Tréteaux Roof Framing Kernel and Claw Lines

The basic roof framing kernel can be used to develop the footprint of the hip rafter rotated into the roof surface. The roof framing kernel can also be used to verify the geometry of the claw lines on the fold down roof surface for the geometric development of the jack rafters, purlin rafters and purlin rafters skewed from the plate line.

tréteau à devers

Here's the basic roof framing kernel.

Add the hip rafter backing triangle to the roof framing kernel.

The red square at the top of the hip rafter backing triangle represents the hip rafter material you're using and it is rotated to align with the top of the hip rafter backing triangle. 

Geometric drawing steps for the rotated hip rafter foot print.

1. Draw line FP #1 parallel with the hip rafter run line.
2. Draw lines TC #1 & TC #2 parallel with the sides of the rotated hip rafter block in the hip rafter backing triangle.
3. Where the TC # 1 line intersects at the bottom of the hip rafter backing triangle draw the line DP #1 to the eave line where it intersects with FP #1.
4. Draw DP #2 parallel to DP #1.
5. Draw the FP #2 line for the footprint line in plan view of the hip rafter. 
6. The hip rafter foot print line intersects the two DP lines and forms the , yellow, hip rafter prism footprint. 

To develop the claw lines for the jack rafters, purlin rafters and skewed purlin rafters develop the roof surface. Use the Tréteaux Angles Check Online Calculator to draw out the claw lines on the roof surface or develop the claw lines from the geometry circled in the following drawings. 

Drawing #1

Roof Eave Angle = 90.00000

SS = Main Rafter Slope Angle = 30.25644

S = Adjacent Rafter Slope Angle = 39.80557

DD = Main Plan Angle = 55.00798

D = Adjacent Plan Angle = 34.99202

DD = arctan (sin W ÷ (tan SS ÷ tan S + cos W)) = 55.00798

R1 = Hip Rafter Slope Angle = 25.54245

C5m Main Hip Rafter Backing Angle = 16.79517

C5a Adjacent Hip Rafter Backing Angle = 31.63186

Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 41.57297

P2m = Main Jack Rafter Side Cut Angle = 31.15906

90° - P2m = Main Roof Sheathing Angle = 58.84094

P2a = Adjacent Jack Rafter Side Cut Angle = 47.66035

90° - P2a = Adjacent Roof Sheathing Angle = 42.33965

Purlin Depth = 1

Hip Rafter Depth = 2

Hip Rafter Width = 2

Purlin Rafter Seat Line Dimension for Plan View = 1.56205

Purlin Rafter Seat Line Dimension for Roof Surface = 1.20000

Hip Rafter Footprint Seat Line Dimension = 3.96927

Hip Rafter Dimension for Claw Lines from A to B = 1.78640

Hip Rafter Dimension C for Upper Claw Lines from A to C = 1.12740

Hip Rafter Dimension D for Lower Claw Lines from B to D = 0.88700

Drawing # 2

Roof Eave Angle = 120.00000

SS = Main Rafter Slope Angle = 30.25644

S = Adjacent Rafter Slope Angle = 39.80557

DD = Main Plan Angle = 76.99608

D = Adjacent Plan Angle = 43.00392

R1 = Hip Rafter Slope Angle = 29.61276

C5m Main Hip Rafter Backing Angle = 6.51019

C5a Adjacent Hip Rafter Backing Angle = 27.91566

Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 55.57415

P2m = Main Jack Rafter Side Cut Angle = 11.28135

90° - P2m = Main Roof Sheathing Angle = 78.71865

P2a = Adjacent Jack Rafter Side Cut Angle = 39.47840

90° - P2a = Adjacent Roof Sheathing Angle = 50.52160

Purlin Depth = 1

Hip Rafter Depth = 3.5

Hip Rafter Width = 3.5

Purlin Rafter Seat Line Dimension for Plan View = 1.56205

Purlin Rafter Seat Line Dimension for Roof Surface = 1.20000

Hip Rafter Footprint Seat Line Dimension = 6.94622

Hip Rafter Dimension for Claw Lines from A to B = 1.39221

Hip Rafter Dimension C for Upper Claw Lines from A to C = 0.68538

Hip Rafter Dimension D for Lower Claw Lines from B to D = 1.45905

Drawing #3
Roof Eave Angle = 90.00000
SS = Main Rafter Slope Angle = 33.69007
S = Adjacent Rafter Slope Angle = 33.69007

DD = Main Plan Angle = 45.00000
D = Adjacent Plan Angle = 45.00000

R1 = Hip Rafter Slope Angle = 25.23940
C5m Main Hip Rafter Backing Angle = 23.09347
C5a Adjacent Hip Rafter Backing Angle = 23.09347
Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 43.81306

P2m = Main Jack Rafter Side Cut Angle = 39.76216
90° - P2m = Main Roof Sheathing Angle = 50.23784
P2a = Adjacent Jack Rafter Side Cut Angle = 39.76216
90° - P2a = Adjacent Roof Sheathing Angle = 50.23784

Purlin Depth = 1
Hip Rafter Depth = 2
Hip Rafter Width = 2

Purlin Rafter Seat Line Dimension for Plan View = 1.80278
Purlin Rafter Seat Line Dimension for Roof Surface = 1.50000
Hip Rafter Footprint Seat Line Dimension = 3.60555

Hip Rafter Dimension for Claw Lines from A to B = 1.81221
Hip Rafter Dimension C for Upper Claw Lines from A to C = 1.04231
Hip Rafter Dimension D for Lower Claw Lines from B to D = 0.95940

Drawing for location of Miter & Claw lines on a roof with a Plumb Hip Rafter.

Roof Eave Angle = 90.00000
SS = Main Rafter Slope Angle = 30.25644
S = Adjacent Rafter Slope Angle = 39.80557

DD = Main Plan Angle = 55.00798
D = Adjacent Plan Angle = 34.99202

R1 = Hip Rafter Slope Angle = 25.54245
C5m Main Hip Rafter Backing Angle = 16.79517
C5a Adjacent Hip Rafter Backing Angle = 31.63186
Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 41.57297

P2m = Main Jack Rafter Side Cut Angle = 31.15906
90° - P2m = Main Roof Sheathing Angle = 58.84094
P2a = Adjacent Jack Rafter Side Cut Angle = 47.66035
90° - P2a = Adjacent Roof Sheathing Angle = 42.33965

Purlin Depth = 2
Hip Rafter Depth = 2
Hip Rafter Width = 2

Hip Rafter Claw & Miter Line Dimensions for Plumb Hip Rafters

Main SS Hip Rafter Offset Perpendicular to Hip Rafter Run Line = 1.34228
Man SS Hip Rafter Offset Along Eave Line = 1.63846
Adjacent S Hip Rafter Offset Perpendicular to Hip Rafter Run Line = 0.65772
Adjacent S Hip Rafter Offset Along Eave Line = 1.14692
Hip Rafter Backing Depth on Side of Hip Rafter = 0.40514

Hip Rafter Claw & Miter Line Dimensions for Plumb Hip Rafter on Main Side SS-DD
Hip Rafter Line Dimensions for Line 1 = 0.00000
Hip Rafter Miter Line Dimensions for Line 2 = 1.40209
Hip Rafter Miter Line Dimensions for Line 3 = 2.00574
Hip Rafter Claw Line Dimensions for Line 4 = 0.29525
Hip Rafter Claw Line Dimensions for Line 5 = 6.92159

Jack Rafter Miter Angle On Stick = 59.74356
Jack Rafter Bevel Angle On Stick= 31.15906
Jack Rafter Claw Angle on Stick = 8.87615
Jack Purlin Rafter Miter Angle On Side Face Perpendicular To Roof Surface On Stick= 70.57176
Jack Purlin Rafter Bevel Angle On Face Set In Roof Surface On Stick = 58.84094
Jack Purlin Rafter Claw Angle on Stick= 14.48201