Find out ratio of strain-energy, Mechanical Engineering

Find out ratio of strain-energy:

A circular rod of diameter d and length l is fixed at one end and a torque T applied at the other. Now, if any close coiled helical spring is built of the same rod & applied same moment T around the axis, find out ratio of strain-energy stored.

E = 200 GPa; G = 80 GPa.

Solution

Circular Rod

J = 2I

θ= Tl  / GJ

U1 = T 2 l  / 2 GJ =        T l /  4 G I                        ------------- (1)

Helical Spring

φ= M l/ E I = T l/ E I

U 2  = (½) M φ = T 2 l / 2 E I                            -------------. (2)

U1 /U2  =   E/ 2 G =   200 / (2 × 80) = 1.25

Posted Date: 1/21/2013 1:22:55 AM | Location : United States







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