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

Let us begin with the computation of I .
xx

2
The MMOI contribution of (I element ) about the ‘x-axis’ is given by: L ∗ H ∗ dz ∗ ρ ∗ z , as shown
in [Fig 2.44].

[Fig 2.44: inertia of element about the 'x-axis' through the CG]

Now summing up the contribution of all the sections along the ‘z-axis’ we get:

W
2
2 3 2
I

xx,elem = L ∗ H ∗ dz ∗ ρ ∗ z = L ∗ H ∗ ρ - - - - (2.38)
3
− W −
2
2
Simplifying equation (2.38), we get:
W

z 3 2 W 3 W 3 W 3
L ∗ H ∗ ρ = L ∗ H ∗ ρ + = L ∗ H ∗ ρ
3 W 24 24 12
−
2
W 2 mW 2
= L ∗ H ∗ ρ ∗ W = - - - - (2.39)
12 12

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