Question

What is the shear stress due to torsion at the surface of a 2-inch diameter solid steel shaft of a home-built high-speed boat that transmits 2500 HP at 2000 RPM? Note: bending and axial loads are negligible. Give the maximum torsional stress, to the nearest psi.

Answer 1

Answer:

The maximum stress is 50154 psi.

Explanation:

Torsional equation is applied for steels haft under given condition for maximum torsional stress.  

Step1

Given:

Diameter of shaft is 2 in.

Power transmission is 2500 HP at rotation 2000 RPM.

Calculation:

Step2

Conversion of power transmission is as follows:

$P=(2500HP)(\frac{6600 lbin/s}{1HP})$

$P = 16.5\times10^{6}$ lbin/s.

Step3

Torque is calculated as follows:

$P=T\omega$

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

$16.5\times10^{6} =T\times\frac{2\pi\times2000}{60}$

T = 78781.69 lbin.

Step4

Apply torsional equation for maximum torsional shear stress as follows:

$\tau=\frac{T}{Z_{p}}$

$\tau=\frac{T}{\frac{\pi d^{3}}{16}}$

$\tau=\frac{78781.69 }{\frac{\pi\times2^{3}}{16}}$

$\tau= 50153.98$ psi.

Or

$\tau= 50154$ psi.

Thus, the maximum stress is 50154 psi.