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A 1/8 inch thick, 1 inch tall ruler is bent on edge instead of flat. How much stiffer is it?

64 times stiffer, for an ideal rectangular cross section.

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  1. About the same
  2. About 2 times
  3. 64 times ✔

Why: For a rectangle, bending stiffness follows bh cubed. Turning this 1 by 1/8 inch section swaps b and h, changing their ratio by (1 divided by 1/8) squared, or 64.

Huh, didn't know that: That is why floor joists stand on edge instead of lying flat.

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My ruler tried to bend on edge. It just couldn't measure up.
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References

Answer: 64 times. For a rectangle, bending stiffness follows bh cubed. Turning this 1 by 1/8 inch section swaps b and h, changing their ratio by (1 divided by 1/8) squared, or 64.

  1. Engineering Statics (Baker and Haynes): 10.1 Integral Properties of Shapes engineeringstatics.org/Chapter_10-integral-properties-of-shapes.html
    is over 20 times more than the bending resistance the other way
    Checked 2026-10-11.
  2. MIT OCW 3.11 Mechanics of Materials (Roylance): Stresses in Beams ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/96d839b02e4a6c63cf8031800e89cccd_MIT3_11F99_bstress.pdf
    I = bh3 /12
    Checked 2026-10-11.

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