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

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

46. Solve Angle y Developing from last week x 90⁰ 90 90⁰ - x x y

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