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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/m2.
Solution
M = 16 N-m = 16 × 103 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 mm4
(a) U = M 2 l / 2 EI = ((16 × 103)2 × 9424.8)/ (2 × (200 × 103) (490.9)) = 12287.4 N-m = 12.3 N-m
(b) σ= 32 M / π d 3 =32 × 16 × 103 / π × 103 = 163 N/mm2
(c) U =( 1 /2 )M φ
⇒ 12.3 = (1 /2)× 16 × φ
∴ φ = 1.54 rad
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