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Strength of Materials
Stress & Strain
GATE 2013
Medium

Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

  • A16
  • 24
  • C36
  • D48

Explanation

Elastic strain energy for an axially loaded bar U=P²L/(2AE) ∝ 1/A ∝ 1/d² (same P, L, E for both bolts). U_A=4U_B ⟹ 1/d_A²=4/d_B² ⟹ d_B²=4d_A² ⟹ d_B=2d_A=2×12=24mm.

Source: GATE ME 2013 (Booklet Code A) (2013)

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