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Octagonal Roof

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Octagonal Roof

- 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

- 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.

- In its most common form

Pitch Angle

- Other Examples

Pitch Angle

Pitch Angle

Pitch Angle

Pitch Angle

½ Span

½ Span

22.5°

½ Span

Plan Lengths

- Determine which side is the “Plan Length”

- Determine which side is the “Plan Length”

- What are the Plan Lengths of these triangles?

Plan Lengths

This Triangle

This Triangle

- A Regular Geometric Shape

- On an A3 drawing sheet conduct the following drafting excercise

Gathering Point is ½ Span Back from edge

Walls are parallel

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

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

Draw Construction Line To Represent End of Building

Draw Construction Line To Represent End of Building

This end is not so important

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

Locate Centring Rafters

(1/2 Span from end)

Find Gathering Point

Scribe Semi Circle with ½ Span as Radius

Draw in Centring Rafters

Draw in Major Crown End

Bisect Centring & Crown End Rafters to form Minor Crown End

Bisect Centring & Crown End Rafters to form Minor Crown End

Extend Lines Perpendicular to Ridge

At ½ End Length

= ½ Span x 0.414

Extend Sides of Building by ½ End Length

= ½ Span x 0.414

Join up external Lines

Draw in Hips

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

Draw Construction Line To Represent End of Building

Draw Construction Line To Represent End of Building

This end is not so important

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

Locate Centring Rafters

(1/2 Span from end)

Find Gathering Point

Scribe Semi Circle with ½ Span as Radius

Draw in Centring Rafters

Draw in Major Crown End

Bisect Centring & Crown End Rafters to form Minor Crown End

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

Extend Lines Perpendicular to Ridge

To intersect with HIP

Extend sides of Building

To intersect with HIP

Clean Up & Draw in HIPS

Join up external lines

- 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

- Retain your drawing for future use and submission.

Angle Between Major Crown End & Centring Rafters = 90⁰

All Angles are plan angles

Angle Between Crown End Rafters = 45⁰

All Angles are plan angles

Angle Between Crowns Ends & Hips = 22.5⁰

All Angles are plan angles

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

All Angles are plan angles

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

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

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

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

- t

22.5° between Roof Members

(a) Top Plate projection = Tan 22.5°

22.5° between Roof Members

(b) Octagonal End = 2 x Tan 22.5°

2X

- 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

- Based on the full size dimensions given to you by your trainer determine,
- Top Plate Projection
- Octagonal End

- 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

- As with all previous roof
- We must solve the 1m triangle

- Rafter Length per 1m = 1 ÷ Cos 22.5°
= 1.082

(This is the Rafter Multiplier)

22.5°

- Rise = 1 x Tan 22.5°
= 0.414

(This is the Rise Multiplier)

1.082

22.5°

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

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 90⁰

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 45⁰

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 22.5⁰

These relationships are constant on all properly built Octagonal Roofs

These angles are always 22.5⁰

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

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

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

½ Span

½ Span

22.5°

½ Span

In ALL Cases Plan Length Hip =1.082 x ½ Span

= Tan 22.5° x 1

= 1.082

Note – This is always the case regardless of Pitch

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°

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

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

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

Click on table below to open Spread sheet

Rise is Calculated to the Pitching Line

(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

(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

Remember that rise is calculated to the pitching line

The full height is calculated by determining 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

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

Total Rise is a 3 Step process

Determine Required Height above Pitching Line Perpendicular to Rafter

Determine Plumb Height

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

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

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

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

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

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

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”

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

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

- 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

- 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

- Centreline Length
- How far does it travel in “Plan” ?

- Centreline Length
- How far does it travel in “Plan” ?

Side Elevation

Rafter Travels to

Gathering Point

Plan View

- Centreline Length
- How far does it travel in “Plan” ?

- Centreline Length, Which Multiplier?

- The Rise must be the same as
- Common Rafter

Plan Length = ½ Span

- 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

- 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

- 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

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

- Centreline Length = ½ Span x Rafter Length per m
- How far does it travel in “Plan” ?

- 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

- Based on data given to you by you trainer determine,
Centreline Length Major Crown

- Based on data given to you by you trainer determine,
Centreline Length Major Crown

Click on Spread Sheet to determine answers

(b) True Length

How far does it Travel in Plan ?

(b) True Length

How far does it Travel in Plan ?

Travels to edge of

Centring Rafter

Major Crown End

(b) True Length

How far does it Travel in Plan ?

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

- 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

- Note Plan Length = ½ Span – ½ Rafter

- Based on data given to you by you trainer determine,
True Length Major Crown End Rafter

- 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

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

- 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

- 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

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

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

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

- 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

- 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

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

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

The other 2 angles must = 90°

(180° – 90° = 90°)

Therefore this angle

Must = 90° - Roof Pitch

Therefore this angle

= 90° - 22.5°

= 67.5°

This Triangle is formed by the Roof

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

This Angle must = 90° - Roof Pitch

= 67.5°

This Angle must = 90° - Roof Pitch

= 67.5°

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

A Triangle is Formed

This angle is the same as the Roof Pitch

This angle must be 90°

This angle must be 90° - Roof Pitch

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

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

1.082

0.414

1.159

22.5°

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

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?

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?

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?

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

- Roof Pitch 22.5°
- Timber Depth190
= (Tan 22.5°) x 190

= 0.414 x 190

= 79mm

- 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)

- Roof Pitch 22.5°
- Timber Depth190
= (Tan 22.5°) x 190

= 0.414 x 190

= 79mm

- 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

- Pattern Rafter (90 x 45)
- Mark Square Line

90

- 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

- 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

- 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

- 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”

- 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

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

Major Crown End Rafter

Minor Crown End Rafter

- Centreline Length
- How Far does it Travel in plan?

Radius = ½ Span

Octagonal End Based on Semi Circle

- Centreline Length
- How Far does it Travel in plan?

Plan Length = ½ Span

Octagonal End Based on Semi Circle

Major Crown is a Radius

- 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

- 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

- 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

- 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

- 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

- 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

Common Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

- 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

- 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

- Based on data given to you by you trainer determine,
True Length Minor Crown End Rafter

- Based on data given to you by you trainer determine,
Centreline Length Major Crown

Click on Spread Sheet to determine answers

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

There are 2 methods to determine the Shortening

Mathematically

Graphically

Major Crown End Rafter

Minor Crown End Rafter

(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

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

- Rafter travels to Intersection of
- Centring Rafter &
- Major Crown

(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

(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

(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

- 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

- 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

(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

- 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

Draw Centrelines

MINOR CROWN END RAFTER

CENTRING RAFTERS

MAJOR CROWN END RAFTER

Gathering Point

MINOR CROWN END

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

Dimension Shortening from Centreline

Note Zoomed in for Clarity

CENTRING RAFTERS

MINOR CROWN END RAFTER

Gathering Point

MAJOR CROWN END RAFTER

MINOR CROWN END

- 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

Side Elevation

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

Side Elevation

Mark Out Centreline Length as determined in 6a

Side Elevation

Mark Out Plumb Cuts as determined in 6c

Side Elevation

Mark Lines square on Top of Rafter

You Rafter should now be marked with

Centreline Length

Centreline Length

Isometric View

These lines are Plumb

Side Elevation

A line 90° to Plumb will be level

Side Elevation

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

Side Elevation

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

All measurements are taken from Centreline Length

Mark Centreline Shortening Distance

Side Elevation

Plan View

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

Mark Line using Plumb Cut Bevel

Side Elevation

Plan View

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

Which represents

this point in PLAN

Mark Line using Plumb Cut Bevel

Side Elevation

Plan View

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

Centreline Length

Mark Line square on Top of Rafter

Isometric View

Mark Out Plumb Cuts as determined in 6c

Centreline Length

Mark Centreline

Isometric View

Mark Out Plumb Cuts as determined in 6c

Mark Edge Bevel Shortening Distance

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

Mark Line using Plumb Cut Bevel

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

Which represents

these points in PLAN

Mark Line using Plumb Cut Bevel

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

Centreline Length

Mark Lines square

on Top of Rafter

Centreline Shortening

Isometric View

You Rafter should now be marked with

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Thickness Centreline Mark

Thickness Centreline Mark

Isometric View

Centreline Length

Plan View

Isometric View

Centreline Length

Centreline Shortening

Plan View

Isometric View

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Plan View

Isometric View

Centreline Length

Centreline Shortening

Edge Bevel Shortening

Thickness Centreline Mark

Plan View

Isometric View

This is the Shape of the

end of the Rafter in Plan

Plan View

Isometric View

This is the Shape of the

End of the Rafter

It is based on the measurements

Determined previously

Plan View

Isometric View

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

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

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

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

- Develop in Plan the Shortening of an Octagonal End Roof
- Timber Widths to be supplied by Trainer is 45mm thick

- Timber to be supplied by Trainer

- 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

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

- Timber to be supplied by Trainer

- Shortening in Plan

- Shortening in Elevation

(c) True Length

- Rafter travels to Intersection of
- Centring Rafter &
- Major Crown

(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

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

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

= (½ Span – (½ Rafter x 1.414))

- 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

- 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

- 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

(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

(c) Plumb Cut Minor Crown

i. Graphically

Extend Construction Lines

Perpendicular to ends of Rafter

(c) Plumb Cut Minor Crown

i. Graphically

Establish False Top Plate

(c) Plumb Cut Minor Crown

i. Graphically

Establish Plan Length

(c) Plumb Cut Minor Crown

i. Graphically

Establish Rise

(c) Plumb Cut Minor Crown

i. Graphically

- Draw in Rafter
- Establish Plumb Cut
- Establish Roof Pitch

- Using your previous drafting exercise determine graphically,
Plumb Cut - Minor Crown End

In Plan this Angle = 45⁰

In Plan this Angle = 45⁰

When can you use the plan angle?

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

Plan Angle = 45⁰

Plan Angle = 90⁰

Plan Angle = 45⁰

Both Sides Must

Be Equal

Plan Angle = 90⁰

Both Sides Must

Be Equal

Plan Angle = 45⁰

Plan Angle = 90⁰

When Can You Use The Plan For the Edge Bevel ?

Both Sides Must

Be Equal

Plan Angle = 45⁰

Plan Angle = 90⁰

When Can You Use The Plan For the Edge Bevel ?

What members form the triangle?

Centreline Length Rafter

What members form the triangle?

Centreline Length Rafter

If this angle is 45⁰

What members form the triangle?

Centreline Length Rafter

This angle must 45⁰

What members form the triangle?

Centreline Length Rafter

Both these sides must be equal

What members form the triangle?

Centreline Length Rafter

This line runs parallel with the top

Of the Rafter

Which is level

What members form the triangle?

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 90⁰

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 45⁰

The Octagonal Roof is a geometric shape

No matter the size the angles are always the same

These angles are always 22.5⁰

These relationships are constant on all properly built Octagonal Roofs

These angles are always 22.5⁰

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

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

- Determine Plan Length of Hip
- Span7600
Plan Length = ½ Span x 1.082

= (7600 ÷ 2) x 1.082

= 3800 x 1.082

= 4112

- Span7600

Hip Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

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

As with all Roof members to determine the length we

Determine how far it travels in plan

Apply the multiplier

As with all Roof members to determine the length we

Determine how far it travels in plan ?

Apply the multiplier

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

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!

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

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

The Rafter travels ½ Span

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

The Rafter travels ½ Span

As with all Roof members to determine the length we

Determine how far it travels in plan = ½ Span

Apply the multiplier

As with all Roof members to determine the length we

Determine how far it travels in plan = ½ Span

Apply the multiplier

Hip Rafter Multiplier

1.082

0.414

1.159

20.9°

22.5°

Hip Rafter Multiplier for 22.5° = 1.159

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

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

Note - Plan Length = ½ Span

- 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

- Determine Centreline length of Hip Rafter
- SpanSupplied by Trainer
- PitchSupplied by Trainer
- Hip MultiplierAs derived from pitch

- Determine Centreline length of Hip Rafter
- SpanSupplied by Trainer
- PitchSupplied by Trainer
- Hip MultiplierAs derived from pitch
Click on Spread Sheet for Answers

Draw in False Top Plate

Establish Rise of Roof

By drawing in Common Rafter

Draw in Ridge Line

Rotate Length of Hip onto Ridge

Extend this length up to false Top Plate

Establish the rise

The Rise will be the same as the

Common Rafter Rise

Draw in Hip Rafter

Plumb Cut Hip

Plumb Cut as Shown

- Using the A3 drawing previously developed using the method outlined
- Develop Plumb Cut - Graphically

- 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

Hip Plumb Cut

1.082

0.414

1.159

Rise

20.9°

22.5°

Hip Run

Reduce Hip Triangle to Steel Square

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

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

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

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

Roof Pitch = 22.5

Hip Pitch= 20.9°

Timber Depth = 190mm

= (Tan 20.9°) x Timber Depth

= 0.382 x 190

= 73mm

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

To determine the True Length

Determine how far it travels

Apply the correct multiplier

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

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

We Reduce from ½ Span

½ Ridge Thickness

To determine the True Length

Determine how far it travels

Apply the correct multiplier

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

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

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

- Based on Data given to you by the Trainer
- Ridge Thickness Supplied by Trainer
- Rafter ThicknessSupplied by Trainer

- Determine the Shortening

This Dimension measured from True Length in Plan

Isometric Elevation

Isometric Elevation

This measurement

Is at 90° to the Plumb Cut

Isometric Elevation

Develop Edge Bevel

- On Page xx develop the edge bevel graphically
- With Timber Supplied
- Mark Plumb Cut
- Mark Centreline Shortening
- Mark Edge Bevels

- 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

Determine Plan Length

= ½ Span - Shortening

To determine the True Length

Determine how far it travels

Apply the correct multiplier

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

- Based on the previous exercise and data supplied by the Trainer
- SpanSupplied by Trainer

- Determine True Plan Length Hip Rafter

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

Centreline Length

Mark Lines square

on Top of Rafter

Centreline Shortening

Isometric View

Determine Plan Length

To determine the True Length

Determine how far it travels

Apply the correct multiplier

- 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

- 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

Apply Multiplier

= Plan Length x Hip per 1m Rafter

To determine the True Length

Determine how far it travels

Apply the correct multiplier

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

- Based on the previous exercises determine
- True Length Hip Rafter

- Determine Creeper Shortening
- Determine Long Point Correction
- Determine 1st Creeper True Length
- Determine all other Creepers

These 2 Triangles are similar

The Ratio between the

Sides must be equal

Plan Shortening = ½ Span

Spacing CL to End

Plan Shortening = 1.000

200 0.414

For an Octagonal Roof

These are always the same

Plan Shortening = 2.414

200

Plan Shortening = 2.414 x 200

- Creeper Shortening
- = (Spacing x 2.414) x Rafter Length /m

- 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

- Determine Creeper Shortening
- PitchSpecified by Trainer
- Spacing Specified by Trainer

- Determine Creeper Shortening
- PitchSpecified by Trainer
- Spacing Specified by Trainer

- Determine Creeper Shortening
- Determine Long Point Correction
- Determine 1st Creeper True Length
- Determine all other Creepers

The simplest way is to draw it

This can be done mathematically but

It is a convoluted process

In this the correction is -3mm

The simplest way is to draw it

This can be done mathematically but

It is a convoluted process

In this the correction is -3mm

On an A3 Sheet

Draw the intersection

Of the member &

Determine the Long Point

Correction

On an A3 Sheet

Draw the intersection

Of the member &

Determine the Long Point

Correction

- Determine Creeper Shortening
- Determine Long Point Correction
- Determine 1st Creeper True Length
- Determine all other Creepers

- = (½ Span + Correction) x Rafter per/m – Creeper Shortening
- = (3800 -3) x 1.082 – 1175
- = 3797 x 1.082 – 1175
- = 4108 – 1175
- = 2933

- Determine Creeper Shortening
- Determine Long Point Correction
- Determine 1st Creeper True Length
- Determine all other Creepers

- = Previous Creeper – Creeper Shortening
- = 2933 – 1175
- = 1758 – 1175
- = 583