Equivalent Radius of Helical Handrail

[PEStructural]

Does anyone know an equation that calculates the equivalent radius for a helical handrail on a set of curved stairs?

 

[ornerynorsk]

Lay it out as a flat arc segment, you should be able to trig it out from there.

 

[Kapitan]

Does Equivalent Radius mean Radius of Curvature at any point ?

If so, then the equation for Curvature K = r / (r^2 + c^2) can be used, where r is the radius of the cylinder that the helix lays on and c is the pitch. As Curvature is 1/R then the Radius of Curvature,

Rc = ( r^2 + c^2 ) / r

As the handrail is a space curve the Radius is rolling over as it moves along the helix, and as the pitch and cylinder radius are fixed the Torsion of the curve is constant.

Development of the helix is a right angled triangle where the hypotenuse is the true length of the curve, the other two sides being Pi*D and Pitch respectively, or multiples of according to the number of helical turns.

 

[Techne]

I have also used 1/r = 4Pi^2R/[H^2+(2PiR)^2]
where:
1/r = curvature of the helix
r = ideal inner radius of annular strip
R = radius of cylinder
H = height of one turn of the helix (2Pi radians)

Would this also give you the equivelent radius?


Referenced:

http://www.math.cornell.edu/~dwh/papers/EB-DG/EB-DG-web.htm