MecMovies 4.0 : M6.19: Shear Stresses in Coaxial Shafts

Diagram shows a shaft A B with aluminum segment marked 1 of length 1,000 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 $30 mm$ .

A concentrated torque of $T = 1, 400 N - m$ is applied to the composite shaft at the free end $B$ .

Determine

• The torques $T_{1}$ and $T_{2}$ developed in the aluminum and bronze shafts.

• The shear stresses $τ_{1}$ and $τ_{2}$ in each shaft.

• The angle of rotation of end $B$ .