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Question

The mass density of the material of a T joint is 2 kg/m. The dimensions of this joint are shown in the figure.


What is the approximate moment of inertia (MI) of the T joint about an axis passing through their common joining point and perpendicular to the plane of structure?

A
120 kg-m2
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B
240 kg-m2
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C
362 kg-m2
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D
426 kg.m2
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Solution

The correct option is C 362 kg-m2
The mass density of the material of the T joint,
λ=2 kg/m
Length of section AB:
LAB=5 m
Mass of section AB
mAB=λ×LAB=2×5=10 kg

Similarly, LCD=8 m
mCD=λ×LCD=2×8=16 kg
For section AB the axis YY is analogous to axis passing through mid point of a rod.
MI of section AB about the axis,
MIAB=mAB×L2AB12
MIAB=10×5212=10×2512=1256 kg-m2

The axis YY is analogous to the axis passing through one end of a rod.
MICD=mCD×L2CD3=16×823

MICD=10243 kg-m2

Net MI of T joint is:
MINet=MIAB+MICD
MINet=1256+10243362 kg-m2

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