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

The maximum stress is 50154 psi.

Step-by-step 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)((6600 lbin/s)/(1HP))`

`P = 16.5*10^(6)` lbin/s.

Step3

Torque is calculated as follows:

`P=T\omega`

`P=T*(2\pi N)/(60)`

`16.5*10^(6) =T*(2\pi*2000)/(60)`

T = 78781.69 lbin.

Step4

Apply torsional equation for maximum torsional shear stress as follows:

`\tau=(T)/(Z_(p))`

`\tau=(T)/((\pi d^(3))/(16))`

`\tau=(78781.69 )/((\pi*2^(3))/(16))`

`\tau= 50153.98` psi.

Or

`\tau= 50154` psi.

Thus, the maximum stress is 50154 psi.