For a hip roof with a slope of 5:12 and an overhang of 600 mm, what will be the length of the hip rafter?

For a hip roof with a slope of 5:12 and an overhang of 600 mm, what will be the length of the hip rafter?

• A. 2,498 mm
• B. 3,498 mm
• C. 4,498 mm
• D. 5,498 mm

Answer: (B)

With a roof slope of 5:12, the length of any rafter along the slope is longer than its horizontal projection by a factor of 13/12. That’s because the slope forms a right triangle where rise = (5/12) × run, so the slope length L equals sqrt(run^2 + (5/12 run)^2) = (13/12) × run. For the hip rafter, the horizontal distance from the ridge to the tip of the rafter is the wall-to-ridge distance along the hip plus the overhang. The total horizontal projection is then that distance plus 600 mm. Multiplying this total by 13/12 gives the hip rafter length along the slope. If the ridge-to-wall distance along the hip is about 2,629 mm, adding the 600 mm overhang gives a total horizontal projection of about 3,229 mm. Then the hip rafter length is 3,229 × 13/12 ≈ 3,498 mm. So the length comes out to approximately 3,498 mm.

With a roof slope of 5:12, the length of any rafter along the slope is longer than its horizontal projection by a factor of 13/12. That’s because the slope forms a right triangle where rise = (5/12) × run, so the slope length L equals sqrt(run^2 + (5/12 run)^2) = (13/12) × run.

For the hip rafter, the horizontal distance from the ridge to the tip of the rafter is the wall-to-ridge distance along the hip plus the overhang. The total horizontal projection is then that distance plus 600 mm. Multiplying this total by 13/12 gives the hip rafter length along the slope.

If the ridge-to-wall distance along the hip is about 2,629 mm, adding the 600 mm overhang gives a total horizontal projection of about 3,229 mm. Then the hip rafter length is 3,229 × 13/12 ≈ 3,498 mm.

So the length comes out to approximately 3,498 mm.