Deformation of Twisted Strips. 



VznW_ 15 K z 

 E 



479 



a 2 cj> 2 = 



or 



or 



a ^\\/v, 



2(1 + fi) cC 

 2(1+ /a) J 



13 



The square root in this expression is equal to 2 \ ifV= ^=, and 



1 . 



is equal to 2\ if cr= ^ ; hence for ordinary substances it is 



o 



intermediate between 2 J- and 2-J. We see that if the strip is 

 thin, so that h is small compared with a, the above value of a<j> 

 will be small. This shows that the maximum value of 6 will 

 occur well within the limits in which our approximation is valid. 

 This maximum value is 



°~ 32h 2 a\/ Ue) 



/\2(l + *)f' 



32nA 2 aV (2(1 + /*) 

 In order that the strip may be sensitive, 6 must be large for 

 a given value of w. If the area Aah of the cross section be 

 kept constant, this result may be brought about by making h 

 as small as possible, and this fact affords a further justification 

 of the present method of treatment. 



When 6 is approaching the maximum, its rate of increase 

 will of course become less rapid, and after this maximum 

 has been passed, 6 will diminish still more slowly than it 

 increased. Thus if we call 6 r the maximum value of 6 and 

 <f> r the corresponding value of <£, the relation between 6 and <£ 

 may be written 



6 _ 2 



This relation may be exhibited graphically by tracing the 

 cubic curve % x 



where as = <p/(j> r , y=0/O / (see figure). 



The greatest negative value of dyjdx is = — J and occurs 

 when x= \Z3, while when x = we have dy\dx—2. This 



