Octagonal Roof.

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 Parameters To 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”

What are the Plan Lengths of these triangles?

Plan Lengths

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

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

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 Octagonal End With Compass

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

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

Clean Up Drawing Angle Between Crowns Ends & Hips = 22.5⁰

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 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 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 (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. Worked Example Based on the dimensions on the example sheet previous drafting exercise determine, Top Plate Projection ½ Span x = 3800 x = 931.5 Octagonal End ½ Span x = 3800 x = 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

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
22.5° Rafter Length per 1m = 1 ÷ Cos 22.5° = 1.082 (This is the Rafter Multiplier)

Solve 1m Triangle - Example 3(b) Rise per plan 1m Travel of Rafter in Plan
1.082 22.5° Rise = 1 x Tan 22.5° = 0.414 (This is the Rise Multiplier)

Solve 1m Triangle - Example 3(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 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

No matter the size the angles are always the same These angles are always 90⁰

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) = per 1m of Rafter Plan Length Hip Rafters 1.082

Plan Hip Length = ½ Span ÷ cos 22.5⁰ = per 1m of Rafter Plan Length 1.082

Plan Hip Length = ½ Span ÷ cos 22.5⁰ = per 1m of Rafter Plan Length 1.082 The Hip Plan Length is Always 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 - Example 2(c) Hip Rafter Plan Length per 1m Travel of Rafter in Plan
= Tan 22.5° x 1 = Note – This is always the case regardless of Pitch

Solve 1m Triangle - Example 2(d) Hip Rafter Length per 1m Travel of Rafter in Plan
1.082 0.414 22.5° Hip Length / m = √( ) = √( ) = (This is the Hip Rafter Multiplier per 1m of Rafter in plan)

Solve 1m Triangle - Example 2(e) Hip Pitch = Tan-1 (Rise per metre ÷ 1
1.082 0.414 1.159 22.5° Hip Pitch = Tan-1(RISE ÷ 1.082) = Tan-1(0.414 ÷ 1.082) = Tan-1(0.383) = 20.9° say 21° Remember this is always 1082

1m Triangle Multipliers - Example
Common Rafter Multiplier Hip Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9° 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 Trainer to Supply Roof Pitch for This Excercise

1m Triangle - Answer Click on table below to open Spread sheet
Ask Learners to demonstrate the Calculations to Confirm Knowledge

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. RISE 4(b) Total Rise Total Rise is a 3 Step process
Determine Required Height above Pitching Line Perpendicular to Rafter Total Rise

4. RISE 4(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

Determine Required Height above Pitching Line Perpendicular to Rafter Total Rise Allowances Rafter = 152 Battens = 45 Custom Orb = 17 Ridge Cap = 10 Total = 224

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height Total Rise

4. RISE 4(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

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height This must be a Right Angle

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height This must be a 90° - Roof Pitch

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height This also must be a 90° - Roof Pitch

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height This must equal the Roof Pitch

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

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”

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

Determine Required Height above Pitching Line Perpendicular to Rafter Determine Plumb Height = 242 Add answer to Rise Rise = 1574 Plumb Height = (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 Span To be Supplied by Trainer Pitch To 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” ?

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

1m Triangle Multipliers
Common Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9°

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

Worked Example Exercise 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 - Answer Exercise 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 Example Exercise 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 = x 1.082 = 4093

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

Establish ½ Span

Establish Rise

Establish Crown End Rafter

Establish Crown End Rafter Rise is Same as Common Rafter Plan Length is Same as Common Rafter

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

Plumb Cut – Steel Square Method 5. (ii) – Worked Example
Common Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9° Rafter Plumb Cut Rise = ÷ 2 = 0.207 Run = ÷ 2 = 0.500 Rise Run

Plumb Cut – Steel Square Method 5. (ii) – Worked Example
Common Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9° Rafter Plumb Cut Rise = 414 ÷ 2 = 207 Run = 1000 ÷ 2 = 500 Rise = 207 Run = 500

Plumb Cut – Steel Square Method 5. (ii)
Common Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9° 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

Plumb Cut Offset Method

5. Major Crown End (ii) Plumb Cut Offset Method
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° ° = 67.5°

This Triangle is formed by the Roof

A SIMILAR triangle is also formed in this position

As the triangles are SIMILAR these angles must be the same

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 = = 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 = x 190 = 77mm

Worked Example - 1 Roof Pitch 22.5° Timber Depth 190
= (Tan 22.5°) x 190 = 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)

Worked Example - 1 Roof Pitch 22.5° Timber Depth 190
= (Tan 22.5°) x 190 = x 190 = 79mm

Worked Example - 2 Roof Pitch 22.5° Timber Depth 190 = 0.414 x 190
= 79mm

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 Out 90 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 = x 190mm = 79mm

Worked Example - 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”

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 The Spreadsheet will allow Timber width to be changed

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

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 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 The Pitch must be the same as 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 The Pitch must be the same as 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 22.5° 20.9°

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 Example Exercise 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

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

(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

(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 = (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 = (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

Draw Centrelines MINOR CROWN END RAFTER CENTRING RAFTERS MAJOR CROWN END RAFTER Gathering Point MINOR CROWN END

Draw Timber Thicknesses at full size In this case all Roof Members Are 35mm thick i.e 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

6. Minor Crown End Rafter b) ii
6. Minor Crown End Rafter b) 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 Rafter b) ii. Shortening from Centreline Length - Graphically Side Elevation Mark Out Centreline Length as determined in 6a

6. Minor Crown End Rafter b) ii. Shortening from Centreline Length - Graphically Side Elevation Mark Out Plumb Cuts as determined in 6c

6. Minor Crown End Rafter d) ii
6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Side Elevation Mark Lines square on Top of Rafter

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically You Rafter should now be marked with Centreline Length Centreline Length Isometric View

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically These lines are Plumb Side Elevation

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically A line 90° to Plumb will be level Side Elevation

6. Minor Crown End Rafter ) ii
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 Rafter d) ii. Shortening from Centreline Length - Graphically Side Elevation Mark Out a level line approximately ½ way down the top plumb cut

Mark Centreline Shortening Distance
6. Minor Crown End Rafter d) 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)

Mark Line using Plumb Cut Bevel
6. Minor Crown End Rafter d) 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 Rafter d) 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 Rafter d) 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 Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Mark Centreline Isometric View Mark Out Plumb Cuts as determined in 6c

Mark Edge Bevel Shortening Distance
6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Mark Edge Bevel Shortening Distance Transfer plan measurements determined in 6 (d) (ii)

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Mark Line using Plumb Cut Bevel Transfer plan measurements determined in 6 (d) (ii)

6. Minor Crown End Rafter d) 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 Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Mark Lines square on Top of Rafter Centreline Shortening Isometric View

6. Minor Crown End Rafter d) 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 Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Plan View Isometric View

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Centreline Shortening Plan View Isometric View

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Centreline Shortening Edge Bevel Shortening Plan View Isometric View

6. Minor Crown End Rafter d) ii. Shortening from Centreline Length - Graphically Centreline Length Centreline Shortening Edge Bevel Shortening Thickness Centreline Mark Plan View Isometric View

6. Minor Crown End Rafter d) 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 Rafter d) 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 Rafter d) 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 Rafter d) 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 Rafter d) 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 Rafter d) 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 Mark Out Plumb Cuts as determined in 6c Isometric View

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

(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))

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

Determine the True Length of the Minor Crown End Rafter based on data given to you by the Trainer. Span To be Supplied by Trainer Pitch To 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. Span To be Supplied by Trainer Pitch To 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

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

Edge Bevel Minor Crown End Rafters Plan Angle

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 ?

Minor Crown True Angle

Edge Bevel Minor Crown End Rafters True Angle
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?

7.Plan Length Hip Rafter The Octagonal Roof is a geometric shape

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 = (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 (That it is equal to the Rafter Multiplier is a coincidence) This is a fixed relationship Regardless of pitch

Worked Example 7. Plan Length of Hip
Determine Plan Length of Hip Span 7600 Plan Length = ½ Span x 1.082 = (7600 ÷ 2) x 1.082 = 3800 x 1.082 = 4112

Hip Rafter Multiplier 1.082 0.414 1.159 22.5° 20.9° 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

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 22.5° 20.9° 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 22.5° 20.9° 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

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 22.5° 20.9° 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

Worked Example Determine Centreline length of Hip Rafter Span 7600mm
Pitch ° Hip Multiplier 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 Span Supplied by Trainer Pitch Supplied by Trainer Hip Multiplier As derived from pitch

Determine Centreline length of Hip Rafter Span Supplied by Trainer Pitch Supplied by Trainer Hip Multiplier As derived from pitch Click on Spread Sheet for Answers

9. Hip Plumb Cut

9a.Hip Plumb - Graphically
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

9b.Hip Plumb – Steel Square Method
Hip Plumb Cut 1.082 0.414 1.159 Rise 22.5° 20.9° Hip Run Reduce Hip Triangle to Steel Square

Hip Plumb Cut 1.082 0.414 1.159 Rise 22.5° 20.9° Hip Run Reduce Hip Triangle to Steel Square Divide by 2

Hip Plumb Cut 1.082 0.414 1.159 Rise 22.5° 20.9° 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 22.5° 20.9° 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 22.5° 20.9° Plumb Cut Offset = Tan(Hip Pitch°) x Timber Depth or = (Timber Depth ÷ 1.082) x Rise

Worked Example 1 Using Derived Hip Pitch
Roof Pitch = 22.5 Hip Pitch = 20.9° Timber Depth = 190mm = (Tan 20.9°) x Timber Depth = x 190 = 73mm

Worked Example 2 Using 1m Trainagle Data
Roof Pitch = 22.5 Rise = Timber Depth = 190mm = (Timber Depth ÷ 1.082) x = (190 ÷ 1.082) x = x = 73mm

10. True Length Hip Rafter To determine the True Length
Determine how far it travels Apply the correct multiplier

10 True Length Hip Rafter a) 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 Rafter a) 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

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

9. True Length Hip Rafter a) Shortening – Worked Example
All members 35mm = ½ Ridge Thickness + (½ Rafter x 1.414) = (17.5 x 1.414) = = 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 Thickness Supplied by Trainer Determine the Shortening

9. True Length Hip Rafter a (i) Edge Bevel – Graphically
This Dimension measured from True Length in Plan

9. True Length Hip Rafter a (iii) Edge Bevel – Graphically
Isometric Elevation

This measurement Is at 90° to the Plumb Cut Isometric Elevation

Develop Edge Bevel Isometric Elevation

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

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 = 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 Span Supplied by Trainer Determine True Plan Length Hip Rafter

9. True Length Hip Rafter c 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 Rafter c) Shortening from Centreline Length - Graphically
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

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

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 = 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

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 = x 200

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

Creepers a) 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 = x 1.082 = 1175

Creepers a) Shortening –at Confirmation of Learning
Determine Creeper Shortening Pitch Specified by Trainer Spacing Specified by Trainer

Creepers - Answer a) Shortening –at Confirmation of Learning
Determine Creeper Shortening Pitch Specified by Trainer Spacing Specified by Trainer

Creepers a) 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

Creepers a) Long Point Correction in plan – Confirmation of Learning
On an A3 Sheet Draw the intersection Of the member & Determine the Long Point Correction

Creepers - Answer a) Long Point Correction in plan – Confirmation of Learning
On an A3 Sheet Draw the intersection Of the member & Determine the Long Point Correction

Creepers (c) 1st Creeper
= (½ Span + Correction) x Rafter per/m – Creeper Shortening = ( ) x – 1175 = 3797 x – 1175 = 4108 – 1175 = 2933

Creepers (d) Determine Creepers
= Previous Creeper – Creeper Shortening = 2933 – 1175 = 1758 – 1175 = 583

Creepers (d) Determine Creepers

Octagonal Roof.

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