StructuralWiki - User contributions [en]

Moment area method

2012-12-04T01:13:07Z

RTFVerterra:

The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]].

== First Theorem ==

[[Image:Moment area method theorem 1(b).gif|right|frame|Picture illustrating the first theorem]]

'''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>
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
</tex>

where

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

== 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.

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

where

* M moment
* EI flexural rigidity
* <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 ==

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

== 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

{{Traditional Analysis Methods}}

[[Category:Glossary]]

Moment area method

2012-12-04T01:09:42Z

RTFVerterra: /* External links */

The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]].

== First Theorem ==

[[Image:Moment area method theorem 1(b).gif|right|frame|Picture illustrating the first theorem]]

'''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>
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
</tex>

where

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

== 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.

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

where

* M moment
* EI flexural rigidity
* <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 ==

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

== 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

{{Traditional Analysis Methods}}

[[Category:Glossary]]

Moment area method

2011-09-16T08:37:35Z

RTFVerterra: /* External links */

The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]].

== First Theorem ==

[[Image:Moment area method theorem 1(b).gif|right|frame|Picture illustrating the first theorem]]

'''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>
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
</tex>

where

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

== 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.

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

where

* M moment
* EI flexural rigidity
* <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 ==

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

== 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
* [http://cereview.info/book/theory-structures/solution-restrained-beams-moment-area-method Solution of Restrained Beams by Moment Area Method]

{{Traditional Analysis Methods}}

[[Category:Glossary]]

Moment area method

2010-05-03T08:06:55Z

RTFVerterra: /* References */

The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]].

== First Theorem ==

[[Image:Moment area method theorem 1(b).gif|right|frame|Picture illustrating the first theorem]]

'''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>
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
</tex>

where

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

== 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.

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

where

* M moment
* EI flexural rigidity
* <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 ==

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

== 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

{{Traditional Analysis Methods}}

[[Category:Glossary]]

Moment area method

2010-05-03T08:03:54Z

RTFVerterra: /* External links */

The method for finding [[deflection|deflections]] in a framed structure by use of the [[moment area|moment area curve]].

== First Theorem ==

[[Image:Moment area method theorem 1(b).gif|right|frame|Picture illustrating the first theorem]]

'''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>
\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx
</tex>

where

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

== 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.

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

where

* M moment
* EI flexural rigidity
* <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 ==

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

=== 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

{{Traditional Analysis Methods}}

[[Category:Glossary]]