Intersecting Roof Framing Principles

Describes the geometrical considerations and mathematical relationships involved in the construction of roof structures where roof planes intersect at an angle other than 90 degrees.

Geometric Principles of Intersecting Roof Planes

Plan Angle: The horizontal angle formed by the intersection of two roof surfaces.
Rise: The vertical distance from the wall plate to the ridge.
Run: The horizontal distance from the wall plate to a point directly below the ridge, measured along the roof plane's horizontal projection.
Slope: The inclination of the roof surface, typically expressed as a ratio of rise to run (e.g., 6:12).
True Hip/Valley Angle: The actual angle the hip or valley rafter makes with the horizontal.

Essential Components and Their Relationships

Common Rafter: Standard rafters that run from the wall plate to the ridge.
Hip Rafter: A rafter that forms the intersection of two roof planes where they meet at an external angle.
Valley Rafter: A rafter that forms the intersection of two roof planes where they meet at an internal angle.
Jack Rafter: Shortened rafters that run from the wall plate to a hip rafter or from a valley rafter to the ridge. They are of varying lengths.

Mathematical Relationships for Determining Component Dimensions

Trigonometric functions and the Pythagorean theorem are essential for calculating lengths and angles.

Pythagorean Theorem: Used to determine the length of the hip or valley rafter based on the run and the rise.
Trigonometry (Sine, Cosine, Tangent): Used to determine angles and adjustments for bevels and cuts.
Run Adjustment: The horizontal run of a hip or valley rafter is different than that of a common rafter. Calculations must account for this adjustment.

Practical Considerations for Construction

Layout Techniques: Methods for accurately marking cuts and angles on the lumber.
Plumb Cuts and Seat Cuts: Ensuring proper fit and support for the rafters.
Material Selection: Choosing appropriate lumber and fasteners.
Safety Precautions: Important measures for working at heights and with power tools.