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Calculating theoretical principle second moments of an L shaped section

  1. Dec 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Hi, I'm trying to complete my laboratory write up over my christmas break, and I'm struggling to understand how to do part of it. I emailed the lab demonstrator on December 9th, and the head of labs on the 18th and I've had no reply off either, so I'd really appreciate it if you guys could try and help me!

    I need to calculate the theoretical value of the principle second moment of area for an L shaped section. Using a Mohr's circle apparently.

    Here is a scan of the lab sheet explaining what I need to do.. I just don't understand how:


    2. Relevant equations

    http://dl.dropbox.com/u/630750/Screen%20Shot%202011-12-23%20at%2010.08.40.png [Broken]

    3. The attempt at a solution

    If someone can try to explain what I'm supposed to do that would be so helpful! Thank you.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 23, 2011 #2

    vela

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    The lab sheet seems pretty straightforward:
    1. Calculate IA.
    2. Calculate IB.
    3. Calculate IAB{/sub].
      [*]Follow the instructions on how to construct Mohr's circle from those values.

    What part are you having trouble with and what specifically is the problem?
     
  4. Dec 23, 2011 #3


    Thanks for the reply, I just don't know how to calculate IA, IB or IAB.

    Is there a formula I should know?
     
  5. Dec 23, 2011 #4

    vela

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    Do you know how to calculate the moment of inertia about an axis?
     
  6. Dec 23, 2011 #5
    It isn't something I've done a considerable amount of work on, I'm used to using the formulas for common shapes such as beams & cylinders.

    But looking through my textbook I've found some examples.

    They demonstrate using Ix and Iy, but they're Ia and Ib in my problem I think.

    They split it up into sections and then sum them?

    using http://dl.dropbox.com/u/630750/Screen%20Shot%202011-12-23%20at%2014.00.29.png [Broken]

    If that's right, how do I get IAB from that? Average them? Or add them?

    Plus how do I convert these values from IA and IB to the proper Ix and Iy?

    Thanks for your help!
     
    Last edited by a moderator: May 5, 2017
  7. Dec 23, 2011 #6

    vela

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    Right. x, y and A, B are just labels for the axes.

    Yes, that's what you want to do to find IA and IB. The moments of inertia about the center of mass for common shapes are tabulated, so there's no need to derive them again. For an axis that doesn't pass through the center of mass, you use the parallel-axis theorem.

    By definition, you have
    $$I_{AB} = \int_A ab\ dA$$which for a rectangular section turns out to be ##I_{AB}=a_\mathrm{cm}b_\mathrm{cm}A##. So, again, calculate IAB for each piece and then sum them.

    (Sometimes, you'll see a negative sign in the definition. It shouldn't matter here though.)

    You use Mohr's circle.
     
    Last edited by a moderator: May 5, 2017
  8. Dec 23, 2011 #7

    Redbelly98

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    Moderator's note: thread moved to Engineering, Comp Sci, & Technology

    In the future, please post engineering homework in Engineering, Comp Sci, & Technology instead of Introductory Physics
     
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