I need some help regarding my problem.
I have a solid shaft with a mounted ring on it. The has a higher E-modulus than the shaft.
A force F is acting downwards on the ring. As seen in the picture. The force could be assumed to be a point load if its easier than a even distributed one?

I want to calculate the circumferencial and radial stress that is acting in the ring due to the applied force and the fact that the shaft is either made of steel or cast iron wich is softer than steel.
I want to make a pretty easy calculation of this, but I want the different lenghts to have an influence on the stress.

I have heard something about "elastic bedding" that takes the fact that the material beneth the ring is softer than the ring, but some contact mechanics could maybe do the trick?
I´ll need some help starting with this.