I have several concerns with this design.
First, having the cage on the floor can be a problem depending on the room it's in. The most obvious problem is if the room is in a basement or is in a single story house on a slab (no basement, crawl space, etc). With either situation having an air space between the bottom of the cage and the floor may be necessary.
Also, for some people having the cage on floor causes access and cleaning problems. If I come home from work late and find a smelly water bowl I'm probably not going to be in the mood to get down on the floor and get the bowl out.
Then there are the concerns with having a bed on top of the cage. Beds have to handle a lot of movement from tossing and turning, etc. This will transfer slight vibrations to the cage which may stress the inhabitants out.
And if the cage requires night-time heating your bed may heat up more than you like.
Lastly, there are the engineering concerns. Not only will you have to design the cage to handle the weight, it also will have to be built flex-free as to allow the door system to operate properly. This will be a concern with almost any door design.
I see the new forum format does not include the original message in the reply box, but I believe you asked for tips etc. on how to build such a cage. Based on that I'm assuming you've never tackled anything like this and am not sure it's a project I'd recommend undertaking.
However, I may have read your post wrong and you may have extensive experience. Either way, I do not feel comfortable attempting to verbalize methods that could be utilized to build such a cage design.
If it were me I'd build an elevated cage and just throw a mattress on the floor underneath it. Or I'd build one of those fold-down beds that could be lowered for sleep.
That would save more room than putting a cage underneath a bed, especially if you require room while handling animals, cage cleaning etc.
Hope I've helped some. I don't necessarily think this is a terrible idea, but I think there are better uses of the material and effort.