Question

A circular solid shaft of span L = 5m is fixed at one end and free at the other end. A twisting moment T=100 kN-m is applied at the free end. The torsional rigidity GJ is 50000 kN-$m^2/$ rad.
Following statements are made of this shaft.
I. The maximum rotation is 0.01 rad
II. The torsional strain energy is 1 kN-m

With referance to the above statements, which of the following applies?

• A. Both statements are ture
• B. Statement I is true but II is a false
• C. Statement II is true but I is false
• D. Both the statements are false

Answer 1

The correct option is B Statement I is true but II is a false


We know $\frac{T}{J}=\frac{G\theta }{L}$
$\Rightarrow \theta =\frac{TL}{GJ}=\frac{100\times 5}{50000}=0.01rad$
Torsional strain energy.
$U=\frac{1}{2}T\times \theta =\frac{1}{2}\times 100\times 0.01$
$=0.5$ kNm