Pattern Rafters & CalculationsGable & Hipped Roof

M.S.MartinNov. 2005,

Revised Feb. 2006

Reviewed March 2010

Explanatory Note

• The Rafters (Timber sections) shown in this slide show will not appear full size in relation to the dimensions given, however

• The overall principle and methods used are precise and have been purposely made larger in scale to aid explanation.

First some simple Terms

SPAN

½ SPAN

Now lets look at some simple Math's

• Lets use 28° as an example for the pitch of our roof.

• Find the tan button on your calculator.

• Now press tan, 28, = and your answer should be .532mm

• You have just given yourself the rise per metre run for the common rafter.

• Lets relate this to a square on the next slide.

Rise per metre run of rafter• This means for every 1.0m you

go along the bottom or span of the roof, you rise up 532mm. (for our example of 28º)

• If you simulate a steel square as the triangle of a roof, you can divide these measurements by two to use on here.

• See opposite• 1.0m = 500mm (goes on the

2 blade of the square)• 532 = 266mm (goes on the

2 tongue of the square)

500mm

266mm

You have also now created the two bevels you need

• Plumb bevel common rafter.

• Level bevel common rafter.

• We can use the square set up like this to set out our pattern rafter. 500mm

266mm

True length per/m and Centre Line Length

• True length per / m• Use your rise per /m run

measurements for this and square root them.

• √ .532² + 1.0²• = √ 1.283• = 1.133mm

• Centre line length• Use the true length per/m and

half span for this.• T/L per/m x ½ span of roof• As an example we will use 3.6m

for the ½ span of our roof.• 1.133 x 3.6• = 4.079m• This is the measurement from

the centre line of the ridge, to the back of the birdsmouth, measured along the top of the rafter.

The Gable Roof

Start with a simple Plumb Bevel

This is the centre line for the top of the rafter (centre of ridge position)

Use your steel square for this bevel, or other means if you prefer.

Measure the centre line length of rafter and place another plumb bevel

This line is the back of the birdsmouth position

Alternatively, step out your length with a steel square

This line is still the same position (back of birdsmouth)

Now we mark the level cut on the birdsmouth (Max. 1/3 Rafter depth)

This is easiest with a builders square, or you can simply mark square off the plumb cut.

Maximum 1/3

Two more things left, 1. Reduction at the ridge, 2. Eaves overhang

This pattern is now ready to cut, so other rafters can be marked off it.The lines shown blue are where you cut the rafter.

Measure half ridge thickness square off plumb cut and place another plumb cut

Now measure eaves overhang square off bottom plumb cut

Your pattern rafter and the Gable Roof.

Now look at the roof and your pattern above, any questions?

The Hipped Roof

Lets first look at the pattern we know, then add to it.

For the hip lets look at it in solid form, for there is marks we need

to place on the edge as well

Cut for eaves overhang

Cut for top end of rafter Centre line

Birdsmouth

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With a hipped roof, we need to add creeper cuts to this pattern

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We can do this with your square or by measurement

The two distances you need are either (1) rafter spacings at base of square, or (2) true length at the top.

Now this becomes the centre line of first creeper

Measurements and calculations• Before we go any further, lets note down some more

figures.• (1) Rafter spacings, for our exercise, lets say they are

at 450mm centres. This means your centre to centre measurement on base of square would be 450mm.

• (2) Now for the true measurement at top, if you choose to do it this way, we need to do a simple calculation. Remember our ‘True length per / m’?

• True length per / m x rafter centres gives you measurement (2) above.

• 1.133 x .450 = .509mm• Lets look at the rafter again

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Steel Square centre to centre measurement

450mm measured at base of square

True length centre to centre measurement

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True length of 509mm is measured at top of rafter.

1st Creeper adjustment

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Centre line of first creeper

From this centre line point we need to mark the ‘long point for the first creeper' and we can do this with two simple measurements.

1) half mitre thickness of the hip

2) Half the thickness of a rafter. First lets look at what this means

Adjustment measurements

Half the mitre thickness of a hip

Half the thickness of a rafter

Adjustments on the rafter

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Centre line of first creeper

Gives you long point of first creeper

Back half mitre thickness of hip

Forward half thickness of rafter

The Geometry as to Why

Now lets look at the rafter again

Pattern Rafter with first Creeper

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Centre line of first creeper

Long point of first creeper

The last step is to mark remaining creepers, which you do with centre to centre measurement, either by square or by measurement of true length.

Marking remaining creepersNote: this will be there long point

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Start from long point of first creeper

Simply mark remaining long points from here, the simplest way is with a steel square

Long point of next creeper, and continue down the length of the rafter for longer lengths

One more item – the Crown end cut

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Simply measure ½ the thickness of a rafter from original centre mark, this is your crown end cut.

Crown end cut

Your finished Pattern for a hipped roof

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Crown end cut

Common Rafter cut

Centre line of ridge

First creeper long point

Second creeper long point

Birdsmouth

Plumb cut for eave overhang

Remember: longer rafter, more creepers marked

Have another look at the Hipped Roof