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 R^{3 }n / Gd^{ 4}
W / Δ = G d ^{4}/ 64 R^{3 }n
100 =(80 × 10^{3 }) d ^{4}/64 (40)^{3} (10) ∴ d = 15 mm
τ_{max} = 16 W R / π d^{3}
200 = 16 W × 40 / π (15)^{3 }∴ W = 3313.4 N = 3.3 kN