A hip roof has common rafters running a horizontal distance (run) of 12 feet from the exterior wall to the ridge. The valley rafter serving the same roof section runs diagonally at a 45-degree angle in plan view. Approximately what horizontal run does the valley rafter span, and what is the design implication?
- AAbout 24 feet, double the common rafter run, requiring doubled rafters
- BAbout 17 feet (12 × 1.414), requiring a larger rafter size than the common rafters
- CAbout 12 feet, the same as the common rafter, requiring no size change
- DAbout 6 feet, half the common rafter run, allowing a smaller member
Show answer & explanationAnswer & explanation
Correct answer: B. About 17 feet (12 × 1.414), requiring a larger rafter size than the common rafters
A valley (or hip) rafter running at 45 degrees in plan spans a horizontal distance equal to the common rafter's run multiplied by √2 (≈1.414), so 12 ft × 1.414 ≈ 17 ft. Because the valley rafter must span this longer distance while also carrying tributary loads from jack rafters on both sides, it typically requires a larger member size than the common rafters to meet span tables.
Why the other options are wrong
- A. Doubling is not the correct geometric relationship for a 45-degree diagonal.
- C. Ignores the geometric lengthening effect of the 45-degree diagonal run.
- D. The valley rafter run is longer, not shorter, than the common rafter run.
Valley/Hip Rafter Span Geometry
A hip or valley rafter running at 45 degrees in plan spans a horizontal distance equal to the common rafter run multiplied by approximately 1.414 (√2), requiring larger sizing to meet span and load requirements.
- Diagonal run = common rafter run × 1.414
- Valley/hip rafters carry tributary loads from jack rafters on both sides
- Typically sized one size larger than common rafters
Memory trick: Forty-five degrees stretches the run by root two.