Bifilar Property of Twisted Strips. 



779 



Let F = total tension to which the strip is subjected, and 



Tjl 



26= breadth of strip; the tension per cm. breadth, T= ^ . 



Over a fibre of breadth dr the total 

 tension is Tdr along the length of fibre. 

 The fibre in displaced position makes an 

 angle <f> with the vertical. 



In the displaced position, the horizontal 

 component of force on the fibre = Tdr sin </>, 



rQ 



since cp and 6 are small. 



The corresponding fibre on opposite 

 side of neutral line gives an equal opposite 

 force, and the two give a couple of moment 

 rQ 



The moment of the resultant couple for 



C b r 2 

 the whole strip = I 2T -j- dr, 



2T6 

 3 I 



Thus the restoring couple per unit angular displacement 



n _ 2 T/> 3 



U -3~ 



(1) 



When this bifilar couple is negligible the strip twists into 

 the form of a helicoid, and the restoring couple 



C 2= ^bd^ 



(2)* 



where n is the torsional rigidity of the material and 2d the 

 thickness of the strip, which is small in comparison with 

 the breadth 2b. 



If the two couples Oi and C 2 are of comparable magnitude, 

 the total restoring couple per unit angular displacement 



n _16bd 3 n 2TP 



(3) 



* Searle, ' Experimental Elasticity.' 

 3E 2 



