Torsion

The twist or deformation of a body set up by a torque.

Torsion Theories

• Saint Venant torsion theory - basic torsion theory for which warping is not restrained
• Vlasov torsion theory - more general torsion theory for which warping can be restrained

Notation

The following notation is used throughout the torsion topic, unless noted otherwise:

• <tex>B</tex> ... bimoment
• <tex>I_{\omega}</tex> ... sectorial moment of inertia
• <tex>\phi</tex> ... angle of rotation due to torsional moment
• <tex>\phi'</tex> ... first derivative of <tex>\phi</tex> with respect to the local X axis of the member
• <tex>\phi</tex> ... second derivative of <tex>\phi</tex> with respect to the local X axis of the member
• <tex>\phi</tex> ... third derivative of <tex>\phi</tex> with respect to the local X axis of the member

Torsion of Closed Thin-Walled Sections

Shear stress due to torsion in a thin-walled noncircular shell can be calculated as follows (Lindeburg 2003):

<tex>\tau = \frac{T}{2At}</tex>

where

• <tex>\tau</tex> ... shear stress
• <tex>T</tex> ... applied torsion
• <tex>A</tex> ... area enclosed by the centerline of the shell
• <tex>t</tex> ... sheel thickness

See Also

• warping
• shear flow

References

• AISC Design Guide 9: Torsional Analysis of Structural Steel Members (1996)
• Michael R. Lindeburg: Civil Engineering Reference Manual for the PE Exam, 9th Edition, 2003, p. 45-14 (eq. 45.54)