TORSION TEST. 217 



This result is, of course, only an approximate demonstration 

 of the truth of the fact that G : E : : 2 : 5 for the same 

 material. The two tests were not made on steel from the 

 same piece, but the two metals were of very similar 

 character. 



When the shaft is still elastic, the shearing stress at any 

 point on a section of the bar is directly proportional to the 

 radial distance of this point from the axis, and, therefore, 

 the maximum stress is always at the outer surface. On 

 this account it is these outer layers that are first strained 

 beyond the elastic limit, while the layers nearer the axis 

 are still in the elastic state. When once these outer layers 

 begin to take permanent set, a greater stress is thrown on 

 those layers coming next to them, and so on, the semi- 

 plastic condition gradually penetrating inwards until the 

 whole bar is in this state. 



It will be readily understood that the commonly 

 accepted formula for torsion, 



* ' T = *" 



is only true so long as the elastic condition is maintained, 

 that is, so long as the stress is proportional to the distance 

 from the axis. 



The further the test progresses, and the nearer the point 

 of fracture is approached, the more nearly is the truly 

 plastic condition approximated to. As was pointed out 

 (par. 16) a significant fact about the plastic condition, so 

 far as a torsion specimen is concerned, is that under this 

 condition the shearing stress at any point in a bar is not 

 proportional to the distance of that point from the 

 axis of the bar, but is sensibly uniform over the whole 

 section of the bar ; and the relations of stress and moment 

 are now expressed-by the formula (XXX.), instead of (IX.). 

 This formula, which has already been given, is 



Between the elastic limit and the maximum twisting 

 moment, the relations of stress are not expressed by either 

 of the two above formulae, but probably by an expression of 

 the form, 



