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.

A composite shaft consists of a hollow aluminum $(G = 26 GPa)$ shaft $(1)$ bonded to a hollow bronze $(G = 38 GPa)$ shaft $(2)$ . The outside diameter of shaft $(1)$ is $50 mm$ and the inside diameter is $42 mm$ . The outside diameter of shaft $(2)$ is $42 mm$ and the inside diameter is $30 mm$ .

The allowable shear stresses for the aluminum and bronze materials are $85 MPa$ and $100 MPa$ , respectively.

Determine:

• The maximum torque $T$ that can be applied to the free end $B$ .

• The stresses $τ_{1}$ and $τ_{2}$ developed in the shafts.

• The angle of rotation of end $B$ .