Principal direction, principal moments

[Anonymous]

Can anyone tell me what these properties mean?

Thanks!

--
Bob Q
Pentium 4 3.33 GHz
1GB RAM
XP Pro SP2
ATI Mobility Radeon 9000 IGP graphics.....
MDT 2004DX

[Anonymous]

Here's the massprop for a wide flange beam (Ixx>Iyy)

---------------- REGIONS ----------------

Area: 5342.0910
Perimeter: 1032.8694
Bounding box: X: -12060.0082 -- -11894.0091
Y: 7203.7780 -- 7408.7789
Centroid: X: -11977.0086
Y: 7306.2785
Moments of inertia: X: 2.8521E+11
Y: 7.6633E+11
Product of inertia: XY: -4.6747E+11
Radii of gyration: X: 7306.8049
Y: 11977.0785
Principal moments and X-Y directions about centroid:
I: 8941997.7944 along [0.0002 1.0000]
J: 41094884.5825 along [-1.0000 0.0002]


and the same beam rotated so that the flanges are vertical (parallel to Y
world)
---------------- REGIONS ----------------

Area: 5342.0910
Perimeter: 1032.8694
Bounding box: X: -11638.2693 -- -11433.2685
Y: 7245.8287 -- 7411.8279
Centroid: X: -11535.7689
Y: 7328.8283
Moments of inertia: X: 2.8694E+11
Y: 7.1093E+11
Product of inertia: XY: -4.5164E+11
Radii of gyration: X: 7328.9425
Y: 11536.1023
Principal moments and X-Y directions about centroid:
I: 8941997.7944 along [1.0000 -0.0002]
J: 41094884.5825 along [0.0002 1.0000]

The principal moments are those at the centroid - in this case along the
prinicpal neutral axis.


Note that in the first example where the web aligns to Y, I is measured
along the vector (0,1) - meaning the the moment of inertai at the centroid
where the acis is aligne with the y axis. Thus J, measured along the X-axis
is the expected larger figure.

In the second example where the beam is rotated 90 we see tgat the vetor for
I is now (1,0) ie reversed.

For AutoCAD, the concept is:

I is the lower moment through the centroid
J is the larger moment.
The direction of the axis for these moments is defined by the vector
associated with them.

rather obtuse really, it should simply have been Ixx and Iyy and every
structural engineer would have understood


TDP



"Bob" wrote in message
news:6146471@discussion.autodesk.com...
Can anyone tell me what these properties mean?

Thanks!

--
Bob Q
Pentium 4 3.33 GHz
1GB RAM
XP Pro SP2
ATI Mobility Radeon 9000 IGP graphics.....
MDT 2004DX

[Anonymous]

Thank you, I see it is relevant for strength and bending stuff..... if my
"mechanics of materials" memory serves me correctly!

Thanks!


"Princess Jamie" wrote in message
news:6146486@discussion.autodesk.com...
Here's the massprop for a wide flange beam (Ixx>Iyy)

---------------- REGIONS ----------------

Area: 5342.0910
Perimeter: 1032.8694
Bounding box: X: -12060.0082 -- -11894.0091
Y: 7203.7780 -- 7408.7789
Centroid: X: -11977.0086
Y: 7306.2785
Moments of inertia: X: 2.8521E+11
Y: 7.6633E+11
Product of inertia: XY: -4.6747E+11
Radii of gyration: X: 7306.8049
Y: 11977.0785
Principal moments and X-Y directions about centroid:
I: 8941997.7944 along [0.0002 1.0000]
J: 41094884.5825 along [-1.0000 0.0002]


and the same beam rotated so that the flanges are vertical (parallel to Y
world)
---------------- REGIONS ----------------

Area: 5342.0910
Perimeter: 1032.8694
Bounding box: X: -11638.2693 -- -11433.2685
Y: 7245.8287 -- 7411.8279
Centroid: X: -11535.7689
Y: 7328.8283
Moments of inertia: X: 2.8694E+11
Y: 7.1093E+11
Product of inertia: XY: -4.5164E+11
Radii of gyration: X: 7328.9425
Y: 11536.1023
Principal moments and X-Y directions about centroid:
I: 8941997.7944 along [1.0000 -0.0002]
J: 41094884.5825 along [0.0002 1.0000]

The principal moments are those at the centroid - in this case along the
prinicpal neutral axis.


Note that in the first example where the web aligns to Y, I is measured
along the vector (0,1) - meaning the the moment of inertai at the centroid
where the acis is aligne with the y axis. Thus J, measured along the X-axis
is the expected larger figure.

In the second example where the beam is rotated 90 we see tgat the vetor for
I is now (1,0) ie reversed.

For AutoCAD, the concept is:

I is the lower moment through the centroid
J is the larger moment.
The direction of the axis for these moments is defined by the vector
associated with them.

rather obtuse really, it should simply have been Ixx and Iyy and every
structural engineer would have understood


TDP



"Bob" wrote in message
news:6146471@discussion.autodesk.com...
Can anyone tell me what these properties mean?

Thanks!

--
Bob Q
Pentium 4 3.33 GHz
1GB RAM
XP Pro SP2
ATI Mobility Radeon 9000 IGP graphics.....
MDT 2004DX

[Anonymous]

Google is your friend.

http://en.wikipedia.org/wiki/Moment_of_inertia

[Anonymous]

>The principal moments are those at the centroid - in this case along the
prinicpal neutral axis.

Jamie-

Not quite right.

The principal moments are the moments along the principal axes, with the
origin at the centroid.

As such they are related to the principal axes, rather than any other
coordinate system which might be defined, which is why MASSPROP, or
(vlax-dump-object) reports them identically, no matter the current UCS. They
are characteristics of the object, in other words.

The principal axes, as you surely know, are the coordinate system which
diagonalizes the inertia tensor, which means the products of inertia (off
diagonal elements) are all zero when calculated in coordinate system defined
by the principal axes. The existence of a principal axis transformation, and
hence of principal moments, is guaranteed by the nature of the inertia
tensor (or matrix, if you prefer), namely that it is real and symmetric.
Since it has been many years since I studied linear algebra, I am not
prepared to prove this, but you can look up the details if you are
interested.:)

In the case of a region (or 3 dimensional body) which has no axes of
symmetry, there will still be principal directions and principal moments,
but it most likely will not be possible (for the average person, at least)
to determine these "by inspection."

A practical example of such a profile would be a metal stair pan (which
eventually gets filled with concrete).

HTH

(I am not sure the OP is vitally interested, but others reading this may
be.)

[Anonymous]

I got pretty close from memory seeing as I haven't studied the definition in
30 years.


TDP

"Herman Mayfarth" wrote in message
news:6146495@discussion.autodesk.com...
>The principal moments are those at the centroid - in this case along the
prinicpal neutral axis.

Jamie-

Not quite right.

The principal moments are the moments along the principal axes, with the
origin at the centroid.

As such they are related to the principal axes, rather than any other
coordinate system which might be defined, which is why MASSPROP, or
(vlax-dump-object) reports them identically, no matter the current UCS. They
are characteristics of the object, in other words.

The principal axes, as you surely know, are the coordinate system which
diagonalizes the inertia tensor, which means the products of inertia (off
diagonal elements) are all zero when calculated in coordinate system defined
by the principal axes. The existence of a principal axis transformation, and
hence of principal moments, is guaranteed by the nature of the inertia
tensor (or matrix, if you prefer), namely that it is real and symmetric.
Since it has been many years since I studied linear algebra, I am not
prepared to prove this, but you can look up the details if you are
interested.:)

In the case of a region (or 3 dimensional body) which has no axes of
symmetry, there will still be principal directions and principal moments,
but it most likely will not be possible (for the average person, at least)
to determine these "by inspection."

A practical example of such a profile would be a metal stair pan (which
eventually gets filled with concrete).

HTH

(I am not sure the OP is vitally interested, but others reading this may
be.)

[stevor]

Normally,

principal direction: X, Y, Z axii;

principal moments: the moments in those directions, see wiki.