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How To Calculate The Length Of Roof Rafters

How To Calculate The Length Of Roof Rafters

Let us calculate the length of the roof rafter as shown in the below drawing.

Roof Rafter

The length of the roof rafters is calculated in three different methods based on the available data. Let us go through, all of them as explained below.

1. Roof rafter with pitch:

Roof With Pitch

Given data:

Span = 20 ft.

Pitch = 7 /12

As you know,

Run = [span ÷ 2]

      = [ 20 ft. ÷ 2]

      = 10 ft. 

 

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Here,

Pitch = [rise / run.]

i.e.   ( 7 / 12 ) = [ rise / 10 ft.]

By cross multiplication,

Rise = [ (7/12 ) × 10 ft.]

       = 5.833 ft.

By Pythagoras theorem,

AB2= AC2 + BC2

i.e. rafter2= rise2 + run2

Rafter = √ rise2 + run2

Rafter = √ (5.833)2 + (10)2

= √ 34.027 + 100

= √ 134.027

= 11.577 ft.

Length of the roof rafter = 11.577 ft.

 

  1. Roof rafter with an angle & span:

Roof with Angle

Given data :

Span = 20 ft.

Angle θ = 25°

As you know,

Run = [span ÷ 2]

= [ 20 ft. ÷ 2]

      = 10 ft.

By trigonometry,

sinθ = opposite / hypotenuse

In the above triangle,

Side AB = rafter = hypotenuse

Side BC = run = opposite.

So, 

Sin25° = [ 10 ft. ÷ hypotenuse]

0.4226 = [ 10 ft. ÷ hypotenuse]

By cross multiplying,

Hypotenuse = [10 ft. ÷ 0.4226 ]

                   = 23.663 ft.

The length of the roof rafter = 23.663 ft.

 

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3. Roof rafter with an angle & rise:

Given data :

Rise = 8 ft.

Angle θ = 25°

By trigonometry,

cosθ = adjacent / hypotenuse

In the above triangle,

Side AB = rafter = hypotenuse

Side AC = rise = adjacent.

So,

Cos25° = [ 8 ft. ÷ hypotenuse]

0.906 = [ 8 ft. ÷ hypotenuse]

By cross multiplying,

Hypotenuse = [8 ft. ÷ 0.906 ]

                   = 8.83 ft.

The length of the roof rafter = 8.83 ft.

 

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Thank you for going through this article. Have a good day.

 

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About Raja Junaid Iqbal

Hi My name is Raja Junaid Iqbal and i am Land Surveyor by Profession but I've specialized in the field of Q,S and land development. As Professional Surveyor I engaged my self in all over the Gulf since 14 years.

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