Flat roof joist design

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Replacing the flat roof on the rear of my property to a warm roof. The window and the patio doors are both full height to joist level so no need for any cavity lintels (confirmed with BC).

Does this joist design look sufficient?

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Thanks!
 
What supports the ends of the cantilevered joists?

I could dig out Superbeam and run a proper design because that's what you need but then I'd be taking bread out of another guy's mouth 'cos I'm retired.

Seriously, my instinct is probably not and you would either need more width or since you're going to go warm deck you could go up to 9x's and trim the insulation around the upstand.
 
Thanks for your reply, if you could help with a design I’d be happy to pay you or make a donation to a chosen charity. Got steels in last week and have just got time lines messed up, weather closing in, no roof on the back of the house and I need to get things water tight. Thought we had a design but the internal leaf on the existing and new cavity wall do not line up (due to cavity sizes) so that’s had to be abandoned.

Any help much appreciated.

Edit. It had to be 8s to marry up with an existing roof on the garage.
 
Thanks for the reply, I’ve redesigned so everything is perpendicular to the 4 main beams (pink).
 

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