Valley Rafter and Purlin Intersections
Studies of the "Purlin Lip Cut Angle" ... Angle P3

Overview of Juxtaposed Tetrahedra modeling the Angles

Main Slope = 10/12     Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90


Bird's-Eye View of Juxtaposed Tetrahedra
Bird's-Eye View of Juxtaposed Tetrahedra

Location Angle P3 (Purlin Lip Cut Angle) on Juxtaposed Tetrahedra
Location Angle P3 (Purlin Lip Cut Angle) on Juxtaposed Tetrahedra

Developments of Tetrahedron modeling Angle P3 (Purlin Lip Cut Angle)

Development of Tetrahedron modeling Angle P3
Development of Tetrahedron modeling Angle P3

Formula for Angle P3
Formula for Angle P3

Jack Purlin intersects Valley Rafter
Example application of Angle P3

Main Slope = 10/12     Adjoining Slope = 10/12
Corner Angle measured between Eaves in Plan View = 90


Jack Purlin housed in the Valley Rafter
Jack Purlin housed in the Valley Rafter

Jack Purlin housing on side face of Valley Rafter
Jack Purlin housing on side face of Valley Rafter

View of Square Housing Cut and Step Tenon on end of Jack Purlin
View of Square Housing Cut and Step Tenon on end of Jack Purlin

Lateral View of Square Housing Cut and Step Tenon
on the Jack Purlin, showing the location of Angle P3

Lateral View of Square Housing Cut and Step Tenon on the Jack Purlin, showing the location of Angle P3

3D Models ... Valley Rafter Peak intersects Principal Purlin
Example application of Angle P3

Main Slope = 10/12     Adjoining Slope = 10/12
Corner Angle measured between Eaves in Plan View = 90


Intersection of Valley Rafter Peak and Principal Purlin
Intersection of Valley Rafter Peak and Principal Purlin

Tenon at Valley Rafter Peak
Tenon at Valley Rafter Peak

Mortise on Principal Purlin to accommodate the Valley Rafter Peak
Mortise on Principal Purlin to accommodate the Valley Rafter Peak

Valley Rafter Peaks intersect Principal Purlin

Main Slope = 12/12     Adjoining Slope = 10/12
Corner Angle measured between Eaves in Plan View = 90


Adjoining Valley Rafter Peaks and Adjoining Side Ridge Beam intersect Principal Purlin
Adjoining Valley Rafter Peaks and Ridge Beam intersect Principal Purlin

Valley Rafter meets intersecting Underpurlins
Note ... intersecting underpurlins are exactly the same as Square Hung Fascia

Main Slope = 7/12     Adjoining Slope = 12/12
Corner Angle measured between Eaves in Plan View = 90


Underpurlin Miter and Saw Bevel Angles to accommodate Valley Rafter
Underpurlin Miter and Saw Bevel Angles to accommodate Valley Rafter

Underpurlin Miter and Saw Bevel angles to accommodate Valley Rafter
... view of Intersecting Purlins abutting one another

Underpurlin Miter and Saw Bevel angles to accommodate Valley Rafter ... view of Intersecting Purlins abutting one another

Underpurlin Miter and Saw Bevel Angles to accommodate Valley Rafter
... relationship of Angle P3 to the Miter Angles

Underpurlin Miter and Saw Bevel Angles to accommodate Valley Rafter ... relationship of Angle P3 to the Miter Angles

Intersecting Underpurlins ... Planes set in the surface of the Roof
Intersecting Underpurlins ... Planes set in the surface of the Roof

Intersecting Underpurlins ... view of the Abutting Faces
Intersecting Underpurlins ... view of the Abutting Faces

Co-Ordinates (Direction Numbers) of Vectors to solve
Saw Blade Bevel = C5a C5m = Difference of Backing Angles

Co-Ordinates (Direction Numbers) of Vectors to solve Saw Blade Bevel = C5a  C5m = Difference of Backing Angles

Joe Bartok