Google SketchUp Plugin -- Roof Framing Geometry Version 1.1

Here's a link to an updated dated version of the Roof Framing Geometry Plugin, version 1.2.

I fixed the dihedral angle, so it draws correctly.

Just unzip it in the Google SketchUp \Plugins directory.
The file structure should look something like this.

C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming.rbC:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\plan_angle.rbC:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\Trapezoidal.rb 
C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\Trapezoidal_Timber.rb 

C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\Tetrahedron_Slice.rb 
C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\Trapezoidal_Timber_Plane.rb 
C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\draw_angle_dim.rbC:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\draw_arc.rbC:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\draw_circle.rb C:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\interior.pngC:\Program Files\Google\Google SketchUp 8\Plugins\RoofFraming\exterior.png




RoofFraming-v-1-2.zip

Ad Quadratum - Seed of Life - Ad Triangulum

We're doing a 600 sq-ft addition/remodel on Knoll Organics farm. There's a granite stone fabrication site down the road from the farm. They paid $55.00 a ton to dispose of the left over pieces of granite. So they give the left over granite to Rick Knoll and he's built a 2,000 sq-ft man cave with granite on all of the walls in his house.  He also built a 500 LF granite wall about 4' high and about 2' wide. It's quite impressive. I'll have to get some pictures of his man cave and his granite wall.

Knoll Organics Farm

On the remodel, we're going to try to add the Ad Quadratum - Seed of Life - Ad Triangulum  geometric symbols to the granite wains coat that is on the front of the remodel below the windows. I'm thinking about using a router with a diamond tip bit to carve the geometric symbols into the granite.

Here's a couple of drawings showing the   Ad Quadratum - Seed of Life - Ad Triangulum  geometric symbols.

Ad Quadratum (square rotated within the circle)

Ad Quadratum (earth geometry)

Ad Triangulum ( equilateral triangle rotated within the circle)

Ad Triangulum (human consciousness)

Seed of Life

(daisy wheel)

Here’s a link with more info on the geometric shapes

and here's a link to the Ad Quadratum - Seed of Life - Ad Triangulum  geometric symbols.

http://www.sbebuilders.com/Traite_De_Charpente/SketchUp/Geometry.pdf

Skewed Rafter Saw Blade Bevel Angle

The Trapezoidal Timber generated from the Roof Framing Geometry plugin based on the Skewed Rafter on page 52 in "Traité Théorique et Pratique de Charpente" by Louis Mazerolle needs a little more work before I build a full scale model. We're not suppose to cut the model with a skill saw, so there wasn't any need to develop the saw blade bevels angles. Well, it 2012 and I'm going to cut my full scale model with a skill saw, so I developed a plugin that develops the saw blade bevel angles for the skewed rafter foot and peak.


In this image I laid out  the two  "trait carré"  , drawing a perpendicular line to a given line to find the peak miter angle of 43.08446° and the bevel angle of 78.82320°.

Then I used the Tetrahedron Slice Tool to find the Saw Blade Bevel Angle 8.21141 for the cut at the peak of the skewed rafter.

For the skewed rafter foot  I laid out  the two  "trait carré"  , drawing a perpendicular line to a given line to find the foot miter angle of 43.33393° and the bevel angle of 77.79889°.

Then I used the Tetrahedron Slice Tool to find the Saw Blade Bevel Angle 8.79189° for the cut at the foot of the skewed rafter.

Here are the links to the Google SketchUp files I used in this article.

Tetrahedron_Slices.skp

Tetrahedron_Slice_1.skp

Tetrahedron_Slice_2.skp

Tetrahedron Extracted From Jack Rafter Side Cut At Hip Rafter

While going through the exercises in  "Traité Théorique et Pratique de Charpente" by Louis Mazerolle it helps me to understand the Stereotomy geometry in 2D by extracting and unfolding tetrahedrons to make sure the 3D Stereotomy in the book is correct.



Here we have a Tetrahedron Extracted From an 8:12 pitched roof (33.69007°) Jack Rafter Side Cut Angle at the Hip Rafter.

Unfold each face.

First draw the line CE that is perpendicular to line AB, trait carré, square to a give line.

Next develop the slope of the tetrahedron by drawing a line from point C that is perpendicular to line CD,  trait carré, square to a give line. The length of line FC = CE, then draw the line FD. The line CD is the common rafter run of the tetrahedron and the angle CDF is the slope of the tetrahedron.

By developing the slope triangle of the tetrahedron you can see all the roof framing angles developed from the unfolded tetrahedron.

The unfolded tetrahedron has

Common Rafter Slope Angle

Jack Rafter Side Cut Angle

Roof Sheathing Angle

Hip Rafter Slope Angle

Hip Rafter Backing Angle

Hip Rafter Square Tail Fascia Miter Angle

Purlin Miter Angle

Using the Roof Framing Geometry , Tetrahedron Angles,  Google SketchUp Plugin  and using 

Rafter Pitch Angle = 66.9065291478°

Plan Angle = 39.7621583409°

we can go full circle and see the plan angle of 45° as the dihedral angle between the two planes.Next time you set your saw to 45° for the jack rafter side cut bevel angle you'll be developing a lot more than just the jack rafter side cut angle.

Tetrahedron Trigonometric Identity Formulas

The Tetrahedron Trigonometric Identity Formulas by Joe Bartok are what I consider the most important roof framing document developed over the last 100 years. The Timber Framing Hawkindale Angle Formulas developed by Rees Hawkins Acheson from the Martindale Hip and Valley Roof Angles were the first Tetrahedron development for roof framing angles, but Joe Bartok's Tetrahedron Trigonometric Identity Formulas gave us the ability to find the roof framing angles in any type of Tetrahedron.

Steps To Extract a Tetrahedron In Google SketchUp

Creating roofs in Google SketchUp in 3D is fairly easy, but sometimes you need more roof framing angle information from your drawings. Here is a step by step example of extracting a  tetrahedron from a 3D drawing in Google SketchUp . In this example we'll use the Trapezoidal Timber generated from the Roof Framing Geometry plugin based on the Skewed Rafter on page 52 in "Traité Théorique et Pratique de Charpente" by Louis Mazerolle. This tetrahedron extraction is also an example of   "trait carré"  , drawing a perpendicular line to a given line.




Step 1.
Use the protractor tool and draw a perpendicular construction line,"trait carré", on the top edge of the rafter from point E.

Step 2. Draw a line from point E to point C and then delete the construction line made by the protractor tool.

Step 3. Use the protractor tool and draw a perpendicular construction line ,"trait carré",on the side of the rafter at point C. Then draw a line from point C to point A and then delete the construction line made by the protractor tool.

Step 4. Select the 3 top edges of the tetrahedron. Line E-C, line C-B and line C-A. Use Edit/Copy then Edit/Plaste.

Step 5. Draw a line from E-A and draw a line from A-B to complete the edges of the tetrahedron.

Step 6. Use the paint bucket tool paint the faces of  the tetrahedron. Then check the angles on the extracted tetrahedron to make sure they match the angles on the rafter.

Step 7. To draw the tetrahedron unfolded start by drawing a construction line at point B using the angle EBC.

Step 8. Draw a construction line at point E using the angle BEC. Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool.

Step 9. Draw a construction line at point C using the angle ECA. Draw a construction line at point E using the angle CEA.Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool.

Sometimes you need to use the protractor tool at a different location to draw the correct angle. After you have drawn the correct angle with the protractor tool use the move tool to place the construction line in the correct position.

Step 10. Draw a construction line at point E using the angle CEB. It helps to paint the face of the triangles to get the protractor tool to position it self correctly on the face of the triangle. Draw a construction line at point A using the angle EAB.Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool. Then paint the face of the triangle.

Step 11. Draw a construction line perpendicular to the line EA. Then use the Move tool and position the construction line at point C. 

Step 12. Draw a construction line perpendicular to the line AC.  Draw the angle BAC at point A.

Step 13. Use the Tape Measure Tool and get the length of line CB. Then use the Tape Measure Tool again along the construction line at point C, to mark off the length CB. In a 2D Cad program we would use the Arc or Circle tool to mark off the location of the new point, but not in Google SketchUp. Then draw a line from D to the new point B.  The triangle DCB is the triangle that we'll use in the next post on Tetrahedrons.

Skewed Rafter Footprint & Stereotomic View

Steps to geometrically develop the Trapezoidal Ground Plan Skewed Rafter on page 52 in "Traité Théorique et Pratique de Charpente" by Louis Mazerolle.


Step 1:
Develop the point PT, swing an arc with center point K and radius equal to KZ. This is the rise of the principal rafters. Draw a line from PT to AC. The angle K-PT-AC is the plane tilt of the skewed rafter (8.68257°). Draw a line thru GC, perpendicular to Q - G to K. Swing an arc from center point AC with radius equal to AC-PT, thru point SP. Draw a line from SP to G, to develop the triangle that gives us the miter angle at the skewed rafter foot.

The dark brown triangle is the plane tilt triangle, the red triangle is the horizontal plane rotation of the the tilted plane, the tan triangle is the miter angle at the skewed rafter foot. The green triangle is just part of a tetrahedron and not significant to the skewed rafter miter or bevel angles. 

Then draw some horizontal trace lines thru g1, g2, g3 and g4. Transfer the lines g1-g2 to the stereotomic view of the skewed rafter and then the lines g1-g4, g2-g3. Then draw the sides of the skewed rafter at the skewed rafter angle (44.33393°).

Here's a link to the Google SketchUp file.

Trapezoidal_Timber_Footprint.skp