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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 R3 n/ Gd 4 (Δ = 1 mm)
∴ W = Gd 4/64 R3 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 R3n/ Gd 4)
= E R2 / 2 G E = 2 G (1 + ν)
M / W = R2 (1 + ν)
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