Roof/ceiling problems

hello i have a flat roof ceiling and i bought this place with it . now i need to fix it some how with out having to replace the entire roof structure . who ever built this add on room did not do it right . the 2x4's span 11'6" NOT good. there starting to sag and hence got a leak now. i can not brice it up from inside as this is a living room area.. i was thinking maybe a beam across the room to support this crazy roof untill a few years down the road when i can maybe get it replaced the right way. the room spans 11'6" X 16' the 2x4's run 11'6" so i need the beam to run 16'. now for the problem of that.. head room is 10 inches and drops to about 5" or 6 " but i think i can get away with a beam in the middle but would have to cut the 2x4's so the beam could be placed right against the roof then the 2x4's would have to be attached to that beam. i know the whole entire roof must come off at some point in time and get fixed right. but thats gunna have to wait a few years. no money for that expense.
so now what ta do with this mess ????

 

Youre right, thats a disaster that should never have been built.

To get by for a while, you would probably want to go with the cross beam to cut the span in half... which will still be too far for 2x4s to span as a roof.

So build a temporary wall maybe 2 feet away from where the beam will be (on each side of where the beam will be). Snap a chalk line to represent where your cuts be. Your beam will be 3" wide, so make your cut 3 1/4" wide. Your cut will need to be perfect so I'd suggest you use an oscillating cutoff saw, like a Fein Multimaster. If you try to use a Sawzall you could cut through the plywood, so... that would be bad.

Once you cut your slot, you are ready to put your beam up. It should be two 2x10s minimum. It really should have a pocket in the wall to fit into, supported with posts within the wall.

Then once the beam is in, use Simpson 2x4 joist hangers (LU24 for single joists LU24-2 for doubles) to attach your ceiling joists to the beam, using the joist hanger nails (or the structural screws) that they specify.

Then take the temporary walls down.

 

I like Xsleeper's suggestion to your very scary looking problem.

I am a huge fan of plywood laminating. Adds a ton of strength. Add a 3/4" plywood layer to both sides of your beam, glued and screwed together, will keep the beam from sagging.

As much as I don't like the 2x4s, given the space it looks like you have to work with, I would suggest laminating most or all the 2x4s with 3/4".

 

If an inspector ever saw this they would condemn the building.

Looks like you also have a problem where roof joists meet the old building they seem to be pulling away..
Check the outside wall if it is leaning outward to confirm that the roof is pulling away from the old building.
At the very least I would install joist hangers but that depends on the size of the gap between the joists and the old building.

As Xsleeper said the beam has to be supported on the ends with a beam. Problem is if this is the what the roof is built lord only knows what the foundation/floor is like.

You also have a problem trying to get the roof level again. Your plywood is now warped to the dip so getting it to straighten up will be nearly impossible unless it is like 1/4 inch thick which would not surprise me.

And what is going on with that electrical box!!!!!

This is definitely a disaster waiting to happen and I am skeptical that any decent repair is worth doing.
Looks more like a rip it down and start over.