If "this" is just the bridge, in the situation with a mass hanging from it, the FBD will have a gravitational force and a tension force downward (this tension force will have the same magnitude as the tension force as the FBD for just the hanging mass in the previous paragraph), and two normal forces upward. In this case, the normal force from each chair will have a magnitude equal to half the sum of the gravitational and tension forces. But since the tension force will have a magnitude equal to the gravitational force on the hanging mass, these normal forces turn out to be the same as for the FBD when we treated the bridge and the hanging mass as one big object. It really as to be that way, because a real thing (normal forces) can't depend on how we divide up the object in our minds.
