The step shaft is subjected to a torque of 710 lb·in. If the allowable shear stress for the material is τallow = 12 ksi, determine the smallest radius at the junction between the cross sections that can be used to transmit the torque.

The smallest radius at the junction between the cross section that can be used to transmit the torque is 0.167 inches.

Explanation:

Torsional shear stress is determined by the following expression:

Where:

- Torque, measured in .

- Radius of the cross section, measured in inches.

- Torsion module, measured in quartic inches.

- Torsional shear stress, measured in pounds per square inch.

The radius of the cross section and torsion module are, respectively:

Where is the diameter of the cross section, measured in inches.

Then, the shear stress formula is now expanded and simplified as a function of the cross section diameter:

In addition, diameter is cleared:

If and , then:

The smallest radius at the junction between the cross section that can be used to transmit the torque is 0.167 inches.

explanation:

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