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