Plate Deflection Formula Question

[aduetto]

Hello,

I'm a hobbiest, not an engineer, and I need some help. I want to calculate some plate deflection numbers on circular plates using excel. I know there are on-line calculators that will do it, but I want to keep it in excel. So, my copy of Machinery's Handbook gives the following 2 formulas.

Stress = 0.39 * W / t^2
deflection = 0.221 * W * R^2/ E * t^3

I had no problems setting up both formulas. I can look up Poisson's ratio (0.39), and the other values are either known from the material or computed.

But I have no idea where the 0.221 comes from!! Google found me a couple of examples of the formula, and the value used in place of 0.221 varies with the plate material. Could someone tell me how to find it? Look it up - where? Calculate it - what's needed?

Thanks,

Alex

 

[Worldtraveller]

If E is included in the formula, that should account for the material differences. It appears that the .221 is an empirical value, probably determined by many tests and curve fitting. Roark's has many similar equations. Many of the engineering equations we use are either determined from first principles (approximate solutions to differential equations, or empirically determined and interpolated).

It's been a number of years since I did in depth DE solutions, but I seem to recall that the only plate with an exact DE solution is triangular (the bi-harmonic equation?), so any other shape will be an approximate solution, reduced to a relatively simple algebraic formula, such as what you are using.

 

[aduetto]

Ok, I think I've read that those formulas are approximate solutions, I don't need greater precision.

But my question is, where can I find this value? The MH example I had above is for steel. I found another example for lexan and the value was 0.0284. It seems there should be a table or something with this value, that's what I'm looking for.

Alex

 

[aduetto]

I think I just misread the deflection formula. I believe 0.221 is a given number which changes depending upon the shape of plate and extent/type of edge support. I would have read MH this correctly except that I found an example on a web site that had a different number for the same plate. It turns out they made an error by using the wrong number and have changed it based on my question there.

Alex

 

[Worldtraveller]

Ok, good. that makes more sense, then. There are many examples like this where rather complex DE solutions are reduced, solved, or approximated with algebraic formulas. Sometimes, they fit to an equation with a factor that varies based on shape, sometimes they have a curve fit to some of the values.

So it sounds like your curiosity helped both you and them.

 

[rb1957]

i'd look in Roark "Formulas for Stress and Strain", the section on plate stress, particularly table 11.4 (7th Ed)

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