welded > to the back of it in a star pattern as below (ribs seperated by 45 > degrees). It is fixed around the outside edge and carries a uniform > pressure p. > > \ | / > - - - > / | \ > > Where do you calc the moment of area? And how do you then backout > equivelant plate thickness? An example would be cool. > > Regards, Tony.
Take a rib plus a section of the plate. It'll form a 'T' section. A simple approach would be to use a width of plate mid-way to the next rib on each side of a rib. Then calculate the moment of interia (I) for the T and equate that to a rectangular plate with the same width and an effective bending thickness. So
I for _____ = I for ===== . | |
Jeff out ...
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Tony,
You've outlined a basic and time-honored approach. Before FEM, these kinds of models were the only practical approach. Unless you're building air- or space-craft, you can usually afford an elevated factor of safety to cover the uncertainty. In support of this contention, I'll cite my 133 page copy of 1962 Section III of the ASME Nuclear Vessels Code, which recommends no special treatment for ligaments in perforated heads (kind of the inverse to your reinforcement problem).
The other plus for hack models like this is the guidance they can give for fabricability. The mega-element FEM model will happily chase ribs into the apex of your star reinforcement - a place no welding torch can follow. Thumbing through Roark, though, might lead you to a short piece of pipe with radial webs to the edge of the plate.
Don't trust an FEM analysis unless there's a copy of Roark within reach of the chair where it was done. Check for dirty page edges and pencil notes.
hth, Fred Klingener, PE (ret)
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