# Radius of curvature of a function

Homework Helper

## Homework Statement

I have a graph of y=lg(x) which is supposed to mimic the curvature of a beam, or I can use y =√x to be more precise. But in essence between two points x2 and x1, I need to find the radius of curvature R so as to find the bending stress on it.

## The Attempt at a Solution

I don't know if it is as simple as taking the arc length and dividing by π or something. Any help would be fine.

Or could I use

E/R = σ/y

and use σ as the yield stress and get R from there, though that is assuming that it is a straight beam.

## Answers and Replies

Homework Helper
You are making this too complicated. If you have y=f(x) there's a reasonably simple formula for radius of curvature. See formula 5 in http://mathworld.wolfram.com/RadiusofCurvature.html

:rofl: oh my, I've seen that equation all my life and I've been using it to find radius, add in the word curvature and I complicate life. Thanks for lessening my work load!

Would it be best to use the average of x1 and x2 and get the curvature then?

Dick
Science Advisor
Homework Helper
Not sure. I don't know the engineering problem. Do you want an average between x1 and x2, or a max between x1 and x2 or something else? What's best depends on the problem.

Homework Helper
Not sure. I don't know the engineering problem. Do you want an average between x1 and x2, or a max between x1 and x2 or something else? What's best depends on the problem.

If I could I'd like to get an average estimate for the entire length from x=1 to some x=x2

EDIT: nvm, I am analyzing the beam at different sections, so those are at certain x points, so I can just reuse the formula throughout. Thank you again.