SBE Builders

Strong Built Establishments Builders

SBE Builders is a commercial and residential framing contractor located in Discovery Bay California. Dedicated to the art of Carpentery & Roof Framing. We are the professionals for the future of the craft of carpentry.

Irregular Hips Geometry
based on Billy Dillon's article in the Sept. 2007 JLC, On Complex Roof Geometry
Major Rafter Pitch Or Major Pitch Angle Minor Rafter Pitch Or Minor Pitch Angle Building Span Building Length  
feet
inches
frac
feet
inches
frac
 
Common Rafter Width Hip Rafter Width Ridge Width Plate Width Rafter O.C. Spacing Major Rafter Pitch Overhang Show Feet Inches
Download Irregular Hip Rafter Geometry DXF
Irregular Hip Geometry Framing.dxf -- auto generated DXF CAD file of irregular hip geometry drawing each time script is run

Irregular Hip Framing Formulas

Variables
----------------------------
Major Pitch 
Minor Pitch 
Major Run 
Jack Rafter Spacing

Formulas
----------------------------------

Eave Angle  = 90
Major Pitch Angle = atan( Major Pitch  12 )
Minor Pitch Angle = atan( Minor Pitch  12 )
Minor Run = ( Major Pitch  Minor Pitch ) * Major Run

Major Plan Angle =  arctan( Minor Pitch  Major Pitch )
Minor Plan Angle =  arctan( major_pitch  Minor Pitch )

Hip Pitch Angle = arctan( tan( Major Pitch Angle ) * sin( Major Plan Angle ))
Major Pitch Hip Backing Angle = arctan( sin( Hip Pitch Angle)  tan( Major Plan Angle ) )
Minor Pitch Hip Backing Angle = arctan( sin( Hip Pitch Angle)  tan( Minor Plan Angle ) )

Major Plan Angle Unit Rise = tan( Major Plan Angle )
Minor Plan Angle Unit Rise = tan( Minor Plan Angle )

Major Pitch Common Unit Run = 12 / tan( Major Pitch Angle )
Minor Pitch Common Unit Run = 12 / tan( Minor Pitch Angle )

Major Pitch Common Unit Length = Major Pitch Common Unit Run  cos( Major Pitch Angle )
Minor Pitch Common Unit Length = Minor Pitch Common Unit Run  cos( Minor Pitch Angle )

Hip Rafter Unit Run = hypotenuse(Major Pitch Common Unit Run , Minor Pitch Common Unit Run )
Hip Rafter Unit Length = hypotenuse( 12 , Hip Rafter Unit Run )

Major Side Shift Unit Ratio = Major Plan Angle Unit Rise  ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ) 
Minor Side Shift Unit Ratio = Minor Plan Angle Unit Rise  ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ) 
Major Side Shift = 0.5 * ( Major Side Shift Unit Ratio - Minor Side Shift Unit Ratio) 
Minor Side Shift = 0.5 * ( Minor Side Shift Unit Ratio - Major Side Shift Unit Ratio) 
Hip Unit Rise Run = 12  sin( Major Plan Angle)
Unit Hip Drop = Major Pitch  (Hip Unit Rise Run * ( Major Plan Angle Unit Rise + Minor Plan Angle Unit Rise ))
Hip Drop = Hip Width * Unit Hip Drop

Major Plumb Backing Angle = arctan( tan( Hip Pitch Angle )  tan( Major Plan Angle ))
Minor Plumb Backing Angle = arctan( tan( Hip Pitch Angle )  tan( Minor Plan Angle ))

Major Plumb Backing Angle Rise = (( Hip_Width * 0.5 ) * tan( Major Pitch Hip Backing Angle ))  cos( Hip Pitch Angle )
Minor Plumb_Backing_Angle_Rise = (( Hip_Width * 0.5 ) * tan( Minor Pitch Hip Backing Angle ))  cos( Hip Pitch Angle )
Major Plumb Backing Angle Run = Major Plumb Backing Angle Rise  tan( Major Plumb Backing Angle )
Minor Plumb Backing Angle Run = Minor Plumb Backing Angle Rise  tan( Minor Plumb Backing Angle )

Major Plan Angle Hip Rafter Side Cut Angle  = arctan( cos( Hip Pitch Angle )  tan( Major Plan Angle )) 
Minor Plan Angle Hip Rafter Side Cut Angle  = arctan( cos( Hip Pitch Angle )  tan( Minor Plan Angle )) 

Major Pitch Jack Rafter Side Cut = acos( sin( Major Plan Angle )  cos( Major Pitch Hip Backing Angle ))
Minor Pitch Jack Rafter Side Cut = acos( sin( Minor Plan Angle )  cos( Minor Pitch Hip Backing Angle )) 

Major Pitch Sheathing Angle = acos( cos( Major Plan Angle ) * cos( Hip Pitch Angle )) 
Minor Pitch Sheathing Angle = acos( cos( Minor Plan Angle ) * cos( Hip Pitch Angle )) 

Major Pitch Sheathing Cut Measurement =  Plywood Width  tan( Major Pitch Sheathing Angle)
Minor Pitch Sheathing Cut Measurement =  Plywood Width  tan( Minor Pitch Sheathing Angle )

Major Pitch Jack Difference =  tan( Major Pitch Sheathing Angle ) * Jack Rafter Spacing
Minor Pitch Jack Difference =  tan( Minor Pitch Sheathing Angle ) * Jack Rafter Spacing

Major Plan Angle Frieze Block Saw Miter Angle  = arctan( sin ( Major Rafter Pitch Angle )  tan( Major Plan Angle )) 
Major Plan Angle Frieze Block Saw Blade Bevel Angle   = arctan( sin( Major Plan Angle Frieze Block Saw Miter Angle )  tan( Major Rafter Pitch Angle )) 

Minor Plan Angle Frieze Block Saw Miter Angle  = arctan( sin(Minor Rafter Pitch Angle )  tan( Minor Plan Angle )) 
Minor Plan Angle Frieze Block Saw Blade Bevel Angle   = arctan( sin( Minor Plan Angle Frieze Block Saw Miter Angle )  tan( Minor Rafter Pitch Angle )) 

Major Common Rafter Rise = Major Run * tan( Major Pitch Angle )
Major Common Rafter Length = Major Run  cos( Major Pitch Angle )
Major Common JackRafter Run = Jack Rafter Spacing * tan( Major Plan Angle )
Major Common JackRafter Length = Major Common JackRafter Runn  cos( Major Pitch Angle )

Minor Common Rafter Rise = Minor Run * tan( Minor Pitch Angle )
Minor Common Rafter Length = Minor Run  cos( Minor Pitch Angle )
Minor Common JackRafter Run = Jack Rafter Spacing * tan( Minor Plan Angle )
Minor Common JackRafter Length = Minor Common JackRafter Run  cos( Minor Pitch Angle )

Hip Rafter Run = Major Run  cos( Major Plan Angle )
Hip Rafter Length = Hip Rafter Run  cos( Hip Pitch Angle )

Example Irregular Hips Geometry DXF Drawing
Irregular hips Geometry
Example Irregular Hips Geometry Dimensions DXF Drawing
Irregular hips Geometry
Example Irregular Hips Geometry Major Plan Angle, Minor Plan Angle, Hip Backing Angle, Sheathing Cut Angle and Jack Rafter Cheek Cut Angle DXF Drawing
Irregular hips Geometry
Example Irregular Hips Geometry Find Jack Rafter Length Difference Drawing
Irregular hips Geometry


Pitch Common Unit Runs at 12'' Rise
Pitch Common Unit Lengths at 12'' Rise

1/12 Pitch Common Unit Run = 144.00000
1/12 Pitch Common Unit Length = 144.49913
2/12 Pitch Common Unit Run = 72.00000
2/12 Pitch Common Unit Length = 72.99315
3/12 Pitch Common Unit Run = 48.00000
3/12 Pitch Common Unit Length = 49.47727
4/12 Pitch Common Unit Run = 36.00000
4/12 Pitch Common Unit Length = 37.94733
5/12 Pitch Common Unit Run = 28.80000
5/12 Pitch Common Unit Length = 31.20000
6/12 Pitch Common Unit Run = 24.00000
6/12 Pitch Common Unit Length = 26.83282
7/12 Pitch Common Unit Run = 20.57143
7/12 Pitch Common Unit Length = 23.81562
8/12 Pitch Common Unit Run = 18.00000
8/12 Pitch Common Unit Length = 21.63331
9/12 Pitch Common Unit Run = 16.00000
9/12 Pitch Common Unit Length = 20.00000
10/12 Pitch Common Unit Run = 14.40000
10/12 Pitch Common Unit Length = 18.74460
11/12 Pitch Common Unit Run = 13.09091
11/12 Pitch Common Unit Length = 17.75871
12/12 Pitch Common Unit Run = 12.00000
12/12 Pitch Common Unit Length = 16.97056
13/12 Pitch Common Unit Run = 11.07692
13/12 Pitch Common Unit Length = 16.33090
14/12 Pitch Common Unit Run = 10.28571
14/12 Pitch Common Unit Length = 15.80493
15/12 Pitch Common Unit Run = 9.60000
15/12 Pitch Common Unit Length = 15.36750
16/12 Pitch Common Unit Run = 9.00000
16/12 Pitch Common Unit Length = 15.00000
17/12 Pitch Common Unit Run = 8.47059
17/12 Pitch Common Unit Length = 14.68846
18/12 Pitch Common Unit Run = 8.00000
18/12 Pitch Common Unit Length = 14.42221
19/12 Pitch Common Unit Run = 7.57895
19/12 Pitch Common Unit Length = 14.19297
20/12 Pitch Common Unit Run = 7.20000
20/12 Pitch Common Unit Length = 13.99428
21/12 Pitch Common Unit Run = 6.85714
21/12 Pitch Common Unit Length = 13.82101
22/12 Pitch Common Unit Run = 6.54545
22/12 Pitch Common Unit Length = 13.66905
23/12 Pitch Common Unit Run = 6.26087
23/12 Pitch Common Unit Length = 13.53508
24/12 Pitch Common Unit Run = 6.00000
24/12 Pitch Common Unit Length = 13.41641

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SBE Builders
SBE Builders
5305 Laguna Ct.
Discovery Bay, California 94505
(925) 634-6022 • Fax: (925) 634-6022
Commercial & Residential Framing Contractor
American Carpenter and Builder
California Licensed General Building Contractor
CA LIC.#  546126


Roof Framing Geometry

  • Roof framing geometry is empirical-type knowledge.
  • Information gained by means of observation, experience, or experiment.
  • From ground Line 0: Z1, Z2, Z3 etc...
  • To Roof Axis 0: A1, A2, A3 etc...
  • To the bring back line 0 for scribing: B1, B2, B3 etc...

Roof Framing Geometry Blog

Rafter Tools for Android
With Quad Tetrahedra Analytic Algorithm Technology.
Helping apprentice carpenters on their journey to becoming master carpenters with Certification in roof framing.

Rafter Tools+ for iPhone

Rafter Tools+ is a rafter calculator for complex roof framing angles that other roof framing calculators don't offer.

RafterTools+

Stair Tangent for iPhone

This iPhone app is for rough frame carpenters that don't build stairs everyday, but could use an stair app calculator to check their stair building calculations. Build a set of stairs that you are gonna be proud of. With Stair Tangent you can elimenate cumulative math errors when building - constructing stairs.

Stair Tangent
stairtangent.com

Crown Molding Tools
crownmoldingtools.com

Crown Molding Tools  

Carpenters Of Steel

Canadian & American Geometric Roof Framing Development
using a Steel Framing Square

Geometric Roof Framing Development for Irregular Hip Roof Calculations
using a Steel Framing Square

Geometric Development of Tetrahedron
using a Steel Framing Square

Hip Rafter Backing Bevel Angles from 1565 to 2013

Applied Geometry and Euclidean GeometryA lesson in Applied Geometry and Euclidean Geometry

This Is Carpentry

We're a member of the Timber Framers Guild

Timber Framers Guild

American College of the Building Arts, carpentry and timber framing programs.

American College of the Building Arts

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