Topic 8 – Ridge Boards and Hip Rafters
Ridge Board for Hip Roofs
The first step in calculating the length of the ridge board is to find its theory length. This is calculated by simply taking the building length and subtracting the building width from it. Because the ridge is terminated inside the building perimeter, we do not take the overhang into account when doing calculations involving the ridge:
Theory Length of Hip Ridge Board = Building Length − Building Width
For example, if we have a building that is 24’-0” x 36”-0”, the theory length of the ridge board would be as follows:
Theory Length of Ridge = 36′ – 24’= 12′
Actual Length of Ridge Board
The actual length for a ridge board in a hip roof is dependent on which method is used for cutting the hip rafters. Where and how the hip intersects the ridge will change its length. There are two methods used, both of which require additions to be made to the theory length of the ridge board:
- ½ the 45° thickness of the hip rafter
- ½ the 90° thickness of the ridge board
***Try to calculate the actual length of the ridge board for the following building using both methods:
- Building 26’-0” x 42’-0”
- 2×10 ridge board
- 2×8 hip rafters
- 2×6 common rafters
Line Length of Hip Rafters
There are two methods used when calculating the line length of the hip rafter:
Square Root Method
This method uses the total rise and total run of a hip rafter to calculate its line length. Just as for common rafters, we take these values and place them in Pythagorean’s theorem, where a = total rise, b = total run, and c = line length of hip rafter:
The total rise is the same as for the common rafters and can be found by multiplying the units of run times the unit rise.
The total run involves a bit more work. If we look at how the hip rafter approaches the ridge at a 45° angle, it forms an equilateral triangle with the exterior wall and common rafter (see figure 3 below). As this means both sides of this triangle are equal, we can use the total run of a common rafter to find the run of the hip rafter using Pythagorean’s theorem again:
In figure three above, the total run of the hip rafter is given; we can double check this using the formula above:
Now that we have the total run and the total rise, we can find the line length of the hip rafter in figure 3:
Unit Line Length
We can also find the line length of hip rafters using unit line length (ULL). This unit line length can be calculated or found on certain framing squares. While finding the ULL is an extra step, this method is advantageous as it allows us to use the same amount of units of run as the common rafters.
For common rafters, the unit run is always 12”. Because hip rafters run at 45° to the common rafters, the unit run must be altered to accommodate the gain in length run in relation to the common rafters (see figure 4 below). We can calculate the unit run by again using Pythagorean’s theorem:
When laying out hip rafters with a framing square, this value is r