570 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



the size of the outside wire is comparable to the size of the terminal 

 and it is obvious that a twist in the terminal is occurring. This is a case 

 of three dimensional stress rather than plane stress and cannot easily 

 be analyzed from the photograph. The photograph does, however, show 

 a twist of the terminal. 



The twisting strain can be most easily analyzed by taking a long 

 section of terminal of low torsional stiffness, winding 100 or more turns 

 on the terminal and measuring the angle of twist as discussed in the 

 paper by Mallina. Calculations by Love^ show that a twist in an ellipti- 

 cal section with its length along the Z axis introduces shearing strains 

 in the X, Z and F, Z planes, i.e., ezx — S^ and eyz = 84, shearing strains 

 equal to 



where 2a is the diameter of the ellipse along the X direction and 26 

 the diameter of the ellipse along the Y direction and r the angle of twist 

 in radians per centimeter. For the terminal with 100 turns of 0.020 mil 

 copper wire discussed by Mallina whose data are given by Fig. 13, 45° 

 angle of twist occurs in 2 inches giving a value of r = 0.157. This causes 

 a shearing strain of about 2 per cent in the worst case which is enough 

 to cause a considerable permanent set. While this twist is useful in 

 studying stress relaxation in the wire, it is undesirable for a solderless 

 wrapped connection to have too much twist since it may cause the ter- 

 minal to twist off in the winding process. According to the data of Fig. 13 

 of MalUna's paper, no terminal set occurs for nickel silver if the twist in 

 radians per centimeter is less than 0.09 which corresponds to a maxi- 

 mum shearing strain in the X, Z plane of 1.1 per cent. Hence in order 

 to avoid excessive permanent set and twisting off of the inner terminal, 

 the size and shape of the terminal should be controlled so that shearing 

 strains due to twisting should be less than 1 per cent. For standard 

 shapes such as rectangles and ellipses formulae are available to relate 

 the maximum strain to the dimensions of the terminals and the moment 

 due to the winding stress. For a given wrapping tension, this moment 

 can be calculated from Appendix I of Mallina's paper. 



Summarizing the results of this section, the necessary conditions 

 that the terminal should meet are: 



1. The wrapped connection is held together by the hoop stress in the 

 outside wrapping wire. This can be locked in if the terminal has a dis- 

 synmietrical shape in which the length-width ratio is 1.5 or greater, 



1 Love, Theory of Elasticity. Chap. XIV, p. 310, 4th Edition, Cambridge Uni- 

 versity Press. 



