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Math Help - Can anyone help with this problem on Force??

  1. #1
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    Can anyone help with this problem on Force??

    A circulur column has a diameter of 80mm outside edge and 60mm inside edge.
    Both ends are fixed with equal force being applied top and bottom.
    Young's Modulus E = 200GN m-2
    Yield Stress deltay = 140 MN m-2

    What is the minimum length of column at which buckling is likely to happen?
    If the column was this length what load would you expect failure to occur?
    If the column is half this length what load would you expect failure to occur?

    Really struggling with this one if anyone can help id really appreciate it
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Can anyone help with this problem on Force??

    Are you familiar with Euler's equations for column critical load?

     F_{crit} = \frac {\pi ^2 EI}{(KL)^2}

    where the factor K depends on how the column is secured. For a column with both ends fixes K = 0.5. You asked for the "minimum length" under which buckling is likely to happen - that's where the length is sufficient to makes this a "long" or "slender" column, which generally means L is ten times the diameter. To find the force that can cause buckling for that length use the Euler equation above - you have the value for E, and can calculate I from the dimensions you were given. The answer to the third question may seem evident from the fact that F is inversely proportional to L^2, so if you halve L the force F that causes buckling will go up by a factor of 4. However I think this is a trick question, because if the length is now only 5 times the diameter the failure mode will be crushing of the material, not buckling. So for this you already have the value for the maximum stress it can withstand, and you simply multiply that stress by the cross-sectional area of the column to get the force.
    Last edited by ebaines; October 3rd 2012 at 02:28 PM.
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  3. #3
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    Re: Can anyone help with this problem on Force??

    thanks ill try it again tonight when ive got kids in bed and let you know
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