Talk:Second moment of area

message: This section must be checked by an expert.
* Deutsch page has any reference and show a - sign for Ixy, which means there are wrong formulae on the web.
* Spanish page refers the same Spanish book ... But I could not trust the formulae against the English one using symbolic computation (Sympy):
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)
thread_title:  Polygon 

message: 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)
thread_title:  first comments 

message: I had several problems with the changes made by 69.251.146.46:
*The lead sentence shouldn't be about what it is confused with.
*Polar moment of area -- much less frequently used than polar moment of inertia... dead linkage
Nephron  T|C 02:49, 25 August 2006 (UTC)
thread_title:  reverting 

message: The definition does not state what areas are to be summed in the integral. 
* The elements of area comprising the surface of a body? 
* The cross sectional areas perpendicular to an axis, such that with a thickness, the volume of the body is accounted for?
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)
replies: text: I think the bit that needed clarifying was that this a property of a cross section of body, not of a body. The area to include in the integral is simply the area of the cross section. Do you have any suggestions for further clarifications? 77.215.191.91 (talk) 17:00, 24 November 2009 (UTC)
thread_title:  The definition is incomplete 

message: Something should be said about the product moment of area in this section. If I remember correctly, the formula used for that transformation is:
I_{xy}'= I_{xy} + Axy
-- Fernando Estel ☆ · 星 (Talk: here- commons- es) 10:21, 13 June 2010 (UTC)
thread_title:  Parallel axis theorem 

message: 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)
replies: text: I agree with everything above, but furthermore the second paragraph of 'Intuition' is not consistent with the first. Rewrite is needed: watch, as they don't say, that space! 86.176.166.181 (talk) 00:37, 17 April 2012 (UTC)
thread_title:  Intuition 

message: 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)
thread_title:  Questionable link 

message: 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)
thread_title:  Readership? 

message: 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:
* if it mentioned any form of beam theory then it doesn't belong here.  
* if it mentioned any form of stress then it has no place in this article
* examples must be exclusively about an area's geometric properties, because that's what any moment of area does
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)
replies: text: < if it mentioned any form of beam theory then it doesn't belong here. > Why is that? It says right on this talk page that this is a Civil Engineering topic! 109.151.253.181 (talk) 21:17, 13 November 2013 (UTC)
thread_title:  Major cleanup 

message: 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)
thread_title:  Major Rework 

message: 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 J_z directly, not I_x or I_y.  I think someone who edited it after me got confused about what I was calculating and changed some stuff to I_z if I recall correctly.  I just wanted to justify why I switched it back. -- Chiraag.nataraj (talk) 23:00, 27 April 2013 (UTC)
thread_title:  Annulus 

message: 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)
thread_title:  Current State of Momentum 

message: 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)
thread_title:  Updated 

message: 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)
thread_title: Polygon