Question

A hollow shaft of 16 mm outside diameter and 12 mm inside diameter is subjected to a torque of 40 N-m. The shear stresses at the outside and inside of the material of the shaft are respectively

• A. $65.75N/m{m}^{2}and50.00N/m{m}^2$
• B. $72.75N/m{m}^{2}and54.54N/m{m}^2$
• C. $79.75N/m{m}^{2}and59.54N/m{m}^2$
• D. $80.00N/m{m}^{2}and40.00N/m{m}^2$

Answer 1

The correct option is B $72.75N/m{m}^{2}and54.54N/m{m}^2$

$D_0=16mm,\frac{\tau }{r}=\frac{T}{J}$

D = 12 mm
T = 40 N-m

$\Rightarrow \tau =\frac{T\times r}{J}$

$J=\frac{\pi ({16}^4-{12}^4)}{32}$

$\Rightarrow {\tau }_0=\frac{40\times {10}^3\times \frac{16}{2}}{\pi \times \frac{({16}^4-{12}^4)}{32}}=72.75N/m{m}^2$

${\tau }_i=\frac{72.7}{\left(\frac{16}{2}\right)}\times \left(\frac{12}{2}\right)=54.54N/m{m}^2$