Help with assumption (thick walled theory)

ladil123

Hello!

I have a solid cylindrical shaft with a mounted ring on it.
My ring is subjected to a point load, I have with this load and the geometry of the ring used a special beam theory called Winkler Bedding. By using that theory I get the deflection of my "beam". This deflection is the deflection of the ring.

Now for my question:
Can I use this deflection as a radial mismatch between the shaft and the ring so that I can derive the hoop stress ?
this gives me pretty good results, with a applied force of 200 kN for a certain geometry I should get around 100 MPa in hoop stress. This I know from testing and experience.
Now with my assumption that the deflection as a radial missmatch I get 100 MPa from my derived equations

Does anybody know if my assumption is correct or is it completly wrong?