A power transmission solid shaft of diameter d, length l and rigidity modulus G is subjected to a pure torque. The maximum allowable shear stress is τ_max . The maximum strain energy/unit volume in the shaft is given by:

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Question

This question was previously asked in

ESE Mechanical 2013 Official Paper - 2

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Answer 1

Concept:

Strain energy: It is the energy stored in a body on account of deformations produced.

Strain energy due to various forces –

(1) Axial force:

(2) Bending Moment:

(3) Torsional Moment:

Now

we have

Taking U/V and eliminating T from the above equations, we get

Torsional strain energy per unit volume in cylindrical shaft =

Note: Torsional strain energy per unit volume in rectangular shaft =

Where , τ = Maximum shear stress produced

G = Modulus of Rigidity.