Question

Calculate area moment of inertia for a circular cross-section with 3 mm diameter:

28 mm4


254 mm4


7 mm4


4 mm4


81 mm4



Calculate the minimum area moment of inertia for a rectangular cross-section with side lengths 6 cm and 4 cm.


52 cm4


72 cm4


32 cm4


24 cm4


2 cm4

Answer 1

Part 1

4 mm⁴

Part 2

32 cm³

Step-by-step explanation:

Part 1

The diameter of the circular cross section, d = 3 mm

The area moment of inertia of a circle,
`I_C`, is given as follows;

`I_x = I_y = (\pi \cdot d^4 )/(64)`

Where;

d = The diameter of the circle

Therefore, the area moment of inertia of the given circular cross section, with d = 3 mm, is found as follows;

`I_x = I_y = (\pi * (3 \, mm)^4 )/(64) \approx 4 \, mm^4`

Part 2

The minimum area moment of inertia for a rectangular cross-section is given as follows;

`I_x = (1)/(12) \cdot b \cdot h^3`

`I_y = (1)/(12) \cdot h \cdot b^3`

The minimum moment of inertia, for the rectangular cross-section is given by placing, the height, h = The short side length and calculating for, Iₓ, and vice versa

Therefore, for the question, where, h = 4 cm, and b = 6 cm, we have;

`I_x = (1)/(12) * 6 \, cm * (4 \, cm)^3 = 32 \, cm^4`