splay end hip
DESCRIPTION
Splay End Hip. Advanced Roofing. Roof Set Out. Hips always bisect corners. Centre an arc on the origin of the 2 lines you want to Bisect. Scribe to cut external walls. Centre 2 arcs on the intersection of the lines you want To bisect & the previous scribed arc. - PowerPoint PPT PresentationTRANSCRIPT
Splay End Hip
Advanced Roofing
Roof Set Out
Hips always bisect corners
Centre an arc on the origin of the 2 lines you want to Bisect
Scribe to cut external walls
Centre 2 arcs on the intersection of the lines you wantTo bisect & the previous scribed arc
Radii need not be the same as the previous arc but both must be equal
Centre 2 arcs on the intersection of the lines you wantTo bisect & the previous scribed arc
Radii need not be the same as the previous arc but both must be equal
Both arcs must cross
Extend a line from the origin of the corner to be bisected thru the furtherest intersection of the arcs
The line formed has bisected the corner
The line formed has bisected the corner
Repeat the process for the other corner
Oblique End Roof
Roof Geometry
Roof Geometry
If we extend ridge (which is central) it will intersect with centre of splay end
Roof Geometry
Two Similar Triangles will be formed, 1 half the size of the other
Roof GeometryRemember for laterTherefore we can say the ridge extension length is half the length of the splay end extension
Roof GeometryRemember for laterWe need to remember this number for later use
Roof Geometry
Walls are parallel
Determine relevant triangle
Walls are parallel
Tan y = Opp/ AdjTan y = 2000 / 900
Roof Geometry
Walls are parallel
Tan y = 2.222Angle y = 65.8⁰
Roof Geometry
Walls are parallel
Angle Z =180 – 90 - 65.8⁰
Roof Geometry
Walls are parallel
Angle Z =180 – 90 - 65.8⁰
Roof Geometry
Walls are parallel
Angle Z = 24.2⁰
Roof Geometry
Walls are parallel
Angle X = 24.2 + 90⁰ ⁰
Roof Geometry
Walls are parallel
Roof Geometry
Walls are parallel
Roof Geometry
Note the 2 angles must add up to 90⁰
Roof Geometry
Walls are parallel
Roof Geometry
This angle = 90 – 57.1⁰
Roof Geometry
This angle = 90 – 32.9⁰
A straight lines = 180⁰
Roof Geometry
Walls are parallel
180 - 57.1 - 32.9 = 90⁰ ⁰ ⁰ ⁰
Roof Geometry
Roof Geometryx
90⁰ -x
90⁰ x
90 90⁰ - x
x
90⁰
Therefore we can say1.When the corners of a splayed end roof are bisected they will intersect at the ridge
2.The angles formed by the hips will be 90⁰
90⁰ - x
Roof Geometry
If we centre a circle on the intersection of the Ridge & skew end
Then make the diameter the lengthOf the skew end
The circle will pass thru the corners
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=
Roof Geometry
Geometric RuleLines from each end of a diameter that intersect on the circumference of the Circle will intersect at 90⁰
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=
Roof Geometry
If we extend lines from these intersectionsTo the centre of the circle
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=
Roof Geometry
If we extend lines from these intersectionsTo the centre of the circle
They must be radii
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=
=
=
=
Roof Geometry
The ridge line extended past the centringRafter must be a radius of this circle
Roof Geometry
The Ridge Extension must equal the half length of the Splay end
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=
=
Roof Geometry
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=
=
Roof Geometry
Previously we determined that the length of The ridge extension was half the splay end extension
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=
1. Determine Splay ExtensionSplay Extension = Long Side – Short Side
SHORT SIDE
LONG SIDE
SP
LAY
EN
D LE
NG
THS
PA
N
SPLAY EXTENSION
1. Confirmation of Learning Determine Splay Extension
Splay Extension = Long Side – Short Side62
94
14162
11329
1. Confirmation of Learning Determine Splay Extension - Answer
Splay Extension = 14162 – 11329
Long Side 14162Short Side 11329
Splay Extension 2833
Determine Splay Extension
283311329
6294
14162
2. Determine Splay End LengthSplay End Length = √((Splay Extension)2 + (Span)2)
SHORT SIDE
LONG SIDE
SP
LAY
EN
D LE
NG
TH
SP
AN
SPLAY EXTENSION
2. Confirmation of Learning Determine Splay End Length
Splay End Length = √(Splay Extension)2 + (Span)2)
283311329
6294
14162
2. Confirmation of Learning Determine Splay End Length - Answer
Splay End Length = √(Splay Extension)2 + (Span)2)
11329
6294
14162
2833
6902
Span 6294Splay Extension 2833
Splay End 6902
2.Determine Splay End Length
Positioning Centring Rafter
Therefore the offset must equalRadius – Half the Splay Extension
=
=
=
Position of Centring RaftersTherefore we can sayIf External walls are parallel
Hips always bisect corners
1.When the corners of a splayed end roof are bisected they will intersect at the ridge
2.The angles formed by the hips will be 90⁰ (This is the same for a conventional roof)
3.The intersection will occur at ½ the length of the splay end from the intersection of the ridge line & top plate.
4.Offset = ½ Spay end – ½ Splay extension
3.Positioning Centring RafterOffset = (Splay End Length – Splay Extension) ÷ 2
SPLAY EXTENSION
SP
LAY
EN
D
OFFSETT
Centring Rafters
3.Confirmation of Learning Positioning Centring Rafter
Offset = (Splay End Length – Splay Extension) ÷ 2
Centring Rafters
11329
6294
14162
2833
6902
OFFSETT
3.Confirmation of Learning Positioning Centring Rafter - Answer
Offset = (Splay End Length – Splay Extension) ÷ 2
11329
6294
14162
2833
6902
2035
Splay End 6902Splay Extension 2833
Offset 2035
3. Position of Centring Rafters
x90⁰
Position Crown End Rafter
90 - x
x90⁰
90 - x
x
Angle is bisected as Hips always bisect corners
Position Crown End Rafter
x90⁰
Position Crown End Rafter
90 - x
x
90⁰Rafters are always 90° to top plates
x90⁰
Position Crown End Rafter
90 - x
x
90 - x90⁰
This angle must = 90 - x
x90⁰
Position Crown End Rafter
90 - x
x
90 - x90⁰
The hypotenuse is the same
x90⁰
Position Crown End Rafter
90 - x
x
90 - x90⁰
The other 2 sides of the triangles must be the same
Triangle A ½ Span = Cos (90-x) x HypotenuseOffset = Sin (90-x) x Hypotenuse
Triangle BCrown Run = Cos (90-x) x HypotenuseCrown Pos = Sin (90-x) x Hypotenuse
A
B
x90⁰
Position Crown End Rafter
90 - x
x
90 - x90⁰
Triangles are the same
x90⁰
90 90⁰ - x
x
4.Position Crown End Rafter
90 - x
x
90 - x90⁰
Position of Crown End = Offset
4.Positioning Crown End Rafter
SPLAY EXTENSION
SP
LAY
EN
D
OFFSETT
Centring Rafters
Ridge
Gathering Point is Intersection ofRidge & Centring Rafters
4.Positioning Crown End Rafter
SPLAY EXTENSION
SP
LAY
EN
D
OFFSETT
90°
OFFS
ET
T
Centring Rafters
Ridge
Crown End RafterRuns from Gathering PointAnd is perpendicular to Splay End
4.Positioning Crown End RafterOffset = (Splay End Length – Splay Extension) ÷ 2
Same Distance to Centring Rafters
SPLAY EXTENSION
SP
LAY
EN
D
OFFSETTO
FFS
ETT
1/2
Spa
n
1/2 Span
1 13 4. 51
Centring Rafters
Ridge
Crown End RafterRuns from Gathering PointAnd is perpendicular to Splay End
x90⁰
90 90⁰ - x
x
Solve Crown End Plan Length
90 - x
x
90 - x90⁰
This must be ½ Span
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
The Hypotenuse of these triangles are the same
x
90⁰
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
The triangles are equal trianglesSo all sides will be equal
x
90⁰
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
Crown End Run = Half Span
x
90⁰
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
Crown End Rafter position willEqual same distance as CentringRafters from the short end
x
90⁰
90⁰
SPLAY EXTENSION
SP
LAY
EN
DOFFSETT
90°
OFF
SE
TT
1/2
Spa
n
1/2 Span
5. Crown End Plan Length
Crown End Rafter Plan Length = ½ Span
SPLAY EXTENSIONS
PLA
Y E
ND
OFFSETT
90°
OFFS
ETT
1/2
Spa
n
1/2 Span
6 . Crown End Rafter Centreline Length
If Plan Length of Both Rafter is1/2 Span and
6 . Crown End Rafter Centreline Length
As in all other pervious Roofs the Rise is the same
RIS
E
PLAN LENGTH PLAN LENGTH
RIS
E
28.57° 28.5
7°RIS
E
6 . Crown End Rafter Centreline Length
Common Rafter Crown End Rafter
If The Plan Length is the Same &If The Rise is the Same thenThe Pitch must be the Same
SPLAY EXTENSIONS
PLA
Y E
ND
OFFSETT
OFFS
ETT
1/2
Spa
n
1/2 Span
RiseR
ise
6 . Crown End Rafter Centreline Length
Crown End Centreline Length = Common Rafter Centreline Length
7.Crown End Development
27
11This Line Represents Centreline Length
Plan Development
Dimensions willVary depending on splay
7.Crown End Development
27
11
This Line Represents Centreline Length
Plan Development
Dimensions willVary depending on splay
7.Crown End Development
27
11This Line Represents Centreline Length
Confirmation of LearningDevelop the Crown End on your drawing
Dimensions willVary depending on splay
8.Plan Length Hip ShortPlan Length of Hip = √(1/2 Span2 + Offset2)
8.Plan Length Hip ShortPlan Length of Hip = √(1/2 Span2 + Offset2)
2035
6294
8.Plan Length Hip ShortPlan Length of Hip = √(1/2 Span2 + Offset2) 2035
6294 37
47
9. Centreline Length Hip ShortCentreline Length of Hip = √(Plan Length Hip2 + Rise2)
10.Plan Length Hip LongPlan Length of Hip = √(1/2 Span2 + (Offset + Extension)2)
2035
6294
2833
10.Plan Length Hip LongPlan Length of Hip = √(1/2 Span2 + (Offset + Extension)2)
10.Plan Length Hip LongPlan Length of Hip = √(1/2 Span2 + (Offset + Extension)2)
11.Centreline Length Hip Long
Centreline Length of Hip = √(Plan Length Hip2 + Rise2)
12 . Develop Hip A
12 . Develop Hip A
27
32
21
11
13 . Develop Hip B
2035
6294
2833Creeper Reduction
• Short Hip
Plan Length = ½ Span x Spacing Dist to Corner
2035
6294
2833Creeper Reduction
• Short Hip
Plan Length = 3147 x 450 2035 = 696 x RLPM
2035
6294
2833
Creeper Bevel
• Short Hip
2035
6294
2833Creeper Reduction
• Long Hip
CS = ½ Span x Spacing Dist to Corner
54
Creeper Bevel
• Short Hip
2035
6294
2833
5796
Creeper Reduction
• Short Hip
Creeper Shortening A
200
200
Shortening
Triangle formed by Shortening & Spacing
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Triangle formed by Shortening & Spacing
Is a similar triangle to triangle formed by Crown End Rafter & Offset
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Ratios between the sides of similar triangle will be the same
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Ratio = Shortening ÷ Spacing
Ratio = Centreline length Crown End ÷ Offset
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Ratio = Shortening ÷ Spacing
Ratio = Centreline length Crown End ÷ Offset
Note we use Centreline length as we want the centreline shortening.If we want plan shortening we use the plan crown end length
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Shortening ÷ Spacing = Centreline length Crown End ÷ Offset
Spacing
200
Shortening
Offset
Plan/Centreline Length Rafter
Creeper Shortening A
Shortening = Centreline length Crown End x Spacing ÷ Offset
Creeper Shortening B
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n / C
enre
line
Ra
fter
Sho
rten
ing
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n /
Ce
nre
line
Ra
fter
Sh
orte
nin
g
Creeper Shortening B
Triangle formed by Shortening & Spacing
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n /
Ce
nre
line
Raf
ter
Sho
rte
ning
Creeper Shortening B
Triangle formed by Shortening & Spacing
Is a similar triangle to triangle formed by Centring Rafter & Offset + Splay End
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n /
Ce
nre
line
Raf
ter
Sho
rte
ning
Creeper Shortening B
Ratios between the sides of similar triangle will be the same
Creeper Shortening B
Ratio = Shortening ÷ Spacing
Ratio = Centreline Centring Rafter ÷ (Offset + Splay Extension)
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n /
Ce
nre
line
Ra
fter
Sho
rte
ning
Creeper Shortening B
Ratio = Shortening ÷ Spacing
Ratio = Centreline Centring Rafter ÷ (Offset + Splay Extension)
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n /
Ce
nre
line
Ra
fter
Sho
rte
ning
Note we use Centreline length as we want the centreline shortening.If we want plan shortening we use the plan crown end length
Creeper Shortening B
Shortening ÷ Spacing = Centreline Centring Rafter ÷ (Offset + Splay Extension)
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n / C
enre
line
Raf
ter
Sho
rten
ing
Creeper Shortening B
Shortening = Centreline Centring Rafter x Spacing ÷ (Offset + Splay Extension)
Plan/Centreline Length Rafter
Spacing
Offset + Splay Extension
1/2
Spa
n / C
enre
line
Raf
ter
Sho
rten
ing
Plan Creeper A Long Point Correction
10
45
Centreline Length
Add Long Point
Deduct Short Point
Mark Up Pattern Rafter
Pattern Rafter Centreline Length
Deduct Creeper Shortening
Pattern Rafter Centreline Length
Creeper Shortening
Add Long Point Correction
Pattern Rafter Centreline Length
Creeper Shortening
10
Add Short Point Correction
Pattern Rafter Centreline Length
Creeper Shortening
10
45
Isometric View
Isometric View
Square short point across to other edge
Isometric View
Join long point & short point to form edge bevel
Isometric View
Plan Creeper B Long Point Correction
11
11
Centreline Length
Long point
Short Point
Mark Up Pattern Rafter
Pattern Rafter Centreline Length
Deduct Creeper Shortening
Pattern Rafter Centreline Length
Creeper Shortening
Add Long Point Correction
Pattern Rafter Centreline Length
Creeper Shortening
11
Add Short Point Correction
Pattern Rafter Centreline Length
Creeper Shortening
11 11
Isometric View
Isometric View
Square short point across to other edge
Isometric View
Join long point & short point to form edge bevel
Isometric View