Find out the strain energy stored, Mechanical Engineering

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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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