The strain energy stored in a solid circular shaft subjected shear stress (τ) is (where C = Modulus of rigidity the shaft material) 

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ISRO URSC Technical Assistant Mechanical 24 March 2019 Official Paper
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  1. τ/2C*volume of shaft
  2. τ2/4C*volume of shaft
  3. τ/4C*volume of shaft
  4. τ2/2C*volume of shaft 

Answer (Detailed Solution Below)

Option 4 : τ2/2C*volume of shaft 
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Detailed Solution

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Explanation:

Strain Energy:

Strain Energy of the member is defined as the internal work done in deforming the body by the action of externally applied forces.

Normal Stress:

Strain energy due to normal stress is given as

where σ = normal stress, E = young's modulus of elasticity

Shear Force:

Strain energy due to shear force is given as

where τ = shear stress due to shear force.

For solid circular shaft due to torsion strain energy is:

where τ = shear stress due to torsion, G = modulus of rigidity

For hollow shaft:

Strain energy

where τ​ = shear stress due to torsion, G = modulus of rigidity.

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