Shed design - advice on rafters

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I am currently designing a combined garden office / storage shed. Due to the location within 1m of a boundary, I'm limited to 2.5m total height, as well as max 15m^2 area. I'd like to get as close to these limits as possible.

I have put some initial designs together using Sketchup, screenshots below. These are not complete but should give a good idea of what I'm trying to achieve. The walls are 2x4 construction with 1/2" ply internally, and I will insulate with 50mm celotex and apply cladding directly to the exterior.

The roof construction is where I would like some advice. I would like to get away with 2x4 for the rafters due to the limited height, but I also intend to insulate with 50mm celotex and leave a 50mm air gap for cross flow, so would also like to avoid a structural ridge beam as this would block the air flow, also I want to avoid using ceiling joists as this would decrease the headroom. I have 1/2 inch ply for the roof on top of the rafters, and would also apply 1/2 inch ply on the underside of the rafters once the insulation is in.

The pitch of the roof is pushing the limits a bit at 2.5 in 12. Again this is due to the space limitations.

So my question is, would the rafter design that I currently have work without causing the roof to sag or the front or rear walls to bow outwards? I can't find any tools or formulas for calculating this sort of span. I would also be adding support for the rafters on each of the end walls and the dividing wall betweem the rooms.

The main 'room' is 3m deep so this is how far the rafters would be spanning (with the rear rafter longer as the shed is lower at the back), and it is 2.8m wide, with the rafters at 450mm centres.

I would really appreciate your comments or suggestions.

 
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You can implement gusset plates like that example, effectively sheets of board at the apex and the rafter ends, a sheet each side and bolted together. You need to be familiar ith structural engineering if you want to calculate the size of the gussets required. Or you just stick your thumb in the air and hope for the best.

I don't know why you don't just have a structural ridge. All this nonsense about trying to retain crossflow. If you wanna get picky then you should have vents at the ridge as well as the eaves. Its only a shed afterall.
 
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OK so what is the normal way of ensuring air flow above insulation if using a ridge beam?

Also, would it need to be bigger than 2x4, would 2x6 be sufficient in this case?
 
OK so what is the normal way of ensuring air flow above insulation if using a ridge beam?

Also, would it need to be bigger than 2x4, would 2x6 be sufficient in this case?

every space between your wall structure will be a self contained "air box"
the idea is not really airflow in this instance its to spread any damp that penetrates
'over a larger area to breath through the wood and dry out
 
Just push the insulation hard up against the underside of the roof deck then. This is typically how a flat roof garage conversion roof would end up. Its not ideal but should be OK.
 

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