Roof framing

A pitched roof in light wood framing is built from a few kinds of sloping members, all cut from one rule. Pairs of rafters lean against each other across the house. Their feet sit on the top plates of the walls, and their heads meet at a board along the peak. Where the roof turns a corner, a heavier member runs up the diagonal and shorter rafters frame into it. The figure frames one small house three ways: a gable roof, a hip roof, and a hipped L that adds a wing and with it a valley, on stud walls already sheathed, with the crew part way through sheathing the roof.

A common rafter runs from the wall plate to the ridge, square to both. At its foot a triangular notch, the birdsmouth, lets it sit on the plate: a level seat cut bears on top of the plate and a vertical plumb cut rests against its outer edge. At the head another plumb cut meets the ridge board. The ridge board does little structural work. It gives the rafters a straight line to land on and something to nail to while the frame goes up. The pair carries its load by pushing against itself through the ridge, like the two sides of a letter A.

The outward thrust needs a complete resisting system, such as properly connected rafter ties. A structural ridge beam provides another arrangement: it supports the rafter heads and carries their reactions to its supports. Slope alone does not settle that choice. Rafters are commonly spaced 12, 16 or 24 in (305, 405 or 610) apart; their size depends on species, grade, loading, span and deflection limits. This model draws 2×8s at 24 in spacing across a 12 ft run each way to explain the geometry.

Slope is given as rise per 12 units of run: a 6 in 12 roof rises 6 in for every foot it runs inward. The dashed triangle beside one rafter in the figure draws it at full size. The house is 24 ft wide, so each slope runs 12 ft, and the rise in feet equals the pitch number. Up to 3 in 12 counts as low slope, mostly covered with roll or membrane roofing. Shingles, tiles and metal shed water from about 4 in 12 up to 12 in 12. A steeper roof sheds snow and rain faster and makes room in the attic, at the cost of more roof area and more wind on its face.

On a hip roof every wall carries an eave and the slopes meet over the corners. The line where two slopes meet over an outside corner is a hip, and a hip rafter runs up it from the corner of the plates to the end of the ridge. A valley is the same line over an inside corner, where two slopes drain toward each other. Both run at 45° in plan, so for every 12 in a common rafter runs, they run the diagonal of a 12 in square: 16.97 in, which framers round to 17. A hip at 6 in 12 rises 6 in for every 17 in of run, which makes it shallower and longer than the commons beside it. It is also cut a size deeper, so the rafters framing into its sides bear on it over their full cut.

Those shorter rafters are jacks. Hip jacks run from the plate up to a hip, valley jacks from a valley up to the ridge, and cripple jacks touch neither plate nor ridge, running between a hip and a valley. Because they keep the 24 in spacing, each jack is shorter than its neighbour by the same amount, the length of 24 in of run along the slope. Each jack also needs an angled cheek cut where it meets the diagonal member. The figure’s L meets with equal spans, so its hip and valley line up and no cripples are needed.

These are line lengths, measured from the outside of the wall plate to the centre of the ridge. Each piece is then shortened by half the thickness of whatever it meets, and the tail for the overhang is added. The figure cuts every member that way: each face stops where it meets the next member, so the cheek cuts come out true.

Load a pair of rafters and it spreads. The heads lock against each other at the ridge, so the feet push outward on the walls, and a wall built to stand upright bends easily at its top. Under 30 lb/ft² of roof load (10 dead, 20 snow), each pair at 24 in pushes each wall outward with

That gives 720 lb (3.2 kN) at 6 in 12. Halve the pitch and the thrust doubles, to 1,440 lb at 3 in 12. Steepen it to 12 in 12 and it halves, to 360 lb. The cure is a tie across the bottom of the triangle. In most houses the ceiling joists are that tie: they lie beside the rafters on the plates, are nailed to each heel, and are lapped or spliced over a bearing partition so that they work in tension from wall to wall.

Collar ties sit higher, in the upper third of the rafters. They are too high to stop the walls spreading. Their job is to hold each pair together when wind lifts the roof and tries to pull the rafters off the ridge. To leave the space open to the rafters for a cathedral ceiling, the ties go and the ridge becomes a real beam on posts. Each rafter then spans from wall to beam and pushes on neither.

Past the wall each rafter runs on as a tail, here 16 in (405) of overhang. Its end gets a plumb cut for the subfascia, the board that lines up the tails and carries the gutter and the fascia trim, and a short level cut for a soffit. On a hip roof the subfascia runs all the way round, mitred at each corner, with the hip tails reaching out diagonally to meet it.

On a gable roof the edge that climbs the slope is the rake. To carry the roof past the gable wall, flat 2×4 lookouts run out over the wall’s sloping top plate from a doubled rafter inside. A fly rafter (or barge rafter) along their ends forms the overhang, 12 in (305) here. Below it, studs at 16 in fill the gable triangle down to the wall’s double top plate.

Choose Seat or Ridge and the rest of the house steps back to a ghost, leaving one pair of common rafters and what they touch. It is the whole roof structure in one slice, and each joint in it does a different job.

• At the seat the rafter bears on the double top plate through its birdsmouth and is toenailed to it. The ceiling joist bears on the same plate beside it and is nailed to its heel. That nailing is the joint that matters most: it is where the rafter’s outward thrust becomes tension in the joist. The wall sheathing runs up to the top of the plate, and the roof sheathing runs out over the tail to the subfascia.
• At the middle the two ceiling joists butt end to end over the bearing partition and are spliced there, so the tie is continuous from wall to wall even though no joist is 24 ft long.
• At the ridge the plumb cuts are nailed through the ridge board to each other. The collar tie, higher up, is nailed across both faces of the pair.

Take away the roof sheathing with Show and the frame is what is left; take away the walls and the rafters stand on their plates alone.

The same members make every other pitched roof. A shed roof is one slope, its rafters spanning from a low wall to a high one. A gambrel breaks each side into a steep lower slope and a shallow upper one, joined at a purlin. A mansard does the same on all four sides. Dormers cut openings that are framed with doubled rafters and headers, like an opening in a floor. Flat roofs are framed like floors, with the slope for drainage built in by tapering the joists or the insulation above them.

The three the figure frames are the ones most houses choose between, and the plan and the wind decide more than taste does:

Most new houses replace this cutting and fitting with trussed rafters, triangulated in a factory and set on the walls in a day. The ceiling joists of this roof are the top floor of the platform frame below it. Rafters still win where the roof is complicated or the space under it is wanted; the two, with panels and timber, are compared under trussed rafters.