Oblique End & Skew End Roof
Oblique End & Skew End Roof
Solve Angles x and y
Walls are parallel
Solve Angles x and y
Walls are parallel
Determine relevant triangle
Solve Angles x and y
Walls are parallel
Tan y = Opp/ AdjTan y = 2000 / 900
Solve Angles x and y
Walls are parallel
Tan y = 2.222Angle y = 65.8⁰
Solve Angles x and y
Walls are parallel
Angle Z =180 – 90 - 65.8⁰
Solve Angles x and y
Walls are parallel
Angle Z = 24.2⁰
Solve Angles x and y
Walls are parallel
Angle X = 24.2 + 90⁰ ⁰
Solve Angles x and y
Walls are parallel
Angle X = 114.2⁰
Oblique End Roof
Determine Position of Centring Rafters
Position Centring Rafter
If we extend ridge (which is central) it will intersect with centre of splay end
Positioning Centring Rafter
Two Similar Triangles will be formed, 1 half the size of the other
Positioning Centring RafterRemember for laterTherefore we can say the ridge extension length is half the length of the splay end extension
Position Centring Rafters
Remember Hips MUST Bisect Corners
Position Centring Rafters
Remember Hips MUST Bisect Corners(Angles will vary)
Positioning Centring Rafterx90⁰ x
Corner is Bisected this must also = x
Positioning Centring Rafterx90⁰ x
To form TriangleѲ = 180 – 90 – xѲ = 90 - x
Ѳ
Positioning Centring Rafterx90⁰ x
Hip is at 90⁰ to Centring Rafters
90⁰ - x
Positioning Centring Rafterx90⁰ x
Ѳ = 90⁰ – 90⁰ - x
90⁰ - x
Ѳ⁰
Positioning Centring Rafterx90⁰ x
Ѳ = x
90⁰ - x
Ѳ⁰
Positioning Centring Rafterx90⁰ x
To form triangleѲ =180⁰ - x – x = 180⁰ - 2x
90⁰ - x
x Ѳ
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
Positioning Centring Rafterx90⁰ x
Centring Rafters are at 90⁰ to Ridge & Wall Plates
90⁰ - x
x 180⁰ - 2x
2x
Positioning Centring Rafterx90⁰ x
The internal angles of a 4 Sided polygon must total 360⁰
90⁰ - x
x 180⁰ - 2x
2x
Positioning Centring Rafter90⁰
x
Ѳ = 360⁰ - 90⁰ - 90⁰ - 2x⁰ = 180⁰ -2x
90⁰ - x
x 180⁰ - 2x
2x
Ѳ
x
Positioning Centring Rafter90⁰
Remember Hips bisect corners
90⁰ - x
x 180⁰ - 2x
2x
180⁰ - 2x
xx
Positioning Centring Rafterx90⁰
Ѳ
Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x
90⁰ - x
x 180⁰ - 2x
2x
180⁰ - 2x
Ѳ
Positioning Centring Rafterx90⁰
90⁰ - x
Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x
90⁰ - x
x 180⁰ - 2x
2x
90⁰ - x
x
Positioning Centring Rafterx90⁰
90⁰ - x
Complete the TriangleѲ = 180⁰ - 90⁰ - (90⁰ - x) = x
90⁰ - x
x 180⁰ - 2x
2x
90⁰ - x
x
Ѳ
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
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
Positioning Centring Rafterx90⁰
90⁰ - x
Angle between Hip Rafters = 90⁰
90⁰ - x
x 180⁰ - 2x
2x
90⁰ - x
x
x
90⁰ - x
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
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
=
=
Positioning Centring Rafter
Lines from each end of a diameter that intersect on the circumference of the Circle will intersect at 90⁰
=
=
Positioning Centring Rafter
If we extend lines from these intersectionsTo the centre of the circle
=
=
Positioning Centring Rafter
If we extend lines from these intersectionsTo the centre of the circle
They must be radiuses
=
=
Positioning Centring Rafter
The ridge line extended past the centringRafter must be a radius of this circle
Positioning Centring Rafter
The Ridge Extension must equal the half length of the Splay end
=
=
=
Positioning Centring Rafter
=
=
=
Positioning Centring Rafter
Previously we determined that the length of The ridge extension was half the splay end extension
=
=
=
Positioning Centring Rafter
Therefore the offset must equalRadius – Half Splay Extension
=
=
=
Positioning Centring Rafter
Better we can sayHalf Splay End Length – Half Splay Extension
1097 – 450 = 647
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)
x90⁰
90 90⁰ - x
x
Solve Angle yDeveloping from last week
y
x90⁰
90 90⁰ - x
x
1. Hips Always Bisect Corners
Solve Angle yDeveloping from last week
y
x
90⁰ - x
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
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
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
x
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
This angle must be 90 - x
x
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
The angles in both these trianglesare the same
x
90⁰
90⁰
x90⁰
90 90⁰ - x
Solve Crown End Run
90- x
90- x
Therefore these triangles are similar triangles
x
90⁰
90⁰
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 Run = Half Span
Crown End Rafter position willEqual same distance as CentringRafters from the short end
x
90⁰
90⁰
Gathering Point
Similar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters
Gathering PointSimilar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters
Gathering Point
Similar to conventional hip roof all members that form the oblique end hip have the same rise as the common rafters
Crown End Rafter Centreline Length
Similar to a conventional hip roof
The Crown End Rafters Centreline Run is the same as the common rafters
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
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
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
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
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
Crown End Rafter True Length
Similar to a conventional hip roof
The Crown End Rafters will butt into the Centring Rafters
Crown End Rafter True Length
Different to a conventional hip roof
The Crown End Rafters do not butt into the Centring Rafters at 90⁰
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
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