State the Problem  
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Diagram shows an aluminum shaft A B with a support at A, marked 1 of length 2,000 millimeters and a brass shaft B C with a support at C, marked 2 of length 800 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 = 86 GPa) shaft (1) connected to a solid bronze (G = 38 GPa) shaft (2) at flange B. The outside diameter of shaft (1) is 75 mm and the inside diameter is 55 mm. The outside diameter of shaft (2) is 75 mm.

A concentrated torque T will be applied to the composite shaft at flange B.

Determine:

• The maximum magnitude of the concentrated torque T if the angle of rotation at flange B cannot exceed 3°.

• The shear stresses τ1 and τ2 in each shaft.