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Opposing Moments on Levered Beam

  1. Mar 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the force F1 to bend the beam AB to a radius of 7.5m. Assume the beam is a steel tube 200mm OD with wall thickness 20mm. The arm's AC and BD can be assumed rigid.

    The force F1 acts on pivots at C and D and is always in the x direction.

    2. Relevant equations

    I = pi (do4 - di4) / 64



    3. The attempt at a solution

    My first thought was to assume the beam was fixed at one end and then work out the deflection required to achieve a a radius of 7.5m. From this I substituted into the deflection formula to work out a point load need on the end of the cantilevered beam to produce the deflection.

    I think i should be calculating the moment at point C and D but I'm struggling a bit, any help would be greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Mar 22, 2012 #2

    rock.freak667

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    Homework Helper

    Why not just use

    M/I = σ/y = E/R

    E is given for the material and you know R. Just get M.
     
  4. Mar 22, 2012 #3
    Thanks rock.freak667.

    i have since found this formula and came out with an answer of 1.25 x 10^6 N/m for the moment required.

    this is using a value of 4.637 x 10^-5 for the second moment of area and a young's modulus of 200GPa for the steel.

    As the arms at the end of the beam are 1.25m long then the required force at points C and D would be 9.9 x 10^5 N.

    This seem a little high?
     
  5. Mar 23, 2012 #4
    When I calculated the second moment of area I got 2.701*10^-5 m^4 based on this:
    [itex]I=\frac{\pi*\left[\left(200mm\right)^{4}-\left(200mm-20mm\right)^{4}\right]}{64}=2.701\times10^{-5}m^{4}[/itex]

    This would change your results a little bit. Solving out the ratio before of M/I = E/R gives:

    [itex]\frac{M}{I}=\frac{E}{R}[/itex]

    [itex]M=\frac{EI}{R}[/itex]

    [itex]M=1.441\times10^{5}N[/itex]

    I would definitely double check what I did. 32,394 pounds of force seems reasonable to me though.
     
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