Question

If
A = Cross-sectional area
E = Young's modulus of elasticity
G = Modulus of rigidity
I = Moment of inertia
J = Polar moment of inertia

then torsional rigidity is given by

• A. AE
• B. GE
• C. EI
• D. GJ

Answer 1

The correct option is D GJ

According to torsion formula

$\frac{T}{J}=\frac{G\theta }{l}=\frac{f_s}{R}$

Let a twisting moment T produce a twist of $\theta$ radian in a length l.

$\frac{T}{J}=\frac{G\theta }{l}$

$\Rightarrow \theta =\frac{TL}{GJ}$

$\Rightarrow GJ=\frac{Tl}{\theta }$

The quantity GJ stands for the torque required to produce a twist of 1 radian per unit length of the shaft.

This quantity GJ is called torsional rigidity.