Moment of Inertia of an I-Section
Mediummoment of inertiaparallel axis theoremcomposite sections
A symmetric I-section has two flanges each 100 mm wide 20 mm thick and a web 20 mm wide 160 mm tall, for an overall depth of 200 mm. The moment of inertia about the horizontal centroidal axis is most nearly:
- A6.96 × 10⁶ mm⁴
- B32.5 × 10⁶ mm⁴
- C39.4 × 10⁶ mm⁴
- D66.7 × 10⁶ mm⁴
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Answer: C. 39.4 × 10⁶ mm⁴
Because the section is symmetric, the centroid sits at mid-depth and the quickest route is subtraction: the I-section is a 100 × 200 rectangle with two 40 × 160 rectangles removed either side of the web. I = [100 × 200³ − 80 × 160³]/12 = (800.0 − 327.7) × 10⁶/12 = 39.4 × 10⁶ mm⁴. The parallel-axis route gives the same result: web 20 × 160³/12 = 6.83 × 10⁶, plus each flange 100 × 20³/12 + (2,000)(90)² = 16.27 × 10⁶, times two. Quoting 6.96 × 10⁶ is the classic error of adding the flanges' own I without their Ad² terms; 66.7 × 10⁶ is the solid 100 × 200 rectangle with nothing removed.
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