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.

The procedure to solve this problem
can be outlined as:

• Equilibrium
Draw a free-body diagram $(FBD)$ of flange $B$ to determine the relationship of internal torques $T_{1}$ and $T_{2}$ to the applied torque $T$ .

• Geometry of deformation
From the angles of rotation at $A$ , $B$ , and $C$ , we will deduce the relationship between the twist angles in shafts $(1)$ and $(2)$ .

• Torque-twist relationships
The relationship between internal torque and angle of twist will be expressed for each shaft.

• Compatibility equation
The torque-twist relationships will be substituted into the geometry of deformation relationship to derive a compatibility equation expressed in terms of the internal torques $T_{1}$ and $T_{2}$ .