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Tough Civil Eng. Problem

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data

    When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 12 MPa, determine the optimal geometry of the column 100m tall made of concrete to support a mass of 1000 tonnes at its top (like the CN tower).


    2. Relevant equations

    Weight concrete: 24Kn/m^3
    Stiffness: 30000MPa
    Cost: $0.05/kg

    3. The attempt at a solution

    well I guess I can find the total force = 1000(#tonnes) x 9.81.

    Also Stress = Force/Area and from that I can find the radius/diameter of the cylinder.

    But the cylinder is suppose to be sort of "cone" shaped I think for optimal geometry (like the CN Tower)

    Also, would there have to be a function to find the minimum cost and volume of building this structure?

    Thanks
     
  2. jcsd
  3. Oct 6, 2009 #2
    I can't say much, but as for the minimum cost, you might want to try some linear programming given your constraints
     
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