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Homework Help: Moment of Inertia: Non Uniform Rod

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

    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


    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


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    Science Advisor
    Homework Helper
    Gold Member

    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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