Putting theory to the test in the real world COMPOUND JOINTS     The trigonometry and linear algebra used to solve the angles for the compound joints shown below is explained in the section COMPOUND JOINERY . Interlocking Trusses Four-branch Convergent Joint Ridge detail ... two 8/12 rafters meet two beams Four-branch Convergent Joint .. matching faces Bird's-eye view of Atrium Atrium detail: Three-branch Convergent Joint 5 21/32/12 Hip rafter meets two beams TIMBER FRAMED ROOF     ANGLE CALCULATORS contains a link to the Excel worksheet Log Angle Generator, and online calculators LAG and Lag , which will generate the angles for the joinery depicted below. Equal 10/12 pitches, cruciform footprint Interior View: Four 7 1/16/12 Valley rafters meet the ridges at the center post LOG ROOF SYSTEMS 9/12 Main pitch intersects 7 1/4/12 Adjacent pitch 90° angle between ridge lines Gazebo: 8/12 pitches, regular octagonal (135°) footprint 73/8/12 Hip rafters meet kingpost     There is no valley rafter in the roof below, the valley line is created by intercepting ridges and purlins. The strength of these roof components was assessed using the mathematics described in LOG BEAM SECTIONS , implemented in the Excel worksheet Log Beam Calculator . Photos courtesy of JOHN DEVRIES LOG HOMES

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