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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics

Let us now compute the MMOI contribution of all the elements about their own axis as shown in
[Fig 2.45].

[Fig 2.45: inertia of element about its own axis]

The contribution of a single element is computed as follows:

H
H
2
2
2 y 3
I

element = L ∗ dy ∗ dz ∗ ρ ∗ y = L ∗ dz ∗ ρ 3 H - - - - (2.40)
− −
2
H
2
Simplifying equation (2.40), we get:
H
y 3 L ∗ dz ∗ ρ H 3
2
L ∗ dz ∗ ρ =
3 H 12
−
2
Integrating the single element’s contribution across the width (W), as shown in [Fig 2.46], we get
the total MMOI contribution of all the elements about their own axis.

[Fig 2.46: MMOI contribution of elements across the width (W)]

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