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Moment of Inertia: Non Uniform Rod

  1. Nov 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello,

    I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1.

    Known variables: L, D, P, t
    Dependent variables: T2, L2
    Design variables: T1, L1

    rod.PNG

    2. Relevant equations
    L2 = L - L1
    T2 = T1 - t

    Standard Moment of Inertia: I = π/4 * (Ro^4 - Ri^4)
    I am looking to modify the above equation to be include 2 sections of variable thickness

    3. The attempt at a solution
    I1 = π/64 * (D^4 - (D - T1)^4)
    I = I1 * (1 - L1/L)^4

    The above solution is valid for a linearly tapered beam, not a beam with 2 discrete sections. I have not been able to find any derived moments of inertia for the above shape. Any help would be greatly appreciated!
     
  2. jcsd
  3. Nov 28, 2016 #2

    haruspex

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    Moments of Inertia are additive. Just break it up into pieces of convenient shape, find the MoI of each (about the same axis) and add them up.
     
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