A good, creative structural PE can save you many times his/her fee by showing you the best solution. In this case, perhaps sistering the joists would be stiffer and cheaper.
Deflection almost always governs. An upturned beam may work. 6" members can rarely span 24' without sagging too much...
If width is not a problem, You may want to consider (2) 5" or 6" Channels back to back. The webs are easier to drill and the flanges greatly increase the stiffness compared to the same weight plate.
How about a W6 steel beam with wood nailers and hangers? Leave a 1/4" space above the top...
I agree w/JAE, here's why.
When performing a peer review, I check and coordinate the plans, never the calcs. As soon as one looks at the calcs they can't help being "sucked into" the same design philosophies and assumptions. The review is no longer independent.
Structures usually fail...
2x10's sistered to each attic joist is the usual method of conversion. Use plywood for flooring(APA)span rated for the joist spacing. The bottoms of the new and old joists should be flush so that the new will reach the exterior wall plates.
Kneewalls can help support undersized rafters common...
I am reinforcing steel angle tower legs by clamping new HSS (steel tube) to each existing. I cannot drill or weld to the legs.
Analysis tells me that 111k will be taken by each new tube and 68k by each original angle leg.
per ( http://www.tensioncontrolbolting.com/TCB.pdf )
If I use 28k per...