I am trying to build a 12' x 8' flat roof held up by 4) 8ft high 4x4s,to cover a bar and grill next to the pool, will a 12' 2x6 header sag? can I use tar paper and planks for the roof? or should I slant the roof to one side with a tin or plastic roofing? do I have to have joists or could I just nail 3)4x8 sheets of plywood on top covered with tar paper and thatch
Having designed a few of these for my clients, I know there will be a couple of important issues at play, particularly when it comes to the grill and venting. If the grill is going to be part of the bar structure (fixed in place, as in an outdoor kitchen) or you intend to cook under there with a portable gas grill, venting has to be looked at. Depending on what you want, you might not need a permanent hood, but the path of the cooking fumes has to be looked at.
Personally I don't recommend flat roofs, because they always end up with headaches. Even more so in a space where the underside is unconditioned and subject to humidity, cold, etc. Have you thought about a kit, or a simple set of plans? Purchased plans can also get you pretty far with getting permits, also.
With regards to your span and rafter questions, the answers you seek lie in an analysis of rain, wind, and snow loads for your area. Roofs always start from there. Even your garden variety tool shed roof or backyard gazebo roof started its life with an analysis of those loads (I've done that engineering work on Summerwood's gazebo line).
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