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.

Polygon Roof Framing Developmental Geometry
Rafter Pitch Or Rafter Pitch Angle Polygon Number of Sides Radius of Polygon or Enter Common Rafter Run of Polygon
Download Polygon Geometry DXF
Polygon Geometry.dxf -- auto generated DXF CAD file of polygon geometry drawing each time script is run


Construction of Backing Angle for Octagon by Joe Bartok
Developmental Geometry for Polygon Roof Framing

S   is the length of any side of the polygon
N   is the number of sides
R   is the Radius of the circumscribed circle
apothem  is the Radius of the inscribed circle
pi is PI, approximately 3.14159

central angle = 360  N
working angle = 360  (N  2)
plan angle = (180 - central angle)  2
apothem multiplier = secant(360  ( N  2 ))
side wall multiplier = tan((360  (N  2 ))  2
projection angle a = 360  N
projection angle b = 90 - projection angle a 
miter angle = 12.0 * tan( working angle)
hip run per foot = 12.0  / cos( working angle)
adjacent run = 12 * tan(working angle)
unit rise = 12 * tan(pitch angle)
CMC irregular pitch angle = arctan( unit rise  adjacent)

working angle multipler  = tan(360  (N  2)) 2
rafter multipler = 1  cos pitch angle
hip multipler = 1  cos hip angle
rise multipler = 1  tan pitch angle

inscribed radius = apothem
inscribed radius = S / (2 * tan(360  N))
inscribed radius = R * cos(360  N)

Common Rafter Run = apothem
Hip Rafter Run = Radius
Hip Rafter Run = Common Rafter Run  apothem multipler
Common Rafter Run = S  working angle multipler
S = Common Rafter Run  working angle multipler
Common Rafter Length = Common Rafter Run  rafter multipler
Hip Rafter Length = Hip Rafter Run  hip multipler
Common Rafter Rise = Common Rafter Run  rise multipler

Common Rafter Span =  Common Rafter Run  2
Common Rafter Length = Common Rafter Run  cos(Pitch Angle)
Common Rafter Rise = Common Rafter Run  tan(Pitch Angle)

Hip Rafter Angle = arctan(Common Rafter Rise  Hip Rafter Run)
Hip Rafter Length = Hip Rafter Run  cos(Hip Rafter Pitch)
                      
The cotangent cot(x) is the multiplicative inverse of tan(x), 1/tan(x).
The cosecant csc(x) is the multiplicative inverse of sin(x),... 1/sin(x).
The secant sec(x) is the multiplicative inverse of cos(x), ... 1/cos(x).


polygonal hip roof developmental geometry
Draw lines in this order for polygonal hip roof developmental geometry
Line C-N = Polygon Side Wall Length
Line A-B = Common Rafter Run 90 to C-N
Line A-E = Common Rafter Rise 90 to A-B
Line E-B = Common Rafter Length
Line A-C = Polygon Hip Rafter Run
Line A-F = Common Rafter Rise 90 to A-C
Line F-C = Polygon Hip Rafter Length
Line B-D = Common Rafter Length 90 to C-N
Line C-D = Polygon Hip Rafter Length
Line N-D = Polygon Hip Rafter Length
Line C-J = Polygon Hip Rafter Side Cut Rise 90 to A-C Intersects Line B-D
Line H-C = Polygon Hip Rafter Side Cut Rise 90 to F-C
Line F-H = Hip Side Cut Angle Line At Ridge

Line A-G = Hip Backing Rise 90 to F-C Also Altitude Of Hip Length Line F-C  (Backing Angle Rise)
Line A-K = Hip Backing Rise At Same Angle As Plan Angle (Backing Angle Rise)
Line A-M = 90 to K-A And Intersects Eave Line N-M (Backing Angle Run)
Line K-M = Intersects Eave Line N-M


Line F-A  Line C-A = Hip Pitch Angle
Line A-B  Line C-B = Plan Angle
Line C-B  Line A-B = Polygon Working Angle
Line B-D  Line C-B = Sheathing Angle
Line D-B  Line C-B = Jack Rafter Side Cut Angle
Line C-B  Line D-B = Jack Rafter Side Cut Angle on Face Of The Plumb Cut
Line K-A  Line M-A = Hip Backing Angle
Line H-C  Line C-F = Hip Side Cut Angle At Ridge

RFI | structural | framing | online tools | company | site map
safety | building resource links | build it green | photo gallery | Octagon | crown molding angles | home
WindsorOne Protected Trim
  
  

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

Website Usage Legal Policy