Circular plate calculation using Roark's formulas

[SaturnVI]

Greetings:

I recently did some calculations for a circular plate with a center hole, the center hole is fixed and the outer edges are free. The load is applied on the outer edge. I used Roark's Forumlas for Stress and Strain (8th Edition), and the Case number for the formula was 1L. The maximum stress value I calculated was about 2.5 times that of the value that was calculated by the efunda online calculator. I noticed that the equation for the maximum moment was different for the efunda calculator, but that the max stress equation was the same as Roark's. So, if I made a mistake, it would be with the moment calculation. Anyhow, I've double checked my work, and unless I missed something (which is possible), I've calculated the values correct to the printed formula. So, my question is, which one is right?

If you want to double check my results, I got -705.52 for the Roarks moment and -16,836.48 lbs/in^2 for stress. The Inputs were 23.625 inches for outer radius and load radius. The Force per unit length was 13.438 lbs/in. The inner radius was 3.25 inches and the thickness was .5 inches. The material is aluminum, with an E of 10,200,000 lbs/in^2 and V of .33. The efunda calculator that I used is listed below. I got a stress value of 6570 lbs/in^2 from the efunda calculator. Any insight (even pointing out that I forgot to carry that pesky 1) is appreciated. Thanks.

http://www.efunda.com/formulae/solid_mechanics/plates/calculators/apFC_PRing.cfm

 

[JStephen]

If it's critical and you have time..
One thing you can do is go look up Roark's source material, he didn't invent all of that on his own.
A second thing to check is that he gives equations for moment versus radius, etc., see if those formulas give the same values as you approach the edge. And make you're not getting any goofy reversed moments in between (which might be happening if the edge moment is off).

And lessee...if you just treated that as radial vanes, what would the moment be? A 1" width at the center would correspond to a 7.27" width at the outside radius, with a load of 97.7 lbs, a moment of 995 in-lbs, a stress of 23,880 psi- so I would suspect your answer is right.

 

[prex]

Your results are correct: see them here.

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

 

[rb1957]

i'm with JS ... checking here is one thing, trying to understand the source material is another. you could also try to FEA it.

Quando Omni Flunkus Moritati

 

[SaturnVI]

Thanks for the information. The formula used by efunda on that annular plate for the moment is listed as M_max = P_r(r_L -r_i), where P_r is the load per unit length, r_L is the radius of the applied load from the center of the plate and r_i is the inner radius of the plate. To me, this equation doesn't account for the larger area of applied load at one end of the plate being supported by the smaller radius where the plate is fixed. It looks like a moment equation for a straight beam instead. It also seams as if the load per unit length is used incorrectly in that equation. Anyhow, I'm glad to see that the calculations that I did look accurate.

rb1957 - I would love to do an FEA of this part (it's certainly simple enough to get some quick results), unfortunately, I don't have access to a decent program at this time. That was my first thought on a double check though.

 

[rb1957]

that'd be load per unit length (circumference)

Quando Omni Flunkus Moritati