Torsion - Revision history

Ok: Text replacement - "" to " $"$

2024-10-22T01:07:27Z Text replacement - "<tex>" to "<math>"

← Older revision		Revision as of 03:07, 22 October 2024
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	The following notation is used throughout the torsion topic, unless noted otherwise:		The following notation is used throughout the torsion topic, unless noted otherwise:

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

2024-10-22T00:42:39Z

Text replacement - "</tex>" to "</math>"

← Older revision		Revision as of 02:42, 22 October 2024
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	The following notation is used throughout the torsion topic, unless noted otherwise:		The following notation is used throughout the torsion topic, unless noted otherwise:

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

2009-09-22T04:19:56Z

2009-09-22T04:19:17Z

← Older revision		Revision as of 06:19, 22 September 2009
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	* <tex>\phi'''</tex> ... third 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 Solid Sections ==~~

	~~== 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

	~~== Torsion of Open Thin-Walled Sections ==~~

	== See Also ==		== See Also ==

2009-09-22T03:27:56Z

Notation

← Older revision		Revision as of 05:27, 22 September 2009
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	The following notation is used throughout the torsion topic, unless noted otherwise:		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> ... 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> ... 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> ... 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		* <tex>\phi'''</tex> ... third derivative of <tex>\phi</tex> with respect to the local X axis of the member
	* <tex>I_{\omega}</tex> ... [[sectorial moment of inertia]]

	== Torsion of Solid Sections ==		== Torsion of Solid Sections ==

2009-09-22T03:20:45Z

Notation

← Older revision		Revision as of 05:20, 22 September 2009
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	* <tex>\phi''</tex> ... second 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		* <tex>\phi'''</tex> ... third derivative of <tex>\phi</tex> with respect to the local X axis of the member
			* <tex>I_{\omega}</tex> ... [[sectorial moment of inertia]]

	== Torsion of Solid Sections ==		== Torsion of Solid Sections ==

2009-09-22T03:16:02Z

Notation

← Older revision		Revision as of 05:16, 22 September 2009
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	== Notation ==		== Notation ==

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

	* <tex>\phi</tex> ... angle of rotation due to torsional moment		* <tex>\phi</tex> ... angle of rotation due to torsional moment

2009-09-22T03:15:10Z

← Older revision		Revision as of 05:15, 22 September 2009
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	* [[Saint Venant torsion theory]] - basic torsion theory for which [[warping]] is not restrained		* [[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		* [[Vlasov torsion theory]] - more general torsion theory for which warping can be restrained

			== Notation ==

			The following notation is used for the torsion topic:

			* <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 Solid Sections ==		== Torsion of Solid Sections ==

2009-09-22T02:35:32Z

Torsion Theories

← Older revision		Revision as of 04:35, 22 September 2009
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	== Torsion Theories ==		== Torsion Theories ==

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

	== Torsion of Solid Sections ==		== Torsion of Solid Sections ==

2009-09-22T02:33:32Z

← Older revision		Revision as of 04:33, 22 September 2009
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	* Michael R. Lindeburg: Civil Engineering Reference Manual for the PE Exam, 9th Edition, 2003, p. 45-14 (eq. 45.54)		* Michael R. Lindeburg: Civil Engineering Reference Manual for the PE Exam, 9th Edition, 2003, p. 45-14 (eq. 45.54)

	{{~~Elements of Design~~}}		{{Torsion}}

	[[Category:Glossary]]		[[Category:Glossary]]
	[[Category:Torsion]]		[[Category:Torsion]]