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A Beam of rectangular cross section 200mm deep and 100mm wide

  1. May 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Please visit my flickr link for a scanned image of the problem statement.

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


    2. Relevant equations

    M/I = σ/y = E/R This is the flexure or bending formula.

    3. The attempt at a solution


    a) = 8.333 kN
    b) = 12.5 kN
    c) = I can do this one

    d)

    This one is giving me some difficulty. If I increase the 200mm dimension by 20% the stress value goes down 8680 Newtons. I have played around with the other dimension but this could be a laborious process. Could someone please explain to me how I would go about this. Is there some sort of optimal ratio here. Can I use calculus and if so just how do i go about it? Much appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 24, 2013 #2

    haruspex

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    Yes, you'll need calculus. It seems intuitive to use as much cross-sectional area as allowed, but we need not assume that. I would approach it as supposing the area is fixed as A and optimising the ratio for that area. Having found that relationship, you can go about optimising the area.
     
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