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


  
  
SBE Builders
SBE Builders


Holy Grail of Roof Framing Geometry & Trigonometry

Book I & Book II. These roof framing books were written to make complex roof framing simple..

The Art of the Line for Carpentry

The book includes step by step instructions on developing stereotomic drawings on Art du Trait de Charpente, Trestles, Tréteau à devers, Canted Trestles, Louis Mozerolles' Joiners Table, Sawhorses, and the Saint Andrews' Cross, twisted crosses. You'll also find theories on hip rafter shift-offset, standard roof framing kernel trait drawings, German Schiften DP-Shadow Line techniques, folding net roof surface and net plane geometric development, when hip rafters collide, the Warlock Cut, and developing upper and lower claws on rafters using Axioms.

HG IV Circular Work in Carpentry

The book includes step-by-step instructions on developing stereotomic double curvature drawings for circular work in carpentry. Some of the techniques presented in this book are thousands of years in the making. As carpenters, we shouldn't have to re-invent the wheel each time we are faced with new challenges. There is a likely hood that someone, that came before us, has already refined a technique that we can use today. The tools might have changed, but the piece of wood that it is twisting and turning remains the same piece of wood.

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  

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