Which of the following terms represents the torque that produces a twist of one radian in a shaft of unit length?

Which of the following terms represents the torque that produces a twist of one radian in a shaft of unit length?

Right Answer is:

Torsional rigidity

SOLUTION

Torsional rigidity as such represents the torsional moment required to produce an angle of twist of one radian per unit length of the shaft. For a given twisting moment T therefore the angle of twist for every unit of its length is constant.

$\frac{T}{j} = \frac{{G \times \theta }}{L} = \frac{\tau }{r}$

where

T is torque
J is the polar moment of inertia of the shaft
τ is the shear stress
r is the radius of the shaft
G is the shear modulus
L length of the shaft
θ is the angle of twist

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