1. ROOFING BCGCA3007B

2. Types of Roofs

5. Problem No1 Calculate Underside of Beams Birdsmouth 30mm Rafter 140 x 45

6. Problem No1 Calculate Underside of Beams

18. Exercise 2 – Draw in Hips & Valleys

19. Exercise 2

25. Review Principles of Roofing 1.Ridges are Level 2.Rafters run at 90⁰ to Wall Plate 3.Hips & Valleys bisect all internal & external Corners 4.Roof members are set out along centerlines

27. Common Rafter Main Roofing Member Calculated same method as Gable Spaced 450mm to 600mm for Tiled Roofs 600mm to 900mm for Sheet Roof Cut using a Pattern Rafter

29. Centering Rafter Layout Roofs are Set out by Centreline Centring Rafters Centering Rafters Set back by Half Span

30. Centering Rafter Layout Half Span Centering Rafters Set back by Half Span

31. Ridge Used to centre Rafters Length = Length – span + Rafter Thickness

32. Determine Ridge Length

33. Crown End Rafters Cut & Fitted Against Ridge Act as Opposing Braces Similar to Common Rafter Half Rafter is Deducted

34. Crown End Rafter Layout What is the Crown End Rafter Centreline Span? Crown End Rafters

35. Crown End Rafter Layout Crown End Rafters Ridge 140 x19 Rafter 90 x 45 CL Span is Half span

36. Crown End Rafter Layout What is the run of Centering Rafter & Crown End Rafter Crown End Rafters Ridge 140 x19 Rafter 90 x 45 CL Span is Half span

37. Crown End Rafter Layout What is the run of Centering Rafter & Crown End Rafter Crown End Rafters Hip Rafters Centering Rafters Ridge

38. Crown End Rafter Layout What is the run of Centering Rafter & Crown End Rafter Centering Rafter Run Deduct Half Ridge Ridge 140 x19 Rafter 90 x 45 Crown End Rafter Run deduct Half Centering Rafter

39. Crown End & Centering Rafter Run Crown End Rafter = Half Span – Half Centering Rafter Width Run Centering Rafter = Half Span – Half Ridge Width

41. Hip Rafter Runs From Corner to Intersection Crown End & Centering Rafter - Centerline Hips Bisect Corners Support Creepers Fixing and Locating of Creepers Distance above Birdsmouth is same as common rafters called “Amount Left On”

42. Hip Rafter Layout Roofs are Set out by Centerline Bisects Corner Hip in Plan

43. Hip Rafter Span of Hip

44. Hip Rafter Hip Span Hip Run

45. Hip Rafter Hip Span Hip Run

46. Hip Rafter Hip Span Hip Run Corner Trimmed to allow a better fit

47. Hip Rafter

48. Hip Rafter Layout Roofs are Set out by Centerline Bisects Corner Determine Centreline Span of Hip

49. Centreline Span of Hip (Z) X = Half span = 2070 Z = √(x 2 ) + (x 2 ) = √(2070 2 ) + (2070 2 ) Z = 2927 X = Half span = 2070 Z = Half span x √2 Z = 2927

50. Centreline Span of Hip (Z) X = Half span = 2070 Z = √(x 2 ) + (x 2 ) = √(2070 2 ) + (2070 2 ) Z = 2927 X = Half span = 2070 Z = Half span x √2 Z = 2927

51. Centreline Length of Hip Methods – Pythagoras – Hip Centreline Length per Meter of Common Rafter Run – Scribing – Measure in Situ

52. Hip by Pythagoras Revision From Gable Roofs Step 1 – Calculate Roof Rise Rise= Tan 25 ⁰ x 2070 = 965mm Pitch 25 ⁰

53. Hip by Pythagoras Step 1 – Calculate Roof Rise Rise= Tan 25 ⁰ x 2070 = 965mm Pitch 25 ⁰ Hip Rise Must Be The Same

54. Hip by Pythagoras Step 1 – Calculate Roof Rise Rise= Tan 25 ⁰ x 2070 = 965mm Pitch 25 ⁰ Hip Rise Must Be The Same as the rest of the roof Hip Centreline Length = √(Hip Span ² + Rise ²) = √(2927 ² + 965²) = 3082mm What is the Hip Pitch ? Rise 965mm

55. Hip by Pythagoras Pitch 25 ⁰ Rise = 965mm Hip CL = 3082 What is the Hip Pitch ? Tan Pitch = 965/2927 Pitch = 18.25 ⁰ Using Tan Tan Pitch = Rise/ Hip Span Using Cos Cos Pitch = Hip Span/ Hip CL Length Cos Pitch = 2927/3082

56. Centreline Length of Hip Mathematically Methods – Pythagoras – Hip Centreline Length per Meter of Common Rafter Run – Scribing – Measure in Situ

57. From Gable Roof Lessons We Know That for the above Roof the Rafter Length per meter can be calculated as follows Rafter per meter run = √(1 ² + 0.577²) = 1.149 Given Rise = 577 per metre

58. From Gable Roof Lessons We Know That for the above Roof the Rafter Length per meter can be calculated as follows Rafter per meter run = √(1 ² + 0.577²) = 1.149 Given Rise = 577 per metre

59. We learnt previously that for every 1 metre run of the common rafter the hip run is 1.414 Given Rise = 577 per metre

60. We learnt previously that for every 1meter run of the common rafter the hip run is 1.414 Given Rise = 577 per metre

61. Using Pythagoras we determine the above triangle Hip per meter of Common Rafter Run = √(1.414² + 0.577²) = 1.527 Given Rise = 577 per metre

62. Using Pythagoras we determine the above triangle Hip per metre of Common Rafter Run = √(√1.414² + 0.577²) = √(2+ 0.333) = √(2.333) = 1.527 Given Rise = 577 per metre We can now say that at this given rise per meter, for every metre of run of the common rafter the hip length will be 1527mm

63. Using Pythagoras we determined on last slide the above triangle Hip per meter of Common Rafter Run = √(1.414² + 0.577²) = √(2+ 0.333²) = √(2.333) = 1.527 Centreline Length of Hip = Half span x Hip Length per meter of Common Rafter Centreline Length of Hip = 2.070 x 1.527 = 3.161 Given Rise = 577 per metre

64. Lets extend this principle Roof Pitch = 30 ⁰ Tan 30 ⁰ = 0.577 Pitch = 30 ⁰

65. Lets extend this principle Roof Pitch = 30 ⁰ Tan 30 ⁰ = 0.577 This Brings Our Triangle from The Previous Example Back Pitch = 30 ⁰ This Triangle represents the Common Rafter Pitch Which by similar triangles we can transfer to our steel square

66. We learnt previously that for every 1meter run of the common rafter the hip run is 1.414 Pitch = 30 ⁰

67. Using Pythagoras we determine the above triangle Hip per meter of Common Rafter Run = √(1.414 2 + 0.577²) = √(2+ 0.577²) = √(2.333) = 1.527 Therefore for every meter of Common Rafter run at 30 ⁰ The Hip Centreline Length = 1.527

68. Centreline Length of Hip = Half span x Hip Length per meter of Common Rafter Centreline Length of Hip = 2.070 x 1.527 = 3.161 ` Given Rise = 577 per metre `

69. Calculate Hip Length per meter of Common Rafter Run

71. Centreline Length of Hip Methods – Pythagoras – Hip Centreline Length per Meter of Common Rafter Run – Scribing – Measure in Situ

72. Scribing

75. Centreline Length of Hip Methods – Pythagoras – Hip Centreline Length per Meter of Common Rafter Run – Scribing – Measure in Situ

76. In-Situ

79. True Length of Centering Rafters Same as Common Rafter Half Ridge Thickness Deducted

80. Calculate Centering Rafters True Length Step 2 – Calculate True Length Centering Rafter = (2070 – 9.5) / Cos 25 = 2060.5/ 0.906 = 2274 Pitch 25 ⁰ Ridge 140 x 19 Step1 – Deterime Run Centering Rafter Run = Half Span – ½ Ridge = 2070 – 9.5 = 2060.5 or 2061

81. Centering Rafter Will always be the same length as Common Rafter Plumb Cut will always same as the Common Rafter Base Cut will always same as the Common Rafter

82. Revision - Determining Angles Mathematically for Common Rafter Roof Pitch Right Angled Triangle This angle must be 65 ⁰ 90 – 25 = 65 This angle must be 25 ⁰ 90 – 65 = 25

83. Determining Plumb Cut Angles Mathematically 1.Extend Line 90⁰ From Rafter

84. Determining Angles Mathematically 1.Extend Line 90⁰ From Rafter 2.Extend Plumb Line from same origin at top of Rafter

85. Determining Angles Mathematically 1.Extend Line 90⁰ From Rafter 2.Extend Plumb Line from same origin at top of Rafter 3.Angle Formed is same as roof pitch

86. Determining Angles Mathematically 1.Extend Line 90⁰ From Rafter 2.Extend Plumb Line 3.Angle Formed is same as roof pitch 4.Offset = Tan (pitch) x width

87. Determining Angles Mathematically 1.Extend Line 90⁰ From Rafter 2.Extend Plumb Line 3.Angle Formed is same as roof pitch 4.Offset = Tan (25⁰) x 90 = 42

88. True Length of Crown End Rafter Similar to Common Rafter Half Centering Rafter Thickness Deducted

89. Calculate Crown End Rafters True Length Step 2 – Calculate True Length Centering Rafter = 2047.5 / Cos 25 = 2047.5/ 0.906 = 2259 Pitch 25 ⁰ Centering Rafter 90 x 45 Step1 – Deterime Run Centering Rafter Run = Half Span – ½ Rafter = 2070 – 22.5 = 2047.5 or 2048

90. Crown End Rafter Will always be the same Pitch as Common Rafter Triangle formed is SIMILAR Plumb Cut will always same as the Common Rafter Base Cut will always same as the Common Rafter

91. Determine Cutting Length of Hip Steps 1.Determine Corresponding Crown End Rafter Run 2.Deductions – Centring Rafters – Corner of Plates

92. Calculate Hip True Length Step 1 Pitch 25 ⁰ Centering Rafter 90 x 45 Crown End Rafter Span = Half Span = 2070

93. Determine Cutting Length of Hip Steps 1.Determine Corresponding Crown End Rafter Run 2.Deductions – Centring Rafters – Corner of Plates

94. Determine Hip Run Ridge 140 x19 Rafter 90 x 45 Hip140 x 19 Deduction = Half Centering Rafter Thickness = 22.5 Hip Run based on Crown End Rafter Run

95. Calculate Crown End Run & Hip Run Pitch 25 ⁰ Centering Rafter 90 x 45 Crown End Rafter Run = Half Span – Centering Rafter Thickness = 2070 – 22.5 = 2047.5 Say 2048 Hip Run = 1414 x 2048 = 2896

96. Calculate Crown End Run & Hip Run Pitch 25 ⁰ Centering Rafter 90 x 45 Crown End Rafter Run = 2048 Hip Run = 1414 x 2048 = 2896 What is the Hip True Length ?

97. Calculate Crown End Run & Hip Run Pitch 25 ⁰ Centering Rafter 90 x 45 Hip True Length = √(Hip Run ² x Rise ²) = √(2896 ² x 955 ²) = 3049

98. Alternate Method to Calculate Hip True Length

99. Previous Centreline Calculation of Hip Pitch 25 ⁰ Rise = 965mm Hip CL = 3082 Centreline Span of Hip = √(Half Span ² + Half Span ²) = √(2070 ² + 2070²) = 2927

100. Determine Hip Run Ridge 140 x19 Rafter 90 x 45 Hip140 x 19 Deduction = √(22.5 ²+ 22.5 ²) = √1012.5 = 31.8 or 32

101. Crown End Rafter Layout Ridge 140 x19 Rafter 90 x 45 Hip140 x 19 Method 1 Deduction = √(22.5 ²+ 22.5 ²) = √1012.5 = 31.8 or 32 Method 2 Deduction = 1.414 x 22.5 = 31.8 or 32

102. Determine Run of Hip Pitch 25 ⁰ Rise = 965mm Hip CL = 3082 Hip Run = 2927 – 32 Hip Run = 2895 32 mm Deduction Centreline Length

103. Determine Run of Hip Pitch 25 ⁰ Rise = 965mm Hip CL = 3082 Hip Run = 2927 – 32 Hip Run = 2895 32 mm Deduction True Length

104. Determine Cutting Length of Hip 1.Determine Corresponding Crown End Rafter 2.Deductions – Centring Rafters – Corner of Plates

105. Hip Plumb Cut Mathematically From previous work we determined the hip as follows Hip Pitch may be determined either Pitch = Tan -1 954/2895 = 0.330 = 18.25 ⁰

106. Deduction for Top Plate Cut Ridge 140 x19 Rafter 90 x 45 Hip140 x 19 Deduction = Hip Width / 2 = 19 / 2 = 9.5`

107. Determining Plumb Cut Mathematically – Hip 140 x 19 1.Extend Line 90⁰ From Rafter 2.Extend Plumb Line from same origin 3.Angle Formed is same as roof pitch 4.Offset = Tan (18.25⁰) x 140 = 46

108. Markng Out Hip 1.Set Out Top Plumb Cut

109. Marking Out Hip 1.Set Out Top Plumb Cut 2.Measure Calculated Hip Length and place Plumb line

110. Marking Out Hip 1.Set Out Top Plumb Cut 2.Measure Calculated Hip Length and place Plumb line 3.Mark same “Amount Left on” as the Common Rafter Common Rafter Hip Rafter

111. Marking Out Hip 1.Set Out Top Plumb Cut 2.Measure Calculated Hip Length and place Plumb line 3.Mark “Amount Left on” 4.Mark deduction for top plate

112. Marking Out Hip

113. Determine Hip Length Using Roofing Square Use Calculator Revise Common Rafter 1.Press Tan 25 – what does this give you 2.Therefore for every 1 metre run there is 0.466m rise 3.The hip rafter, Crown End Rafter & Common Rafter have the same rise

114. Hip has same rise as Common Rafter & Crown End Rafter

115. 1.Therefore for every 1 metre run of Common Rafter there is 1 metre of run for the Crown End Rafter and there is 1.414 metres of run for the hip 2.For both members there is 0.466m rise 3.Using the principle of similar triangles we reduce the size of the triangle 4.In this case to fit on the steel square we need to divide by 3

116. 1.As we reduce hip by 3 we reduce Crown End/ Common Rafter by 3 (1000 / 3 = 333) 2.There are (2048 / 333 =) 6.150 step outs for the Crown End rafter 3.There will also be 6.150 step outs for the Hip Rafter or 6 step outs + remainder(.189 x 471) 71 4.Plumb Cut Hip

117. Set Out Hip with Steel Square Step 2 Using Steel Square for Hip step out six times Step 3 Using Tape measure out along a square line of Steel Square and mark Plumb Cut Step 1 Mark Plumb Cut to Back of Birdsmouth 1 2 3 4 5 6

118. 1.Eaves Allowance 2.Eaves Width = 600mm 3.There are (600 / 333 =) 1.802 step outs for the Eave Overhang 4.There will also be 1.802 step outs for the Hip Rafter or 1 step outs + remainder(.802 x 471) 378 5.Plumb Cut Hip

119. Set Out Hip with Steel Square Eaves Allowance Eaves Width 600mm As Overhangs are never pre-cut, we need leave enough say 2 Step Outs + Plumb Cut

120. Creeper Rafters

122. Determine Creepers 1.Creepers Spacing Same as Common Rafter 2.Creepers usually of same material as Common Rafter Pitch 25 ⁰

123. Determine Creepers 1.The Centreline Run of 1st Creeper is 1 Rafter Spacing less than the Centering Rafter 2.If take a view in this direction Pitch 25 ⁰

124. Determine Creepers 1.This reduction in length can be represented by this triangle 2.The hypotenuse = Rafter Spacing/ Cos Pitch 3.450mm/Cos 25 ⁰= 497mm 4.This is called the CREEPER SHORTENING Pitch 25 ⁰

125. Determine Creepers 1.All pairs of Creepers are reduced by the creeper shortening

126. Determine Creepers Setting Out 1.It is impractical to use centreline to measure creepers for cutting 2.Typically you would set out to the long point 3.The Run of the Long Point of the Creeper is longer by Half Thickness of the Creeper Rafter Centerline Pitch 25 ⁰

127. Determining Creepers Run Determine First Creeper Run 1.Deduct Rafter Spacing Pitch 25 ⁰ Hip 140x19

128. Determining Creepers Run Determine First Creeper Run 1.Deduct Rafter Spacing 2.Deduct Half Hip x 1.414 Pitch 25 ⁰ Hip 140x19

129. Determining Creepers Run Determine First Creeper Run 1.Deduct Rafter Spacing 2.Deduct Half Hip x 1.414 3.Deduction = 9.5 x 1.414 = 13mm Pitch 25 ⁰ Hip 140x19

130. Determine Creepers Setting Out 1.The Run of the Long Point of the Creeper is longer by Half Thickness of the Creeper Rafter Pitch 25 ⁰

131. Determine Creepers Setting Out Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 1.Deduct Rafter Spacing 2.Deduct Half Hip x 1.414 3.Deduction = 9.5 x 1.414 = 13mm 4.Add ½ thickness of creeper

132. Determine Creepers Setting Out Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 The run of the 1 st Creeper = Centering Rafter Run Less Rafter Spacing Less Half Ridge x 1.414 Plus Half Creeper Thickness

133. Creeper Rafters Determine 1 st Creeper 1 st Creeper Rafter Run = Centering Rafter Run = 2061 Minus Creeper Spacing = 450 Minus Half Ridge x 1.414 =13 Plus Half Creeper Thickness = 22.5 1 st Creeper Rafter Run = 1620.5 True Length = 1620.5/ Cos 25 = 1788 Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm

134. Creeper Rafters 2nd Creeper Rafter True Length = 1 st Creeper True Length = 1788 Less Creeper Shortening - 497 2nd Creeper Rafter True Length = 1291 Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm

135. Creeper Rafters 3rd Creeper Rafter True Length = 2nd Creeper True Length = 1291 Less Creeper Shortening - 497 3rd Creeper Rafter True Length = 794 Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm

136. Creeper Rafters 4th Creeper Rafter True Length = 3rd Creeper True Length = 794 Less Creeper Shortening - 497 4th Creeper Rafter True Length = 297 Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm

137. Creeper Rafters 4th Creeper Rafter True Length = 3rd Creeper True Length = 794 Less Creeper Shortening - 497 4th Creeper Rafter True Length = 297 Note – If distance from hip to last creeper is excessive an extra creeper may be placed to support eaves– This is called a DUMMY CREEPER Pitch 25 ⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm

138. Edge Bevel Creeper Mathematically Edge Bevel Angle Angle = Tan-1(True Length Rafter) Half Span

139. Edge Bevel Creeper Mathematically Edge Bevel Angle Angle = Tan-1( Half Span ) True Length Rafter Angle = Tan-1(2070) 2280 Angle = Tan-1(0.907894) = 42.24 ⁰

140. Edge Bevel Creeper Mathematically Edge Bevel Angle Angle = Tan-1( Half Span ) True Length Rafter Angle = Tan-1(2070) 2280 Angle = Tan-1(0.907894) = 42.24 ⁰

141. Review Determining Angles Mathematically 1.From Our Common Rafter Example 2.Note – Plumb Cut is not Roof Pitch 3.We require 65⁰ 4.To use Bevel, angle needs to be in this position 5.Therefore 90⁰ – (Required Angle ) = Offset Angle

142. Edge Bevel Creeper Mathematically OFFSETT Angle = 90 ⁰ - (Required Angle) = 90 ⁰ - 42.24 ⁰ = 47.76 ⁰ OFFSETT = Tan 47.76 ⁰ = 99