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Have i got the right Units

  1. Sep 30, 2015 #1
    1. The problem statement, all variables and given/known data
    This is the problem I am working through. I am up to (b). I am struggling with the units.

    https://www.flickr.com/photos/93763273@N05/8815418518/lightbox/

    My question is, why is the final answer in N/m^2? and why does the workbooks list stress in the units of N/m^-2

    the beam is 100mm wide and 200mm deep

    2. Relevant equations
    m/I=σ/y

    σ=(my)/I

    I = (bd^3)/12

    3. The attempt at a solution

    I have drawn out the bending moment diagram, and calculated a max bending moment to be m = 8.333kN. This is the same as other people attempting this question are getting. So I am happy with that.
    y = 100mm or 0.1m

    I = (0.1x0.2^3)/12 = 6.66667x10^-5m^4

    so, σ=(my)/I

    σ=(8333 x 0.1) / 6.66667x10^-5
    σ=12499499.94 N/m^2 or 12.5x10^6N/m^2
    or
    σ= 12.5 MN/m^2 or 12.5 N/mm^2

    Thanks,
    Craig
     
  2. jcsd
  3. Sep 30, 2015 #2

    SteamKing

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    Are you sure the workbook isn't using units of Nm-2 for stress? {No slash}
     
  4. Sep 30, 2015 #3
    Argh, yeah they are, so my answer shouldn't have a slash either? the units are MNm-2

    So ignoring the slash in my question, can you explain the units to me and what is the -2?

    Kr
    Craig
     
  5. Sep 30, 2015 #4

    SteamKing

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    Remember the Laws of Exponents? How 1/x2 = x-2 ?
     
  6. Sep 30, 2015 #5
    umm you have confused me a little more now, Stress is force per unit area, so should the answer as I have written it be MN/m2?

    Argh, think I have it!
    a/b2 is the same as ab-2

    so my answer is 12.5MN/m2 or 12.5MN m-2
     
  7. Sep 30, 2015 #6
    haha was typing out my reply at the same time! thanks SteamKing for pointing me in the right direction!
     
  8. Sep 30, 2015 #7

    SteamKing

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    Or 12.5 MPa
     
  9. Sep 30, 2015 #8
    Just on this subject, if in σ=(my)/I we got (Newtons x Metres)/Metres4, then why do we end up with Newton/Metres2??
     
  10. Sep 30, 2015 #9
    think I got it now, we actually have ((N x m) x m) / m4

    so using
    an/am=an-m

    so it comes down to Nm2/m4 = N (m2/m4) = N/m2
     
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