Simply Supported (SS) Rectangular Plate Stress Distribution
Simply Supported (SS) Rectangular Plate Stress Distribution
(OP)
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,
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,






RE: Simply Supported (SS) Rectangular Plate Stress Distribution
"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 ?
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
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,
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
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 ?
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
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.
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
Thanks for your comment!
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
another day in paradise, or is paradise one day closer ?
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
Thanks for your time rb1957 and JStephen!
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
another day in paradise, or is paradise one day closer ?
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
RE: Simply Supported (SS) Rectangular Plate Stress Distribution
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 ?