CSLB General Building (B)Planning and EstimatingHard
A contractor is preparing to order lumber for roof rafters for a gable roof. The building is 30 feet wide, and the roof has a 6/12 pitch. What is the approximate length of the common rafters needed, assuming no overhang and not accounting for ridge board deduction?
- A13.4 feet
- B18.0 feet
- C16.8 feet
- D15.0 feet
Show answer & explanationAnswer & explanation
Correct answer: C. 16.8 feet
The building width is 30 feet, so the run for one side of the roof is half of that: 15 feet. A 6/12 pitch means for every 12 inches of run, there are 6 inches of rise. This forms a right triangle where the run is 15 feet and the rise is (6/12) * 15 feet = 0.5 * 15 = 7.5 feet. Using the Pythagorean theorem (a² + b² = c²), the rafter length (c) is the square root of (run² + rise²). So, c = sqrt(15² + 7.5²) = sqrt(225 + 56.25) = sqrt(281.25) = 16.77 feet. Rounded to one decimal place, this is 16.8 feet.
Why the other options are wrong
- A. Incorrect. This would be a much flatter pitch or shorter span.
- B. Incorrect. This would imply a steeper pitch or longer span.
- D. Incorrect. This is just the run length, not the rafter length.
Rafter Length Calculation (Pythagorean Theorem)
Determining the length of a common rafter using the roof's run and rise, forming a right triangle.
- Half the building width is the 'run' for one side of the roof.
- The 'rise' is calculated from the run and the roof pitch.
- Rafter length is the hypotenuse: sqrt(run² + rise²).
- This doesn't include overhang or ridge board deduction.
Memory trick: Run, rise, then hypotenuse, for rafter length, no excuse!