That's one hell of a beam for a shed. a 12x16' roof can hold a lot of snow! when you start calculating the loads a structure can support, it's really kind of amazing how much weight they hold without collapsing. actually, if you make the end walls with 2x6's, that would put your free span awefully close to a 15 foot span.. However, when i built my shed (8'x12'), i made some simple site built roof trusses. no ridge board needed. you could always order trusses from a truss company too. for a 12' deep shed, i'd use 2x4 rafters, a 2x6 ridge, and a 2x6 ceiling joist, spaced at 24" oc.. Insulation and roof sheathing. soffit vents and ridge vent for air circulation. also has a working cupola that was used when it was an unpaneled and uninsulated garden shed. the cupola still works but it is not open to the ceiling, only to the air space below the roof sheathing, as does the ridge vent..
This step by step diy project is about 12x16 shed roof plans. this is part 2 of the 12x16 storage shed, where i show you how to build the gable roof. i recommend you to build the rafters. mark the cut lines on the 2

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