Trussed rafters

Assemble repeated roof trusses into a restrained roof system.

Individual trusses need temporary and permanent restraint as the roof is erected and enclosed.

Context. An educational model. Geometry, material assumptions and the reference building are described in the illustrated study.

Most house roofs built today arrive on a truck. Each truss is a flat frame of 2×4s, cut and assembled in a factory to a drawing made for that one roof, and the crew’s job on site is to stand them up, space them, tie them down and brace them. Where a framer once cut every rafter and ceiling joist by hand, a crane now sets a truss every few minutes. The figure builds the roof of a small 24 ft (7.3 m) wide house that way, one truss at a time, and then finishes it: deck, shingles, eaves and gutters outside, ceiling and insulation inside. Use Show to take away whatever hides the part you are looking at.

A trussed rafter does the work of a rafter, a ceiling joist and the wall that would otherwise hold them up in the middle. Its sloped top chords carry the roof; its bottom chord carries the ceiling and ties the two heels together so they cannot spread; and the webs between them cut the space into triangles. A triangle cannot change shape unless one of its sides changes length, so every member ends up pushed or pulled along its length rather than bent. That is why 2×4s can cross 24 ft.

Framed by hand, the same roof would typically need deeper rafters, ceiling joists that lap over a bearing wall down the middle of the building, and a day of cutting. The trusses span from outside wall to outside wall, so every wall inside is free to go anywhere, or nowhere. Step through the figure and the room underneath stays empty from start to finish. This model spans 24 ft (7.3 m); actual spans depend on the engineered truss design.

Trusses are not the only way to hold up a pitched roof, and they cost the house its attic. When the roof is complicated, or the space under it is wanted, the old ways come back:

The joints are made with connector plates: galvanized steel, usually 20 gauge (about 0.9 mm), punched so that rows of sharp teeth stand up from one face. At the factory the members are laid out in a jig and a press drives a plate into each face of every joint. Choose Heel in the figure to see one up close. The teeth grip the wood like dozens of short nails, and because there is a plate on both faces the joint carries load without twisting.

The plates are sized by the truss designer for the force in each joint. The biggest are at the heels, where the thrust of the sloping top chord turns into tension in the bottom chord, and at the peak. A loose or missing plate is a broken truss, which is why damaged trusses go back to the yard instead of up on the wall.

The web pattern is chosen by span and by what has to happen under the roof. All five in the figure span the same 24 ft; change the truss and the whole row is rebuilt in the new pattern.

Fink

The W truss, and the common house truss. Its webs are short, so all of it can be 2×4, and of these five only the king post has fewer joints.

Howe

Vertical webs and diagonals leaning toward the middle. Under a roof load the verticals are stretched and the diagonals squeezed. More joints than a Fink, used where loads or spans are larger.

King post

One post from the peak to the middle of the bottom chord. Its panels are long, so here its chords step up to 2×6s; it suits short spans and low loads.

Scissors

The bottom chords slope up toward the middle too, at half the pitch of the roof, so the ceiling inside can be vaulted. The truss is shallower in the middle, which costs it stiffness: scissors trusses spread more at the heels than flat-bottomed ones.

Attic

Leaves a room inside the truss: the bottom chord becomes a floor, posts become knee walls, and a tie becomes the ceiling. The room cannot be crossed by webs, so the chords get much deeper and the joints much larger. Attic trusses in this model are steep, at 12:12, to create the headroom the room needs.

Why some webs are stretched and others squeezed, and how the load divides among them, is the subject of Trusses.

Trussed rafters usually go at 24 in (610) on centre, which suits 4 × 8 ft sheathing: every sheet edge lands on a truss. They can go farther apart, up to 4 ft (1220), if the decking can span it. They bear only on the outside walls, through the double top plate, which spreads each truss’s load to the studs below wherever it falls. Here the walls are framed at 16 in and the trusses at 24 in, and the top plate takes care of the mismatch.

At each end of the building a gable-end truss stands over the end wall. It has the same top chords as the others, but since it is supported along its whole length it needs no webs: vertical studs at 24 in fill it and carry the siding. At each heel of every other truss a hurricane tie, a strap of bent steel nailed to the truss and to the top plates, keeps the roof on the walls when wind tries to lift it.

A truss is stiff in its own plane and almost floppy out of it. A 24 ft frame of 2×4s is only 1½ in (38) thick; standing on its edge it has nothing to stop it toppling but its nails. If the first truss of a row goes over, it lands on the second, and the pair on the third. When trusses collapse during construction, missing or late bracing is almost always the reason.

So the bracing goes in as the trusses go up, in a fixed order, and the figure follows it.

1. The first truss is the hardest to hold, because there is nothing yet to tie it to. The crane holds it while it is braced, outside to stakes in the ground or, as here, inside down to the floor. Only then is it let go.
2. Each following truss is set at 24 in and nailed to 2×4 restraints running along the top chords back to the first one. Under the usual guidance from the truss industry, these rows are at most about 10 ft (3 m) apart along the top chord for spans up to 30 ft, and closer for longer spans.
3. Restraints alone only keep the trusses at the same spacing. The whole row can still lean together, like a stack of books. Diagonal bracing laid across the top chords locks the restraint lines into a triangulated plane.
4. Permanent bracing stays in the finished roof: a continuous restraint along each long web that the designer marks as needing one, so it cannot buckle sideways under its compression, anchored by diagonals.
5. The sheathing finally braces every top chord along its whole length, and the ceiling does the same for the bottom chords. The temporary restraints come off as the sheathing covers them.

Every member of a truss is working, and none is spare. Notching a chord or cutting out a web to fit a duct, an attic hatch or a skylight can take away the triangle that holds a joint in place, and the truss can fold under its next snow load. A truss that has to be changed needs a repair detail from the truss designer, usually extra lumber and plates fixed across the damage.

Once the row is braced, the roof is closed in from the bottom up, and every layer laps over the one below it so that water running down always lands on top of the next piece, never behind it.

1. A 2×6 sub-fascia is nailed across the plumb-cut truss tails, lining them up and giving the fascia, soffit and gutter something to fix to. At the gable a ladder of 2×4 rungs, nailed through the gable sheathing into the gable-end truss, carries a fly rafter 12 in (305) out: the rake overhang.
2. The deck goes on in 4 × 8 ft sheets from each eave, stopping 1 in (25) short of the ridge on both sides to leave a slot for air.
3. Metal drip edge along the eaves, then underlayment rolled out from the eave up, each course lapping the one below, then drip edge up the rakes on top of it. At the eave the drip edge is under the underlayment and at the rake it is over it, so in both places water is led outward.
4. Shingles from a starter course at the eave, each course nailed just above the butts of the one below so the nails are covered, with 5⅝ in (143) left to the weather. A ridge vent covers the slot.
5. Fascia, a level soffit with a vent strip, and gutters hung on the fascia under the drip edge. Windows and doors go in once the roof keeps the rain off.
6. Inside, gypsum board is screwed to the bottom chords, a baffle is fitted in every bay at the eaves, and insulation is blown in over the whole ceiling.

Shingles suit this roof: a 6 in 12 pitch sheds water well under them, and they are the cheapest roofing there is. Where snow is heavy, fire is a risk or the roof should outlast the house’s first owners, something else goes on the same deck:

Choose Eave to see the junction cut through the last truss, where three systems lock together: the structure, the weather skin and the insulated envelope. Read it from the inside out.

• The bottom chord bears on the double top plate, which carries the load to the studs. The hurricane tie fastens the truss to the plates, so wind pulling up on the roof is passed down into the wall.
• Blocking between the heels closes each bay over the wall, with holes in it for air. The baffle above it does two jobs: its lip dams the insulation, and its sheet holds a 1¾ in (44) channel open under the deck, so air from the soffit vent can run up every bay to the ridge vent. The roof deck stays cold and dry, and in snow country ice dams are less likely to form.
• The deck, underlayment and shingles run out over the sub-fascia. The drip edge laps over the fascia and sheds into the gutter; the soffit runs back from the fascia to the wall, where it meets the housewrap, which runs up behind it to the top plate.
• Inside, the ceiling board goes up first and the wall board butts up under its edge, so the wall board holds the ceiling’s edge up.

The weak spot is the insulation. Over the middle of the ceiling it is 14 in (355) deep. Over the wall it can only be as deep as the heel allows: with a standard heel, the top chord meets the wall just 3.9 in (100) above the top plate. That leaves about 4 in (100) of insulation over the inside face of the wall and 3 in (75) at the baffle, right where the warm room meets the cold eave. A raised heel lifts the truss at the wall line, with a short vertical web at each end, so the full depth can run out over the plates. It costs little in the factory and a lot to fix afterwards.

Choose Gable, then hide the roofing and the deck. The gable-end truss arrived with its OSB already on; that sheathing meets the wall sheathing at the top plate, and the housewrap runs over both. The ladder’s rungs pass through to the gable truss, the deck runs over them out to the fly rafter, and the rake board covers its face. The same principle holds as at the eave: whatever is higher laps over whatever is lower.

From the model in the figure: a 24 ft (7315) span between the outside faces of the walls, 18 in (457) overhangs, and lumber at about 500 kg/m³ with 20-gauge plates.

Every joint has a plate on each face, so the Fink carries 14 plates. Its 74 ft (22.4 m) of 2×4 is about what two workers can lift by hand, which is why short-span trusses are often set without a crane. The attic truss is more than twice as heavy and is not.