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What would be required for a beam to have a span of 6.5 meters without a mid-support on a patio roof?

The roof I am considering will be 6.5 meters x 3 meters. A beam at the back by the facade with only two pillars and at the front a beam with three supports.

snozon: Sthlm
 
So the back edge "by the facade," and not "in the facade"?

If you attach the roof to the house in some way, then it becomes a non-problem (if possible, that is)

no clear answers from me then, but fun to know :)
 
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Those are some real beams.
 
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12mm, that is if there is 200 kg/m2 of snow
 
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I think I need to rethink.

There will be three posts at the back.
I don't dare to attach the terrace roof to the facade. I previously made a six-meter beam replacement right where the terrace roof will be built.
 
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