Calculation for Deflection of a Ring under Compression 1

[dcstang]

I am looking for the formula for deflection of a ring under point load. I have ID, OD, E, G, and the load. If anyone has it or can point me in the right direction I would appreciate it.

 

[stanier]

Roark & Young Stress and Strain contains all the formulas

 

[Cockroach]

You need to use Curved Beam Theory, which falls under Castigliano's Method. I recently solved this problem for tangential forces deflecting a snap ring.

Google the subject under this topic heading. There is lots of websites that probably have the exact equation needed.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[zekeman]

You do this with the energy application using Castigliano which is far easier than curved beam theory. You first split the the ring in quarters using the second quadrant assuming the force is north south. If the load is north P, then you have a built in edge on the north point and a moment M1, undetermined and a south vertical force of P/2 at the west position. You write the energy integral M^2/2EI*rd@ over the 90 degrees where
M=m1-(P/2)r(1-cos@)The partial derivative with respect to M1 would be the slope at the west position is zero due to symmetry and the partial with respect to P is the vertical displacement, your problem. After all this I get
y=Pr^3(pi/4-2/pi)

 

[zekeman]

Correction,
I left off EI in the denominator; it should read:
y=Pr^3((pi/4-2/pi)/EI

 

[DAVIDSTECKER]

There is an equation in the Machinist's Handbook

 

[dcstang]

Thanks all, I passed the info on to my co-worker.

 

[JStephen]

The formulas in Stress and Strain are fairly simple and straightforward, and much preferred over deriving your own solution.