How to Calculate the Radius of a Long Steel Section Curved Less Than 180 Degrees

The definition of a radius of a circle is the length of a line from the center of a circle to its perimeter.  When measuring a curved steel section (e.g. a curved steel angle, beam, bar, channel, etc.), you can measure from the inside of the curved steel section or from the outside to yield the inside or outside radius respectively.  When the curved steel section has 180 degrees or more of arc, you can simply measure the diameter and divide by 2 to obtain the radius.  But what if we have less than 180 degrees of arc?  How do we measure the radius of a long steel section then?

Here’s how:

Tools needed:
One string
Two magnets
One measuring tape

Step One:
Create a chord:
A chord is a straight line connecting two points on a curve.  Take a magnet and secure a string at one end of the curved steel section, and then use the other magnet to secure the sting taut at the other end of the steel section.  Using a measuring tape, measure the distance between the two end points of the string.  This measurement will be the chord length.  The longer the chord you create, the better your radius calculations will turn out.

Step Two:
Create a midpoint:
The midpoint is the middle point of a line segment.  To find the midpoint on your string simply take the number in step one (the chord measurement) and divide this number by two.  You will then have the midpoint of the chord.

Step Three:
Create a rise:
Measure the distance 90 degrees off the midpoint of the chord to the curved steel section.  This is called the “mid-ordinate rise” or simply the “rise.”  The more accurate you are in creating this right angle with your measuring tape and string, the more accurate your radius calculations will be.

To calculate the radius of the curved surface, we will use a math formula along with the chord you found in step one and the rise you found in step three.  Radius = 1/2 (rise2 + 1/4 chord2) / rise.[maxbutton id=”4″]


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