Housing layout for Valley Rafter intercepts Beam

Porch intersects Log Wall
Porch intersects Log Wall
Photos courtesy of John Devries Log Homes

Major Pitch = 10/12       Minor Pitch = 3/12
Angle in Plan between Valley Ridges = 90°
Valley Rafter Shift: Plan and Section Views
Valley intercepts Beam Assembly
Valley Rafter Section Dimensions
Valley Rafter Section detailing intercept with Beam
Valley Housing layout on Beam
Valley Housing layout on Beam
Non-Rectangular Sections Calculator
Entries
Miter Angle
μ = 72.85600° (R4Ba ... Valley Side Cut Angle)
Bevel Angle
Note the NEGATIVE value entered for β
β = – 76.53371° (90° - R1 ... 90° - Valley Pitch Angle)
Slope Angle of Cross-Section
α = 3.99630° (C5a ... Backing Angle)
Width of Rectangular Face = 6
Height of Rectangular Face = Variable
Returns
Miter Angle on Sloped Face (backed face of Valley rafter)
MIT = 73.77275° (90° - P2a ... Sheathing Angle)
Angles on Projected Triangle created by cutting the compound angle at the Valley rafter foot
Projected 90° - α
BEV = 90.00000°
Note the NEGATIVE sign and orientation of R5Ba on the stick with respect to Backing Angle C5a
Projected α
ρ = – 3.93617° (R5Ba)
Angles on Parallelogram created by cutting the compound angle at the Valley rafter foot (Supplementary pair of projected Right Angles)
93.93617° , 86.06383° (90° R5Ba)
Dihedral Angle along line of MIT on Sloped Face
(Backed face of Valley rafter)
XDIH = 104.03624°, the angle between the 3/12 Roof Plane and the plumb plane along the length of the Beam
Blade Angle = 14.03624° (S ... Common Pitch Angle)
Dihedral Angle along Line of β
(Plumb face of Valley rafter)
YDIH = 73.30076° (D ... Plan Angle)
Blade Angle = 16.69924° (90° - D ... 90° - Plan Angle)
Dihedral Angle along Line of μ
(Bottom shoulder of Valley rafter)
ZDIH = 77.11164° (90° - A5Ba)
Blade Angle = 12.88836° (A5Ba)

Cross-Section Triangle Dimensions: the dimensions of the triangle created by cutting the Backing Angle (right triangle of C5a)
Rise = .41917
Run = 6
Slope = 6.01462
Projected Triangle Dimensions: the triangle of the Backing Angle projected to the sloped face formed by cutting the compound angle at the Valley rafter foot (right triangle of R5Ba)
Note the NEGATIVE sign and the location on the stick of the projected Rise
projected Rise to Line of β = – .43102
projected Run to Line of μ = 6.27900
length along Slope of MIT = 6.26418

Joe Bartok
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