Moment area method - Revision history

Ok: Text replacement - "" to ""

2024-10-22T01:32:45Z

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

← Older revision		Revision as of 03:32, 22 October 2024
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	<math>		<math>
	\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx		\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
	</~~tex~~>		</math>

	where		where
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	* M moment		* M moment
	* EI flexural rigidity		* EI flexural rigidity
	* <math>\theta_{AB}</~~tex~~> ... change in slope between points A and B		* <math>\theta_{AB}</math> ... change in slope between points A and B
	* A, B ... points on the elastic curve		* A, B ... points on the elastic curve

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	[[Image:Moment area method theorem 2.gif\|right\|frame\|Picture illustrating the second theorem]]		[[Image:Moment area method theorem 2.gif\|right\|frame\|Picture illustrating the second theorem]]

	'''Theorem 2:''' The deviation of the tangent at point B on the elastic curve with respect to the tangent at point A equals the "moment" of the <math>M/EI</~~tex~~> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <math>t_{A/B}</~~tex~~> is to be determined.		'''Theorem 2:''' The deviation of the tangent at point B on the elastic curve with respect to the tangent at point A equals the "moment" of the <math>M/EI</math> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <math>t_{A/B}</math> is to be determined.

	<math>		<math>
	t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx		t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx
	</~~tex~~>		</math>

	where		where
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	* M moment		* M moment
	* EI flexural rigidity		* EI flexural rigidity
	* <math>t_{A/B}</~~tex~~> ... deviation of tangent at point B with respect to the tangent at point A		* <math>t_{A/B}</math> ... deviation of tangent at point B with respect to the tangent at point A
	* <math>\bar{x}</~~tex~~> ... centroid of M/EI diagram measured horizontally from point A		* <math>\bar{x}</math> ... centroid of M/EI diagram measured horizontally from point A
	* A, B ... points on the elastic curve		* A, B ... points on the elastic curve

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

2024-10-22T00:35:37Z

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

← Older revision		Revision as of 02:35, 22 October 2024
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	'''Theorem 1:''' The change in slope between any two points on the [[elastic curve]] equals the area of the M/EI diagram between these two points.		'''Theorem 1:''' The change in slope between any two points on the [[elastic curve]] equals the area of the M/EI diagram between these two points.

	<~~tex~~>		<math>
	\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx		\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
	</tex>		</tex>
Line 15:		Line 15:
	* M moment		* M moment
	* EI flexural rigidity		* EI flexural rigidity
	* <~~tex~~>\theta_{AB}</tex> ... change in slope between points A and B		* <math>\theta_{AB}</tex> ... change in slope between points A and B
	* A, B ... points on the elastic curve		* A, B ... points on the elastic curve

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	[[Image:Moment area method theorem 2.gif\|right\|frame\|Picture illustrating the second theorem]]		[[Image:Moment area method theorem 2.gif\|right\|frame\|Picture illustrating the second theorem]]

	'''Theorem 2:''' The deviation of the tangent at point B on the elastic curve with respect to the tangent at point A equals the "moment" of the <~~tex~~>M/EI</tex> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <~~tex~~>t_{A/B}</tex> is to be determined.		'''Theorem 2:''' The deviation of the tangent at point B on the elastic curve with respect to the tangent at point A equals the "moment" of the <math>M/EI</tex> diagram between points A and B computed about point A (the point on the elastic curve), where the deviation <math>t_{A/B}</tex> is to be determined.

	<~~tex~~>		<math>
	t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx		t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx
	</tex>		</tex>
Line 32:		Line 32:
	* M moment		* M moment
	* EI flexural rigidity		* EI flexural rigidity
	* <~~tex~~>t_{A/B}</tex> ... deviation of tangent at point B with respect to the tangent at point A		* <math>t_{A/B}</tex> ... deviation of tangent at point B with respect to the tangent at point A
	* <~~tex~~>\bar{x}</tex> ... centroid of M/EI diagram measured horizontally from point A		* <math>\bar{x}</tex> ... centroid of M/EI diagram measured horizontally from point A
	* A, B ... points on the elastic curve		* A, B ... points on the elastic curve

RTFVerterra at 01:13, 4 December 2012

2012-12-04T01:13:07Z

← Older revision		Revision as of 03:13, 4 December 2012
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	<tex>		<tex>
	t_{A/B} = ~~\bar{x}~~ {\int_A}^B \frac{M}{EI}\;dx		t_{A/B} = {\int_A}^B \frac{M}{EI} \bar{x} \;dx
	</tex>		</tex>

RTFVerterra: /* External links */

2012-12-04T01:09:42Z

External links

← Older revision		Revision as of 03:09, 4 December 2012
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	* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-in-simply-supported-beams-area-moment-method Deflection of Simply Supported Beam by Area Moment Method]		* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-in-simply-supported-beams-area-moment-method Deflection of Simply Supported Beam by Area Moment Method]
	* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007		* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007
	* [http://cereview.info/book/theory-structures/solution-restrained-beams-moment-area-method Solution of Restrained Beams by Moment Area Method]

	{{Traditional Analysis Methods}}		{{Traditional Analysis Methods}}

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

RTFVerterra: /* External links */

2011-09-16T08:37:35Z

External links

← Older revision		Revision as of 10:37, 16 September 2011
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	* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-in-simply-supported-beams-area-moment-method Deflection of Simply Supported Beam by Area Moment Method]		* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-in-simply-supported-beams-area-moment-method Deflection of Simply Supported Beam by Area Moment Method]
	* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007		* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007
			* [http://cereview.info/book/theory-structures/solution-restrained-beams-moment-area-method Solution of Restrained Beams by Moment Area Method]

	{{Traditional Analysis Methods}}		{{Traditional Analysis Methods}}

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

RTFVerterra: /* References */

2010-05-03T08:06:55Z

References

← Older revision		Revision as of 10:06, 3 May 2010
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	* Russel C. Hibbeler: Structural Analysis, 3rd Edition, Prentice Hall, 1995, chapter 8, p. 354-569, ISBN 0-02-354041-9		* Russel C. Hibbeler: Structural Analysis, 3rd Edition, Prentice Hall, 1995, chapter 8, p. 354-569, ISBN 0-02-354041-9

	=== External links ===		== External links ==

	* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-of-cantilever-beams-area-moment-method Deflection of Cantilever Beam by Area Moment Method]		* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-of-cantilever-beams-area-moment-method Deflection of Cantilever Beam by Area Moment Method]

RTFVerterra: /* External links */

2010-05-03T08:03:54Z

External links

← Older revision		Revision as of 10:03, 3 May 2010
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	=== External links ===		=== External links ===

			* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-of-cantilever-beams-area-moment-method Deflection of Cantilever Beam by Area Moment Method]
			* [http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/deflection-in-simply-supported-beams-area-moment-method Deflection of Simply Supported Beam by Area Moment Method]
	* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007		* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007

Ok at 02:56, 22 March 2009

2009-03-22T02:56:07Z

← Older revision		Revision as of 04:56, 22 March 2009
Line 39:		Line 39:

	* Russel C. Hibbeler: Structural Analysis, 3rd Edition, Prentice Hall, 1995, chapter 8, p. 354-569, ISBN 0-02-354041-9		* Russel C. Hibbeler: Structural Analysis, 3rd Edition, Prentice Hall, 1995, chapter 8, p. 354-569, ISBN 0-02-354041-9

			=== External links ===

			* Colin Caprani: [http://www.colincaprani.com/files/notes/SAIII/Mohrs%20Theorems.pdf Structural Analysis III The Moment Area Method – Mohr’s Theorems] (lecture notes), 2007

	{{Traditional Analysis Methods}}		{{Traditional Analysis Methods}}

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

Ok: /* First Theorem */

2009-03-22T02:48:52Z

First Theorem

← Older revision		Revision as of 04:48, 22 March 2009
Line 16:		Line 16:
	* EI flexural rigidity		* EI flexural rigidity
	* <tex>\theta_{AB}</tex> ... change in slope between points A and B		* <tex>\theta_{AB}</tex> ... change in slope between points A and B
			* A, B ... points on the elastic curve

	== Second Theorem ==		== Second Theorem ==

Ok: /* Second Theorem */

2009-03-22T02:48:38Z

Second Theorem

← Older revision		Revision as of 04:48, 22 March 2009
Line 32:		Line 32:
	* EI flexural rigidity		* EI flexural rigidity
	* <tex>t_{A/B}</tex> ... deviation of tangent at point B with respect to the tangent at point A		* <tex>t_{A/B}</tex> ... deviation of tangent at point B with respect to the tangent at point A
			* <tex>\bar{x}</tex> ... centroid of M/EI diagram measured horizontally from point A
			* A, B ... points on the elastic curve

	== References ==		== References ==