eje principal de inercia

11:00 Nov 14, 2014 

and the reason for confusion,
http://mathworld.wolfram.com/AreaMomentofInertia.html

11:45 Nov 10, 2014 

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.

11:05 Nov 10, 2014 

;@)

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

Neil

11:03 Nov 10, 2014 

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.

10:42 Nov 10, 2014 

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".

10:39 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the Eurocode does not mention "inertia" once, https://law.resource.org/pub/eur/ibr/en.1999.1.1.2007.html (possibly outdated version))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?

10:25 Nov 10, 2014 

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)

02:09 Nov 10, 2014 

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

21:04 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.

20:56 Nov 9, 2014 

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!)

20:51 Nov 9, 2014 

["axis of inertia" about an axis] wouldn't make sense - but I don't think it's saying that is it?

20:45 Nov 9, 2014 

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.

20:15 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??