MecMovies 4.0 : M6.21: Maximum Torque for Composite Shaft

Diagram shows an aluminum shaft A B with a support at A, marked 1 of length 4,000 millimeters and a brass shaft B C with a support at C, marked 2 of length 3,000 millimeters with a flange in between at B. The shafts are centered on the x axis. A torque T is applied at B.

A composite shaft consists of a hollow steel $(G = 76 GPa)$ shaft $(1)$ connected to a solid bronze $(G = 38 GPa)$ shaft $(2)$ at flange $B$ . The outside diameter of shaft $(1)$ is $80 mm$ and the inside diameter is $65 mm$ . The outside diameter of shaft $(2)$ is $80 mm$ .

The allowable shear stresses for the steel and bronze materials are $90 MPa$ and $50 MPa$ , respectively.

Determine:

• The maximum torque $T$ that can be applied to flange $B$ .

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

• The angle of rotation of flange $B$ .