Checking the load capacity of the existing rafters
The main worry I had about the studio build as a whole was on how to ensure that the existing ceiling framework would be able to bear the additional "double plasterboard skin" false ceiling that I was going to install on it. Clearly, it was pretty imperative for this not to collapse under the additional weight...
Being an engineer, I wanted to do some calculations myself, rather than calling in a professional structural engineer which would have been very costly. Helpfully, I was told about a piece of software called The Timber Beam Calculator, which does all the calculations for you, instead of having to spend hours researching/remembering all the various formulas.
The calculator that I used was the "Ceiling Joist Calculator". Here I inputted the clear span, the joist spacing, the timber grade (C16 or C24, normally printed on the wood itself), and the specific dead load that represented the plasterboard that would be hanging from the ceiling. I won't tell you what my values were as each situation is different, and I wouldn't want someone to just copy mine! However, the process for the calculations is described below.
In order to calculate the load, which is needed in kN/m^2, I first calculated the weight of the plasterboard - knowing the weight of one sheet, I found a weight per m^2 by dividing by the area of one sheet. I then doubled this - for the double skin roof. Finally, using my total load per square metre, I converted this to kN/m^2 simply by multiplying by gravity (a factor of 9.81) to get N/m^2, and then dividing by 1000 to get kN/m^2.
The results showed that although nearly all the load conditions were satisfied, the system would fail (only just) on the "long term deflection" criteria. My solution to this was the installation of a second level of rafter collars which would then be tied together with the existing collars using some steel straps to strengthen them and reduce the deflection. Much more on this here, but the diagram below gives the rough idea:
Designing the ceiling structure of the new inner room
The second point that I was unsure about was the design of the inner room ceiling. Although this wouldn't have to endure any wind/snow loading that the outer roof did (something that The Timber Beam Calculator takes into account already), it would again need to bear the weight of another double plasterboard layer skin. For this calculation I also needed to account for the additional weight of the rockwool which would attach to the inner room ceiling. In my case I used 10cm slabs of RW3 which has a density of 60kg/m^3, so a 10cm slab weighs 6 kg/m^2.
To begin with, I used a rafter spacing of 40cm and tried the load calculation using different sized timber beams to see whether they would be strong enough. As I wouldn't to be able to use the same "Double rafter collar" trick as I used on the outer room, and given the long 5m span that they beams needed to cover, the calculator told me that I would need to use 2by8 members of C24 - even bigger than the 2by6 rafters of the inner room!
The plan for the inner room thus looked like this (very much not to scale):
In hindsight, had I known that I was going to add a purlin to the inner room as well - thus vastly reducing the free span of the rafters - I probably would have got away with 2by6s. But at this stage I was expecting a "purlin-free" design, so went ahead and ordered a load of 4.8m lengths of 2by8. This finally dictated the dimensions of the inner room, and I was able to go ahead with the build safe in the knowledge that my planned structure would be both safe enough, and also conform to the British Standards that the Timber Beam Calculator are based on.