Verkanteter Gratsparren DP Line

Drawings showing the development of the DP Line for the Verkanteter Gratsparren, canted hip rafter.

Roof Framing Geometry Proposition – Axioms  # 8:
The intersection of the Rafter Run Line & TC Line locates Hip Rafter DP Line.

Verkanteter Gratsparren

Verkanteter Gratsparren translates to canted hip rafter in German. In these drawings the canted hip rafter is rotated into the roof surface plane on a ground plan with equal roof slope angles and the eave angle is 60°. This example uses my Roof Framing Geometry Propositions – Axioms on a jack rafter that's plumb to the earth and the German Shiften method for locating the upper and lower claw angles from the width of the jack rafter in plan view.

California Valley Sleeper Saw Blade Bevel Angle

On this job, a 1200 square foot addition to an existing house the built in the 1950's the structural engineer called out the 2x beveled sleeper on the plans. This is the first time I've seen a structural engineer call out a beveled California Valley Sleeper.

It's fun to draw out the California Valley Sleeper Bevel Angle using geometry, but on the jobsite you need to know the actual California Valley Sleeper Saw Blade Bevel Angle. You can use one of my iPhone or Android apps to get the California Valley Sleeper Bevel Angle or use trigonometry. The California Valley Sleeper Bevel Angle is 90° minus the sum of the main roof hip rafter backing angle plus the adjacent roof hip rafter backing angle. You also need to know the California Valley Sleeper Bevel offset dimension, to snap a line on the California Valley Sleeper Material.

4:12 Equal Pitched Roof Slope Example:

C5m Main Hip Rafter Backing Angle = 12.92097
C5a Adjacent Hip Rafter Backing Angle = 12.92097

Valley Sleeper Saw Blade Bevel Angle = 90° - (C5m + C5a) = 64.15807

The California Valley Sleeper Bevel offset dimension is:

Material Depth × tan(Valley Sleeper Saw Blade Bevel Angle)

in this example the material thickness is 1.5"

1.5" × tan(64.15807) = 3.09711" or 3 1/8"

In this picture you can see the red snap line on the face of the 2x12 valley sleeper material for the California Valley Sleeper Bevel offset dimension. However, the Valley Sleeper Saw Blade Bevel Angle was greater than the bevel angle settings on my saw, so I use 90° - 64.15807° = 25.84193° or 25.8° and cut the material from the edge of the material instead of using the 64.15807° on the face of the material. First I used my 7 1/4" SkillSaw to cut the bevel angle, then I used my Bigfoot Saw with the 10" blade to finish off the cut. You could also use a Bigfoot saw with a swing table to make the 64.15807° bevel angle on the face of the material. 

California Valley Sleeper with the roof sheathing miter angle on the face of the sleeper and the bevel angle for the plumb cut using the roof slope angle.

The existing house built in the 1950's has California-Okie Valley Framing. 1x8 vrustic for the sleeper, 2x4 jack rafters and 1x4 ridge that's sagging 2" or 3" from the roof spreading apart. 

New 2013 California Valley framing requirements.

Install flat blocking below the new California Valley Sleeper.

Nail off the new roof sheathing at the Shear Wall Schedule nailing pattern. 6" O.C. in this example. Then nail off the valley sleeper material at 6" O.C.  The level cut of the valley jack rafters must be fully supported. For this house it meant using a 2x12 valley sleeper that's beveled and a 2x8 sleeper to support the  level cut of the valley jack rafters.

Install hangers or clips at the ridge and the level cut at the foot of the valley jack rafters.

Roof Framing Geometry Propositions – Axioms #4

Testing the Roof Framing Geometry Propositions – Axioms  on a rotated purlin rafter intersecting two rotated hip rafters. The DP Line of the purlin rafter is drawn using the Roof Framing Geometry Propositions – Axioms. However, laying down the purlin rafter plane onto the plan view requires a couple of more steps. To lay down the purlin rafter plane in plan view you have to swing two arcs or circles using the lengths of the vertical plane tilt for the radius of the arcs. Then you have to draw a line that is tangent to the two arcs-circles to establish the correct purlin rafter plane in plan view. Then the standard  Roof Framing Geometry Propositions – Axioms work for the upper and lower claw angles on the rotated purlin rafter.

 Swing arcs from Point V  with radius equal to V-A then draw the tangent line to the two arcs thru Point B to establish the purlin rafter plane in plan view.

The Roof Framing Geometry Propositions – Axioms also work for a Jack Rafter Plumb to the Earth Skewed from the Plate Line with Edge Bevel.