Question

A circular shaft of diameter 'D' is made of a material for which Young's Modulus of Elasticity is 'E' and Poisson's Ratio is 'v'. The ratio of flexural rigidity to torsional rigidity for the shaft is

• A. $4(1+v)$
• B. $15(1-2v)$
• C. $(1+v)$
• D. $0.25(1+v)$

Answer 1

The correct option is C $(1+v)$

$\because \frac{\text{Flexural rigidity}}{\text{Torsional rigidity}}=\frac{El}{GJ}=\frac{E\frac{\pi }{64}{D}^4}{G\frac{\pi }{32}{D}^4}=\frac{E}{2G}$
$\therefore G=\frac{E}{2(1+v)}$

$\because \frac{\text{Flexural rigidity}}{\text{Torsional rigidity}}=\frac{El}{2\times \frac{E}{2(1+v)}}$
$=1+v$