GATE ME 2016 Set 3 — Question 17
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Strength of Materials → Beams & Columns → Bending & Shear Stresses
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Question
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 , while the circular cross-section has flexural rigidity . Both sections have the same cross-sectional area. The ratio is
Correct answer
(C) π/3
Solution
Flexural rigidity is defined as . Since both bars are made of the same material, the Young's modulus is the same for both. Therefore, the ratio of their flexural rigidities is simply the ratio of their area moments of inertia: .Let the cross-sectional area of both bars be .
Taking the ratio:
.
1.For the square section with side :
2.For the circular section with radius :
Taking the ratio:
.
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