Question

The area moment of inertia of shaded area about horizontal centroidal x axis in mm4
is
20 mm
40 mm 40 mm + 40 mm
k
Answer:​

Answer 1

Answer:

The area moment of inertia of shaded area about horizontal centroidal x axis is 106.66mm

Explanation:

The moment of inertia of a rectangular section about an horizontal axis through C.G is

bd3/12.

Here breadth b=20mm

depth D=40 mm

The moment of inertia of a rectangular section about an horizontal axis through C.G is

$\frac{b {d}^{3} }{12}$

$\frac{20 \times {40}^{3} }{12}$

106.66mm

The area moment of inertia of shaded area about horizontal centroidal x axis is 106.66mm

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Answer 2

Answer:

$1,06,666.67 \mathrm{~mm}^{4}$

Explanation:

A rectangle with dimensions of b and d has the following moment of inertia (MOI) about each of its centroidal axes:

$\mathbf{I}_{\mathbf{x x}}=\frac{\mathbf{b d}^{3}}{12}$ and $\mathbf{I}_{\mathbf{y y}}=\frac{\mathbf{d b}^{3}}{12}$, where$\mathrm{b}=$width and $\mathrm{d}=$ depth of the section

Given data,

$b=20 \mathrm{~mm}, \mathrm{~d}=40 \mathrm{~mm}$

Now, we are aware that MOI around the $\mathrm{X}$-axis, which is a centroidal axis parallel to the breadth, is provided by

$\mathbf{I}_{\mathrm{xx}}=\frac{\mathrm{bd}^{3}}{12}=\frac{20 \times 40^{3}}{12}$

$\therefore \mathrm{I}_{\mathrm{xx}}=1,06,666.67 \mathrm{~mm}^{4}$

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