I'm renovating my 1930s semi and have taken down the old lath and plaster ceiling in one of the rooms, as it was crumbling to pieces. I want to put plasterboard up but the ceiling joists are warped and sagging slightly, so it's not a flat surface to work with. I also want to install 270mm of insulation in the loft and board over it for storage, so I'm not convinced that the joists are strong enough to take the added weight.
The existing joists measure about 40x105mm (2x4s?) and are inconsistently spaced between 350-450mm, but at around 400mm centres on average - the longest unsupported span is 3.6m. Based on these span tables for ceiling joists, if they're roughly equivalent to C16 at 400mm centres, even at light load the maximum recommended span is < 2m?
I'd like to either replace the existing joists, or install some new ones alongside them so that I have a strong and level surface for a plasterboard ceiling and for loft boarding (C24 2x6 or 2x8?). I don't need them to be up to the standard needed for loft conversion floor joists, but I'd like to be able to use the loft for more than just light Christmas decorations.
I'm not sure if the wooden lintel over the bay window can take much additional weight either - it's constructed from two 50x180mm timbers doubled up to make 100x180mm x 2.7m long (unsupported span is 2.25m), and is possibly already sagging slightly.
I've measured everything up and put together a rough model in SketchUp (front and top views attached) - I haven't bothered modelling the ground floor, or windows other than the bay opening. Colour coding as follows:
White walls are made of brick and are load bearing
Yellow walls are made of cinder blocks, seemingly built after the lath and plaster ceilings were put up, so not load bearing
Red joists are "short" (~3.7m)
Green joists are "long" (~4.3m)
Pink joists just rest on the chimney breasts, so don't seem to be helping structurally
Blue is the bay window lintel
Brown is the wall plate
The joists are just nailed together in the middle where they overlap, and are connected to the wall plate with a single skew nail - they don't seem to be connected directly to the rafters, which possibly explains why they've warped away from them. The rafters are presumably connected to the wall plate, so indirectly supported by the joists?
Would it be best to pay a structural engineer to do some calculations? Any suggestions would be much appreciated!