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Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

(OP)
I am looking for a fourier series formula that calculates the deflection and moments for plate (simply supported (pinned) on two opposite edges & free on the two other edges) [like the navier solution]. I looked at Theory of Plates and Shells by Timoshenko and Woinowsky-Krieger, but was not able to find it there. Does anyone know of a reference that might have this information?

I want to use these formulas so i can calculate the deflection and moments for non-uniform (in both x and y direction) distributed load (using MATLAB).

I found a thread with the same question, but it was closed and unanswered:
http://www.eng-tips.com/viewthread.cfm?qid=334844

Thanks!

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Roark's Formulas for Stress and Strain

Faith is taking the first step even when you can't see the whole staircase. -MLK

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Definitely Roark's has what you're after.

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

(OP)
could you point out what formula i should use?
i need to find the deflection formula w(x,y) for a uniform load over x=x1+- delta_x/2 and y=y1+-delta_y/2.

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

google "moody rectangular plates" ... he (Moody) is the source of Roark's data and he covers more examples.

but thinking about your case (2 sides free, 2 sides pinned) ... why wouldn't you model as a SS beam, 1" wide ?

note if deflections exceed 1/2 thickness then the plate is behaving like a membrane (axial load on the NA) as opposed to a plate in bending, so a different theory applies.

another day in paradise, or is paradise one day closer ?

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

DaDuck:
Come on, what gives here? First you want a “fourier series formula” for solving a plate bending problem, and then you want/need us to tell you what formula to pick from Roark’s book to best fit and approximate your problem. And then the “the navier solution” too, along with a full review of “Theory of Plates and Shells by Timoshenko and Woinowsky-Krieger”? This sounds like lots of big impressive words, without much idea what you are really doing. I’ll bet that problem has been solved before, but we are not running a research library here.

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

(OP)
@rb1957
thanks for your answer. i have foud the book. i will read it after the weekend.

@dhengr
I dont know if you saw that thread i refered to, but i just copied that question. In the older post they also said it would be in Roarks book. So i read the book and saw the solution isnt in that book. Probably you havent read Roarks book, so you dont know.
I know this simple problem probably has been solved before, but i cannot find a direct solution anywhere. since i saw the same question already on this website I thought I could ask again.

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Roark, 7th Ed, table 11.4 case 15, with theta = 0 ... but I'm not faulting you for not finding it (or discarding it as it is a specific geometry that might not suit your application). I'm not that surprised that Roark doesn't have much on this, as your plate is very easy to analyze (as a SS beam).

another day in paradise, or is paradise one day closer ?

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

(OP)
so thats why i mentioned the navier solution. that solution can be used for partially loaded plate (and than be extended for ANY non-uniform loading in both directions). I could never use the formula you have mentioned since its for an entire loaded plate.

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

try xcalcs.com

another day in paradise, or is paradise one day closer ?

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

SS & held...will have a combination of bending and membrane forces depending on the amount of deflection..
SS & not held....will just have typ bending...
I may be wrong on this, but, I doubt if there is a simple formula that would represent the various combination of stresses at each stage of deflection....

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

I don't know why this question got the aggressive response, since it clearly stated the loading was non-uniform in both directions, so a beam analysis is not applicable, and as far as I can see nothing in Roarke or Pilkey (Formulas for Stress, Strain, and Structural Matrices) covers this case.

As far as I can see FEA would be the easiest way to do it.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Deflection and Moments for Plate (Two Simply Supported (pinned) Edges and Two Free Edges)

Quote:

As far as I can see FEA would be the easiest way to do it.

It occurs to me that if the slab in question was a bridge in the USA it would be designed using distribution factors published by AASHTO, so that might be a good place to look.

Anywhere else it would probably be done with FEA, possibly in the form of a grillage analysis.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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