Octagonal Roof. Notes to this Lesson. This demonstration develops from knowledge gained from the development of Gable & Hip Roofs This PowerPoint does not explain the development of the Basic Roof Members
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Octagonal Roof
Pitch Angle
Pitch Angle
Pitch Angle
Pitch Angle
Pitch Angle
½ Span
½ Span
22.5°
½ Span
Plan Lengths
Plan Lengths
This Triangle
This Triangle
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
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
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
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
(Click on Spread Sheet Below to Check Answers)
Entry only allowed in this cell
Note minor discrepancies are rounding errors
= 1.082
(This is the Rafter Multiplier)
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
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
Timber Depth is used to determine amount left on
Determine
Click on Spread sheet to determine answers
Timber Depth is used to determine amount left on
Determine
Click on Spread sheet to determine answers
Side Elevation
Rafter Travels to
Gathering Point
Plan View
Plan Length = ½ Span
Plan Length = ½ Span
Plan Length = ½ Span
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
Centreline Length = 3800 x 1.082
= 4112
Centreline Length Major Crown
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
True Length = (3800 – (35 ÷ 2)) x 1.082
= (3800 – 17.5) x 1.082
= 3782.5 x 1.082
= 4093
True Length Major Crown End Rafter
True Length Major Crown End Rafter
Click on Spread Sheet to determine answers
Establish False Top Plate
Establish ½ Span
Establish Rise
Plumb Cut
Establish Crown End Rafter
Plumb Cut
Plumb Cut
Plumb Cut - Major Crown End
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
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
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
= (Tan 22.5°) x 190
= 0.414 x 190
= 79mm
(The first formula is probably the easiest as the second formula gets complicated with hips)
= (Tan 22.5°) x 190
= 0.414 x 190
= 79mm
= 0.414 x 190
= 79mm
5. Major Crown End(ii) Plumb Cut Offset Method
90
90
= 90 x 0.414
= 37mm
90
37
Plumb Cut
90
37
Plumb Cut Offset- Major Crown End
= 190 x Rise per 1 metre of Rafter in plan
= 0.414 x 190mm
= 79mm
Plumb Cut Offset- Major Crown End
On the Supplied A4 sheet demonstrate the set out of the “Plumb Cut”
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
Radius = ½ Span
Octagonal End Based on Semi Circle
Plan Length = ½ Span
Octagonal End Based on Semi Circle
Major Crown is a Radius
Plan Length = ½ Span
Octagonal End Based on Semi Circle
Major Crown is a Radius
Minor Crown also is a Radius
Minor Crown End
Minor Crown End Rafters travel to Gathering Point
Minor Crown End
Plan Length = ½ Span
Minor Crown End
Minor Crown End
Plan Length = ½ Span
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
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
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°
Plan Length = ½ Span
Centreline Length = Plan Length x Rafter Length per m
Note– Plan Length = ½ Span
Centreline Length = 3800 x 1.082
= 4112
True Length Minor Crown End Rafter
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
(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
(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
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
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
Submission should be as Answer 1
(c) True Length
(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))
= (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
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
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
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
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
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
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
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
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
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
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
- Using Any Method
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
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
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