If this is a long roof with hips on the ends, there will be common rafters in the center. The first thing to do is to layout the common rafters, so you need to know the length of the ridge board. This is found by measuring the length of the building and subtracting the span and adding the thickness of the ridge board. Nail the common rafters flush on the ends of the ridge board and at 90 degrees to it in the center of the span.
Now let's put on the hips. The hip rafter is a diagonal of the square formed from the two common rafters and the two outside wall lines. The length of the diagonal is the run of the hip rafter. Since the hip forms the diagonal of a square with a 12" run, the diagonal of this square measures 17". This is what we use on the framing square as our run for the hip, 17". For every 12" of run on a common rafter we have a hip or valley run of 17".
In the third column of the rafter table (see my article: Rafter Tables on the Framing Square) on the framing square is the length of hip or valley rafter. For a 5/12 roof we look across at the 5 and find 17.69. Multiply 17.69 times the decimal equivalent (.25 instead of 1/4, for example) of the run to get the distance from the center of the ridge to the outside of the wall line. Shorten the hip by half the 45 degree horizontal thickness of the ridge.
The angle of the side cut of the hip and valley rafters are also given on the rafter table. For a 5/12 roof pitch the side cut is 11.5". Use this number with 12" on the framing square to find the side cut. This is the angle of the side cut which is marked on the top edge of the rafter. The plumb cut for the hip and valley uses 5" and 17" on the framing square, which is marked on the side of the rafter. This is a compound angle best cut with a circular saw or radial arm. Set the side cut angle on the bevel of the saw and cut along the plumb cut.
Okay, now let's go to the wall end of the hip and cut the seat cut (also called bird's mouth). You should have your length marked for the outside of the wall. You will notice that if the hip or valley was installed now the outer edges of the board is higher than the center of the board where the sheathing will lay. To compensate for this, the hip is dropped so the edges will support the sheathing, rather than the center, about 1/4" for a 1 1/2 inch board. To arrive at this drop height follow this simple procedure:
With the framing square, align 17" on the body and the 5" mark on the tongue (for our 5/12 roof pitch example) on the bottom edge of the hip rafter (or any other straight edge you can find--we generally use an edge of the rafter because it's right there). Scribe along the outside body of the framing square, marking a short line from the edge of the board. Mark the inside tongue of the framing square at the edge. Measure from the tongue and mark the distance of half the thickness of the rafter (3/4" in our example). Now shift the framing square along the board, maintaining the 17" and 5" marks along the edge of the board, until the tongue of the framing square is half the thickness (3/4") away from the first tongue mark. Scribe along the outside the body of the framing square as before. The distance between the two lines is the amount of the drop required for the hip. It works out about 1/4" for a 1 1/2" thick rafter. Layout the seat cut in the usual way, but drop it the extra 1/4", as in our example.
The plumb cut for the bird's mouth must also be moved to compensate for the 90 degree angle of the intersection of the outside walls. We will cut a straight cut instead of a 90 degree notch. So move this plumb cut toward the tail by a half thickness of the rafter again. Mark the plumb cut here with the 5 and 17 configuration. The length of the tail is dependent on the overhang. This is found by using the rafter table and multiplying the horizontal overhang by the unit run on the hip, which is 17.69". For example, a 2' overhang would be 17.69 x 2 = 35.38" less the 45 degree thickness of the rafter trim (backing for the fascia board, usually the same size as the common rafter). Cut this end back from this mark 45 degrees each way. Then finally trim the hip tail to fit the 2x6 trim by squaring back off the tail plumb cut to the same length of cut as on the common rafter tail. This prevents the wider hip bottom from hitting the soffit material later on. Now install the hips or valleys on the roof. The valleys are cut with the same cuts as the hip, except the tail. The seat cut doesn't have to be lowered either since the sheathing will rest on the center of the valley rafter and not on the edges as the hip.
Now the jack rafter must be cut and installed. The hip jack is the same as the common rafter on the tail, but the side cut is different since it goes from the wall to the hip instead of to the ridge as the common rafter does. When rafters or studs come from a square line to an angled line (the hip) the amount to cut off or add on is referred to as the common difference. This common difference is given in the rafter table on the framing square under the unit run. (For 5/12 in our example, under 5 the common difference is given for 16" centers on rafters as 17 5/16" and for 24" centers as 26". Start at the common rafter and go down the hip layout two jacks opposite to each other on the side cut. Remember to start at the center of the hip and allow for half the 45 degree thickness again. Once this first one is cut the remaining ones can be cut exactly the common difference shorter. Check it out first though. Before installing the ceiling joists to the jacks, sight along the hip rafter to make sure it is straight. Usually by hammering the jack tighter or looser the hip can be easily straightened. When everything is nailed and secured, lay on the sheathing. It should look something like this drawing.
When installing the ceiling joists, you will notice that near the end of the building (on the drawing, where the hip jacks are located), there is no room for the joists. To counteract this just double up the last ceiling joist, then run short ceiling joists from this girder joist 90 degrees to the wall and nailed to the side of the hip jacks and the one common rafter. Use joist hangers on the girder joists. Just trim off any part of the ceiling joist that extends above the rafter. In the 'old days' I used to trim these pieces off with a hatchet. Also a very important tip: Always either overlap and nail the ceiling joists together in the center of a long span or butt them together and nail a scab over the joint. This ties the two walls together to prevent them from kicking out when a load comes on the roof. If there is a center wall, it may be a good idea to support the ridge with 2x4 posts. Also on long spans collar ties are used to shorten the span by nailing 2x4's across the rafters near the top. Or pony walls are also used to shorten the span. Your building inspector will advise you on that. Since the 1970's most builders use trusses and stay away from rafters. A truss roof can be made up to fit almost any configuration of hip and valley roofs. The truss roof, of course, is not dependent on walls under it as is a rafter roof.
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