CSLB General Building (B)Framing and CarpentryMedium
A contractor is installing a pitched roof with a 6:12 slope. The common rafters have a horizontal run of 10 feet. What is the approximate length of the common rafters required, assuming no overhang and not accounting for birdsmouth cuts or ridge board thickness?
- A10 feet 0 inches
- B14 feet 2 inches
- C11 feet 2 inches
- D13 feet 5 inches
Show answer & explanationAnswer & explanation
Correct answer: C. 11 feet 2 inches
For a 6:12 pitch, the diagonal length (rafter length) for every 12 inches of run is the square root of (6^2 + 12^2) = square root of (36 + 144) = square root of 180 = 13.416 inches. So, for a 1-foot run, the rafter length is 13.416 inches. For a 10-foot run, it's 10 * 13.416 inches = 134.16 inches. 134.16 inches / 12 inches/foot = 11.18 feet, which is approximately 11 feet 2 inches (11' + 0.18*12" = 11' 2.16").
Why the other options are wrong
- A. This is the horizontal run, not the rafter length.
- B. This would be the approximate rafter length for a much steeper pitch or a significantly longer run.
- D. This would be the approximate rafter length for a steeper pitch or a longer run.
Common Rafter Length Calculation (Pythagorean Theorem)
Determining the true length of a common rafter by using the Pythagorean theorem, where the run and the rise form the two legs of a right triangle, and the rafter length is the hypotenuse.
- Rafter length = sqrt(Run^2 + Rise^2).
- Rise = (Run / 12) * Pitch (e.g., 6 for 6:12 pitch).
- Often simplified using a rafter factor for different pitches.
Memory trick: Run, Rise, Rafter: The roof's right triangle.