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We're turning a 13x13 area of attic space into livable space. The new 13x13 area joins an existing room. The attic floor structure is: 2x8 floor joists and OSB board on top.

There is a ~5 inch step down from the current room into the attic space area. Someone presented the idea of keeping the OSB board on top of the 2x8 joists and running 2x4 joists on top of the OSB board. The 2x4s would run opposite of the 2x8's and the OSB would be sandwiched in between the existing 2x8s and the new 2x4's. On top of the 2x4's, we would place two layers of plywood to bring it flush with the existing room.

Should the OSB be removed first?

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    I can appreciate the desire to have the floors even but sometimes loosing 5" of floor to ceiling height can be a problem. This could be even more of an issue in an attic space. Does the existing room sit on a different joist structure than this added area and is it under a different roof structure? – Michael Karas Jan 22 '17 at 1:17
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    Have you got an engineer's report on this? You are talking about adding a large static load on the 2x8 ceiling joists. Why is the top of the 2x8 joists 5 inches lower than the other room? Does the other room have trusses or much larger joists? – Jim Stewart Jan 22 '17 at 1:29
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You've asked one specific question here, and I'll start by answering that: No. Unless you have a particular reason to do so, do not bother removing the existing OSB.

From there I'd say your plan is reasonable. Running the 2x4s perpendicular should pose no problem, as they're supported every 2 feet. They'll span that with no detectable sag. Be sure to butt join them over joists.

Rather than two expensive layers of 3/4" OSB, though, I'd rip 2x6 lumber to the appropriate height so that you can use just one layer of t&g OSB as the new subfloor. This mitigates the overload risk, too.

Note: I assume that you've had the roof system inspected for use as a living space (or even for storage). With 2x8 bottom chords I assume that either 1) it's a very long span, or 2) it was designed for use as such. That's a critical point here.

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"Should the OSB be removed first?" Absolutely.

Imagine some situation that causes the OSB to deteriorate or otherwise give cause for removal/replacement (moisture, mold,...whatever). What would then support the 2x4's? Also, how would one remove the OSB?

As for the background of your question, "The 2x4s would run opposite of the 2x8's". I think you mean, "The 2x4's would run perpendicular to the 2x8's".

There's a potential problem here.

There's going to be one to three 2x8's supporting the overlapped ends of two, 8'0" long 2x4's. The 2x4's will flex downward in the middle of the 13'x13' room (even if one braces them together where they sister for 3'0").

I'd also be concerned how the load of this room is carried downward. The ends of the 2x4's need to rest on a load bearing wall/beam which is, in turn, supported by load-bearing columns to grade.

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