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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. Draw line FP #1 parallel with the hip rafter run line. Draw lines TC #1 & TC #2 parallel with the sides of the rotated hip rafter block in the hip rafter backing triangle. Where the TC # 1 line intersects at the bottom of the hip rafter backing triangle draw the line DP #1 to th

We're getting closer to defining the claw lines on the  Tréteaux  Fold Down Roof Surface correctly. Once the claw lines on the fold down roof surface are drawn correctly you can place the lines for the timber in plan view at any skewed angle from the eave line and still develop the timber angle cuts on the the fold down roof surface. tréteau à devers First, here's an example of a purlin rafter on the DP side of the hip rafter rotated into the roof surface and a jack rafter on the rotated side of the hip rafter. Here's a drawing using the same folding roof surfaces with the purlin rafters skewed from the plate line. Here's the drawing of how the claw lines on the folding roof surface are developed from the seat lines in plan view and the seat lines on the folding roof surface. There should always be 4 lines that define the claw-miter-bevel angles of the rafters on the roof surface. These four lines represent the center line of the hip rafter, the edge of the hip rafter,

Tréteaux Angles Trigonometry Formulas Link to Online Script to check the Tréteaux Angles Input Variables Works for any Roof Eave Angle with equal or unequal rafter slope angles. Roof Eave Angle SS = Main Rafter Slope Angle S = Adjacent Rafter Slope Angle DD = Main Plan Angle D = Adjacent Plan Angle R1 = Hip Rafter Slope Angle C5m Main Hip Rafter Backing Angle C5a Adjacent Hip Rafter Backing Angle Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) P2m = Main Jack Rafter Side Cut Angle 90° - P2m = Main Roof Sheathing Angle P2a = Adjacent Jack Rafter Side Cut Angle 90° - P2a = Adjacent Roof Sheathing Angle Tréteaux Angles tréteau à devers R8-DP = Tilted Hip Rafter Slope Angle on DP Side = arctan( tan ( Hip Rafter Backing Angle) ÷ tan (Jack Rafter Side Cut Angle )) R8-DP = arctan( tan ( C5m ) ÷ tan ( P2m )) R9-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line R9-DP = arctan( sin ( R1 ) × tan ( C5m )) D-DP = Horizontal Plane Rotation for Tilted Hip Rafter on DP Line fr

I asked Joe Bartok to help me with the saw blade bevel angle on the  Tréteaux Dit Cadet task model .  I had some inconsistencies in my SketchUp drawings and it resulted in inconsistencies in the results of Joe's formulas. So I made drew up some new control files and sure enough Joe's formulas for the saw blade bevel angle at the foot of the trestle-sawhorse-hip rafter rotated into the roof surface plane for the Parallelogram Prism were correct. tréteau à devers Research notes: ----------------------------------------------------------------------------- Parallelepiped In three dimensional geometry a parallelepiped is a prism whose faces are all parallelograms. In  geometry , a  parallelepiped  is a three-dimensional figure formed by six  parallelograms . Trihedral Angle ----------------------------------------------------------------------------------------------------- First I drew out an equal pitched 8:12 roof. Angular Dimension (27.13381°) Hip Rafter Rotated Slope Angle = a