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Glossary entry

Spanish term or phrase:

eje principal de inercia

English translation:

major/minor principal inertia axis [for \"area moment of inertia\" - not to be confused with rotational inertia]

Added to glossary by Neil Ashby
Nov 9, 2014 20:06
9 yrs ago
3 viewers *
Spanish term

eje principal de inercia

Spanish to English Tech/Engineering Construction / Civil Engineering Eurocode structural calculations
Hi Kudozers,

I'm going a bit crazy over this!
From Spanish Spanish to UK English, please.

Taken from the structural calculations for an aluminium enclosure which use "Eurocode 9: design of aluminium structures" as a guide.

My problem is that "axis of inertia" is incorrect (no?) as the moment of inertia acts about (or is relevant to) an axis - I don't believe there is a such a thing as an "axis of inertia".
Below are a few examples of how the expression is used:

1) Mu,Ed: es el momento flector solicitante de cálculo alrededor del eje principal de inercia 'u' de la sección
bruta.

2) iv: es el radio de giro de la sección bruta respecto al eje principal de inercia 'v'.

3) Vv,Ed: es el esfuerzo cortante solicitante de cálculo en la dirección del eje principal de menor inercia 'v' de la sección bruta.

As an example my understanding of 1) would be: "Mu,Ed: is the design value of the bending moment about the gross cross-section's main axis of inertia 'u'. " >>> BUT "main axis of inertia", like I say it just doesn't make sense. Example 3) "eje principal de menor inercia 'v' " has me even more flummoxed.

My feeling is to just drop "of inertia" because I think that is what is being referred to - "the main axis 'u' (of the gross cross-section)", but this a 200 page document and it occurs 100s of times and I'm not keen on cutting it without checking!

https://law.resource.org/pub/eur/ibr/en.1999.1.1.2007.html
this a link to Eurocode 9 but I'm not sure if it the most recent version.

Any help appreciated.
TIA
Proposed translations (English)
3 +1 principal axis of inertia
References
findings

Discussion

Neil Ashby (asker) Nov 14, 2014:
This page explains the two different "inertias" and the reason for confusion,
http://mathworld.wolfram.com/AreaMomentofInertia.html
Neil Ashby (asker) Nov 10, 2014:
For those who are interested: I've finally found evidence in my source text of the incorrect use of the phrase "eje principal de inercia".

Iu: es el momento de inercia de la sección bruta respecto al eje principal de inercia 'u'.
>>>
Iu: is the gross cross-section's moment of inertia about the major principal axis 'u'. (the second "de inercia" is OTT).

From this definition I can see that the source adds "de inercia" where it is simply not needed, which has always been my suspicion (see original Q).

Another possibility is "major principal inertia axis" (which of course = 'axis of inertia', but seems more common and clearer, in my head at least) - this is the option I think I shall use, explain the first instances a bit more and then use "major/minor principal inertia axis/es"

Thank you all for your time and input.
Neil Ashby (asker) Nov 10, 2014:
Thanks to the four of you for your time and help ;@)

I'll let you know what I decide after re-submerging the old grey matter in the translation.

Neil
Neil Ashby (asker) Nov 10, 2014:
It's a good possibility Donal, and I think a real one to avoid massively complicating my life (I don't want to drastically length the 1000s of sentences in the calculations or it would mean a lot of re-formatting!!!). One full clear explanation at the beginning could be a good solution although the paper defines new terms which include the phrase "eje principal de inercia" hundreds of times.

I'll check out the practicality of the situation.
DLyons Nov 10, 2014:
Just define it it at the beginning and then use the shortest term. So, "in the following we use 'u' to mean ..." and subsequently "principal axis 'u' ". So 'u' presumably is the axis with lower moment of inertia, and 'v' the one with greater. Or as Star Trek says, "Make it so".
Neil Ashby (asker) Nov 10, 2014:
I'm thinking of the following options:

1) "principal axis 'u' about which inertia acts"

2) "principal axis of inertia 'u' " (taking it to be assumed as "principal axis 'u' about which moment of inertia acts")

3) "principal axis 'u' " i.e. do away with "de inercia" (the assumption being that it is the axis about which the moment of inertia acts, curiously the Eurocode does not mention "inertia" once, https://law.resource.org/pub/eur/ibr/en.1999.1.1.2007.html (possibly outdated version))

Any thoughts?
Neil Ashby (asker) Nov 10, 2014:
'u' and 'v' are the principal axes. As per Liz's last ref. - "just find the principal moments, not the axes. 6. ..... ***the principal axes and which ones have the least moment of inertia*** and the .."
The moments of inertia and the principal axes are two different parameters to be calculated (in all of my cases the principal axes are defined and do not need to be calculated). So I'm not keen on the term "axes of inertia", Liz's second ref. also explains what moment of inertia is in the context force calculations (as opposed to rotational accelerations). "The Moment of Inertia (I) is a term used to describe the capacity of a cross-section to resist bending. It is always considered with respect to a reference axis such as X-X or Y-Y." > Ixx or Iyy. (I for an axis perpendicular to the cross-section, J in the plane of the cross-section)
TravellingTrans Nov 10, 2014:
Maybe incorrect parsing is the problem? in number 1) & 2) the "of inertia 'u' and of inertia 'v'" may not be referring to the principal axis but instead the 1) es el momento flector solicitante de cálculo; and 2) es el radio de giro de la sección bruta

in other words, could it be rewritten:

1) alrededor del eje principal, es el momento flector solicitante de cálculo de inercia 'u' de la sección

2) respecto al eje principal, es el radio de giro de la sección bruta de inercia 'v'

or if that doesn't help see it, try:

1) es el momento flector solicitante de cálculo, alrededor del eje principal, de inercia 'u' de la sección
bruta.

2) es el radio de giro de la sección bruta, respecto al eje principal, de inercia 'v'.

I'm cuing off the way 1) & 3) put "inercia 'v' de la sección bruta" but 2) splits it

anyway it's offered as an alternate idea
Neil Ashby (asker) Nov 9, 2014:
Donal, the long way of saying "inertia" (in my head at least) is "moment of inertia about an axis", that's where I was getting my logic for the Spanish "ejes de inercia" = "axis of inertia" [about an axis]. Not wanting to be argumentative just explain better.

I'm not making myself easy to help!!!
Sorry but I do appreciate it.
Neil Ashby (asker) Nov 9, 2014:
Donal I think that ref. and the expression might only be correct for rotational inertia - moment of inertia applied to force calculations in construction members is the "second moment of area / area moment of inertia" - sorry I should have mentioned that before.

This is part of my problem - the definition of the "area moment of inertia", is that of being a plane (the cross-section) and so "axis of inertia" sticks in my throat.....

https://en.wikipedia.org/wiki/Second_moment_of_area

Having said that something is starting to clear in my head...just need to figure how to say it - having re-read the definition in Wiki 20 times I think I'm getting it! I'll sleep on it (tossing and turning due to the moment of inertia about the longitudinal axis of my body!)
DLyons Nov 9, 2014:
Hasta mañana ["axis of inertia" about an axis] wouldn't make sense - but I don't think it's saying that is it?
Neil Ashby (asker) Nov 9, 2014:
Donal, Liz, thanks for you input.... The way I understand it is that "inertia" is a moment (force) about an axis. So "axis of inertia" about an axis, doesn't hold sense for me.

You can find examples of "principle axes of inertia" (thanks Liz) but they really mean the "principle axes of the moment of inertia" and as you say Donal it's just shorthand.

Another problem for is why aren't there more examples of "axis/es of inertia" (just a few hundred) if it were a typical expression used in structural calcs. (all the expression occur frequently on the internet)?

Moment of inertia and the (arbitrary direction of the) principle axes are two different parameters, "main axis/es of inertia" appears to combine them when they can't be combined.

I'll have a look at your refs. and see if I can figure it out in the morning (fortunately no rush...) when I think coffee might help more than Ribera del Duero is currently doing.
DLyons Nov 9, 2014:
I think it's valid to say "axis of inertia" as a shorthand
http://www2.eng.cam.ac.uk/~hemh/gyroscopes/momentinertia.htm...

There are three principal axes X, Y,Z around which roll/pitch/yaw happen. Each has a moment of inertia and so can (I don't say should) be called an axis of inertia.

Main axis of inertia would just be the smallest of these? Or might it be the greatest??

Proposed translations

+1
23 mins
Selected

principal axis of inertia

My feeling is that this is the principal axis of rotation which has the minimum moment of inertia (smallest eigenvalue of the Inertia Matrix).

--------------------------------------------------
Note added at 2 hrs (2014-11-09 22:51:44 GMT)
--------------------------------------------------

In principle, it's the same in 2D - there's a moment of inertia tensor J [19] http://mathworld.wolfram.com/AreaMomentofInertia.html . We then diagonalize J to get the directions of the shape’s principal axes (same thing as the axes of its best-fit ellipse).

I agree it sounds even odder in 2D, but I don't see what else it can be. For "eje principal de menor inercia 'v' de la sección bruta" I suggest "the minimum inertia principal axis, v, of the gross section" (I'm assuming that v is a 2D vector).

--------------------------------------------------
Note added at 9 hrs (2014-11-10 05:21:51 GMT)
--------------------------------------------------

See P878 et seq of http://books.google.ie/books?id=kNwe9z06ZLkC&pg=PA878 This and Wolfram are much more reliable than Wiki. It uses standard notation which reinforces my feeling that u and v are to be read as vectors rather than scalar values.
Note from asker:
You mean for my third example? I agree with that, but the problem is "del eje principal de menor inercia 'v' de la sección bruta." Where do we stick "v" ? ;@) "principal axis of rotation which has the minimum moment of inertia" it's straying quite a long way from the source, which scares me a bit if I'm going to do it a few hundred times!
"the minimum inertia principal axis, v, of the gross section" I like that.... thanks. Yes I think they are vectors but directly from Eurocode 9: "x - x axis along a member y - y axis of a cross-section z - z axis of a cross-section u - u major principal axis (where this does not coincide with the y-y axis) v - v minor principal axis (where this does not coincide with the z-z axis)" (https://law.resource.org/pub/eur/ibr/en.1999.1.1.2007.html) It's difficult to get clear information, different sources use different terminology, notation, etc...
Your last ref. has the solution, I think, "the moments of inertias with respect to principal axes are called 'principal moments of inertia' " - this gives them a name without using "axis" :@)
Peer comment(s):
agree Jennifer Levey : Yes, it's the axis around which the interia is acting circumferentially. This certainly fits the second example.
2 hrs
Thanks Robin.
Something went wrong...
3 KudoZ points awarded for this answer. Comment: "Thanks for the discussion D. Liz's sources were also useful in confirming things in my mind. In the end I've given a slightly longer explanation at the beginning and then used "major principal inertia axis U / minor principal inertia axis V" or "the principal axes of inertia". "

Reference comments

8 mins
Reference:

findings

norma española - Escuela Universitaria de Ingeniería ...
www.op.upm.es/index.php?option=com...
•
Translate this page
Eurocode 3: Calcul des structures en acier. Partie 1-1: Règles ...... EN 1999 Eurocódigo 9: Proyecto de estructuras de aluminio. 1) Acuerdo entre la ..... eje principal mayor (cuando éste no coincida con el eje y-y);. v-v ..... momento de inerciadel ala comprimida reducida respecto al eje débil de la sección;. Aeff,f área del ala ...

http://fp.optics.arizona.edu/optomech/references/OPTI_222/OP...

Moment of Inertia and Properties of Plane Areas
The Moment of Inertia (I) is a term used to describe the capacity of a cross-section to
resist bending. It is always considered with respect to a reference axis such as X-X or
Y-Y. It is a mathematical property of a section concerned with a surface area and how
that area is distributed about the reference axis (axis of interest). The reference axis is
usually a centroidal axis.
1. Structural Analysis - Moment of Inertia of a section
civilengineer.webinfolist.com/str/mi.htm
o
o
31 Jan 2013 - Moment of Inertia about y-y axis. Moment of Inertia of some standard areas can be found below. 1. Rectangular section;. (a) Ixx = (bd3)/12.


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Note added at 12 mins (2014-11-09 20:19:28 GMT)
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http://www.monografias.com/trabajos35/momentos-inercia/momen...

SELECCIÓN DE LA POSICIÓN DE LOS EJES DE REFERENCIA
Se necesitan tres ejes de referencia para definir el centro de gravedad, pero sólo se necesita un eje para definir el momento de inercia. Aunque cualquier eje puede ser de referencia, es deseable seleccionar los ejes de rotación del objeto como referencia. Si el objeto está montado sobre soportes, el eje está definido por la línea central de los soportes. Si el objeto vuela en el espacio, entonces ***este eje es un "eje principal"*** (ejes que pasan por el Cg y están orientado de forma que el producto de inercia alrededor de ese eje es cero). Si el eje de referencia se va a utilizar para calcular el momento de inercia de la forma compleja, se debe elegir un eje de simetría para simplificar el cálculo. Este eje puede ser trasladado, más tarde, a otro eje si se desea, utilizando las reglas descritas en el apartado


Leer más: http://www.monografias.com/trabajos35/momentos-inercia/momen...

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Note added at 13 mins (2014-11-09 20:20:13 GMT)
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Lecture 34: Principal Axes of Inertia
www.physics.arizona.edu/~varnes/Teaching/321Fall2004/.../Le...
Lecture 34: Principal Axes of Inertia. • We've spent the last few lectures deriving the general expressions for L and T rot in terms of the inertia tensor.

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Note added at 15 mins (2014-11-09 20:21:56 GMT)
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HW 9
www.physics.uci.edu/~tanedo/files/teaching/P3318S13/HW9_sol...
H&F 8.3 For the physical tensor, just find the principal moments, not the axes. 6. ..... ***the principal axes and which ones have the least moment of inertia*** and the ..

I think you may be right about the Spanish wording not being clear, but you will need to clarify in the translation what the exact meaning is:)
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