Flat Plate Bending when submerged 2

[twylks]

Hi

I'm trying to calculate the worst case bending of a simple flat plate, which would be used to hold back a head of water. It will be fixed within an open channel at the sides and bottom and submerged up part of it's height.

The dimensions are:

Plate Height: 2000mm
Plate Width: 2150mm
Plate Thickness: 10mm
Water Depth: 1150mm

I know the fundamentals and can do simple bending calcs on beams etc... I know how to calculate the force of the water against the plate. I just don't know how to apply that and produce a deflection given this scenario.

Any advise would be greatly appreciated.

 

[chicopee]

I would assume the pate to be fixed only by the two vertical sides and forget about the influence of the bottom connection; then develop an equivalent force and moment at the middle of the plate to evaluate deflection and stresses. then

 

[rb1957]

"within an open channel" ... does this mean moving water ? how fast ??

"submerged part of the way up" ... how is the part of the plate that is not in the water supported ?

how are the sides of the plate supported ? clamped (restrained from rotating) or pinned (like in a wide groove so that the plate edge is pushed against one side of the groove but the plate is able to bend in the groove).

google (seriously) "moody rectangular plates" he's the reference roark uses.

 

[twylks]

Thanks for quick replies so far.

The 3 supported edges (bottom and sides) will be supported along their entire length and will be bolted (i.e. prevented from moving). The water will only come up to 1150mm of the entire 2000mm height of the plate.

I will check out the moody rectangular plates. If only there was a "clamped three sides, free one side, triangular load" one, I'd be laughing.

Thanks again.

 

[drawoh]

twylks,

Flat plate bending is explained in Roark's Equations for Stress and Strain. I actually bought this book because my college machine design book had an absolutely cursory explanation of flat plates, followed by a recommendation for Roark's.

--
JHG

 

[prex]

twylks, look here in the first site below. (and do not choke when laughing)

prex
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[rb1957]

actually i believe moody does cover that case. as i remember he was working for the Corps of Engineers on levee walls.

 

[dhengr]

Twylks:
Why is the plate 2000mm high if the water can never approach that height? And, if it can/might, shouldn’t you design for that max. water pressure? While the single, simple plate, is a pretty clean design arrangement, you could use a thinner plate if you provided some horiz. stiffeners spanning in the 2150mm width direction, with varied spacing in the height direction to account for the water pressure change. This might also simplify your connection detail requirements on the sides and bottom, since that connection no longer has to take a tension component from the plate.

 

[zekeman]

For what it'e worth
Timoshenko&Winowsky-Krieger,2nd edition,1959 , Plates and Shells,has a solution for the case where the water reaches to the top of the plate
Table p216.
For that case I found max deflection an moment

w=.00065*Qo*a^4/D
M=.0095*Qo*a^2
Qo pressure at bottom
D =Eh^3/12/(1-nu^2)

 

[Cockroach]

You would go to Roark's Formulae for Stress & Strain and look up the case study for a flat plate held by three sides. The load intensity on the flat plate is not uniform, for water force would increase with depth, hence pressure on the plate increases uniformily with depth. Find that load case in the flat plate section, three edges rigidly held. Follow the recipe equations given.

Or you model your situation in CAD and apply a FEA package. You should see a very close agreement between your hand calculation and the FEA simulation. You should do this anyway, never take a FEA study for truth unless you support that output with a hand calculation, typically done at a simple feature.

This is not a hugely difficult problem. There should be several website solutions as provided by members of the forum. But you need to do the work yourself and make an effort.

Regards,
Cockroach