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Homework Help: Radius of curvature of a function

  1. Apr 6, 2010 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations



    3. 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.
     
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  3. Apr 6, 2010 #2

    Dick

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  4. Apr 6, 2010 #3

    rock.freak667

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    :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?
     
  5. Apr 6, 2010 #4

    Dick

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    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.
     
  6. Apr 6, 2010 #5

    rock.freak667

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    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.
     
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