532 Dr. J. Prescott on the Torsion of 



The stress is greatest at the ends of the minor axis, and 

 its value at these points is, by (32), 



Q 



S =2A, 



Q 



lirab . kb 

 2ma 2 b 



aUb* <"> 



The two particular examples we have worked out show 

 that equation (34) gives, in every case, the value of the 

 torque obtained on the assumption that £ is so small compared 

 with the greatest dimension of the section of the tube (or with 

 the perimeter of the section) that powers of t beyond the first 

 may be neglected. 



Torsion of thin unclosed Tubes. 



The approximate results that we have obtained for closed 

 tubes fail altogether when we come to deal with unclosed or 

 split tubes. For a split tube there is only one boundary to 

 the section and f has one constant value over the whole of 

 this boundary. Thus, in fig. fi, £ has the same value at P as 



Fig. 6. 



at P', whereas if the tube were closed by fastening A and B 

 together there would be a continuous increase <>r decrease 

 of f from P to P'. Any shear line that crosses PP' in fig. 6 

 crosses that line twice since it has the form of a closed 

 curve lying entirely within the boundary of the section. If, 

 however, the tube were closed each shear line would only 

 cross PP' once, since it could close up by encircling the 

 inner boundary. Then across approximately one half of 

 PP' there are shear lines going in one direction, and over 

 the remainder the shear lines cross in the opposite direction, 

 and there are the same number of lines crossing each way 



