Find out the strain energy stored:
A close coiled spring is subjected into an axial moment of 16 N-m. If the spring contains 15 coils with wire diameter of 10 mm and mean coil radius of 10 cm. Find out the following:
(a) the strain energy stored,
(b) maximum bending stress,
(c) axial twist.
Take E = 200 GN/m^{2}.
Solution
M = 16 N-m = 16 × 10^{3} N-mm , n = 15, d = 10 mm, R = 100 mm,
l = 2 π R n = 2π × 100 × 15 = 9434.8 mm , I = (π/64) d^{ 4} = (π/64) (10)^{4} = 490.9 mm^{4}
(a) U = M 2 l / 2 EI = ((16 × 10^{3})^{2} × 9424.8)/ (2 × (200 × 10^{3}) (490.9)) = 12287.4 N-m = 12.3 N-m
(b) σ= 32 M / π d ^{3 } =32 × 16 × 10^{3} / π × 10^{3 }= 163 N/mm^{2}
(c) U =( 1 /2 )M φ
⇒ 12.3 = (1 /2)× 16 × φ
∴ φ = 1.54 rad