The deflection (δ) of a cylindrical spring per turn when subjected to a tensile force (F) is considered to be a function of the following variables:              δ = ψ1 (F, D, d, G) where: D =...

The deflection (δ) of a cylindrical spring per turn when subjected to a tensile force (F) is considered to be a function of the following variables:

             δ = ψ1 (F, D, d, G)

where:

D = diameter of the coil

d = diameter of the wire

G = shear modulus of the wire

a) Perform a dimensional analysis.

b) Simplify this result by use of an obvious fact. c) Using a straightened paper clip wire, form two circular rings one having a diameter (D) and the other twice as large (dia = 2D). Load the rings with the same tensile force (F) as shown in Fig. P12.13. Use this relationship to further simplify the relation for δ. A convenient way of applying the same force (F) is to hold one end of a wire and load the other with a soft rubber band. When the deflection of the rubber band is the same in the two cases the forces will be the same. Care must be taken not to load the rings into the plastic region.