Question

The maximum shear stress induced in a solid circular shaft of diameter $15cm$ while transmitting $150kW$ power at $180rpm$ is ____ $N/m{m}^2$

• A. $10$
• B. $14.4$
• C. $11.32$
• D. $12$

Answer 1

The correct option is D $12$

Power $\left(P\right)=T\times \omega$

$T=\frac{P\times 60}{2\pi N}$

$=\frac{150\times 60}{2\pi \times 180}=7.96kN-m$

Now, $\frac{\tau }{r}=\frac{T}{I_p}=\frac{G\theta }{L}$

$\tau =\frac{T\times r}{I_p}=\frac{T}{\left(\frac{\pi }{16}{D}^3\right)}=\frac{(7.96\times {10}^6)N-mm}{\frac{\pi }{16}\times (150{)}^{3}m{m}^3}$

$=12.01N/m{m}^2$