Question

A solid shaft of 100 mm diameter in a small hydraulic turbine is subjected to an axial compressive load of $100\pi kN$ and a torque of $5\pi kN-m$. The maximum shearing stress induced in the shaft is

• A. $20\sqrt{3}N/m{m}^2$
• B. $20\sqrt{8}N/m{m}^2$
• C. $20\sqrt{15}N/m{m}^2$
• D. $20\sqrt{17}N/m{m}^2$

Answer 1

The correct option is D $20\sqrt{17}N/m{m}^2$

$Axialstress=\frac{100\pi }{\frac{\pi \times {100}^2}{4}}=0.04kN/m{m}^2$

$=40N/m{m}^2$

$Shearstress=\frac{16T}{\pi d^3}=\frac{16}{\pi \times (100{)}^3}\times 5\pi \times {10}^6$

$=80N/m{m}^2$

Maximum shear stress is the radius of Mohr's circle.

$Maximumshearstress=\sqrt{{\left(\frac{40}{2}\right)}^2+(80{)}^2}$

$=20\sqrt{17}N/m{m}^2$