Plan the Solution  
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Diagram shows a shaft A B with aluminum segment marked 1 of length 400 millimeters inside which is a brass shaft marked 2. Both the shafts are centered on the central axis x. A torque T is applied at B.

The procedure to solve this problem can be outlined as:

• Compatibility equation
The torque-twist relationships will be substituted into the geometry of deformation relationship to derive a compatibility equation expressed in terms of the internal torques T1 and T2.

• Stress relationship
Expressions for shaft torques can be obtained from the elastic torsion formula. Substituting these expressions into the compatibility equation gives a relationship between the shear stresses in the shafts.

• Controlling shear stress
Using the relationship between shear stresses in the two shafts and the allowable stresses, the shaft that controls the design can be determined.