What is the correct method to determine the moment of inertia of a symmetrical Tsection about its centroidal axis?
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A.
Consider only the moment of inertia of the flange, as it dominates the shape
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B.
Assume it behaves as a solid rectangular section of the same overall dimensions
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C.
Use the perpendicular axis theorem directly
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D.
Use the parallel axis theorem to sum the moments of inertia of the flange and web
Correct Answer:
D. Use the parallel axis theorem to sum the moments of inertia of the flange and web
Explanation:
The correct answer is Use the parallel axis theorem to sum the moments of inertia of the flange and web.
To find the moment of inertia for a symmetrical T-section, the shape is divided into two simpler parts: the flange and the web. Since the individual centroidal axes of these components do not coincide with the overall centroidal axis of the T-section, the parallel axis theorem must be applied. This theorem allows you to calculate the moment of inertia for each part relative to the section's central axis by adding the product of the component's area and the square of the distance from its own axis to the main axis. Finally, the total moment of inertia is obtained by summing the results for both the flange and the web.
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