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XXV. Twisted Strips. 

 By Professor John Perky, F.R.S.* 



IN a paper read at the British Association Meeting this 

 year, and also at a former meeting of the Physical Society, 

 I referred to the curious behaviour of a twisted strip. The 

 twisted strip must not be confounded with what has been 

 called the Ayrton and Perry Spring. It is a straight strip of 

 metal to which a permanent twisted appearance has been 

 given, a twisting moment being applied about the axis of the 

 strip to give it the permanent twist, care being taken to pre- 

 vent the axis of the strip from lateral motion. In fact the 

 axis remains straight, and is the axis of all the spiral lines now 

 formed by the lines which were originally straight and parallel 

 to the axis. When an axial force is employed to elongate a 

 twisted strip, a slight elongation takes place accompanied by 

 a large relative rotation of the ends of the strip. The only 

 simple hypothesis on which, as I told the Society on a former 

 occasion, I could see my way to building a possible theory 

 was to consider in any very short length of the strip any two 

 spiral filaments equally distant from the axis as two threads 

 in a bifilar suspension. Under the action of any axial force 

 these two threads tend to produce untwisting, and the sum of 

 all these untwisting moments is equal to the torsional rigidity 

 of the cross section multiplied by the angle of untwist. 



The phenomena are so complicated that I never hoped to 

 explain them all by this or any other hypothesis. I was 

 seeking for a roughly correct theory only. 



The breadth being b and thickness t, we may roughly 



assume that the section remains rectangular ; and as b is 



always more than ten times t, we may take the torsional 



N 

 rigidity as -~ bt s . If then 6 is the angular amount of un- 

 o 



twisting produced per unit length of the strip, the moment of 

 torsional resistance is 



N 



Let w be the axial force. If (f> is the twist of the strip per 

 unit length, then for a filament whose horizontal section is 

 t . has, at the distance x from the axis (as t is small compared 

 with b I take the filament as extending quite across the sec- 

 tion), if p is the vertical tensile stress on the section, it is 



* Communicated by the Physical Society: read November 1, 1889. 



