MecMovies 4.0 : M6.18: Motor-driven Shafts

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Diagram shows two shafts marked 1 and 2 of length 36 inches and 96 inches respectively. They are connected by two gears at B which has 24 teeth on the shaft 1 and at C which has 72 teeth on the shaft 2. The shaft 1 is connected to a motor at A. The shaft 2 has a gear at D on which a torque T subscript D is applied.

The shear stress magnitude in shaft $(1)$ is:

$τ_{1} = \frac{T_{1} c_{1}}{J_{1}} = \frac{(43.768 lb - ft) (0.75 in . / 2) (12 in . / ft)}{0.031063 {in.}^{4}} = 6, 340.455 psi = 6, 340 psi$