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Moment of inertia for T shaped object

  1. Dec 26, 2009 #1
    h have a T shaped object (2-d) for which i need to find the moment of enertia,
    i used a parallel axis theorem, then to check myself i found i site which had a direct equation for it
    http://www.efunda.com/designstandards/beams/SquareTbeam.cfm

    what i did

    b1=100mm
    h1=12mm
    b2=12mm
    h2=75mm
    q=12.643mm(the distance from the joint of the 2 shapes to the centroid of the T)

    >> ((b1*h1^3)/12)+((b1*h1)*(q+h1/2)^2)+((b2*h2^3)/12)+((b2*h2)*(h2/2-q)^2)

    1.4094e-006 m4

    using their equation

    t=12mm
    y=75-12.643=62.357mm
    b=100mm
    s=12mm
    d=87mm

    >> (t*y^3+b*(d-y)^3-(b-t)*(d-y-s)^3)/3

    7.6247e-006m4


    where have i gone wrong here?
     
  2. jcsd
  3. Dec 26, 2009 #2

    PhanthomJay

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    I don't know what you may have done wrong, but did you calculate the centroid correctly? Once you have calculated the centroid of the T-shape using moment areas, the I of the T-shape, about the xx axis thru its centroid, is the sum of the I + Ad^2 of each rectangle, where d is the distance from the centroid of that rectangle to the centroid of the T shape. It's all number or letter variable crunching from there. I'd avoid the cookbook solution, as you lose track of how the equation is derived.
     
  4. Dec 26, 2009 #3
    the centroid is correct, using their"recipe" i got the same centroid, only i took the centroid from the joint of the 2 shapes and they took from the base of the T
     
  5. Dec 26, 2009 #4

    PhanthomJay

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    Ok, if you are sure of the centroid, calculate I, using I_T = sum of I + Ad^2. Don't forget that d is the distance from the centroid of each rectangle to the centroid of the T. Please show your calculation using numbers, and define h1, h2, etc., so we can check your math. Your equation appears correct, although i haven't checked the numbers yet.
     
  6. Dec 26, 2009 #5

    PhanthomJay

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    I checked your numbers and your result looks good. I didn't check the recipe nor the numbers you may have entered into it. Your way is better anyway. Toss out the cookbook!:mad:
     
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