Determine the deflection of the spring:

A close coiled helical spring deflects 25 mm under a certain axial load. Determine the deflection of the second spring under the similar load if the effective length of the wire is same but the diameter of coils is 20% greater and that of the wire is 10% greater.

Solution

Δ= 64 W R³ n/ Gd ⁴

R₂ = 1.20 R₁,   d₂ = 1.1 d₁

l₁ = l₂

G and W are same for two springs.

If we call two springs 1 and 2 then they contain the same length but different coil radius and number of coils

∴          l₁  = l₂ or  2π R₁ n₁  = 2π R₂ n₂

But       R₂ = 1.2 R₁       (20% greater)

∴          R₂ n₁ = 1.2 R₁ n₂  or    n₁ / n₂ = 1.2

Take the ratio of deflections of two springs

 ( Δ₂/25 ) = 1.20 R₁/R₁)³ (1/1.20) (d₁/1.1d₁)⁴ = ((1.2)²/(1.2)). (1/1/1)⁴= 0.984

∴ Δ₂  = 0.984 × 25 = 24.59 mm