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Therefore total torque required = (0.793 + 3.53 + 2.23)103

Since the angle of twist is assumed constant across the whole shaft its value may be determined by application of the simple torsion theory to either the case or the elastic core.

Example 3.6

A hollow circular bar of 100 mm external diameter and 80 mm internal diameter (Fig. 3.42) is subjected to a gradually increasing torque T. Determine the value of T:

(a) when the material of the bar first yields;

(b) when plastic penetration has occurred to a depth of 5 mm;

(c) when the section is fully plastic.

Fig. 3.42.

The yield stress in shear of the shaft material is 120 MN/m2.

Determine the distribution of the residual stresses present in the shaft when unloaded from conditions (b) and (c).

Solution

(a) Maximum elastic torque from eqn. (3.11)

(b) Partially plastic torque, from eqns. (3.11) and (3.13),

(c) Fully plastic torque from eqn. (3.16) or eqn. (3.13)

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