What is the maximum load the spring may carry:

Any close coiled helical spring has mean diameter of 80 mm, has spring constant of 100 kN/m. It contains 10 coils. The maximum shear stress is equal to 200 MPa. Find out diameter of spring wire? What is the maximum load the spring may carry?

Take G = 80 GPa.

Solution

D = 80 mm, R = 80 /2 = 40 mm , k = 100 kN/m, n = 10

Δ= 64 W R³ n / Gd ⁴

W / Δ = G d ⁴/  64 R³ n

100 =(80 × 10³ ) d ⁴/64 (40)³ (10)        ∴ d = 15 mm

τ_max      = 16 W R  / π d³           

200 = 16 W × 40 / π (15)³         ∴ W = 3313.4 N = 3.3 kN