Determine the ratio between moment and load:
Any close coiled helical spring of circular section extends 1 mm while subjected to an axial load of W and then given an angular rotation of 1 radian while a moment M is independently applied around the axis. Determine the ratio M / W
Solution
For a close coiled spring :
Δ=64 W R^{3} n/ Gd ^{4} (Δ = 1 mm)
∴ W = Gd ^{4}/64 R^{3} n ------------- (1)
φ= 128 M Rn / Ed ^{4}
∴ M = E d ^{4}/128 R n -------------- (2)
Eq. (2) divided by Eq. (1), we get
M/ W = (Ed^{ 4}/128 R n) × (64 R^{3}n/ Gd ^{4})
= E R^{2} / 2 G E = 2 G (1 + ν)
M / W = R^{2} (1 + ν)