MecMovies 4.0 : M6.20: Shear Stresses in End-to-end Shafts

Diagram shows an aluminum shaft A B with a support at A, marked 1 of length 1,500 millimeters and a brass shaft B C with a support at C, marked 2 of length 1,000 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 $(G = 75 GPa)$ shaft $(1)$ connected to a solid brass $(G = 40 GPa)$ shaft $(2)$ at flange $B$ . The outside diameter of shaft $(1)$ is $50 mm$ and the inside diameter is $40 mm$ . The outside diameter of shaft $(2)$ is $50 mm$ .

A concentrated torque of $T = 1, 000 N - m$ is applied to the composite shaft at flange $B$ .

Determine

• The torques $T_{1}$ and $T_{2}$ developed in the steel and brass shafts.

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

• The angle of rotation of flange $B$ .