Statically Indeterminate Structure by Superposition

Hint: Suppose the uniform load was horizontal. What would the moment be at "A?"

You would, of course need the length of the vertical member in order to calculate the moment at A. The structure is indeterminate to the first degree.

One way is to make the structure determinate by removing the roller support (call that point B), then solve for Δ_B, the deflection at point B. Calculate the deflection at point B under a unit horizontal force at B. What horizontal force is needed at B to restore point B back to its original position?

Another way is to make the structure determinate by changing the fixed support at A to a hinged support. Solve for Θ_A (rotation at A) for the applied loading. Solve for Θ_A for a unit moment at A. What moment is needed at point A to restore it to zero rotation?

Since the title of your thread includes the words "by superposition", you should consider the horizontal and vertical components of the sloping applied loading separately and simply add the effects of each. Be sure to keep track of the algebraic signs as you do this.

A third method is to consider the moment at the crank point (point C) to be redundant. Make the structure determinate by adding a hinge at point C and leaving the other supports as they are, i.e. fixed support at A and roller support at B. Solve for all of the reactions and M_A (moment at A) for the determinate structure.

Calculate the rotation of each member meeting at point C by standard methods and from that, the angle change at point C (the difference between the two rotations). Place a unit moment in opposing directions on each member (watch the signs) and calculate the resulting angle change. Determine M_C to make the angle change zero, then modify M_A accordingly.

I think this is the method a practicing engineer would prefer because the determinate structure resembles the indeterminate structure more closely than the other two methods.