False ceiling

I had a question and I can't see any reasons not to move forward but I haven't seen it anywhere. In my shop I have a large garage style door, the kind that goes from vertical to horizontal as you raise it. This door has no opener but lifts quite easily. 

I was thinking of building a ceiling just below the horizontal portion. This would do two things, give me a place to put some insulation in (it's a metal pole barn) and provide me with a surface to mount up some shop lights in that area. I would of course need to make it low enough to allow for clearance and have an opening for the door to go through. 

Do other people do this? What's it called? Any problems I'm not thinking of? 

Included a "drawing" below. 

Thanks in advance!