Radius of Circle from Secant Line

[KGordon899]

Not a home work question but rather a "real world" math problem. I am a construction superintendent and I need to determine a common radius of 3 separate as-built radii. I have a set of 2 story steps that I need to have wood paneling that is continuous from the lower level through the upper level. There are 3 different as build radii, Lower level stairs, ground floor slab radius and upper level stairs. On each of the set of stairs I set up a secant line (string line) from the upper tread and lower tread of each set of stairs and measured distance between each rise of the stair and the distance back to the secant line following the angle of the stair tread. For the ground floor slab I have measured distance from the tread above (thought was once stair above radius was determined the difference between the two would determine my ground floor slab radius). Can the radius of each as-built condition be determined from the dimension provided? See attachment for all dimensions of as-built conditions on details 1, 2, & 3

 

[blamocur]

Am I the only one who can't understand the question? I am not good at reading architectural drawings, no do I know what are "as-build radii"

 

[KGordon899]

Am I the only one who can't understand the question? I am not good at reading architectural drawings, no do I know what are "as-build radii"

sorry if I didn't frame the question correctly. And as built is just the term used of actual built condition that my vary from the design drawings. For example drawings attached show design radius of 22'-1" to face of wall + 3'-6" tread width making the design radius of 25'-7". However I need to determine what the actual installed radius of the stairs are, so I can determine at what radius the the wood panels need to be built at that will allow me to meet all radius. measuring the radius back to the center of circle is no longer an option because material has been installed which obstructs me from doing so.

basically, I just was asking if the radius can be determined based off the dimensions shown in red and blue on details 1 & 3.

any help is appreciated.

 

[Deleted member 4993]

sorry if I didn't frame the question correctly. And as built is just the term used of actual built condition that my vary from the design drawings. For example drawings attached show design radius of 22'-1" to face of wall + 3'-6" tread width making the design radius of 25'-7". However I need to determine what the actual installed radius of the stairs are, so I can determine at what radius the the wood panels need to be built at that will allow me to meet all radius. measuring the radius back to the center of circle is no longer an option because material has been installed which obstructs me from doing so.

basically, I just was asking if the radius can be determined based off the dimensions shown in red and blue on details 1 & 3.

any help is appreciated.

Staircases are in general "helical screw". I would strongly suggest consulting "face-to-face" with an engineer or professor at the nearest university. There would be many more questions - a face-to-face consultation will save you time and wasted-effort and wasted-material.

 

[Dr.Peterson]

basically, I just was asking if the radius can be determined based off the dimensions shown in red and blue on details 1 & 3.

any help is appreciated.

With so much data, it's more likely that you'll find that it isn't a perfect circle in the first place! You probably won't be able to calculate one exact radius. So any calculation you do will be only an approximation.

The fact that the distances are measured in different directions (relative to the unknown center of arc!) makes the data particularly awkward to use.

I'm assuming you are talking about the radius of the actual horizontal circle on the plan, not of individual arcs along the helix in three dimensions.

There are ways to get an approximate radius, assuming it really is circular; for example given a chord (the horizontal projection of your secant line) and sagitta (the distance of the wall at its center), you can find the radius:

Sagitta (geometry) - Wikipedia

en.wikipedia.org