Geometry question

How do you obtain a radius given only two points???

Had an engineer call wanting the raidus placement of some columns and I was
totally lost. We have a regtangular shaped building. At both ends there is a
circular beam (basicly an arc) overhead that is supported by two columns
placed at either side of the entry way. Our discussion was concerning the
foundation sheet but I had to go to the roof sheet, offset the beam by half
to place an arc dead center over the columns and get the radius of that.
This guy was obtaining a radius from the center point of the two columns
somehow.... can anyone explain or post an example of how to do this?

 

There are literally an infinite number of arcs that can pass through two
points; all will have radii greater than half the distance between the
points, but the value of the radius is, of course, indeterminate.

.... unless, of course there is some other constraint, such as the arc being
a semi-circle (180 deg.), or subtending some other known angle.
___

 

How about posting the dwg - really not sure, but think I know what you're
talking about. Need to look at the dwg.

 

Tried three time to unzip, but each time get message says "No files
found".

 

Well.....I am having difficulty understanding what you have posted, i.e.,

"At both ends there is a circular beam (basicly an arc) overhead that is supported by two columns
placed at either side of the entry way. Our discussion was concerning the foundation sheet but I
had to go to the roof sheet, offset the beam by half to place an arc dead center over the columns
and get the radius of that. This guy was obtaining a radius from the center point of the two
columns
somehow"

Some of the confusion is due to me because there is a difference between beams and columns. You say
"circular beam" - is that the arc over the entrance?
You say "two columns placed at either side of the entry way" - are those the partial arcs?

 

This is the foundation drawing (plan view), the beam is shown on the roof
framing sheet.
The (2) C2/C4 columns (grid line A2 and A3) support a circular shaped beam
overhead. The beam starts at the half circle shaped bump out (green- layer
is S-COL-CONC-BELOW) and you see two yellow dots [vert. rebar], runs over
the two columns and back to the wall again. Given the center points of the
two 4x4 TS columns, can you obtain a radius value?

 

Let me look at it again now that I have a better guide.

 

Let me know if what I sent is right.

 

Excellent, center point for the start and end are obvious enough, but how
did you obtain the third point for the arc?

 

Looks like a 3P circle drawn through 3 of the centers... and then trimmed.

 

Two points define a line in space. If you want to define an explicit
radius, you must have three minimum.

If you only have two points, then a design assumption must be made. I think
in your case, you would offset an existing arc (or radius) the distance from
the existing radius center line to the new radius center line. Thus ending
with a new radius with a radius larger by the offset amount (this assumes
the two points are not on the same arc center line of the existing arc.

Stephen R.

 

Awww...light comes on....Excellent. Thanks Tracy and Walt.

 

No, not a three point circle - a three point ARC, starting with center of
either half-circle, second point mid-point of line (you drew) through 4x4TS
and third point center of other half-circle.

 

I don't know if this will help.

1.) draw a line (chord=C) between the two points.
2.) draw a line (middle ordinate=M) form the mid point of the chord,
perpendicular to the chord to the arc.
3.) radius=(C squared/8M) + (M/2)
JoeB