The following data refers to an open – coiled helical spring:

Pitch of the coils=27mm
Number of coils=12
Mean coil diameter=54mm
Diameter of wire=8mm
Modulus of elasticity spring material=208GN/m2
Modulus of rigidity of spring material=72GN/m2
The spring is subjected to a pure axial twisting moment of 9M-m.

Determine:

The resulting angle of twist. (8 marks)
The extension produced. (31/2 marks)
The bending stress in the surface of the wire. (41/2 marks)
The shear stress in the surface of the wire. (4 marks)

a) i) State any FOUR assumptions made in the theory of torsion.
ii) Show that the strain energy ‘u’ stored in a solid shaft of diameter ‘d’, length ‘l’ and modulus of rigidity G, when subjected to pure torque T, is given by the expression:

u=T2 x Volume of the shaft
4G
where T is the maximum shear stress. (7 marks)

b) A composite shaft is used to transmit 380KW at a speed of 750 rev/min. The composite shaft is made by passing a solid cylindrical shaft of 65mm diameter and 1.8m long, 65mm and 75mm internal and external diameters respectively. They are then rigidly joined together at their ends. The solid shaft is made of steel and the hollow shaft is made of brass.

Determine:
The maximum and minimum stresses in the two shafts.
The angle of twist.
The total strain stored:
Take G for brass=35GN/m2
and G for steel=78 GN/m2 (13 marks)

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