Octagonal end 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
PLAN LENGTH
27°
Pitch Angle

Example
• Other Examples
PLAN LENGTH
27°
PLANLENGTH
27°
PLAN
LENG
TH
27°
PLAN
LENGTH
27°
Pitch Angle
Pitch Angle
Pitch Angle
Pitch Angle

Hip Rafter per 1m of Common Rafter
Plan Length
½
Span
½ Span
½
Span
22.5°Plan Lengths

Confirmation of Learning
• Determine which side is the “Plan Length”
27°
27°
63°
90°
63°

Confirmation of Learning - Answer
• Determine which side is the “Plan Length”
27°
PLAN
LENGTH
27°
63°
90°
63°
PLAN
LENG
TH
PLANLENGTH
PLANLENGTH

• What are the Plan Lengths of these triangles?

Plan Lengths

25°
247
This Triangle

25°
247
PLANLENGTH
This Triangle

Octagonal Roof
• A Regular Geometric Shape
1/2 SPAN

Roof Members can be Determined
MAJOR CROWN END
CENTREINGRAFTERCENTREINGRAFTER
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
R
O
W
N
EN
D
HIPRAFTER
HIP RAFTER
HIP RAFTER
HIPRAFTER

Class Works
• On an A3 drawing sheet conduct the following
drafting excercise

1/2 SPAN
Walls are parallel
Determine Set Out Points
Gathering Point is ½ Span Back from edge

1/2 SPAN
Walls are parallel
Determine Set Out Points
Gathering Point is ½ Span Back from edge
This 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

BUILDING LENGTH
Draw Construction Line To
Represent End of Building

BUILDING LENGTH
Draw Construction Line To
Represent End of Building
This end is not so important

BUILDING LENGTH
==
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
45°
45°45°
45°
Bisect Centring & Crown
End Rafters to form
Minor Crown End

MAJOR CROWN END
45°
45°45°
45°
Extend Lines
Perpendicular to Ridge
At ½ End Length
= ½ Span x 0.414

MAJOR CROWN END
45°
45°45°
45°
Extend Sides of Building
by ½ End Length
= ½ Span x 0.414

MAJOR CROWN END
45°
45°45°
45°
Join up external Lines

MAJOR CROWN END
45°
45°45°
45°
Draw in Hips

Draw Octagonal End With Compass

MAJOR CROWN END
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
RO
W
N
EN
D
22,5°
22,5°
22,5°
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
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
RO
W
N
EN
D
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
Extend Lines
Perpendicular to Ridge
To intersect with HIP

MAJOR CROWN END
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
RO
W
N
EN
D
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
Extend sides of Building
To intersect with HIP

MAJOR CROWN END
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
RO
W
N
EN
D
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
22,5°
Clean Up & Draw in HIPS

MAJOR CROWN END
M
IN
O
R
C
R
O
W
N
EN
D
M
IN
O
R
C
RO
W
N
EN
D
22,5°
22,5°
22,5°
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 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

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
FullEnds
NOTE – These are all Centreline Measurements

3. Set Out Roof
• t
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°
2X

2. Worked Example
• Based on the dimensions on the example
sheet previous drafting exercise determine,
½ Span x 0.414 = 3800 x 0.414 = 931.5
Octagonal End
½ Span x 0.828 = 3800 x 0.828 = 1863

• Based on the full size dimensions given to you
by your trainer determine,
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) 7600
1/2 Span 3800
Top Plate Projection 1574
Octagonal 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°

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

3(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
1.082
0.414

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 45⁰

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

Method 2
Plan Hip Length = ½ Span ÷ cos 22.5⁰
1.082

Method 2
1.082
The Hip Plan Length is
Always 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 Span
½
Span
22.5°

= Tan 22.5° x 1
= 1.082
Note – This is always the case regardless of Pitch
2(c) Hip Rafter Plan Length per 1m Travel of Rafter in Plan

2(d) Hip Rafter Length per 1m Travel of Rafter in Plan
Hip Length / m = √(0.4142
+ 1.0822
)
= √(0.171 + 1.171)
= 1.159
(This is the Hip Rafter Multiplier per 1m of Rafter in plan)
1.082
22.5°
0.414

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

1m Triangle Multipliers - Example
1.082
22.5°
1.159
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
0.414

• 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 Plan
d. Hip Rafter Length per 1m Travel of Rafter in Plan
e. Hip Pitch 23.315
Answers
1.103
0.466
1.082
1.178

4. RISE
22.5°
1/2 SPAN
RISE
Rise is Calculated to the Pitching Line

22.5°
3800
RISE=
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°
3800
RISE=1574
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°
3800
RISE=1574
Remember that rise is calculated to the pitching line

4. RISE
22.5°
3800
TOTALRISE
The full height is calculated by determining Total Rise

4. RISE
4(b) Total Rise
22.5°
3800
TOTALRISE
Total Rise is a 3 Step process
1.Determine Required Height above Pitching Line
Perpendicular to Rafter Total Rise

224
38
45
17
10
152
Total Rise
Perpendicular to Rafter
Pitching Line
Allowances
Rafter = 152
Battens = 45
Custom Orb = 17
Ridge Cap = 10
Total = 224
Note Rafter 190 x 35
38mm Birdsmouth
152 above Pitching Line
(All measurements perpendicular to Rafter)
4. RISE
4(b) Total Rise

4. RISE
4(b) Total Rise
22.5°
3800
TOTALRISE
224
Perpendicular to Rafter Total Rise
Allowances
Rafter = 152
Battens = 45
Custom Orb = 17
Ridge Cap = 10
Total = 224

4. RISE
4(b) Total Rise
22.5°
3800
PLUMBHEIGHT
224
2.Determine Plumb Height
Total Rise

4. RISE
4(b) Total Rise
22.5°
3800
PLUMBHEIGHT
224
90°
67.5°
To determine Plumb Height
We must solve the Hypotenuse
Of this Triangle

4. RISE
4(b) Total Rise
22.5°
3800
PLUMBHEIGHT
224
90°
67.5°
This must be a Right Angle

4. RISE
4(b) Total Rise
22.5°
3800
PLUMBHEIGHT
224
90°
67.5°
This must be a 90° - Roof Pitch

4. RISE
4(b) Total Rise
22.5°
3800
PLUMBHEIGHT
224
90°
67.5°
This also must be a 90° - Roof Pitch

4. RISE
4(b) Total Rise
224
67.5°
22.5°
242
This must equal the
Roof Pitch

4. RISE
4(b) Total Rise
224
67.5°
22.5°
This is a similar triangle that
We used to determine the
Rafter Multiplier

4. RISE
4(b) Total Rise
224
67.5°
22.5°
242
1.Determine Required Height above Pitching Line Perpendicular to
Rafter
Plumb Height = Amount Left On x Rafter Length per metre
= 224 x 1.082
= 242
To determine Hypotenuse
We multiply “Amount Left on
By Rafter Multiplier”

4. RISE
4(b) Total Rise
22.5°
3800
224
90°
67.5°
67.5°
22.5°
2421574
TOTALRISE=1816
Rafter
2.Determine Plumb Height = 242
3.Add answer to Rise
Rise = 1574
Plumb Height = 242
Total Rise = 1816

4. RISE
4(b) Total Rise
22.5°
3800
90°
67.5°
67.5°
22.5°
1641574
1738
152
Rafter
2.Determine Plumb Height = 242
3.Add answer to Rise
Rise = 1574
Plumb Height = 164 (152 x 1.082)
Total Rise = 1738
If you wanted to find the height to
Top of Rafter – you would
substitute the perpendicular
distance to the top of Rafter

• Based on data
– 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
1.Rise
2.Amount Left On Plumb Height
3.Total Rise
Click on Spread sheet to determine answers

• Based on data
– Timber Depth To be Supplied by Trainer
Timber Depth is used to determine amount left on
Determine
1.Rise
2.Amount Left On Plumb Height
3.Total Rise
Click on Spread sheet to determine answers
Roof Pitch 22.5
Span 7600
Amount Left On 152
Amount Left On
Plumb Height 165
Rise 1574
Total Rise 1739

(5) Major Crown End Rafter
RAFTER
MAJOR CROWN
½ SPAN
½SPAN
(a)Centreline Length
How far does it travel in “Plan” ?

(a)Centreline Length
1/2SPAN
1/2 SPAN
RISE
1/2 SPAN
PLUMB CUT
ROOF PITCH
RIDGE
Rafter Travels to
Gathering Point
Plan View
Side Elevation

(a) Centreline Length
RAFTER
MAJOR CROWN
½ SPAN
½SPAN

1/2SPAN
1/2 SPAN
RISE
1/2 SPAN
PLUMB CUT
ROOF PITCH
RIDGE
(a) Centreline Length, Which Multiplier?
Plan Length = ½ Span
The Rise must be the same as
1.Common Rafter

1/2SPAN
1/2 SPAN
RISE
1/2 SPAN
PLUMB CUT
ROOF PITCH
RIDGE
1.Common Rafter
The Plan Length is the same as
1. Common Rafter

1/2SPAN
1/2 SPAN
RISE
1/2 SPAN
PLUMB CUT
ROOF PITCH
RIDGE
1.Common Rafter
1.Common Rafter
The Pitch must be the same as
1. Common Rafter

1/2SPAN
1/2 SPAN
RISE
1/2 SPAN
PLUMB CUT
ROOF PITCH
RIDGE
1.Common Rafter
1.Common Rafter
1. Common Rafter
We use the Common Rafter Multiplier = Rafter Length per metre

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

(a) Centreline Length = ½ Span x Rafter Length per m
RAFTER
MAJOR CROWN
½ SPAN
½SPAN

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

Exercise 5a
• Based on data given to you by you trainer
determine,
Centreline Length Major Crown

Exercise 5a
determine,
Click on Spread Sheet to determine answers
°
= 4113
Span
Pitch
7600
22.5

5. Major Crown End
(b) True Length
How far does it Travel in Plan ?
RAFTER
MAJOR CROWN
½ SPAN
½SPAN

5. Major Crown End
(b) True Length
CentringRafter
½ Span – ½ Rafter
RISE
½ Span – ½ Rafter ROOF PITCH
RIDGE
True Length Rafter
Travels to edge of
Centring Rafter
Major Crown End

5. Major Crown End
(b) True Length
RAFTER
MAJOR CROWN
½ SPAN - ½ Rafter
½SPAN

5. Major Crown End
(b) True Length= (½ Span – ½ Rafter) x Rafter Length per m
RAFTER
MAJOR CROWN
½ SPAN - ½ Rafter
½SPAN

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
= 3782.5 x 1.082
= 4093

Exercise 5a
determine,
True Length Major Crown End Rafter

Exercise 5a
determine,
True Length Major Crown End Rafter
°
Rafter Thickness mm
= 4094
Span
Pitch
7600
22.5
35

5. Major Crown End
(i) Plumb Cut Graphically

Establish False Top Plate
5. Major Crown End

Establish ½ Span
5. Major Crown End

Establish Rise
5. Major Crown End

Plumb Cut
Establish Crown End Rafter
5. Major Crown End

Plumb Cut
•Rise is Same as Common Rafter
•Plan Length is Same as Common Rafter
5. Major Crown End

Plumb Cut
•Rise is Same as Common Rafter
•Plan Length is Same as Common Rafter
•Plumb Cut must be the same as Common Rafter
5. 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,
• (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°

15°
20°
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 Method
5. (ii) – Worked Example
1.082
22.5°
0.414
1.159
20.9°
Run
Rafter Plumb
Cut
Rise = 0.414 ÷ 2
= 0.207
Run = 1.000 ÷ 2
= 0.500
Rise

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

5. (ii)
1.082
22.5°
0.414
1.159
20.9°
Run
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

• 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 207
Run 500

22.5°
224
38
45
17
10
3800
152
90°
5. Major Crown End
(ii) Plumb Cut Offset Method
Total of Internal angles of Triangle formed by Roof = 180°

22.5°
224
38
45
17
10
3800
152
90°
67.5°
5. Major Crown End
In a Right Angled Triangle one of the angles = 90°

22.5°
224
38
45
17
10
3800
152
90°
5. Major Crown End
The other 2 angles must = 90°
(180° – 90° = 90°)

22.5°
224
38
45
17
10
3800
152
90°
5. Major Crown End
Therefore this angle
Must = 90° - Roof Pitch

22.5°
224
38
45
17
10
3800
152
90°
67.5°
5. Major Crown End
Therefore this angle
= 90° - 22.5°
= 67.5°

22.5°
224
38
45
17
10
3800
152
90°
67.5°
5. Major Crown End
This Triangle is formed by the Roof

22.5°
224
38
45
17
10
3800
152
90°
67.5°
5. Major Crown End
A SIMILAR triangle is also formed in this position

22.5°
224
38
45
17
10
3800
152
90°67.5°
22.5°
224
38
45
17
10
3800
152
90°
67.5°
5. Major Crown End
As the triangles are SIMILAR these angles must be the same

22.5°
224
38
45
17
10
3800
152
90°
67.5°
This Angle must = 90° - Roof Pitch
= 67.5°
5. Major Crown End

224
38
45
17
10
152
67.5°
5. Major Crown End
This Angle must = 90° - Roof Pitch
= 67.5°

If we mark a square line at Top of Rafter & Extend Base
5. Major Crown End
224
38
45
17
10
152
67.5°

38
45
17
10
152
67.5°
22.5°
90.0°
A Triangle is Formed
5. Major Crown End

38
45
17
10
152
67.5°
22.5°
90.0°
This angle is the same as the Roof Pitch
5. Major Crown End

38
45
17
10
152
67.5°
22.5°
90.0°
This angle must be 90°
5. Major Crown End

38
45
17
10
152
67.5°
22.5°
90.0°
This angle must be 90° - Roof Pitch
5. Major Crown End

38
45
17
10
152
67.5°
22.5°
90.0°
This triangle MUST BE A SIMILAR TRIANGLE to the 1m triangle formed by the Rafter
5. Major Crown End

38
17
152
67.5°
22.5°
90.0°
5. Major Crown End
1.082
22.5°
0.414

38
17
152
67.5°
22.5°
90.0°
5. Major Crown End
1.082
22.5°
0.414
Therefore we can use the same multipliers to determine its dimensions

38
45
17
10
152
67.5°
22.5°
90.0°
5. Major Crown End
What is the Pitch angle of this triangle?

38
45
17
10
152
67.5°
22.5°
90.0°
5. Major Crown End
What is the Plan Length?
Pitch Angle = 22.5°

38
45
17
10
152
67.5°
22.5°
90.0°
5. Major Crown End
What is the Plan Length?
Plan Length
= 152 + 38
= 190

38
45
17
10
152
67.5°
22.5°
90.0°
5. Major Crown End
Offset = Rise Multiplier x Plan Length
= 0.414 x 190
= 77mm
This length is
Similar to
The 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)
5. Major Crown End

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

• Pattern Rafter (90 x 45)90
5. Major Crown End

• Pattern Rafter (90 x 45)
1. Mark Square Line
90
5. Major Crown End

1. Mark Square Line
2. Determine Plumb Cut Offset and Mark Out
= 90 x Rise per 1m of Rafter in plan or 90 x (Tan 22.5°)
= 90 x 0.414
= 37mm
90
37
5. Major Crown End

1. Mark Square Line
2. Determine Plumb Cut Offset and Mark Out
90 x 0.414= 37mm
3. Mark Plumb Cut
90
Plumb Cut
5. Major Crown End
37

Worked Example
• Based on the pitch of 25°and using a 150mm
Deep Rafter determine ,
Plumb Cut Offset- Major Crown End
= 190 x Rise per 1 metre of Rafter in plan
= 0.414 x 190mm
= 79mm

• Based on the pitch & Timber Width supplied
by the Trainer determine ,
On the Supplied A4 sheet demonstrate the set
out of the “Plumb Cut”

• 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

CENTREINGRAFTER
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTER
(6) Minor Crown End Rafters
Radius = ½ Span
Octagonal End Based on
Semi Circle
How Far does it Travel in plan?

CENTREINGRAFTER
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTER
Plan Length =
½ Span
Semi Circle
Major Crown is a Radius

CENTREINGRAFTER
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTER
Semi Circle
Major Crown is a Radius
Minor Crown also is a Radius

1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
Minor Crown End Rafters
travel to Gathering Point
M
inor C
row
n
End
M
inorCrown
End

1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
Determine Centreline Length: Which Multiplier?
The Rise be same as
1.Common Rafter &
2.Major Crown End Rafter
M
inor C
row
n
End
M
inorCrown
End

1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
The Rise be same as
Common Rafter &
Common Rafter &
M
inor C
row
n
End
M
inorCrown
End

1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
The Rise be same as
Common Rafter &
Common Rafter &
Common Rafter &
M
inor C
row
n
End
M
inorCrown
End

1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
The Rise be same as
Common Rafter &
Common Rafter &
Common Rafter &
M
inor C
row
n
End
M
inorCrown
End
We use the Common Rafter Multiplier = Rafter Length per metre

CENTREINGRAFTER
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTER
(a) Centreline Length = Plan Length x Rafter Length per m
Note - Plan Length = ½ Span (Which is the same as the Major Crown)

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
= 4112

Exercise 6a
determine,
True Length Minor Crown End Rafter

Exercise 6a
determine,
°
= 4113
Span
Pitch
7600
22.5

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.Mathematically
II.Graphically
(b) Shortening

(b)(i) Shortening of Crown End Rafters from Centreline Length -
Mathematically
Remember Centreline Plan Length = ½ Span

(b)(i) Shortening of Crown End Rafters from Centreline Length - Mathematically
1/2SPAN
1/2 SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTERS
Rafter travels to Intersection of
•Centring Rafter &
•Major Crown

½ RAFTER
½RAFTER
½
R
AFTER
x
1.414
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
M
inorC
rown
End
R
after
Shortening

½ RAFTER
½RAFTER
½
R
AFTER
x
1.414
Shortening = ½ Rafter x 1.414
Shortening
Note
1.414 = √2
M
inorC
rown
End
R
after

½ RAFTER
½RAFTER
½
R
AFTER
x
1.414
Worked Example
Rafter = 35mm
= (35 ÷ 2) x 1.414
= 17 x 1.414
= 24mm
Shortening
Note
1.414 = √2
M
inorC
rown
End
R
after

• 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
=
42
Width ÷ 2
21
29.694

½ RAFTER
½RAFTER
½
R
AFTER
x
1.414
Worked Example
Rafter = 35mm
= (35 ÷ 2) x 1.414
= 17 x 1.414
= 24mm
Shortening
Note
1.414 = √2
M
inorC
rown
End
R
after
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”

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
CENTRINGRAFTERS
M
IN
O
R
C
R
O
W
N
EN
D
R
AFTER
M
IN
O
R
C
R
O
W
N
EN
D
MAJOR CROWN END RAFTER
Draw Centrelines

17.5
Gathering Point
CENTRINGRAFTERS
M
IN
O
R
C
R
O
W
N
EN
D
R
AFTER
M
IN
O
R
C
R
O
W
N
EN
D
Draw Timber Thicknesses at full size
In this case all Roof Members
Are 35mm thick
i.e. 17.5 either side of Centreline

25
42
42
Gathering Point
CENTRINGRAFTERS
M
IN
O
R
C
R
O
W
N
EN
D
R
AFTER
M
IN
O
R
C
R
O
W
N
EN
D
Dimension Shortening from Centreline
Note Zoomed in for Clarity

25
42
42
Gathering Point
CENTRINGRAFTERS
M
IN
O
R
C
R
O
W
N
EN
D
R
AFTER
M
IN
O
R
C
R
O
W
N
EN
D
To put this drawing into practical use
you need to understand that
1.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

b) 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
22.5°
Side Elevation

Mark Out Plumb Cuts as determined in 6c
CENTRELINE LENGTH
22.5°
Side Elevation

d) ii. Shortening from Centreline Length - Graphically
Mark Lines square on Top of Rafter
CENTRELINE
LENG
TH
22.5°
Side Elevation

CENTRELINE
LENG
TH
22.5°
Isometric View
Centreline Length
You Rafter should now be marked with
1.Centreline Length

CENTRELINE LENGTH
22.5°
These lines are Plumb
Side Elevation

CENTRELINE LENGTH
22.5°
90°
A line 90° to Plumb will be level
Side Elevation

) ii. Shortening from Centreline Length - Graphically
CENTRELINE LENGTH
22.5°
90° The measurements on the drawing
are 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
22.5°
90°
Side Elevation

25
42
42
25
Transfer plan measurements determined in 6 (b) (ii)
Mark Centreline
Shortening Distance
Side Elevation
Plan View
All measurements are
taken from Centreline
Length

25
42
42
25
Transfer plan measurements determined in 6 (d) (ii)
Mark Line using
Plumb Cut Bevel
Side Elevation
Plan View

25
42
42
25
Mark Line using
Plumb Cut Bevel
Which represents
this point in PLAN
Side Elevation
Plan View

25
90°
Isometric View
Mark Line square
on Top of Rafter
Centreline Length

25
90°
Isometric View
Mark Centreline
Centreline Length

25
42
42
42
25
Mark Edge BevelShortening Distance

25
42
42
42
25
Mark Line using
Plumb Cut Bevel

25
42
42
42
25
Mark Line using
Plumb Cut Bevel
Which represents
these points in PLAN

42
90°
Isometric View
Mark Lines square
on Top of Rafter
Centreline Shortening
Centreline Length

CENTRELINE
LENG
TH
22.5°
25
42
Isometric View
You Rafter should now be marked with
1.Centreline Length
2.Centreline Shortening
3.Edge Bevel Shortening
4.Thickness Centreline Mark
Thickness Centreline Mark

25
42
42
25
42
Isometric ViewPlan View
Centreline Length

25
42
42
25
42
Centreline Length

25
42
42
25
42
Centreline Length
Edge Bevel Shortening

25
42
42
25
42
Isometric View
Thickness Centreline Mark
Plan View
Centreline Length
Edge Bevel Shortening

CENTRELINELENGTH
CENTRELINESHORTENING
EDGEBEVELSHORTENING
Isometric View
This is the Shape of the
end of the Rafter in Plan
Plan View

25
42
42
CENTRELINELENGTH
EDGEBEVELSHORTENING
Isometric View
End of the Rafter
It is based on the measurements
Determined previously
Plan View

25
42
42
CENTRELINELENGTH
EDGEBEVELSHORTENING
Isometric View
End of the Rafter
Plan View
We now replicate
what we see in Plan
on the Actual Rafter

25
42
42
CENTRELINELENGTH
EDGEBEVELSHORTENING
Isometric View
End of the Rafter
Plan View
Draw Lines Starting From
1.Edge Bevel Shortening

25
42
42
CENTRELINELENGTH
EDGEBEVELSHORTENING
Isometric View
End of the Rafter
Plan View
Draw Lines Starting From
1.Edge Bevel Shortening to Intersection of
2.Centreline Shortening & Thickness Centreline to

CENTRELINELENGTH
EDGEBEVELSHORTENING
Isometric View
The Rafter is then cut to
This Shape
The length has also been shortened
And 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 1
2.On Timber Supplied Develop shortening based
on a pitch of 27° & ½ Span of 300mm
a) Timber to be supplied by Trainer

Confirmation of Learning – Answer 1
• Shortening in Plan
32
54
54

Confirmation of Learning – Answer 2
• Shortening in Elevation
CENTERLINE LENGTH = 337MM
27°
32
54
EDGEBEVELSHORTENING
CENTRELINELENGTH

(c) True Length
1/2SPAN
1/2 SPAN
½
SPAN
–
(½
R
AFTER
x
1.414)
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
CENTREINGRAFTERS
Rafter travels to Intersection of
•Centring Rafter &
•Major Crown

½ RAFTER
½RAFTER
½
R
AFTER
x
1.414
(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
Rafter Plan Reduction
M
inorC
rown
End
R
after

45,0°
(½
Span
–
(½
R
afterx
1.414))x
R
afterLength
perm
(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.
– 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.
– 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 - Shortening
True Length = x Rafte Length per m
= ( 3800 - 25 ) x
= 3775 x
= 4086
35
24.745
1.082
22.5
7600
Plan Length
Width ÷ 2 1.414
1.414
1.082
1.082

(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
1/2SPAN
1/2 SPAN
1/2
SPAN
1/2
SPAN

i. Graphically
1/2SPAN
1/2 SPAN
1/2
SPAN
1/2
SPAN
Extend Construction Lines
Perpendicular to ends of Rafter

i. Graphically
1/2SPAN
1/2 SPAN
1/2
SPAN
1/2
SPAN
Establish False Top Plate

i. Graphically
1/2SPAN
1/2 SPAN
1/2
SPAN
1/2
SPAN
1/2
SPAN
Establish Plan Length

i. Graphically
1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
1/2
SPAN
1/2
SPAN
Establish Rise

i. Graphically
1/2SPAN
1/2 SPAN
R
ISE
1/2
SPAN
PLU
M
B
C
U
T
R
O
O
F
PITC
H
1/2
SPAN
1/2
SPAN
Draw in Rafter
•Establish Plumb Cut
•Establish Roof Pitch

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

1/2SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
45°
6. Minor Crown End Rafters
(e) Edge Bevel Development
In Plan this
Angle = 45⁰

1/2SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
45°
In Plan this
Angle = 45⁰
When can you use the plan angle?

1/2SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
IN
O
R
C
R
O
W
N
45°
In Plan this
Angle = 45⁰
When can you use the plan angle?
When you use a power tool such as
1.Drop Saw
2.Power Saw etc

Edge Bevel Minor Crown End Rafters
Plan Angle
Plan Angle = 45⁰
Plan Angle = 90⁰

Plan Angle
Plan Angle = 45⁰
Plan Angle = 90⁰
Both Sides Must
Be Equal

Plan Angle
Plan Angle = 45⁰
Plan Angle = 90⁰
Both Sides Must
Be Equal
When Can You Use The Plan For
the Edge Bevel ?

Plan Angle
Plan Angle = 45⁰
Plan Angle = 90⁰
Both Sides Must
Be Equal
When Can You Use The Plan For
the Edge Bevel ?
1/2SPAN
MAJOR CROWN
M
IN
O
R
C
R
O
W
N
M
INO
R
C
R
O
W
N

True Angle
What members form the triangle?

True Angle
Centreline Length Rafter

True Angle
If this angle is 45⁰

True Angle
This angle must 45⁰

True Angle
Both these sides
must be equal

True Angle
This line runs
parallel with the top
Of the Rafter
Which is level

7.Plan Length Hip Rafter

7. Plan Length Hip Rafter

These angles are
always 90⁰

These angles are
always 45⁰

These angles are
always 22.5⁰

These relationships are constant on all properly built Octagonal Roofs
These angles are
always 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
MAJOR CROWN
½ SPAN - ½ Rafter
½SPAN
1/2 Span x 1.082
22.5°

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
MAJOR CROWN
½ SPAN - ½ Rafter
½SPAN
1/2 Span x 1.082
22.5°

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

1.082
22.5°
0.414
1.159
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 plan
2.Apply the multiplier

1.Determine how far it travels in plan ?

1.082
22.5°
0.414
1.159
20.9°
If we remember our multiplier is derived on the following premise
Hip Rafter Length for every 1m metre of Rafter in Plan

1.082
22.5°
0.414
1.159
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

1.Determine how far it travels in plan = ½ Span

1.082
22.5°
0.414
1.159
20.9°
Hip Rafter Multiplier for 22.5° = 1.159

1.Determine how far it travels in plan = ½ Span
2.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 22.5°
– Hip Multiplier 1.159
Centreline Length of Hip = Plan Length x Hip Rafter Length per m
Note - Plan Length = ½ Span
= (7800 ÷ 2) x 1.159
= 3800 x 1.159
= 4404

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

– Pitch Supplied by Trainer
– Hip Multiplier As derived from pitch
Click on Spread Sheet for Answers
Span
Pitch °
Hip Multiplier
Hip Centreline = 3800 x 1.159
= 4404
22.5
7600
1.159

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
Roof Pitch 25 °
Hip Pitch 23.3 °

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

Rise
Hip Run
Hip Plumb Cut
1.082
22.5°
0.414
1.159
20.9°
Divide by 2

Rise
Hip Run
Hip Plumb Cut
1.082
22.5°
0.414
1.159
20.9°
Divide by 2
Rise = 207
Hip Run = 541

207
541
Hip Plumb Cut
1.082
22.5°
0.414
1.159
20.9°
Divide by 2
Rise = 207
Hip Run = 541

9b.Hip Plumb – Offset Method

9b.Hip Plumb – Offset Method
1.082
22.5°
0.414
1.159
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
= 0.382 x 190
= 73mm

Worked Example 2
Using 1m Trainagle Data
Roof Pitch = 22.5
Rise = 0.414
Timber Depth = 190mm
= (Timber Depth ÷ 1.082) x 0.414
= (190 ÷ 1.082) x 0.414
= 175.6 x 0.414
= 73mm

10. True Length Hip Rafter
CentreingRafter
MAJOR CROWN
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
To determine the True Length
1.Determine how far it travels
2.Apply the correct multiplier

10 True Length Hip Rafter
a) Shortening
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
We must determine how
Far in the direction of the
Rafter does the hip travel

a) Shortening
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
We must determine the
Distance from ½ Span to
The plan length
This is called the shortening

HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
a) Shortening
We Reduce from ½ Span
1.½ Ridge Thickness

a) Shortening
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
2.½ Rafter x 1.414

a) Shortening
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
2.½ Rafter x 1.414
This Reduction is call the Shortening
= ½ Ridge Thickness + ½ Rafter x 1.414

a) Shortening – Worked Example
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
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

a (i) Edge Bevel – Graphically
This Dimension measured from True Length in Plan
EDGEBEVELSHORTENING

TRUELENGTH
Isometric Elevation
a (iii) Edge Bevel – Graphically

TRUELENGTH
EDGEBEVELSHORTENING
EDGE BEVEL SHORTENING
Isometric Elevation
This measurement
Is at 90° to the Plumb Cut

TRUELENGTH
EDGEBEVELSHORTENING
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 22.5
Span (mm) 7600
Rafter Thickness (mm) 35
Hip Thickness (mm) 35
Centreline Length (mm) 4404
Shortening in Plan 45.7297
Edge Bevel in Plan 42.24874
All measurements from Centreline Length

(b) True Plan Length
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
Determine Plan Length
= ½ Span - Shortening

(b) True Plan Length – Worked Example
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
= ½ Span – Shortening
= 3800 – 42.5
= 3757.5

• Based on the previous exercise and data
supplied by the Trainer
• Determine True Plan Length Hip Rafter

SHORTENING
EDGEBEVELSHORTENING
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

c) Shortening from Centreline Length - Graphically
90°
Isometric View
Mark Lines square
on Top of Rafter
Centreline Length

(b) True Plan Length
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414

• 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

(b) True Length
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
Apply Multiplier
= Plan Length x Hip per 1m Rafter

(b) True Length – Worked Example
HIP RAFTER
M
IN
O
R
C
R
O
W
N
HIPRAFTER
PLANLENGTH
1/2SPAN
½RIDGE
½RAFTERx1.414
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 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

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
• = 1086.3 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
3
The simplest way is to draw it
This can be done mathematically but
It is a convoluted process
In this the correction is -3mm

22.5°
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

22.5°
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
Hip Thickness 35
Rafter Thickness 35
centerline short 45.7297
Long Point Extenstion 42.24874
Long Point Correction -3.48097

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
1. Determine Creeper Shortening
2. Determine Long Point Correction
3. Determine 1st Creeper True Length
4. Determine all other Creepers

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

Creepers
(d) Determine Creepers
84

Octagonal end roof

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