6"x11" Shed with Green Roof advice (pics)

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Tyne and Wear
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United Kingdom
Hi everyone,

I've decided to build a shed for my garden, a pretty big shed. To make it a little more interesting I would like to add a green roof to it. My current design (images attached) has a 10 degree slope with beans of 3.4m in length.
Structure:
- Footings using 4x4 beams
- 2x4 cross beams
- 12mm floor
- All stud work to be done using 2x4s
- 12mm roof base

I think I would need to tie the roof beams together, to avoid/reduce twisting. I've not added that to the design.

Reading online about sedum mats/roofs it seems that the roof would need to support around 60-70kg per 1m2.

The surface area of the roof is 3.4mx1.8m giving 6.12m2 x 70 ~ 430kg.

Am I being optimistic that 2x4s would support such weight at 3.4m length?
Has anyone done a green roof on a shed before?

Thanks
 

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