Plate Deflection Calulation help

[jazz330]

I have a 3/16" plate with a 2x2x3/16 angle iron frame with a pressure of 8psi on the surface as shown in the attached picture.

How do I calculate the max deflection in the plate?

 

[JStephen]

There are flat-plate formulas in Roark's Formulas For Stress And Strain, among other sources.
For a long narrow plate, figure a strip of it in the short direction as a beam and use beam formulas.

 

[arbreen]

You need a copy of Roark's Formulas for Stress and Strain.

 

[rb1957]

google "moody rectangular plates" ... that's the source for Roark and has more info in it.

the two important dim'ns are the width and the length of the plate (together with the thickness and the pressure).

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

 

[kingnero]

@ JStephen, (and others),

How would you choose the width of such an arbitrary strip?

 

[arbreen]

@kingnero,

Because OP's loading is even pressure and not a concentrated load, the deflection is the same for the beam method no matter the width. I would choose a width of 1 inch to drop a dimension out of the calculations.

 

[arbreen]

What I'd really do is create a complete 3D model with proper loads and constraints, run FEA, and just use Roark/Moody to validate the results. Now that everyone and their mother has FEA built into their CAD system, it's so quick and easy it seems foolish not to use it for quick iteration of your virtual prototypes.

 

[IFRs]

FEA is usually based on small deflections. Garbage in / garbage out.

 

[arbreen]

@IFRs, the OP's not hydroforming. My quick FEA spits out around .25" max deflection for a 18"x36" steel plate (roughly scaled from illustration). Unless the plate's in danger of buckling or yielding, that's definitely a small deflection. If you got a large deflection for a result, you'd know it warranted further investigation.

Plus, pencil and paper methods also make small-angle approximations.

 

[IFRs]

1/4" is greater than the material thickness by 25%. Is your FEA accurate for those deflections? Assuming it is, how does one not skilled in the art of FEA know what "small" deflections are and when the equations become less accurate? Maybe I'm just stuck in the past...

 

[GregLocock]

...note that the Roark's equation does not account for membrane stiffness either!

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[prex]

No one above cared to ask how is the plate supported, possibly at the four corners?
Definitely solvable with formulae, but, jazz330, please first state some more data: supports, dimensions...

prex
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]http://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]http://www.levitans.com[/url] : Air bearing pads

 

[GregLocock]

I jumped to the conclusion it was ss along the edges, but as you point out that is dangerous.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[mekafime]

Hi jazz330,
We need more information like measurements, I assumed that is 1x0.2m welded in 4 corners, you will have problems because the deflection is 10.77 mm and von mises stress is 310 MPa. (I assumed that material is A36 too).

P.D.: My english is very bad

 

[jazz330]

The plate is 3/16" Thick x 96" Wide x 240" High. The frame is made from 2"x2"x1/4" Angle Iron mitered and welded at the corners. The pressure is 8 psi coming from the side with the angle iron frame. All 4 sides are fixed not simply supported.

I have done hand calculations and FEA but I get a ridiculous value for Stress and deflection and I may be doing it wrong so any help would be great.

Thanks

 

[prex]

I don't see how a plate that big, with a so small thickness, could resist that pressure.
You should better describe the context and the goal of your analysis, as what you described is out of question.
Anyway your source is definitely the Roark, but also other sources online, google 'flat plates in bending' (example here, from the first site below).
If you insist with those dimensions and loading, you'll need to take into account the membrane action, and state whether the boundary is also fixed in the plane of the plate. Here a calc sheet for this condition.

prex
[URL unfurl="true"]http://www.xcalcs.com[/url] : Online engineering calculations
[URL unfurl="true"]http://www.megamag.it[/url] : Magnetic brakes and launchers for fun rides
[URL unfurl="true"]http://www.levitans.com[/url] : Air bearing pads

 

[Sparweb]

You need thicker plate and more members spanning across it. Many more.
Unless the plate gets used once and is then discarded...

STF

 

[mekafime]

I think that you must make a better drawing and post it.

 

[rb1957]

I think we're jumping the gun to say "your plate's no good ..."

Assume a deflection of 1", then the plate has formed to a radius of 1152" = (48^2+1)/2

Then hoop stress is 8*1152/0.1875 = 50ksi; so it is looking dodgy,but then maybe 1" dflection is on the small side, given the scale of this plate. a 2" deflection would about 1/2 the stress ... 1/48, about 2% ... not unreasonable.

stiffeners running across the plate (96" long) provide lots of bending strength to the plate, and reduce the stress in the plate.

But, don't count a simple angle to fix the edge, even if you support the standing leg all around the perimeter; the angle would easily "open up". A tube section around the perimeter would give you more fixity (plate bending is torque of the tube ...)

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

 

[IFRs]

You are getting into membrane stress, large deflections and edge distortions. Maybe that's all OK for the OP but we don't know. I'm still skeptical of basic, simple, quick FEA being of much use...