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HIP ROOFING. BCGCA3007B. Common Rafter. For a detailed explanation of determining the common rafter, review the “Gable Roof Presentation”. Problem No1 Lets warm your brain up. Calculate Underside of Beams Birdsmouth 30mm Rafter 140 x 45. Problem No1. Calculate Underside of Beams. - PowerPoint PPT Presentation
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HIP ROOFING
BCGCA3007B
Common Rafter
• For a detailed explanation of determining the common rafter, review the “Gable Roof Presentation”
Problem No1Lets warm your brain up
Calculate Underside of BeamsBirdsmouth 30mmRafter 140 x 45
Problem No1
Calculate Underside of Beams
Review Principles of Roofing
1. Ridges are Level2. Rafters run at 90⁰ to Wall Plate3. Hips & Valleys bisect all internal & external Corners4. Roof members are set out along centerlines
Ridges are Level
Golden Principles of Roofing
1. Ridges are Level2. Rafters run at 90⁰ to Wall Plate3. Hips & Valleys bisect all internal & external Corners4. Roof members are set out along centerlines
Rafters at 90° to top plate
Golden Principles of Roofing
1. Ridges are Level2. Rafters run at 90⁰ to Wall Plate3. Hips & Valleys bisect all internal & external Corners4. Roof members are set out along centerlines
Hips & Valleys bisect all internal & external Corners
Golden Principles of Roofing
1. Ridges are Level2. Rafters run at 90⁰ to Wall Plate3. Hips & Valleys bisect all internal & external Corners4. Roof members are set out along centerlines
Roof members are set out along centerlines
Types of Roofs
Types of Roofs
Types of Roofs
Exercise 2 – Draw in Hips & Valleys
Exercise 2
Hips & Valleys always Bisect Corners
Hips & Valleys always Bisect CornersThis also applies to complex roofs we will construct in Stage 3
Splay End Hip
Review Principles of Roofing
1. Ridges are Level2. Rafters run at 90⁰ to Wall Plate3. Hips & Valleys bisect all internal & external Corners4. Roof members are set out along centerlines
Centreline Plan Length of Hip (Z)
X = Half span = 2070
Z = √(x2) + (x2) = √(20702) + (20702)
Z = 2927
X = Half span = 2070
Z = Half span x √2
Z = 2927
Determining Hip Roof Members
Common Rafter
• Main Roofing Member• Calculated same method as Gable• Spaced Usually at 450mm to 600mm for Tiled
Roofs & 600mm to 900mm for Sheet Roof– This is dependant on span tables found in AS
1684.2
• Cut using a Pattern Rafter
Determine Common Rafter
Determine Common Rafter
Step 1 - Solve 1m Triangle
25°
1
Rise = 1 x Tan 25° = 0.466
Rafter Length / m = 1 ÷ Cos 25° = 1.103
0.4661.103
Step 1 - Solve 1m Triangle
25°
1
Rise = 1 x Tan 25° = 0.466
Rafter Length / m = 1 ÷ Cos 25° = 1.103
0.4661.103
Determine Centreline LengthRidge
Step 2 – Determine Plan LengthCentreline Length
25°
1
Plan Length= 2070
0.4661.103
2070(1/2 Span)Plan Length
Step 3 – Determine Rafter LengthCentreline Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2070 x 1.103
Rafter Length = 2283
0.4661.103
2070(1/2 Span)Plan Length
2283
Step 4 – Determine Rise (If Required) Centreline Length
25°
1
Total Rise = Horizontal Travel x Rise per metre
Total Rise = 2070 x 0.466
Total Rise = 964
0.4661.103
2283
964
2070(1/2 Span)Plan Length
Determine True Length
Step 2 – Determine Plan LengthTrue Length
25°
1
Plan Length = ½ Span – ½ Ridge ThicknessPlan Length = 2070 – 9.5Plan Length = 2060.5
0.4661.103
2060.5Plan Length
Plan Length = Distance from Top Plate to Edge of Ridge
Ridge 190 x 19
½ Ridge = 9.5mm
Step 3 – Determine Rafter LengthTrue Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2060.5 x 1.103
Rafter Length = 2273
0.4661.103
2060.5Plan Length
2273
Step 4 – Determine Rise (If Required) True Length
25°
1
Total Rise = Plan Length x Rise per metre
Total Rise = 2060.5 x 0.466
Total Rise = 960
0.4661.103
2283
960
2060.5Plan Length
Note – Rise is measured to pitching line only and IS NOT THE FULL HEIGHT OF THE ROOF
Centreing Rafter LayoutRoofs are Set out by Centreline
Centring Rafters
Centering Rafters Set back by Half Span
Centreing Rafter Layout
Centering Rafters Set back by Half Span
Centreing Rafter Layout
Centering Rafters Set back by Half Span
Centring Rafters are determined in the same manner as Common Rafter
Centreing Rafter Layout
Centering Rafters Set back by Half Span
Centring Rafters are determined in the same manner as Common Rafter
Exercise – Determine Centring Rafters at 25˚
Centering Rafters Set back by Half Span
Centring Rafters are determined in the same manner as Common Rafter
Step 1 - Solve 1m Triangle
25°
1
Rise = 1 x Tan 25° = 0.466
Rafter Length / m = 1 ÷ Cos 25° = 1.103
0.4661.103
This is the Same triangle as,•Common Rafter
Determine Centreline LengthRidge
Step 2 – Determine Plan LengthCentreline Length
25°
1
Plan Length= 2070
0.4661.103
2070(1/2 Span)Plan Length
Step 3 – Determine Rafter LengthCentreline Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2070 x 1.103
Rafter Length = 2283
0.4661.103
2070(1/2 Span)Plan Length
2283
Step 4 – Determine Rise (If Required) Centreline Length
25°
1
Total Rise = Horizontal Travel x Rise per metre
Total Rise = 2070 x 0.466
Total Rise = 964
0.4661.103
2283
964
2070(1/2 Span)Plan Length
Determine True Length
True Length of Centering Rafters
•Same as Common Rafter
•Half Ridge Thickness Deducted
Step 2 – Determine Plan LengthTrue Length
25°
1
Plan Length = ½ Span – ½ Ridge ThicknessPlan Length = 2070 – 9.5Plan Length = 2060.5
0.4661.103
2060.5Plan Length
Plan Length = Distance from Top Plate to Edge of Ridge
Ridge 190 x 19
½ Ridge = 9.5mm
Step 3 – Determine Rafter LengthTrue Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2060.5 x 1.103
Rafter Length = 2273
0.4661.103
2060.5Plan Length
2273
Step 4 – Determine Rise (If Required) True Length
25°
1
Total Rise = Plan Length x Rise per metre
Total Rise = 2060.5 x 0.466
Total Rise = 960
0.4661.103
2283
960
2060.5Plan Length
Note – Rise is measured to pitching line only and IS NOT THE FULL HEIGHT OF THE ROOF
Ridge Centreline Length• Used to centre Rafters• Length = Length – Number of Hip Ends x ½ Span
Confirmation of Learning
• On A3 drawing paper draw a plan view of a roof showing
1.Centring Rafters - Centreline
2.Ridge – Centreline
Example on Next Slide
Determine Ridge True Length
Determine Ridge True Length
The Ridge Extends past the centre of the centring rafter by ½ Rafter thickness
Confirmation of Learning
• On A3 drawing paper draw a plan view of a roof showing
1.Centring Rafters – Actual Thickness
2.Ridge – Actual Thickness
Example on Next Slide Rafter 35mm ThickRidge 19mm Thick
Crown End Rafters
•Cut & Fitted Against Ridge•Act as Opposing Braces•Similar to Common Rafter•Half Rafter is Deducted
True Length of Centering Rafters
•Same as Centreline as Common Rafter
•Half Rafter Thickness Deducted
Crown End Rafter LayoutWhat is the Crown End Rafter Centreline Plan Length?
Crown End Rafters
Crown End Rafter LayoutWhat is the Crown End Rafter Centreline Run?
Crown End Rafters
2070 ½ Span
Confirmation of Learning• On A3 drawing paper draw a plan view of a roof showing
1.Centring Rafters – Actual Thickness
2.Ridge – Actual Thickness
3.Crown End Rafter - Centreline
Example on Next Slide
Rafter 35mm ThickRidge 19mm Thick
Confirmation of Learning• On A3 drawing paper draw a plan view of a roof showing
1.Centring Rafters – Actual Thickness
2.Ridge – Actual Thickness
3.Crown End Rafter – Actual Thickness
Example on Next Slide
All Rafters 35mm ThickRidge 19mm Thick
350
250
12535
350
250
12535
Crown End Rafter LayoutWhat is the Crown End Rafter Plan Length?
Crown End Rafters
350
250
12535
Plan Length
Crown End Rafter LayoutWhat is the Crown End Rafter Plan Length?
Crown End Rafters
Plan Length = Distance from top plate to edge of member
Confirmation of Learning
Crown End Rafters
Determine Plan Length of Crown End Rafter Ridge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
Crown End Rafter True LayoutWhat is the PLAN Length of the Crown End Rafter
Crown End Rafter
Hip Rafters
Centering Rafters
Ridge
Plan length measuredTo edge of Centring Rafter
Confirmation of Learning
Crown End Rafters
Determine Plan Length of Crown End Rafter Ridge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
Plan Length
Confirmation of Learning
Crown End Rafters
Determine Plan Length of Crown End Rafter Ridge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
½ Span – ½ Rafter
Confirmation of Learning
Crown End Rafters
Determine Plan Length of Crown End Rafter Ridge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
2070 – 22.5
Confirmation of Learning
Crown End Rafters
Determine Plan Length of Crown End Rafter Ridge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
2047.5
Determine Crown End Rafter
Step 1 - Solve 1m Triangle
25°
1
Rise = 1 x Tan 25° = 0.466
Rafter Length / m = 1 ÷ Cos 25° = 1.103
0.4661.103
This is the Same triangle as,•Common Rafter•Centring Rafter
Determine Centreline LengthCrown End Rafter
Ridge
Step 2 – Determine Plan LengthCentreline Length
25°
1
Plan Length= 2070
0.4661.103
2070(1/2 Span)Plan Length
Step 3 – Determine Rafter LengthCentreline Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2070 x 1.103
Rafter Length = 2283
0.4661.103
2070(1/2 Span)Plan Length
2283
Determine True LengthCentring Rafter
90 x 45
Step 2 – Determine Plan LengthTrue Length
25°
1
Plan Length = ½ Span – ½ Rafter ThicknessPlan Length = 2070 – 22.5.5Plan Length = 2047.5
0.4661.103
2047.5 Plan Length
Plan Length = Horizontal Distance from Top Plate to Edge of Centring Rafter
Centring Rafter
90 x 45
½ Rafter = 22.5mm
True Length
REVIEW - Crown End Rafter LayoutWhat is the run of Centring Rafter & Crown End Rafter
Centering Rafter Run
Deduct Half Ridge
Ridge 140 x19 Rafter 90 x 45
Crown End Rafter Run deduct Half Centering Rafter
Step 3 – Determine Rafter LengthTrue Length
25°
1
Rafter Length = Plan Length x Rafter Length per metre (RL/m)
Rafter Length = 2047.5 x 1.103
Rafter Length = 2258
0.4661.103
2047.5Plan Length
2258
Step 4 – Determine Rise (If Required) True Rise for Crown End
25°
1
Total Rise = Plan Length x Rise per metre
Total Rise = 2047.5 x 0.466
Total Rise = 954mm
0.4661.103
2258
954
2047.5Plan Length
Note – Rise of the Crown Rafter is lower than the Common & Centring Rafters
Detail on Next Slide
Detail Explaining Rise of Centring Rafter
• Why isn’t the “TRUE” rise of the Crown End Rafter the same as the Common Rafters
• It depends!
Crown End Rafter LayoutRidge 140 x19 Rafter 90 x 45
CL Span is Half span CL Span is Half span
A
AB
B
A
Rafter Rise
4
19
45
10
22.5
10
45
22.5
As the crown end is further from the centre it must be lower
Section A-A
Section B-B
Centring Rafter
Ridge
Crown End Rafter
Crown End Rafter
Rafter Rise
4
19
45
10
22.5
As the crown end is further from the centre it must be lower
Section A-A
Section B-B
Centring Rafter
Ridge
Crown End Rafter
Crown End Rafter
If the Centring & Crown Rafter are the same thickness they should meet at this point
10
45
22.5
Crown End & Centring Rafter• Plan Length Crown End Rafter =
Half Span – Half Centring Rafter Width• Plan Length Centring Rafter =
Half Span – Half Ridge Width
Hip Rafter
• Runs From Corner to Intersection Crown End & Centering Rafter - Centerline
• Hips Bisect Corners• Support Creepers• Fixing and Locating of Creepers• Distance above Birdsmouth is same as
common rafters called “Amount Left On”
Hip Rafter LayoutRoofs are Set out by Centerline
Bisects Corner
Hip in Plan
Hip Rafter – Plan Length
Span of Hip
Hip Rafter – Plan Length
Hip Centreline Plan Length
Hip True Plan Length
Hip Rafter
Start Point for Hip
Hip Rafter
Corner Trimmed to allow a better fit
Hip Rafter
Hip Rafter LayoutRoofs are Set out by Centerline
Bisects Corner
Determine Centreline Span of Hip
Hip & Rafter Fixed Relationship
1.00
0
1.000
90°
Hip & Rafter Fixed Relationship
1.00
0
1.000
90°
Using Pythagoras Theorem
Z = √(12 + 12)
Z = √2 or 1.414
Using Similar Triangle
1.000
1.00
0
2.000
2.00
0
1 x
√2
2 x
√2
3.145
3.14
500
0
3.14
5 x
√2
Note these triangles are not to scale
45°
45°
90° 45°
45°
90° 45°
45°
90°
Confirmation of Learning
Express the Plan Length of the Hip as multiples of √2
½ Span Hip Length
1.000
4.563
7.896
12.546
Confirmation of Learning
Express the Plan Length of the Hip as multiples of √2
½ Span Hip Length
1.000 1 x √2
4.563 4.563 x √2
7.896 7.896 x √2
12.546 12.546 x √2
Centreline Plan length of Hip (Z)
½ Span = 2070
Z = 2070 x √2
Z = 2927
Confirmation of Learning
Determine Actual the Plan Length of the Hips Below
½ Span Hip Length
1.000
4.563
7.896
12.546
Confirmation of Learning
Express the Plan Length of the Hip as multiples of √2
½ Span Hip Length
1.000 1 x √2 = 1.414
4.563 4.563 x √2 = 6.453
7.896 7.896 x √2 = 11.167
12.546 12.546 x √2 = 17.743
Centreline Length of Hip
• Methods– Hip Centreline Length per Meter of Common
Rafter Run– Pythagoras– Scribing– Measure in Situ
From Gable Roof Lessons
We Know That for the above Roof the Rafter Length per meter can be calculated as follows
Rafter per meter run = √(1² + 0.577²) = 1.149
Roof Pitch = 30° Rise = 577 per metre
Given Rise = 577 per metre
The Hip must rise to the same height
½ Span
√2
1.000
0.5
77
30°
From Gable Roof Lessons
We Know That for the above Roof the Rafter Length per meter can be calculated as follows
Rafter per meter run = √(1² + 0.577²) = 1.149
Rafter per meter run = √(1 ÷ Cos 30°) = 1.149
Given Rise = 577 per metre
Roof Pitch = 30° Rise = 577 per metre
Given Rise = 577 per metre
The Hip must rise to the same height
½ Span
√21.000
0.5
77
30°
We learnt previously that for every 1meter of Plan Length of the common rafter the hips plan length is run √2 or 1.414.
√2 = √(12 + 12)
1.0001.000
Given Rise = 577 per metre
Roof Pitch = 30° Rise = 577 per metre
1.000 √2
1.155
We can draw the triangles formed as below
We learnt previously that for every 1meter of Plan Length of the common rafter the hips plan length is run √2 or 1.414.
√2 = √(12 + 12)
30°
0.57
7
Given Rise = 577 per metre
Roof Pitch = 30° Rise = 577 per metre
1.000 √2
1.155
We can draw the triangles formed as below
Previously demonstrated there is a fixed relationship between the Plan Length of the Common Rafter and the Plan Length of the Hip Rafter.
Plan Length of Hip = Plan Length of Common Rafter x √(2)
30°
0.57
7
Given Rise = 577 per metre
Roof Pitch = 30° Rise = 577 per metre
1.000 √2
1.155
If the Triangle is Solved using Pythagoras Theorem
Hip Length per metre of Rafter = √(Rise2 + √(2)2) = √(0.5772 + 2) = √(0.5772 + 2)
= 1.527
30°
Hip Length per metre of Rafter0.57
7
Given Rise = 577 per metre
Roof Pitch = 30° Rise = 577 per metre
1.000 √2
1.155
If the Triangle is Solved using Pythagoras Theorem
Therefore for every for a 30°,
• For 1m of Plan Length of the Common Rafter • the Hip Rafter Length is 1.527
The Hip Rafter will change with the Pitch
30°
1.527
0.57
7
Pitch = 30⁰
Using Pythagoras we determine the above triangle
Hip per meter of Common Rafter Run = √(1.4142+ 0.577²)= √(2+ 0.577²)
= √(2.333) = 1.527
Therefore for every meter of Common Rafter run at 30⁰The Hip Centreline Length = 1.527
1.527
Pitch = 30⁰
If the Roof is Twice the size (2x) all numbers will be multiplied by 2
1.527
1 m Triangle
3.054
2 x
1.5272.824
1.15
4
Pitch = 30⁰
If the Roof is 3600 times the size all numbers will multiplied by 3.6
1.527
1 m Triangle
5497
3600 x
36005091
2077
Using Pythagoras we determined on last slide the above triangle
Hip per meter of Common Rafter Run = √(√(2)² + 0.577²)= √(2+ 0.333²)
= √(2.333) = 1.527
Centreline Length of Hip = ½ span x Hip Length per 1 metre of Common Rafter Plan Length
Centreline Length of Hip = 2.070 x 1.527 = 3.161
Given Rise = 577 per metre
IN SUMMARY
5497
3600 x
36005091
2077
1.155
1m Triangle
1.0001.414
0.57
7
5257
3600 x
36005091
2077
1.460
1m Triangle
1.0001.414
0.36
4
20°20°
When Pitch Changes Plan dimensions do not change
IN SUMMARY
5497
3600 x
36005091
2077
1.155
1m Triangle
1.414 1.000
0.57
7
5257
3600 x
36005091
2077
1.460
1m Triangle
1.0001.414
0.36
4
20°20°
When Pitch Changes Rise & Hip dimensions do change
Centreline Length of Hip = Half span x Hip Length per meter of Common Rafter
Centreline Length of Hip = 2.070 x 1.527
= 3.161
`
Given Rise = 577 per metre
`
Confirmation of LearningDetermine the Following
Pitch Span Hip Length per Meter Hip C.L Length30 545015 2370
22.5 1056025 600032 459045 11300
Confirmation of LearningDetermine the Following
Pitch Span Hip Length per Meter Hip C.L Length30 5450 1.528 416315 2370 1.439 1706
22.5 10560 1.474 778125 6000 1.489 446732 4590 1.546 354845 11300 1.732 9786
Centreline Length of Hip
• Methods– Hip Centreline Length per Meter of Common
Rafter Run– Pythagoras– Scribing– Measure in Situ
Hip by Pythagoras
Step 1 – Calculate Roof RiseRise = Tan 25 x 2070⁰
= 965mm
Pitch 25⁰
Hip Rise Must Be The Same
Hip by Pythagoras
Step 1 – Calculate Roof RiseRise = Tan 25 x 2070⁰
= 965mm
Pitch 25⁰
Hip Rise Must Be The Same as the rest of the roof
Hip Centreline Length = √(Hip Span² + Rise²) = √(2927² + 965²) = 3082mm
What is the Hip Pitch ?
Rise 965mm
Hip by Pythagoras
Step 1 – Calculate Plan Length of Hip
= √(20702 x 20702)= 2927
Pitch 25⁰ Rise 965mm
Hip by Pythagoras
Step 1 – Calculate Plan Length of Hip
= √(20702 x 20702)= 2927
Pitch 25⁰ Rise 965mm
Step 2 – Determine Rise= 2070 Tan 25°= 965
Hip by Pythagoras
Step 1 – Calculate Plan Length of Hip
= √(20702 x 20702)= 2927
Pitch 25⁰
Hip Rise Must Be The Same as the rest of the roof
Hip Centreline Length = √(Hip Span² + Rise²) = √(2927² + 965²) = 3082mm
What is the Hip Pitch ?
Rise 965mm
Step 2 – Determine Rise= 2070 Tan 25°= 965
1.527
Determine Pitch of Hip
1.5271.155
1.155
√2 1.000
Or √2
0.57
7
If the hip uses a large distance to get to the rise it cannot be the same pitch as the Common Rafter
Determine Pitch of Hip
Adjacent
Opposite
Pitch°
Tan (Pitch)° = Opposite ÷ Adjacent
1.527
Determine Pitch of Hip
1.5271.155
1.155
√2 1.000
Or √2
0.57
7
Tan (Pitch)° = Opposite ÷ Adjacent = √2 ÷ 0.577
= 0.408
Use your Calculators Inverse Trigonometry FunctionInv Tan-1 (0.408) = 22°
Adjacent
Opposite
Centreline Length of Hip
• Methods– Hip Centreline Length per Meter of Common
Rafter Run– Pythagoras– Scribing– Measure in Situ
Scribing
Scribing
Scribing
Centreline Length of Hip
• Methods– Pythagoras– Hip Centreline Length per Meter of Common
Rafter Run– Scribing– Measure in Situ
In-Situ
In-Situ
In-Situ
Determine Plumb Cut Mathamatically
Revision - Determining Angles Mathematically for Common Rafter
Roof Pitch
Right Angled Triangle
This angle must be 65⁰90 – 25 = 65
This angle must be 25⁰90 – 65 = 25
Determining Plumb Cut Angles Mathematically
1. Extend Line 90⁰ From Rafter
Determining Angles Mathematically
1. Extend Line 90⁰ From Rafter2. Extend Plumb Line from
same origin at top of Rafter
Determining Angles Mathematically
1. Extend Line 90⁰ From Rafter2. Extend Plumb Line from
same origin at top of Rafter3. Angle Formed is same as
roof pitch
Determining Angles Mathematically
1. Extend Line 90⁰ From Rafter2. Extend Plumb Line3. Angle Formed is same as
roof pitch4. Offset = Tan (pitch) x width
Determining Angles Mathematically
1. Extend Line 90⁰ From Rafter2. Extend Plumb Line3. Angle Formed is same as
roof pitch4. Offset = Tan (25⁰) x 90
= 42
Determine Cutting Length of Hip
Steps1. Determine Corresponding
Crown End Rafter Plan Length
2. Determine True Length
Calculate Hip True LengthStep 1 – Determine Plan Length of Crown End
Pitch 25⁰Centering Rafter 90 x 45
Crown End Rafter Plan Length = Half Span – ½ Rafter Thickness= 2070 – 22.5= 4047.5 or 2048
Hip runs to edge of Crown End Rafter
Determine Hip RunHip Run Plan Length is based on Crown End Rafter’s Plan Length
Calculate Hip True LengthStep 2 – Determine True Length
Pitch 30⁰Centring Rafter 90 x 45
Hip True Length = Crown End Rafter Plan Length x Hip Length per m of Rafter= 2048 x 1.527= 3.127
Hip runs to edge of Crown End Rafter
1.527
√2 1.0000.
577
30°
Alternate Method to Calculate Hip True Length
Previous Centreline Calculation of Hip
Pitch 25⁰Rise = 965mmHip CL = 3082
Centreline Plan Length of Hip = √(Half Span² + Half Span²) = √(2070² + 2070²) = 2927
Crown End Rafter LayoutRidge 140 x19 Rafter 90 x 45Hip 140 x 19
Method 1Deduction = √(22.5²+ 22.5²)
= √1012.5= 31.8 or 32
Method 2Deduction = 1.414 x 22.5
= 31.8 or 32
Determine Run of HipPitch 25⁰Rise = 965mmHip CL = 3082
Hip Run = 2927 – 32
Hip Run = 2895
32 mm Deduction
Centreline Length
Determine Run of HipPitch 25⁰Rise = 965mmHip CL = 3082
Hip Run = 2927 – 32
Hip Run = 2895
32 mm Deduction
True Length
Determine Cutting Length of Hip
1. Determine Corresponding Crown End Rafter
2. Deductions
– Centring Rafters
– Corner of Plates
Deduction for Top Plate CutRidge 140 x19 Rafter 90 x 45Hip 140 x 19
Deduction = Hip Width / 2= 19 / 2= 9.5`
Hip Plumb CutMathematically
From previous work we determined the hip as follows
Hip Pitch may be determined either
Pitch = Tan-1 954/2895 = 0.330 = 18.25⁰
Determining Plumb Cut Mathematically – Hip 140 x 19
1. Extend Line 90⁰ From Rafter2. Extend Plumb Line from
same origin3. Angle Formed is same as
roof pitch4. Offset = Tan (18.25⁰) x 140
= 46
Markng Out Hip
1. Set Out Top Plumb Cut
Marking Out Hip
1. Set Out Top Plumb Cut2. Measure Calculated Hip Length
and place Plumb line
Marking Out Hip
1. Set Out Top Plumb Cut2. Measure Calculated Hip Length
and place Plumb line3. Mark same “Amount Left on”
as the Common Rafter
Common Rafter Hip Rafter
Marking Out Hip
1. Set Out Top Plumb Cut2. Measure Calculated Hip Length
and place Plumb line3. Mark “Amount Left on”4. Mark deduction for top plate
Marking Out Hip
Determine Hip LengthUsing Roofing Square
Use Calculator
Revise Common Rafter
1.Press Tan 25 – what does this give you2.Therefore for every 1 metre run there is 0.466m rise3.The hip rafter , Crown End Rafter & Common Rafter have the same rise
Hip has same rise as Common Rafter & Crown End Rafter
1. Therefore for every 1 metre run of Common Rafter there is 1 metre of run for the Crown End Rafter and there is 1.414 metres of run for the hip
2. For both members there is 0.466m rise3. Using the principle of similar triangles
we reduce the size of the triangle4. In this case to fit on the steel square we
need to divide by 3
1. As we reduce hip by 3 we reduce Crown End/ Common Rafter by 3 (1000 / 3 = 333)
2. There are (2048 / 333 =) 6.150 step outs for the Crown End rafter
3. There will also be 6.150 step outs for the Hip Rafter or 6 step outs + remainder( .189 x 471) 71
4. Plumb Cut Hip
Set Out Hip with Steel Square
Step 2
Using Steel Square for Hip step out six times
Step 3Using Tape measure out along a square line of Steel Square and mark Plumb Cut
Step 1 Mark Plumb Cut to Back of Birdsmouth
1
2
34
5
6
1. Eaves Allowance2. Eaves Width = 600mm3. There are (600 / 333 =)
1.802 step outs for the Eave Overhang
4. There will also be 1.802 step outs for the Hip Rafter or 1 step outs + remainder( .802 x 471) 378
5. Plumb Cut Hip
Set Out Hip with Steel Square
Eaves AllowanceEaves Width 600mm
As Overhangs are never pre-cut, we need leave enough say 2 Step Outs + Plumb Cut
Determine Hip Edge Bevel
Determine Hip Edge Bevel
This angle is in the Plane as the roof
Pitch 25⁰
Determine Hip Edge Bevel
Top Edge of Hip is not in the same plane as the Main Roof
Determine Hip Edge Bevel
Extend base of Hip to plane formed by Crown End Rafter
This line is Level
Determine Hip Edge Bevel
Plan View
Extend base of Hip to plane formed by Crown End Rafter
Determine Hip Edge Bevel
Plan View
New Line Formed is same length as Hip Run
Determine Hip Edge Bevel
Hip Centreline Length
Hip Centreline Run
Pitch 25⁰
Determine Hip Edge Bevel
Hip Centreline Length
Hip Centreline Run
Hip Edge Bevel
Pitch 25⁰
Determine Hip Edge Bevel
Hip Centreline Length
Hip Centreline Run
Hip Edge BevelEdge Bevel = Tan-1 Hip Run
Hip Length= Tan-1 2928 3082= Tan-1 0.950
= 43.53⁰
Pitch 25⁰
Review Determining Angles Mathematically
1. From Our Common Rafter Example
2. Note – Plumb Cut is not Roof Pitch
3. We require 65⁰4. To use Bevel, angle needs
to be in this position5. Therefore 90⁰ – (Required
Angle ) = Offset Angle
Edge Bevel HipMathematically
OFFSETT Angle = 90 - (Required Angle)⁰
= 90 - 43.53⁰ ⁰
= 46.47⁰
OFFSETT = Tan 46.47 x 90
= 95
Creeper Rafters
Creeper Rafters
Determine Creepers
1. Creepers Spacing Same as Common Rafter
2. Creepers usually of same material as Common Rafter
Pitch 25⁰
Determine Creepers
1. The Centreline Run of 1st Creeper is 1 Rafter Spacing less than the Centering Rafter
2. If take a view in this direction
Pitch 25⁰
Determine Creepers
1. This reduction in length can be represented by this triangle
2. As the pitch is the same as the common Rafter we can use the 1m Triangle
3. The hypotenuse = Rafter Spacing x Rafter Length per m
= 450 x 1.103 = 496mm
This is called the CREEPER SHORTENING
Pitch 25⁰
1.000
1.103
45° in Plan
Section V
iew
This is the same pitch as Common Rafter
Determine Creepers
1. All pairs of Creepers are reduced by the creeper shortening
Determine CreepersSetting Out
1. It is impractical to use centreline to measure creepers for cutting
2. Typically you would set out to the long point
3. We need to 1st determine the plan length of the Creeper at the “LONG POINT” as a distance from the top plate
Pitch 25⁰
Determining Creepers RunDetermine First Creeper Plan Length
1. Deduct Rafter Spacing
Pitch 25⁰Hip 140x19
Gets us to here
Dis
tanc
e fr
om T
op P
late
½ S
pan
– R
aft
er S
paci
ng
Determining Creepers RunDetermine First Creeper Plan Length
1. Deduct Rafter Spacing
2. Deduct Half Hip x 1.414
Pitch 25⁰Hip 140x19
We now need to get here
Determining Creepers RunDetermine First Creeper Run
1. Deduct Rafter Spacing
2. Deduct Half Hip x √2
3. Deduction = 9.5 x √2 = 13mm
Pitch 25⁰Hip 140x19
We now need to get here
½ S
pan
– R
aft
er S
paci
ng
– (
Hip
Th
ickn
ess
x √
2)
We now need to get here
Determine CreepersRafter 90 x 45
We now need to getto the long point
½ S
pan
– R
aft
er S
paci
ng
– (
Hip
Th
ickn
ess
x √
2) +
½ R
afte
r T
hick
ness
Determine CreepersSetting Out
Pitch 25⁰Hip 140 x19Creeper 90 x 45
1. Deduct Rafter Spacing
2. Deduct Half Hip x 1.414
3. Deduction = 9.5 x 1.414 = 13mm
4. Add ½ thickness of creeper
Determine CreepersSetting Out
Pitch 25⁰Hip 140 x19Creeper 90 x 45
The Plan Length of the 1st Creeper =
Centring Rafter RunLess Rafter SpacingLess Half Hip x 1.414Plus Half Creeper Thickness
Creeper RaftersDetermine 1st Creeper
1st Creeper Rafter Plan Length =
Half Span = 2070Minus Creeper Spacing = 450Minus Half Hip x 1.414 = 13Plus Half Creeper Thickness = 22.5
1st Creeper Plan Length = 1629.5
True Length = 1629.5 x Rafter /m = 1629.5 x 1.103 = 1797
Pitch 25⁰Hip 140 x19Creeper 90 x 45Rafter Spacing 450mmCreeper Shortening 497mm
1.000
1.103
Creeper Rafters
2nd Creeper Rafter True Length =
1st Creeper True Length = 1797Less Creeper Shortening - 497
2nd Creeper Rafter True Length = 1300
Pitch 25⁰Hip 140 x19Creeper 90 x 45Rafter Spacing 450mmCreeper Shortening 497mm
Creeper Rafters
3rd Creeper Rafter True Length =
2nd Creeper True Length = 1300Less Creeper Shortening - 497
3rd Creeper Rafter True Length = 803
Pitch 25⁰Hip 140 x19Creeper 90 x 45Rafter Spacing 450mmCreeper Shortening 497mm
Creeper Rafters
4th Creeper Rafter True Length =
3rd Creeper True Length = 803Less Creeper Shortening - 497
4th Creeper Rafter True Length = 306
Pitch 25⁰Hip 140 x19Creeper 90 x 45Rafter Spacing 450mmCreeper Shortening 497mm
Creeper Rafters
4th Creeper Rafter True Length =
3rd Creeper True Length = 794Less Creeper Shortening - 497
4th Creeper Rafter True Length = 307
Note – If distance from hip to last creeper is excessive an extra creeper may be placed to support eaves– This is called a DUMMY CREEPER
Pitch 25⁰Hip 140 x19Creeper 90 x 45Rafter Spacing 450mmCreeper Shortening 497mm
Edge Bevel Creeper
When we look in plan at a roofWe do not see its true shape
In this case we see a triangle With 2 sides appearing to equalLengths of half span
Pitch 25⁰
Edge Bevel Creeper
The true shape of the hipEnd is in fact defined byHalf Span andTrue Length Rafter
Pitch 25⁰
Edge Bevel Creeper
Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter
Pitch 25⁰
Edge Bevel Creeper
Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter
Angle = Tan-1(2070) 2284
Angle = Tan-1(0.9063)
= 42.19⁰
Pitch 25⁰
Edge Bevel Creeper
Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter
Angle = Tan-1(2070) 2284
Angle = Tan-1(0.9063)
= 42.19⁰
Pitch 25⁰
Determine Creeper Edge Bevel
Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter
Angle = Tan-1(2070) 2284
Angle = Tan-1(0.9063)
= 42.19⁰
Edge Bevel CreeperMathematically
OFFSETT Angle = 90 - (Required Angle)⁰
= 90 - 42.19⁰ ⁰
= 47.81⁰
OFFSETT = Tan 47.81 x 90⁰
= 99
Determine Purlin Edge Bevel
Plan View
Purlins Intersect at 90⁰ across Hip Rafter
Determine Purlin Edge Bevel
Plan View
Purlins Intersect at 90⁰ across Hip Rafter
Determine Purlin Edge Bevel
Purlins are parallel to top plate
Determine Purlin Edge Bevel
Angles are the same for all purlins on an equally pitched roof
Determine Purlin Edge Bevel
Angles formed at Top Plate is the same as formed at Purlin
Determine Purlin Edge Bevel
Triangle formed by Purlin, Hip & Centering Rafter
Triangle formed by Top Plate, Hip & Centering Rafter
Similar Triangles
Determine Purlin Edge Bevel
Determine Purlin Edge Bevel
Edge Bevel Angle
Angle = Tan-1(Rafter Centerline) Half Span
Angle = Tan-1(2284) 2070
Angle = Tan-1(1.103)
= 47.81⁰
Pitch 25⁰
Determine Purlin & Creeper Edge Bevel
Out of Same Triangle
Creeper Edge Bevel
Purlin Edge Bevel
Pitch 25⁰