Problem: A torque of magnitude T = 100 Nm is applied to shaft AB of the gear train shown below. The diameters of the three solid shafts are: dAB = 21 mm, dCD = 30 mm, dEF = 40 mm. Determine the maximum shearing stress in: a) shaft AB b) shaft CD c) shaft EF

Solution: a) This is just substitution into a formula...

The factor 10-9 is a correction to make the units come out in Pa; I have eliminated the power of ten in the result to express the answer in MPa. To determine the shearing stresses in the other shafts, the torques need to be computed. The radius of gear B is rB = 25 mm, and the force that gear C exerts on gear B is TAB:

By Newton's Third Law, this is also the force on gear C:

Using this torque with gear D,

Finally, I move to gear E and shaft EF:

b) The shearing stress in shaft CD is given by

c) The shearing stress in shaft EF is: