Housing layout for Valley Rafter intercepts Beam

Photos courtesy of John Devries Log Homes

Major Pitch = 10/12       Minor Pitch = 3/12
Angle in Plan between Valley Ridges = 90°

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