Torsion: Difference between revisions

Latest revision as of 03:07, 22 October 2024

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

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

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

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

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)

Home > Topics > Traditional Analysis Methods > Torsion e
Overview	Torsion · Saint Venant torsion theory · Vlasov torsion theory · Torsion formulas
Topics	Warping · Bimoment

@@ Line 6: / Line 6: @@
 * [[Vlasov torsion theory]] - more general torsion theory for which warping can be restrained
-== Torsion of Solid Sections ==
+== Notation ==
-== Torsion of Closed Thin-Walled Sections ==
+The following notation is used throughout the torsion topic, unless noted otherwise:
-Shear stress due to torsion in a thin-walled noncircular shell can be calculated as follows (Lindeburg 2003):
+* <math>B</math> ... [[bimoment]]
+* <math>I_{\omega}</math> ... [[sectorial moment of inertia]]
+* <math>\phi</math> ... angle of rotation due to torsional moment
+* <math>\phi'</math> ... first derivative of <math>\phi</math> with respect to the local X axis of the member
+* <math>\phi''</math> ... second derivative of <math>\phi</math> with respect to the local X axis of the member
+* <math>\phi'''</math> ... third derivative of <math>\phi</math> with respect to the local X axis of the member
-<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
-== Torsion of Open Thin-Walled Sections ==
 == See Also ==
-* [[warping]]
 * [[shear flow]]