Torsional Deformation

Torque is a moment that tends to twist a member about its longitudinal axis. Two parallel longitudinal lines on the outer surface of the tube are used to show the twist. From the above animation, we can observe the deformation process of the rectangular element on the outer surface of the tube when it is subjected to the torque.

Two radial lines are connected to the parallel lines. Please know that radial lines remain straight during deformation.

Thus, if the shaft is fixed at one end as in this animation and a torque is applied to its other end, the yellow plane will distort into a skewed form as shown.

The torsion formulas:

The shear stress at any point with the intermediate distance ρ can be determined from following equations.

τ = Tρ/J

J = πc4/2

Where, τ = the shear stress at radius ρ,
T = the torque at cross section,
J = the polar moment of inertia of the cross-sectional area,
c = the outer radius.

This material is based upon work supported by the National Science Foundation under Grant No. 0633602. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

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Pennsylvania State University
Department of Engineering Science and Mechanics
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