GATE ME 2016 Set 1 — Question 43
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Engineering Mechanics → Beams & Columns → Bending & Shear Stresses
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Question
The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in ) of this cross-section about its base is ____________
Correct answer
1873 to 1879
Solution
The area moment of inertia about the base () is calculated by subtracting the moment of inertia of the cutouts from the moment of inertia of the full square.
Using the parallel axis theorem for the circle:
The value is approximately .
1.Moment of inertia of the square () about its base:
2.Moment of inertia of the two semi-circular cutouts:
The two semi-circles of radius are equivalent to one full circle of radius centered at a height from the base.Using the parallel axis theorem for the circle:
3.Net Moment of Inertia:
The value is approximately .
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