Creation of incidentally habitable loft floor with additional joists - does this work?

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To provide a little context - we applied for and were granted planning permission for a dormer conversion to create a master w/ensuite, walk-in wardrobe and small office in our loft a couple of months ago. I also have the engineers report and calculations in hand. Since putting the conversation out to tender, I have had a couple of builders (to their credit) question me on whether the conversion will be a good idea. The head height in the finished conversion will be around 2.00 - 2.10 m, I am 1.94m, there is a little concern that spending much of my time in a world which ends a couple of inches above my head will become a little oppressive with time. We have high ceilings on the first floor but would be unable to lower them due to us also having large windows to the front of the house which extend right up to only a few inches below the roof, which we wouldn't be able to make smaller as we need to have a similar appearance to our neighbours on that side.

The preferred plan now is to spend the money elsewhere in the house but we are still keen to make something of the loft if we can (and some of the sunk costs in getting this far). We planning to carry out a mostly-DIY Velux conversion which will be used mostly for light storage but also as an occasional bedroom when we have guests (the plan with the dormer was for my wife and I to move up there, our children to move around on the first floor, and the existing box room to become the spare/guest room).

We will have the staircase that would have lead up to the dormer conversion installed (which meets building regulations), we will then carry out the rest of the conversion ourselves. We will try to meet building regulations as closely as possible - installing a fire rated door/fire rated plasterboard, a smoke alarm, exit will be via the veluxes in case of emergency, we will also install the required level of insulation etc etc. The one thing we don't plan on doing however is installing the floor that the SE designed as it would require us to touch existing roof support etc which would undoubted end in disaster. We are planning to (which is where someone in this forum can talk sense into me/say it isn't a completely terrible idea) add additional joists alongside the existing ceiling joists, which will span between the external walls and an internal load bearing which is pretty much bang in the middle of the house (see simplified drawing for detailed) - these can't be put in in a single piece as we wont be able to get them up there/manoeuvre them into place, 3m sections however should be possible with a little persuasion.

The existing ceiling joists are 4" x 2" at 360mm centres (closer together than is typical I think?), any additional joists cannot exceed 4" due to a beam which sits perpendicular to the ceiling and just above which is supporting the roof (which I don't want to touch for obvious reasons), we also can't replace all of the joists for thicker ones for similar reasons. I'm planning to install two C24 4" x 3" joists between each of the existing joists (so they are effectively at 180mm centres), which I think/hope will be strong enough (see crude calculations and assumptions below).

I cannot find span tables which have 75mm x 97mm joists, or 360mm or 180mm centres so I have had to do a little fiddling (which may be my downfall, hopefully someone can correct me).

- Plotting the maximum span of 63mm x 97mm joists for 1.5kN/m^2 imposed load and 0.5kN/m^2 dead load at 400, 450 and 600mm centres from the available tables gives a fairly straight line, I have extrapolated back to estimate that at 180mm centres the maximum span would be 2.83m (and the absolutely maximum if they were separated by 1mm would be 3.19m - which doesn't feel completely unreasonable?) - the spans from the tables at 400mm, 450mm and 600mm centres are 2.41m, 2.29m and 2.01m, respectively.
- Taking ratios of the maximum spans of 63mm x 122mm and 75mm x 122mm, 63mm x 147mm and 75mm x 147mm, and 63mm x 170mm and 75mm x 170mm (as 75mm x 97mm does not appear in the tables) suggests that the difference between 63mm and 75mm thickness beams is around 6%
- Multiplying the 2.83m found by extrapolation down to 180mm centres for 63mm x 97mm beams by 106% gets to almost precisely 3m, which is the largest span between the external walls and internal load bearing walls that I would have to cover.


I appreciate that a building inspector will never come and sign this off for me but the aim is to create an occasional space which is safe to sleep once in a while, we have no plans to move house in the next 20 or so years so whether it can be classes as a bedroom or not isn't a concern, just that we have insulated it properly, it is fire safe and the bed isn't going to come crashing through the ceiling the middle of the night if someone sleeps up there.

The approach to extrapolate is probably way off but I have also assumed that the existing ceiling joists have no load bearing capability whatsoever which should hopefully plug any deficient, all of the load up there will be within about 5ft either side of the load bearing wall too (which hopefully further reduces the chance of a catastrophic failure).

If anyone has any words of wisdom before I risk the lives of my wife and kids that would be great, likewise is anyone can offer the actual span of the beams, I would appreciate any help.
 

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Have you considered lowering the ceilings slightly back from the windows - commonly done in older properties.
 
Your best bet is to go back to the SE and explain your problem.
They might have a better solution giving you enough head space.
Lowering the first floor ceilings is common in these situations and can be done without much of a mess if everything is properly cleaned from above in advance.
Your only issue then should be to clear most of the first floor, but this can be a good chance to declutter.
A good builder could lower and finish the ceiling in a few days, but you best organise alternative accommodation in the meantime (temporary beds on the ground floor).
A bodged loft conversion can put off potential buyers.
 
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