How long should the 2 x 6 rafter stock be to frame a gable roof on a 24' x 42' building with a 4-in-12 slope and 1' overhang?

To determine the correct length for the 2 x 6 rafter stock for framing a gable roof on a building of the specified dimensions, it is essential to consider the slope of the roof and the overhang.

A roof with a 4-in-12 slope means that for every 12 horizontal inches, the roof rises 4 vertical inches. This gives us the rise per foot and helps in calculating the diagonal length of the rafters needed to accommodate that slope.

First, we need to calculate the total run of the roof. Since the building is 24 feet wide, the run will be half of that, which is 12 feet. To find the height of the roof at its peak, we can use the rise of the roof based on the given slope. For a 12-foot run, the vertical rise will be:

[ \text{Rise} = \frac{4}{12} \times \text{Run} = \frac{4}{12} \times 12 = 4 \text{ feet} ]

Next, we have to account for the 1-foot overhang. This overhang adds additional horizontal distance that the rafters must reach. Therefore, the total horizontal dimension from the wall