Simply Supported (SS) Rectangular Plate Stress Distribution

[ABV97]

Hi All,
I am analyzing a rectangular plate under uniform liquid pressure in order to evaluate its max deflection and stress. My approach was using "Roark's Formulas...." and for my panel (25.0" x 13.0"), with p = 29.61 psi, I got a panel stress of f = 585,184 psi. I double checked with Timoshenko, having very close result of f = 590,478 psi. In Timoshenko, the bend moment, from where the stress is calculated, is per unit length. So in my case, this high stress is per inch of width, would it be correct to divide that stress to the panel width (b = 13"), so my panel stress would be f = 585,184 / 13 = 45,014 psi?
Thank you all,

 

[rb1957]

no, it's a high stress because a plate plate doesn't like pressure loads.

"per inch width" means than each inch is seeing that stress ... Roark uses a piece of the plate 1" wide and t thick to calc I (as t3/12).

you'll probably find that the deflection is greater than the thickness of the plate, so "simple" plate bending is "hopelessly" conservative. the plate is probably a "large deflection" problem, and should be reacting the pressure is in-plane membrane tension.

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

 

[ABV97]

Thank you rb1957,
so my stress is 585,184 psi and I have a failure. That's it! So, I guess, have to reduce the panel size, or applied load...(just for the record, for another panel configuration, I triple checked with Michael Niu (page 196), and the stress result from his graphic, I multiplied by panel width and got similar result from Roark stress, probably M.Niu output stress is not per inch of width, as Roark is...)
Thank you again,

 

[rb1957]

"and I have a failure" ... maybe, maybe not !?

you're using small deflection plate bending. This calc can produce very high stresses (just as Euler column can for very short columns) that are not real. if the deflection is greater than the plate thickness (or 1/2 the thickness, depending on who you ask) then you need to use a large deflection solution (similar to how you limit column stress to fcy or fcc).

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

 

[ABV97]

...my panel thickness is 0.071' 2024-T3, and my deflection is 23.63". So looks like it is a large deflection problem - any hint where I could look at to solve my problem? Thank you rb1957!!!...I feel like standing in front of a big concrete wall with no way out...

 

[JStephen]

In both references, the moment calculated should be moment per unit length, with stress being 6M/t^2.

For a rectangular plate, as it gets longer and narrower, the stress near the center will be similar to that in a beam spanning the short direction. So if you check stresses in a 1" wide bar 13" long with that loading, it should come out somewhat higher than the plate bending stresses, and that can be a quick check.

 

[ABV97]

Thank you JStephen - I quickly did it, so for 1" wide, 13" long beam, with a w = p*b = 29.61 x 1 = 29.61 lb/in, the bend moment is 626 in-# and stress f = 6*626/(0.071^2) = 745,090 psi, which is relatively close to my 585,184 psi. As rb1957 mentioned, probably my problem would be under "large deflection" one...to use a membrane stress ones the plate start bending, I don't know!
Thanks for your comment!

 

[rb1957]

i'm sure if you look you can find references for "plates with large deflections". for example Roark has some info (in 7th Ed, section 11.11 "effect of large deflection".

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

 

[ABV97]

thanks rb1957, I am on it right now, appreciate your thoughts!!!

 

[ABV97]

...from all the information I was able to get - Timoshenko Large Deflection of Plates, Roarks, Effects of Large Deflection and Bending of Rectangular Plates with large Deflection Tech Note 846, all large deflection are limited to pb^4/Et^4 = 250 or 300. For my case, this value is 3169, not even close. On the other hand I did check for rectangular plate with DIA D = 13" and I got stress of 49,155 psi...Maybe, end od the day, I have to reduce the panel size!
Thanks for your time rb1957 and JStephen!

 

[rb1957]

adding stiffeners to the flat panel would help it carry bending. a 0.07" thk panel will not behave like a plate, because it deflects too easily (doesn't have enough thickness to develop a bending stress field) but like a membrane ... it'll deflect out-of-plane and react the pressure with an in-plane "hoop" stress.

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

 

[ABV97]

...I am in Bruhn A17.6, hope it will help. Another thing, which a friend recommended me is, to look at it like a cable, and substantiate the end reactions, which might be a problem due to the high end magnitude of this reaction. Hope in Bruhn to find some answer, other than that a stiffeners, as you said is the next step. Thanks rb1957

 

[rb1957]

bruhn para A17.8 might help explain the difference between plate and membrane problems.

creating a "story" for membrane is easy enough (assume a central pt deflection, put a circular arc to the edges (supports), calc hoop stress, > strain, compare to the arc length, and iterate.

the problem is the real world ... how will the edges allow this to happen ? is the plate large enough and loosely held so the plate will deflect, and slide over the edges (and deflect out-of-plane) ? or are the edges constrained (much more likely) so they'll develop (amazingly high) reactions ?

a 0.07" plate really won't like 30psi pressure (i would like to see more than 10psi on it). i think you need stiffeners ... 3 or 4 stiffernera preferably about the 25" side (so they're 13" long) ... UDL = 30*25/3 = 250 lbs/in ... that a lot !! max moment = qL2/8 = 250*169/8 = 5300in.lbs ...



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