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GATE 2016 ME (ME3) – Question 17

Mechanics of Materials · Bending and shear stresses, shear centre · 1 mark · Multiple choice

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1, while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I1/I2 is

Diagram for GATE 2016 ME (ME3) question 17
  1. $1/\pi$
  2. $2/\pi$
  3. $\pi/3$
  4. $\pi/6$

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Show answer and explanation

Correct answer: (C) $\pi/3$

Explanation

Equal areas give a²=πr². The square has I=a⁴/12=π²r⁴/12, while the circle has I=πr⁴/4 about a diameter. Thus I_square/I_circle=**π/3, C**. Equal area does not imply equal bending stiffness.