Before starting the calculation, we need to know some technical terms related to a pitched roof.
Rafter Of Roof:
Rafter is the distance between the ridge or hip of the roof to the wall plate of the external wall.
Span Of Roof:
Span is the clear distance between the supports of an arch, beam or roof truss.
Rise Of Roof:
It is the vertical distance between the wall and the top of the ridges.
Pitch Of Roof:
The pitch of a roof is its vertical rise over its horizontal span. The angle, or pitch of a roof, is calculated by the number of inches it rises vertically for every 12 inches it extends horizontally. For example, a roof that rises 6 inches for every 12 inches of horizontal run has a 6/12 pitch.
There is no standard, universal pitch of roof. It varies depending on culture, climate, style, and available materials. The most common roof pitch is designed with a pitch ranging from 4/12 to 9/12.
Pitch = Rise/Run
Run Of Roof:
In roof framing, the run is the distance from the outside of the wall’s top plate to a point directly below the center of the ridge. In simple words, the run is the half distance of span.
Run = Span/2
Exmple 1:
Given,
Span = 30 ft.
Pitch = 5/12
Run = Span/2 = 30/2 = 15 ft.
Rafter length =??
According to Pythagoras theorem, a ² + b ² = c ²
Run ² + Rise ² = Rafter ²
Rafter = √ (Run ² + rise ² )
Pitch = 5/12
Rise/Run = 5/12
∴ Rise = Run x 5/12 = 15 x 5/12 = 6.25 ft.
Rafter ² = Run ² + Rise ² = 15 ² + 6.25 ² =264.0625
∴ Rafter = √ 264.0625 = 16.25 ft.
Example 2:
Calculate Rafter Length Using Angle:
Given,
Length of roof = 30 ft.
Rise = 6 ft.
Angle = 20°
We know,
Sinθ = Opposite/Hypotenuse
Cosθ = Adjacent/Hypotenuse
tanθ = Opposite/Adjacent
In the above triangle,
a = Opposite = Run
b = Adjacent = Rise
c = Hypotenuse = Rafter
Cosθ = Adjacent/Hypotenuse = b/c
c = b/Cosθ = 6/Cos20° = 6.38 ft.
∴ Rafter length = 6.38 ft.
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