Equalizer hitch. where do you store when not in use?

dumb question and that's a good idea, but when you put that big 100 pound hitch head in the coupler do you put any support underneath that? or is the coupler ok to support that weight and wont stress it? like is said, I am brand new to this, and not sure what can be supported weight was or not. and you don't worry about the bars being stolen while sitting on the aframe? maybe im not sure what the a-frame is, im assumimg that's the front frame by the battery and propane?.thanks