Hi, I'm Dave Osborne. With over 50 years experience as a journeyman carpenter, foreman and contractor in heavy construction I enjoyed working with apprentices and sharing the tricks of the trade that others shared with me. Now I get emails from Members all over the world and we include many of my answers in our Free Monthly Newsletters. Some of my answers include drawings and instructions specific to a project, but may also answer your questions. I use correct construction terminology, so you can confidently inform your building supply dealers or contractors exactly what you need.
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Carpenters don't refer to the angle of a roof, such as 30° or 45°, but to the pitch of the roof, which is just the ratio of vertical to horizontal measurements. I say this because it's quite an important distinction. Angles are pretty hard to measure, but roof pitch is simple. An average and easy roof pitch to work with is a 5-12. The 5 refers to the rise of the roof and the 12 refers to the run of the roof. With the framing square (rafter square) we can use these numbers directly without having to compute angles.
In your example of a 6' span or a 3' run (half the span) we could use a 2x4 for the rafters and a 1x6 for the ridge board. Refer to my article on the Framing Square for some background information. For a 5-12 roof pitch take your framing square and with the 5 on the tongue and the 12 on the body with the heel of the framing square below the rafter, scribe along the tongue to give the plumb cut. From this point along the top of the rafter, measure 3'-3" and put another plumb cut at this mark.
Now measure back up the rafter 3/8", which is half the thickness of the ridge board. On the face of the rafter, square off a line from this last measure. This is the outside wall line.
For a tree house of this size a 6" overhang should be enough. So come down from this outside wall line 6 1/2" and scribe another plumb line. Scribe another line the thickness of your rafter trim, usually 1 1/2", parallel to this plumb line to shorten the rafter. Now go back to the wall line and scribe the bird's mouth and cut it out. This is the pattern for your rafters. Try two out first before you cut the rest.
Dave(Ask Dave) (About Dave)
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