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Strength of Materials
Bending of Beams
GATE 2016
Hard

The cross-sections of two solid bars made of the same material are shown: a square cross-section with flexural rigidity I1, and a circular cross-section with flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I1/I2 is

  • A1/π
  • B2/π
  • π/3
  • Dπ/6

Explanation

For equal area A: square side a=√A, I1=a^4/12=A²/12. Circle radius r=√(A/π), I2=πr^4/4=A²/(4π). Ratio I1/I2 = (A²/12)/(A²/(4π)) = 4π/12 = π/3.

Source: GATE ME 2016 Set-3 (2016)

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