Okay Tom, insulation first. We only use Celotex, so will stick with that. Celotex has brought out the 5000 range that has a lambda of 0.021W/mK, but according to our figures, pound for pound the 4000 range still works out cheapest. plus the 5000 range has not yet found its way into LABC Technical Note 10.
You can either go cold or warm deck. Material wise cost very little difference. Labour wise cost cheaper and easier with cold deck
You have a number of choices with Celotex to achieve 0.18W/m2K. Permeable breather felt over rafters.
1. 165mm XR4000 between the rafters and P/B
2. 100mm GA4000 between the rafters and either 35mm GA4000 under rafter and P/B or 35mm PL4000 under rafter. PL4000 has 12.5 plasterboard laminated to insulation.
3. 50mm GA4000 between rafters and 70mm GA4000 under and P/B or 70mm PL4000 under.
Rafters. 5x4m external footprint Assume 300mm cavity walls, therefore overall span of plate 3600 with run of 1800 at 20 degree pitch (half thickness of ridge not deducted as rafters need to meet at apex) gives rafter length of 1915 from top plumb cut to birds mouth heel cut plus whatever overhang you require. We usually allow 450, so you will require 2700 lengths if you can get them, but you may have to buy 3000.
For your information, on a close coupled roof with a pitch length of 1915 and snow load of 0.75KN/m2, and the worst scenario roof tile dead load of 1.0KN/m2, then C16s 47x 125 at 600/C or 47x100 at 400/C would be sufficient, how ever considering your U values and that roof is vaulted, this is the way we would do it.
Using the same loading tables as above C16s 47x200 regulised to 47x195 at 600/C. Permeable roof felt over rafters, 25mm gap down to insulation, 165mm XR4000 insulation flush with bottom of rafters and 12.5 plasterboard. We do not bother with VB as pig to get up, but run 100mm aluminium foil tape down each rafter with 25mm lap over insulation. Acts as VP and will stop ghosting if any.
For structural ridge we never use glulam beam, only USBs with 50x100 plate (wider if necessary) either gunned to top or coach bolted up through flange. Will leave size of beam and calcs to you.
With 20 degree pitch and standard two thirds down to pitch line leaves you a long seat cut on birds mouth, so go four fifths down with your pitch line on your pattern rafter and this will give you HAP of 167mm, heel cut of 39mm deep and seat cut of 105mm long. Use the same pitch line on top birds beak and you should have heel cut of 39mm deep and seat cut 50mm long.
For each pair of rafters at the apex cut, laminate and nail each side 6mm ply gusset from top of apex to bottom of beam plate. One restraint strap each side for gable and holding down straps at 1m centres, not 2m centres.
Sorry its so long but you have all you want, although we think that relaxing PD is going to be a pipe dream.
One other thing you could increase pitch if you can get in under first floor window cills.
Regards oldun