Circular plate calculation using Roark's formulas
Circular plate calculation using Roark's formulas
(OP)
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/pla...
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/pla...





RE: Circular plate calculation using Roark's formulas
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.
RE: Circular plate calculation using Roark's formulas
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RE: Circular plate calculation using Roark's formulas
Quando Omni Flunkus Moritati
RE: Circular plate calculation using Roark's formulas
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.
RE: Circular plate calculation using Roark's formulas
Quando Omni Flunkus Moritati