Top Banner
Oblique End & Skew End Roof
70

CPCCCA3009A Construct Advanced Roofs Oblique roof

Jan 13, 2015

Download

Education

jbusse

 
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: CPCCCA3009A Construct Advanced Roofs Oblique roof

Oblique End & Skew End Roof

Page 2: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Page 3: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Determine relevant triangle

Page 4: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Tan y = Opp/ AdjTan y = 2000 / 900

Page 5: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Tan y = 2.222Angle y = 65.8⁰

Page 6: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Angle Z =180 – 90 - 65.8⁰

Page 7: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Angle Z = 24.2⁰

Page 8: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Angle X = 24.2 + 90⁰ ⁰

Page 9: CPCCCA3009A Construct Advanced Roofs Oblique roof

Solve Angles x and y

Walls are parallel

Angle X = 114.2⁰

Page 10: CPCCCA3009A Construct Advanced Roofs Oblique roof

Oblique End Roof

Page 11: CPCCCA3009A Construct Advanced Roofs Oblique roof

Determine Position of Centring Rafters

Page 12: CPCCCA3009A Construct Advanced Roofs Oblique roof

Position Centring Rafter

If we extend ridge (which is central) it will intersect with centre of splay end

Page 13: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

Two Similar Triangles will be formed, 1 half the size of the other

Page 14: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring RafterRemember for laterTherefore we can say the ridge extension length is half the length of the splay end extension

Page 15: CPCCCA3009A Construct Advanced Roofs Oblique roof

Position Centring Rafters

Remember Hips MUST Bisect Corners

Page 16: CPCCCA3009A Construct Advanced Roofs Oblique roof

Position Centring Rafters

Remember Hips MUST Bisect Corners(Angles will vary)

Page 17: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

Corner is Bisected this must also = x

Page 18: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

To form TriangleѲ = 180 – 90 – xѲ = 90 - x

Ѳ

Page 19: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

Hip is at 90⁰ to Centring Rafters

90⁰ - x

Page 20: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

Ѳ = 90⁰ – 90⁰ - x

90⁰ - x

Ѳ⁰

Page 21: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

Ѳ = x

90⁰ - x

Ѳ⁰

Page 22: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

To form triangleѲ =180⁰ - x – x = 180⁰ - 2x

90⁰ - x

x Ѳ

Page 23: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

If the angles formed by a T intersection must total 180⁰Ѳ =180 ⁰ - (180⁰ - 2x) = 2x

90⁰ - x

x 180⁰ - 2x

Ѳ

Page 24: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

Centring Rafters are at 90⁰ to Ridge & Wall Plates

90⁰ - x

x 180⁰ - 2x

2x

Page 25: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰ x

The internal angles of a 4 Sided polygon must total 360⁰

90⁰ - x

x 180⁰ - 2x

2x

Page 26: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter90⁰

x

Ѳ = 360⁰ - 90⁰ - 90⁰ - 2x⁰ = 180⁰ -2x

90⁰ - x

x 180⁰ - 2x

2x

Ѳ

x

Page 27: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter90⁰

Remember Hips bisect corners

90⁰ - x

x 180⁰ - 2x

2x

180⁰ - 2x

xx

Page 28: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

Ѳ

Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x

90⁰ - x

x 180⁰ - 2x

2x

180⁰ - 2x

Ѳ

Page 29: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

90⁰ - x

Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x

90⁰ - x

x 180⁰ - 2x

2x

90⁰ - x

x

Page 30: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

90⁰ - x

Complete the TriangleѲ = 180⁰ - 90⁰ - (90⁰ - x) = x

90⁰ - x

x 180⁰ - 2x

2x

90⁰ - x

x

Ѳ

Page 31: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

90⁰ - x

Angle between Rafters & Ridge is 90⁰ Ѳ = 90⁰ - x

90⁰ - x

x 180⁰ - 2x

2x

90⁰ - x

x

x

Ѳ

Page 32: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

90⁰ - x

Angle between Hip RaftersѲ = 90⁰ - x + x = 90⁰

90⁰ - x

x 180⁰ - 2x

2x

90⁰ - x

x

x

90⁰ - x

Page 33: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx90⁰

90⁰ - x

Angle between Hip Rafters = 90⁰

90⁰ - x

x 180⁰ - 2x

2x

90⁰ - x

x

x

90⁰ - x

Page 34: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx

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

Page 35: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

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

=

=

Page 36: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

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

=

=

Page 37: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

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

=

=

Page 38: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

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

They must be radiuses

=

=

Page 39: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

The ridge line extended past the centringRafter must be a radius of this circle

Page 40: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

The Ridge Extension must equal the half length of the Splay end

=

=

=

Page 41: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

=

=

=

Page 42: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

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

=

=

=

Page 43: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

Therefore the offset must equalRadius – Half Splay Extension

=

=

=

Page 44: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafter

Better we can sayHalf Splay End Length – Half Splay Extension

1097 – 450 = 647

Page 45: CPCCCA3009A Construct Advanced Roofs Oblique roof

Positioning Centring Rafterx

90⁰ -x

90⁰ x

90 90⁰ - x

x

90⁰

Therefore 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)

Page 46: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

x

Solve Angle yDeveloping from last week

y

Page 47: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

x

1. Hips Always Bisect Corners

Solve Angle yDeveloping from last week

y

x

90⁰ - x

Page 48: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

x

1. Hips Always Bisect Corners2. Rafters are always at 90° to wall plates

Solve Angle yDeveloping from last week

y

x

90⁰

Page 49: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

x

1. Hips Always Bisect Corners2. Rafters are always at 90° to wall plates

Solve yDeveloping from last week

90 -x

x

90⁰This angle must = 90 - x

Page 50: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

x

90⁰

Page 51: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

This angle must be 90 - x

x

90⁰

Page 52: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

The angles in both these trianglesare the same

x

90⁰

90⁰

Page 53: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

Therefore these triangles are similar triangles

x

90⁰

90⁰

Page 54: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

The Hypotenuse of these triangles are the same

x

90⁰

90⁰

Page 55: CPCCCA3009A Construct Advanced Roofs Oblique roof

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

Page 56: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

Crown End Run = Half Span

x

90⁰

90⁰

Page 57: CPCCCA3009A Construct Advanced Roofs Oblique roof

x90⁰

90 90⁰ - x

Solve Crown End Run

90- x

90- x

Crown End Run = Half Span

Crown End Rafter position willEqual same distance as CentringRafters from the short end

x

90⁰

90⁰

Page 58: CPCCCA3009A Construct Advanced Roofs Oblique roof

Gathering Point

Similar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters

Page 59: CPCCCA3009A Construct Advanced Roofs Oblique roof

Gathering PointSimilar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters

Page 60: CPCCCA3009A Construct Advanced Roofs Oblique roof

Gathering Point

Similar to conventional hip roof all members that form the oblique end hip have the same rise as the common rafters

Page 61: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter Centreline Length

Similar to a conventional hip roof

The Crown End Rafters Centreline Run is the same as the common rafters

Page 62: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter Centreline Length

Similar to a conventional hip roof

The Crown End Rafters Centreline Rise is the same as the Common Rafters

The Crown End Rafters Centreline Run is the same as the Common Rafters

Page 63: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter Centreline Length

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = CL Run ÷ Cos PitchCrown CL = 1000 ÷ Cos 25⁰Crown CL =1000 ÷ 0.906Crown CL =1.103

Pitch 25⁰

Page 64: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter Centreline Length

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = CL Run ÷ Cos PitchCrown CL = 1000 ÷ Cos 25⁰Crown CL =1000 ÷ 0.906Crown CL =1.103 (Note that this length also represents the length per metre

Pitch 25⁰

Page 65: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter Centreline Length using Pythagoras

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = √(CL Run² + Rise²)Crown CL = √(1² + 0.466²)Crown CL = √(1 + 0.217) = √(1.217) Crown CL =1.103

Pitch 25⁰

Page 66: CPCCCA3009A Construct Advanced Roofs Oblique roof

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = CL Run ÷ Cos PitchCrown CL = 1000 ÷ Cos 25⁰Crown CL =1000 ÷ 0.906Crown CL =1.103

Pitch 25⁰

Crown End Rafter Centreline Length using Trigonometry

Page 67: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter True Length

Similar to a conventional hip roof

The Crown End Rafters will butt into the Centring Rafters

Page 68: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter True Length

Different to a conventional hip roof

The Crown End Rafters do not butt into the Centring Rafters at 90⁰

Page 69: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter True Length

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = CL Run ÷ Cos PitchCrown CL = 1000 ÷ Cos 25⁰Crown CL =1000 ÷ 0.906Crown CL =1.103 (Note that this length also represents the length per metre

Pitch 25⁰

Page 70: CPCCCA3009A Construct Advanced Roofs Oblique roof

Crown End Rafter True Length

The Centreline Line (CL) Length can be calculated in the same way

Crown CL = √(CL Run² + Rise²)Crown CL = √(1² + 0.466²)Crown CL = √(1 + 0.217) = √(1.217) Crown CL =1.103

Pitch 25⁰