# stress and deflection calculations

I know how to calculate stress and deflection on simple beam cross sections but I'm not sure how to do this...
Suppose you have a hydraulic cylinder pushing against a round plate that
has an evenly distributed load on the other side, how do you figure the stress in a plate of a given thickness and diameter. If the calculation for having the load at the outer edges of the round plate is easier that would probably get me close enough.
the example I am wanting to work on now is a 12" diameter plate with a 60,000 lbs force from a 2" diameter hydraulic cylinder rod pushing on the center. I want to know how thick the plate needs to be to keep the stress to about 15,000 psi and also how much the plate will deflect.
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Chris W

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The simplest way would be to use a finite element analysis tool. The problem is that you do not have a constant value for your moment of inertia.

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YouGoFirst wrote:

It's a circular plate problem. Moment of interia is not a factor here.
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get your hands on a copy of Roark's Formulas--it should have most everything you need....

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I have the 4th edition of Roark's. In Table X - Formulas for Flat Plates, Case number 3 looks like your answer. You need the modulus elasticity and Poisson's ratio (reciprocal) for the material of your 12" dia. plate. The rest is plug and play on a pocket calculator. I assume the 2" cylinder rod has a flat end which will create a circular ring load condition as it deflects the plate
Jim Y
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Jim Y wrote:

Sorry I should have included that bit of information in my first post. I will be using A36 steel, I have never used Poisson's ratio before so I don't know what it is for steel. As for the 2" cylinder rod, it is actually threaded on the end so I will probably take some 3 or 4" round and tap the inside and screw the it onto the rod after it is welded to the 12" diameter plate. That way the load will be spread out a little and keep the stress down. Do you mind posting the formula for that BTW?
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Chris W

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Chris W said the following on 8/29/2005 5:45 PM: <snip>

:) You've never seen a formula from Roark have you? It's asking a lot.
Lance *****
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Quicky estimate: 15 thou deflection of 0.31 inch plate for 15 kpsi radial stress max