When applying the moment distribution method also known as the Hardy Cross method, how do I take into account the self-weight of columns? In the case of the beams, I can just apply the weight load laterally. However, for the column the load is axial, therefore causing 0 fixed end moment even when there is a difference in the support bending moment reaction.
I'm not sure what system of columns and beams you're describing, but the answer appears to be in the question: the self-weight of the columns has no effect on the support bending moment reactions. You will use it in reactions at the column footings, but otherwise ignore it.