Unequally Pitched Roofs

Name: Unequally Pitched Roofs
Uploaded: 2017-07-12T01:17:26+00:00
Duration: PTM40S18
Channel: Avice Anderson
Description: Unequally Pitched Roofs

Unequally Pitched Roofs

Ridge Set Out Determine the Rise Roofs Set out On x- y line A
(Pitch A)Rise = (2000 – Y) Tan 30˚

Ridge Set Out Determine the Rise Roofs Set out On x- y line a b
(Pitch A)Rise = (2000 – B) Tan 30˚ (Pitch B)Rise = (2000 – A) Tan 40˚

Ridge Set Out Determine the Rise Roofs Set out On x- y line a b
(Pitch A)Rise = (2000 – B) Tan 30˚ (Pitch B)Rise = (2000 – A) Tan 40˚ Or we can restate as (Pitch A)Rise = (2000 – B) Tan 30˚ (Pitch B)Rise = B Tan 40˚

Ridge Set Out Roofs Set out On x- y line Or we can restate as
Rise = (2000 – B) Tan 30˚ Rise = B Tan 40˚ As both rises are equal we can state (2000 – B) Tan 30˚ = B Tan 40˚

Ridge Set Out Roofs Set out On x- y line Solve the Equation
(2000 – B) Tan 30˚ = B Tan 40˚ -Divide by both sides by Tan 30˚ -Divide by both sides by B -B ÷ B = 1 -Add 1 to each side -Make B the subject of the formula -Solve the equation

Ridge Set Out Roofs Set out On x- y line a b
Centerline Position of Ridge OR

Ridge Set Out Unequal pitch causes an problem Roofs Set out
On x- y line

Ridge Set Out When lines are offset from the x – y line, the edges of the rafters will misalign

Ridge Set Out The top of rafter intersection will move
x-y line intersection

Ridge Set Out As will the bottom intersection move

Ridge Set Out When the tops of the Rafters are intersected the Ridge always moves towards the steeper pitch side.

Ridge Set Out When the tops of the Rafters are intersected the Ridge moves towards the steeper pitch side. The intersection of the bottom moves towards the lower pitch side

Ridge Set Out Generally you would want the top of the roof to align
If the bottom is exposed you may want the bottom to align

Ridge Set Out b a Determining the correction Mathematically Where
a⁰ = Lower Pitch b⁰ = Higher Pitch T = Amount Left on

Ridge Set Out a b Determining the correction Mathematically = 6.388
Where a⁰ = Lower Pitch = 30⁰ b⁰ = Higher Pitch = 40⁰ T = Amount Left on =60 = 6.388

Ridge Correction a b Remember the correction always moves towards the steeper pitch

Centreline Ridge Correction
a b Remember the correction always moves towards the steeper pitch A = B = 815 – 6

Determine Rafter Cut Length
Ridge 120 x 19 ½ Ridge = 9.5 a b We need to deduct the ridge as for an equally pitched roof A = 1191 – 9.5 B = 809 – 9.5

Rafter True Length Ridge 120 x 19 a b
Rafters are then calculated as normal Rafter A = ÷ cos 30⁰ Rafter B = ÷ cos 40⁰

Eaves Set Out If level Eaves are required i.e. Hipped Roof
Steeper O/H is lower a b Eaves should be set out from the top of the rafter Due to the different pitches if the overhang is the same one will be lower

Steeper O/H is lower a b For the eaves to finish at the same height the eave to the steeper pitch must be reduced

Steeper O/H is lower a b To do this we must look at the hatched triangle and solve x & y

Z = 300 x Tan 30⁰ Z = 173

This angle = 60⁰ This angle = 30⁰ y = Amount Left On ÷ sin (90 ⁰ - pitch) y = 60 ÷ sin (60 ⁰ ) y = 69 y = Amount Left On ÷ cos (pitch) y = 60 ÷ sin (30 ⁰ ) y = 69

x = z - y X = X = 104

b To determine matching eave on steeper side we must solve the highlighted triangle

This angle = 50⁰ a b This angle = 40⁰ y = Amount Left On ÷ sin (90 ⁰ - pitch) Y = 60 ÷ sin (50 ⁰ ) Y = 78 y = Amount Left On ÷ cos (pitch) Y = 60 ÷ sin (40 ⁰ ) Y = 78

X must be the same on both side of the roof

Z = X + Y Z = Z = 182

O/H = Z ÷ tan pitch⁰ O/H = 182 ÷ tan 40⁰ O/H = 217

Where a = Lower pitch b = Steeper pitch m = O/H Steeper Pitch t = Amount left on

Set Out The Steeper Roof hip is always at 45⁰ in plan view

Set Out The Hip to the lower pitch will always be less than 45⁰
The Steeper Roof hip is always at 45⁰ in plan view

This rafter has a run 809 & pitch of 40⁰
Set Out This rafter has a run 809 & pitch of 40⁰

Set Out If the Crown End rafters also have a run 809 and the same rise as the common rafter. What is the pitch of the Crown ends?

Set Out They must also be pitched at 40⁰
If the Crown End rafters also have a run 809 and the same rise as the common rafter. What is the pitch of the Crown ends?

Set Out They must also be pitched at 40⁰
If the Crown End rafters also have a run 809 and the same rise as the common rafter. What is the pitch of the Crown ends? The Steeper roof is pitched in a similar manner to a conventional pitched roof

Gathering Point Similar to Equally Pitched Roof
All members centrelines meet at the gathering point Note – Hip to lower pitch is not at 45⁰ in plan

True Length of Crown End Rafter Gathering Point
Similar to Common Rafter Half Centering Rafter Thickness Deducted

Calculate Crown End Rafters True Length
Pitch 40⁰ & 30⁰ Centering Rafter 90 x 45 Hips 190 x 45 Crown End 90 x 45 Step1 – Deterime Run Centring Rafter Run = Half Span – ½ Rafter = 809 – 22.5 = or 787 Step 2 – Calculate True Length Centering Rafter = / Cos 40 = / 0.766 = 1027

Crown End Rafter Same Pitch as Common Rafter of the Steeper pitch
Plumb Cut same as the Common Rafter Steeper Pitch Base Cut same as the Common Rafter Steeper Pitch

Hip Rafter

Creeper Rafters Pitch 40⁰ & 30⁰ Centering Rafter 90 x 45 Hips 190 x 45
Crown End 90 x 45 As the steeper part the roof is pitched as per an equally pitched roof The same method to determine creepers is used

Determine Creepers Pitch 25⁰ Creepers Spacing Same as Common Rafter
Creepers usually of same material as Common Rafter

Determine Creepers Pitch 25⁰
The Centreline Run of 1st Creeper is 1 Rafter Spacing less than the Centering Rafter If take a view in this direction

Determine Creepers Pitch 25⁰
This reduction in length can be represented by this triangle The hypotenuse = Rafter Spacing/ Cos Pitch 450mm/Cos 25⁰= 497mm This is called the CREEPER SHORTENING

Determine Creepers All pairs of Creepers are reduced by the creeper shortening

Determine Creepers Setting Out
Pitch 25⁰ It is impractical to use centreline to measure creepers for cutting Typically you would set out to the long point The Run of the Long Point of the Creeper is longer by Half Thickness of the Creeper Rafter Centerline

Determining Creepers Run Determine First Creeper Run
Pitch 25⁰ Hip 140x19 Deduct Rafter Spacing

Pitch 25⁰ Hip 140x19 Deduct Rafter Spacing Deduct Half Hip x 1.414

Pitch 25⁰ Hip 140x19 Deduct Rafter Spacing Deduct Half Hip x 1.414 Deduction = 9.5 x = 13mm

Pitch 25⁰ The Run of the Long Point of the Creeper is longer by Half Thickness of the Creeper Rafter

Pitch 25⁰ Hip 140 x19 Creeper 90 x 45 Deduct Rafter Spacing Deduct Half Hip x 1.414 Deduction = 9.5 x = 13mm Add ½ thickness of creeper

Pitch 25⁰ Hip 140 x19 Creeper 90 x 45 The run of the 1st Creeper = Centering Rafter Run Less Rafter Spacing Less Half Hip x 1.414 Plus Half Creeper Thickness

Creeper Rafters Determine 1st Creeper
Pitch 25⁰ Hip 140 x19 Creeper 90 x 45 Rafter Spacing 450mm Creeper Shortening 497mm 1st Creeper Rafter Run = Centering Rafter Span Or Half Span = 809 Minus Creeper Spacing = 450 Minus Half Hip x = Plus Half Creeper Thickness = 22.5 1st Creeper Rafter Run = 368.5 True Length = 368.5/ Cos 25 = 407

Edge Bevel Creeper Pitch 25⁰ When we look in plan at a roof
We do not see its true shape In this case we see a triangle With 2 sides appearing to equal Lengths of run of steeper pitch

Edge Bevel Creeper Pitch 25⁰ Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter

Edge Bevel Creeper Pitch 25⁰ Edge Bevel Angle
Angle = Tan-1( Half Span ) True Length Rafter Angle = Tan-1(809) 893 Angle = Tan-1(0.9066) = 42.19⁰

Determine Creeper Edge Bevel
Edge Bevel Angle Angle = Tan-1( Half Span ) True Length Rafter Angle = Tan-1(809) 893 Angle = Tan-1(0.9066) = 42.19⁰

Determine Creeper to Lower Side Plan Side Cut (A)
Angle is defined by Run of Crown End & O/H A

Angle is defined by Run of Crown End & O/H Run of Rafter (lower) + O/H A

Angle is defined by Run of Crown End & O/H Run of Rafter (lower) + O/H Run of Hip A

Angle is defined by Run of Crown End & O/H Run of Rafter (lower) + O/H Run of Hip Determine Angle x = x = 1191 y = 809 Ѳ = Tan-1 Opposite Adjacent Ѳ = Tan Ѳ = Tan Ѳ = ⁰ A

Determine Creeper to Lower Side Plan Side Cut (A) - Formula
Creeper A Plan side cut angle = Tan – 1((x + k)/(y + L) Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch A

Determine Creeper to Lower Side True Side Cut (A)
Angle is defined by True Length of Crown End & O/H A

Angle is defined by True Length of Crown End & O/H Run of Rafter (lower) + O/H A

Angle is defined by True Length of Crown End & O/H Run of Rafter (lower) + O/H True Length of Hip A

Angle is defined by True Length of Crown End & O/H Run of Rafter (lower) + O/H True Length of Hip Determine Angle x = x = 1191 y = 809 Ѳ = Tan-1 Opposite Adjacent Ѳ = Tan ( )/Cos 40⁰ Ѳ = Tan Ѳ = ⁰ A

Determine Creeper to Lower Side True Side Cut (A) - Formula
Creeper A True side cut angle = Tan – 1((x + k)/ ((y + L)/cos b⁰))) Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch A

Determine Creeper to Lower Side Plan Side Cut (B)
Angle is defined by Run of Rafter (lower) + O/H B A

Angle is defined by Run of Rafter (lower) + O/H Run of Crown End & O/H B A

Angle is defined by Run of Crown End & O/H Run of Rafter (lower) + O/H Run of Hip B A

Angle is defined by Run of Crown End & O/H Run of Rafter (lower) + O/H Run of Hip Determine Angle x = x = 1191 y = 809 Ѳ = Tan-1 Opposite Adjacent Ѳ = Tan Ѳ = Tan Ѳ = ⁰ B A

Determine Creeper to Lower Side Plan Side Cut (A) - Formula
Creeper A Plan side cut angle = Tan – 1((x + k)/(y + L) Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch A

Determine Creeper to Lower Side True Side Cut (B)
Angle is defined by True Length of Rafter (lower) + O/H B A

Angle is defined by True Length of Crown End & O/H Run of Crown End & O/H B A

Angle is defined by True Length of Crown End & O/H Run of Rafter (lower) + O/H True Length of Hip B A

Angle is defined by True Length of Crown End & O/H Run of Rafter (lower) + O/H True Length of Hip Determine Angle x = x = 1191 y = 809 Ѳ = Tan-1 Opposite Adjacent Ѳ = Tan ( )/Cos 30⁰ Ѳ = Tan Ѳ = ⁰ A

Determine Creeper to Lower Side True Side Cut (A) - Formula
Creeper A True side cut angle = Tan – 1((x + k)/ ((y + L)/cos b⁰))) Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch A

Determine Creeper to Lower Side Creeper Shortening side (A)
Creeper to side A is shortened by distance “h” A

Distance “h” is defined by blue triangle A

Blue Triangle is a similar triangle to purple triangle A

Blue Triangle is a similar triangle to purple triangle In a Similar Triangle Angles are the same. Ratios between the sides will be the same. A

The relationship between the side of the triangle can be described as follows y+L = (x+k) x (y+L)/ (x+k) Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening A

The relationship between the side of the triangle can be described as follows y+L = (x+k) x (y+L)/ (x+k) Note that this ratio is constant for all triangles similar to this one Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening A

As the smaller blue triangle is a similar triangle, the following will be true h = f x (y+L)/ (x+k) h = 450 x (( )/( )) h = This is the plan length True Length Creeper Shortening = 310/ cos 40⁰ = 404 Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening A

Determine Creeper Long point Correction Creeper Shortening side (A)
Hip 190 x 19 Rafter 90 x 45 t = ½ Hip (x+k)/(y+L) u = ½ Rafter (y+L)/(x+k) These 2 triangles are similar Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay Detail View Unequal Hip End

Detail View Unequal Hip End
Determine Creeper Long point Correction Creeper Long Point Correction Side A Hip 190 x 19 Rafter 90 x 45 Where t = √((½ Hip)2 + (½ Hip ((y+L)/(x+K)))2) u = ½ Rafter ((y+L)/(x+k)) These 2 triangles are similar Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay Detail View Unequal Hip End Correction = ½ Rafter ((y+L)/(x+k)) - √((½ Hip)2 + (½ Hip ((y+L)/(x+K)))2)

Determine Creepers Creeper Spacing side B
We know that h = f ((y+L)/(x+k)) i.e. plan length of the creeper shortening B Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A Plan View Unequal Hip End

Determine Creepers Creeper Spacing side B
We know that h = f ((y+L)/(x+k)) i.e. plan length of the creeper shortening If the creepers are to meet on the hip. The creepers on side B must be spaced at the plan length of the Creeper Shortening side A B Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A Plan View Unequal Hip End

Determine Creepers Creeper Shortening Side B
Creepers to side B are shortened in plan by “f” B Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A Plan View Unequal Hip End

Creepers to side B are shortened in plan by “f” Distance f is the Creeper Spacing of Side A B A Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay Plan View Unequal Hip End

Creepers to side B are shortened in plan by “f” Distance f is the Creeper Spacing of Side A B Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A Plan View Unequal Hip End Shortening= f/cos a⁰ = 450 / cos 30 ⁰ = 520

Determine Creepers Long Point Correction Side B
Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A In all 3 Triangle Highlighted all angles are equal

Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A In all 3 Triangle Highlighted all angles are equal They must be similar triangles

Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A In all 3 Triangle Highlighted all angles are equal They must be similar triangles The ratio’s between the sides must be the same

Where s = span x = c/l run of lower pitch rafter y = c/l run of steeper pitch rafter k = Overhang Lower pitch L = Overhang Steeper pitch a⁰ = Lower Pitch b⁰ = Steeper Pitch h = Plan len of Creeper Shortening t = ½ Hip across splay u = ½ Rafter across splay A Where t = √((½ Hip)2 + (½ Hip ((x+k)/(y+L)))2) u = ½ Rafter ((x+k)/(y+L)) Shortening = ½ Rafter ((x+k)/(y+L)) - √((½ Hip)2 + (½ Hip ((x+k)/(y+L)))2)

Edge Bevel Creeper Mathematically
OFFSETT Angle = 90⁰ - (Required Angle) = 90⁰ ⁰ = 47.81⁰ OFFSETT = Tan 47.81⁰ x 90 = 99

Determine Purlin Edge Bevel
Purlins Intersect at 90⁰ across Hip Rafter Plan View

Purlins are parallel to top plate

Angles are the same for all purlins on an equally pitched roof

Angles formed at Top Plate is the same as formed at Purlin

Triangle formed by Purlin, Hip & Centering Rafter Triangle formed by Top Plate, Hip & Centering Rafter Similar Triangles

Determine Purlin & Creeper Edge Bevel
Pitch 25⁰ Out of Same Triangle Creeper Edge Bevel Purlin Edge Bevel

Pitch 25⁰ Edge Bevel Angle Angle = Tan-1(Rafter Centerline) Half Span Angle = Tan-1(2284) 2070 Angle = Tan-1(1.103) = 47.81⁰

Creeper Rafters Pitch 40⁰ & 30⁰ Centering Rafter 90 x 45 Hips 190 x 45
Crown End 90 x 45 As the steeper part the roof is pitched as per an equally pitched roof The same method to determine creepers is used

To determine an unknown pitch
Set Out Unknown Pitch Pitch 40⁰ Pitch 40⁰ Pitch 40⁰ To determine an unknown pitch

b We must determine the amount left on (y)

This angle = 50⁰ This angle = 40⁰ b y = Amount Left On ÷ sin (90 ⁰ - pitch) Y = 60 ÷ sin (50 ⁰ ) Y = 78 y = Amount Left On ÷ cos (pitch) Y = 60 ÷ sin (40 ⁰ ) Y = 78

Ridge Set Out B A We must determine the hatched triangle
Rise = 809 x Tan 40˚

Ridge Set Out A B Total Rise B = Run (B) x tan B˚ + Amount Left On (B) x sin B˚ Total Rise A= (Span – Run(B)) x Tan A˚ + Amount Left On (A) x sin A˚ Both are the same

Ridge Set Out A B Run (B) x tan B˚ + Amount Left On (B) x sin B˚ = (Span – Run(B)) x Tan A˚ + Amount Left On (A) x sin A˚

Ridge Set Out A B Rise B= 809 x Tan 40˚ Rise = Tan a˚ (2000 – 809)

Ridge Set Out A B Rise B = 809 x Tan 40˚ = Tan a˚ (2000 – 809)

Ridge Set Out A B Rise B = 809 x Tan 40˚ 0.570 = Tan 30˚

Ridge Set Out A B Rise = 809 x Tan 40˚ = Tan a˚ (2000 – 809)

Unequally Pitched Roofs

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