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

[DaDuck]

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!

 

[Bagman2524]

Roark's Formulas for Stress and Strain

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

 

[jayrod12]

Definitely Roark's has what you're after.

 

[DaDuck]

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.

 

[rb1957]

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 ?

 

[dhengr]

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.

 

[DaDuck]

@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.

 

[rb1957]

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 ?

 

[DaDuck]

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.

 

[rb1957]

try xcalcs.com

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

 

[SAIL3]

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....

 

[IDS]

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/

 

[IDS]

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/