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Octagonal Roof. Notes to this Lesson. This demonstration develops from knowledge gained from the development of Gable & Hip Roofs This PowerPoint does not explain the development of the Basic Roof Members

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Octagonal Roof

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Octagonal Roof


Notes to this Lesson

  • This demonstration develops from knowledge gained from the development of Gable & Hip Roofs

  • This PowerPoint does not explain the development of the Basic Roof Members

  • If you require an understanding of these you should first look at the Gable & Hip Roof presentations


Lesson ParametersTo be Provided by Trainer and used in Confirmation Excercises


Critical Definition

  • Plan Length

  • Is the distance a roofing member travels, measured along the base of the Right Angled Triangle that it forms adjacent to the Pitch angle.


Example

  • In its most common form

Pitch Angle


Example

  • Other Examples

Pitch Angle

Pitch Angle

Pitch Angle

Pitch Angle


Hip Rafter per 1m of Common Rafter Plan Length

½ Span

½ Span

22.5°

½ Span

Plan Lengths


Confirmation of Learning

  • Determine which side is the “Plan Length”


Confirmation of Learning - Answer

  • Determine which side is the “Plan Length”


Confirmation of Learning

  • What are the Plan Lengths of these triangles?


Confirmation of Learning - Answer

Plan Lengths


Confirmation of Learning

This Triangle


Confirmation of Learning

This Triangle


Octagonal Roof

  • A Regular Geometric Shape


Roof Members can be Determined


Class Works

  • On an A3 drawing sheet conduct the following drafting excercise


Determine Set Out Points

Gathering Point is ½ Span Back from edge

Walls are parallel


Determine Set Out Points

This will mean for our Practical Class Exercise, the Gathering Point will be ½ Rafter in from edge of the Table Frame

Gathering Point is ½ Span Back from edge

Walls are parallel


Drawing Octagonal Roof without Compass


Drawing An Octagonal End Roof

Draw 2 Construction Lines to scale to represent the Width of The Building


Drawing An Octagonal End Roof

Draw Construction Line To Represent End of Building


Drawing An Octagonal End Roof

Draw Construction Line To Represent End of Building

This end is not so important


Drawing An Octagonal End Roof

Draw a Construction Line Mid Span to Represent the Ridgeline (i.e. Centre Span)


Drawing An Octagonal End Roof

Locate Centring Rafters

(1/2 Span from end)


Drawing An Octagonal End Roof

Find Gathering Point


Drawing An Octagonal End Roof

Scribe Semi Circle with ½ Span as Radius


Drawing An Octagonal End Roof

Draw in Centring Rafters


Drawing An Octagonal End Roof

Draw in Major Crown End


Drawing An Octagonal End Roof

Bisect Centring & Crown End Rafters to form Minor Crown End


Drawing An Octagonal End Roof

Bisect Centring & Crown End Rafters to form Minor Crown End


Drawing An Octagonal End Roof

Extend Lines Perpendicular to Ridge

At ½ End Length

= ½ Span x 0.414


Drawing An Octagonal End Roof

Extend Sides of Building by ½ End Length

= ½ Span x 0.414


Drawing An Octagonal End Roof

Join up external Lines


Drawing An Octagonal End Roof

Draw in Hips


Draw Octagonal End With Compass


Drawing An Octagonal End Roof

Draw 2 Construction Lines to scale to represent the Width of The Building


Drawing An Octagonal End Roof

Draw Construction Line To Represent End of Building


Drawing An Octagonal End Roof

Draw Construction Line To Represent End of Building

This end is not so important


Drawing An Octagonal End Roof

Draw a Construction Line Mid Span to Represent the Ridgeline (i.e. Centre Span)


Drawing An Octagonal End Roof

Locate Centring Rafters

(1/2 Span from end)


Drawing An Octagonal End Roof

Find Gathering Point


Drawing An Octagonal End Roof

Scribe Semi Circle with ½ Span as Radius


Drawing An Octagonal End Roof

Draw in Centring Rafters


Drawing An Octagonal End Roof

Draw in Major Crown End


Drawing An Octagonal End Roof

Bisect Centring & Crown End Rafters to form Minor Crown End


Drawing An Octagonal End Roof

Bisect Centring & all Crown End Rafters to form Hip Rafters as extended “Light” Construction Lines


Drawing An Octagonal End Roof

Extend Lines Perpendicular to Ridge

To intersect with HIP


Drawing An Octagonal End Roof

Extend sides of Building

To intersect with HIP


Drawing An Octagonal End Roof

Clean Up & Draw in HIPS


Drawing An Octagonal End Roof

Join up external lines


Confirmation of Learning

  • On the A3 Paper Supplied, Draw to scale and Octagonal End Roof based on the following

  • Building Length = 7600mm

  • Building Width = 4500mm

  • Correctly Label all Roof Members


Answer

  • Retain your drawing for future use and submission.


Review Geometry

Angle Between Major Crown End & Centring Rafters = 90⁰

All Angles are plan angles


Clean Up Drawing

Angle Between Crown End Rafters = 45⁰

All Angles are plan angles


Clean Up Drawing

Angle Between Crowns Ends & Hips = 22.5⁰

All Angles are plan angles


Angles formed by the Roof

These angles are the same no matter the size of Roof as it is a Geometric Shape

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

We can say in all cases, no matter the size of the roof

½ End = ½ Span x tan 22.5⁰

= ½ Span x 0.414

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

We can say in all cases, no matter the size of the roof

½ End = ½ Span x 0.414

The Triangles are the same

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

We can say in all cases, no matter the size of the roof

½ End = ½ Span x 0.414

The Triangles are the same

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

We can say in all cases, no matter the size of the roof

½ End = ½ Span x 0.414

Top Plate Projection

= ½ End

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

In all cases, we can say

Full End = ½ Span x 0.414 x 2

All Angles are plan angles


Octagonal Roof Theory

If the angle between the members is constant 22.5⁰

Also in all cases, the full end will be

Full End = ½ Span x 0.828

All Angles are plan angles


Octagonal Roof Theory

These formulas are the same no matter the size of the Roof

Top Plate Projection = ½ Span x 0.414 (Also ½ End)

Full End = ½ Span x 0.828

Top Plate Projection

Full Ends

NOTE – These are all Centreline Measurements


3. Set Out Roof

  • t

22.5° between Roof Members


2. Set Out Roof

(a) Top Plate projection = Tan 22.5°

22.5° between Roof Members


2. Set Out Roof

(b) Octagonal End = 2 x Tan 22.5°

2X


2. WorkedExample

  • Based on the dimensions on the example sheet previous drafting exercise determine,

    Top Plate Projection

    ½ Span x 0.414 = 3800 x 0.414 = 931.5

    Octagonal End

    ½ Span x 0.828 = 3800 x 0.828 = 1863


Confirmation of Learning

  • Based on the full size dimensions given to you by your trainer determine,

  • Top Plate Projection

  • Octagonal End


Confirmation of Learning - Answer

  • Based on the full size dimensions used in your previous drafting exercise determine,

    (Click on Spread Sheet Below to Check Answers)

Entry only allowed in this cell

Note minor discrepancies are rounding errors


Determine Roof Members

  • As with all previous roof

  • We must solve the 1m triangle


Solve 1m Triangle - Example(3a) Rafter Length per plan 1m of Travel of Rafter in Plan

  • Rafter Length per 1m = 1 ÷ Cos 22.5°

    = 1.082

    (This is the Rafter Multiplier)

22.5°


Solve 1m Triangle - Example3(b) Rise per plan 1m Travel of Rafter in Plan

  • Rise = 1 x Tan 22.5°

    = 0.414

    (This is the Rise Multiplier)

1.082

22.5°


Solve 1m Triangle - Example3(c) Hip Rafter Plan Length per 1m Travel of Rafter in Plan

1.082

0.414

Lets have a close look at why the Plan Length of Hip is ALWAYS 1.082 for every 1m of Rafter plan length


Plan Length Hip Rafter

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same


Plan Length Hip Rafter

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 90⁰


Plan Length Hip Rafter

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 45⁰


Plan Length Hip Rafter

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 22.5⁰


Plan Length Hip Rafter

These relationships are constant on all properly built Octagonal Roofs

These angles are always 22.5⁰


Plan Length Hip Rafter

Calculate Plan Length of Hip

Method 1

Plan Hip Length = √((1/2 Span)² (1/2 Span x 0.414)²)

= 1.082 per 1m of Rafter Plan Length

Hip Rafters

1.082


Plan Length Hip Rafter

Calculate Plan Length of Hip

Method 2

Plan Hip Length = ½ Span ÷ cos 22.5⁰

= 1.082 per 1m of Rafter Plan Length

1.082


Plan Length Hip Rafter

Calculate Plan Length of Hip

Method 2

Plan Hip Length = ½ Span ÷ cos 22.5⁰

= 1.082 per 1m of Rafter Plan Length

1.082

The Hip Plan Length is

Always 1.082 x ½ Span


Hip Rafter per 1m of Common Rafter Plan Length

½ Span

½ Span

22.5°

½ Span

In ALL Cases Plan Length Hip =1.082 x ½ Span


Solve 1m Triangle - Example2(c) Hip Rafter Plan Length per 1m Travel of Rafter in Plan

= Tan 22.5° x 1

= 1.082

Note – This is always the case regardless of Pitch


Solve 1m Triangle - Example2(d) Hip Rafter Length per 1m Travel of Rafter in Plan

Hip Length / m = √(0.4142 + 1.0822 )

= √(0.171 + 1.171)

= 1.159

(This is the Hip Rafter Multiplier per 1m of Rafter in plan)

1.082

0.414

22.5°


Solve 1m Triangle - Example2(e) Hip Pitch = Tan-1 (Rise per metre ÷ 1.082)

Hip Pitch = Tan-1(RISE ÷ 1.082)

= Tan-1(0.414 ÷ 1.082)

= Tan-1(0.383)

= 20.9°say 21°

1.082

0.414

1.159

22.5°

Remember this is always 1082


1m Triangle Multipliers - Example

Hip Rafter Multiplier

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

As with previous Roofs the 1m triangle will be the basis of your calculation of Roof Members


Confirmation of Learning

  • On your worksheet Solve the 1m triangle and determine the multipliers for the Roof Pitch given to you by your trainer


1m Triangle - Answer

Click on table below to open Spread sheet


4. RISE

Rise is Calculated to the Pitching Line


4. Rise

(a) Rise = ½ Span x Rise per metre (Note –Rise is calculated to pitching line)

Rise Multiplier

For every 1m of Plan Travel, the Roof Rises 0.414m


4. Rise

(a) Rise = ½ Span x Rise per metre (Note –Rise is calculated to pitching line)

Rise = 3800 x 0.414

= 1574

For every 1m of Plan Travel, the Roof Rises 0.414m


4. RISE

Remember that rise is calculated to the pitching line


4. RISE

The full height is calculated by determining Total Rise


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Total Rise


4. RISE4(b) Total Rise

Allowances

Rafter = 152

Battens = 45

Custom Orb = 17

Ridge Cap = 10

Total = 224

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Note Rafter 190 x 35

38mm Birdsmouth

152 above Pitching Line

(All measurements perpendicular to Rafter)

Total Rise

Pitching Line


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Total Rise

Allowances

Rafter = 152

Battens = 45

Custom Orb = 17

Ridge Cap = 10

Total = 224


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

Total Rise


4. RISE4(b) Total Rise

To determine Plumb Height

We must solve the Hypotenuse

Of this Triangle

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

This must be a Right Angle


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

This must be a 90° - Roof Pitch


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

This also must be a 90° - Roof Pitch


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

This must equal the

Roof Pitch


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

This is a similar triangle that

We used to determine the

Rafter Multiplier


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

Plumb Height = Amount Left On x Rafter Length per metre

= 224 x 1.082

= 242

To determine Hypotenuse

We multiply “Amount Left on

By Rafter Multiplier”


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height = 242

Add answer to Rise

Rise = 1574

Plumb Height = 242

Total Rise = 1816


4. RISE4(b) Total Rise

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height = 242

Add answer to Rise

Rise = 1574

Plumb Height = 164 (152 x 1.082)

Total Rise = 1738

If you wanted to find the height to

Top of Rafter – you would substitute the perpendicular distance to the top of Rafter


Confirmation of Learning

  • Based on data

    • SpanTo be Supplied by Trainer

    • PitchTo be Supplied by Trainer

    • Timber Depth To be Supplied by Trainer

      Timber Depth is used to determine amount left on

      Determine

  • Rise

  • Amount Left On Plumb Height

  • Total Rise

    Click on Spread sheet to determine answers


Confirmation of Learning - Answer

  • Based on data

    • SpanTo be Supplied by Trainer

    • PitchTo be Supplied by Trainer

    • Timber Depth To be Supplied by Trainer

      Timber Depth is used to determine amount left on

      Determine

  • Rise

  • Amount Left On Plumb Height

  • Total Rise

    Click on Spread sheet to determine answers


(5) Major Crown End Rafter

  • Centreline Length

  • How far does it travel in “Plan” ?


(5) Major Crown End Rafter

  • Centreline Length

  • How far does it travel in “Plan” ?

Side Elevation

Rafter Travels to

Gathering Point

Plan View


(5) Major Crown End Rafter

  • Centreline Length

  • How far does it travel in “Plan” ?


(5) Major Crown End Rafter

  • Centreline Length, Which Multiplier?

  • The Rise must be the same as

  • Common Rafter

Plan Length = ½ Span


(5) Major Crown End Rafter

  • Centreline Length, Which Multiplier?

  • The Rise must be the same as

  • Common Rafter

  • The Plan Length is the same as

  • 1. Common Rafter

Plan Length = ½ Span


(5) Major Crown End Rafter

  • Centreline Length, Which Multiplier?

  • The Rise must be the same as

  • Common Rafter

  • The Plan Length is the same as

  • 1.Common Rafter

  • The Pitch must be the same as

  • 1. Common Rafter

Plan Length = ½ Span


(5) Major Crown End Rafter

  • Centreline Length, Which Multiplier?

  • The Rise must be the same as

  • Common Rafter

  • The Plan Length is the same as

  • 1.Common Rafter

  • The Pitch must be the same as

  • 1. Common Rafter

We use the Common Rafter Multiplier = Rafter Length per metre


1m Triangle Multipliers

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°


(5) Major Crown End Rafter

  • Centreline Length = ½ Span x Rafter Length per m

  • How far does it travel in “Plan” ?


Worked ExampleExercise 5a

  • Determine Major Crown End Centreline Length

  • Span = 7600

  • Pitch = 22.5°

    Centreline Length = Plan Length x Rafter Length per m

    Note– Plan Length = ½ Span

    Centreline Length = 3800 x 1.082

    = 4112


Confirmation of Learning Exercise 5a

  • Based on data given to you by you trainer determine,

    Centreline Length Major Crown


Confirmation of Learning - AnswerExercise 5a

  • Based on data given to you by you trainer determine,

    Centreline Length Major Crown

    Click on Spread Sheet to determine answers


5. Major Crown End

(b) True Length

How far does it Travel in Plan ?


5. Major Crown End

(b) True Length

How far does it Travel in Plan ?

Travels to edge of

Centring Rafter

Major Crown End


5. Major Crown End

(b) True Length

How far does it Travel in Plan ?


5. Major Crown End

(b) True Length= (½ Span – ½ Rafter) x Rafter Length per m


Worked ExampleExercise 5b

  • Determine Major Crown End Centreline Length

  • Span = 7600

  • Pitch = 22.5°

  • Rafter Width = 35mm (1/2 Rafter = 35 ÷ 2)

  • True Length= Plan Length x Rafter Length per m

    • Note Plan Length = ½ Span – ½ Rafter

      True Length = (3800 – (35 ÷ 2)) x 1.082

      = (3800 – 17.5) x 1.082

      = 3782.5 x 1.082

      = 4093


Confirmation of LearningExercise 5a

  • Based on data given to you by you trainer determine,

    True Length Major Crown End Rafter


Confirmation of Learning - AnswerExercise 5a

  • Based on data given to you by you trainer determine,

    True Length Major Crown End Rafter

    Click on Spread Sheet to determine answers


5. Major Crown End(i) Plumb Cut Graphically


  • 5. Major Crown End(i) Plumb Cut Graphically

Establish False Top Plate


  • 5. Major Crown End(i) Plumb Cut Graphically

Establish ½ Span


  • 5. Major Crown End(i) Plumb Cut Graphically

Establish Rise


  • 5. Major Crown End(i) Plumb Cut Graphically

Plumb Cut

Establish Crown End Rafter


  • 5. Major Crown End(i) Plumb Cut Graphically

Plumb Cut

  • Establish Crown End Rafter

  • Rise is Same as Common Rafter

  • Plan Length is Same as Common Rafter


  • 5. Major Crown End(i) Plumb Cut Graphically

Plumb Cut

  • Establish Crown End Rafter

  • Rise is Same as Common Rafter

  • Plan Length is Same as Common Rafter

  • Plumb Cut must be the same as Common Rafter


Confirmation of Learning

  • On the Drawing previously developed based on data given to you by your Trainer by the Graphical Method shown to you develop on an A3 Sheet,

  • (Trainer should select a pitch between 15 to 35°)

    Plumb Cut - Major Crown End


Confirmation of Learning - Answer

  • On the Drawing previously developed based on data given to you by your Trainer by the Graphical Method shown to you develop on an A3 Sheet,

    Plumb Cut - Major Crown End

    - Print Answer Drawing 1 on a clear sheet to compare with learners submissions will provide angles from 15 to 35°


Answer Drawing 1 – Click on Drawing to Open File


  • 5. Major Crown End(ii) Plumb Cut – Steel Square Method


Plumb Cut – Steel Square Method5. (ii) – Worked Example

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

Rafter Plumb Cut

Rise = 0.414 ÷ 2

= 0.207

Run = 1.000 ÷ 2

= 0.500

Rise

Run


Plumb Cut – Steel Square Method5. (ii) – Worked Example

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

Rafter Plumb Cut

Rise = 414 ÷ 2

= 207

Run = 1000 ÷ 2

= 500

Rise = 207

Run = 500


Plumb Cut – Steel Square Method5. (ii)

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

Rafter Plumb Cut

The Steel Square relies on principle of similar triangles

If we reduce the 1m by half the angles will stay the same

Rise

Run


Confirmation of Learning

  • Based on the Roof Pitch given to you by the Trainer, Determine the required measurements to set the Steel Square for

    • Plumb Cut Major Crown


Confirmation of Learning - Answer

  • Based on the Roof Pitch given to you by the Trainer, Determine the required measurements to set the Steel Square for

    • Plumb Cut Major Crown

    • Click on Spread Sheet for Answers


Plumb Cut Offset Method


5. Major Crown End(ii) Plumb Cut Offset Method

Total of Internal angles of Triangle formed by Roof = 180°


5. Major Crown End(ii) Plumb Cut Offset Method

In a Right Angled Triangle one of the angles = 90°


5. Major Crown End(ii) Plumb Cut Offset Method

The other 2 angles must = 90°

(180° – 90° = 90°)


5. Major Crown End(ii) Plumb Cut Offset Method

Therefore this angle

Must = 90° - Roof Pitch


5. Major Crown End(ii) Plumb Cut Offset Method

Therefore this angle

= 90° - 22.5°

= 67.5°


5. Major Crown End(ii) Plumb Cut Offset Method

This Triangle is formed by the Roof


5. Major Crown End(ii) Plumb Cut Offset Method

A SIMILAR triangle is also formed in this position


5. Major Crown End(ii) Plumb Cut Offset Method

As the triangles are SIMILAR these angles must be the same


5. Major Crown End(ii) Plumb Cut Offset Method

This Angle must = 90° - Roof Pitch

= 67.5°


5. Major Crown End(ii) Plumb Cut Offset Method

This Angle must = 90° - Roof Pitch

= 67.5°


5. Major Crown End(ii) Plumb Cut Offset Method

If we mark a square line at Top of Rafter & Extend Base


5. Major Crown End(ii) Plumb Cut Offset Method

A Triangle is Formed


5. Major Crown End(ii) Plumb Cut Offset Method

This angle is the same as the Roof Pitch


5. Major Crown End(ii) Plumb Cut Offset Method

This angle must be 90°


5. Major Crown End(ii) Plumb Cut Offset Method

This angle must be 90° - Roof Pitch


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

1.082

0.414

1.159

22.5°


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

1.082

0.414

1.159

22.5°

Therefore we can use the same multipliers to determine its dimensions


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

1.159

What is the Pitch angle of this triangle?


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

Pitch Angle = 22.5°

1.159

What is the Plan Length?


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

Pitch Angle = 22.5°

Plan Length

= 152 + 38

= 190

1.159

What is the Plan Length?


5. Major Crown End(ii) Plumb Cut Offset Method

This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter

Pitch Angle = 22.5°

This length is

Similar to

The Rise

1.159

Offset = Rise Multiplier x Plan Length

= 0.414 x 190

= 77mm


Worked Example - 1

  • Roof Pitch 22.5°

  • Timber Depth190

    = (Tan 22.5°) x 190

    = 0.414 x 190

    = 79mm


5. Major Crown End(ii) Plumb Cut Offset Method

  • There 2 Formulas to Determine the Plumb

  • = Tan (Roof Pitch°) x Timber Depth or

  • = Rise per m of Rafter x Timber Depth

    (The first formula is probably the easiest as the second formula gets complicated with hips)


Worked Example - 1

  • Roof Pitch 22.5°

  • Timber Depth190

    = (Tan 22.5°) x 190

    = 0.414 x 190

    = 79mm


Worked Example - 2

  • Roof Pitch 22.5°

  • Timber Depth190

    = 0.414 x 190

    = 79mm


5. Major Crown End(ii) Plumb Cut Offset Method

  • Pattern Rafter (90 x 45)

90


5. Major Crown End(ii) Plumb Cut Offset Method

  • Pattern Rafter (90 x 45)

  • Mark Square Line

90


5. Major Crown End(ii) Plumb Cut Offset Method

  • Pattern Rafter (90 x 45)

  • Mark Square Line

  • Determine Plumb Cut Offset and Mark Out= 90 x Rise per 1m of Rafter in plan or 90 x (Tan 22.5°)

    = 90 x 0.414

    = 37mm

90

37


5. Major Crown End(ii) Plumb Cut Offset Method

  • Pattern Rafter (90 x 45)

  • Mark Square Line

  • Determine Plumb Cut Offset and Mark Out90 x 0.414= 37mm

  • Mark Plumb Cut

Plumb Cut

90

37


Worked Example

  • Based on the pitch of 25°and using a 150mm Deep Rafter determine ,

    Plumb Cut Offset- Major Crown End

    = 190 x Rise per 1 metre of Rafter in plan

    = 0.414 x 190mm

    = 79mm


Worked Example - Answer


Confirmation of Learning

  • Based on the pitch & Timber Width supplied by the Trainer determine ,

    Plumb Cut Offset- Major Crown End

    On the Supplied A4 sheet demonstrate the set out of the “Plumb Cut”


Confirmation of Learning - Answer

  • Based on the pitch & Timber Width supplied by the Trainer determine ,

    Plumb Cut Offset- Major Crown End

    On the Supplied A4 sheet demonstrate the set out of the “Plumb Cut”

    Click on Spreadsheet below to generate Answers


6.Minor Crown End Rafters

Minor Crown End Rafters join in a similar manner to a hip rafter

Major Crown End Rafter

Minor Crown End Rafter


(6) Minor Crown End Rafters

  • Centreline Length

  • How Far does it Travel in plan?

Radius = ½ Span

Octagonal End Based on Semi Circle


(6) Minor Crown End Rafters

  • Centreline Length

  • How Far does it Travel in plan?

Plan Length = ½ Span

Octagonal End Based on Semi Circle

Major Crown is a Radius


(6) Minor Crown End Rafters

  • Centreline Length

  • How Far does it Travel in plan?

Plan Length = ½ Span

Octagonal End Based on Semi Circle

Major Crown is a Radius

Minor Crown also is a Radius


(6) Minor Crown End Rafters

  • Centreline Length

  • How Far does it Travel in plan?

  • Plan Length = ½ Span

Minor Crown End

Minor Crown End Rafters travel to Gathering Point

Minor Crown End

Plan Length = ½ Span


(6) Minor Crown End Rafters

  • Centreline Length

  • Determine Centreline Length:Which Multiplier?

  • The Rise be same as

  • Common Rafter &

  • Major Crown End Rafter

Minor Crown End

Minor Crown End

Plan Length = ½ Span


(6) Minor Crown End Rafters

  • Centreline Length

  • Determine Centreline Length:Which Multiplier?

The Rise be same as

Common Rafter &

Major Crown End Rafter

The Plan Length is the same as

Common Rafter &

Major Crown End Rafter

Minor Crown End

Minor Crown End

Plan Length = ½ Span


(6) Minor Crown End Rafters

  • Centreline Length

  • Determine Centreline Length:Which Multiplier?

The Rise be same as

Common Rafter &

Major Crown End Rafter

The Plan Length is the same as

Common Rafter &

Major Crown End Rafter

The Pitch must be the same as

Common Rafter &

Major Crown End Rafter

Minor Crown End

Minor Crown End

Plan Length = ½ Span


(6) Minor Crown End Rafters

  • Centreline Length

  • Determine Centreline Length:Which Multiplier?

The Rise be same as

Common Rafter &

Major Crown End Rafter

The Plan Length is the same as

Common Rafter &

Major Crown End Rafter

The Pitch must be the same as

Common Rafter &

Major Crown End Rafter

Minor Crown End

Minor Crown End

We use the Common Rafter Multiplier = Rafter Length per metre


1m Triangle Multipliers

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°


(6) Minor Crown End Rafters

  • Centreline Length = Plan Length x Rafter Length per m

  • Note - Plan Length = ½ Span(Which is the same as the Major Crown)

Plan Length = ½ Span


Worked ExampleExercise 6a

  • Determine Minor Crown End Centreline Length

  • Span = 7600

  • Pitch = 22.5°

    Centreline Length = Plan Length x Rafter Length per m

    Note– Plan Length = ½ Span

    Centreline Length = 3800 x 1.082

    = 4112


Confirmation of LearningExercise 6a

  • Based on data given to you by you trainer determine,

    True Length Minor Crown End Rafter


Confirmation of Learning - AnswerExercise 6a

  • Based on data given to you by you trainer determine,

    Centreline Length Major Crown

    Click on Spread Sheet to determine answers


(6) Minor Crown End Rafters

To Determine the True Length we must determine the reduction in length from the Centreline Length

This is called the Shortening

Major Crown End Rafter

Minor Crown End Rafter


(6) Minor Crown End Rafters(b) Shortening

There are 2 methods to determine the Shortening

Mathematically

Graphically

Major Crown End Rafter

Minor Crown End Rafter


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

Remember Centreline Plan Length = ½ Span

Major Crown End Rafter

Minor Crown End Rafter


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

  • Rafter travels to Intersection of

  • Centring Rafter &

  • Major Crown


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

The Rafters Plan length is reduced by

√(½ Rafter2 + ½ Rafter2)

We know form our previous study

Of HIP ROOFS that this can be

simplified to

½ Rafter x 1.414

Note

1.414 = √2

Major Crown End Rafter

Shortening

Minor Crown End Rafter


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

Shortening = ½ Rafter x 1.414

Note

1.414 = √2

Major Crown End Rafter

Shortening

Minor Crown End Rafter


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

Shortening = ½ Rafter x 1.414

Worked Example

Rafter = 35mm

Shortening = ½ Rafter x 1.414

= (35 ÷ 2) x 1.414

= 17 x 1.414

= 24mm

Note

1.414 = √2

Major Crown End Rafter

Shortening

Minor Crown End Rafter


Confirmation of Learning

  • Determine the shortening of the Rafter Width nominated by your trainer.

  • Note – this is a mathematical exercise and the width need not be an orderable width


Confirmation of Learning - Answer

  • Determine the shortening of the Rafter Width nominated by your trainer.

  • Note – this is a mathematical exercise and the width need not be an orderable width.

    • Click On Spread sheet to generate answers


(6) Minor Crown End Rafters

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically

Shortening = ½ Rafter x 1.414

Worked Example

Rafter = 35mm

Shortening = ½ Rafter x 1.414

= (35 ÷ 2) x 1.414

= 17 x 1.414

= 24mm

Note

1.414 = √2

Major Crown End Rafter

Shortening

This is a relatively easy calculation if all Roof members are the same thickness

If the Centring & Major Crown Rafters are different thicknesses you should consider

Using the “Graphical Method”

Minor Crown End Rafter


6. Minor Crown End Rafter(b)(ii) Shortening of Crown End Rafters - Graphically

  • You should develop an understanding of this method

    • It works on any Roof

    • It develops all bevels & shortenings

    • No formulas to remember only a method


6. Minor Crown End Rafter(b)(ii) Shortening of Crown End Rafters - Graphically

Draw Centrelines

MINOR CROWN END RAFTER

CENTRING RAFTERS

MAJOR CROWN END RAFTER

Gathering Point

MINOR CROWN END


6. Minor Crown End Rafter(b)(ii) Shortening of Crown End Rafters - Graphically

MINOR CROWN END RAFTER

Draw Timber Thicknesses at full size

In this case all Roof Members

Are 35mm thick

i.e. 17.5 either side of Centreline

CENTRING RAFTERS

Gathering Point

MAJOR CROWN END RAFTER

MINOR CROWN END


6. Minor Crown End Rafter(b)(ii) Shortening of Crown End Rafters - Graphically

Dimension Shortening from Centreline

Note Zoomed in for Clarity

CENTRING RAFTERS

MINOR CROWN END RAFTER

Gathering Point

MAJOR CROWN END RAFTER

MINOR CROWN END


6. Minor Crown End Rafter(b)(ii) Shortening of Crown End Rafters - Graphically

  • To put this drawing into practical use

  • you need to understand that

  • This is a TRUE representation of the actual

  • Intersection of Roof members in PLAN

  • If we can transfer these dimension to our

  • Rafter we can determine the True length and

  • All required edge bevels

CENTRING RAFTERS

MINOR CROWN END RAFTER

Gathering Point

MAJOR CROWN END RAFTER

MINOR CROWN END


6. Minor Crown End Rafterb) ii. Shortening from Centreline Length - Graphically

Side Elevation

Select a timber of Suitable Length to use as the Minor Crown Rafter


6. Minor Crown End Rafterb) ii. Shortening from Centreline Length - Graphically

Side Elevation

Mark Out Centreline Length as determined in 6a


6. Minor Crown End Rafterb) ii. Shortening from Centreline Length - Graphically

Side Elevation

Mark Out Plumb Cuts as determined in 6c


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Side Elevation

Mark Lines square on Top of Rafter


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

You Rafter should now be marked with

Centreline Length

Centreline Length

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

These lines are Plumb

Side Elevation


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

A line 90° to Plumb will be level

Side Elevation


6. Minor Crown End Rafter) ii. Shortening from Centreline Length - Graphically

The measurements on the drawing

are in the level plane.

The set out must also be in the level plane

Side Elevation

Mark Out Plumb Cuts as determined in 6c


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Side Elevation

Mark Out a level line approximately ½ way down the top plumb cut


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

All measurements are taken from Centreline Length

Mark Centreline Shortening Distance

Side Elevation

Plan View

Transfer plan measurements determined in 6 (b) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Mark Line using Plumb Cut Bevel

Side Elevation

Plan View

Transfer plan measurements determined in 6 (d) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Which represents

this point in PLAN

Mark Line using Plumb Cut Bevel

Side Elevation

Plan View

Transfer plan measurements determined in 6 (d) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Mark Line square on Top of Rafter

Isometric View

Mark Out Plumb Cuts as determined in 6c


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Mark Centreline

Isometric View

Mark Out Plumb Cuts as determined in 6c


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Mark Edge Bevel Shortening Distance

Transfer plan measurements determined in 6 (d) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Mark Line using Plumb Cut Bevel

Transfer plan measurements determined in 6 (d) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Which represents

these points in PLAN

Mark Line using Plumb Cut Bevel

Transfer plan measurements determined in 6 (d) (ii)


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Mark Lines square

on Top of Rafter

Centreline Shortening

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

You Rafter should now be marked with

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Thickness Centreline Mark

Thickness Centreline Mark

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Centreline Shortening

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Thickness Centreline Mark

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

This is the Shape of the

end of the Rafter in Plan

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

This is the Shape of the

End of the Rafter

It is based on the measurements

Determined previously

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

We now replicate what we see in Plan on the Actual Rafter

This is the Shape of the

End of the Rafter

It is based on the measurements

Determined previously

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Draw Lines Starting From

Edge Bevel Shortening

This is the Shape of the

End of the Rafter

It is based on the measurements

Determined previously

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

Draw Lines Starting From

Edge Bevel Shortening to Intersection of

Centreline Shortening & Thickness Centreline to

This is the Shape of the

End of the Rafter

It is based on the measurements

Determined previously

Plan View

Isometric View


6. Minor Crown End Rafterd) ii. Shortening from Centreline Length - Graphically

The Rafter is then cut to

This Shape

The length has also been shortened

And ready to be installed

Plan View

Isometric View

Mark Out Plumb Cuts as determined in 6c


Confirmation of Learning

  • Develop in Plan the Shortening of an Octagonal End Roof

    • Timber Widths to be supplied by Trainer is 45mm thick

  • On Timber Supplied Develop required shortening based on a pitch of 27° & ½ Span of 300mm

    • Timber to be supplied by Trainer


  • Confirmation of Learning - Answers

    • Develop in Plan the Shortening of an Octagonal End Roof

      • Timber Widths to be supplied by Trainer is 45mm thick

        Submission should be as Answer 1

  • On Timber Supplied Develop shortening based on a pitch of 27° & ½ Span of 300mm

    • Timber to be supplied by Trainer


  • Confirmation of Learning – Answer 1

    • Shortening in Plan


    Confirmation of Learning – Answer 2

    • Shortening in Elevation


    (6) Minor Crown End Rafters

    (c) True Length

    • Rafter travels to Intersection of

    • Centring Rafter &

    • Major Crown


    (6) Minor Crown End Rafters

    (c) True Length

    How far does it travel in plan?

    Remember Centreline Plan Length = ½ Span

    True Length in Plan = ½ Span – ½ Rafter x 1.414

    Major Crown End Rafter

    Rafter Plan Reduction

    Minor Crown End Rafter


    (6) Minor Crown End Rafters

    (b) True Length = Plan Length x Rafter Length per m

    Note – Plan Length = (½ Span – Shortening)) or

    = (½ Span – (½ Rafter x 1.414))


    Worked Example

    • Minor Crown True Length =

      • Plan Length x Rafter Length per m

      • Plan Length = (½ Span – ½ Rafter x 1.414)

        = (3800 –(35 ÷ 2) x 1.414) x 1.082

        = (3800 – 17.5 x 1.414) x 1.082

        = (3800 – 25) x 1.082

        = 3775 x 1.082

        = 4085


    Confirmation of Learning

    • Determine the True Length of the Minor Crown End Rafter based on data given to you by the Trainer.

      • SpanTo be Supplied by Trainer

      • PitchTo be Supplied by Trainer

      • Timber Width To be Supplied by Trainer


    Confirmation of Learning - Answer

    • Determine the True Length of the Minor Crown End Rafter based on data given to you by the Trainer.

      • SpanTo be Supplied by Trainer

      • PitchTo be Supplied by Trainer

      • Timber Width To be Supplied by Trainer

        Click on Spread Sheet to check answers


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    As we use the Common Rafter multiplier we can use the Common Rafter Plumb Cut

    The following slides demonstrate how to develop the plumb cut


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    i. Graphically

    Extend Construction Lines

    Perpendicular to ends of Rafter


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    i. Graphically

    Establish False Top Plate


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    i. Graphically

    Establish Plan Length


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    i. Graphically

    Establish Rise


    (6) Minor Crown End Rafters

    (c) Plumb Cut Minor Crown

    i. Graphically

    • Draw in Rafter

    • Establish Plumb Cut

    • Establish Roof Pitch


    Confirmation of Learning

    • Using your previous drafting exercise determine graphically,

      Plumb Cut - Minor Crown End


    6. Minor Crown End Rafters(e) Edge Bevel Development

    In Plan this Angle = 45⁰


    6. Minor Crown End Rafters(e) Edge Bevel Development

    In Plan this Angle = 45⁰

    When can you use the plan angle?


    6. Minor Crown End Rafters(e) Edge Bevel Development

    In Plan this Angle = 45⁰

    When can you use the plan angle?

    When you use a power tool such as

    Drop Saw

    Power Saw etc


    Edge Bevel Minor Crown End RaftersPlan Angle

    Plan Angle = 45⁰

    Plan Angle = 90⁰


    Edge Bevel Minor Crown End RaftersPlan Angle

    Plan Angle = 45⁰

    Both Sides Must

    Be Equal

    Plan Angle = 90⁰


    Edge Bevel Minor Crown End RaftersPlan Angle

    Both Sides Must

    Be Equal

    Plan Angle = 45⁰

    Plan Angle = 90⁰

    When Can You Use The Plan For the Edge Bevel ?


    Edge Bevel Minor Crown End RaftersPlan Angle

    Both Sides Must

    Be Equal

    Plan Angle = 45⁰

    Plan Angle = 90⁰

    When Can You Use The Plan For the Edge Bevel ?


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Minor Crown True Angle


    Edge Bevel Minor Crown End RaftersTrue Angle

    What members form the triangle?


    Edge Bevel Minor Crown End RaftersTrue Angle

    Centreline Length Rafter

    What members form the triangle?


    Edge Bevel Minor Crown End RaftersTrue Angle

    Centreline Length Rafter

    If this angle is 45⁰

    What members form the triangle?


    Edge Bevel Minor Crown End RaftersTrue Angle

    Centreline Length Rafter

    This angle must 45⁰

    What members form the triangle?


    Edge Bevel Minor Crown End RaftersTrue Angle

    Centreline Length Rafter

    Both these sides must be equal

    What members form the triangle?


    Edge Bevel Minor Crown End RaftersTrue Angle

    Centreline Length Rafter

    This line runs parallel with the top

    Of the Rafter

    Which is level

    What members form the triangle?


    7.Plan Length Hip Rafter

    The Octagonal Roof is a geometric shape

    No matter the size the angles are always the same


    7. Plan Length Hip Rafter

    The Octagonal Roof is a geometric shape

    No matter the size the angles are always the same


    7.Plan Length Hip Rafter

    The Octagonal Roof is a geometric shape

    No matter the size the angles are always the same

    These angles are always 90⁰


    7.Plan Length Hip Rafter

    The Octagonal Roof is a geometric shape

    No matter the size the angles are always the same

    These angles are always 45⁰


    7.Plan Length Hip Rafter

    The Octagonal Roof is a geometric shape

    No matter the size the angles are always the same

    These angles are always 22.5⁰


    7.Plan Length Hip Rafter

    These relationships are constant on all properly built Octagonal Roofs

    These angles are always 22.5⁰


    7.Plan Length Hip Rafter

    Calculate Plan Length of Hip

    Plan Hip Length = ½ Span ÷ cos 22.5⁰

    = ½ Span ÷ 0.924

    = 1.082 (That it is equal to the Rafter Multiplier is a coincidence in this case)

    This is a fixed relationship

    Regardless of pitch


    7.Plan Length Hip Rafter

    Calculate Plan Length of Hip

    Simple Rule

    Plan Hip Length = ½ Span x 1.082 (That it is equal to the Rafter Multiplier is a coincidence)

    This is a fixed relationship

    Regardless of pitch


    Worked Example7. Plan Length of Hip

    • Determine Plan Length of Hip

      • Span7600

        Plan Length = ½ Span x 1.082

        = (7600 ÷ 2) x 1.082

        = 3800 x 1.082

        = 4112


    1m Triangle Multipliers

    Hip Rafter Multiplier

    1.082

    0.414

    1.159

    20.9°

    22.5°

    When we solved the 1m Triangle we developed the Hip Multiplier


    8.Centerline Length of Hip Rafter

    As with all Roof members to determine the length we

    Determine how far it travels in plan

    Apply the multiplier


    8.Centerline Length of Hip Rafter

    As with all Roof members to determine the length we

    Determine how far it travels in plan ?

    Apply the multiplier


    1m Triangle Multipliers

    Hip Rafter Multiplier

    1.082

    0.414

    1.159

    20.9°

    22.5°

    If we remember our multiplier is derived on the following premise

    Hip Rafter Length for every 1m metre of Rafter in Plan


    1m Triangle Multipliers

    Hip Rafter Multiplier

    1.082

    0.414

    1.159

    20.9°

    22.5°

    If we remember our multiplier is derived on the following premise

    Hip Rafter Length for every 1m metre of Rafter in Plan

    It is the Plan Length of the Rafter that we must determine!


    8.Centerline Length of Hip Rafter

    How far does the Rafter Travel in plan to intersect the Hip in plan?


    8.Centerline Length of Hip Rafter

    How far does the Rafter Travel in plan to intersect the Hip in plan?

    The Rafter travels ½ Span


    8.Centerline Length of Hip Rafter

    How far does the Rafter Travel in plan to intersect the Hip in plan?

    The Rafter travels ½ Span


    8.Centerline Length of Hip Rafter

    As with all Roof members to determine the length we

    Determine how far it travels in plan = ½ Span

    Apply the multiplier


    8.Centerline Length of Hip Rafter

    As with all Roof members to determine the length we

    Determine how far it travels in plan = ½ Span

    Apply the multiplier


    1m Triangle Multipliers

    Hip Rafter Multiplier

    1.082

    0.414

    1.159

    20.9°

    22.5°

    Hip Rafter Multiplier for 22.5° = 1.159


    8.Centerline Length of Hip Rafter

    As with all Roof members to determine the length we

    Determine how far it travels in plan = ½ Span

    Apply the multiplier = As per 1m triangle multiplier


    8.Centerline Length of Hip Rafter

    Centreline Length of Hip = Plan Length x Hip Rafter Length per m

    Note - Plan Length = ½ Span


    Worked Example

    • Determine Centreline length of Hip Rafter

      • Span7600mm

      • Pitch22.5°

      • Hip Multiplier1.159

        Centreline Length of Hip = Plan Length x Hip Rafter Length per m

        Note- Plan Length = ½ Span

        = (7800 ÷ 2) x 1.159

        = 3800 x 1.159

        = 4404


    Confirmation of Learning

    • Determine Centreline length of Hip Rafter

      • SpanSupplied by Trainer

      • PitchSupplied by Trainer

      • Hip MultiplierAs derived from pitch


    Confirmation of Learning - Answer

    • Determine Centreline length of Hip Rafter

      • SpanSupplied by Trainer

      • PitchSupplied by Trainer

      • Hip MultiplierAs derived from pitch

        Click on Spread Sheet for Answers


    9. Hip Plumb Cut


    9a.Hip Plumb - Graphically

    Draw in False Top Plate


    9a.Hip Plumb - Graphically

    Establish Rise of Roof

    By drawing in Common Rafter


    9a.Hip Plumb - Graphically

    Draw in Ridge Line


    9a.Hip Plumb - Graphically

    Rotate Length of Hip onto Ridge


    9a.Hip Plumb - Graphically

    Extend this length up to false Top Plate


    9a.Hip Plumb - Graphically

    Establish the rise

    The Rise will be the same as the

    Common Rafter Rise


    9a.Hip Plumb - Graphically

    Draw in Hip Rafter


    9a.Hip Plumb - Graphically

    Plumb Cut Hip

    Plumb Cut as Shown


    Confirmation of Learning

    • Using the A3 drawing previously developed using the method outlined

    • Develop Plumb Cut - Graphically


    Confirmation of Learning - Answer

    • Using the A3 drawing previously developed using the method outlined

    • Develop Plumb Cut – Graphically

    • Click on Spread Sheet to determine Hip pitch based on Common Rafter Pitch, Using Pitching template on next slide to confirm


    Answer Drawing 1 – Click on Drawing to Open File


    9b.Hip Plumb – Steel Square Method

    Hip Plumb Cut

    1.082

    0.414

    1.159

    Rise

    20.9°

    22.5°

    Hip Run

    Reduce Hip Triangle to Steel Square


    9b.Hip Plumb – Steel Square Method

    Hip Plumb Cut

    1.082

    0.414

    1.159

    Rise

    20.9°

    22.5°

    Hip Run

    Reduce Hip Triangle to Steel Square

    Divide by 2


    9b.Hip Plumb – Steel Square Method

    Hip Plumb Cut

    1.082

    0.414

    1.159

    Rise

    20.9°

    22.5°

    Hip Run

    Reduce Hip Triangle to Steel Square

    Divide by 2

    Rise = 207

    Hip Run = 541


    9b.Hip Plumb – Steel Square Method

    Hip Plumb Cut

    1.082

    0.414

    1.159

    207

    20.9°

    22.5°

    541

    Reduce Hip Triangle to Steel Square

    Divide by 2

    Rise = 207

    Hip Run = 541


    9b.Hip Plumb – Offset Method


    9b.Hip Plumb – Offset Method

    Common Rafter Multiplier

    1.082

    0.414

    1.159

    20.9°

    22.5°

    Plumb Cut Offset = Tan(Hip Pitch°) x Timber Depth or

    = (Timber Depth ÷ 1.082) x Rise


    Worked Example 1Using Derived Hip Pitch

    Roof Pitch = 22.5

    Hip Pitch= 20.9°

    Timber Depth = 190mm

    = (Tan 20.9°) x Timber Depth

    = 0.382 x 190

    = 73mm


    Worked Example 2Using 1m Trainagle Data

    Roof Pitch = 22.5

    Rise = 0.414

    Timber Depth = 190mm

    = (Timber Depth ÷ 1.082) x 0.414

    = (190 ÷ 1.082) x 0.414

    = 175.6 x 0.414

    = 73mm


    10. True Length Hip Rafter

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    10 True Length Hip Raftera) Shortening

    We must determine how

    Far in the direction of the

    Rafter does the hip travel

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Raftera) Shortening

    We must determine the

    Distance from ½ Span to

    The plan length

    This is called the shortening

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Raftera) Shortening

    We Reduce from ½ Span

    ½ Ridge Thickness

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Raftera) Shortening

    We Reduce from ½ Span

    ½ Ridge Thickness

    ½ Rafter x 1.414

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Raftera) Shortening

    We Reduce from ½ Span

    ½ Ridge Thickness

    ½ Rafter x 1.414

    This Reduction is call the Shortening

    = ½ Ridge Thickness + ½ Rafter x 1.414

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Raftera) Shortening – Worked Example

    All members 35mm

    = ½ Ridge Thickness + (½ Rafter x 1.414)

    = 17.5 + (17.5 x 1.414)

    = 17.5 + 25

    = 42.5mm

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    Conformation of Learning

    • Based on Data given to you by the Trainer

      • Ridge Thickness Supplied by Trainer

      • Rafter ThicknessSupplied by Trainer

    • Determine the Shortening


    9. True Length Hip Raftera (i) Edge Bevel – Graphically

    This Dimension measured from True Length in Plan


    9. True Length Hip Raftera (iii) Edge Bevel – Graphically

    Isometric Elevation


    9. True Length Hip Raftera (iii) Edge Bevel – Graphically

    Isometric Elevation

    This measurement

    Is at 90° to the Plumb Cut


    9. True Length Hip Raftera (iii) Edge Bevel – Graphically

    Isometric Elevation

    Develop Edge Bevel


    Confirmation of Learning

    • On Page xx develop the edge bevel graphically

    • With Timber Supplied

      • Mark Plumb Cut

      • Mark Centreline Shortening

      • Mark Edge Bevels


    Confirmation of Learning - Answer

    • On Page xx develop the edge bevel graphically

      • Pitch

      • Span

    • With Timber Supplied

      • Mark Centreline Length

      • Mark Plumb Cut

      • Mark Centreline Shortening

      • Mark Edge Bevels


    9. True Length Hip Rafter(b) True Plan Length

    Determine Plan Length

    = ½ Span - Shortening

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Rafter(b) True Plan Length – Worked Example

    Determine Plan Length

    = ½ Span – Shortening

    = 3800 – 42.5

    = 3757.5

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    Confirmation of Learning

    • Based on the previous exercise and data supplied by the Trainer

      • SpanSupplied by Trainer

    • Determine True Plan Length Hip Rafter


    9. True Length Hip Rafterc Develop Rafter Graphically

    It is possible to not bother with the maths

    And develop from the centreline length all measurements.

    This is the easiest method for complex roof


    9. Minor Crown End Rafterc) Shortening from Centreline Length - Graphically

    Centreline Length

    Mark Lines square

    on Top of Rafter

    Centreline Shortening

    Isometric View


    9. True Length Hip Rafter(b) True Plan Length

    Determine Plan Length

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    Confirmation of Learning

    • On the Supplied sheet of Paper

      • Draw the shortening & edge bevels for the hip

      • On the supplied piece of Timber based on data given to you by your trainer mark out a Hip Rafter Completely

        - Using Any Method


    Confirmation of Learning

    • On the Supplied sheet of Paper

      • Draw the shortening & edge bevels for the hip

      • On the supplied piece of Timber based on data given to you by your trainer mark out a Hip Rafter Completely


    9. True Length Hip Rafter(b) True Length

    Apply Multiplier

    = Plan Length x Hip per 1m Rafter

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    9. True Length Hip Rafter(b) True Length – Worked Example

    Apply Multiplier

    = Plan Length x Hip per 1m Rafter

    = 3757.5 x 1.159

    = 4355

    To determine the True Length

    Determine how far it travels

    Apply the correct multiplier


    Confirmation of Learning

    • Based on the previous exercises determine

    • True Length Hip Rafter


    Creepers

    • Determine Creeper Shortening

    • Determine Long Point Correction

    • Determine 1st Creeper True Length

    • Determine all other Creepers


    Determine Shortening

    These 2 Triangles are similar


    Determine Shortening

    The Ratio between the

    Sides must be equal


    Determine Shortening

    Plan Shortening = ½ Span

    Spacing CL to End


    Determine Shortening

    Plan Shortening = 1.000

    200 0.414

    For an Octagonal Roof

    These are always the same


    Determine Shortening

    Plan Shortening = 2.414

    200


    Determine Shortening

    Plan Shortening = 2.414 x 200


    Creepersa) Shortening

    • Creeper Shortening

    • = (Spacing x 2.414) x Rafter Length /m


    Creepersa) Shortening – Worked Example

    • Creeper Shortening

      • Pitch 22.5°

      • Spacing = 450mm

    • = (Spacing x 2.414) x Rafter Length /m

    • = (450 x 2.414) x 1.082

    • = 1086.3 x 1.082

    • = 1175


    Creepersa) Shortening –at Confirmation of Learning

    • Determine Creeper Shortening

      • PitchSpecified by Trainer

      • Spacing Specified by Trainer


    Creepers - Answera) Shortening –at Confirmation of Learning

    • Determine Creeper Shortening

      • PitchSpecified by Trainer

      • Spacing Specified by Trainer


    Creepers

    • Determine Creeper Shortening

    • Determine Long Point Correction

    • Determine 1st Creeper True Length

    • Determine all other Creepers


    Creepersa) Long Point Correction in plan

    The simplest way is to draw it

    This can be done mathematically but

    It is a convoluted process

    In this the correction is -3mm


    Creepersa) Long Point Correction in plan

    The simplest way is to draw it

    This can be done mathematically but

    It is a convoluted process

    In this the correction is -3mm


    Creepersa) Long Point Correction in plan – Confirmation of Learning

    On an A3 Sheet

    Draw the intersection

    Of the member &

    Determine the Long Point

    Correction


    Creepers - Answera) Long Point Correction in plan – Confirmation of Learning

    On an A3 Sheet

    Draw the intersection

    Of the member &

    Determine the Long Point

    Correction


    Creepers

    • Determine Creeper Shortening

    • Determine Long Point Correction

    • Determine 1st Creeper True Length

    • Determine all other Creepers


    Creepers(c) 1st Creeper

    • = (½ Span + Correction) x Rafter per/m – Creeper Shortening

    • = (3800 -3) x 1.082 – 1175

    • = 3797 x 1.082 – 1175

    • = 4108 – 1175

    • = 2933


    Creepers

    • Determine Creeper Shortening

    • Determine Long Point Correction

    • Determine 1st Creeper True Length

    • Determine all other Creepers


    Creepers(d) Determine Creepers

    • = Previous Creeper – Creeper Shortening

    • = 2933 – 1175

    • = 1758 – 1175

    • = 583


    Creepers(d) Determine Creepers


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