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Strength of Materials
Stress & Strain
GATE 2011
Hard

A torque T is applied at the free end of a stepped rod of circular cross-sections: a fixed segment of length L and diameter 2d, in series with a free-end segment of length L/2 and diameter d, with the torque T applied at the very end. The shear modulus of the material is G. The expression for d to produce an angular twist θ at the free end is

  • A(32TL/(πθG))^(1/4)
  • (18TL/(πθG))^(1/4)
  • C(16TL/(πθG))^(1/4)
  • D(2TL/(πθG))^(1/4)

Explanation

Both segments carry the same torque T (series). J1=π(2d)⁴/32=πd⁴/2 for the length-L segment, J2=πd⁴/32 for the length-L/2 segment. θ = TL/(GJ1) + T(L/2)/(GJ2) = 2TL/(Gπd⁴) + 16TL/(Gπd⁴) = 18TL/(Gπd⁴). Solving for d: d=(18TL/(πθG))^(1/4).

Source: GATE ME 2011 (2011)

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