applied load shall elongate the springdesign a

Question

Applied load shall elongate the spring:

Design a close coiled helical spring which shall deflect 100 mm under a load of 600 N. The radius of the coil is 6 times the wire diameter. The maximum shear stress is not to exceed 8 MPa. G = 80 GPa. What suddenly applied load shall elongate the spring by 100 mm?

Solution

Δ = 100 mm, W = 600 N, R = 6d, τ_max  = 80 N/mm² ,

G = 90 GPa = 80 × 10³ N/mm²

τ_max      = 16 W R / π d³

⇒         80 = 16 × 600 × (6d )/ π d ³

∴          d = 15.14 mm

R = 6d = 90.84 mm

Δ= 64 W R³ n / Gd ⁴

⇒         100 =64 × 600 × 90.84³ × n/(80 × 10³ ) (15.14)⁴

                        = n = 14.6

A suddenly applied load shall cause double the stress caused by same load if applied gradually. Therefore, in this case if same stress is to be induced in spring wire cross-section by suddenly applied load it shall be W/2  = 600/2 = 300 N .