Radius of curvature of a function

[rock.freak667]

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.

Homework Equations

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.

 

[Dick]

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

 

[rock.freak667]

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]

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.

 

[rock.freak667]

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.