The bar — torsional loading

In this chapter, we study structural elements loaded in torsion. A common example is a transmission shaft used to transfer a torque from one part to another. Geometrically, a shaft is relatively long compared to its cross-sectional area, just like the bar. Actually, we will often use expressions such as “a bar loaded in torsion” and “axially loaded bar”.

The following sections will introduce important concepts such as external and internal torque, sectional moment, shear stress, angle of twist/rotation, shear strain.

However, before continuing we point out one limitation:

The equations derived in this chapter are valid for circular cross-sections. The corresponding theory is often called St. Venant’s theory of torsion.


Torsion of thin-walled circular bars

Torsion of thick-walled circular bars

Elastoplastic behavior during torsion

Differential equation for torsion of a bar



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