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This section must be checked by an expert.
E1 = sympify('(yi**2 + yi*yi1 + yi1**2)*(xi * yi1 - xi1 * yi)')
E2 = sympify('(xi1-xi)*(yi1+yi)*(yi1**2+yi**2)') — Preceding unsigned comment added by 90.43.11.93 ( talk) 21:18, 2 October 2018 (UTC)
The calculation of "y" the distance to the centroid is incorrect. It should be:
y=(h+h1)/4
John.g.taylor 04:30, 28 May 2007 (UTC)
I think the second moment of area is different to the second moment of inertia.
John.g.taylor 04:29, 28 May 2007 (UTC)
Specifically:
Second moment of inertia = rather than dA. ..
The second moment of area is a more general concept. For example the static roll stability of a ship depends on the second moment of area of the waterline section - short fat ships are stable, long thin ones are not. Gordon Vigurs 08:10, 11 July 2006 (UTC)
As a Swede I find it strange that "area moment of inertia" is the last choice. In Swedish that is what we call it: "yttröghetsmoment". Compare to moment of inertia = sum up all the infinitesimal mass elements multiplied by the lever squared, versus area moment of inertia = sum up all the infinitesimal area elements multiplied by the lever squared. — Preceding unsigned comment added by 83.223.9.100 ( talk) 11:51, 23 October 2023 (UTC)
I had several problems with the changes made by 69.251.146.46:
Nephron T| C 02:49, 25 August 2006 (UTC)
'I' in the stress bending eqn should be for 2nd moment of area. I referred this from 'Mechanics of solids and structures', Benham, P.P. ISBN: 0273361910
It is requested that a physics diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
This article needs some diagrams to go with the formulas, to make the variables clear.
Some body needs to translate and lift the diagrams from the De page on this
Comment moved from article to talk ( RJFJR 15:14, 2 May 2007 (UTC)) "I-beam" cross section
I have found the math here too sloppy to be understandable. I suggest to put (7) from http://www.dynamore.de/documents/papers/euro4/implicit-new-developments/ls-dyna-beam-elements-default-and-user-defined as an example of rectangular cross section beam. This was what made me understand the concept. —Preceding unsigned comment added by 145.236.252.34 ( talk) 10:45, 14 October 2009 (UTC)
This material on the "product moment of area" was int eh article but seems to lack context and explanation:
What is this used for? Is it really related to the second moment because an object with both x-axis and y-axis symmetry would have a value of zero, whcih is certainly not true of the second moment (it more resembles a first moment). Can we clearify this before we put it back in teh article, if this is where it belongs. And why does this have a redlink? RJFJR 13:48, 6 May 2007 (UTC)
There is a discussion of mast calculations in here under the section on the second moment of area of a circular cross section. Everything the section mentions is true but are mast calculations really an important enough consideration to warrant a mention here? I think it adds unnecessary length to the article. I am cleaning the section up some but it needs to be considered for deletion anyway.
The definition does not state what areas are to be summed in the integral.
At each point with coordinates (x,y,z), there are infinitely many surfaces including that point, each with a different orientation. Which of them should be included in the sum?
Can the sum include area elements that overlap?
The definition lacks every hint of context. It is understandable only for those who already know what it means. Cacadril ( talk) 16:25, 24 November 2009 (UTC)
This page is not about second moment of area any more, it is about bending stress and strain.
I think it should be possible to define this concept mathematically, and then proceed to show how it is applied in various contexts, and notably for computation of bending stresses, with limitations and conditions. Perhaps the article should be renamed, and a new article about the specific mathematical concept be written. Cacadril ( talk) 05:15, 15 February 2010 (UTC)
Something should be said about the product moment of area in this section. If I remember correctly, the formula used for that transformation is:
-- Fernando Estel ☆ · 星 (Talk: here- commons- es) 10:21, 13 June 2010 (UTC)
As a non-expert I would like to know why the 'moment of inertia' of the cross-section of a beam is important in relation to stiffness or laibility to failure (Strength). I found the introduction of elastic stored energy unhelpful. Its relevance is not at all clear from what is written. What is required is an explanation of 2 independent relationships to radius. For example, in the case of rotational moment of inertia, I could explain how moment of inertia relates to torque and angular acceleration and then show that a particle of mass at radius r accelerates more as r is increased, and also how the moment of the accelerating force increases with r, thus giving an overall dependence on r^2. I would appreciate an analogous approach with 2nd moment of area, bending moment, and deflection (or condition of failure), or whatever the concepts are which are most relevant. Why is integral(r^2)da a significant metric; why is the square of the radius of an element of area important ? At present the underlying principles of the analysis remain obscure (to me at least). I think that the effective explanation of concepts in simple terms is a particular skill and needs more careful thought than is being used at present. —Preceding unsigned comment added by G4oep ( talk • contribs) 09:04, 24 October 2010 (UTC)
In the section "Product moment of area", the linked reference to "Pilkey 2002" does not seem to work, and I cannot find a book by that title or an book on a related subject by "Pilkey". Please clarify.
NextThreshold ( talk) 12:31, 5 July 2011 (UTC)
I'd be interested to know for whom the article in its current state - with 'a symmetric tensor' in the third paragraph and 'Minimum total potential energy principle' in the fourth - is intended. You really don't need to know about the Kronecker delta before you can form a working understanding of second moment of area. 86.185.64.17 ( talk) 01:55, 2 April 2012 (UTC)
I've cleaned up the article, which included a whole lot of nonsense and stuff which was simply wrong. The criteria for the cleanup was:
This article is still a bit incomplete, but at least now it doesn't include blatant errors and misconceptions about its subject. -- Mecanismo | Talk 13:00, 10 February 2013 (UTC)
If your work removed the blatant errors, etc, could you change the cleanup tag to reflect its current state? 165.121.80.228 ( talk) 10:35, 1 April 2013 (UTC)
I've reworked a lot of what was in the article to get rid of mentions to cross-section (still remnant of the beam-theory days). Also fixed some of the linkages. Added simple sections about parallel and perpendicular axis theorems and composite shapes. And removed the unnecessary example that just pulls from the list. I only kept (and reorganized) examples that exploit some calculation of the second moment of area.
The only thing I have a question about is the product of inertia. Should this article include this? Or should we rewrite the existing page for product of inertia that just links here?
Also, I didn't remove the messages at the top. I would like someone else to review the article and clear them if they feel it's cleared up the issues. — Preceding unsigned comment added by BeaumontTaz ( talk • contribs) 04:13, 14 April 2013 (UTC)
So I changed some stuff in the Annulus section of the page. One thing to keep in mind (and I clarified this in a later edit) is that with that integral, I was calculating directly, not or . I think someone who edited it after me got confused about what I was calculating and changed some stuff to if I recall correctly. I just wanted to justify why I switched it back. -- Chiraag.nataraj ( talk) 23:00, 27 April 2013 (UTC)
- Hey. I'm the user who edited it after you changed it. Honestly, I think I was looking at an older version of your series of edits, not the final one. What I saw reflected
this edit. My apologies for the confusion. I believe the article looks good. Thank you for the edit! — Preceding
unsigned comment added by
BeaumontTaz (
talk •
contribs) 02:18, 28 April 2013 (UTC)
Ah I see. Thanks for the clarification! :) -- Chiraag.nataraj ( talk) 18:02, 28 April 2013 (UTC)
I have looked at the recent edits and can see major improvements, that result in a clarity of understanding. Keep up the Good Work! DPHutchins ( talk) 05:44, 11 July 2013 (UTC)
I have read through the formulae and confirmed that all are correct (up to the polygons -- I didn't check that one.)
It's worth noticing here that there are two communities playing tug-of-war over this article: the math/physics people who keep saying that it is fundamentally wrong and the engineering-type folks who are trying to make it useful for us. The formulae that are here now match both the basic fundamental mathematics and principally the useage in engineering. I'd propose that the big warning at the top of the page be removed.
I also tried to clean up some of the references. Annahoward ( talk) 13:54, 24 March 2015 (UTC)annahoward
I found an appropriate reference.
https://apps.dtic.mil/dtic/tr/fulltext/u2/a183444.pdf
I will program these equations and verify them against known results.
Also, there are some explanations on how to deal with disconnected polygons and polygons with holes.
Diego Torquemada ( talk) 16:48, 19 May 2019 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
This section must be checked by an expert.
E1 = sympify('(yi**2 + yi*yi1 + yi1**2)*(xi * yi1 - xi1 * yi)')
E2 = sympify('(xi1-xi)*(yi1+yi)*(yi1**2+yi**2)') — Preceding unsigned comment added by 90.43.11.93 ( talk) 21:18, 2 October 2018 (UTC)
The calculation of "y" the distance to the centroid is incorrect. It should be:
y=(h+h1)/4
John.g.taylor 04:30, 28 May 2007 (UTC)
I think the second moment of area is different to the second moment of inertia.
John.g.taylor 04:29, 28 May 2007 (UTC)
Specifically:
Second moment of inertia = rather than dA. ..
The second moment of area is a more general concept. For example the static roll stability of a ship depends on the second moment of area of the waterline section - short fat ships are stable, long thin ones are not. Gordon Vigurs 08:10, 11 July 2006 (UTC)
As a Swede I find it strange that "area moment of inertia" is the last choice. In Swedish that is what we call it: "yttröghetsmoment". Compare to moment of inertia = sum up all the infinitesimal mass elements multiplied by the lever squared, versus area moment of inertia = sum up all the infinitesimal area elements multiplied by the lever squared. — Preceding unsigned comment added by 83.223.9.100 ( talk) 11:51, 23 October 2023 (UTC)
I had several problems with the changes made by 69.251.146.46:
Nephron T| C 02:49, 25 August 2006 (UTC)
'I' in the stress bending eqn should be for 2nd moment of area. I referred this from 'Mechanics of solids and structures', Benham, P.P. ISBN: 0273361910
It is requested that a physics diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
This article needs some diagrams to go with the formulas, to make the variables clear.
Some body needs to translate and lift the diagrams from the De page on this
Comment moved from article to talk ( RJFJR 15:14, 2 May 2007 (UTC)) "I-beam" cross section
I have found the math here too sloppy to be understandable. I suggest to put (7) from http://www.dynamore.de/documents/papers/euro4/implicit-new-developments/ls-dyna-beam-elements-default-and-user-defined as an example of rectangular cross section beam. This was what made me understand the concept. —Preceding unsigned comment added by 145.236.252.34 ( talk) 10:45, 14 October 2009 (UTC)
This material on the "product moment of area" was int eh article but seems to lack context and explanation:
What is this used for? Is it really related to the second moment because an object with both x-axis and y-axis symmetry would have a value of zero, whcih is certainly not true of the second moment (it more resembles a first moment). Can we clearify this before we put it back in teh article, if this is where it belongs. And why does this have a redlink? RJFJR 13:48, 6 May 2007 (UTC)
There is a discussion of mast calculations in here under the section on the second moment of area of a circular cross section. Everything the section mentions is true but are mast calculations really an important enough consideration to warrant a mention here? I think it adds unnecessary length to the article. I am cleaning the section up some but it needs to be considered for deletion anyway.
The definition does not state what areas are to be summed in the integral.
At each point with coordinates (x,y,z), there are infinitely many surfaces including that point, each with a different orientation. Which of them should be included in the sum?
Can the sum include area elements that overlap?
The definition lacks every hint of context. It is understandable only for those who already know what it means. Cacadril ( talk) 16:25, 24 November 2009 (UTC)
This page is not about second moment of area any more, it is about bending stress and strain.
I think it should be possible to define this concept mathematically, and then proceed to show how it is applied in various contexts, and notably for computation of bending stresses, with limitations and conditions. Perhaps the article should be renamed, and a new article about the specific mathematical concept be written. Cacadril ( talk) 05:15, 15 February 2010 (UTC)
Something should be said about the product moment of area in this section. If I remember correctly, the formula used for that transformation is:
-- Fernando Estel ☆ · 星 (Talk: here- commons- es) 10:21, 13 June 2010 (UTC)
As a non-expert I would like to know why the 'moment of inertia' of the cross-section of a beam is important in relation to stiffness or laibility to failure (Strength). I found the introduction of elastic stored energy unhelpful. Its relevance is not at all clear from what is written. What is required is an explanation of 2 independent relationships to radius. For example, in the case of rotational moment of inertia, I could explain how moment of inertia relates to torque and angular acceleration and then show that a particle of mass at radius r accelerates more as r is increased, and also how the moment of the accelerating force increases with r, thus giving an overall dependence on r^2. I would appreciate an analogous approach with 2nd moment of area, bending moment, and deflection (or condition of failure), or whatever the concepts are which are most relevant. Why is integral(r^2)da a significant metric; why is the square of the radius of an element of area important ? At present the underlying principles of the analysis remain obscure (to me at least). I think that the effective explanation of concepts in simple terms is a particular skill and needs more careful thought than is being used at present. —Preceding unsigned comment added by G4oep ( talk • contribs) 09:04, 24 October 2010 (UTC)
In the section "Product moment of area", the linked reference to "Pilkey 2002" does not seem to work, and I cannot find a book by that title or an book on a related subject by "Pilkey". Please clarify.
NextThreshold ( talk) 12:31, 5 July 2011 (UTC)
I'd be interested to know for whom the article in its current state - with 'a symmetric tensor' in the third paragraph and 'Minimum total potential energy principle' in the fourth - is intended. You really don't need to know about the Kronecker delta before you can form a working understanding of second moment of area. 86.185.64.17 ( talk) 01:55, 2 April 2012 (UTC)
I've cleaned up the article, which included a whole lot of nonsense and stuff which was simply wrong. The criteria for the cleanup was:
This article is still a bit incomplete, but at least now it doesn't include blatant errors and misconceptions about its subject. -- Mecanismo | Talk 13:00, 10 February 2013 (UTC)
If your work removed the blatant errors, etc, could you change the cleanup tag to reflect its current state? 165.121.80.228 ( talk) 10:35, 1 April 2013 (UTC)
I've reworked a lot of what was in the article to get rid of mentions to cross-section (still remnant of the beam-theory days). Also fixed some of the linkages. Added simple sections about parallel and perpendicular axis theorems and composite shapes. And removed the unnecessary example that just pulls from the list. I only kept (and reorganized) examples that exploit some calculation of the second moment of area.
The only thing I have a question about is the product of inertia. Should this article include this? Or should we rewrite the existing page for product of inertia that just links here?
Also, I didn't remove the messages at the top. I would like someone else to review the article and clear them if they feel it's cleared up the issues. — Preceding unsigned comment added by BeaumontTaz ( talk • contribs) 04:13, 14 April 2013 (UTC)
So I changed some stuff in the Annulus section of the page. One thing to keep in mind (and I clarified this in a later edit) is that with that integral, I was calculating directly, not or . I think someone who edited it after me got confused about what I was calculating and changed some stuff to if I recall correctly. I just wanted to justify why I switched it back. -- Chiraag.nataraj ( talk) 23:00, 27 April 2013 (UTC)
- Hey. I'm the user who edited it after you changed it. Honestly, I think I was looking at an older version of your series of edits, not the final one. What I saw reflected
this edit. My apologies for the confusion. I believe the article looks good. Thank you for the edit! — Preceding
unsigned comment added by
BeaumontTaz (
talk •
contribs) 02:18, 28 April 2013 (UTC)
Ah I see. Thanks for the clarification! :) -- Chiraag.nataraj ( talk) 18:02, 28 April 2013 (UTC)
I have looked at the recent edits and can see major improvements, that result in a clarity of understanding. Keep up the Good Work! DPHutchins ( talk) 05:44, 11 July 2013 (UTC)
I have read through the formulae and confirmed that all are correct (up to the polygons -- I didn't check that one.)
It's worth noticing here that there are two communities playing tug-of-war over this article: the math/physics people who keep saying that it is fundamentally wrong and the engineering-type folks who are trying to make it useful for us. The formulae that are here now match both the basic fundamental mathematics and principally the useage in engineering. I'd propose that the big warning at the top of the page be removed.
I also tried to clean up some of the references. Annahoward ( talk) 13:54, 24 March 2015 (UTC)annahoward
I found an appropriate reference.
https://apps.dtic.mil/dtic/tr/fulltext/u2/a183444.pdf
I will program these equations and verify them against known results.
Also, there are some explanations on how to deal with disconnected polygons and polygons with holes.
Diego Torquemada ( talk) 16:48, 19 May 2019 (UTC)