Which of the following expressions is correct to compute the moment of inertia (Iyy) of a hollow section shown in the figure?
F2 Vinanti Engineering 17.08.23 D1

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DDA JE Civil 01 Apr 2023 Shift 1 Official Paper
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  1. \(\frac{\pi}{64}\)(D4 - d4)
  2. \(\frac{\pi}{8}\)(D4 - d4)
  3. \(\frac{\pi}{16}\)(D4 - d4)
  4. \(\frac{\pi}{32}\)(D4 - d4)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\pi}{64}\)(D4 - d4)
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Detailed Solution

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Concept:

Moment of inertia is the sum of the product of mass of each particle with the square of its distance from the axis of the rotation.

M.O.I for hollow circular cross-section 

\( = \frac{\pi }{{64}}\left( {D^4 - d^4} \right)\)

Where D = outer diameter of cross section

d = inner diameter of cross section

Additional Information

Formula of moment of inertia for various other figures is given below.

S.No.

Shape of cross-section

INA

Ymax

Z

1

Rectangle

\(I = \frac{{b{d^3}}}{{12}}\)

\({Y_{max}} = \frac{d}{2}\)

\(Z = \frac{{b{d^2}}}{6}\)

2

Circular

\(I = \frac{\pi }{{64}}{D^4}\)

\({Y_{max}} = \frac{d}{2}\)

\(Z = \frac{\pi }{{32}}{D^3}\)

3

Triangular

\(I = \frac{{B{h^3}}}{{36}}\)

\({Y_{max}} = \frac{{2H}}{3}\)

\(Z = \frac{{B{H^3}}}{{24}}\)

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