﻿Shaft moving with Uniform Speed along its Axis. 747 

 When we refer to a point x = ?', y = 0, we get 



r-e('+-£) + frg. .... (6) 

 n '=er)+err& (7) 



r-/t (») 



The radial strain at any point is determined by equa- 

 tion (6). To find the principal axes o£ strain in the plane 

 of (j/, z) we need only consider equations (7) and (8), which 

 mav be written 



V= «■?+*& .......... (9) 



C=/fc (io) 



where 5 = erT, (11) 



/= Vl-^/c 2 by deduction (IT.). (12) 



The next step is to express e, /i 5 in terms of the position 

 of the principal axes and their contractions. Since the strain 

 is not pure, the principal axes will be rotated from their 

 initial positions, and both their final and initial positions will 

 have to be considered. 



Fig. l. 



\ \ Final , 



t wX position 



Y 



Initial 

 position 



We assume this part of the strain is produced by contrac- 

 tions along and perpendicular to axes Y and Z, which in 

 consequence of the strain have been rotated into positions y 

 and z, as shown in the diagram. 



