Question
Download Solution PDFWhich of the following expressions is correct to compute the moment of inertia (Iyy) of a hollow section shown in the figure?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 |
\(I = \frac{{B{h^3}}}{{36}}\) |
\({Y_{max}} = \frac{{2H}}{3}\) |
\(Z = \frac{{B{H^3}}}{{24}}\) |
Last updated on May 28, 2025
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