Framing an Octagonal Roof, continued After cutting and accurately setting a "blank" hip rafter against a common at one end of the frame, I used a straightedge with an attached pencil to transfer the correct profile from the commons to the hip.

Where the curvature exceeded the width of the hip rafter, we again added LVL blocking, attached with screws and adhesive. We developed the interior ceiling profile the same way.

With the hip and common patterns completed, we fabricated the rest of the rafters. We first set the hips, securing them at the plate below and the center block above. The common jacks were a little trickier. Each octagonal section had four jacks, two longer and two shorter ones. There was an equal number of rights and lefts. The level cut at the bottom was already made, but the rafters needed to be shortened at the top. With no straight edge to work from, we needed a way to make an accurate plumb cheek cut.

Rather than fuss with a mathematical approach, I cut a 14 1/4-inch-long gauge stick to represent the standard spacing between 16-inch-on-center LVL rafters. I positioned this stick between a pair of hips an equal distance down from the top. At the points where the gauge just contacted the face of each hip, I made pencil marks to target with my LeveLite plumb laser, set up on the deck. The laser line, marked with pencil, became the long point of the jack rafter cut. I then set a short full-scale heel pattern on the plate to measure from, up to the mark, to find the overall jack length. I cut 16 of these longer jacks, half lefts and half rights (see "Cutting Acute Rafter Angles," below).

Cutting Acute Rafter Angles

When cutting acute angles on jack rafters, I first make the plumb cut square to the stock. (I make sure that I'm cutting to the long point of the compound angle.) Then I find the distance back to the short point of the bevel using a calculator and the tangent method: Tan = Opp ÷ Adj I know the length of the opposite side -- the thickness of the LVL rafter, 1 3/4 in. -- as well as the rafter angle in plan -- 22.5 degrees. Plugging in the numbers, the formula looks like this: Tan 22.5 degrees = 1.75 ÷ X .4142 = 1.75 ÷ X X = 1.75 ÷ .4142 = 4.225, or 4 1/4 in. This is the distance I measure back from the plumb cut to find the short point of the compound angle. Because we're working in plan, I have to measure perpendicular to the plumb cut. I then transfer this dimension to the edge of the rafter stock. Finally, I secure the rafter on edge across a pair of sawhorses, with the short point of the angle facing up. Setting the circ saw at the correct bevel -- 22.5 degrees -- I cut down the face of the angle, with the shoe riding on the plumb cut. The circular saw will only cut deep enough to establish an initial kerf, so I finish up with a recip saw. To make sure I'm getting an accurate cut, I typically draw the cut line all the way around the rafter and cut a little strong, preserving the line. If need be, the cut cleans up perfectly with a power planer, if you're careful to keep the edge mark visible as a guide. Remember to keep track of left and right side jacks; the octagon requires an equal number of each.

A series of shorter jacks completed the layout; these were simply traced from the lower end of the common pattern.

The framing members went together neatly with a little belt-sanding and power-planing here and there to fine-tune the cheek cuts. We shot the cheeks in with 3 1/4-inch gun nails following a liberal application of PL Premium. On the side of the roof that would coincide with the steel girder, I shortened the rafter tails to butt against the face of a double 2x10 let-in header that replaced one side of the plate, and connected the rafters with metal Simpson hangers (Figure 6).

Figure 6.A steel beam in the main roof forced the author to face-hang the rafters from a header on one side of the octagon.

Sheathing

The roof was sheathed with a double layer of 3/8-inch-thick "wacky wood," or bendable plywood, made to flex and bend along one axis or the other, parallel to the face grain (Figure 7).

Figure 7.The author used glue and screws to sheathe the roof with 3/8-inch-thick "wacky wood." The plywood can be ordered to bend either across or along the sheet but not both. Bending requires an extremely uniform framing surface for solid contact at all points.

It can be ordered to bend either across the sheet or along its length but not both. Small discrepancies in contour from one rafter to the next interfered with a smooth bend, so we had to spend a considerable amount of time fine-tuning the curves with a belt sander before the bendable ply would cooperate. Next time around, I'll stack all the common rafters and belt-sand them together to a perfectly uniform surface -- the slightest bumps and discrepancies created problems at the hips. When building a complex shape like this one, you can't be too precise.

Wacky wood does very wacky things if it gets wet, so we immediately covered the sheathing with a layer of Ice & Water Shield. A custom copper roof would go over it later.

Lifting. We decided that the best way to lift the roof into place was via a central lift ring. We had Rob Crowell, a talented local welder, make a custom "star" plate that tied into the underside of each hip to prevent possible spreading (Figure 8).

Figure 8.A custom-welded steel "star" plate distributed the lifting forces to each hip rafter. The plate was welded to a central eyebolt that penetrated the roof's crown (inset).

The plate was welded to a long eyebolt that rose through the top of the center block. Somehow, the wind failed to notice what we were up to, and the actual lift went off without a hitch (Figure 9).

Figure 9.Thanks to meticulous calculations and cooperative weather, the roof sailed into place on lift day.

I'd already checked and rechecked all the protrusions and other critical points of interest and notched and adjusted the roof accordingly. The roof settled into place as nice as can be, and we secured it with three 5/8-inch-diameter machine bolts per side, drilled up through the plate and drawn up tight.