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- 1. Oblique End & Skew End Roof
- 2. Solve Angles x and y Walls are parallel
- 3. Solve Angles x and y Walls are parallel Determine relevant triangle
- 4. Solve Angles x and y Walls are parallel Tan y = Opp/ Adj Tan y = 2000 / 900
- 5. Solve Angles x and y Walls are parallel Tan y = 2.222 Angle y = 65.8 ⁰
- 6. Solve Angles x and y Walls are parallel Angle Z =180 – 90 - 65.8 ⁰
- 7. Solve Angles x and y Walls are parallel Angle Z = 24.2 ⁰
- 8. Solve Angles x and y Walls are parallel Angle X = 24.2⁰ + 90⁰
- 9. Solve Angles x and y Walls are parallel Angle X = 114.2⁰
- 10. Oblique End Roof
- 11. Determine Position of Centring Rafters
- 12. Position Centring Rafter If we extend ridge (which is central) it will intersect with centre of splay end
- 13. Positioning Centring Rafter Two Similar Triangles will be formed, 1 half the size of the other
- 14. Positioning Centring Rafter Remember for later Therefore we can say the ridge extension length is half the length of the splay end extension
- 15. Position Centring Rafters Remember Hips MUST Bisect Corners
- 16. Position Centring Rafters Remember Hips MUST Bisect Corners (Angles will vary)
- 17. Positioning Centring Rafter x 90⁰ x Corner is Bisected this must also = x
- 18. Positioning Centring Rafter x 90⁰ x To form Triangle Ѳ = 180 – 90 – x Ѳ = 90 - x Ѳ
- 19. Positioning Centring Rafter x 90⁰ x Hip is at 90⁰ to Centring Rafters 90⁰ - x
- 20. Positioning Centring Rafter x 90⁰ x Ѳ = 90⁰ – 90⁰ - x 90⁰ - x Ѳ⁰
- 21. Positioning Centring Rafter x 90⁰ x Ѳ = x 90⁰ - x Ѳ⁰
- 22. Positioning Centring Rafter x 90⁰ x To form triangle Ѳ =180⁰ - x – x = 180⁰ - 2x 90⁰ - x x Ѳ
- 23. Positioning Centring Rafter x 90⁰ x If the angles formed by a T intersection must total 180⁰ Ѳ =180 ⁰ - (180⁰ - 2x) = 2x 90⁰ - x x 180⁰ - 2x Ѳ
- 24. Positioning Centring Rafter x 90⁰ x Centring Rafters are at 90⁰ to Ridge & Wall Plates 90⁰ - x x 180⁰ - 2x 2x
- 25. Positioning Centring Rafter x 90⁰ x The internal angles of a 4 Sided polygon must total 360⁰ 90⁰ - x x 180⁰ - 2x 2x
- 26. Positioning Centring Rafter 90⁰ x Ѳ = 360⁰ - 90⁰ - 90⁰ - 2x⁰ = 180⁰ -2x 90⁰ - x x 180⁰ - 2x 2x Ѳ x
- 27. Positioning Centring Rafter 90⁰ Remember Hips bisect corners 90⁰ - x x 180⁰ - 2x 2x 180⁰ - 2x x x
- 28. Positioning Centring Rafter x 90⁰ Ѳ Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x 90⁰ - x x 180⁰ - 2x 2x 180⁰ - 2x Ѳ
- 29. Positioning Centring Rafter x 90⁰ 90⁰ - x Ѳ = 180⁰ - 2x 2 2 = 90⁰ - x 90⁰ - x x 180⁰ - 2x 2x 90⁰ - x x
- 30. Positioning Centring Rafter x 90⁰ 90⁰ - x Complete the Triangle Ѳ = 180⁰ - 90⁰ - (90⁰ - x) = x 90⁰ - x x 180⁰ - 2x 2x 90⁰ - x x Ѳ
- 31. Positioning Centring Rafter x 90⁰ 90⁰ - x Angle between Rafters & Ridge is 90⁰ Ѳ = 90⁰ - x 90⁰ - x x 180⁰ - 2x 2x 90⁰ - x x x Ѳ
- 32. Positioning Centring Rafter x 90⁰ 90⁰ - x Angle between Hip Rafters Ѳ = 90⁰ - x + x = 90⁰ 90⁰ - x x 180⁰ - 2x 2x 90⁰ - x x x 90⁰ - x
- 33. Positioning Centring Rafter x 90⁰ 90⁰ - x Angle between Hip Rafters = 90⁰ 90⁰ - x x 180⁰ - 2x 2x 90⁰ - x x x 90⁰ - x
- 34. Positioning Centring Rafter x 90⁰ -x 90⁰ x 90 90⁰ - x x 90⁰ <ul><li>Therefore we can say </li></ul><ul><li>When the corners of a splayed end roof are bisected they will intersect at the ridge </li></ul><ul><li>The angles formed by the hips will be 90⁰ </li></ul>
- 35. Positioning Centring Rafter If we centre a circle on the intersection of the Ridge & skew end Then make the diameter the length Of the skew end The circle will pass thru the corners = =
- 36. Positioning Centring Rafter Lines from each end of a diameter that intersect on the circumference of the Circle will intersect at 90 ⁰ = =
- 37. Positioning Centring Rafter If we extend lines from these intersections To the centre of the circle = =
- 38. Positioning Centring Rafter If we extend lines from these intersections To the centre of the circle They must be radiuses = =
- 39. Positioning Centring Rafter The ridge line extended past the centring Rafter must be a radius of this circle
- 40. Positioning Centring Rafter The Ridge Extension must equal the half length of the Splay end = = =
- 41. Positioning Centring Rafter = = =
- 42. Positioning Centring Rafter Previously we determined that the length of The ridge extension was half the splay end extension = = =
- 43. Positioning Centring Rafter Therefore the offset must equal Radius – Half Splay Extension = = =
- 44. Positioning Centring Rafter Better we can say Half Splay End Length – Half Splay Extension 1097 – 450 = 647
- 45. Positioning Centring Rafter x 90⁰ -x 90⁰ x 90 90⁰ - x x 90⁰ <ul><li>Therefore we can say If External walls are parallel Hips always bisect corners </li></ul><ul><li>When the corners of a splayed end roof are bisected they will intersect at the ridge </li></ul><ul><li>The angles formed by the hips will be 90⁰ (This is the same for a conventional roof) </li></ul>
- 46. Solve Angle y Developing from last week x 90⁰ 90 90⁰ - x x y
- 47. Solve Angle y Developing from last week x 90⁰ 90 90⁰ - x x <ul><li>Hips Always Bisect Corners </li></ul>y x 90⁰ - x
- 48. Solve Angle y Developing from last week x 90⁰ 90 90⁰ - x x <ul><li>Hips Always Bisect Corners </li></ul><ul><li>Rafters are always at 90° to wall plates </li></ul>y x 90⁰
- 49. Solve y Developing from last week x 90⁰ 90 90⁰ - x x <ul><li>Hips Always Bisect Corners </li></ul><ul><li>Rafters are always at 90° to wall plates </li></ul>90 -x x 90⁰ This angle must = 90 - x
- 50. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x x 90⁰
- 51. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x This angle must be 90 - x x 90⁰
- 52. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x The angles in both these triangles are the same x 90⁰ 90⁰
- 53. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x Therefore these triangles are similar triangles x 90⁰ 90⁰
- 54. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x The Hypotenuse of these triangles are the same x 90⁰ 90⁰
- 55. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x The triangles are equal triangles So all sides will be equal x 90⁰ 90⁰
- 56. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x Crown End Run = Half Span x 90⁰ 90⁰
- 57. Solve Crown End Run x 90⁰ 90 90⁰ - x 90- x 90- x Crown End Run = Half Span Crown End Rafter position will Equal same distance as Centring Rafters from the short end x 90⁰ 90⁰
- 58. Gathering Point Similar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters
- 59. Gathering Point Similar to a conventional hip roof the gathering point is at the centreline of the Ridge & Centring rafters
- 60. Gathering Point Similar to conventional hip roof all members that form the oblique end hip have the same rise as the common rafters
- 61. Crown End Rafter Centreline Length Similar to a conventional hip roof The Crown End Rafters Centreline Run is the same as the common rafters
- 62. 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
- 63. Crown End Rafter Centreline Length The Centreline Line (CL) Length can be calculated in the same way Crown CL = CL Run ÷ Cos Pitch Crown CL = 1000 ÷ Cos 25 ⁰ Crown CL =1000 ÷ 0.906 Crown CL =1.103 Pitch 25 ⁰
- 64. Crown End Rafter Centreline Length The Centreline Line (CL) Length can be calculated in the same way Crown CL = CL Run ÷ Cos Pitch Crown CL = 1000 ÷ Cos 25 ⁰ Crown CL =1000 ÷ 0.906 Crown CL =1.103 (Note that this length also represents the length per metre Pitch 25 ⁰
- 65. Crown End Rafter Centreline Length using Pythagoras The Centreline Line (CL) Length can be calculated in the same way Crown CL = √(CL Run ² + Rise ²) Crown CL = √(1 ² + 0.466 ²) Crown CL = √(1 + 0.217 ) = √(1.217 ) Crown CL =1.103 Pitch 25 ⁰
- 66. Crown End Rafter Centreline Length using Trigonometry The Centreline Line (CL) Length can be calculated in the same way Crown CL = CL Run ÷ Cos Pitch Crown CL = 1000 ÷ Cos 25 ⁰ Crown CL =1000 ÷ 0.906 Crown CL =1.103 Pitch 25 ⁰
- 67. Crown End Rafter True Length Similar to a conventional hip roof The Crown End Rafters will butt into the Centring Rafters
- 68. Crown End Rafter True Length Different to a conventional hip roof The Crown End Rafters do not butt into the Centring Rafters at 90 ⁰
- 69. Crown End Rafter True Length The Centreline Line (CL) Length can be calculated in the same way Crown CL = CL Run ÷ Cos Pitch Crown CL = 1000 ÷ Cos 25 ⁰ Crown CL =1000 ÷ 0.906 Crown CL =1.103 (Note that this length also represents the length per metre Pitch 25 ⁰
- 70. Crown End Rafter True Length The Centreline Line (CL) Length can be calculated in the same way Crown CL = √(CL Run ² + Rise ²) Crown CL = √(1 ² + 0.466 ²) Crown CL = √(1 + 0.217 ) = √(1.217 ) Crown CL =1.103 Pitch 25 ⁰

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