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 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

PLAN LENGTH

Pitch Angle

Example

• Other Examples

PLAN LENGTH

PLAN L

PLAN LENGTH

Pitch Angle

Hip Rafter per 1m of Common Rafter Plan Length

½ Span

½ Span½ Span

°Plan Lengths

Confirmation of Learning

• Determine which side is the “Plan Length”

Confirmation of Learning - Answer

• Determine which side is the “Plan Length”

PLAN LENGTH

• What are the Plan Lengths of these triangles?

Plan Lengths

25° 247

This Triangle

25° 247

This Triangle

Octagonal Roof

• A Regular Geometric Shape

1/2 SPAN

Roof Members can be Determined

MAJOR CROWN END

OR CROW

MINOR CROW

HIP RAFTER

Class Works

• On an A3 drawing sheet conduct the following drafting excercise

1/2 SPANWalls are parallel

Determine Set Out Points

Gathering Point is ½ Span Back from edge

1/2 SPANWalls are parallel

Determine Set Out Points

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

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 RoofBUILDING LENGTH

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)

1/2 SPAN

BUILDING LENGTH

Locate Centring Rafters(1/2 Span from end)

1/2 SPAN

BUILDING LENGTH

Find Gathering Point

1/2 SPAN

BUILDING LENGTH

Scribe Semi Circle with ½ Span as Radius

1/2 SPAN

Draw in Centring Rafters

MAJOR CROWN

Draw in Major Crown End

MAJOR CROWN END

Bisect Centring & Crown End Rafters to form Minor Crown End

MAJOR CROWN END

Extend Lines Perpendicular to RidgeAt ½ End Length= ½ Span x 0.414

MAJOR CROWN END

Extend Sides of Building by ½ End Length= ½ Span x 0.414

MAJOR CROWN END

Join up external Lines

MAJOR CROWN END

Draw in Hips

Draw Octagonal End With Compass

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

This end is not so important

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

1/2 SPAN

BUILDING LENGTH

Locate Centring Rafters(1/2 Span from end)

1/2 SPAN

BUILDING LENGTH

Find Gathering Point

1/2 SPAN

BUILDING LENGTH

Scribe Semi Circle with ½ Span as Radius

1/2 SPAN

Draw in Centring Rafters

MAJOR CROWN

Draw in Major Crown End

MAJOR CROWN END

OR CROW

MINOR CROW

22,5°22,5°

22,5°

22,5°22,5°

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

MAJOR CROWN END

OR CROW

MINOR CROW

22,5°22,5°

22,5°

22,5°22,5°

Extend Lines Perpendicular to RidgeTo intersect with HIP

MAJOR CROWN END

OR CROW

MINOR CROW

22,5°22,5°

22,5°

22,5°22,5°

Extend sides of BuildingTo intersect with HIP

MAJOR CROWN END

OR CROW

MINOR CROW

22,5°22,5°

22,5°

22,5°22,5°

Clean Up & Draw in HIPS

MAJOR CROWN END

OR CROW

MINOR CROW

22,5°22,5°

22,5°

22,5°22,5°

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

Octagonal Roof TheoryIf the angle between the members is constant 22.5⁰

We can say in all cases, no matter the size of the roof½ End = ½ Span x tan 22.5⁰

= ½ Span x 0.414

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

Octagonal Roof Theory

The Triangles are the same

½ End = ½ Span x 0.414

The Triangles are the same

½ End = ½ Span x 0.414

Top Plate Projection= ½ End

In all cases, we can say

Full End = ½ Span x 0.414 x 2

Also in all cases, the full end will be

Full End = ½ Span x 0.828

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

NOTE – These are all Centreline Measurements

3. Set Out Roof

22.5° between Roof Members

2. Set Out Roof

22.5° between Roof Members

(a) Top Plate projection = Tan 22.5°

2. Set Out Roof(b) Octagonal End = 2 x Tan 22.5°

2. Worked Example

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

Top Plate Projection½ 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,

1.Top Plate Projection

2.Octagonal End

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

(Click on Spread Sheet Below to Check Answers)

Span (mm) 76001/2 Span 3800

Top Plate Projection 1574Octagonal End 3148

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)

22.5°

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

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

Plan Length Hip Rafter

These angles are always 90⁰

These angles are always 22.5⁰

These relationships are constant on all properly built Octagonal Roofs

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

Method 2

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

Method 2

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

The Hip Plan Length isAlways 1.082 x ½ Span

Hip Rafter per 1m of Common Rafter Plan Length

In ALL Cases Plan Length Hip =1.082 x ½ Span

½ Span

½ Span½ Span

= Tan 22.5° x 1= 1.082Note – This is always the case regardless of Pitch

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

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)

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°

22.5°

Remember this is always 1082

1m Triangle Multipliers - Example

22.5°

20.9°

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

Common Rafter Multiplier Hip Rafter Multiplier

• 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

Pitch Given to Learners 25.0 °

a. Rafter Length per 1m Travel of Rafter in Plan b. Rise per plan 1m Travel of Rafter in Plan c. Hip Rafter Plan Length per 1m Travel of Rafter in Pland. Hip Rafter Length per 1m Travel of Rafter in Plane. Hip Pitch 23.315

Answers1.1030.4661.0821.178

4. RISE

22.5°

1/2 SPAN

Rise is Calculated to the Pitching Line

22.5°

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

22.5°

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

22.5°

Remember that rise is calculated to the pitching line

4. RISE

22.5°

The full height is calculated by determining Total Rise

4. RISE4(b) Total Rise

22.5°

Total Rise is a 3 Step process

1.Determine Required Height above Pitching Line Perpendicular to Rafter Total Rise

152Total Rise

1.Determine Required Height above Pitching Line Perpendicular to Rafter

Pitching Line

AllowancesRafter = 152Battens = 45Custom Orb = 17Ridge Cap = 10

Total = 224Note Rafter 190 x 3538mm Birdsmouth152 above Pitching Line

(All measurements perpendicular to Rafter)

22.5°

1.Determine Required Height above Pitching Line Perpendicular to Rafter Total Rise

AllowancesRafter = 152Battens = 45Custom Orb = 17Ridge Cap = 10

Total = 224

22.5°

1.Determine Required Height above Pitching Line Perpendicular to Rafter2.Determine Plumb Height

Total Rise

22.5°

67.5°

To determine Plumb HeightWe must solve the HypotenuseOf this Triangle

22.5°

67.5°

This must be a Right Angle

22.5°

67.5°

This must be a 90° - Roof Pitch

22.5°

67.5°

This also must be a 90° - Roof Pitch

67.5°

22.5°

This must equal the Roof Pitch

67.5°

22.5°

This is a similar triangle thatWe used to determine the Rafter Multiplier

67.5°

22.5°

1.Determine Required Height above Pitching Line Perpendicular to Rafter2.Determine Plumb Height Plumb Height = Amount Left On x Rafter Length per metre = 224 x 1.082 = 242

To determine HypotenuseWe multiply “Amount Left onBy Rafter Multiplier”

22.5°

67.5°

22.5°

1.Determine Required Height above Pitching Line Perpendicular to Rafter2.Determine Plumb Height = 2423.Add answer to Rise

Rise = 1574Plumb Height = 242Total Rise = 1816

22.5°

67.5°

22.5°

1574 17

1.Determine Required Height above Pitching Line Perpendicular to Rafter2.Determine Plumb Height = 2423.Add answer to Rise

Rise = 1574Plumb Height = 164 (152 x 1.082)Total Rise = 1738

If you wanted to find the height toTop of Rafter – you would substitute the perpendicular distance to the top of Rafter

Confirmation of Learning• 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

Determine1.Rise2.Amount Left On Plumb Height

3.Total Rise

Click on Spread sheet to determine answers

Confirmation of Learning - Answer• 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

Determine1.Rise2.Amount Left On Plumb Height

3.Total Rise

Click on Spread sheet to determine answers

Roof Pitch 22.5Span 7600Amount Left On 152

Amount Left On Plumb Height 165Rise 1574Total Rise 1739

(5) Major Crown End Rafter

MAJOR CROWN

½ SPAN

(a)Centreline Length

How far does it travel in “Plan” ?

(a)Centreline Length

1/2 SPAN

PLUMB CUT

ROOF PITCH

Rafter Travels toGathering Point

Plan View

Side Elevation

(a) Centreline Length

MAJOR CROWN

½ SPAN

1/2 SPAN

PLUMB CUT

ROOF PITCH

(a) Centreline Length, Which Multiplier?

Plan Length = ½ Span

The Rise must be the same as

1.Common Rafter

1/2 SPAN

PLUMB CUT

ROOF PITCH

1.Common Rafter

The Plan Length is the same as

1. Common Rafter

1/2 SPAN

PLUMB CUT

ROOF PITCH

1.Common Rafter

The Pitch must be the same as

1. Common Rafter

1/2 SPAN

PLUMB CUT

ROOF PITCH

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

22.5°

20.9°

Common Rafter Multiplier

(a) Centreline Length = ½ Span x Rafter Length per m

MAJOR CROWN

½ SPAN

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

Centreline Length Major CrownClick on Spread Sheet to determine answers

SpanPitch

760022.5

5. Major Crown End(b) True LengthHow far does it Travel in Plan ?

MAJOR CROWN

½ SPAN

½ Span – ½ Rafter

½ Span – ½ Rafter ROOF PITCH

True Length Rafter

Travels to edge ofCentring Rafter

Major Crown End

MAJOR CROWN

½ SPAN - ½ Rafter

5. Major Crown End(b) True Length= (½ Span – ½ Rafter) x Rafter Length per m

MAJOR CROWN

½ SPAN - ½ Rafter

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

True Length Major Crown End Rafter

True Length Major Crown End RafterClick on Spread Sheet to determine answers

°Rafter Thickness mm

SpanPitch

760022.5

5. Major Crown End(i) Plumb Cut Graphically

Establish False Top Plate

Establish ½ Span

Establish Rise

Plumb Cut

Establish Crown End Rafter

Plumb Cut

•Rise is Same as Common Rafter•Plan Length is Same as Common Rafter

Plumb Cut

•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°

25°30°

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

22.5°

20.9°

Rafter Plumb Cut

Rise = 0.414 ÷ 2 = 0.207

Run = 1.000 ÷ 2 = 0.500

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

22.5°

20.9°

Run = 500

Rafter Plumb Cut

Rise = 414 ÷ 2 = 207

Run = 1000 ÷ 2 = 500

Rise = 207

Plumb Cut – Steel Square Method5. (ii)

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

• 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

Roof Pitch 22.5

Rise 207Run 500

Plumb Cut Offset Method

22.5°

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

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

22.5°

67.5°

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

22.5°

The other 2 angles must = 90°(180° – 90° = 90°)

22.5°

Therefore this angleMust = 90° - Roof Pitch

22.5°

67.5°

Therefore this angle= 90° - 22.5°= 67.5°

22.5°

67.5°

This Triangle is formed by the Roof

22.5°

67.5°

A SIMILAR triangle is also formed in this position

22.5°

3800152

67.5°

22.5°

67.5°

As the triangles are SIMILAR these angles must be the same

22.5°

67.5°

This Angle must = 90° - Roof Pitch = 67.5°

67.5°

This Angle must = 90° - Roof Pitch = 67.5°

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

67.5°

67.5°22.5°90.0°

A Triangle is Formed

67.5°22.5°90.0°

This angle is the same as the Roof Pitch

67.5°22.5°90.0°

This angle must be 90°

67.5°22.5°90.0°

This angle must be 90° - Roof Pitch

67.5°22.5°90.0°

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

67.5°22.5°90.0°

22.5°

67.5°22.5°90.0°

22.5°

Therefore we can use the same multipliers to determine its dimensions

67.5°22.5°

90.0°

What is the Pitch angle of this triangle?

67.5°22.5°

90.0°

What is the Plan Length?

Pitch Angle = 22.5°

67.5°22.5°

90.0°

What is the Plan Length?

Plan Length = 152 + 38= 190

67.5°22.5°

90.0°

Offset = Rise Multiplier x Plan Length = 0.414 x 190 = 77mm

This length isSimilar toThe Rise

Worked Example - 1

• Roof Pitch 22.5°• Timber Depth 190

= (Tan 22.5°) x 190= 0.414 x 190= 79mm

• There 2 Formulas to Determine the Plumb

1.= Tan (Roof Pitch°) x Timber Depth or

2.= 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

= (Tan 22.5°) x 190= 0.414 x 190= 79mm

Worked Example - 2

= 0.414 x 190= 79mm

• Pattern Rafter (90 x 45)90

• Pattern Rafter (90 x 45)1. Mark Square Line

• Pattern Rafter (90 x 45)1. Mark Square Line2. 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

• Pattern Rafter (90 x 45)1. Mark Square Line2. Determine Plumb Cut Offset and Mark Out

90 x 0.414= 37mm3. Mark Plumb Cut

Plumb Cut

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

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

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 ,

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

Click on Spreadsheet below to generate Answers

Roof Pitch 25 °Timber Width 90

Offsett(mm) 42

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

6.Minor Crown End Rafters

Major Crown End Rafter

Minor Crown End Rafter

MAJOR CROWN

MINOR CROW

OR CROW

(6) Minor Crown End Rafters

Radius = ½ Span

Octagonal End Based on Semi Circle

(a) Centreline Length How Far does it Travel in plan?

MAJOR CROWN

MINOR CROW

OR CROW

Major Crown is a Radius

MAJOR CROWN

MINOR CROW

OR CROW

(6) Minor Crown End RaftersPlan Length = ½ Span

Major Crown is a Radius

Minor Crown also is a Radius

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

Minor Crown End Rafters travel to Gathering Point

(a) Centreline Length How Far does it Travel in plan?Plan Length = ½ Span

wn End

Minor Crown End

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

(a) Centreline Length Determine Centreline Length: Which Multiplier?

The Rise be same as1.Common Rafter &2.Major Crown End Rafter

wn End

Minor Crown End

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

The Rise be same asCommon Rafter &Major Crown End Rafter

The Plan Length is the same asCommon Rafter &Major Crown End Rafter

wn End

Minor Crown End

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

The Pitch must be the same asCommon Rafter &Major Crown End Rafter

wn End

Minor Crown End

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

(6) Minor Crown End Rafters(a) Centreline Length Determine Centreline Length: Which Multiplier?

The Pitch must be the same asCommon Rafter &Major Crown End Rafter

wn End

Minor Crown End

We use the Common Rafter Multiplier = Rafter Length per metre

22.5°

20.9°

MAJOR CROWN

MINOR CROW

OR CROW

(a) Centreline Length = Plan Length x Rafter Length per m

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

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

Confirmation of LearningExercise 6a

True Length Minor Crown End Rafter

Centreline Length Major CrownClick on Spread Sheet to determine answers

SpanPitch

760022.5

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

This is called the Shortening

There are 2 methods to determine the Shortening

I.MathematicallyII.Graphically

(6) Minor Crown End Rafters(b) Shortening

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

Remember Centreline Plan Length = ½ Span

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

MAJOR CROWN

OR CROW

MINOR CROW

Rafter travels to Intersection of

•Centring Rafter &•Major Crown

½ RAFTER

½ RAFTER x 1.414

The Rafters Plan length is reduced by

√(½ Rafter2 + ½ Rafter2)

We know form our previous studyOf HIP ROOFS that this can be simplified to

½ Rafter x 1.414

Note 1.414 = √2

Shortening

½ RAFTER

½ RAFTER x 1.414

Shortening = ½ Rafter x 1.414

Shortening

Note 1.414 = √2

½ RAFTER

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

Shortening

Note 1.414 = √2

• 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

Timber Width (mm)

Shortening = x 1.414= ( 42 ÷ 2 ) x 1.414= x 1.414=

Width ÷ 2

2129.694

½ RAFTER

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

Shortening

Note 1.414 = √2

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 considerUsing the “Graphical Method”

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

Gathering Point

OR CROW

N END R

MINOR CROW

MAJOR CROWN END RAFTER

Draw Centrelines

Gathering Point

OR CROW

N END R

MINOR CROW

Draw Timber Thicknesses at full size

In this case all Roof MembersAre 35mm thick

i.e. 17.5 either side of Centreline

Gathering Point

OR CROW

N END R

MINOR CROW

Dimension Shortening from Centreline

Note Zoomed in for Clarity

Gathering Point

OR CROW

N END R

MINOR CROW

To put this drawing into practical use you need to understand that

1.This is a TRUE representation of the actualIntersection 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

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

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

Side Elevation

Mark Out Centreline Length as determined in 6a

CENTRELINE LENGTH

Side Elevation

Mark Out Plumb Cuts as determined in 6c

CENTRELINE LENGTH

Side Elevation

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

Mark Lines square on Top of Rafter

CENTRELINE LENGTH

Side Elevation

CENTRELINE LENGTH

Isometric View

Centreline Length

You Rafter should now be marked with1.Centreline Length

CENTRELINE LENGTH

These lines are Plumb

Side Elevation

CENTRELINE LENGTH

A line 90° to Plumb will be level

Side Elevation

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

CENTRELINE LENGTH

The measurements on the drawingare in the level plane.

The set out must also be in the level plane

Side Elevation

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

CENTRELINE LENGTH

Side Elevation

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

Mark Centreline

Shortening Distance

Side Elevation

Plan View

All measurements are taken from Centreline Length

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

Mark Line using Plumb Cut Bevel

Side Elevation

Plan View

Which represents this point in PLAN

Side Elevation

Plan View

Isometric View

Mark Line square on Top of Rafter

Centreline Length

Isometric View

Mark Centreline

Centreline Length

Mark Edge Bevel Shortening Distance

Which represents these points in PLAN

Isometric View

Centreline Shortening

Centreline Length

CENTRELINE LENGTH

Isometric View

You Rafter should now be marked with1.Centreline Length2.Centreline Shortening3.Edge Bevel Shortening4.Thickness Centreline Mark

Thickness Centreline Mark

Isometric ViewPlan View

Centreline Length

Edge Bevel Shortening

Isometric View

Thickness Centreline Mark

Plan View

Centreline Length

Edge Bevel Shortening

Isometric View

This is the Shape of theend of the Rafter in Plan

Plan View

Isometric View

This is the Shape of theEnd of the Rafter

It is based on the measurementsDetermined previously

Plan View

Isometric View

Plan View

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

Isometric View

Plan View

Draw Lines Starting From 1.Edge Bevel Shortening

Isometric View

Plan View

Draw Lines Starting From 1.Edge Bevel Shortening to Intersection of2.Centreline Shortening & Thickness Centreline to

Isometric View

The Rafter is then cut to This Shape

The length has also been shortenedAnd ready to be installed

Mark Out Plumb Cuts as determined in 6cPlan 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

1. Develop in Plan the Shortening of an Octagonal End Roof

a) Timber Widths to be supplied by Trainer is 45mm thick

Submission should be as Answer 12.On Timber Supplied Develop shortening based on a pitch of 27° & ½ Span of 300mmb) Timber to be supplied by Trainer

Confirmation of Learning – Answer 1

• Shortening in Plan

Confirmation of Learning – Answer 2

• Shortening in Elevation

CENTERLINE LENGTH = 337MM

(c) True Length

1/2 SPAN

½ SPAN – (½

RAFTER x 1.414)

PLUMB CUT

ROOF PITCH1/2 SPAN

MAJOR CROWN

OR CROW

MINOR CROW

Rafter travels to Intersection of

•Centring Rafter &•Major Crown

½ RAFTER

½ RAFTER x 1.414

(c) True Length

How far does it travel in plan?

Remember Centreline Plan Length = ½ SpanTrue Length in Plan = ½ Span – ½ Rafter x 1.414

Rafter Plan Reduction

°(½ Span – (½

Rafter x 1.414)) x Rafter Length per m

(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.– Span To be Supplied by Trainer– Pitch To 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.– 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

Timber Width (mm)Span (mm)Pitch°Rafter per m

Shortening = x= ( 35 ÷ 2) x 1.414= 17.5 x=

Note Plan Length = 1/2 Span - ShorteningTrue Length = x Rafte Length per m

= ( 3800 - 25 ) x = 3775 x= 4086

24.745

1.08222.57600

Plan Length

Width ÷ 2 1.414

1.0821.082

(c) Plumb Cut Minor Crown

As we use the Common Rafter multiplier we can use the Common Rafter Plumb CutThe following slides demonstrate how to develop the plumb cut

1/2 SPAN

(c) Plumb Cut Minor Crowni. Graphically

1/2 SPAN

Extend Construction LinesPerpendicular to ends of Rafter

1/2 SPAN

Establish False Top Plate

1/2 SPAN

Establish Plan Length

1/2 SPAN

Establish Rise

1/2 SPAN

PLUMB CUT

ROOF PITCH1/2 SPAN

Draw in Rafter•Establish Plumb Cut•Establish Roof Pitch

• Using your previous drafting exercise determine graphically,

Plumb Cut - Minor Crown End

MAJOR CROWN

MINOR CROW

OR CROW

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

In Plan this Angle = 45⁰

MAJOR CROWN

MINOR CROW

OR CROW

When can you use the plan angle?

MAJOR CROWN

MINOR CROW

OR CROW

When can you use the plan angle?

When you use a power tool such as1.Drop Saw2.Power Saw etc

Edge Bevel Minor Crown End RaftersPlan Angle

Plan Angle = 45⁰

Plan Angle = 90⁰

Plan Angle = 45⁰

Plan Angle = 90⁰

Both Sides MustBe Equal

Plan Angle = 45⁰

Plan Angle = 90⁰

When Can You Use The Plan For the Edge Bevel ?

Plan Angle = 45⁰

Plan Angle = 90⁰

When Can You Use The Plan For the Edge Bevel ?

MAJOR CROWN

MINOR CROW

OR CROW

Minor Crown True Angle

Edge Bevel Minor Crown End RaftersTrue Angle

What members form the triangle?

Centreline Length Rafter

If this angle is 45⁰

This angle must 45⁰

Both these sides must be equal

This line runs parallel with the top Of the Rafter

Which is level

7.Plan Length Hip Rafter

7. Plan Length Hip Rafter

These relationships are constant on all properly built Octagonal Roofs

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 relationshipRegardless of pitch

MAJOR CROWN

½ SPAN - ½ Rafter

1/2 Span x 1.082

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 relationshipRegardless of pitch

MAJOR CROWN

½ SPAN - ½ Rafter

1/2 Span x 1.082

Worked Example7. 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

22.5°

20.9°

Hip Rafter Multiplier

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 1.Determine how far it travels in plan2.Apply the multiplier

As with all Roof members to determine the length we 1.Determine how far it travels in plan ?2.Apply the multiplier

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

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?

The Rafter travels ½ Span

As with all Roof members to determine the length we 1.Determine how far it travels in plan = ½ Span2.Apply the multiplier

22.5°

20.9°

Hip Rafter Multiplier for 22.5° = 1.159

As with all Roof members to determine the length we 1.Determine how far it travels in plan = ½ Span2.Apply the multiplier = As per 1m triangle multiplier

Centreline Length of Hip = Plan Length x Hip Rafter Length per mNote - Plan Length = ½ Span

Worked Example• Determine Centreline length of Hip Rafter

– Span 7600mm– Pitch 22.5°– Hip Multiplier 1.159

Centreline Length of Hip = Plan Length x Hip Rafter Length per mNote - Plan Length = ½ Span

= (7800 ÷ 2) x 1.159= 3800 x 1.159= 4404

Confirmation of Learning• Determine Centreline length of Hip Rafter

– Span Supplied by Trainer– Pitch Supplied by Trainer– Hip Multiplier As derived from pitch

Confirmation of Learning - Answer• Determine Centreline length of Hip Rafter

– Span Supplied by Trainer– Pitch Supplied by Trainer– Hip Multiplier As derived from pitchClick on Spread Sheet for Answers

SpanPitch °Hip Multiplier

Hip Centreline = 3800 x 1.159= 4404

22.57600

9. Hip Plumb Cut

9a.Hip Plumb - Graphically

Draw in False Top Plate

Establish Rise of RoofBy 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 theCommon 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

Roof Pitch 25 °Hip Pitch 23.3 °

25°30°

35°Answer Drawing 1 – Click on Drawing to Open File

9b.Hip Plumb – Steel Square Method

Hip Run

Hip Plumb Cut

22.5°

20.9°

Reduce Hip Triangle to Steel Square

Hip Run

Hip Plumb Cut

22.5°

20.9°

Reduce Hip Triangle to Steel SquareDivide by 2

Hip Run

Hip Plumb Cut

22.5°

20.9°

Rise = 207Hip Run = 541

Hip Plumb Cut

22.5°

20.9°

Rise = 207Hip Run = 541

9b.Hip Plumb – Offset Method

22.5°

20.9°

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

Worked Example 1Using Derived Hip Pitch

Roof Pitch = 22.5Hip 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 = 22.5Rise = 0.414Timber 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

MAJOR CROWN

HIP RAFTERM

INOR CROWN

HIP RAFTER

OR CROW

To determine the True Length 1.Determine how far it travels 2.Apply the correct multiplier

10 True Length Hip Raftera) Shortening

HIP RAFTERM

INOR CROWN

To determine the True Length 1.Determine how far it travels2.Apply the correct multiplier

We must determine howFar in the direction of the Rafter does the hip travel

9. True Length Hip Raftera) Shortening

HIP RAFTERM

INOR CROWN

We must determine theDistance from ½ Span to The plan length

This is called the shortening

HIP RAFTERM

INOR CROWN

We Reduce from ½ Span1.½ Ridge Thickness

HIP RAFTERM

INOR CROWN

We Reduce from ½ Span1.½ Ridge Thickness2.½ Rafter x 1.414

HIP RAFTERM

INOR CROWN

We Reduce from ½ Span1.½ Ridge Thickness2.½ Rafter x 1.414

This Reduction is call the Shortening

= ½ Ridge Thickness + ½ Rafter x 1.414

9. True Length Hip Raftera) Shortening – Worked Example

HIP RAFTERM

INOR CROWN

All members 35mm= ½ Ridge Thickness + (½ Rafter x 1.414)= 17.5 + (17.5 x 1.414)= 17.5 + 25= 42.5mm

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 Raftera (i) Edge Bevel – Graphically

This Dimension measured from True Length in Plan

Isometric Elevation

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

EDGE BEVEL SHORTENING

Isometric Elevation

This measurementIs at 90° to the Plumb Cut

EDGE BEVEL SHORTENING

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

Pitch 22.5Span (mm) 7600Rafter Thickness (mm) 35Hip Thickness (mm) 35Centreline Length (mm) 4404

Shortening in Plan 45.7297Edge Bevel in Plan 42.24874

All measurements from Centreline Length

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

HIP RAFTERM

INOR CROWN

Determine Plan Length= ½ Span - Shortening

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

HIP RAFTERM

INOR CROWN

Determine Plan Length= ½ Span – Shortening= 3800 – 42.5= 3757.5

• 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 Rafterc Develop Rafter Graphically

It is possible to not bother with the mathsAnd 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

Isometric View

Centreline Length

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

HIP RAFTERM

INOR CROWN

Determine Plan Length

• 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

HIP RAFTERM

INOR CROWN

Apply Multiplier= Plan Length x Hip per 1m Rafter

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

HIP RAFTERM

INOR CROWN

Apply Multiplier= Plan Length x Hip per 1m Rafter= 3757.5 x 1.159= 4355

• Based on the previous exercises determine

• True Length Hip Rafter

Creepers

1. Determine Creeper Shortening

2. Determine Long Point Correction

3. Determine 1st Creeper True Length

4. Determine all other Creepers

Determine Shortening

These 2 Triangles are similar

The Ratio between theSides must be equal

Plan Shortening = ½ Span Spacing CL to End

Plan Shortening = 1.000 200 0.414

For an Octagonal RoofThese are always the same

Plan Shortening = 2.414 200

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– Pitch Specified by Trainer– Spacing Specified by Trainer

Creepers - Answera) Shortening –at Confirmation of Learning

• Determine Creeper Shortening– Pitch Specified by Trainer– Spacing Specified by Trainer

Creepers

Creepersa) Long Point Correction in plan

The simplest way is to draw it

This can be done mathematically butIt 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 butIt is a convoluted process

In this the correction is -3mm

Creepersa) Long Point Correction in plan – Confirmation of Learning

On an A3 SheetDraw the intersection Of the member &Determine the Long PointCorrection

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

On an A3 SheetDraw the intersection Of the member &Determine the Long PointCorrection

Hip Thickness 35Rafter Thickness 35

centerline short 45.7297Long Point Extenstion 42.24874

Long Point Correction -3.48097

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

Creepers(d) Determine Creepers

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

Creepers(d) Determine Creepers

octagonal roof

end of buildingthis

octagonal end rooffind

hipsdraw octagonal end

octagonal end roofjoin

end of buildingdrawing

octagonal roofnotes

ridgeat end length

construction line mid

Documents

how to build your own octagonal poker table……

crashworthiness analysis of octagonal inner double tube

tdining, octagonal stamford dining, octagonal table...

octagonal drawing johan van rooij. overview what is an...

d efortmonroe.org/wp-content/uploads/g_4c-resource...gable...

octagonal ring antenna (ora) development for aamid ·...

an archaeological investigation of the roman octagonal...

octagonal end roof

reinforcing the octagonal web openings of castellated beam

zeus electrostatic system: cabina zeus octagonal

octagonal roof. notes to this lesson this demonstration...

equivalent circuit model of octagonal ultra...

proceso de optimización de un prisma octagonal

cfd simulations of flow around octagonal shaped...

project oscar octagonal speech-controlled autonomous robot...

gold 2013 sydney - octagonal resources asx: ors

delta®-garden roof system with delta®-floraxx ·...

octagonal knotworks a mathematical approach - … ·...

gold investment symposium 2012 - company presentation -...

fundacion tanque placa octagonal