Rotated Rafters intersecting Rotated Hip Rafters

Joe Bartok's Study on Rotated Rafters intersecting Rotated Hip Rafters.
Download Rafters Rotated To Roof Surface PDF file
______________________________________________________



Rectangular Section Calculations

Main Slope Angle = 9/12

Adjacent Slope = 12/12

Corner Angle = 90°

.............................

 SS = 36.86990°
DD = 53.13010° 
P2m = 30.96376° 
C5m = 21.10020° 
R1 = 30.96376°

S = 45.00000°
D = 36.86990°
P2a = 43.31386°
C5a = 34.44990°
R1 = 30.96376°
...........................
The 9/12 Side of the central (30.96376°) Hip Rafter is rotated to the roof surface
Dihedral Angle between Hip upper shoulder and Roof Surface on 12/12 Side
= 90° – (C5m + C5a) = 90° – (21.10020° + 34.44990°) = 34.44990°
.............................

Rotated Rafter Offset on 9/12 Eave = 60°
Rotated Rafter Slope Angle = arctan (tan 36.86990° sin 60°) = 33.00449° Rotated Rafter Backing
Bevel = arctan (sin 33.00449° ÷ tan 60°) = 17.45760° Rotated Rafter P2 Angle = arctan (cos
36.86990° ÷ tan 60°) = 24.79128° Rotated Rafter 90° – P2 Angle = arctan (tan 60° ÷ cos 36.86990°) =
65.20872°

Rotated Rafter Peak Calculations:
Sum of P2 Angles at Rotated Rafter Peak = 30.96376° + 24.79128° = 55.75504° Blade Bevel along Sum
of P2 Angles = 0°
Angle on Adjoining Face = 90°
Blade Bevel for Adjoining Face = 90° – 55.75504° = 34.24496° Trace Angle = arccos (cos 55.75504°
cos 90°) = 90°
Rotated Rafter Foot Calculations:
DDP = arctan (sin 33.00449° tan 17.45760°) = 9.72052° Angle on shoulder of Rotated Rafter @ DP Line
= arccos (cos 33.00449° cos 9.72052°) = 34.25020°
Blade Bevel = arctan (sin 34.25020° ÷ tan 65.20872°) = 14.57152° Angle on adjoining shoulder of 
Rotated Rafter
= arctan (sin 34.25020° ÷ tan 14.57152°)
= 65.20872° = 90° – P2
Blade Bevel along 90° – P2
= DD = arctan (sin 65.20872° ÷ tan 34.25020°)
= 53.13010° = 90° – SS
Rotated Rafter Footprint Angle
= arccos (cos 65.20872° cos 34.25020°) = 69.72052° Offset Angle + DDP = 60° + 9.72052°


.............................


Rotated Rafter Offset on 12/12 Eave = 70°
Rotated Rafter Slope Angle = arctan (tan 45° sin 70°) = 43.21918°
Rotated Rafter Backing Bevel = arctan (sin 43.21918° ÷ tan 70°) = 13.99545° Rotated Rafter P2 Angle 
= arctan (cos 45° ÷ tan 70°) = 14.43276°
Rotated Rafter 90° – P2 Angle = arctan (tan 70° ÷ cos 45°) = 75.56724°


Rotated Rafter Upper Claw Calculations:
Sum of P2 Angles at Rotated Rafter Peak = 43.31386° + 14.43276° = 57.74662° Blade Bevel along Sum 
of P2 Angles
= C5m + C5a = 21.10020° + 34.44990° = 55.55010°
Angle on Adjoining Face = arctan (sin 57.74662° ÷ tan 55.55010°) = 30.11986° Blade Bevel for 
Adjoining Face = arctan (sin 30.11986° ÷ tan 57.74662°) =
17.57093°
Trace Angle on shoulder of 30.96376° Hip Rafter arccos (cos 30.11986° cos 57.74662°) = 62.50910°


Rotated Rafter Lower Claw Calculations:
Sum of P2 Angles at Rotated Rafter Peak = 43.31386° + 14.43276° = 57.74662°
Blade Bevel along Sum of P2

Blade Bevel for Adjoining Face = arctan (sin 50.95245° ÷ tan 57.74662°) =
26.10841°°
Trace Angle on shoulder of 30.96376° Hip Rafter arccos (cos 50.95245° cos 57.74662°) = 70.35508°
Rotated Rafter Foot Calculations:
DDP = arctan (sin 43.21918° tan 13.99545°) = 9.68589° Angle on shoulder of Rotated Rafter @ DP Line
= arccos (cos 43.21918° cos 9.68590°) = 44.08148°
Blade Bevel = arctan (sin 44.08148° ÷ tan 75.56724°) = 10.15094° Angle on adjoining shoulder of 
Rotated Rafter
= arctan (sin 44.08148° ÷ tan 10.15094°)
= 75.56724° = 90° – P2
Blade Bevel along 90° – P2
= DD = arctan (sin 75.56724° ÷ tan 44.08148°)
= 45.00000° = 90° – S
Rotated Rafter Footprint Angle
= arccos (cos 75.56724° cos 44.08148°) = 79.68589°
= Offset Angle + DDP = 70° + 9.68589°

____________________________________________________________
NR Section Calculator
The rafters are treated as if the bevel were applied to the side face (the face not set
in the roof surface).
.............................
9/12 Side Rotated Rafter Peak
μ  = 90° (Angle on Rectangular Section)
ß  = 30.96376° + 24.79128° = 55.75504° (Sum of P2)
α  = 17.45760° (Backing Bevel)
MIT = 78.45754° (Angle on Plumb Face of Rotated Rafter)
BEV = 69.17126° (Trace Angle on face of 30.96376° Hip)
= 20.82874°
Projected Right Angle = 90° (Trace Angle for Rectangular Section)
Supplementary Angle = 90°
Blade Bevel for XDIH = 32.46690° (90° – 55.75504° ... Blade Bevel remains the
same)
Blade Bevel for YDIH = 0° (Dihedral Angle between faces of 30.96376° Hip =
90°)
Blade Bevel for ZDIH = 34.24496° (Blade Bevel for Rectangular Section)
.............................
9/12 Side Rotated Rafter Foot
μ  = 34.25020° (Angle on Rectangular Section)
ß = 65.20872° (90° – P2)
α  = 17.45760° (Backing Bevel)
MIT = 33.00449° (Rotated Rafter Slope Angle)
BEV = 60.00000° (Rotated Rafter Footprint)
= 9.72052° (DDP )
Projected Right Angle = 110.27948°
Supplementary Angle = 69.72052° (BEV + = 60° + DDP)
Blade Bevel for XDIH = 0.00000°
Blade Bevel for YDIH = 53.13011° (90° – SS ... Blade Bevel for Rectangular
Section)
Blade Bevel for ZDIH = 14.57152° (Blade Bevel for Rectangular Section)
.............................
12/12 Side Rotated Rafter Peak – Upper Claw
μ  = 30.11986° (Angle on Rectangular Section)
ß = 43.31386° + 14.43276° = 57.74662° (Sum of P2)
α  = 13.99544° (Backing Bevel)
MIT = 28.71825° (Upper Claw Angle on Plumb Face of )
BEV = 55.50766° (Trace Angle on face of 30.96376° )
= 7.00143°
Projected Right Angle = 117.49090°
Supplementary Angle = 62.50910° (Trace Angle for Rectangular Section)
Blade Bevel for XDIH = 5.36467° (Blade Bevel along 28.71825°)
Blade Bevel for YDIH = 55.55010° (Blade Bevel remains the same)
Blade Bevel for ZDIH = 17.57092° (Blade Bevel for Rectangular Section)
.............................
12/12 Side Rotated Rafter Peak – Lower Claw
μ = 180 – 50.95244° = 129.04756° (Angle on Rectangular Section)
ß = 43.31386° + 14.43276° = 57.74662° (Sum of P2)
α  = 13.99544° (Backing Bevel)
180° – MIT = 57.60620° (Lower Claw Angle on Plumb Face of )
BEV = 96.49999° (Trace Angle on face of 30.96376° )
= 13.14492°
Projected Right Angle = 70.35508° (Trace Angle for Rectangular Section)
Supplementary Angle = 109.64491°
Blade Bevel for XDIH = 34.32007° (Blade Bevel along 57.60620°)
Blade Bevel for YDIH = 34.44991° (Saw Blade Bevel remains the same)
Blade Bevel for ZDIH = 26.10840° (Blade Bevel for Rectangular Section)
.............................
12/12 Side Rotated Rafter Foot
 μ = 44.08148° (Angle on Rectangular Section)
 ß = 75.56724° (90° – P2)
 α = 13.99544° (Backing Bevel)
MIT = 43.21918° (Rotated Rafter Slope Angle)
BEV = 70.00000° (Rotated Rafter Footprint)
= 9.68589° (DDP)
Projected Right Angle = 100.31411°
Supplementary Angle = 79.68589° (BEV + = 60° + DDP)
Blade Bevel for XDIH = 0.00000°
Blade Bevel for YDIH = 45.00000° (90° – S ... ... Blade Bevel for Rectangular
Section)
Blade Bevel for ZDIH = 10.15094° (Blade Bevel for Rectangular Section

























































Komentar

Posting Komentar

Postingan populer dari blog ini

Layover Valley Rafter Basics

Gambar
Before I get into the Hexenschnitt for the Layover Valley Rafter I needed to review the basic geometry that defines the layover valley rafter. I needed to make sure I could draw the layover valley rafter correctly in plan view (ground plan). Here's one method of a basic drawing using the layover valley rafter backing triangle to position the layover valley rafter material on the roof surface that defines the  layover valley rafter in plan view. The  layover valley rafter top bevel is easily defined by extending the  layover valley rafter backing triangle to the top of the  layover valley rafter. The other  layover valley rafter line in plan view is defined by the bottom edge of the  layover valley rafter material sitting on the  layover valley rafter backing triangle. (Roof Surface). The  layover valley rafter plan view lines at the intersection of the two roofs. I tried this method for drawing the  layover valley rafter, but this method seems to be slow of a process for determinin
Baca selengkapnya

Hip Rafter Edge Bevel and Backing Angle

Gambar
In complex roof framing there are 7 main roof framing angles. Hip Rafter Backing Angle Valley Sleeper Bevel Angle Plain Titl (DP) Main Plan Angle Adjacent Plan Angle  Main Profile Rafter Slope Angle Adjacent Profile Rafter Slope Angle In this article I will discuss the hip rafter backing angle and the valley sleeper bevel angle. These two angles determine the miter angle and and saw blade bevel angles for jack rafters and purlin rafters that are plumb to the earth and for jack rafters and purlin rafters that are skewed from the eave line. A thorough knowledge of these two angles is critical in complex roof framing using geometry or trigonometry. The hip rafter edge bevel was avoided in the 12th century on some roof structures by rotating the hip rafter into the roof surface plane. However, by avoiding the hip rafter edge bevel, the carpenters-builders had to have a knowledge of the Valley Sleeper Bevel Angle. They didn't call it the Valley Sleeper Bevel Angle, but it's the same
Baca selengkapnya

Layover Valley Rafter Hexenschnitt #3

Gambar
In the book Das neue Buch vom alten Wissen der Schiftung The new book on the ancient knowledge Schiftung The new book on the ancient knowledge Roof Framing The new book on the ancient knowledge Roof Framing Geometry by Bernd Küppers I'm stuck on page 23. The geometry in the book, just doesn't return the correct miter angle for the Layover Valley Rafter Witches Cut (Hexenschnitt). I don't know if I'm drawing it incorrectly, or the BE (Bottom Edge Plane of the Layover Valley Rafter) should be drawn differently. Similar drawing at File: Kehlbohle mit Hexenschnitt.jpg There's 3 canted planes that define the Layover Valley Rafter Witches Cut Miter Angle. The main roof surface, the square tail fascia plane of the main roof and the the square tail fascia plane of the adjacent roof.  I think the problem with my geometric drawings is defining the intersection of the roof surface with the adjacent  square tail fascia plane.
Baca selengkapnya