# Virtual work method for a disk with axisymmetric distributed and concentrated loads

I'm trying to determine all forces/reactions on a disk with a hole in the center.

The disk is loaded with a (known) uniform distributed load from A to C (all around the disk), a concentrated (known) load at D (all around the disk), is either simply supported (only force reactions, $$M_W = 0$$) at A and B or simply supported at A and rigidly supported (force and moment reactions) at B.

Bellow is a depiction of the problem:

I'm trying to determine the reactions $$F_N$$, $$F_W$$ and $$M_W$$ (if fixed and not simply supported at B).

I know how to do that for line problems with a sum of forces and moments.

In this axisymmetric case however, the dum of moments does not see easy to obtain. How could I do this?

I'm trying to get the reaction by the virtual work method. The sum of the product of force and virtual displacements needs to equal zero:

$$\sum F \cdot \delta = 0$$

I'm getting however strange results with this method, and I'm probably doing some erros in the derivation of the equations.

What would the virtual work equation look for this axisymmetric case?

Is there any resource were a similar problem is solved by this method?