Lesson 5 of 6 · Chapter 5
The Roof, Simplified
A roof is triangles. Rise over run gives the pitch, the pitch gives every cut, and half the span, measured along the slope, gives the rafter's length. This lesson lays out and cuts a common rafter with a framing square, then chooses between a ridge board and a ridge beam.
Step one
Read the material
Six ideas: rise, run and pitch; setting the framing square; rafter length; the three cuts; ridge board or ridge beam; and installing with the right ties.
Idea one
Inches up for every 12 across
Rise is how far the roof climbs; run is the level distance it climbs over. Pitch is written as the rise for every 12 inches of run.
A roof that rises 4 inches for every 12 is a 4:12 roof, common in homes. 6:12 rises half a foot for every foot.
As an angle, 4:12 is about 18.4° and 6:12 about 26.6°. The pitch sets every cut on the rafter.
Find the pitch on the architectural plans. It is chosen for the look and for structural needs such as snow.
Idea two
Rise on the tongue, run on the blade
The rafter square, or framing square, has a long leg, the blade, and a shorter leg, the tongue, both marked in inches.
To lay out a pitch, set the square on the face of the rafter with the rise on the tongue and 12 on the blade, both marks on the same edge of the board. For 6:12: 6 on the tongue, 12 on the blade.
A line along the tongue is a plumb cut: it will stand vertical when the rafter is in place. A line along the blade is a level cut.
Swap them, 6 on the blade and 12 on the tongue, and you have laid out a 12:6 roof: four times as steep. Measure twice, cut once.
Idea three
Half the span, along the slope
A common rafter runs from the wall to the ridge, so its run is half the span of the building. A 12-foot span gives a 6-foot run.
The rafter climbs as it runs, so it is longer than its run. For every foot of run it is √(144 + rise²) inches long: 12.65 at 4:12, 13.42 at 6:12.
A 12-foot span at 6:12: 6 × 13.42 = about 80-1/2 inches to the plate. The overhang adds its own run times the same factor. Span plus overhang (12 + 1 = 13 feet) is nowhere near right: that is a rafter for twice the building.
Framers also take off half the ridge board’s thickness at the top. Add a few inches of stock for adjustment, and cut the first rafter as a pattern.
Idea four
Plumb at the ridge, bird's mouth at the wall, tail at the eave
A common rafter has three cuts. At the top, the plumb cut meets the ridge board.
At the wall, the bird’s mouth is a notch of two cuts: a level seat cut that sits flat on the top plate, and a plumb heel cut that bears against the outside of the plate.
Lay out the seat on the bottom edge, about the width of the top plate (3-1/2 inches on a 2x4 wall). Don’t notch away more than about a third of the rafter’s depth, or it will split and sag.
At the bottom end, the tail cut finishes the overhang at the eave. Cut clean, check the angles against the pitch, and test the first rafter in place before cutting the rest.
Idea five
Connector or structure
A ridge board runs along the peak and gives the rafters something to meet. It carries no load itself; the rafters carry the roof down to the walls. It must be at least as deep as the rafter’s plumb cut, so each rafter bears on it fully.
Because a ridge board holds nothing up, the rafters push outward on the walls. Rafter ties or ceiling joists low in the roof tie the walls together so they cannot spread.
A ridge beam is structural: sized, often LVL or solid timber, it carries the roof itself and passes the load down posts or columns to the foundation. That allows vaulted and cathedral ceilings without ties.
A ridge beam must be sized from local code and engineering for its span and loads. A ridge board is simpler and cheaper; a ridge beam gives open space below.
Idea six
Spacing, the ridge, and the right ties
Rafters are set along the top plate at regular spacing, 16 or 24 inches on center depending on the design, and fastened at the ridge and at the plate.
Know your ties. Rafter ties (or ceiling joists) near the plates stop the walls spreading. Collar ties in the upper third of the roof help hold the rafter pairs together against wind and uplift. They are not interchangeable.
Snow country and high wind make these connections more important, not less.
Complex roofs add hip rafters, which run diagonally from the ridge to an outside corner, and valley rafters, where two slopes meet; the square lays them out with different angles. How all of this carries weight to the ground is the next lesson: the load path.
The whole of chapter 5 is free to read or hear on the Residential Framing reader page.
Step two
Work it with your hands on it
The Rafter Bench. Set the building span, the pitch, the overhang and the rafter size. The bench lays out one common rafter: its run, its length along the slope, the plumb cut angle, and the bird's mouth, and warns you if the notch cuts away too much of the rafter. It also shows what the book's "span plus overhang" would have given.
Span:
Pitch:
Overhang (level):
Rafter
Hands on it, off the screen. Hold a framing square on a scrap board: 6 on the tongue, 12 on the blade, both on the same edge. Draw along the tongue: that is a 6:12 plumb cut. Draw along the blade: the level cut.
Look up at a roof overhang, or into an attic: find the ridge, the bird’s mouths on the wall plates, and whether there are ties low in the roof.
Step three
Prove you understood it
One question per idea, a new situation every time. Miss one and you are sent back to the idea it was testing.
All six solid.
You can read a pitch, set a framing square, figure a rafter's length, lay out its three cuts, choose a ridge board or ridge beam, and tie the roof correctly. Next: the load path.
Residential Framing
Lesson five of six, from chapter five. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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