Yhe solution is very simple. As long as the loads are verticle, the
shape of the moment diagram is the same as the catenary (This is a
thrust line, an important principle). So draw the moment diagram for
all loads and rescale to the height of the arch. The 19th Century stone
arches were designed this way. As long as the thrust line lies within
the kern of the secrion, the arch was free of tension.