528 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



F F SPRING ANALOGUE 



Fig. 2 — Screw tightened and wire compressed (with accompanying "Spring 

 Analogue")- 



connections, the forces which hold the wire and terminal together are 

 provided by the springiness or elasticity of the materials. The elasticity 

 in a Fahnestock clip is quite apparent because of the long spring mem- 

 ber. On the other hand, a screw connection, such as shown in Fig. 2, 

 does not appear to have spring members of any kind. Analysis, however, 

 shows that there is considerable elastic deformation. Most of this elas- 

 tic deformation is in the elongation of the screw shank and there is also 

 some bending in the screw head and some compression in the screw 

 threads. When the screw is tightened, the wire which is interposed be- 

 tween screw head and nut is also elastically deformed. Since in most 

 electrical connections the wire is a soft material such as copper or alu- 

 minum, it is nearly always compressed beyond the yield point and only 

 the recovery of the overstressed material can be considered as elastic 

 reserve. 



To determine the usefulness of a connection and compare pressure 

 connections of different kinds, the elastic reserve in the deformed wire 

 and the deformed terminal must be measured or computed. Elastic re- 

 serve might be expressed either in terms of stiffness or the potential 

 energy stored in the system. Stiffness S is defined as the ratio of the 

 ''applied force F to the elastic return Z)"; potential or elastic energy 

 E is "one half of the product of the force F and the elastic return D." 

 {E = H™.) 



Example: A wire is placed under a screw (Fig. 2) and compressed by 

 the screw head to a thickness Di . The screw is then loosened so that 

 it just touches the wire. The wire now has expanded to a certain extent 

 and its new thickness is D2. (Fig. 3.) The difference (D2 — Di = Dw) 

 is the elastic return and the ratio F/Dw = Sw is the useful stiffness of 

 the wire. 



A preferred way of expressing elastic reserve is in terms of stored 

 energy. (Strictly speaking the equation E = J^FD holds only for 

 springs with constant stiffness. A round wire compressed by a screw 

 head becomes stiffer as the compression increases). The distance, Ds = 

 Di — Dir , is the elongation of the screw (see Fig. 3). The total energy 



