flat plate solutions 4

[jp99]

Hi, I am looking for some references regarding the calculation of stresses in flat plates under various loading and boundary conditions. I have the Roark's book but I often run into situations where this book is not sufficient. Does anyone have specific titles that they have used or could recommend?

We typically handle such cases with FEA but I prefer to check the solutions from FEA with a backup hand calc.

My specific problem this time is a flat plate, fixed or simply supported on three edges, with a circular load at the centroid of the plate.

 

[sailoday28]

Have you tried advanced (classical) texts by the authors, Timeshinko and or Goodier?

 

[IRstuff]

Roark and Young is pretty much the compendium of most that's available. I would think that trying to find someone who solved the exact same problem as you, and published the answer, is highly unlikely.

One would think that it might be more fruitful to try and see if your problem can be bounded by one of R&Y's examples.

TTFN

FAQ731-376

 

[Twoballcane]

I agree with IRstuff, I have found R&Y to be all inclusive. For FEA, you have to be careful on how you constrain your edges between fix for fixed edge and let it rotate but fixed in the vertical for simple supported. If you still did not correlate, switch around the fix and rotation.

Tobalcane
"If you avoid failure, you also avoid success."

 

[zekeman]

Try Timoshenko and Wonofsky-Krieger, 2nd edition, McGrwaw Hill, 1959, the grandfather of plates and shells, entitled
"Theory of Plates and Shells"
There are numerous examples for loading of plates with most boundaries. This is truly the most wonderful book I have seen in any engineering discipline, a classic.
It is out of print and occasionally it is sold on Ebay.

 

[prex]

You may try the first site below, under Plates -> Simple bending -> Rectangular -> 3 supp.,1 free (or 3 clamped, 1 free) -> Part.load.
This will give you a load acting on a rectangular (not circular) area placed anywhere on the plate.

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[eureka]

The following are three usefull references for future use:

Analysis of Plates and Shells
Philip L. Gould
Prentice Hall, 1999

Beams, Plates and Shells
Lloyd Hamilton Donnell
McGraw-Hill, 1976

Analysis of Plstes
David McFarland
Bert L. Smith
Walter D. Bernhart
Spartan Books, 1972

 

[FILGUEIRAS]

AALAMI, B.; WILLIAMS, D.G. (1975). Thin plate design for transverse loading.
London, Beccles and Colchester. 194p.

 

[BarryEng]

I would like to refer you to a site that I often use for rectangular plates - a USBR pub that has many support conditions & many loading conditions. I have found the site (directed to me by 'bridgebuster' in another thread).

http://www.usbr.gov/pmts/hydraulics_lab/pubs/EM/EM27.pdf

This pub was originally produced for the skin wall of counterfort retaining walls, but has such a universal application to the design of rectangular plates, that I must direct the site to you.

I agree (with previous threads) that you MUST be careful of FEA that cannot be verified. I am an advocate of elastic solutions (method that have stood the test of time & the results that are reproducible).

My guides have always been: -
Theory of plates & shells by timoshenko
Stresses by Rourke & Young

 

[JoeTank]

jp99,
You might be able to make-do with an approximation of the load. Use the load case for a square load pattern (use equivalent area of your circlular load area) and check if max stress is at support lines. If that's the case your approximation should be sufficent for use (per St Venant's principle). If the max stresses are in the loaded areas you should continue to search for a solution, but I suspect that the reseults would be close anyway.

Joe Tank

 

[Cockroach]

Try this absolute classic textbook:

Theory of Plates & Shells
Timoshenko, Woinowsky-Krieger
McGraw-Hill 1959, re-issued 1987
ISBN 0-07-064779-8

She's a beauty, pal, an absolute requirement for any work with flat plate including rounds. (i.e. pressure vessel)

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada