MecMovies 4.0 : M6.22: Maximum Torque Applied to Coaxial Shaft

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:

• Torque-twist relationships
The relationship between internal torque and angle of twist will be expressed for each shaft.

• 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 $T_{1}$ and $T_{2}$ .

• 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.