splay end hip

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

=

=

Roof Geometry

Geometric RuleLines from each end of a diameter that intersect on the circumference of the Circle will intersect at 90⁰

=

=

Roof Geometry

If we extend lines from these intersectionsTo the centre of the circle

=

=

Roof Geometry

If we extend lines from these intersectionsTo the centre of the circle

They must be radii

=

=

=

=

=

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

=

=

=

Roof Geometry

=

=

=

Roof Geometry

Previously we determined that the length of The ridge extension was half the splay end extension

=

=

=

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