Solve Simple Torsion Problem: Calculate Maximum Torque on 25mm Shaft

[Iclaudius]

Hiya friends,

so i have a little problem,

A shaft is made from tube 25 mm outer diameter and 20 mm inner diameter. The shear stress must not exceed 150 Mpa. Calculate the maximum torque that should be placed on it

ok so we have T/J = tau/r
so T = (tau/r)*J - this should give me my answer right I'm using tau = 150Mpa, r= 20mm, and J = (pi/32)(25^(4)-20^(4)), this however does not give me the answer which is 271.69 Nm

ps i have tried using both 25 and 20 respectively for the r value without any sucess, any help advice is appreciated, thanks in advance

Claudius

 

[Iclaudius]

Nevermind people, a foolish oversight on my part

 

[Studiot]

Is this not a shear flow problem

T=2aS_flow

$$T = \frac{\pi }{4}*{\left( {22.5} \right)^2}*5*150*{10^{ - 3}}*{10^{ - 3}}*{10^{ - 3}}*{10^6} = 298.2$$

 

[Iclaudius]

Ah nope, page 5 on this link has the question - nice little resource on torsion

http://www.freestudy.co.uk/c103/t3.pdf

 

[Studiot]

Sorry the I can't open the link.

However you have to admit that if your link provides a more accurate solution the shear flow approximation gets pretty close, pretty easily.

What shear distribution are you assuming?

 

[Iclaudius]

The link unfortunately just gives a straight answer without working, to answer your question however the shear distribution is assumed to be linear